LIFECON DELIVERABLE D 3.2 Service Life Models

Transcription

1 LIFECON DELIVERABLE D 3.2 Service Life Models Instructions on methodology and application of models for the prediction of the residual service life for classified environmental loads and types of structures in Europe Sascha Lay, Prof. Dr.-Ing. Peter Schießl cbm Technische Universität München Shared-cost RTD project Project acronym: Project full title: LIFECON Project Duration: Co-ordinator: Life Cycle Management of Concrete Infrastructures for Improved Sustainability Technical Research Centre of Finland (VTT) VTT Building Technology Professor, Dr. Asko Sarja Date of issue of the report : Project funded by the European Community under the Competitive and Sustainable Growth Programme ( )

2 Project Information CONTRACT N : ACRONYM: PROJECT TITLE: G1RD-CT LIFECON Life Cycle Management of Concrete Infrastructures for Improved Sustainability PROJECT CO-ORDINATOR: PARTNERS: The Finnish Road Administration, Finland CT LAASTIT Oy Ab, Finland; Optiroc Oy Ab, Finland Technische Universität München, Germany OBERMAYER PLANEN+BERATEN, Germany Norwegian University of Science and Technology, Norway Interconsult Group ASA, (Since : Interconsult Norgit AS), Norway Technical Research Centre of Finland (VTT), VTT Building Technology Professor, Dr. Asko Sarja Norwegian Building Research Institute, Norway Kystdirektoratet, Norway Millab Consult A.S., Norway Centre for Built Environment, Sweden Gävle Kommun, Sweden Ljustech Konsults AB, Sweden L.Öhmans Bygg AB, Sweden British Energy Generation Ltd, UK Heriot-Watt University, UK Centre Scientifique et Technique du Batiment CSTB, France. PROJECT DURATION: FROM TO Project funded by the European Community under the Competitive and Sustainable Growth Programme ( )

3 Deliverable Information Programme name: Sector: Project acronym: Contract number: Project title: Growth Programme TRA 1.9 Infrastructures LIFECON G1RD-CT Life Cycle Management of Concrete Infrastructures for Improved Sustainability Deliverable number: D 3.2 Deliverable title: Deliverable version number: Work package contributing to deliverable: Nature of the deliverable: (PR/RE/SP/TO/WR/OT) Dissemination level (PU/RE/CO): Type of deliverable (PD/WR): Service Life Models Instructions on methodology and application of models for the prediction of the residual service life for classified environmental loads and types of structures in Europe Updated Final Report WP 3 RE PU PD Project Deliverable Contractual date of delivery: Final Delivery: Month 36 Date of delivery: Author(s): Project co-ordinator: Sascha Lay; Prof. Dr.-Ing. Peter Schießl, Prof. John Cairns Asko Sarja Nature: PR - prototype (demonstrator), RE - report, SP - specification, TO - tool, WR - working report OT - other Dissemination level: PU - public usage, RE - restricted to project participants, CO - restricted to commission Type: PD - project deliverable, WR - working report

4 Deliverable ID D 3.2 Quality Assurance Form Title Deliverable type Author (s) of deliverable (Name and organisation) Reviewer(s) Probabilistic service life models for reinforced concrete structures FINAL REPORT Dipl.-Ing. Sascha Lay (Center for Building Materials Technical University of Munich) Christine Kühn, Erkki Vesikari, Arne Gussias, Christer Sjöström Approved by reviewer(s) (Reviewer s name and date) Sign.: Sign.: Date: Sign.: Date: Sign.: Date: Date: Approved for release WP Leader / Co-ordinator Sign.: Sign.: Date: Date:

5 Lifecon Deliverables Deliverable No D1.1 D1.2 Title of the Deliverable Generic technical handbook for a predictive life cycle management system of concrete structures (Lifecon LMS) Generic instructions on requirements, framework and methodology for IT-based decision support tool for Lifecon LMS D1.3 IT-based decision support tool for Lifecon LMS D2.1 Reliability based methodology for lifetime management of structures D2.2 Statistical condition management and financial optimisation in lifetime management of structures Part 1: Markov chain based LCC analysis Part 2: Reference structure models for prediction of degradation Methods for optimisation and decision making in lifetime management of structures D2.3 Part I: Multi attribute decision aid methodologies (MADA) Part II: Quality function deployment (QFD) Part III: Risk assessment and control D3.1 Prototype of condition assessment protocol D3.2 Probabilistic service life models for reinforced concrete structures D4.1 Definition of decisive environmental parameters and loads D4.2 D4.3 D5.1 D5.2 Instructions for quantitative classification of environmental degradation loads onto structures GIS-based national exposure modules and national reports on quantitative environmental degradation loads for chosen objects and locations Qualitative and quantitative description and classification of RAMS (Reliability, Availability, Maintainability, Safety) characteristics for different categories of repair materials and systems Methodology and data for calculation of life cycle costs (LCC) of maintenance and repair methods and works D5.3 Methodology and data for calculation of LCE (Life Cycle Ecology) in repair planning D6.1 Validation of Lifecon LMS and recommendations for further development

6 Keywords concrete, deterioration, model, reliability Abstract This report comprises the mathematical modeling of corrosion induction due to carbonation and chloride ingress, corrosion propagation, frost (internal damage and surface scaling) and alkaliaggregate reaction. Models are presented on a semi-probabilistic and a full-probabilistic level. Semi-probabilistic models only include parameters obtainable throughout structure investigations, without making use of default material and environmental data. Full-probabilistic models are applicable for service life design purposes and for existing objects, including the effect of environmental parameters. For each full-probabilistic model a parameter study was performed in order to classify environmental data. The application of the models for real structures is outlined. The objects of the case studies have been assessed in order to obtain input data for calculations on residual service life. Each degradation mechanism will be treated separately hereby demonstrating: - possible methods to assess concrete structures - the sources for necessary input data - approach used in durability design - application of models for existing structures - the precision of the applied models - necessary assumptions due to lack of available data - possible method to update data gained from investigations throughout condition assessment - default values for input data - output of the calculations The use of full-probabilistic models for the calibration of the Markov Chain approach is described. 6(169)

7 List of Contents Abstract... 6 List of Contents... 7 List of terms, definitions and symbols Introduction Aim of the Report Strategy for the Development Framework General Probabilistic Safety Concept General Reliability Requirements Model Updating Deterministic Safety Concept Deterioration Mechanisms affecting Concrete and Reinforced Concrete Structures Semi-probabilistic Model on Carbonation of Concrete Mathematical Model Spatial Deviation of Carbonation Depth Calculation Procedure Full-Probabilistic Model on Carbonation of Concrete Mathematical Model Inverse Carbonation Resistance Weather Exponent w Relative Humidity Factor k RH Surface Concentration of Carbon Dioxide C S Curing Parameter k c Test Method Factors k t and t Concrete Cover d c Shortcomings of the Model Case Studies on Carbonation induced Corrosion Television Tower Old Structure Provided Information Description of the Object Exposure Zones Overview of Performed Investigations Measurement of Concrete Cover, d cover Measurement of the Carbonation depth, X c Semi-Probabilistic Reliability Calculation (169)

8 5.1.8 Inverse Carbonation Resistance of Concrete, R ACC, Relative Humidity Factor, k RH Weather Function W Curing Factor, k c Carbon Dioxide Concentration of the Environment, C S Concrete Cover, d cover Calculation without Data Update Boundary Conditions for Calculations with Bayesian Update Example for Calculation with Bayesian Update - Exposure Zone 4 South Evaluation of Calculation Results "Young Bridge Provided Information Description of the Object Exposure Zones Overview of Performed Investigations Core Drilling and Accelerated Carbonation Testing Measurement of the Concrete Cover, d cover Inverse Carbonation Resistance, R ACC, Environmental Parameter Relative Humidity Factor, k RH Curing Factor, k c Carbon Dioxide Concentration, C s Calculations and Results Semi-Probabilistic Model on Chloride Ingress Mathematical Background Fick s First Law Fick s Second Law Types of Diffusion Coefficients Choice of Model Scatter for the Depth of the Critical Chloride Concentration x crit Calculation Procedure Full-Probabilistic Model on Chloride Ingress Mathematical Model Material Input Parameter D RCM,0 (t) General Effect of Water-Binder Ratio Effect of Binder Type Derivation of a Model for Chloride Migration Coefficient Application of the Model Environmental and Material dependent Input Parameters Depth of the Convection Zone x Temperature Parameter k T The Age Factor n Influence of a Partial Water Saturation - Parameter k w Separation of Age Exponent n 1 and Factor k w Chloride Concentration C x (169)

9 7.10 Critical Chloride Content C crit Shortcomings of the Model Case Study on chloride induced corrosion Description of the Object Hofham Brücke Reliability Analysis Conclusions for the Praxis Models on Propagation of Corrosion Introduction Corrosion Rate in Dependence of Exposure Classes Direct Measurement of the Corrosion Rate Empirical Modelling of the Corrosion Rate Regression Parameter k Concrete resistivity Model Approach Material Dependent Resistivity Curing Factor k c Test Method Factor k t Humidity Factor k R,RH Temperature Factor k T Chloride Factor k R,Cl Chloride Concentration Factor F Cl The Galvanic Factor F Galv The Oxygen Factor F O Aspects not treated by the Chosen Model Models on Structural Consequences of Reinforcement Corrosion Introduction Corrosion Process Section Loss Volumetric Expansion Weak Interfacial layer Influence of Conditioning and Damage Parameters Effect of corrosion on residual strength Strength and Ductility of Reinforcement Longitudinal Cracking and Cover Integrity Bond Semi-Probabilistic Model on Alkali-Aggregate-Reaction Introduction Predictions using Core Tests Predictions from Monitoring of Movement of Affected Members Predictions with known Expansion Behavior of Similar Concrete Full-Probabilistic Model on Alkali-Aggregate-Reaction Frost Attack (169)

10 13.1 Semi-Probabilistic Model on Internal Frost Damage Full-Probabilistic Model on Internal Frost Damage Semi-Probabilistic Model on Frost induced Scaling Full-Probabilistic Model on Frost induced Scaling Parameter Study for Environmental Classification General Procedure Classification for Carbonation induced Corrosion Procedure Input Data for Parameter Study Classification of Relative Humidity RH Classification of the Time of Wetness ToW Classification of Carbon Dioxide Concentration C S Classification of Temperature T Classification for Chloride induced Corrosion Procedure Input Data for Parameter Study Classification of Temperature T Modelling with a Markov Chain Approach Introduction Principal of the Markov Chain Procedure for Calibration of the Transition Probability Matrix Conclusions Proposal for further development Acknowledgements References (169)

11 List of terms, definitions and symbols AAR Alkali-silica reaction Beta-D Beta distribution CoV D Log-N Coefficient of variation (ratio of standard deviation and mean value in percent) Deterministic value (single constant value) Log-Normal distribution µ Mean value ND StD W Normal distribution Standard Deviation Standard deviation Weibull distribution 11(169)

12 1 Introduction 1.1 Aim of the Report This report intends to provide models regarding deterioration processes of concrete structures. In a major EU research project called DuraCrete a full-probabilistic approach for the durability design was developed. This was achieved by first reviewing current deterioration models covering the mechanisms of carbonation and chloride induced corrosion (separately for initiation and propagation phase), frost and alkali-silica reaction. These models were evaluated to choose the most suitable approach on an engineering level. Using literature data a large number of input parameters was quantified in a statistical manner. For those parameters which may be measured in the laboratory to achieve a more reliable estimate for a certain concrete composition existing compliance tests were evaluated and chosen. The results of the DuraCrete project, which was finished in 1999, were disseminated by the Thematic Network DuraNet. LIFECON focuses on structures in the service life phase. Hence, existing models for durability design need to be adopted for this purpose. The following will be provided: general concept for the calculation of probability of failure and residual service life description of deterioration models case studies to demonstrate the application of the concepts. Deterioration processes are oftentimes divided into two stages, the initiation and the propagation phase. Regardless of the considered phase the development of models for deterioration mechanism comprises the following steps: derivation of equations representing the physical and chemical mechanisms and analytical or numerical procedures for application of these collection of data through condition assessment of existing independent (will not be used for verification of model) structures in their exposure environment to obtain default values for input parameters in models sensitivity analysis to identify critical parameters and range of values collection of new data throughout the condition assessment of existing structures to update and thus improve predictions evaluation of the model accuracy by comparison of predictions with the actual behavior in the field. 1.2 Strategy for the Development This report summarizes the results of existing Service Life Prediction Methods and adds further developments. The focus is set on the necessary input parameters and procedures for their 12(169)

13 determination throughout the investigation and monitoring of existing concrete structures in order to provide: 1. mathematical models for the prediction of the remaining service life of existing structures 2. procedures to collect data from structure investigations in order to provide an extended basis for future durability design applications. 2 Framework 2.1 General Models for the prediction of the residual service life require input data, which may be provided by default data found in literature references and/ or from structure investigations. Hence, service life modeling is closely connected to a Condition Assessment Protocol (CAP), which provides the procedure for the determination of input data throughout structure investigations, as is presented in [i]. The models are integral part of a stepwise condition assessment procedure and are applied on two levels of sophistication: semi-probabilistic and full-probabilistic level. In the semi-probabilistic level time-dependant deterioration functions are used on a basic engineering level. Input for these is inspection data only. The observed response data combines the material resistance and the environmental action. As the input data is based on a low sample scope, scatter is accounted for by safety factors, which are a function of expected scatter and desired level of reliability. As scatter of results can not be reliably calculated for a low number of samples, deviations need to be assumed on the "safe side" (on basis of a literature study on spatial scatter of more extensive inspection data). The output of such calculations is the time until a regarded limit state (which is part of the condition rating scale) is reached with a predefined level of reliability. These calculations may be done at the structure site, e.g. with a simple pocket calculator. On a higher inspection level full-probabilistic models are applied during the condition assessment procedure. The models separate material resistance and environmental loads. This requires the collection and processing of environmental input data as well as specification of material properties for calibration of the empirical equations. Based on this each parameter is defined by the distribution type, mean value, standard deviation and statistical moments by fitting the data to pre-chosen statistical distributions. The necessary data for quantification of input parameters can be divided into data: which can/ must be measured at each individual structure which may/ has to be applied to every structure, originating from statistical analysis of sets of on-site investigations Full-probabilistic models require the application of special software and trained personnel. Input data is updated throughout structure investigations. The reader will first be introduced to the mathematical deterioration models and the constituting parameters. Subsequently the parameters of the particular models are described. The application 13(169)

14 of the chosen models will be demonstrated on case studies, which have been investigated. Hereby the reader will be introduced to: possible methods to investigate concrete structures the source of necessary input data approaches used in durability design application of models for existing structures the precision of the applied models necessary assumptions due to lack of available data possible method to update data obtained from inspections range of magnitude of input data output from the calculations The author included notes giving indications on possible future tasks within the various work packages (WP) of the project. 2.2 Probabilistic Safety Concept General The basic limit state equation: Design problems are in general solved by comparison of two variables. The variable S represents the load onto the component, whereas the variable R expresses the resistance towards the regarded load. A reliability problem occurs, if the resistance R is lower than the load S. Both, load S and resistance R are subjected to scatter. This circumstance leads to a probabilistic approach. The evaluation of the problem is usually performed on basis of limit state related failure probabilities. p{failure} = p f = p {R(x 1, x 2, ) S(y 1, y 2,...) 0} p Target (1) p: probability f: failure R: resistance of component depending on several variables x i S: load onto component depending on several variables y i The failure probability is the probability p that the resistance R may fall below the load S. Both variables may be time- and site-dependent. The failure probability p f must be limited to a predefined target probability p target. Following this approach failure probability must be explicitly calculated. A common procedure starts with the definition of a limit state equation: 14(169)

15 Z = R - S (2) Z: Reliability of component First of all one seeks to know the probability p that the resistance R is lower than a certain value x. This is expressed by the probability distribution function of the resistance F R (x): P(R < x) = F R (x) (3) The probability that the load S = x is calculated as the value of the probability distribution density: P(S=x) = f S (x) (4) The probability that both conditions are met yields: p f (x) F (x) dx f S R (5) Resistance R and load S are introduced in form of mean and deviation. The variable Z represents the reliability, with which the component fulfils the required limit state. If R and S are both normal distributed, die variable Z as the sum of both is a normal distributed variable too. Z R S Z 2 2 R S (6) (7) : : mean value deviation S S R R p f 0 r, s 0. Z Z Z S Z. Z R z Figure 1. Probabilistic performance concept The mean value and deviation of the reliability Z form the reliability index, which is the factor by which the deviation of Z fits into the distance of the mean value and the axis of abscissa, [ii]. Z Z (8) 15(169)

16 If the reliability Z is normal distributed, the variable may be transformed into a standard-normal distributed one, for which µ = 0 and = 1. The failure probability is then equal to the probability distribution function of the standard-normal distribution for the value. 1 u 2 Z 1 2 p f ( ) ( ) e du 2 Z u (9) (.): : Z : Z : Probability distribution function of standard normal distribution Reliability index Mean value of reliability Z Deviation of reliability Z The cumulative frequency of the standard normal distribution can not be solved analytically, but values are tabled in current statistical literature, Figure 2. reliability index [-] 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 0,01 0, failure probability pf [%] Figure 2. Relationship of failure probability p f and reliability index for a normal distributed reliability function Of further interest are so called weight factors i which indicate the importance of a variable regarding the failure probability p f. For two variables (resistance R; stress S) these can be calculated from: R S R and 2 2 S R 2 2 S S R (10) For normal distributed variables the results are correct, whereas for others they are usually very good approximations. This procedure can be transformed into a design equation. In reliability analysis it is of common approach to use for evaluation purposes. The requirement is that 0, with 0 being the safety level required in standards as e.g. in [iii]. Using the above stated equations the following relationship can be postulated: R ( R 0 R S 1 S 0 S 1 ) ( ) (11) 16(169)

17 The reliability Z is only in few cases normal distributed. The solution of the integral in (9) is then by no means a trivial matter. In most cases numerical approximate approaches must be pursued. Numerical integration techniques are not appropriate due to the fact that the effort to solve the problem with sufficient accuracy becomes tremendous. Methods of structural reliability are applied usually FORM (First Order Reliability Method) and SORM (Second Order Reliability Method), which are integral part of today s software. These methods will be only shortly outlined in this report. For further details the interested reader is recommended [iv]. A different way of presenting the above discussed relations is to depict the distributions of the variables R and S as a two-dimensional probability density. Figure 3. Probability density functions of resistance R and stress S in 2- and 3- dimensional space, [ii] With respect to durability the material resistance and the load onto the component are usually both time dependent. This fact must be accounted for by deterioration models. R, S R(t) S(t) Average Service Life Failure Probability p f Technical Service Life Z µ Z Reliability Z Time Figure 4. Time dependant behavior of resistance R(t) and load S(t) during service life and resulting probability density function of reliability Z A major computational advance is achieved by the transformation of the limit state equation into the so called standard space. The variables in the limit state equation are transformed as follows: 17(169)

18 U i Xi x i x i (12) U i : X i : standardized variable variable in limit state equation µ xi : mean value of variable X i xi : standard deviation of variable X i The variables then posses a mean value of µ = 1 and a standard deviation of = 1. The so called design point u * is defined as the point on the limit state function which shows the largest probability density. The limit state equation cuts of an area in which failure is probable. The point which is nearest to the rotation axis is the design point u + for which is searched for. f (u ) U 1 1 u 1 g (u, u ) = u 2 u* p f u 2 f (u ) U 2 2 Figure 5. Design point u * and reliability index of a 2-dimensional probability density function transformed to standard normal space The distance of u * and the centre of the probability density function equals the reliability index. Extensions: The general safety concept comparing two variables R and S is in its basic form only rarely applicable. The above discussed is only valid for linear limit state equations and for independent normal distributed variables X i. For all other cases the results are good approximations. To solve more complex reliability problems, as we face them for durability problems, extensions must be made which include the transition of: - two variables into various variables 18(169)

19 - linear limit state equations to non-linear equations - normal distributed variables to arbitrary distribution types. In case of multiple variables X i in the limit state functions n-dimensional integrals must be solved. In general three methods can be applied to solve these integrals: 1. Numerical Integration (exact method) 2. Approximations of 1. and 2. order (FORM: First Order Reliability Method, SORM: Second Order Reliability Method) 3. Monte-Carlo-Simulation In the calculations of this report only approximations have been applied. In FORM the n- dimensional integrals are approximated by linear limit state functions in the design point u *. In SORM a 2 nd order curve is used for approximation. A linear limit state equation L with various variables can be formulated as: n L a 0 a X 0 i i i 1 (13) As for the two dimensional case the following parameters need to be determined: L 0 i i i1 n µ a a X 0 (14) n 2 L (aix i) i1 1/2 L f L x i p ( ) n i 2 ai 1 i L i1 * i i i i (15) (16) (17) (18) In case of non-linear limit state equations these are linearised by developing a Taylor series in the area of the design point x i *. If the distributions of the variables are not normal distributed, they are replaced by so called equivalent normal distributions in the design point. Equivalent in this respect means that the probability density function and the probability distribution function must be equivalent in the design point x i : 19(169)

20 f (x ) f (x ) N * i i i i and F (x ) F(x ) (19) N * i i i i It is obvious that the complexity of the calculations is out of the scope of manual calculations. But commercial software to solve these problems is already available, as e.g. the software package STRUREL used by the author. In summary the following general information is required for the calculation of the residual service life on a probabilistic level: 1. Models which describe the time dependent deterioration process 2. Time- and site-dependant loads S must be statistically quantified 3. Component resistance R, which depends on geometry and the over time changing physical and chemical properties of the construction material, must be quantified by measurements and statistically analyzed. 4. Relevant limit states need to be formulated, i.e. undesired conditions must be identified. 5. The maximum acceptable failure probability p f or the corresponding reliability index need to be chosen. Statistical quantification of input parameters: A classical approach for the identification of an appropriate distribution function is to [iv]: 1. Postulate a hypothesis for the distribution family 2. Estimate the parameters for the selected distribution on the basis of statistical data 3. Perform a statistical test attempting to reject the hypothesis In many engineering applications this procedure may not be followed in a straightforward manner due to the lack of a sufficient amount of data. In practice it is rather common that physical arguments can be formulated for the choice of distribution functions. A practically applicable approach for the selection of the distribution function for the modeling of random variables is therefore: 1. Consider the physical reasons why the variable may belong to a certain distribution family: May infinite values occur? If not so, what are the physical boundaries? Where is the parameter applied? Does the mathematical structure of the model require boundaries (e.g.: division by zero)? 2. Check whether the statistical data is in gross contradiction with the assumed distribution e.g. by using probability papers, which today is easily possible by commercial software, 20(169)

21 e.g. with the here applied software STATREL included in the software package STRUREL [xix]. The result of a statistical analysis can either be expressed in form of moments (e.g. mean value µ, standard deviation ) or parameters of the distribution, each always accompanied with the specification of the boundaries, see Table 1. Table 1. Examples for probability density function fx with corresponding parameters and moments Distribution Type Parameters/ Moments Range Rectangular a a b a x b a x b b 2 1 fx(x) b a b a 12 Normal µ µ x 2 1 1x 1 x fx(x) exp 2 2 Lognormal >0 ² 0 x 2 µ exp 1 1lnx 2 fx(x) exp x 2 2 µ exp( ²) 1 Beta (B) a r a x b r1 s1 (r s) (x a) (b x) b µ a (ba) r 1 fx(x) r s 1 (r) (s) (b a) r>1 b a rs s>1 with Gamma function: rs rs1 x1 (x) exp( t) t dt Reliability Requirements General: In the construction business usually two types of limit states are distinguished which are connected to different reliability levels: Serviceability Limit State (SLS) Ultimate Limit State (ULS) In general considerations regarding the SLS s are related to function or aesthetics deviations. For maintenance planning as in Lifecon SLS s might also be related to applicability of maintenance, repair and rehabilitation actions, as well as replacement criteria. These limit states are often set based on a complex set of sub criteria such as: maintainability, economy and environmental impacts. The ULS regards the case that the bearing components may not yield the requirements 21(169)

22 regarding load bearing capacity. The result of the calculations is the reliability index vs. exposure time t. Figure 6. Reliability index versus exposure time t. Example of chloride induced corrosion initiation for various concrete cover depths d C [v] The service life of a component follows from the comparison of the minimum target reliability 0 and the reliability over exposure time t, as depicted in Figure 6. The technical service life T depends strongly on the target reliability level 0. The question which target reliability level is appropriate must thus be answered. In general the following must be considered when assigning target reliabilities to possible limit states: possibility to detect damage possibility of corrective actions in case of failure consequence of failure. Please note, that failure is here used in the sense of exceeding a predefined limit state and not in the sense of structural collapse! Serviceability Limit States: With respect to reinforcement corrosion the following states are regarded as service ability limit states [xiv]: SLS 1: SLS 2: SLS 3: depassivation of reinforcement crack formation spalling of concrete, if no risk emerges from falling pieces (otherwise this is regarded an ultimate limit state) The European standardization sets up a fixed reliability index of SLS,T = 1,50 regardless of the type of serviceability limit state. Since passing a serviceability limit state always is accompanied by economic costs an economic optimization of the target reliability should be performed. By 22(169)

23 superposition of production costs (curve A) and maintenance costs (curve b) which are both connected to the reliability level, the optimal reliability level can be calculated from a economical point of view (economic optimization), Figure 7. Figure 7. Determination of the optimal reliability level Based on these considerations the reliability indices may be scaled introducing a proportionality factor, [vi]: C P C RiskM Repair (20) P: proportionality factor [-] C RiskM : costs for risk minimization [Euro] C R : repair costs, caused by limit state based failure [Euro] Table 2. Minimum reliability index SLS during service life P [-] SLS [-] Low 2,0 Normal 1,5 high 1,0 The cost C RiskM include all the costs to obtain additional protection, which shall be outlined by the following examples: If the concrete cover is enhanced the net section is reduced for the same concrete geometry, which will require more reinforcement and thus raises the price of the component. Reducing the w/c-ratio of concrete, in order to reduce the porosity, requires the application of superplasticizer (for equal compactability) increasing the production costs. In the TG 5.6 of fib the requirements the following connection between exposure class according to EuroCode 2 and the reliability index was established, Table 3. The reasoning behind the assignment shall be explained for the example of carbonation induced corrosion: 23(169)

24 1. The carbonation process is accelerated with decreasing relative humidity. Nevertheless the subsequent corrosion process will be comparably slow due to the high electrical resistance of the dry concrete. If repair measures do to depassivation will be necessary, this will only be the case at rather late times compared to the desired service life. Repair costs C R throughout the service life will be low, giving a high value of P in (20). 2. In an environment with frequent wet-dry cycles the carbonation process is rather slow. However, once the reinforcement will be depassivated the damage rate and thus the rate of repair costs will be high, which requires high levels for the reliability index. Table 3. Required reliability index SLS for the state of depassivation of reinforcement according to TG 5.6 of fib P [-] Exposure class SLS [-] Low XC4, XD1, XS1, XS3, XD3 2,0-3,5 Normal XC2, XC3, XS2, XD2 0,0-3,5 high XC1 0,0-2,5 This approach is as such only applicable for the durability design, where production costs may be still be chosen and were only the state of depassivation may be regarded. For existing structures the cost for risk minimization may be exchanged by other types of monetary costs as e.g. user costs (costs in Euro burdened to users due to traffic detours, etc.), see LIFECON deliverable D1.1 [vii]. Ultimate Limit State (ULS): Various ULS can be regarded, which are here exemplified for the corrosion process: ULS 1: Spalling of the concrete cover if risk emerges from falling pieces ULS 2: Loss of bond between concrete and reinforcement ULS 3: Fracture of structural component The two last mentioned states are considered as the classical ultimate limit states, which lead to the total destruction of the structural element. Indices for the ULS are given in national standards. In EC 1 [iii] the reliability index is set to = 3,8. A classification of the reliability as shown for the SLS seems also reasonable Model Updating The conditional probability p(ab) expresses the probability that an event A will occur, if the event B already took place: P(A B) P(A B) P(B) (21) From the above given relationship the mathematician Thomas Bayes ( ) developed the following rule: 24(169)

25 P(A E i) P(E i) P(Ei A) n P(A E ) P(E ) j1 j j (22) E i i-th of n mutually exclusive events In (22) the term P(AE i ) is referred to as the likelihood, i.e. the probability of observing a certain state given the true state. The term P(E i ) is called the prior probability of the event E i, i.e. prior to the knowledge of the event A. Structure investigations can provide additional information. A model without any investigation data, as it is used for the durability design, is called a priori model. If additional information is introduced as a conditional constraint a more reliable post priori model is obtained. To demonstrate the concept of Bayesian Updating the example of a reinforced pillar is considered [iv]: Calculations with a service life model for chloride induced corrosion showed that after 30 years a probability of corrosion initiation (CI) of the reinforcement is expected to be P(CI) = 0,01. The electrochemical potential of the pillar was mapped. The quality of this inspection method may be characterized by the: probability that the inspection method will indicate corrosion given that corrosion was really initiated; P(ICI) probability that corrosion will be indicated, although corrosion actually took not place, P(I CI). An inspection of the pillar took place, which indicated that active corrosion is taking place. What is the probability that corrosion is really taking place? The answer is found by applying the Bayes s rule: The probability of obtaining an indication of corrosion at the inspection is: P(I) P(I CI) P(CI) P(I CI) P(CI) 0,80,010,1 (1 0,01) 0,107 (23) The probability that corrosion is indicated and corrosion is also actually taking place is: P(ICI) P(I CI) P(CI) 0,80,01 0,008 (24) Hence, the probability that corrosion of the reinforcement has initiated given an indication of corrosion at the inspection is: 0,008 P(CI I) 0, 075 0,107 (25) 25(169)

26 The probability of initiated corrosion given an indication of corrosion seems quite low on the first sight. This is mainly due the here assumed high probability of an erroneous indication of corrosion. In the above given example the probability of corrosion initiation P(CI) was calculated for a certain moment in time (30a). This may be also be done over the considered service life span. Using appropriate software, e.g. SYSREL in the software package STRUREL [xix], various types of inspection data obtained at different moments in time can be incorporated in such calculations. 2.3 Deterministic Safety Concept The full-probabilistic concept requires commercial software solutions. But the full-probabilistic concept can be transformed into a simpler, deterministic concept, as it is today common practice in the field of structural design, i.e. calculations with partial safety factors. Deterministic calculations with partial safety factors can be performed manually. The basis are three fundamental equations: R d S d 0 (26) R d R c R (27) S d S c S (28) R, S: Resistance and stress variable Index d: Index c: : Design value Characteristic value Partial safety factor Resistance R and stress S are compared on the level of design values. The design values X d are calculated taking into account partial safety factors. But to determine partial safety factors, further information is required: - Weight factors i, are a measure for the importance of a variable regarding the failure probability and are provided by full-probabilistic calculations. - Target reliability 0 (safety level) which shall be reached after the end of the technical service life. - Mean value µ of the respective parameter. - Deviation of the respective parameter. The design values are in general calculated according to: X d = - = k t d (29) From here on the partial safety factors are calculated as follows: 26(169)

27 X X d c (30) 2.4 Deterioration Mechanisms affecting Concrete and Reinforced Concrete Structures Concrete structures are exposed to environmental conditions which may lead to deterioration of the materials (concrete and steel) and hence the entire structure: Reinforcement Corrosion Concrete Deterioration Chem. & Electrochem. Attack Phy. Attack Chem. Attack Carbonation Chloride penetration Stray current Mech. attack Therm. attack Acid. attack Sulfate attack Alkali reaction Reinforcement corrosion Abrasion Internal Frost Damage Scaling (de-icing salt) Dissolution Internal expansion Figure 8. Overview of basic species and mechanisms leading to deterioration The mechanisms highlighted in Figure 8 will be treated separately with respect to semiprobabilistic and full-probabilistic models as well as possible synergetic effects between those. 3 Semi-probabilistic Model on Carbonation of Concrete 3.1 Mathematical Model Most of today's models on carbonation of concrete are based on Fick's 1 st law of diffusion. The amount of CO 2 which penetrates the concrete due to the CO 2 -gradient between the outer air of the environment and the content in the concrete can be balanced: c c x 1 2 dm -D A dt (31) dm: Mass increment of CO 2 transported by diffusion during the time interval dt [kgco 2 ] D: CO 2 -diffusion coefficient of carbonated concrete [m 2 /s] A: regarded surface area [m 2 ] c 1 : CO 2 -concentration of the environment [kgco 2 /m 3 ] c 2 : CO 2 -concentration at the carbonation front in the concrete [kgco 2 /m 3 ] dt: time interval [s] x: depth of carbonated concrete [m] 27(169)

28 At the carbonation front CO 2 reacts with alkalis of the pore water solution to form various types of carbonate phases, which can be balanced as follows: dm a A dx (32) dm: mass of CO 2 required for the complete carbonation of the depth increment dx [kgco 2 ] a: CO 2 -binding capacity of non-carbonated concrete [kgco 2 /m 3 ] A: regarded surface area [m 2 ] dx: depth increment [m] The balances of the diffusion and the reaction process can be combined: D xdx - c1c2dt a (33) Assuming D, a and (c 1 -c 2 ) to be neither time- nor depth-dependent integration leads to: 2D x c c t a 2 * 1 2 (34) Combining the single concentrations c 1 and c 2 into the concentration gradient C S and solving for the penetration depth gives: x(t) c 2D C a S t * (35) Combining the material parameters D and a with the environmental parameter C S and expressing the exposure time t* as the difference of the age t and the moment once the surface was exposed to CO 2 finally leads to a simple square-root of time approach including only the carbonation rate K, which can be determined by structure investigations without further knowledge of the environmental conditions or material properties. x(t) K (t-t ) c exp (36) K: carbonation rate [mm/(s)] t: Age of concrete at time of inspection [s] t exp : Duration until surface was exposed to CO 2 [s] Usually the time until exposure t exp can be set to zero, as it is negligible short compared to the service life. But for coated surfaces t exp equals the time at which coating failed. From structure investigations with a low sample scope (e.g. three readings) the mean value of the carbonation depth X c at the respective concrete surface can be measured. With the knowledge of the structure age and the exposure time the equation can be solved for K. For concrete surfaces in a dry atmosphere, sheltered from rain (e.g. laboratory climate of T = 20 C, RH = 65%) the carbonation process is in fairly well agreement with the square-root of time law. The variables D, C S and a can be considered to be more or less independent of time 28(169)

29 and site. Precipitation at concrete surfaces will hinder the carbonation process for a certain period. Bearing this in mind the t-law is a simple model, which is always on the safe side. 3.2 Spatial Deviation of Carbonation Depth When performing calculations on the service life of concrete components, this is only possible if data was collected from surfaces produced with the same concrete quality and which are exposed to the same environmental conditions. Deviations of the carbonation depth will under these circumstances mainly be influenced by: - the inhomogeneous character of the concrete - measurement accuracy of personal - inspection technique In [xiv] the variation coefficient of the inverse carbonation resistance R ACC,0-1 was determined as an input to full-probabilistic design models, as will be dealt with later. It could be demonstrated that coefficient of variation decreases with increasing carbonation depth. This fact can be explained with the relatively constant inaccuracy of the carbonation depth measurement. The larger the penetration depth, the lesser is the influence of the measurement accuracy. Therefore the coefficient of variation must be expressed as a function of the carbonation resistance itself: 2 1 b XC 11 CoV 1 a R R ACC,0m a 10 Acc,o b (37) CoV: Coefficient of variation [%] a: Regression parameters [10 11b m 5 /(s kgco 2 )], here a = 68,9 b: Regression parameter [-]; here b = -0,22 R -1 ACC,0m : Mean value of inverse carbonation resistance [10-11 m 5 /(s kgco 2 )] X C : Carbonation depth measured in accelerated carbonation test [m] : Time constant [(s kgco 2 /m³) 0,5 ]; here 420 for a CO 2 -concentration of 2 V.-% and a test duration of 28 days. The carbonation depth X C of laboratory specimens is measured after accelerated carbonation tests, thus taking into account the inhomogeneity of the concrete. As the carbonation depth is the only variable subjected to deviations in the test (test conditions and duration can be considered as constant) the above stated relationship can be adopted to the penetration depth itself: CoV 1 CoV R X C (38) Acc,o The regression analysis was based on data obtained at a single laboratory (level of repeatability). The deviation of these measurements are below those which would be obtained at the construction site by various personal (level of reproducibility). It was assumed that the level of reproducibility can be set to the 90%-quantile of the level of repeatability. Under these conditions the regression parameters yield the above given values. 29(169)

30 3.3 Calculation Procedure In Table 4 a summary of the necessary input data is given. The calculation procedure will be demonstrated by an example. Table 4. Summary of necessary data input for the semi-probabilistic model on carbonation ingress Parameter Unit Format Source Carbonation depth X C [mm] ND(µ, ) Measurements according to Annex of D3.1 [i] Age of concrete t [s] D Structure documentation Concrete Cover d Cover [mm] ND(µ, ) Measurements according to D3.1 The following information is given: - Concrete cover d cover, which is a resistance parameter, was measured with a mean value of µ cover = 30 mm and a standard deviation of R = 8 mm. For the sake of simplicity the distribution is assumed to be normal. - Carbonation depth X C, which is considered as the stress variable, was measured at three spots at an age of 30 a. The mean value was determined to be µ S = 12 mm. The standard deviation should not be based on only these three measurements. Instead the variation should be determined following the approach of the prior chapter. With an average CO 2 -content in the air of around kgco 2 /m³ the time constant in (37) yields: (39) 4 2 CS t which leads to a coefficient of variation for the carbonation depth of: 2 0,22 0, CoVX 68, % C 1065 (40) The mean value of the carbonation rate K can be determined from: x (t) K (t - t ) K (30 0) 12mm (41) c exp leading to µ K = 2,191 mm/a. The standard deviation then yields K = 0,39µ K. The target service life is assumed to be 100 years, with a minimum reliability index of 0 = 1,8. The flow of the calculation to prove whether the requirements will be fulfilled is as follows: 1. Calculation of the stress variable S (Carbonation depth at age T = 100 a): x (t) 2,191 (100 0) 21,9mm c (t) 21,9 39% 8,5mm (42) x c 30(169)

31 2. Transformation to standard space: U R 30 8 U 1 2 S 21,9 8,5 (43) L(U 1,U 2) R S 8U18,5U2 8,1 AU1BU2 C 0 (44) 3. Calculation of the distance of the limit state line from origin using the so called Hesse normal format (comparison of coefficients A, B, C): C 0, 69 1,8 2 2 A B (45) This means that after 100 years the reliability index will drop to a level below the target reliability. If the residual service life is searched for, the reliability has to be set to = 0 = 1,8. The stress S equals the time dependant carbonation depth X C : U R 30 8 U 1 2 S 2,191 t 2,191 t 0,39 (46) Comparison of the coefficients (A, B, C) as above leads to: (30 2,191 t ) 8 (0,85 t) 2 2 1, 8 (47) With a little algebra (or MS-Excel solver option) this results in a service life of t= 35 years. 4 Full-Probabilistic Model on Carbonation of Concrete 4.1 Mathematical Model The carbonation model combines two mechanisms: diffusion and binding of carbon dioxide, being influenced by e.g. the relative humidity, drying and wetting of the concrete, inhomogeneity, etc. In project DuraCrete [viii] the model was extracted from [ix] because it provided the greatest convenience for the daily application by practical engineers and shows reasonable fit to data obtained from exposure tests, [x]. The model, refined in [xiv], is based on Fick s 1st law of diffusion and considers influencing aspects as environmental action, execution and testing by introducing: a carbonation resistance as a measurable concrete property and factors for 31(169)

32 environment execution test method 1 t0 XC 2kRHk c(ktr ACC,0 t) CS t t w [m] (48) X C Carbonation depth [m] Index 0 material parameter has been prepared, cured and tested under defined reference conditions k RH influence of the realistic moisture history at concrete surface on D eff [-] k c influence of the execution on D eff (e.g. curing) [-] k t test-method factor [-] t error term [-] R ACC,O -1 inverse effective carbonation resistance of concrete, determined in accelerated carbonation conditions (ACC) [m 5 /(skgco 2 )] R k R 1 1 NAC,0 t ACC,0 t (49) R NAC,0-1 C S t t 0 w inverse effective carbonation resistance of dry concrete, determined with specimens under defined preparation and storing conditions under natural carbonation conditions (NAC) [m 5 /(skgco 2 ] gradient of the CO 2 -concentration [kg CO 2 /m³] time in service [s] reference period [s] weather exponent, taking into account the micro climatic conditions of the regarded concrete surface (e.g. w = f(tow, p splash with Tow: Time of wetness; p splash = probability of splashed surface due to rain event), introduced by [xiv] [-] The carbonation resistance comprises the effective diffusion coefficient D eff,0 and the binding capacity a of the concrete: R NAC,0 a D eff,0 (50) a D eff,0 where CO 2 -binding capacity of concrete [kgco 2 /m³] effective diffusion coefficient of dry carbonated concrete [m²/s] M a 0,75CcDH M CO 2 CaO (51) C CaO content in cement [M.-%/cement] c cement content [kg/m³] DH degree of hydration [-] M molar masses of respective substance [kg/mol] 32(169)

33 In (55) the inverse carbonation resistance R ACC,0-1 of concrete prepared, cured and tested in an accelerated test under defined laboratory conditions, is transformed to a carbonation resistance R NAC,0-1 under natural carbonation conditions (NAC). The resistance R NAC,0-1 will then be multiplied by a factor k c, accounting for concreting and curing procedures on construction site, deviating from the reference laboratory conditions. As the carbonation resistance of concrete sampled form existing structures already comprises the effect of curing, the following arrangement is proposed: X C 1 t0 2 krh kc ( kt RACC, 0 t ) CS t [m] (52) t w leading to X C 1 t0 2 krh ( kt kc RACC, 0 t ) CS t [m] (53) t w where: R ACC -1 = k c R ACC,0-1 (54) R ACC -1 and inverse carbonation resistance for concrete with a given curing, determined in ACC-Test k c R NAC,0-1 = (k t k c R ACC,0-1 + t ) (55) R NAC,0-1 inverse carbonation resistance for concrete with defined preparation and curing conditions, determined in NAC-Test The degree of water saturation controls the penetration rate of CO 2 into the concrete. The water saturation degree is a function of the concrete composition, the relative humidity (RH) and the Time of Wetness (ToW). The degree of water saturation of concrete may be considered as constant in a certain depth x of the concrete, [xiv]. Since carbonation is restricted to the outer portion of the concrete cover, the approximation of using meteorological data on the quantity of rain events and the relative humidity of the surrounding air seems reasonable. For the carbonation of concrete, the following limit state can be considered [xi]: pf p(xc d cover ) ( ) pt arget (56) p Probability [-] p f failure probability [-] X c carbonation depth [m] cover depth [m] d cover probability distribution function of standard normal distribution reliability index p target target failure probability which has to be defined by the principal or a national standard [-] 33(169)

34 Explicitly (56) expresses the probability that the carbonation front X C reaches or exceeds the cover depth d cover, which should be smaller than a predefined value. The parameters to be statistically defined are given in Table 5: Table 5. Input parameters for the carbonation model according to [xi]: Parameter family Parameter Material -1 R AAC,0 Environmental k RH, w, C S Execution/ Curing k c Test k t, t Geometry d cover 4.2 Inverse Carbonation Resistance The effective carbonation resistance of the concrete can either be measured by an accelerated carbonation test (ACC), as is done for the durability design of new structures, or by measuring the carbonation depth of an existing structure. In the later case, the parameters may then be grouped according to: X C 2 C s R t t t 1 0 Carb w (57) with R 1 Carb k RH R 1 NAC k RH ( k c k R t 1 ACC,0 t ) (58) R Carb effective carbonation resistance of concrete on site [m 5 /(skgco 2 )] The effective carbonation resistance parameter R Carb is dependent on the composition, placement and curing of the concrete as well as on the relative humidity. The Accelerated Carbonation has been chosen as a compliance test for new structures [xii]. The carbonation resistance R ACC,0 is the result of this test, which can be regarded as the potential resistance. 34(169)

35 100 Average inverse carbonation resistance [10-11 m 5 /(s kgco 2 )] w/b: , , , ,4 16,9 13,4 9,8 8,3 5,2 6,8 8,3 6,5 5,5 3,1 3,5 0,3 1,9 2,4 CEM I 42.5R CEM I 42.5R+15%FA CEM I 42.5R+5%SF CEM III/B Figure 9. Default data for the inverse carbonation resistance R ACC,0-1 [10-11 m 5 /(skgco 2 ] determined in accelerated carbonation (ACC) test, [xiv] A detailed description of the test procedure is presented in LIFECON Condition Assessment Protocol, deliverable D3.1 [i]. For existing structures the following investigation options are proposed: (a) If concrete composition is known R ACC,0 may be chosen from database or existing literature data [xiv]. (b) Direct measurement of the carbonation depth at the existing structure (see Inspection Catalogue in Appendix of D3.1 [i]) (c) Accelerated carbonation testing with specimens (e.g. cores) from structure (see Inspection Catalogue in Appendix of D3.1 [i]) Application of option (a), as is performed for new structures, determines the carbonation resistance at defined curing and environmental conditions (R ACC,0 ) and demands for the knowledge of the concrete composition (most important binder type and w/b-ratio). Option (b) - Direct Measurement of Carbonation Depth - is a simple and non-expensive test, which can be applied to any concrete structure. The effective carbonation resistance R carb of the concrete includes the influence of the concrete quality (R ACC,0 ), relative humidity (k RH ) and curing (k c ). Structures with high resistance and/ or low exposure aggressiveness (e.g. high humidity and/ or high Time of Wetness) may show carbonation depth readings close to zero, because carbonation is not the decisive deterioration mechanism. However, it must be kept in mind that in "young" concrete structures carbonation may not yet have taken place to an extent which may already be measured, but may do so within the service life. In this special case this option should not be applied yet. 35(169)

36 Applying option (c) - Accelerated Carbonation Testing - will determine R ACC -1 with inherent influence due to curing and production procedure (k c ). This approach has to be followed especially for young structures, where carbonation has not taken place yet in a sufficient degree to be measured precisely. In general can be stated, that with increasing degree of information the quality of the prediction model is increased, as these can be used for a Bayesian model update, see chapter Weather Exponent w In [xiv] the exponent w is called a weather condition factor, due to the fact, that a rain event will lead to a saturation of the concrete surface which will, at least temporarily, prevent a further carbonation progress since the pores are widely filled with water, Figure 10. effectivecarbonation periods x v t 1 t 2 outdoor exposure, unsheltred stored in laboratory x c3 x c2 x c1 t d1 t w1 td2 t w2 Figure 10. Progress of carbonation of specimens stored under different exposure conditions (laboratory, outdoor-unsheltered) The weather function W(w, t) considers the derivation of the carbonation process of unsheltered structures from the square-root of time law, see Figure 11: t 0 W t w (59) W weather function [-] t time [s] t 0 reference time [s], age when ACC-test is performed (28 d) w weather exponent The carbonation evolution depends strongly on the frequency and the distribution of the wetting periods [xiv]: w a w ToW b w (60) w weather exponent [-] 36(169)

37 ToW Time of Wetness [-] a w Regression parameter [-], D (µ = 0,50) b w Regression parameter [-], ND (µ = 0,446; = 0,163) Figure 11. Progress of carbonation in different exposure environments,[x] To quantify the time of wetness ToW a criterion is required to register a rain event (duration, intensity) as such. The moisture content prior to the rain event, as well as the moisture saturation content of the concrete are decisive for the zone being affected by a certain amount of precipitation, which leads to a high degree of model complexity. For reasons of simplicity all days with amounts of rain above values of h rain = 2.5 mm/d were chosen in [xiv]: Amount of days with rain h 2,5mm / d ToW 365 (61) Data of carbonation depths of unsheltered structures have to be related to meteorological data in order to determine values for the regression parameters a w, b w in (60). In this procedure two boundary conditions have to be met: Boundary 1: ToW = 0 w = 0 For the case of a sheltered structures the time of wetness will be ToW = 0. The carbonation will proceed according to the t-law, resulting in a weather exponent of w = 0, see (57). 37(169)

38 Boundary 2: ToW = 1,0 w = 0,50 For a continuous rain load the time of wetness equals to ToW = 1. A progress of the carbonation mechanism is not to be expected, leading to the boundary of w = 0,50 (hereby canceling the time variable), see (57). For vertical components the probability to splashed by driving rain, has to be taken into account, yielding the above stated boundary conditions: (psplash ToW) w 2 w weather exponent [-] ToW Time of wetness [-] b w b w regression parameter [-],ND (µ = 0,446; = 0,163) p splash probability of a splash event in the case of a decisive rain event, dependent on the orientation of the structure [-] p splash,i d(wir) d(r) d(w i r): sum of days during one year with wind in considered direction i, while at the same day a decisive rain event (precipitation above a level of h rain 2,5mm) is taking place d(r): sum of days during one year with decisive rain events 4.4 Relative Humidity Factor k RH The quantification of the relative humidity factor may be performed by comparing data obtained in the considered climate with data of a reference climate. The parameter k RH describes the effect of the average level of humidity, with k RH = 1 for a reference climate, usually set to T= +20 C/ 65% RH, [xiii]: (62) (63) k RH g f xc,obs 1 RH f xc,lab 1 RHref (64) with x c,obs and x c,lab are observations of the carbonation depth made in the field and in the laboratory: X C,obs observed carbonation depth in the field [-] X C,lab carbonation depth measured in the laboratory at reference climate (T= +20 C/ 65% RH RH relative air humidity obtained at the nearest weather station [-] RH ref reference humidity, here 65% [-] f exponent in the range of 1-10 [xiii] [-] g exponent in the range of 2-5 [xiii] [-] 38(169)

39 1.60 parameter k RH k RH (f RH =5, g RH =2,5) k RH (f RH =5, g RH =2) k e (f RH =5, g RH =3) relative humidity RH real [%] Figure 12. Functional relationship of the relative humidity and the parameter k RH according to (64), [xiv] Data regarding RH must be collected from the nearest weather station and statistically analyzed (e.g. using a Weibull (W) distribution [xiv]). 1,00 0,030 0,80 0,020 0,60 0,010 0,40 0,20 0, , Figure 13. Relative frequency and cumulative frequency of the relative humidity in the city of Aachen (Germany) for the year of 1996, [xiv] 4.5 Surface Concentration of Carbon Dioxide C S The CO 2 concentration of the atmosphere is influenced by two major factors: - combustion of fossil fuels - global reduction of the vegetation Currently the average CO 2 content of the air varies between 350 to 380 ppm, which equals 0,00057 to 0,00062 kgco 2 /m³. Data in [xv] indicates a rather constant standard deviation of 10 ppm. Nevertheless on a micro environmental scale these values may considerably change, due to natural dips (processes reducing CO 2 content: e.g. absorption from sea, photosynthesis of vegetation) or low air exchange rates (e.g. in tunnels). 39(169)

40 Extrapolating the current trends an estimation of the increase rate in CO 2 concentration of the atmosphere C S,Atm may be in the range of e.g. 1,5 ppm/a (1, kgco 2 /m³a) [xv]. C S = C S,Atm + C S, Em (65) C S,Atm C S, Em CO 2 concentration of atmosphere [kgco 2 /m³] local additions, due to special emissions (e.g. in tunnels) must be measured [kgco 2 /m³] (C S,Atm ) = 5, t2, [kgco 2 /m³] (C S,Atm ) = 1, (66) t time [a] 4.6 Curing Parameter k c The curing influence on the diffusion properties of the concrete depends on the chosen material, as well as on the environment and the curing conditions. In order to analyze data of carbonation depths sorting criteria have to be introduced, as e.g.: - time of inspection - environmental classification (e.g. according to EN 206: XC1-4) - material classification (binder type, w/c) The data is related to a reference execution procedure, which in [xi] was chosen to 7 day moist curing, for which k c,ref = 1 (without differentiation of the moist curing method): x x c,t c,ref k k c,t c,ref k c,t (67) Based on a Bayesian linear regression the relation of the curing time and the curing factor k c was determined in [xi]: k a t b c c c c (68) k c curing factor [-] t c duration of the curing [d] regression parameter, a c = 7 bc [1/d], [xiv] a c b c regression parameter, b c : ND ( = -0,567; = 0,024) [-], [xiv] 4.7 Test Method Factors k t and t The factors k t and t (slope and y-intercept in ) relate data obtained in tests with Accelerated Carbonation (ACC, increased CO 2 -concentration) to conditions of a Natural Carbonation (NAC). 40(169)

41 R NAC,0-1 [10-11 m 2 /s/kgco 2 /m 3 ] CEM III CEM I R -1 NAC,0 = k t R -1 ACC,0 + k t : ND (1,25; 0,35) [ - ] : ND (1,0; 0,15) [10-11 m²/s/kgco 2 /m³] R ACC,0-1 [10-11 m 2 /s/kgco 2 /m 3 ] Figure 14. Relationship of the inverse carbonation resistances, obtained under natural conditions (NAC) and in an accelerated test (ACC) [xiv] The regression analysis shows that those inverse carbonation resistances R NAC,O -1 determined with natural carbonation conditions will be larger by an average factor of k t = 1,25 (slope). This may be explained by the fact, that in an accelerated test, due to the reduced test duration by increasing the CO 2 -concentration the drying front has not yet penetrated as deep, as it is the case under natural conditions (though testing under the same climatic conditions being 20 C/65 RH). This will slightly retard the carbonation process under ACC conditions. This theoretically implies values of R ACC,0-1 = 0. As concrete may not possess an infinite resistance, this leads to a so called error term t > 0 (y-intercept in Figure Concrete Cover d c The concrete cover is chosen during the design phase but will always be subjected to variations due to the labor precision. Values of the concrete cover are restricted to the positive domain (negative values are not possible) [xiv]. Additionally the domain should have a maximum boundary, as the cover can not exceed the geometric boundaries of the component. These conditions lead to the application of a beta-distribution for the concrete cover. The case that reinforcing steel may be situated right next to the formwork can not be considered with this type of distribution. These cross-errors need to be avoided by quality management for. Three levels for a statistical quantification of the cover depth are proposed for durability design purposes, [xiv]: Without requirements for the workmanship: Beta: = d cover, nom ; = 10,0 mm; a = 0 mm; b = 5c nom d element 41(169)

42 Regular requirements for the workmanship: Beta: = d cover, nom ; = 8,0 mm; a = 0 mm; b = 5c nom d element Special requirements for the workmanship: Beta: = d cover, nom ; = 6,0 mm; a = 0 mm; b = 5c nom d element mean value standard deviation For existing structures and are derived from measurements of the cover depth, as explained in the Appendix of D3.1 [i]. 4.9 Shortcomings of the Model The following aspects are neglected: - Different moisture properties of the carbonated and non-carbonated cover zone - Effect of the concrete temperature: Due to higher temperatures mainly the chemical reaction of CO 2 with the hydroxides of the pore solution is accelerated. The chemical reaction is a process which takes place much faster as the ingress of CO 2. Temperature effects are thus of minor importance. - A change of the carbonation resistance with increasing age due to hydration: Age dependent data is not available on this topic. So far only default data of concrete tested at an age of 28 days is provided for various binder types. - Interaction of carbonation and other degradation mechanisms as e.g. frost 5 Case Studies on Carbonation induced Corrosion 5.1 Television Tower Old Structure Provided Information The treated object is a television tower with an age of 32 years at the time of investigation. The tower is of a common age, when damages due to carbonation usually start to occur. This implies that a carbonation depth can actually be measured on-site. This part is meant to demonstrate what type of information usually can/ will be provided by the principal. Here the owner provided: - extracts of the service specifications - data on the geometry of the tower - general notes on the concrete composition 42(169)

43 5.1.2 Description of the Object The tower was opened to the public in the area of Munich. The shank is a reinforced concrete tube with a diameter of 16,50 m on ground level (GL). Up to a height of 145 m the tower is designed as a cubic parboil. Further above the shape is conical. The thickness varies from bottom to top between 2,0 and 0,65 m, Figure 15. Platform for visitors 192,6 m III Antenna platform 167,7 m II Antenna platform 159,8 m I Antenna platform 151,9 m Ground Figure 15. Scheme of television tower in Munich-City The concrete of the shank was placed in sections with a width of 2 m using a climbing formwork. Three of theses sections in various heights were chosen as investigation areas Exposure Zones A major impact on the carbonation process and the subsequently induced corrosion is given by the moisture state of the component. In areas with high degree of water saturation lower carbonation depths will be determined for the same concrete quality. Due to the fact that a tower is exposed to different loads of driving rain, distinct exposure zones are to be separated. Thus a durability calculation of a unsheltered vertical concrete surface, as is the case here, has to be performed for each orientation separately, since the concrete resistance and the environmental loading varies (see "Modular Systematic" in D3.1 [i]). The following exposure zones were investigated. The surface of the tower was divided in four zones according to the orientation: east (1), north (2), west (3) and south (4). 43(169)

44 5.1.4 Overview of Performed Investigations The tower has been investigated as follows: - visually up to a height of 30 m (not treated in this report) - measurements of the concrete cover and of the carbonation depths were performed in three levels from ground level:1,0 m, 8,0 m and 28,0 m The inspections and service life calculations of the structure were performed by [xvi] and published in [xvii] Measurement of Concrete Cover, d cover The measurement of the concrete cover has been executed with commercially available equipment [xviii], following the procedure as explained in the appendix of D3.1 [i]. In each investigation section a field of width/ height b = 2 m/ h = 1 m has been investigated for each orientation. The planned nominal concrete cover was supposed to yield c nom = 50 mm. The entrance square is situated at the east side of the tower. A measurement of the concrete cover could therefore not be performed at a height up to h = 1 m above GL. Table 6. Compilation of concrete cover data StD D ND Exposure Zone 1 East 2 North 3 West 4 South Level Height above GL Min/ Max values Result of data analysis h d cover, min d cover, max d cover, mean StD D-Type [m] [mm] [mm] [mm] [mm] [-] 1 1 Entrance ,2 8,0 ND ,9 5,7 ND ,8 17,8 ND ,3 17,2 ND ,2 8,7 ND ,1 8,0 ND ,8 11,1 ND ,2 10,2 ND ,8 17,3 ND ,4 10,1 ND ,9 4,3 ND Standard deviation Distribution Normal Distribution Measurement of the Carbonation depth, X c The determination of the carbonation depth was performed by drilling two holes close to each other. The holes were cleaned with a high pressure air blower. The web between the two holes was broken out with a hammer and a chisel and cleaned up with compressed air. The surfaces were sprayed with a solution of phenolphthalein. The distance from the concrete surface to the depth of the characteristic color was recorded. Readings of the carbonation depth were taken for 44(169)

45 all of the investigation areas, four times each, at sites C1- to C4, except at a height h = 1 m above GL of the north, south and east side (Entrance Area). The methods and respective accuracy are explained and benchmarked in the appendix of D3.1 [i]. Table 7. Carbonation depth X of the television tower. Gray colored cells display values in the area of obviously porous concrete Site X1 X2 X3 X4 Mean StD for area Mean for area Orient. H a. GL [m] [mm] [mm] [mm] [mm] [mm] [mm] [mm] 1 not determined (n.d.) - N ,5 1,3 3, , n.d. 2,3 W ,0 1,0 2, ,3 1 n.d. - S ,3 1,2 4, ,0 1 n.d. (Entrance Area) - E ,5 4,4 10, ,0 Note: areas with porous appearance are displayed in grey n.d. not determined Semi-Probabilistic Reliability Calculation With the information from the structure investigations the current reliability level can be checked according to the procedure already presented in chapter 3.3. The calculation will be performed for the exposure zone 4 South side, because the analysis revealed that the relatively low concrete cover of the southern parts of the tower caused the lowest reliability index over time t. Transforming the stress variable (carbonation depth) and the resistance (concrete cover) into standard space gives: U R 38,4 10,1 U 1 2 S11,5 1, 2 (69) L(U 1,U 2) R S 10,1U11,2U 2 26,9 AU1BU2 C 0 (70) 4. Calculation of the distance of the limit state line from origin using the so called Hesse normal format (comparison of coefficients A, B, C): C 2, 65 1,8 2 2 A B (71) 45(169)

46 Currently the target reliability of 0 = 1,8 is fulfilled and a further in depth investigation would not be required. However, for demonstration purposes a full-probabilistic calculation is demonstrated in the next step Inverse Carbonation Resistance of Concrete, R ACC,0-1 From service specifications arose: - the concrete quality is a B450 (obsolete terminology), with a compressive strength of 45 N/mm² - the cement is a Z 375 (obsolete terminology), with a compressive strength of 37,5 N/mm² - the w/c ratio had to be chosen as low as possible, but requirements were not quantified (in the case study it was assumed to w/c = 0,50) According to investigations performed on different concrete compositions [xiv] the carbonation resistance R -1 ACC,0 of the concrete may be evaluated according to the following reference mixture: CEM I, c = 320 kg/m³, w/c = 0,50 giving: Distribution Type: normal distributed (ND) Mean value: = 6, [m 5 /(skg CO 2 )], [xiv] Standard deviation (StD): = 0,45 = 3, [m 5 /(skg CO 2 )], [xiv] Relative Humidity Factor, k RH The parameter k RH describes the effect of the average level of humidity. For a reference climate (T= +20 C/ 65% RH) the factor k RH = 1, as outlined in chapter 4.4 (Relative Humidity Factor k RH ). The position of the nearest weather station is Munich City, only existing since July Therefore data from the weather station Munich-Nymphenburg of the period from 1991 to 1996 was added. As an example the distribution plot of the relative humidity RH for the year 1999 measured in Munich City is given in Figure 16. As can be seen in Figure 16the relative humidity varies in the range of RH min = 34% to RH max = 100%. According to the data of the past 10 years the following input data was calculated with the software package STRUREL [xix], which is used as an ADD-In Tool for the LIFECON project: Distribution Type: Beta Mean value: µ = 74 [%] 46(169)

47 Standard deviation: = 14 [%] Boundaries: 34 RH 100 [%] Probability 1.0 Distribution Plot (Beta) - [RH] Valid Observations of[import_data][rh] Figure 16. Probability distribution function of daily relative humidity RH [%] of year 1991 measured at station Munich-City Weather Function W The necessary input data in the weather function for each of the four considered exposure zones are given in Table 8. The time of wetness ToW has been calculated from data of the weather stations Munich-City and Munich-Nymphenburg according to chapter 4.3. The probability of driving rain in a considered direction i" p i was determined by the mean distribution of the wind direction p wind during a rain event (for sufficient duration; here 10 years), see deliverable D4.3 [xx]. Table 8. Input data for the determination of the weather exponent w Exposure Zone Position ToW [-] p i [-] b w [-] [xiv] 1 North 27,3 0,021 ND 2 West 27,3 0,375 = 0,446 3 South 27,3 0,037 = 0,163 4 East 27,3 0, Curing Factor, k c For the current structure data on the curing duration was not available and was thus assumed to t c = 1 day. The assumption can be regarded to be on the safe side, but rather reasonable for a climbing formwork. k a t 3,011 b c c c c bc (72) a c b c regression parameters[-], set to a c = 3,01 according to [xiv] regression parameters[-]; normal distributed: = -0,567; = 0,024 according to [xiv] 47(169)

48 Carbon Dioxide Concentration of the Environment, C S In the calculations for the television tower the CO 2 concentration is assumed as constant. On the safe side a value for the year 2100 has been calculated to: (C S,Atm ) = 5, t2, = 8,210-4 [kgco 2 /m³] (C S,Atm ) = 1, (73) Concrete Cover, d cover As input for the service life prediction a statistical description of the concrete cover is essential. The measured data has been evaluated with the software STATREL [xix] (Add-In Tool for LIFECON). The data fits well with to a Normal Distribution (ND) although distribution types with bottom and top limits (e.g. beta distributions) are physically more reasonable, see Figure 17. Probability 1.0 Distribution Plot (Normal (Gauss)) - [cover ea] Valid Observations of[import_data][c] Figure 17. Statistical analysis of the actual concrete cover of the investigation level 3 (28 m above GL) for the East side (Exposure Zone 1) Calculation without Data Update The calculation of the time dependant development of the carbonation depth, which may be performed with a simple pocket calculator or an excel spreadsheet using the mean values of the quantified data in chapter (Calculation without Data Update), indicates that the calculated carbonation depths exceeds the actually measured values, Figure 18 and Table 9. 48(169)

49 25 East North Depth of Carbonation x c [mm] South West Time of Inspection Time [a] Figure 18. Calculated time dependant development of the carbonation depth and actually measured values at an age of t = 33 a Table 9. Comparison of calculated mean values and actually measured carbonation depths after t = 33 a in four exposure zones Carbonation depth at an age of t = 33 a [mm] Exposure 1 East Exposure 2 North Exposure 3 West Exposure 4 South calculated mean 12,8 12,0 4,8 9,7 measured value (see Table 7) 10,6 3,0 2,8 4,1 One explanation for the deviations of calculated and measured values is the fact, that some of the input parameters were safe assumptions (e.g. w/c ratio, curing time t c ) since no reliable information was available. In the axis of the common wind direction West-East the results of the prediction fit fairly well with the actual measurements. However, the deviations in the North-South axis are probably due to the structure geometry. This may be explained by the parameter p i in the weather function (see chapter ). The probability p i of driving rain hitting a surface facing the direction i describes the average distribution of the wind direction during rain events. The data is collected separately for each orientation. For a round geometry, as it is the case for the investigated television tower, the water hitting the structure will run along the surface. This effect will especially influence the surfaces at the north and south side (uncommon wind direction). Water which mainly hits the west side, causing low carbonation depths (see Table 9) will reach the northern and southern surfaces as well, hereby reducing the carbonation rate in these zones. 49(169)

50 main wind direction west - east Figure 19. Scheme of wind streams around a round structure Boundary Conditions for Calculations with Bayesian Update By introduction of inspection data as a boundary condition following the ideas detailed in chapter 2.2.3, the precision of calculations of the remaining service life will be increased. The implementation of inspection data (carbonation depth) is called Bayesian Update and can be performed e.g. with the program SYSREL of the STRUREL software package [xix]. Additionally to the limit state function the formulation of boundary conditions can be inserted, which account for the actual investigations. For the present case study the carbonation data from inspections at an age of t inspection = 33 a (Table 7) are included. The boundary condition to be considered (Equality Constraint) is: t 0 X (t 33a) 2k (k k R ) C t 33a C,inspection RH t c ACC,0 t S t 33a w (74) Example for Calculation with Bayesian Update - Exposure Zone 4 South The calculation including an data update will be demonstrated for the exposure zone 4 South side, because the analysis revealed that the relatively low concrete cover of the southern parts of the tower caused the lowest reliability index over time t. The quantified input parameters are given in Table 44. The result of the calculation is the reliability index and the failure probability p f respectively over time t in the time domain of t target (which here has been set to 100 years). For this decisive level in each exposure zone the time dependent reliability index [-] and failure probability p f [%] have been calculated as displayed for the South side. 50(169)

51 Table 10. Input data for calculation of remaining service life, lines 10 and 11 are equality constrains considering inspection data on carbonation depth No Input Sub- Input Unit Source of data D-Type Mean StD 1 d cover [mm] Inspection ND see Table 6 Weibull RH [%] [xv] (max) 76,9 12,2 2 k RH RH ref = 100 [%] [xiv] Const g RH [-] [xiv] Const. 2,5 - f RH [-] [xiv] Const. 5,0-3 k c b c [-] [xiv] ND -0,567 0,024 tc [-] [xiv] ND k t [-] [xiv] ND 1,25 0,35 [m 5 (skgco 5 2 )] 1,010 t ([mm 5 [xiv] ND 0, (akgco 2 )]) (315,5) (48) 6 C S [kgco 2 /m³] [xv] ND 8, , t target [a] choice Const. here ToW [-] [xiv] Const. 27,3 - b w [-] [xiv] ND 0,446 0,163 W p i [-] [xv] Const. 0,014 - t 0 [a] time at ACC 0,0767 Const. test is fixed (equals 28d) - -1 [m 5 (skgco 9 R 2 )] 6,810 ACC,o ([mm 5 [xiv] ND 3, (akgco 2 )]) (2145) (969) 10 x c,insp [mm] Inspection ND 4,1 1,2 11 t insp [a] Inspection Const D-Type: Std: distribution type standard deviation 5,0 4,5 Basic calculation 4,0 Bayessches updating considering the inspection data reliability index [-] 3,5 3,0 2,5 2,0 1,5 1, inspection time of exposure [a] Figure 20. Time dependent reliability index [-] of exposure zone 4 South 51(169)

52 0,10 0,09 probability failure p f [%] 0,08 0,07 0,06 0,05 0,04 0,03 Bayessches updating considering the inspection data 0, inspection time of exposure [a] Figure 21. Time failure probability p f [%] of exposure zone 4 South Evaluation of Calculation Results The calculations demonstrated that due to the relatively low concrete cover the south side of the tower has to be considered as the most critical area. The results were verified by the symptoms discovered during visual examinations, revealing corrosion stains in this exposure zone. At an age of t target = 100 years approx. 0,09% of the reinforcement will be depassivated. The calculation with the simple semi-probabilistic approach indicated a reliability index of around = 2,6 at the time of inspection, which is slightly higher than the result obtained with the a priori model (without knowledge of inspection data), whereas the model which was improved by a Bayesian update showed a significant higher reliability level at the time of inspection. The reason for this effect is that the a priori model includes a high level of uncertainty in the various input parameters. The semi-probabilistic calculation include only two stochastic variables which were determined by measurements. However the least amount of uncertainty is inherent in the updated full-probabilistic model, which thus gives the highest reliability level. The calculated results can be compared to requirements stated in codes of practice or by the owner. As a Code of practice the EuroCode 1 [iii] may be consulted: Table 11. Planed Service Life according to EC 1 (Part 1, Table 2.1 [iii]) Class Planed Service Life [a] Examples 1 1 to 5 Structures with limited use 2 25 Exchangeable components: e.g. bearings 3 50 Buildings and other common structures Monumental structures, bridges and other engineering structures 52(169)

53 Table 12. Value indications for the reliability index according to EC1 (Part 1, Appendix A, Table A2, [iii]) 1) Limit State [-] (at end of planned service life) [-] (after one year) ULS 3,8 4,7 Fatigue 1,5 to 3,8 1) - Serviceability 1,5 3,0 dependent on the degree of inspection and repair possibilities 5.2 "Young Bridge Provided Information The treated object is a bridge, which is less than one year old. Due to insufficient cover depth, as was detected during acceptance inspection, the necessity of calculating the remaining service life arose. The following data was accessible prior to the investigations: 1. design documents: - shuttering plan - reinforcement plans 2. As built specifications: - concrete catalogue - extract of the construction diary - information on quality management 3. Inspection reports: - list of insufficiencies Description of the Object The bridge is a crossing of two municipal roads situated in a township close to Munich. The construction process was finished at the beginning of the fourth quarter of the year The bridge is designed as a frame with a total length amounting to l tot = 30 m and a span of l s = 18 m, see Figure 22 and Figure (169)

54 Figure 22. Longitudinal section of the bridge Figure 23. Cross section of the bridge The frame designed of a concrete B35 (compressive strength 35 N/mm² determined according to the German standard DIN 1045). The water-cement-ratio was set to w/c = 0,50. According to the German additional technical contract requirements (ZTV-K 1996) the nominal value of the concrete cover was set to c nom = 45 mm, with a minimum cover depth of c min = 40 mm. During the first assigned bridge investigation it was recognized that the minimum cover depth had partly been fallen short. Areas with low concrete cover were: - cantilevers - bottom areas of the abutments 54(169)

55 Background of suchlike investigations is that a contractor may not have to provide additional repair measures on its own cost, if prove can be provided that due to the concrete quality a local undershooting of the minimum cover depth will be compensated and therefore the costs on maintenance and repair will not exceed a general accepted degree Exposure Zones In the present case study a division into exposure zones (see "Modular Systematic" in D3.1 [i]) took place. The following surface areas were investigated: 1. abutment at West and East sides 2. bottom of the cantilevers at North and South side 3. Cantilevers North and South Figure 24. Example for the division of the bridge into components and exposure zones Overview of Performed Investigations The following investigations were performed by [xvi]: 1. core drilling: - bridge deck - both abutments 2. Accelerated Carbonation Tests on cores 3. Measurement of the concrete cover - sides of the cantilevers - bottom of the cantilevers - both abutments 55(169)

56 5.2.5 Core Drilling and Accelerated Carbonation Testing In Case Study One Television Tower, see chapter 5.1, the Inverse Carbonation Resistance R ACC,o -1 has been extracted from literature (data base) studies and was updated with measured data on the carbonation penetration front obtained throughout structure investigations. This approach is only applicable for structures for which a response to the environmental loading, i.e. an exposure to CO 2, can be measured in form of a penetration depth. For the present object under observation a penetration depth was not detectable, due to the short exposure duration. Therefore accelerated carbonation testing had to be performed in order to determine the real carbonation resistance. In every exposure zone (see chapter 5.2.3) a core with diameter = 50 mm was sampled with a length of l = 50 mm. The test procedure took place according to []: The cores were stored for 21 days under constant climatic conditions (T = 20 C/ RH = 65%). Afterwards these were kept for 28 days in a carbonation chamber with a CO 2 -concentration of C s = 2,0 Vol.-%, hereby accelerating the carbonation process. After 28 days the cores were split and the carbonation depth determined using a phenolphthalein indicator. The carbonation depth was measured at four positions for every core with a precision of 0,5 mm, see Table 13. Table 13. Mean values of the penetration depth measured in ACC test Location of withdrawal Carbonation depth Xc [mm] Core1 Core2 Core3 Core4 Mean Abutment East 5,0 6,5 6,0 2,0 southern cantilever of 7,0 5,0 5,0 5,5 superstructure 5,5 northern cantilever of 4,5 7,0 7,0 5,0 superstructure Measurement of the Concrete Cover, d cover The average concrete cover of all investigated areas was above a value of d cover = 45 mm. Low cover depths were measured for the western abutments and the southern cantilevers amounting to d cover = 42 mm and d cover = 36 mm Inverse Carbonation Resistance, R ACC,0-1 In order to determine the actual carbonation resistance of the built in concrete quality, accelerated carbonation tests (ACC) were performed, see chapter The Inverse Carbonation Resistance R ACC,0-1 is calculated according to [xii] by inserting the mean of the penetration depth into the following equation. 56(169)

57 1 Xc R ACC,0 T 2 (75) X C mean of penetration depth determined with ACC-test T constant = 419,45 [((skgco 2 )/m³) 0,5 ] This yields: R ACC,0-1 : normal distributed (ND) Mean: = 6, [m 5 /(skg CO 2 )] Standard deviations (StD): = 0,45 = 3, [m 5 /(skg CO 2 )], [xiv] Environmental Parameter Relative Humidity Factor, k RH For the calculations of k RH the same meteorological data as for Case Study One Tower (Chapter 5.1.9) could be utilized Curing Factor, k c In the ACC-test specimens were tested in which the curing conditions were inherent. Therefore a curing factor could be set constant to k c = Carbon Dioxide Concentration, C s For C s the same assumptions were made, as for Case Study One (see chapter ) Calculations and Results In contrast to Case Study 1 Television Tower the calculations of the remaining service life including a Bayesian Update (Chapters and ) can not be performed, because data on the carbonation penetration depths is not obtainable at early structure age. The only updated information considered is the real concrete resistance of the structure, tested in an ACC test, see chapter Inserting all of the input data to the limit state function the result of the computations with the software package STRUREL [xix] is the reliability index or the failure probability p f over time, as already shown in e.g. Figure Semi-Probabilistic Model on Chloride Ingress 6.1 Mathematical Background Fick s First Law In water dissolved chloride follow in a stochastic manner the Brown molecular movement. In case of a concentration gradient, chloride ions are aim for an equilibrium and thus move from 57(169)

58 high levels of concentration to lower concentrations [xxi]. The diffusion of chloride in concrete can be expressed by means of the ionic flow J, which is by definition positive, if the chlorides move in positive x-direction. If the concentration decreases in x-direction the flow is negative: c J D x (76) J ionic flow [kg/m²s] D Diffusion coefficient [m²/s] c Chloride concentration in solution [kg/m³] x distance [m] Fick s Second Law The diffusion process is fully described, if the particle density is given as a function of space and time t. Starting with Fick s 1 st law and considering the law of mass conservation Fick s 2 nd law is obtained: c 2 c D 2 (77) t x The application of Fick s laws of Diffusion to describe the transport processes in concrete are based on the simplified assumption that concrete is homogeneous, isotropic and inert [xxii]. Furthermore the movement of negatively charged ions induces the movement of positively charged ions. It is a well known fact that sodium and chloride move at different velocity [xxiii], which is neglected when applying Fick s law. While chlorides are diffusing in the pore system they are chemically and physically bound: c t J c x t b (78) c b portion of the bound chlorides within concrete If (76) is inserted to (78) and the diffusion coefficient is considered as time dependent the transport is described as follows: c c t t b 2 D(x, t) c c D(x, t) 2 x x x (79) Chloride binding may for instance be described with the so called Freundlich-Isotherm. If the isotherm is related to the pore volume of concrete one obtains [xxiv]: C b 0 1 W α f B B 1 f c n W 0 n a α V P c A c (80) W n 0 Portion of bound water [-] 58(169)

59 Hydration degree [-] V P Pore volume [m³/kg dry concrete] f c Binder content [kg binder/ kg concrete] which results in: c b B 1 t A B c c t (81) If (81) is inserted to (79) the general relationship for the time dependent non-steady state diffusion of chlorides under consideration of chloride binding is obtained: c t 1 1 A B c 2 D(x, t) c c D(x, t) x x x B1 2 (82) An analytical solution is hard to derive, which calls fort he application of numerical approaches Types of Diffusion Coefficients In the current literature tremendous disagreement is observed when it comes to the terminology of diffusion coefficients. There are real (D), effective (D eff ), apparent or achieved (D app or D a ), steady state (D SS ), non-steady state (D nss ), potential (D p ), etc. diffusion coefficients. A consistent definition of these terms is aimed for currently in the RILEM-TC-178. In order to prevent any bewilderment of the reader, here only the following terms are used: a) effective diffusion coefficient D eff : is a steady state diffusion coefficient including the effect of: different transport velocity of anions and cations The effective diffusion coefficient is the result of diffusion cell tests. In these a thin concrete specimen separates a chloride free and a chloride containing solution. The chloride concentration of the at first chloride free solution is measured vs. time. Once a steady ingress rate is reached, D eff is calculated according to Fick s 1 st law. The obtained value must then be related to the porosity of the concrete. b) apparent diffusion coefficient D app is a non-stationary diffusion coefficient including the effects of: different transport velocity of anions and cations hydration of cement paste 59(169)

60 concentration dependent and hence time dependent chloride binding This parameter is derived by evaluating chloride profiles which can be obtained in immersion tests or structure investigations applying a solution of Fick s 2 nd law of diffusion. 6.2 Choice of Model Due to the extreme complexity of the evolution and interactions of the mechanisms contributing to the ingress of chlorides into concrete, all current models are based on simplifications and assumptions and hence are more or less empirical. With the: time constraint: depth x > 0 and time t = 0 follows that the concentration c is equal to the initial concentration: c = c i and the geometrical constraint: for x = 0 and t > 0 the concentration c is equal to the surrounding environment: c = c 0 the most common approach known as the error function solution of Fick s 2 nd law can be derived: c c 0 x erf c c 4(t t ) D 0 i exp app (83) c o chloride concentration of surrounding solution [g/l] c free chloride concentration of pore solution in depth x [g/l] i initial concentration in pore solution [g/l] erf error function x distance from concrete surface [m] t age of concrete [s] t exp time until concrete is exposed to chloride environment [s] D app "apparent" diffusion coefficient [m²/s] This model is based on numerous simplifications: First of all the model is only valid for a constant apparent diffusion coefficient D app and a constant surface concentration C S. The approach is only valid for semi-infinite conditions, i.e. the regarded object is sufficiently large, so that a constant concentration will be reached in the inner concrete zone. The approach assumes in its pure mathematical form that the ingress is a stationary process, hereby neglecting the binding of chlorides. As the binding of chlorides is a non- 60(169)

61 linear process the free chloride concentration c may not be substituted by the total chloride content, which is convenient to measure [xxv]: c c 0 0 cc c c 0 0c c i i C C c c ts t 0 C C c c ts ti 0 i (84) t s i c o c, total surface initial chloride concentration of surrounding solution free chloride concentration in pore solution in depth x regression parameters of Freundlich binding isotherm As throughout chloride analysis usually only the total soluble chloride content is measured the application of the error function solution is physically not correct. However, from an engineering point of view it is a good approximation and convenient to use. Typically the error function solution is written in the following way: C(x, t) C (C C ) erf 1 i S i 2 (t t exp ) D app x (85) C(x,t) C i C S D app t exp t erf where chloride concentration at depth x at age t in e.g. [M.-%/c] initial chloride background level in e.g. [M.-%/c] surface chloride content [M.-%/c] time dependent apparent diffusion coefficient [m²/s] time until first exposure to chlorides [s] concrete age [s] error function 2 2 x³ x ( 1) x 1! 3 2! 5 n! (2n 1) x 5 n 2n1 2 t erf x ( 2x ) e dt x... 0 (86) The chloride ingress in concrete results in a chloride penetration profile, which is the distribution of the chloride content (e.g. related to the weight of concrete specimen or weight of binder) vs. depth measured from the concrete surface. As a sample with infinitely small thickness can not be taken, the surface concentration of the concrete is determined by extrapolation of the profile unto the depth x = 0. The surface concentration C S is therefore not the real concentration at the time, but rather a regression parameter. In practice, the surface chloride concentration C S changes with time under certain environmental conditions, but usually reaches a constant value during a period which is relatively short compared to the intended service life of the structure. This commonly leads to the approach of assuming C S to be constant. Nevertheless, there are cases for which a time-dependence of C S should be regarded. In the case of low chloride loads of the environment (e.g. in the spray-zone 61(169)

62 of road environments with de-icing salt application) the surface level may take many years to reach its maximum. evaporation concrete surface RH [%] 100 moisture profile "convection zone" splash water evaporation 60 - c(cl ) [M.-%/b] depth x [mm] deviation from 2nd Fick's law of diffusion chloride profile concrete x splash water d c reinforcement Figure 25. Distribution of the moisture content and the chloride concentration, as commonly observed in the splash-zone, [xiv] Especially for the case of an intermittent impact of chlorides on concrete structures, practical observations have shown that the approach of the 2nd Fick s law of diffusion may not be applied without restrains. Close to the concrete surface of a component situated in a spray-environment, the concrete is exposed to a continuous change of wetting and subsequent evaporation. This zone is usually referred to as the convection-zone. Due to the changes of the moisture content in the convection zone, the following effects may take place: - so called piggyback transport caused by capillary penetration of solutions trailing chlorides (convection) - wash off at times when the surface is subjected to chloride free water, for instance structures in the splash zone of the road environment during periods without salt application - change of the chloride binding capacity induced by carbonation and leaching In order to still describe the penetration of chlorides for a intermittent loading with the Fick s 2 nd law of diffusion, the data of the convection zone, which deviates from diffusion behavior, may be neglected in the fitting process. The calculation starts with the substituted surface concentration C s,x in the depth x. This effect may be due to variations of the chloride loading (mainly wash out with chloride free water) or carbonation of the surface zone. This type of profile may also be fitted applying Fick s 2 nd law, by neglecting the data points in surface near area, Figure (169)

63 Figure 26. Detailed chloride profile in the splash zone of a bridge[xxvi] which was fitted by neglecting outer data points The output parameters are then the chloride concentration C x, the depth of the so called convection zone x and the apparent diffusion coefficient D app. A simple engineering model which incorporates the effect of capillary suction is thus [xiv]: xx C(x, t) C (C C ) erf 1 i S i 2 (t t exp ) D app (87) The chloride concentrations determined in the chemical analysis are inserted with the corresponding drilling depth to a data sheet (e.g. MS-Excel), Figure 27. C Chlorid [wt.-%/binder] 3,0 2,5 2,0 1,5 1,0 chloride analysis Fitting with erf V i 0,5 0, distance from concrete surface x [mm] Figure 27. Typical chloride distribution in concrete and result of curve fitting obtained by minimizing the sum of the squared deviations v i between (87) and the measured data These chloride profiles are fitted to (87) using an optimization program, e.g. the solver-option of MS-Excel. Five variables are included in the equation: exposure duration (t-t exp ), apparent diffusion coefficient D app, surface concentration C S, the initial chloride concentration C i and depth of the convection zone x. 63(169)

64 As can be seen in Figure 27 the chloride profile converges with increasing depth towards the initial chloride concentration C i. The initial chloride content is the sum of the particular components of the concrete. This value must be chosen visually from the given data points. For this reason it is important to collect a sufficient amount of data points in the tail of a profile, but at least two for the estimation of C i. If chloride profiles have not been determined in a sufficient depth, this value must be assumed. For concrete produced with Portland cement a statistical analysis of approx. 640 chloride profiles in Germany results in a mean value of around 0,1 [wt.-%/cement] or approx. 0,015 [wt.-%/concrete]. The depth of the convection zone x is also visually determined from the regarded chloride profile. The choice of this parameter may have a significant impact upon the result of the regression. The exposure duration (t-t exp ) is the difference of the total age of the concrete and the moment of first contact with chlorides, which may usually be set equal to the concrete age t. If the exposure time t, the initial concentration C i and the depth of the convection zone x are fixed, the remaining Variables C S and D app can be calculated, as shown in the example below. Table 14. Example for spread sheet to fit chloride profiles (data from case study object Hofham Bridge pillar exposed to de-icing salts Sample interval Depth X C(x) measured C(x) 1) calc 2 V i from [mm] to [mm] [mm] [wt.-%/cem] [wt.-%/cem] [wt.-%/cem]² =((4-5)/4)² 0 5,6 2,8 2,250 2,250 0, ,6 10,8 8,2 2,243 2,338 0, ,8 15,0 12,9 1,950 2,061 0, ,0 29,8 22,4 1,635 1,528 0, ,8 45,0 37,4 0,945 0,847 0, ,0 59,6 52,3 0,405 0,424 0, ,6 75,8 67,7 0,203 0,210 0, ,8 90,6 83,2 0,143 0,130 0, ,6 106,2 98,4 0,090 0,100 0,01235 Sum (minimize!): 0,0443 Set input parameters Regression variables (result) t [a] C i [wt.-%/cem] x [mm] D app [10-12 m²/s] C S [wt.-%/cem] 38 0,10 8,0 0,385 2,350 1) according to (87) If these regression variables are known, the future chloride profiles may be predicted by extrapolation: 64(169)

65 C Chlorid [wt.-%/binder] 3,0 2,5 2,0 1,5 1,0 chloride analysis (t=38a) Fitting with erf extrapolation (t=100a) 0,5 0, distance from concrete surface x [mm] Figure 28. Chloride profile at inspection time of 38a, and predicted profile at t = 100a Today numerous models and modifications of these exist, which may be categorized as follows [xxvii, xxviii]: a) Empirical models: Chloride profiles are predicted by means of analytical or numerical solutions of Fick s 2 nd law of diffusion: 1) Error function methods: with a constant diffusion coefficient D and surface concentration C S [xxix] D(t) and constant C S [xxx, xxxi] 2) analytical solutions of Fick s 2nd law besides the error function solution: D a (t) und C S (t) [xxxii] 3) numerical solutions of Fick s 2 nd law: D(t) und C S (t) [xxxiii] D(t) und C S (t) + Binding isotherms[xxxiv] b) Physical methods: The chloride transport and the binding of chloride is described by separate sub-models: 1) based on Fick s 1 st law of diffusion: Binding isotherms [xxiv] Convection [xxxv] 2) based on the Nernst-Planck equation: Ion equilibrium [xxxvi] 65(169)

66 On a the semi-probabilistic level within the LIFECON concept an approach with constant values for D app and C S seems most appropriate. This is because: a decrease of the diffusion coefficient with time is neglected on the safe side the model is the most simple for application However, even the simple error function solution is not convenient when it comes to manual calculations. For this purpose (87) may be simplified exchanging the error function (erf) approach by a parabolic function: xx C(x, t) C (C C ) 1 i x i 2 3(t t exp ) D app (t) 2 for x x i (88) which is of course only valid in the domain of constantly decreasing values of the chloride concentration, i.e. until the depth x i where C(x,t) = C i : x 2 3 (tt ) D x i exp app (89) Beyond the depth x i the chloride concentration C(x,t) is equal to the initial concentration C i. Figure 29 clearly demonstrates that even an extrapolation over large periods using the parabolic approach according to (88) results in nearly the identical chloride profile. C Chlorid [wt.-%/binder] 3,0 2,5 2,0 1,5 1,0 chloride analysis (t=38a) Fitting with erf (t=38a) extrapolation erf (t=100a) extrapolation parabolic approach (t=100a) 0,5 0, depth x [mm] Figure 29. Chloride distribution at inspection time and predicted distributions using either the error function solution (87) or the parabolic relation given in (88) for identical values of the apparent diffusion coefficient D app and the surface concentration C S The target is not to predict the future development of the chloride distribution in concrete, but rather to determine the probability of chloride induced depassivation at any given time! Therefore the chloride concentration C(x,t) in (88) must be set equal to the critical chloride concentration and solved for penetration depth, hereby resulting in the penetration depth of the critical chloride concentration x crit : 66(169)

67 C C C C S i crit i x 2 3(t t ) D (t) 1 x crit exp app (90) which is compared to the concrete cover d C. 6.3 Scatter for the Depth of the Critical Chloride Concentration x crit From (90) follows that the penetration depth of the critical chloride concentration x crit is a random variable which itself is a function of various random variables. For manual calculations of the probability of depassivation, the most simple way is to compare the random penetration depth x crit (stress variable - S) and the random concrete cover d C (resistance variable - R) following the basic safety concept outlined in chapter 2.2. The mean value of the time dependent penetration depth follows directly from (90) when inserting the regression parameters obtained by fitting chloride profiles (C i, C S,, D app, x) and the critical chloride concentration C crit. The critical chloride concentration C crit depends on the concrete composition and the environmental exposure conditions, as will be outlined more in detail when treating the full-probabilistic model approach, see chapter 7. On the safe side a very simple but convenient method is to assume a mean value of C crit = 0,48 [wt.-%/cement] regardless of the exposure environment. However, the standard deviation of the critical chloride penetration depth x crit can not be determined directly without application of professional software tools, e.g. [xix]. The problem of modeling chloride induced corrosion contains numerous and significant uncertainties. To overcome this problem, the statistical distribution of x crit has been studied for case study objects using a full-probabilistic model as detailed in the later chapters. Distance from concrete surface x [mm] f R (x) 90%- F mean value of concrete cover d R (x) c mean value of penetration depth f S (x) 10%-quantile x crit Age of structure [a] Figure 30. Comparison of constant concrete cover d C (resistance R) and time dependent penetration depth of critical chloride concentration x crit (stress S) for a case study object in the road environment The coefficient of variation CoV (ratio of standard deviation and mean value µ) of the penetration depth x crit must cover up all the uncertainties including the aspects of: spatial scatter of all variables in (90) 67(169)

68 deviations of chloride analysis from the real values model uncertainties The calculations indicated that CoV of the penetration depth is nearly constant over time CoV = 50% is a good assumption on the safe side. 6.4 Calculation Procedure The calculation procedure is comparable to the example already demonstrated for the carbonation induced depassivation and will likewise be exemplified. Table 15. ingress Summary of necessary input data for the semi-probabilistic model on chloride Parameter Unit Format Source Apparent diffusion [10-12 m²/s] ND(µ, ) Fitted from chloride profile as outlined in chapter 0 coefficient Dapp(t=38a) Surface concentration [wt.-cement] ND(µ, ) Fitted from chloride profile as outlined in chapter 0 CS Initial chloride [wt.-cement] ND(µ, ) Assumed for fitting as outlined in chapter 0 concentration Ci Critical chloride [wt.-cement] ND(µ, ) Assumed as outlined in chapter 0 concentration Concrete Cover dcover [mm] ND(µ, ) Measurements according to D3.1 The following information shall be available: - A chloride profile was taken at an age of t = 38a and fitted as shown in Table The critical chloride concentration is assumed to be in average C crit = 0,48 [wt.-cement]. - Concrete cover d cover, which is a resistance parameter, was measured with a mean value of µ cover = 70 mm and a standard deviation of cover = 8 mm. For the sake of simplicity the distribution is assumed to be normal. From this information the mean value of the time dependent penetration depth of the critical chloride concentration can be estimated according to: 0, 48 0,1 2,350 0, µ(x ) 2 3(t ) 0, ,1 t 8 crit [mm] (91) t age of structure [a] The standard deviation is thus: (x ) 50% µ(x ) 3, 6 t 4, 0 [mm] (92) crit crit 68(169)

69 The minimum reliability index is set to min = 1,8. The flow of the calculation to prove whether the requirements are currently fulfilled is as follows: 1. Calculation of the stress variable S (penetration depth at age t = 38 a): µ(x ) 7, (x ) 3, , 0 26 [mm] crit crit (93) 2. Transformation of resistance and stress variables into standard space: U R 70 8 U 1 2 S (94) 3. Limit state equation in standard space: L(U 1,U 2) RS8U126U2 18AU1BU2 C 0 (95) 4. Calculation of the distance of the limit state line from origin using the so called Hesse normal format (comparison of coefficients A, B, C): C 0, 66 1,8 2 2 A B (96) This means that at the current age the reliability requirements are not fulfilled and more thorough investigations are necessary. 7 Full-Probabilistic Model on Chloride Ingress 7.1 Mathematical Model The basic model concept is identical as for the semi-probabilistic approach outlined in the previous chapter. Depassivation of the reinforcement will start when the critical corrosion inducing chloride content C crit will be exceeded in the depth of the concrete cover d cover, which is expressed by a limit state function: p p C C(x d,t) 0 p depassivation crit cov er set (97) where C(x,t) is calculated according to (87). The major difference is that all input parameters: are considered as random variables follow the performance concept, i.e. can be measured have been statistically quantified for durability design purposes and must thus not be determined throughout structure investigations The apparent diffusion coefficient is inserted according to the following sub-model: 69(169)

70 D app t t 0 t (t) (t t ) n1 t 0 * D (t) k k dt RCM,0 T RH 0 (98) D app (t) apparent diffusion coefficient of concrete at the time of the inspection [m²/s] D RCM,0 chloride migration coefficient of water saturated concrete prepared and stored under predefined conditions, determined at the reference time t 0 n 1 exponent regarding the time-dependence of D app due to the environmental exposure [-] k T temperature parameter, introduced in [xiv] [-] k w factor to account for degree of water saturation w of concrete [-] t age of concrete [s] reference time [s] t 0 Please note that D app is introduced to the error function solution as the average over a regarded time period, This topic will be emphasized, when treating the age exponent n. A clear classification of the input parameters is not possible in a straightforward manner (as is the case for the carbonation model), because some of these are influenced by the concrete composition as well as by the environmental exposure conditions, Table 16. Table 16. Summary of input parameters for the chloride ingress model Type of parameter Parameter Material D RCM,0 (t) Material/ Environmental k RH, k T, n, C S,x, x, C crit Test k t, Geometry d cover 7.2 Material Input Parameter D RCM,0 (t) General The chloride diffusion coefficient is highly dependent on the concrete composition. The experimental determination of chloride diffusion coefficients of concrete by conventional methods, as there are diffusion-cell tests or immersion tests, are very time consuming. In immersion tests concrete samples are kept submerged in a chloride containing solution to measure the chloride ingress after certain testing periods by withdrawal and chemical analysis of dust samples, hereby obtaining chloride ingress profiles. An effective diffusion coefficient can be derived by making use of curve fitting methods based on Fick s 2 nd law of diffusion on the obtained chloride profiles, see Figure (169)

71 electr. potential [V] chloride free solution anode chloride containing solution Cl - Cl - Cl - concrete cylinder h = 50 mm d = 100 mm s cathode Figure 31. Experimental design of the Rapid Chloride Migrations test (RCM) For design purposes of new structures the Rapid Chloride Migration (RCM) test (see Figure 31) has been chosen because [xii]: - for equal concrete compositions the chloride migration coefficient D RCM,0 shows a strong statistical correlation with effective diffusion coefficients D eff (determined by time consuming immersion tests), Figure 32 Apparent Chloride Diffusion Coefficient D app,0 [10-12 m 2 /s] Frederikson et al. Gehlen and Ludwig Chloride Migration Coefficient D RCM,0 [10-12 m 2 /s] Figure 32. Correlation of the apparent diffusions coefficient obtained by immersion tests and the chloride migration coefficient D RCM,0 71(169)

72 - a short test duration is achievable with the RCM test - the RCM test is a robust and precise method Details on the RCM test method and further investigation methods concerning the effective diffusion coefficient are provided in the Appendix of D3.1 [i]. For existing structures the following investigations may be performed in order to obtain the apparent diffusion coefficient D app (t): (a) Using literature data with respect to D RCM, if the concrete composition is known. (b) withdrawal of dust samples and curve fitting of the obtained chloride ingress profiles, if exposure time was sufficiently large ("old structures") (c) Performing the RCM test with specimens (e.g. cores) from the structure, which is necessary for "young structures" but should be performed for every object. Extensive time dependent studies with respect to D RCM have been performed by the author [v, xxxvii], which shall be summarized in the following section. In essence the content of cement, superplasticizer and air voids as well as the aggregate type can be neglected, whereas the binder type and the w/b-ratio are of decisive relevance Effect of Water-Binder Ratio Following the results from exposure tests in sea water [xxxviii] an exponential approach seemed to be most suitable to describe the effect the w/b-ratio: D RCM,t=28d [10-12 m²/s] CEM I 42.5R (Gehlen) CEM I 42.5R ( Lay) CEM I 42.5R+FA (Gehlen) CEM III/B 42.5 LH-SR (Gehlen) k w/b,t=28d [-] CEM I 42.5R (Gehlen) CEM I 42.5R (Lay) CEM I 42.5R+FA (Gehlen) CEM III/B 42.5 LH-SR (Gehlen) w/b-ratio [-] w/b-ratio [-] Figure 33 (Left). Figure 34 (Right). D RCM, t = 28d versus w/b-ratio for different binder types; data of Gehlen [xiv] and Lay [v] Binder specific factor k w/b, t = 28d to account for changes in w/b-ratio calculated by relating original data given in Figure 33 to the value measured at w/b = 0.45 which lead to the derivation of: 72(169)

73 D k expa (w/b0,45) (99) RCM,w / bi w/b w/b w/b DRCM,w / b0.45 k w/b factor accounting for a change in water-binder ratio with respect to the chosen reference value w/b = 0,45 [-] a w/b regression parameter [-] w/b error term [-] [mean value = 1, coefficient of variation CoV w/b according to The regression parameter a w/b expresses the sensitivity with respect to a change in w/b-ratio. The model uncertainty of the function compared to the actually measured values is incorporated by means of the error term w/b. This way (99) describes the dependence of D RCM as a random subfunction. Table 17. Regression parameters describing the influence of the w/b-ratio upon the Rapid Migration Coefficient D RCM of concrete for various binder types eligible according to [xxxix] CEM a w/b [-] CoV w/b [%] I 1) 6,0 11 I + FA (18 %, k = 0,5) 1) 5,0 11 II/A-LL 42,5 R 2) 4,2 8 II/B-S 32,5 R 2) 3,8 11 II/B-T 32,5 R 2) 4,4 10 CEM III/B 1) 4,2 15 1) 2) valid for 0,40 w/b 0,60 valid for 0,40 w/b 0,50 The degree of hydration and therefore the degree of hydration at infinite concrete age theoretically increase for larger values of the w/b-ratio, [xl]. However, in the practically relevant domain the effect of the w/b-ratio can be regarded as independent of the concrete age, which leads to the conclusion that (99) can be applied regardless of the considered moment in time. This relationship is exemplified in, as the curves for various w/b-ratios can be shifted parallel along the ordinate. D RCM [10-12 m 2 /s] II/B-S Plant B II/B-S Plant B II/B-S Plant B II/B-S Plant B Fit II/B-S Plant B Fit II/B-S Plant B Fit Age [d] Figure 35. Chloride migration coefficients of concrete at different ages for three w/bratios produced with 360 kg/m³ CEM II/B-S 32.5 (plant B) and corresponding fitted functions (Fit) 73(169)

74 7.2.3 Effect of Binder Type The cements used for the studies were CEM I (Portland cement) of strength class 32.5, 42.5, 52.5 and blended cements of the type CEM I+FA (15, 20 or 40% fly ash), CEM II/A-L 42.5R (15 % limestone), CEM II/B-S 32.5R and 42.5R (31 % slag), CEM II/B-T 32.5R (23 % oil shale), CEM III/A 32.5 (51 % slag) and CEM III/B 32.5 (72 % slag). The investigations revealed that a classification is most reasonable according to the type of binder, whereas data with different cement strength class and cement factory should be grouped, as was done to obtain the relationships given in. D RCM [%] d w/b = 0,45 365d * * 3 3 I I+FA II/A-LL II/B-T II/B-S III/A III/B CEM Figure 36. Mean values for D RCM at an age of 28 and 365 days for various binder types (all concretes with w/b = 0,45) given in % related to CEM / (Portland cement) at an age of 28 days. *) Data at an age of 182 days was used if measurements was not possible at 365d (colorimetric reaction failed) [v] Derivation of a Model for Chloride Migration Coefficient As a starting point for a regression analysis concerning the time dependent decrease of D RCM the commonly used reference age of t 0 = 28 days was chosen. In the following the migration coefficient at this age will be referred to as D RCM, t = 28d. The hydration of concrete proceed in theory for a very long time. However, when compared to the common service life of concrete structures, the effect of hydration upon D RCM becomes insignificant rather early, see e.g. Figure 35. To solve this problem an finite value, which is referred to as D RCM, t = may be introduced, leading to the following expression: n 2 0 D (t) D D D RCM RCM,t28d RCM,t RCM,t t t (100) D RCM, t = 28d binder specific migration coefficient at reference age t 0 [m²/s] D RCM, t = binder specific migrations coefficient after the end of hydration [m²/s] T concrete age t 0 reference age, here 28d [s] 74(169)

75 n 2 age exponent due to hydration [-] As currently data is only available at an age of 365 days the migration coefficient at this moment in time is set equal to D RCM, t =, which is good approximation on the safe side. The velocity of a decrease from D RCM, t = 28d to D RCM, t = due to hydration of the cement paste, is expressed with the age exponent n 2. Table 18. Binder specific chloride migration coefficients D RCM, t = 28d und D RCM, t = (w/b = 0,45) CEM I I+FA II/A-LL II/B-T II/B-S III/A III/B Additions [M.-%] ) Number of samples Age [d] ) ) Mean m [10-12 m²/s] 9,2 4,8 8,2 1,1 12,7 8,2 7,7 2,6 7,3 1,7 3,9 0,3 1,7 0,3 CoV [%] ) Data at an age of 182 days was used if measurements was not possible at 365d (colorimetric reaction failed) [v] If the values for D RCM, t = 28d and D RCM, t = known, the age exponent n 2 can be calculated by fitting the measured results according to (100). The results indicated that a classification is only reasonable with respect to the binder type,. Table 19. Binder specific age exponent n 2 CEM I I+FA II/A-LL II/B-T II/B-S III/A III/B Number of samples Mean m [-] 0,964 1,244 1,303 0,860 1,041 1,159 1,624 CoV [%] Application of the Model To apply the given relationships in a full-probabilistic model for the prediction of the residual service life, all variables must be quantified in terms of statistical distribution type, mean value and coefficient of variation (or standard deviation) and where necessary boundaries of the distribution. Due to the low amount of available data at present, an analysis of the best suitable distribution function is not possible. However, as negative values for D RCM are physically impossible a log-normal distributions seems reasonable for application. Binder specific mean values for D RCM with w/b = 0,45 are provided. The amount of samples is however too low to calculate the coefficient of variation for all binder types. Meanwhile it is proposed to use values determined for CEM I irrespective of the regarded binder type, which means 50% at an age of 28d and 70% at infinite age. If for durability design purposes the actual concrete quality is tested or cores are sampled from an existing structure, the actual concrete quality can be tested for, which will be outlined in the later chapters. For this case the coefficient of variation of the test method obtained from repeated tests of identical concrete under identical conditions should be used, which is only around 20% [xiv]. 75(169)

76 7.3 Environmental and Material dependent Input Parameters There are six input parameters which dependent on the type of environmental exposure and on the concrete composition, which have to be quantified statistically: the age factor n, the chloride concentration C x, the depth of the convection zone x in which the chloride profile deviates from behavior according to the 2nd law of diffusion, the critical chloride concentration C crit and the environmental factor k T. The statistical quantification of environmental parameters based on data obtained throughout structure investigations may be performed as follows [xi]: - providing parameters in form of mean value and standard deviation of the corresponding distribution type presenting parameters as a function of time applying a Bayesian regression analysis on data of the same classification providing parameters as a function of other parameters (material, environmental) by multiple regression analysis The exposure environment may be classified as: (a) Marine environment Submerged zone Tidal zone Splash zone Atmospheric zone (b) Road environment Splash zone (exposed/ not exposed to rain) Spray zone (exposed/ not exposed to rain) The most important aspects for classification with respect to the concrete composition are the binder type and the water-binder ratio. 7.4 Depth of the Convection Zone x The convection zone x is the outer portion of the concrete cover where significant deviations from pure diffusion is taking place. This zone can be identified by means of chloride profiles as a maximum of the chloride concentration is observable in the inner zone of the concrete cover. The main reason for this visible effect is wash-out of chlorides in times without or low chloride loading, which will only be possible if the concrete surface is subjected to chloride free water. 76(169)

77 More important it must be reckoned that in periods with chloride loading chlorides will penetrate very fast by means of capillary suction onto the depth of the convection zone. Beyond this depth diffusion is the decisive transport mechanism. In marine structures this is the case in the atmospheric zone. For structures in the road environment chlorides are washed-out close to the road edge by splash and spray water of the traffic or rain if the structures is not sheltered. The occurrence of a convection zone is therefore dependent on the position of the regarded surface with respect to the source of chloride free water. Gehlen [xiv] analyzed 127 chloride profiles in the marine environment without distinguishing for the distance to chloride source. Since negative values for x are not possible and convection is limited to a finite suction depth, a beta-distribution (B) seemed most appropriate for analysis: B(µ = 8,9; = 63%µ; a = 0; b = 50) Lay [v] analyzed the convection zone for mainly sheltered concrete surfaces in the road environment. If a surface is situated within the domain of 3 m above the road level and 2 m from the road edge, a convection zone will most likely occur. The statistical analysis resulted in: a 3 m and h 2 m: x = B(µ = 9,03; = 100%µ; a = 0; b = 60) [mm] a > 3 m or h > 2 m: x = 0 [mm] For structures, which are not sheltered from rain only few data was available at current. However these showed the same order of magnitude for x, [v]. Hence, the same statistical distributions as given above should be used for these. Systematic data with respect to the influence of concrete composition on the depth of the convection zone is scarce, Figure 37. Figure 37. Effect of binder type and water-binder ratio on depth of convection zone x. Chloride profiles from exposure tests (field station Träslövsläge, Sweden) in atmospheric and tidal marine zone [xli] and wet-dry cycles in laboratory tests [xlii] (26 cycles; 1 day in 3%NaCl; 6 days dry at 20 C/50%RH; each data point reflects the average of 6 chloride profiles) From Figure 37 can be concluded that a rise by 1/10 in w/b-ratio will lead to an increase of the convection zone of around 2-4 mm. Even at water-binder ratios as low as w/b = 0.30 a convection zone of 2-3 mm must be expected. The use of additions as silica fume, fly ash or 77(169)

78 blast furnace slag (CEM III/A or B) will reduce the depth of the convection zone up to around 60% compared to ordinary Portland cement (CEM I). Surprising in the results of Polder is the fact that low slag contents didn t show an improvement but rather the opposite. This should however not be overestimated having in mind the large scatter when evaluating the convection zone. 7.5 Temperature Parameter k T In [xiv] the influence of the air temperature upon the diffusion coefficient has been taken into by using the Arrhenius equation: k T 1 1 exp b T T T ref (101) k T temperature parameter [-] b T T ref T regression parameter (Normal distribution: µ = 4800; = 700, [xiv]) [K] reference temperature [K] temperature of the environment (micro climate) [K] Figure 38. Function k T accounts for of the dependence of the apparent diffusion coefficient on the temperature of the surrounding environment (air, water) 7.6 The Age Factor n As can be seen in (98) the apparent diffusion coefficient D app is a time dependent variable. It has been shown, that D app may considerably decrease with increasing age of the concrete. There are several general effects which may contribute to an decrease of the diffusion coefficient with increasing time, e.g.: 1. the development of a denser pore structure due to the hydration process subsequent to the reference time t 0, which can be separately accounted for according to chapter swelling of the cement paste and deposition effects in the pore structure [xliii] 78(169)

79 3. A pore blocking effect due to the chloride ingress [xliv]: Zhang et al. discovered that the electrical double-layer, which is formed by anions when these are bound to the pore structure, reduce the effective pore diameter. This electrical repulsion effect, which is referred to as the zeta-potential, hence results in a decrease of the diffusion coefficient [xlv]. 4. concentration dependence of the binding capacity inherent in the effective diffusion coefficient [lv] 5. oversimplification of model (assumption of constant C x ), which will be outlined more in detail Gehlen [xiv] and Bamforth [xlvi] collected chloride profiles in various marine exposure zones and fitted these as described in chapter 6.2. As an output the apparent diffusion coefficient D app is obtained, which can be plotted vs. time,. Cement with additions of fly ash apparent chloride diffusion coefficient D [10-12 app m 2/s] ,1 0,01 0, exposure time t [a] Figure 39. Apparent diffusion coefficient plotted vs. exposure time Apparently the fitted diffusion coefficients seem to decrease over various orders of magnitude during the exposure to a chloride containing environment. This relation can be expressed as follows [xlvii]: D 1 D app,2 app,1 n t t 2 (102) D app,i : apparent diffusion coefficient at exposure time t i [m²/s] t i : exposure time [s] n: age exponent [ - ] If the apparent diffusion coefficient at two times is known the age exponent n 1 can be calculated: D ln D n t ln t app,2 app,1 1 2 (103) 79(169)

80 If more than two results are given, as is the case in Figure 39, a regression analysis can be performed. Starting point of such a regression analysis is the migration coefficient obtained at the reference age, which was chosen to be t 0 = 28d, [xiv]: apparent diffusion coefficient D [10-12 app m 2/s] (1) (2) 1 0,1 0,01 t exposure time t [a] Figure 40. Regression analysis of time dependent apparent diffusion coefficient. With (1) being the starting value obtained from chloride migration tests at t 0 = 28d and (2) being the slope of the regression line on a double-logarithmic scale, which is equal to the age exponent n According to the approach given in (102) the age exponent is only valid in the domain of 0 n 1. For the case of n = 1, time t is cancelled out from (87), which means that the chloride concentration C(x,t) remains constant. This is referred to blocking of the chloride ingress [xlviii]. For a value of n > 1 the concentration in any depth x would decrease in the next time interval. This implies that chlorides would flow out of the concrete which is not consistent with the boundary condition for which the error function solution was derived, i.e. that C x remains constant over time. For n < 0 the diffusion coefficient would increase with time, which is not the case either. Therefore a beta distribution with the above mentioned boundaries is used for the statistical analysis of the age exponent. The above described approach neglects the fact, that the apparent diffusion coefficient obtained from fitting chloride profiles, is the average diffusion coefficient in the regarded time interval. D * t t 0 D (t D(t)dt 0 * t ) D(t) t0 t* t Figure 41. Relationship of time dependent diffusion coefficient an the resulting average 80(169)

81 This value should therefore be plotted vs. the time when this average value was achieved, which is unknown, as the age exponent n 1 remains unknown at the time of plotting the value. The exact procedure for determining the age exponent is thus an iterative procedure as recently outlined in [xlix]. However, plotting D app vs. the time of inspection always results in lower values for the age exponent, which is an approach on the safe side. However, the time dependent decrease in chloride diffusion coefficient may not only behave material dependent (type of cement and additions) but has to be evaluated considering the actual exposure conditions as well (e.g. chloride loading intensity because of the concentration dependence of D app ). Therefore it is advisable to determine the age factor n 1 for separated concrete compositions and exposure conditions [xiv]. Table 20. Result of the statistical quantification of age exponent n for the exposure in the submerged, splash and tidal marine exposure zone Binder type Age exponent n 1 CEM I (OPC) Beta(µ = 0,30; = 0,12; a = 0; b = 1) CEM I + FA 1) Beta(µ = 0,60; = 0,15; a = 0; b = 1) CEM III/B (GBFS) Beta(µ = 0,45; = 0,20; a = 0; b = 1) 1) Fly ash content FA 20% 7.7 Influence of a Partial Water Saturation - Parameter k w By introducing a convection zone x according to [xiv] the deviations from the diffusion transport mechanisms in the surface near layer have been accounted for. In the layers beyond x a constant humidity may be assumed. Nevertheless a saturation of the concrete, as provided by the curing and storing conditions throughout the RCM test, may not be assumed in the inner layers of the structures. The moisture conditions of the concrete have to be accounted for. There are very few systematic investigations regarding the influence of a partial water saturation of concrete upon the apparent diffusion coefficient D app as these are quiet difficult to perform. Climent [l] provided a rather simple but effective method. Concrete specimens (CEM II/ALL, c = 350 kg/m³, w/c = 0,6) were produced and stored until a constant mass was achieved in different relative humidity. Subsequent these specimens were exposed to combustion gases of burned PVC and stored once over in the previous relative humidity condition. At different times dust samples were collected and analyzed to obtain chloride profiles. These profiles were fitted to a solution of Fick s 2 nd law which takes into account that a initial chloride surface concentration decreases with time. Additionally the degree of water saturation was measured. The ratio of the rapid migration coefficient D RCM of the tested concrete, which is measured under water saturation, and the apparent diffusion coefficient D app for a particular relative humidity was expressed is referred to the factor k w : k w DRCM D (RH) app (104) which is course restricted to the domain of 0 k RH 1: 81(169)

82 water saturation degree [-] 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0, relative humidity RH [%] Figure 42. water saturation degree w [-] 1,0 0,9 0,8 /Climent/: t=180d 0,7 /Lay/: RCM-Test 0,6 0,5 0,4 0,3 0,2 0,1 0,0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 k w [-] Influence of the relative humidity upon the degree of water saturation of concrete (left) and the reduction factor for the apparent diffusion coefficient as a function of the water saturation degree (right). Data from [l] The data in Figure 42 was used to derive the following deterministic relationship: kw w a RH (105) k RH factor to take into account the effect of a partial water saturation of concrete upon the apparent diffusion coefficient [-] c Regression parameter, here a RH = 4,297 [-] However, the water saturation degree is not only dependent on the relative air humidity but depends even more on the amount and frequency of liquid water reaching the concrete surface, which is the medium in which Chlorides are always transported onto the concrete surface. The water saturation degree w, as an input to (105), must thus be determined as a function of the relative humidity and the time of wetness ToW (see chapter 4.3) in dependence of the concrete composition (binder type, w/b-ratio). Simulations to obtain the water saturation degree are already possible today by using commercial software, e.g. WUFI [li]. It should be realized however that these work well for materials as sandstone which do not react with the penetrating substance (water). This is not so for concrete, which swells and seals up. Calculations with such programs will thus usually overestimate the water ingress into concrete. As (a) there is currently not enough data existing for the concrete specific effect of the water saturation degree w upon the apparent diffusion coefficient D app and (b) the water saturation degree is difficult to predict it seems not yet appropriate to introduce (105) into the fullprobabilistic concept for service life calculations. The simple approach of applying a constant value of k RH for concrete which is splashed or sprayed with chloride containing water seems to be an adequate solution, having in mind that for actually existing structures the actual apparent diffusion coefficient can be measured to update the model, as will be shown in later sections. This constant value can be determined by means of a regression analysis as will be shown in the following chapter. 7.8 Separation of Age Exponent n 1 and Factor k w In the concept of formerly described in chapter 7.6 the age exponent n includes the effects of cement paste hydration and marine environmental effects which lead to a decrease of the apparent diffusion coefficient with time. In chapter it was shown that the decreasing effect 82(169)

83 due to hydration can be neglected after a certain point in time, which depends on the binder type. However, environmental effects still seem to cause a decrease of D app after the contribution of the hydration process has come to an end. Lay took these relationships into account and developed the following relationship: n D (t) k k D (t) dt t (t t ) t 1 t0 1 app T w RCM t 0 0 (106) D app (t) apparent diffusion coefficient of concrete at the time of the inspection [m²/s] D RCM(t) binder specific, time dependent chloride migration coefficient of water saturated concrete prepared and stored under predefined conditions k w environmental parameter accounting for the moisture influence on D app [-] n 1 age exponent describing the time-dependent decrease of D app due to the environmental exposure [-] k T temperature parameter, introduced in [xiv] [-] t age of concrete [s] reference time [s] t 0 As the modeling of the chloride ingress in the road environment, i.e. under conditions for which concrete is most of the time in a unsaturated state, i.e. with having a water saturation degree w < 1, the factor k w was introduced. The apparent diffusion coefficient D app obtained from collected chloride profiles was plotted versus the structure age, Figure 43. A regression analysis on the data was performed applying (106), which includes numerous variables: The average effect of the temperature k T was accounted for according to chapter 7.5 using the average daily air temperature in Germany. The time dependent rapid chloride migration coefficient was modeled according to chapter assuming as an average composition concrete produced with CEM I and w/b = 0,50. Hence, k RH and the age exponent n 1 remained as the only variables which had to be fit to the data. To simplify the analysis of the age exponent n 1, for which (106) must be solved by iteration, the factor k w is considered a deterministic (D) variable (single number). Figure 43. Quantification of relative humidity factor k RH and age exponent n 1. White dots from exposure tests (CEM I only) in Sweden (Nilsson[lii]), black dots from structures in Germany 83(169)

84 Negative values for n 1 are hardly possible, as for these values the diffusion coefficient would increase with time. For a value of n 1 = 1 chlorides will not be transported at all the concrete would be blocked. The age exponent is hence restricted to the domain of 0 n 1 1, which can be accounted for by a beta-distribution. Own in depth investigations (Lay 2003b) indicated the following relationships for the average water saturation degree in the depth interval x = 0 to 50 mm and the age exponent n 1 : in a depth of around 10 to 40 mm the water content reaches a constant level with rising height above road level the degree of water saturation increases within a narrow range the age exponent n 1 behaves inversely to the degree of water saturation in the bottom parts of sheltered vertical surfaces the age exponent may even drop to the minimum value of n 1 = 0 the intensity of chloride loading seems not to influence D app. Chloride migration tests with chloride containing specimens, for which a special test procedure was developed, showed the same results (Lay 2003b). Based on these observations, it appears that the exponent n 1 expresses the frequency of dry periods. During times at which the concrete dries out considerably, D app is almost reduced to zero. With increasing distance form the road, the ratio of dry/wet-periods is enlarged, leading to an increase in n 1. The age exponent n 1 should therefore be a site dependent parameter. Due to the large scatter of data collected from road administrations no dependence of the age exponent n 1 with respect to the distance from the road could be established. Nevertheless, as most of the chloride profiles used for statistical analysis were sampled close to the road (average height above street level h = 85 cm; average horizontal distance a = 170 cm), which is the decisive domain for design, the age exponent n 1 can be applied independent of the distance to the road according to the results in Figure Chloride Concentration C x General: The chloride concentration C x in the depth x depends on the concrete composition and on the environmental conditions. The decisive material parameters are the binder type and w/b-ratio, which define the chloride binding capacity, as well as the pore volume. The most important environmental variables influencing the chloride concentration of the concrete is the chloride concentration of the water to which a concrete surface is subjected. However, the resulting concentration C x in the concrete also depends on the rate of loading with chloride containing water, which is a function of various environmental influences, which will be discussed in the following sections. 84(169)

85 Chloride Concentration of the environment C env : In the case of already existing structures the chloride concentration of the concrete C x can be directly determined from the evaluation of chloride profiles. For "young" structures or durability design purposes C x must be estimated by models. The first step may be to determine the chloride concentration of the water reaching the concrete surface. For Off-shore structures the chloride load can be considered to be equal to the chloride content of the sea water: C water = C sea (107) C water C sea average content of the chloride source [g/l] chloride content of sea water [g/l] The chloride load of structures in a road environment is controlled by the de-icing salt applications [xiv]: C water C road n M h Chloride S (108) n quantity of de-icing salt application incidents [-] C road M Chloride h s average concentration of the chloride containing water on a street [g/l] average mass of chlorides spread during each application of de-icing salts [g/m²] average precipitation (rain, snow) during salt application period [l/m²] The approach above neglects the facts that: - salt may be removed from the street by wind and driving cars and - salt containing water and snow slush will be drained, hereby reducing the salt concentration C water. For durability design purposes the above mentioned approach is on the safe side. The average mass of chlorides spread M Chloride depends on: - climatic conditions - road type (degree of importance, velocity) - road maintenance policy and must thus be based on data provided by the nearest road administration office. Data should be collected for the longest period available, as the scatter of annual data is extremely high. If no data is available from nearby stations, empirical models can be applied which link meteorological data and salt spread data, as e.g. [liii]: M = 1000 C (-9,56+0,52 SF+0,38 SL+0,14 FD-0,20 ID)/w Chloride [g/m²] Salt (109) Index FR M Chloride federal roads average mass of chlorides spread during a single application event on federal roads[t/km] 85(169)

86 C Salt chloride concentration of de-icing salt spread [%] SF number of days per month with snow fall above 0,1 mm [-] SL number of days per month with a layer of snow above 1,0 cm [-] FD number of days per month with average daily temperature below 0 C ID number of days per month with ice on road surface [-] w average spread width (can be set equal to average street width) [m] The correlation between salt spread data for federal roads (FR) and highways (HW) was found to be: M Chloride, HW =1,51+0,235 M [g/m²] Chloride,FR (110) The chloride concentration of the water and slush may also be measured directly. From Figure 44 the large variation of the chloride concentration of snow slush during the winter becomes evident. chloride concentration C in chloride containing slush (Stockholm, winter 96/97) [g/l] 0,R event of application of de-icing salt Figure 44. Chloride concentration in snow-slush and melted water (Stockholm, Winter 96/97) [liv] Chloride Saturation Concentration of Concrete C S,0 : For structures which are submerged or in constant contact with chloride containing water the chloride concentration C x can directly be set equal to chloride saturation concentration C S,0, which can be estimated if the following information is given: chloride concentration of surrounding water C Water chloride adsorption isotherm concrete composition Chloride adsorption isotherms can be taken from literature data, as e.g. given in [lv], or determined in the laboratory: 86(169)

87 Figure 45. Chloride saturation concentration C S,0 (free, bound and total) in dependence of the chloride concentration in the surrounding water C water. Data of Tang [lv] Tang describes the ratio of free chlorides to bound ones as a so called Freundlich-Isotherm, in dependence of binder type and porosity of the concrete: c b f b WGel 1000 ε c β (111) c b bound chlorides in cement paste [g/l] f b, Regression parameter W Gel cement paste content [kg/m³] concrete porosity [m³ pores / m³ concrete ] c concentration of solution (water) [g/l] Table 21. Parameters of chloride binding isotherm [lv] Binder type f b 100% CEM I (OPC) 3,57 0,38 30% slag + 70% CEM I 3,82 0,37 50% slag + 50% CEM I 5,87 0,29 30% fly ash + 70% CEM I 5,73 0,29 However, concrete surfaces which are not in constant contact with chloride containing water as is the case for structures in the splash-zone of the sea or structures in the road environment, will show lower concentrations, which depend on a number of influences. In the marine environment the main influences are: concrete composition distance of the regarded surface to the sea (vertical and horizontal), Figure 46 87(169)

88 orientation with respect to wind direction Figure 46. Maximum recorded chloride concentration C x at different heights above sea level of Gimsøystraumen bridge and 35 other coastal bridges in Norway (for details see D4.2). Data includes both windward and leeward effects. The data represents 850 chloride profiles. Four 4 environmental zones are distinguished. Table 22. Zone Height above sea level [m] Chloride concentration C x in dependence of the height above sea level, see Figure 46 Mean value [wt.-%/concrete] > Standard deviation [wt.-%/concrete] As negative values may not occur a log-normal distribution seems to be most appropriate to describe the chloride concentration C x. The effect of the so-called windward/leeward effect causes chlorides to be deposited at the leeward side. During rain events deposited chlorides are washed of at the windward side whereas the rain will not reach the leeward side, which even emphasizes this effect, Figure 47. The given values in Table 22 must thus be corrected for by means of a so called turbulence factor, which highly depends upon the geometry of the regarded structure. 88(169)

89 Height above sea level: 11.9 m SOUTH % % NORTH % 5.4 m 3.01 m % % % % % % Figure 47. Influence of orientation on C x (Gimsøystraumen bridge, Norway) In the road environment the chloride concentration C x is a function of: concrete composition amount of de-icing salt spread drainage behavior of the street (texture of street surface, pot holes, etc.) distance to the road traffic density climate orientation Possibilities to predict a long term average of the chloride concentration of water and snow slush on the roads during de-icing salt applications were treated above. However, the transformation from the concentration of the street water and slush 5nto the one at the concrete surface seems hard to be developed, having in mind all the above mentioned influences. The most promising solution to this problem seems be to statistically analyze the chloride concentration in the depth x of the concrete directly. Lay collected 640 chloride profiles from German road administrations (160 structures), which were analyzed with respect to the most relevant influences. Although the particular concrete composition of each investigated structure was usually unknown it can be assumed that CEM I (OPC) with water-binder ratios of w/b = 0,40 to 0,50 were usually used. Site dependent information as traffic volume and velocity as well as regime of de-icing salt application was not available and was not incorporated to the analysis. The chloride profiles were thus only analyzed with respect to exposure time and distance to the road. The analysis revealed for the concentration C x : a linear decrease with increasing height (h) above street level a logarithmic decrease with increasing horizontal distance (a) from the street edge 89(169)

90 no trend with respect to exposure time These relationships were picked up to derive a function in the form of C x = f(horizontal, vertical distance to the road): C (a, h) ln(a 1) (a 1) h x, mean C x,mean (a,h) mean chloride concentration in depth x [wt.%/concrete] a horizontal distance to the roadside [cm] h height above road level [cm] (112) Figure 48. Chloride concentration C x as a function of height above street level (h) and horizontal distance to the street edge (a) A model uncertainty c [-] was calculated, which is the ratio of each measured value C x,measured [wt.%/concrete] and the calculated mean value according to (112): C C C x,measured x,mean (a,h) (113) The statistical analysis showed that a log-normal-distribution (L) gives the best description the model uncertainty c. Due to the large scatter of the analyzed data the coefficient of variation (CoV = 100/µ) is quite high with CoV = 75%. The statistical distribution of the concentration in depth x is thus defined as follows: L(mean µ = C x,mean ; standard deviation = µ0,75) in [wt.%/concrete]. From extrapolation of (112) can be seen that elevated chloride concentrations above the initial background level are to be expected up to a height of h Max = 7 m and as far as a horizontal distance of around a Max = 70 m. However, (112) should only be used within the limits of the collected data (0 h 5.5 m; 0 a 12 m). 90(169)

91 The mean value of the presented site dependent function for the concentration C X is as such only valid in Germany and for concrete produced with CEM I and water-binder-ratios of around = 0,40 to 0,50. If the salt application regime differs considerably from the Germane average or a different binder type is considered the values may be adapted by using binding isotherms, which expresses the relationship between chloride supply, C free, and the resulting total content C total (see Figure 49). The standard deviation with the inherent spatial scatter should meanwhile still be based on the model uncertainty obtained for CEM I, see (113). Figure 49. Procedure to determine concentration C x,mean for any concrete composition to be expected in the road environment Example: If a concrete produced with 360kg OPC and w/b = 0.50 shows a surface concentration of around 1.5 wt.-%/concrete in a certain environment, the use of cement with 50% slag (CEM III/A) would lead to a value of around 1.66 wt.-%/concrete according to the above given binding isotherms. A quite similar result is to be expected when changing the w/b ratio from 0.40 to 0.50 while all other parameters are kept equal, Figure 50. Total chloride content C total [M.-%/CEM] 3,0 2,5 2,0 1,5 1,0 CEM III/A - w/b=0.40 CEM I - w/b=0.50 CEM I - w/b= z=360 kg/m³ 0,5 0, Concentration of solution [g/l] Figure 50. Using binding isotherms to estimate chloride surface concentration 91(169)

92 7.10 Critical Chloride Content C crit Chloride concentration at the depth of the reinforcement is compared with published information on threshold concentrations for the initiation of corrosion. If chloride concentration exceeds the threshold, it may be assumed that the steel has been depassivated, and that corrosion is possible. The exact value for the chloride threshold required to initiate corrosion is unclear and is best judged on a risk of corrosion. A number of factors affect the chloride threshold level including, the chloride/hydroxyl ratio, chloride binding capability of the cement, use of replacement materials, admixtures, carbonation of the concrete and the condition of the reinforcing steel. The critical level is generally taken as falling in the range 0.2% to 0.4% chloride by weight of cement but values as high as 1% have been found in structures where corrosion has not been initiated while corrosion has been evident in structures with values as low as 0.1% [lvi, lvii]. BS 8110 [lviii]sets limits of chloride concentration of between 0.1% and 0.4% by mass of cement, depending on the type of structural member, curing regime, and cement type. These limits are intended for new construction. BS 7361 [lix] states that no satisfactory threshold value for chloride concentration has been established, and notes that some authorities impose a limit of 0.3% as allowable before remedial action is necessary. BS 7361 also states that the presence of any chloride should always be assumed to place the structure at risk. Chloride concentration thresholds are generally quoted by proportion of cement, but it is samples of concrete which are weighed and analyzed in tests. This means that either assumptions must be made of the cement content of the mix or analysis of the hardened concrete undertaken to determine cement content. Chemical analysis of the cement content of hardened concrete is notoriously tricky, particularly if a sample of the aggregate is unavailable. Where chlorides are transported from the outside environment but has yet to reach the reinforcement, knowledge of the variation of chloride concentration with depth will enable an estimate of diffusion coefficient and hence of time to depassivation to be made. Computer based programs are available to assist in this process [lx]. No information on the critical chloride content for rebar corrosion in high alumina cement concrete is known. Sulfate resisting cement has a low binding capability, and critical (acid soluble) chloride content can be expected to be significantly lower than for Portland cements [lxi] 37. Similarly, blended cements containing PFA or silica fume also tend to have lower binding capabilities [lxii]. The lesser binding capacity is more than offset by a reduction in permeability, however. The critical chloride content, is here considered as: the content, leading to a depassivation of the steel surface, irrespective of whether corrosion damages become visible or not. According to [lxiii] the critical chloride content mainly is controlled by: the moisture content of the concrete quality of concrete cover. 92(169)

93 Cl - Crit [M.-%/b] good quality quality = f (cover depth, type and amount of cement curing, w/b-ratio) ~ 0,5 poor quality moisture content permanently dry ~50 % RH e.g. indoor prevention of electrolytic process permanently wet % RH frequent wet-dry cycles e.g. splashzone permanently saturated e.g. submerged lack of oxygen Figure 51. Qualitative relationship of the critical chloride content, the environmental conditions and quality of concrete cover, [lxiii] As a statistical parameter the critical chloride content (following definition 1) may be given according to [lxiv]: Beta distribution (m = 0,48; s = 0,15; a = 0,20; b = 2,0) Shortcomings of the Model - Lack of knowledge for the dependence of the apparent diffusion coefficient D app on the humidity conditions of the environment, i.e. the degree of saturation of the concrete. - Effect of carbonation on chloride binding capacity is only indirectly treated by introducing the parameter x, being the depth in which data deviates from diffusion behavior. - Interaction of chloride ingress and other degradation mechanisms as e.g. frost is not included. - Effect of concrete on effective diffusion coefficient is properly modeled. Temperature of concrete is assumed to be equal to environmental temperature. This is a sufficiently correct assumption for surfaces, which are sheltered from direct radiation. Effect of radiation must still be incorporated. A good starting point can be the proposal in [xiii]. 8 Case Study on chloride induced corrosion 8.1 Description of the Object Hofham Brücke The model was applied to a bridge column, which was not part of the data analysis and can thus be regarded as independent for the purpose of verification. The bridge column is situated 1,8 m from the edge of a federal road in Bavaria (near Landshut) with a speed limit of 100 km/h. The concrete was composed of 320 kg/m³ CEM I with w/b = 0,48. The structure was built June (169)

94 and inspected in June 1982 and June The target of the durability design is either the mean value of the concrete cover d C or the apparent diffusion coefficient D app. In the case study we assume that the structure was planned with a mean value of µ = 45 mm for the concrete cover. For regular workmanship a standard deviation of = 8,0 mm can be assumed today for the concrete cover [xiv]. Regarding the height above the road level, the bottom with h = 0 cm, is decisive, as here the highest concentration C x is to be expected, see (112). However, since in 1982 and 2001 chloride profiles were only taken at a height of h = 60 cm, this is used as a reference site for model verification. As an input to the temperature function (101), the daily average air temperature measured by the German weather service (DWD) at the nearest weather station (Landshut), was analyzed for the last 10 years, see also D4.2 [xx]. Table 23. 1) Summary of input parameters for the durability design Parameter Units Distribution 3) Mean StD Source µ C ini [wt.-%/cem] L 0,108 0,057 Analysis 1) C x [wt.-%/cem] L 1,39 1,04 Chapter 7.9 C crit [wt.-%/cem] B 0,48 0,15 [xiv] 0.2 C crit 2.0 x [mm] B 9,03 9,36 Analysis 1) 0 x 60 d c [mm] B 45,0 8,0 Assumption 0 d C 700 D RCM (28d) [10-12 m²/s] L 9,28 4,83 Chapter D RCM (t=) [10-12 m²/s] L 4,88 3,56 Chapter k [-] L 1,20 0,13 Chapter n 2 [-] L 0,964 0,212 Chapter T Air [K] B Analysis 2) 260 T 302 b T [K] N [xiv] k RH [-] D 0,90 - Chapter 7.8 n 1 [-] B 0 1 0, Chapter 7.8 Statistical analysis of 640 chloride profiles of German Road Administrations 2) 3) Statistical analysis of the daily average air temperature Distribution types: N (Normal); B (Beta); L (Log-normal); D (Deterministic) 8.2 Reliability Analysis In a first step the service life of the case study column is calculated using the information, which is available without any further structure investigations. In a second step the additional information of investigations are used to improve the precision of the model. Regarding the height of the road level, the bottom area is the decisive domain for service life calculations. As in the years 1982 and 2001 chloride profiles were taken at a height of h = 60 cm, this domain is taken as a reference for checking the model precision. If only the mean values given in Table 23 are inserted to (87) (semi-probabilistic approach) the in average expected chloride profile can be predicted. 94(169)

95 Figure 52. Measured and predicted chloride profiles (average values) in the year 1982 and 2001 at nearby sampling sites The comparison of chloride profiles (mean values until a certain moment in time) of the year 1982 and 2001 revealed, that the depth dependent chloride loading of the concrete was overestimated by the a priori model (without inspection data), especially in the domain of the depth 10 x 70 mm. When comparing predicted and measured values the considerable spatial scatter must be taken into account. More over, deviations from the real values due to the chemical analysis should be considered. Round robin tests [lxv, lxvi] showed that for concentrations in the domain of the critical chloride threshold average deviations of around 25% will occur (for the most common technique of titration). With decreasing chloride concentration the deviations of the analysis will increase even more. The probability density of the chloride concentration and the resulting quantile values can be calculated for every depth x according to the full-probabilistic model using the data given in Table 23. Figure 53. Scatter in the prognosis of chloride profiles 95(169)

96 Having the various sources of scatter in mind when modeling chloride induced depassivation of the reinforcement, it becomes obvious that only probabilistic methods are appropriate to tackle the problem. This is done by comparing the critical chloride depth x crit and the concrete cover, as already shown for the semi-probabilistic model in chapter 6.4. The probability of depassivation p depassivation is calculated according to (97). However, today it is common practice to regard the reliability index instead of p depassivation. As chloride profiles were determined in the years 1982 and 2001 (age 19 and 38 years) the apparent diffusion coefficient D app, the chloride concentration C X and the depth of the convection zone x were known at these moments in time. Measurements of the concrete cover resulted in a somewhat lower mean value as expected of µ = 44 mm and a relatively high standard deviation of = 12 mm. Furthermore the chloride migration coefficient D RCM of the actually built in concrete can be measured. For young concrete structures, which were not yet subjected to a considerable chloride load (e.g. before first application of de-icing salt in the road environment) this is possible with the regular method according to Tang, see chapter 7.2. For those concretes already loaded with chlorides, as was the case for the considered structure in the year 2001, a new test method was developed [lxvii]. Using all of the additional investigation data improves the prediction of the velocity of chloride penetration considerably, Figure 54. Figure 54. Bayesian update with data of structure investigation (until current age) and monitoring with corrosion sensors (assumption for future) Compared to the a priori model the post priori model results in a higher reliability index versus time. The reason for this effect compared to the assumptions for design are a lower mean value and standard deviation of the convection zone x and of the apparent diffusion coefficient D app. This positive influence overwhelms the effect of a higher scatter of the concrete cover. 96(169)

97 The level of reliability, which was determined with the post priori model 2 at t = 38a, lies in the domain of today s requirements of min = 1,5. As the structure was expected to fulfill these requirements throughout the entire service life, maintenance measures need to be taken if the expected service life is not achieved. The uncertainty with respect to the chloride penetration velocity was reduced by inspections at an age of t = 19 and 38 years. Besides the penetration velocity of chlorides, also the variable critical chloride concentration in concrete is afflicted with uncertainty with respect to the mean value and standard deviation. This uncertainty can not be reduced by collecting chloride profiles, but very well so by integrating data of corrosion sensors [lxviii] (monitoring data). In the present case study such sensors were not installed. Still, for demonstration purposes it is assumed that sensors were installed during the second inspection. The sensor elements, which are installed in different depths, give a corrosion current signal once the critical corrosion inducing chloride content is reached in a certain depth. This information can be monitored continuously over time and be inserted for future predictions [lxix]. 8.3 Conclusions for the Praxis The prognosis of chloride profiles revealed that the developed model for durability design ( a priori model ) gives in average a sufficiently good estimation for the penetration velocity of chlorides. Under consideration of the variability of each input parameter the reliability can be estimated using full-probabilistic methods. A verification of the time dependent penetration depth (mean value and standard deviation) by means of structure investigations will perforce lead to an increase of the reliability index, because the uncertainty in the model is reduced. An improvement of an a priori model will however not always result in an increase of the reliability level. This is the case, if assumptions in the a priori model with respect to the structure resistance (concrete cover) were overestimated and/ or the stress variable (critical penetration depth) was underestimated. Moreover the case study demonstrates the necessity of inspection data, which are obtained at different times with different inspection methods, Figure 55. quality control and acceptance ("birth certificate") age or degree of damage of structure information for model improvement from... chloride profile monitoring (corrosion sensors) potential mapping Figure 55. Moment in time and method to obtain additional information for a model update using Bayesian methods 97(169)

98 For new built structures the necessary concrete cover and material resistance is chosen according to the environmental exposure. Right after completion of the structure the: concrete cover chloride migration coefficient should be tested for within the quality control system. The results of these investigations should be documented in a birth certificate and be used for another calculation of the residual service life. When evaluating chloride profiles the chloride contamination versus the penetration depth is obtained and thus information regarding the penetration velocity of the chlorides. This information is also provided by corrosion sensors, whereas in such sensors also provide information of the critical chloride content under the particular environmental conditions. If the probability of depassivation of the reinforcement is high a mapping of the electrochemical potential may be performed. The result of these measurements supplies site dependent information regarding the corrosion activity of the reinforcement over the entire surface area of a component, which means that the obtained information is obtained at certain depth. The combination of corrosion sensors and chloride profiles with data of potential mapping gives a rather good picture of the condition state of the component. 9 Models on Propagation of Corrosion 9.1 Introduction The propagation period t prop is the time during which the rebar is actively corroding. The main parameter which has to be determined is the corrosion rate. Neglecting the propagation period in Service Life calculations is a common approach for the durability design of new structures until now. This procedure is sufficient when indications are given, that the corrosion of steel will propagate at such a rapid rate, that the propagation period is relatively short compared to the initiation phase or when design considerations will not tolerate any form of re-bar corrosion. Since in most existing structures cases suffer from re-bar corrosion to a certain degree and decisions on necessary measures have to be taken, the corrosion phase must be included in calculations of the residual service life. The corrosion process can be modeled by an equivalent circuit of a galvanic element with a serial connection of resistances representing the anodic and cathodic charge transfer resistances R ct of the steel surface, the electrical conductive resistance of the reinforcement R steel and the concrete resistance R concrete. The corrosion current I corr, which is proportional to the corroded mass of steel, depends on the potential difference U between the anodic and cathodic areas, as well as on the resistances in the equivalent circuit. The corrosion rate V corr can be expressed in terms of the current density i corr [A/cm²] (corrosion current I corr related to the steel surface area) or in terms of the rate of 98(169)

99 loss in bar section [mm/a]. The relationship between electrical current and loss of steel section is as follows: Mass of a single iron ion: MFe 55, 847 m 9,27210 Fe 23 N 6, L 26 [kg] (114) M Fe Relative atom mass of iron [g/mol] N L Loschmid constant [mol -1 ] Electrical current set free in the reaction Fe Fe 2e : F L 2e 2 2 3,20410 N 6, Fe 23 L 19 [C = As] (115) F Faraday constant [C/val = As/val] Corroded mass of steel for 1 amp per year: m 3,15410 s / a Fe 9, ,15410 m 9,127 corr 19 3, L Fe [kg/aa] (116) Corrosion rate related to surface area: m 9,127 mm³ mm/a µm/a 7,8510 Aa A / mm² µa / cm² corr 6 v 1,16 10 corr 6 11,6 Fe (117) Fe Density of steel [kg/mm 3 ] For a known corrosion current density i corr [µa/cm²]the annual penetration rate is thus: V corr = i corr 11,6 [µm/a] (118) icorr corrosion rate density [µa/cm²] V corr may be constant along the propagation period or vary following different events suffered by the structure (environmental changes). There are numerous parameters related to the concrete quality and the environment influencing V corr. The mutual influences may be additive, synergistic or opposite. In [xiii] four main parameters have been identified: - resistivity of concrete - galvanic effects - chloride content of concrete - humidity/ temperature in concrete The resistivity of the concrete is the major factor affecting the corrosion of depassivated steel, being in turn influenced by the mix composition and the moisture content of the concrete. 99(169)

100 The damage function P(t) represents the loss of re-bar diameter at time t: P( t) V t t i corr ( ) d (119) P(t) corrosion depth [mm] t i initiation period [a] V corr corrosion rate [mm/a] Due to the presence of chlorides or partial depassivation induced by carbonation the loss of rebar diameter may locally vary because of the occurrence of pitting corrosion. The pitting factor is the ratio of the maximum pit depth and the average loss of re-bar diameter. Considering a constant corrosion rate, the progressive loss of re-bar diameter is given by [viii]: P(t) V t V (t t ) corr prop corr ini (120) pitting factor accounting for a non-uniform corrosion of the rebar [-] t prop duration of propagation phase [s] t age of structure [s] t ini time until initiation of corrosion [s] The initiation time t ini is inserted to (120) by solving the models for the onset of corrosion due to carbonation or chloride ingress for t. This is not possible for the model on chloride ingress in an analytical way for the proposed model structure, see (87) and (106). There are two solutions to overcome this problem: 1. change the structure for the model on chloride ingress by neglecting the fact hydration only proceeds for a certain time and that the apparent diffusion coefficient is the average diffusion coefficient in a regarded period 2. not to solve these equations for time and rather determine t ini in a different way. The second option is proposed here. To do so the user has to calculate and plot the probability of depassivation versus time. This data can be fit to the probability distribution function of the time until depassivation. As distribution type a Weibull (min. Type III) seems to fit rather well as shown in Figure 56. The result of the fitting are the parameters of the distribution (here, w and k) which characterize the distribution for the time of depassivation unambiguously. 100(169)

101 Probability p [-] 1,0 0,8 0,6 Fit Weibull-min Data of depassivation model 0,4 0,2 0, Age [a] Figure 56. Probability distribution plot for the time until depassivation In the DuraCrete project [xi] the pitting factor being the ratio of the maximum penetration depth P max and the mean penetration depth P mean was analyzed, Table 24. As negative values for the pitting factor can not occur a lognormal distribution is proposed here. Table 24. Pitting factor, according to DuraCrete [xi] Environment Distribution Mean StD Carbonation Deterministic 2,00 - Chloride Log-Normal 9,28 4,04 A procedure to determine the pitting factor by on-site investigations is provided in the appendix of D3.1 [i]. The main task of modeling the damage function P(t) concerns the establishment of the value of V corr. Three general ways of determining V corr are proposed in [viii]. For durability design applications or for "young" structures (corrosion has not yet started) it is possible to: a) assume values in dependence of exposure classes b) use empirical expressions c) perform direct measurements of specimens exposed under accelerated conditions simulating the considered environment For existing objects data obtained from alternatives of a) to c) can be updated by: d) data from direct measurement on-site For alternative d) various possibilities exist, which are benchmarked and described in the appendix of D3.1 [i]. 9.2 Corrosion Rate in Dependence of Exposure Classes The corrosion rate may be given as: 101(169)

102 V corr = V corr,a ToW (121) ToW wetness period given as the fraction of the year [-], see paragraph 0 mean corrosion rate when corrosion is active [mm/year] V corr,a Based on experience, values for ToW and V corr,a are given for the following classification, [xi]: Table 25. Distribution of corrosion rate V corr and weather exponent w for carbonation induced corrosion independent of concrete type and quality Exposure Class V corr [mm/a] w [-] mean StD DT mean StD DT Sheltered 0,002 0,003 0,50 0,12 W Unsheltered 0,005 0,007 0,75 0,20 N Table 26. Distribution of corrosion rate V corr and weather exponent w for chloride induced corrosion independent of concrete type and quality for different exposure classes Exposure Class Vcorr,a [mm/a] w [-] mean StD DT mean StD DT Wet-rarely dry 0,004 0,006 1,00 0,25 Cyclic wet-dry 0,030 0,040 W 0,75 0,20 N Airborne sea water 0,030 0,040 0,50 0,12 Submerged Not expected, unless bad concrete quality or low cover Tidal zone 0,070 0,070 W 1,00 0,25 N mean Std DT W N Mean value Standard deviation Distribution Type Weibull distribution Normal distribution 9.3 Direct Measurement of the Corrosion Rate Applying Faraday s law the corrosion rate can be used from direct measurement [lxx]: V corr = 11,6k t i corr (122) k t testing factor [-] mean value of the corrosion current [ma/cm²] i corr The corrosion current can be directly measured in specimens or structures by means of: - the linear polarization technique - electrochemical impedance (EIS) - intersection method of the polarization curve The above stated methods measure the polarization resistance R P, which is used for the calculation of the corrosion current i corr by means of: i corr = B/ R P (123) 102(169)

103 B constant varying between 13 and 52, usually 26 is applied [mv] The most frequently used method is the linear polarization technique, which is the only one applicable for the measurement on real structures. Two possibilities of the test are feasible: - Laboratory test with simulated climates for new structures - Measurement in-situ of existing structures at several locations for a period of one year at least, in order to estimate the scatter with variation of the climatic conditions, because the values of I corr may change by several orders of magnitude due to changes in the moisture content and the temperature of the concrete. The values of I corr change considerably in time due to changes in the moisture content of concrete and because corrosion is a dynamic process. In consequence, single measurements must be corrected for deviations due to these influences: Table 27. Values for I corr and k t Case Parameter Unit Distribution Mean StD Lab-specimen I corr µa/cm² LN - 0,86 k t - LN 1,0 0,80 On-site I corr µa/cm² W - 1,38 k t - LN 1,0 0, Empirical Modelling of the Corrosion Rate In order to model the corrosion rate the following relationship can be used: i corr k0 F ( t) Cl F Galv F O2 (124) i corr k 0 corrosion rate [A/cm²] constant regression parameter [mm/a] (t) actual resistivity of concrete at time t [m] F cl accounting for the influence of the chloride content [-] F galv influence of galvanic effects [-] F O2 availability of oxygen [-] The model for corrosion rate contains two main environmental and material dependent parameters k 0 and (t). A reasonable approach to model the material and environmental effects upon the concrete resistivity (t) is to introduce a potential resistivity 0 for a reference concrete and defined environmental conditions (20 C/ 100% RH) Regression Parameter k 0 The regression parameter k 0 can be obtained by performing a regression analysis of the corrosion current i corr versus the resistivity. 103(169)

104 In [xi] Nilsson and Gehlen propose a deterministic value of k 0 = 882 for the time being. The scatter of the corrosion rate model is included in all other parameters. Should this parameter be quantified more precisely in the future, it would be a simple task to incorporate it as a stochastic parameter. 9.5 Concrete resistivity Model Approach This material parameter can be obtained with a low amount of effort and is already quantified for numerous concrete compositions [xii]. The difference in environmental conditions is covered by a number of environmental parameters. Since the potential resistivity is measured at an age of 28 days, an age factor n, analogous to the chloride ingress model (see chapter 7.6) is introduced: (t) (t) k k k k k 0 c t R,T R,RH R,Cl (125) 0 time dependent potential concrete resistivity for a reference concrete and defined environment (T=+20 C; immersed in chloride free water) k c curing factor [-] k t test method factor [-] k R,T temperature factor [-] k R,RH relative humidity factor [-] k R,Cl chloride factor [-] In a similar way as for the onset of corrosion, a limit state can be considered: p f = p (P(t)>P crit ) (-) (126) P(t) loss of rebar section (120) critical loss of rebar section, depending on the structural geometry and the chosen limit state P crit Table 28. Overview of parameters in corrosion propagation model Type of parameter Material/ environment material execution test method environment Parameter k 0, F cl, F O2, F Galv 0, n k c k t k R,T ; k R,RH ; k R,Cl Material Dependent Resistivity 0 Applicable test procedures are given in the appendix of D3.1 [i]. The binder type has been identified to be the dominating material factor influencing the resistivity. In [xi] measurements were continuously performed with the Multi-Ring-Method during the first 91d days of hydration, Figure 57, and fitted according to the potential approach (127), to obtain the statistical input parameters given in Table (169)

105 Electrolytical Resistivity in Electrolytical Resistance of Different Concretes (MRE) Time in d A1-R (CEM I 42.5 R), D A2-R (CEM I 42.5 R), D A3-R (CEM I 42.5 R), D B2-R (CEM I 42.5 R HS), D C2-R (CEM III/B 32.5 NW HS), D D2-R (CEM I 42.5 R HS), D E2-R (CEM III/B 32.5 NW HS NA), D F1-R (CEM III/B 42.5 LH SR), NL F2-R (CEM III/B 42.5 LH SR), NL G2-R (CEM I 42.5 BV LH SR), S H2-R (CEM I 42.5 R), GB I2-R (CEM I 42.5 Sulfate), GB Figure 57. Electrolytic resistivity vs. time (early hydration phase) for different concrete mixes submerged in chloride free water at T = 20 C, [xi] (t) 0 0,t28d n t t 0 (127) 0, t = 28d specific resistance at an age of t 0 = 28 days [kcm] n influence of aging of concrete on resistivity [-] Table 29. 1) 2) Statistical results for the specific electrical resistivity 0, TEM and the aging exponent n according to results shown in Figure 57, [xi] Binder w/b 0, TEM 2) [kcm] n [-] DT 1) Mean StD DT 1) Mean StD OPC (CEM I) 7,7 1,2 0,23 0,04 GGBS (CEM III) 0,5 ND 35,2 15 ND 0,54 0,12 CEM I + FA (20% replacement) 9,2 3,0 0,62 0,13 Distribution type Resistivity measured with the Two-Electrode-Method (TEM) Long-term observations indicate that the time dependent increase in electrolytic resistivity of concrete stored in water will end with the termination of the hydration period, which is not taken into account with the potential approach according to (127), see Figure (169)

106 Figure 58. Electrical resistivity (Wenner-Method) vs. time of concrete produced with CEM II/B-T 32,5R (oil slag cement) CEM II/A-LL (limestone cement) and under variation of the w/c-ratio The time until the hydration process does not contribute anymore to the increase in electrical resistivity of the concrete depends on the type of binder and the w/b-ratio. As investigations of Lay [v] lead to the conclusion that only the binder type and w/b-ratio are significant, whereas cement strength class, cement content, air void content, aggregate type and superplasticizer content showed to be negligible with respect to the electrical resistance of concrete. The following simplified linear model is proposed: t < t hyd : 0,t 0,t (t) 28d 0 0,t 28d t 28 t t hyd : (t) 0 0,t (t 28) hyd (128) index 0 indicates reference condition (water saturation) 0, t = 28d specific resistance at an age of t 0 = 28 days [kcm] 0, t = specific resistance at infinite age [kcm] t 0 reference age, here 28 days [s] t concrete age [s] t hyd Age until an increase in resistivity due to hydration can be measured [s] To calculated with this approach, the average value of the concrete resistance during a regarded time period has to be calculated: AVG (t) 0,t 0,t28d 2 (t 28) (tt ) hyd hyd 0,t (t 28) (129) Table 30. Amount of investigated mixes n, mean value [kcm] and coefficient of variation [%] of 0, Ref, t = 28d for w/b = 0,45 and various binder types CEM I II/A-LL II/B-T II/B-S III/A III/B I+FA Additions [wt.-%] n m( 0, Ref, t = 28d ) 13,4 11,2 15,4 15,0 30,1 62,5 15,2 CoV( 0, Ref, t = 28d ) (169)

107 Table 31. 1) Amount of investigated mixes n, mean value [kcm] and coefficient of variation [%] of 0, Ref, t = for w/b = 0,45 and various binder types CEM I II/A-LL II/B-T II/B-S 2) III/A 2) III/B 2) I+FA Additions [wt.-%] n m( 0, Ref, t = ) 22,7 18,7 27,7 55,5 166,9 201,3 90,3 CoV( 0, Ref, t = ) Value at the end of investigations (2 years). Hydration process is not yet finished (approach on safe side) Table 32. 1) Amount of investigated mixes n, mean value m [d] and coefficient of variation [%] for the end of hydration for various binder types CEM I II/A-LL II/B-T II/B-S III/A III/B I+FA Additions [wt.-%] n m(t hyd ) ) - 1) - 1) - 1) CoV(t hyd ) ) - 1) - 1) - 1) Not yet quantified as hydration still proceeds after 2 years of measurement The relationship of the electrical resistance of concrete and the w/b-ratio can be expressed by means of an exponential approach, which corrects the results given in Table 30 and Table 31 for a change in w/b-ratio: a (w / b 0.45) w/b,t28d exp 0, 40 w / b 0,60 0 WER,w/b0,45 (130) 0,w/b = 0,45 binder specific electrical resistivity (Wenner) for w/b = 0,45 [-] a w/b, regression exponent (CEM I: -2,9, CEM I+FA: -6,4, CEM III: -2,2) [-] Curing Factor k c The curing factor is not available at present Test Method Factor k t It is necessary to provide information concerning the method used testing for the electrolytic resistivity 0. In DuraCrete [xii] relations between the following test-methods haven been determined: - TEM: Two-Electrode Method - MRE: Multi Ring Electrode - WER: Wenner Method The relation factors can be determined by testing identical materials with all of the above stated methods. All quantifications should always be related to the Wenner method, as hereby capacitive charge effects are reduced. The following relations are given in [xi]: TEM = A WER + A (131) 107(169)

108 MRE = B WER + B (132) specific electrolytic resistivity either measured by the Two-Electrode-Method (TEM), Wenner-probe (WER) or Multi-Ring-Electrode (MRE) in [kcm] A regression parameter; A = 0,68 B regression parameters; B = 0,721 A A offset; ND (0; 3,4) [kcm] offset; ND (0; 2,8) [kcm] Humidity Factor k R,RH For sheltered concrete structures the humidity factor, which serves to correct the electrolytic resistivity 0 (determined for saturated concrete) for the actual relative humidity on-site, can be derived by comparing the resistivity of the concrete at different relative humidity with a reference humidity (100% RH). A reasonable assumption is to estimate RH from the annual average air humidity close to the structure. Due to lack of data a quantification has so far only been performed for two binder types, i.e. an OPC (CEM I) and a blast furnace slag cement (CEM III). Water cement ratio varied from 0,45 to 0,65. The statistical quantification of the factor k RH is performed for different relative humidity as given in Table 33. Table 33. Relative humidity factor k R,RH to correct the resistivity 0 given in the form distribution type(mean value [-], coefficient of variation [%], limit value []) RH CEM I CEM III 50 sln (17; 145; 3,2) sln (15; 120; 4,9) 65 sln (6; 100; 2,41) sln (7; 70; 3,57) 80 sln (3,2; 48; 1,33) sln (3,8; 27; 2,36) 95 LN (1,08; 13) sln (1,2; 10; 0,24) 100 D (1) D (1) sln LN D shifted lognormal distribution (moments:,, ) lognormal distribution deterministic Mean k RH [-] Mean value CEM I Mean value CEM III CoV CEM I CoV CEM III CoV k RH [%] Relative Humidity RH [%] Figure 59. Mean value and coefficient of variation (CoV) of k R,RH as a function of the relative air humidity for concrete (w/c ranging from 0,45 to 0,65) produced with OPC and BFSC 108(169)

109 From Figure 59 can be seen that the mean value of the factor k R,RH increases exponentially and the coefficient of variation increases linearly with decreasing relative humidity. A fitting of the data from [xi] has been performed according to the following equations: 100 µ(k ) R,RH RH a (133) µ(k R,RH ) mean value of relative humidity factor [-] RH relative humidity [%] a regression parameter CoV(k ) b (100 RH) R,RH (134) CoV(k R,RH ) coefficient of variation of relative humidity factor [%] b regression parameter As a distribution type a log-normal-distribution is proposed. The results indicate that a distinction in between binder types is not necessary for the factor k R,RH so that the above given regression parameters can be applied regardless of the binder type (a = 4,0; b = 2,6). From (133) can be derived: RH = 0 k R,RH = = (dry concrete) RH = 100 k R,RH = 1 = 0 (saturated concrete) For unsheltered conditions the time of wetness ToW, i.e. the duration of rain and condensation at the concrete surface, must be considered. A possibility to account for wet periods in the model is to introduce the time of wetness ToW as follows: d 0 R,RH (t) (t) k k (135) with k being the product of all other influences apart of the relative humidity: k kc kt kr, T kr, Cl (136) The exponent d expresses the time of dry periods. When formulating an expression for the duration of periods in which the concrete is wet, it must be realized that concrete is saturated rather fast once wetted but needs considerably more time to dry out afterwards. 109(169)

110 Figure 60. Measurement of concrete resistance in different depth x during cyclic wetting and drying The effect of a slow drying process may be accounted for by the following expression: b d 1ToW (137) d dry period exponent ToW Time of Wetness [-] b retardation parameter [-] The duration until concrete dries out to the same level as was the case before a wetting event depends on the concrete quality (binder type, w/c-ratio). As sufficient data for the estimation of the retardation effect is lacking it is proposed to: set the exponent d = 0 if concrete is not sheltered from rain or is wetted by further sources set d = 1, if concrete is not wetted Temperature Factor k T An increase in temperature will decrease the electrolytic resistivity of concrete. It is a common approach to use the Arrhenius-equation to model the temperature effect upon the electrolytic resistivity: k R,T 1 1 expb R,T T T0 (138) k R,T factor to account for a change of the concrete resistance with temperature [-] b R,T regression parameter [K] T temperature of environment [K] T 0 reference temperature, here 20 C (273 K) [K] 110(169)

111 To obtain the regression parameter b R,T data on the resistivity at different temperatures (with a reference temperature of usually T = +20 C) has to be compared. A literature study of Raupach [lxxi] resulted in a range values between 2130 b R,T 5500 [K]. Here it is proposed to use the following quantification: Log-N(µ = 3815; = µ0,15 = 560) [K] The following relation is used in DuraCrete, [xi]: k R, T 1 1 K ( T 20) (139) K temperature dependence of conductivity [ C -1 ] T temperature in [ C] Table 34. Parameter K [ C -1 ] in (139) Environment Distribution Mean µ StD T > +20 C ND 0,073 0,015 T < +20 C ND 0,025 0,001 However, a quantification dependent of different temperature regions is not suitable for a parameter study as conducted in later chapters. The relationship given in (138) is thus recommended Chloride Factor k R,Cl The effect that an increasing chloride content reduces the electrolytic resistivity, can be modeled as a function of the chloride content c Cl ; [xi]: 1 a 2 Cl k 1 c R,Cl Cl (140) c cl chloride content [wt.-%/cem] a Cl regression parameter [-] Table 35. Chloride factor k R,Cl [-] and parameter a [-] in (140) Environment Parameter Values c Cl 2% k R,Cl ND (0,72; 0,11) 0% < c Cl < 2% a ND (0,72; 0,11) Chloride Concentration Factor F Cl The parameter F Cl describes the effect of the chloride content on the corrosion rate, apart from the effect upon the resistivity (see chapter 9.5.7, Chloride Factor k R,Cl ). The corrosion rate will increase with increasing chloride content for the same resistivity values. A simple approach may be a linear function, starting from F Cl = 1 at a chloride content equal to the chloride threshold level C crit with a slope of k [xi]: 111(169)

112 F Cl = 1+k(C-C crit ) with C > C crit (141) k regression parameter, here shifted Lognormal distribution (Min = 1,09; µ = 2,63; = 3,51) C chloride concentration C crit critical chloride content The Galvanic Factor F Galv There is so far no information available on the galvanic factor, which shall account for the effect that corrosion products may produce lower values of the corrosion rate, because the oxides already generated may impede a further access of aggressive media, hereby reducing the corrosion rate. Neglecting this factor, i.e. setting F Galv = 1, is thus on the safe side The Oxygen Factor F O2 The influence of the availability of oxygen my be taken into account by the factor F O2. Data is not yet available. Nevertheless, except for submerged concrete, the oxygen supply usually is not limited, thus leading to F O2 = 1 in most cases. 9.6 Aspects not treated by the Chosen Model influence of cracks quantification of parameters is partly missing 10 Models on Structural Consequences of Reinforcement Corrosion (Co-author: Prof. John Cairns, Heriot-Watt University) 10.1 Introduction This section of the report describes the manner in which reinforcement corrosion influences the strength of structural concrete elements, and the models available to estimate the change in structural behavior and strength. The models described here must be integrated with those described in chapter 9 for the propagation of corrosion in order to derive predictions of the future condition. It is fair to say that greater attention has been devoted to modeling the earlier stages of the deterioration process: the greatest attention has been devoted to models up to the initiation of corrosion, somewhat less up to the point at which longitudinal cracking initiates, and least to the propagation phase after the initiation of longitudinal cracking. Certainly models for residual strength are much simpler and more empirical than for earlier stages of corrosion induced deterioration. For this reason the experimental techniques used to obtain the data from which the empirical expressions are derived are also reviewed. The direct effects of corrosion are loss of bar cross section, increase in bar diameter resulting from the volumetric expansion of the corrosion products and a change in the mechanical 112(169)

113 characteristics of the bar/concrete interface on formation of corrosion products [lxxii]. Effects of corrosion on residual structural capacity are divided into those aspects which affect the reinforcement itself, those which affect the surrounding concrete, and those which affect interaction (or bond) between the two. The consequences of each of these aspects and their interrelated effects on the load carrying capacity of reinforced concrete structures are summarized in Figure 61. Corrosion Volumetric expansion Loss of bar section Weak interfacial layer Disengagement of ribs Local General Bond Cover cracking => loss of integrity of cover Ductility, strength Strength Anchorage capacity Composite interaction Loss of concrete cross section Reduction of load carrying capacity Further reductions in corrosion resistance Figure 61. Effects of corrosion on residual strength 10.2 Corrosion Process Section Loss Dissolution of iron from steel reinforcement results in a loss of bar cross section which may either be predominantly uniformly distributed over the length and circumference of the bar (general corrosion) or show concentration at localized sites (pitting corrosion), Figure 62. p(t) d 0 p(t) Uniform section loss : general corrosion Local section loss at pit Figure 62. Section loss due to uniform and pitting corrosion The structural effects of these two forms of corrosion damage differ significantly, and will be examined in more detail. In general corrosion is caused by ingress of chlorides or carbonation of concrete. It is generally associated with formation of brown rust iron oxides which occupy a greater volume than the parent metal, and expansion of the bar as it corrodes, which leads to cracking and eventually spalling of the concrete cover. The residual cross sectional area A res may be evaluated by: 113(169)

114 res 0 corr b 2 A A A d 2p(t) / 4 (142) A 0 original cross section area [mm²] A corr loss in cross section area [mm²] d b original bar diameter [mm] p(t) corrosion penetration depth [mm] Local or pitting corrosion is invariably associated with chloride contamination and not with carbonation. In local corrosion, the area of the anode (where dissolution of metal occurs) may be relatively small. Once a pit has initiated the resulting electric field attracts negative (Cl - ) ions towards the pit. Hydrolysis of the corrosion product in the pit causes a decrease in ph. In the resulting saline and acidic conditions, very rapid corrosion may occur. The need to balance the release and consumption of electrons at anode and cathode means that current density, and hence rate of loss of metal at the anode will be relatively high. Anodic and cathodic sites are separated by tens of millimeters up to meters, and may develop on a single bar or between different layers of reinforcement. Because the corrosion rate is rapid and the supply of oxygen restricted, the products of the corrosion reactions exhibit a lower degree of volumetric expansion as brown rust, and the tendency to split the concrete cover is consequently less. Extreme loss of bar section may occur without external visual signs of cracking, although surface staining will usually be noticeable. However, local corrosion sites are readily detectable by the half cell method where it appears as a strongly negative potential surrounded by a high potential gradient. Local corrosion can only be sustained where resistivity of the concrete is low. The residual cross sectional area A res from local corrosion may be evaluated with the help of Figure 63 if the pitting depth P(t) is known. Figure 63. Calculation of residual area of an idealized pitted bar A d /4 A A [mm²] (143) 2 res b 1 2 where 114(169)

115 2 d b A ad cos 1 b 4180 [mm²] (144) A 2 2 P(t) ap(t) cos[mm²] (145) 180 = 2 arcsin(p(t)/d ) [ ] b (146) a = d b 2 sin [mm] (147) a arcsin p(t) [ ] (148) Although it is convenient to describe the two forms of section loss separately here, both will occur together with chloride induced corrosion, and loss of section will never be completely uniform. Note that the rate of corrosion penetration dp(t)/dt will be different for general and for pitting corrosion, as quantified in chapter Volumetric Expansion The corrosion of steel in concrete is an electrochemical process. Dissolution of the iron at anodic sites, can be represented by: 2+ - Fe Fe +2e (149) At cathodic sites, oxygen is reduced to form hydroxyl ions, consuming the electrons supplied from the anode: O +2H O+4e 2 2 4OH - - (150) The hydroxyl ions migrate through the solution (electrolyte) to the anode where they combine with the metallic ions released by the anodic reaction to form iron oxides. One possible is the formation of. Fe 2 O 3, which is the brown rust ferrous oxide compound. Another alternative reaction results in the formation of black magnetite iron oxide Fe 3 O 4. Note that these reactions do not form part of the electrochemical process, but follow the dissolution of the iron. Fe +2OH Fe(OH) +O 6Fe(OH) +O Fe(OH) Fe O +4H O 2Fe O +6H O (151) (152) (153) As the oxygen demand of the reaction in (152) is greater than that of (153), the latter tends to occur where the supply of oxygen is restricted, generally when the concrete is wet. It also tends to form as the product of pitting corrosion. The products of (153) are less expansive than those of (152). The environment in which corrosion takes place may thus exert an influence on the products of the corrosion reaction, and hence on the deterioration process. 115(169)

116 The ratio of the volume of the corrosion products (rust) to that of parent metal is dependent on density and chemical composition, and can be assumed to usually range in the order of 4-6 [lxxiii]. A volume ingress factor thus ranges in between 3 and 5. There does not appear to have been any attempt to correlate expansiveness to conditioning environment. The volume ingress obviously includes a considerable extent of uncertainty and is further more one of the most important variables when modeling crack initiation as will be shown in chapter Weak Interfacial layer It has been suggested that the formation of corrosion products on the bar surface could produce a mechanically weak layer at the interface between reinforcement and concrete [lxxiv]. However, in an as yet unpublished report, Cairns and Du [lxxv] describe measurements of the coefficient of friction between concrete and steel plates subjected to corrosion while in contact with the concrete. Three different conditioning regimes were used. No reduction in friction was measured despite corrosion being followed until the equivalent of cracks with a width of over 1,0 mm was reached. This aspect is therefore not considered further Influence of Conditioning and Damage Parameters Preceding sections have identified that loss of section and cracking are affected by conditioning environment. This section therefore reviews conditioning procedures used in research into residual strength capacity. In the majority of tests on corroded affected concrete structural elements, the corrosion process has been activated by chloride salts and accelerated by electrical polarization of reinforcement. In this technique, a positive electrical potential is applied to the bars to make the reinforcement anodic and encourage dissolution of Fe 2+ ions (the process may be considered the opposite of cathodic protection, where a negative potential is applied to reinforcement to make it cathodic and thus attract/retain Fe 2+ ions). Conditioning has been carried out with test specimens wholly or partially submerged in some instances, and with ponding of salt solution or by spraying in others. Submersion will tend to restrict the availability of oxygen to the post-dissolution reactions, and corrosion products and the expansive forces generated may thus differ from those found under cyclic wetting and drying, as will be the case in many field exposures. Results of accelerated tests must therefore be treated with caution, as they may be unrepresentative of field conditions. Clark & Saifullah [lxxvi] have demonstrated that the current density applied to accelerate corrosion exerts a significant influence on bond strength. The amount of corrosion (expressed as percentage weight loss) to cause cracking over bars with a cover/bar diameter ratio of 1.0 ranged from 0.2% for high rates of corrosion (current density of 4 ma/cm 2 and a few hours to cracking) to 1.2% at low rates (current density of 0.04 ma/cm 2 and 8-12 days to cracking). This means that for strongly accelerated tests low values of weight loss (and thus short testing time) are necessary to initiate a crack and vice versa. A possible explanation for this effect is the circumstance that corrosion products are generated so fast that these may not expand fast enough 116(169)

117 into the concrete pores as would be the case under natural conditions. Even the lowest of these corrosion rates is appreciably higher than the highest rates of corrosion recorded in service. Corrosion rates measured which typically are of the order of 1- /cm 2 in chloride contaminated concrete, though values up to /cm 2 have been observed in field measurements by Rodriguez et al [lxxvii]. However, values larger than /cm 2 are rarely observed in practice, either on site or in non-accelerated laboratory experiments. In initial guidelines of corrosion rates the medium range had a characteristic current density in the range 1- /cm 2 and the high range above /cm 2 [lxxviii]. This has been revised with a current density of greater than /cm 2 now being regarded as high [lxxix]. In conclusion, accelerated tests will give rather conservative values for the attack penetration to induce cracks. Rates tend to be appreciably lower in structures affected by carbonation. Bond strengths at cracking, expressed as a proportion of the non-corroded specimen strength, ranged between 0.5 and 1.2 for high and low corrosion rates respectively. At high rates of corrosion, there was a large initial drop in bond strength at time of cracking and a gradual subsequent strength reduction with further corrosion. However, at low rates of corrosion, the opposite occurred. The variation was attributed to differences in the chemistry of corrosion products, to their ability to disperse into the cement matrix, and to creep of concrete. Cabrera has also criticized use of high corrosion currents for conditioning [lxxx]. Work carried out at the Institute Torroja and at Geocisa has examined current densities within the range of values between 1-3 A/cm 2, which are more representative of values found in practice. In addition they have also investigated values ranging up to 100 A/cm 2, which are a factor of 5-10 greater than those maximum values seen in service. The influence of current density on cracking initiation and on crack width is reported to be negligible when compared to other parameters such as cover/bar diameter ratio and concrete strength [lxxxi, lxxxii]. Coronelli [lxxxiii] has suggested that current densities should be limited to a maximum of 0.05mA/cm 2 to avoid mechanical damage when conditioning corrosion bond specimens. The most widely adopted measure of corrosion is the weight of metal lost after completion of strength tests. Some investigators quantify corrosion simply as Section Loss, i.e. weight loss divided by original weight, expressed as a percentage. This is evidently an appropriate parameter to adopt where residual tensile strength of the bars is of principal concern. However, there is evidence that average corrosion penetration, i.e. the thickness of steel lost through corrosion, assessed as an average over the original bar surface, offers a better measure of corrosion for assessment of residual bond strength, Figure (169)

118 Weight Loss (%) European Community. Fifth Framework Program: GROWTH 6 Wt Loss (Y1) Rad. Loss (Y2) Radial Loss (mm.) Bar Diameter (mm) 0 Figure 64. Amount of corrosion necessary for crack initiation, Al-Sulaimani et al [lxxxiv] Weight loss per unit area of bar surface provides an equivalent measure. Figure 64 compares the amount of corrosion to cracking required by bars of different diameter (but with constant cover). The results are quantified by weight loss on the left y-axis and by radius of steel lost to corrosion (corrosion penetration) on the right y-axis. Corrosion to cracking is almost constant when assessed by corrosion penetration, but increases markedly with reducing bar diameter when assessed by section loss, suggesting that the first parameter may be a more useful measure. Bond strength will certainly be affected by crack width, and the relationship between loss of bar section and thickness of corrosion products depends on environment. An understanding of the mechanisms affecting bond strength of corroding bars and the establishment of an appropriate measure of damage is clearly a priority in reconciling conflicting test data and development of assessment guidelines Effect of corrosion on residual strength Strength and Ductility of Reinforcement It is evident that loss of section will affect strength of reinforcement and hence member strength. Perhaps less obviously, non-uniform corrosion may also affect ductility. Models for loss of strength and ductility are at present confined to empirical correlations with section loss, expressed as a percentage of original cross section: f=(1.0- A )f y y corr y0 (154) f=(1.0- A )f u u corr u0 (155) = (1.0- A ) l corr 0 (156) f y, f u yield strength, ultimate tensile strength in corroded state [N/mm²] strain in corroded state [-] f y0, f u0, 0 yield strength, ultimate tensile strength and elongation of non-corroded bar A corr section loss [-] y, u, l regression coefficients [-] To model the uncertainty in such variables the Model Code of the Joint Committee of Structural 118(169)

119 Safety (JCSS) [lxxxv] can be consulted: Table 36. Uncertainty in structural parameters according to JCSS [lxxxv] Parameter Unit Distribution CoV [%] Yield stress f y [N/mm²] Log-normal 7 Ultimate stress f u [N/mm²] Log-normal 4 Elastic modulus of steel E S [N/mm²] Log-normal 3 Ultimate strain of steel u [-] Log-normal 6 Nominal steel cross section area [mm²] Log-normal 2 Table 37. Empirical coefficients for strength and ductility reduction of reinforcement assembled by Du [lxxxvi] Authors Cover? Exposure A corr y u l Maslehuddin Bare Service, marine 0-1% [lxxxvii] Andrade [lxxxviii] Bare Accelerated, 1.0 ma/cm % Lee [lxxxix] Concrete Accelerated, 13.0 ma/cm % NS NS Concrete Accelerated, 0.5 ma/cm % NS Clark & Saifullah and 1) and 1) [xc] Morinaga [xci] Concrete Service, chlorides 0-25% Zhang [xcii] Concrete Service, carbonation 0-67% Du [lxxxvi] Bare Accelerated, ma/cm % Concrete Accelerated, 1.0 ma/cm % Mean 0,011 0,013 0,029 CoV [%] NS 1) not stated Clark and Saifullah tested both plain and ribbed bars. The two steels produced slightly different coefficients Almost all authors report reductions in yield strength, ultimate tensile strength and elongation with corrosion. Maslehuddin alone concluded that corrosion did not significantly affect mechanical characteristics. Given the relatively low weight loss of his test samples, any trend may have been obscured by materials variations. These results were thus not regarded for the above given mean values and coefficient of variation (CoV). All Authors except Maslehuddin report the reduction in bar strength to exceed the reduction in average cross sectional area, in other words, corrosion effectively reduces the strength of the steel. The largest reduction in strength was reported by Morinaga, the least by Du. Example: Let s assume a loss in section of 10%. In the case of Du this leads to a residual force of F y = 0.9A 0 ( ) = 0.86F y,0, in the case of Morinaga of F y = 0.9A 0 ( ) = 0.76F y,0. If only the loss of section is considered the residual force would be F y = 0.9F y,0. Consequently Du s result indicate that the reduction in the force at which a bar yields is around 40% greater than would be estimated on the basis of the average loss of section. Morinaga s results even suggest the reduction would be 1.4 times greater than estimated from average loss of cross section. Others have proposed intermediate values. The reduction in elongation is always greater than the reduction in strength. Du reported a tendency for greater reductions (i.e. larger values of coefficients) to be measured with smaller diameter bars. 119(169)

120 The reductions are attributable to the non-uniform nature of corrosion attack (Du also carried out tests on machined bars to verify that the changes observed were not due to removal of a stronger outer layer of steel from the bar). Yielding of the bar develops first at the points of local attack where the cross sectional area is most highly reduced, while the remainder of the bar is still elastic. As load is further increased, strain hardening at the pitted section allows stress to increase above yield. Strains increase much more rapidly post-yield, and even if the length of the defect is not particularly large the overall axial stiffness of the bar is altered and reduces the apparent yield strength of the steel f y. Bar force can be increased until fracture occurs at the UTS at the reduced section. Fracture load will be controlled by the narrowest section, when strains throughout the remainder of the bar are still well below the fracture strain. Ductility and elongation at fracture are thus reduced. The reduction will be dependent on the ratio of local to mean corrosion penetration, and also on the mechanical characteristics of the steel, including the ratio of yield to ultimate tensile strength and strain at maximum stress. Cross-study conclusions regarding the effect of other parameters must be highly tentative, due to the several differences in exposure/conditioning of test samples, test procedures, steel properties, bar diameters and concrete qualities between studies. For the present, models must remain semiempirical, and their predictions must be treated with caution. The effect of reinforcement section loss on residual strength of statically determinate structural elements may be estimated using conventional calculation procedures, but allowing for the reduction in cross sectional area of the bar and of the reduction in apparent yield strength (Ultimate tensile strength is not used in conventional strength calculations). It should also be verified that ductility is not reduced below the value assumed by the design standard in use. Where design assumes development of plastic deformations at the ultimate limit state, i.e. if based on yield line or redistribution, the reduction in residual capacity may be markedly greater as a reduction in ductility of a corroded bar affects the ability of a member to redistribute moments at a plastic hinge. It is essential to verify that bar ductility complies with the design standard in use. Should this not be the case, special measures which recognize the limitation on ductility will be required to verify strength. It may also be necessary to reduce the strength of longitudinal compression bars if links become ineffective either through loss of section to corrosion or because spalling of cover affects anchorage of links Longitudinal Cracking and Cover Integrity Modelling Crack Initiation: The increase in the diameter of a bar as a result of the volumetric expansion of the products of the corrosion reactions generates tensile hoop strains in the concrete surrounding the bar. Once strain capacity of the concrete is exhausted cracking develops along the line of the bar. If corrosion is allowed to continue, spalling of the concrete cover eventually results. Spalling concrete would be a direct hazard to anyone in the immediate vicinity of an affected structure. Structural capacity of members will be impaired as a result of loss of concrete cross section from the compression zone or from the web of a member. Member strength will also be impaired 120(169)

121 where a reduction in confinement to a bar affects bond resistance or the dowel action component of shear resistance. The onset of longitudinal cracking along a corroding bar has been investigated experimentally and analytically. Table 38 compares section loss and corrosion penetration to the onset of cracking reported in various experimental studies. Table 38. 1) Investigation Al-Sulaimani et al [lxxxiv] Cabrera & Ghodussi [lxxiv] Corrosion to cause cracking of concrete cover bar [mm] Cover/ bar ratio [-] Impressed Current [ma/cm 2 ] Section Loss [%] Corrosion depth [mm] Time until cracking 1) [a] , , ,24 12 Large 3 Volts Clark & Saifullah [xc] , , ,45 Andrade et al [xciii] , ,31 Clark & Saifullah [xc] , ,19 Rodriguez et al. [xciv] ,47 Almusallam et al [xcv] ,07 Mean 1,6 0,049 0,84 CoV [%] assuming that a corrosion current density of i corr = 5 µa/cm² is realistic average value The time until crack initiation in Table 38 was calculated using the relationships between corrosion current density i corr [µa/cm²], penetration depth [mm] and test duration given in chapter 9.1, correcting for the fact that the corrosion current while testing was accelerated in by a factor (i corr,test /(5 µa/cm²) between 2 to 2000, in average 350. The results indicate the very short time until first cracking occurs, when compared to the initiation phase. At impressed currents of up to 0.5 ma/cm 2, corresponding to corrosion rates up to 50 times maximum values observed in the field, it can be concluded with a fair degree of confidence that cracking first develops at corrosion penetrations (i.e. reductions in bar radius) of between 0.01 mm and 0.04 mm. It can also be surmised that cover cracking is delayed by increased cover, concrete tensile strength, by more rapid impressed corrosion, and where bars are cast near the top of the pour (Note that beneficial effects of cover on time to cracking reported in these studies concern only the propagation phase of the deterioration process, and exclude the beneficial effect on the initiation phase). Andrade et al [xciii] reported similar corrosion to first cracking, but found cover/bar diameter ratio to have a negligible effect. High corrosion rates probably produce less expansive corrosion products, and hence greater corrosion penetrations are required to split the cover. Concrete is weaker and more porous near the top of a pour, and sedimentation of fresh concrete may leave a 121(169)

122 void under top cast bars, hence allowing dispersion and space for corrosion products which delays splitting. A number of researchers have attempted to use Finite Element numerical models to investigate longitudinal cracking. The models aimed to describe the progression of cracking through the concrete cover and to determine the thickness of corrosion products or the internal pressure for cracking through 2-dimensional plane-strain analysis of concrete sections containing corroding bars. The models idealized the expansive behavior of corrosion products either as an internal pressure or as a prescribed displacement. The FEM penetrations for cracking were generally appreciably lower than measured values, probably because they ignore the dispersion of corrosion products into the cement matrix. A summary is given in [xcvi]. It is worth pointing out, however, that the significance of initiation of longitudinal cracking as a limit state criterion remains a matter of debate. There are currently only very few engineering models existing which tackle the problem of crack initiation on a probabilistic basis, e.g. [xi, xcvii, xcviii]. The most suitable seems to be the one of Gehlen and Banholzer who established the following limit state equation: p p( r r 0) crack initiation r s (157) P probability [-] r r increase of steel radius necessary for initial cracking of concrete (resistance R) [µm] r S increase of steel radius due to the on setting corrosion products (stress S) [µm] Basically the increase of the rebar radius is determined by the penetration depth of the reinforcement due to corrosion and a factor describing the expansion (K E ). Moreover the parameter V P takes account of the volume of pores in which corrosion products may expand without inducing hoop stresses. Possible influences of external radial loads are considered by the variable L: r L (V t V ) K S corr Prop P E (158) V corr corrosion rate, see chapter 0 [µm/a] V P volume of pores available for corrosion products to be accommodated without development of expansion stress [µm] K E expansion factor [-] K E = R-1 R volume ratio of corrosion products and corroded steel [-] L load dependent regression variable for extra radial load upon concrete [xcix] [-] t prop propagation period (difference of structure age and initiation period) [a] The model for the resistance of the concrete against the formation of cracks is based on the elastic theory of material behavior and complemented by variables to account for non-linear behavior (K n ), relaxation (K R ) and reinforcement configuration (K S ). The quantification of these variables was performed by using FEM analysis: r r ' K K K r r n R S (159) 122(169)

123 r r maximal increase of the radius according to the elastic theory bearable [µm] by the concrete without formation of cracks K n correction factor for non-linear material behavior [-] K R correction factor for relaxation ability of concrete [-] K S factor to account for reinforcement detailing [-] d r 2 f E r C S t c S r ' 0,60 0, 40 r r S f t tensile strength of concrete [N/mm²] E C E-Modulus of concrete [N/mm²] d C concrete cover [mm] r S radius of reinforcement [mm] K n rs 1 C1 C 2 d c C 3 r S C 4 (160) (161) C 1 regression parameter, = 3, [-] C 2 regression parameter, = 5, [1/mm] C 3 regression parameter, = 2, [1/mm] C 4 regression parameter, = 1,48 [-] s K C 1 S 5 2r S (162) C 5 regression parameter, = 1, [-] S spacing of reinforcement [mm] The model is only valid to determine the time until a first micro crack of 0,005 mm is developed, which runs from the steel surface to the concrete surface. The tensile strength of concrete f t, elastic E-Modulus E C of concrete and relaxation parameter depends upon the concrete composition. Mean values of these input variables can be derived from current standards or may be determined from measurements of specimens withdrawn from the actual structure. To model the uncertainty in such variables the Model Code of the Joint Committee of Structural Safety (JCSS) [lxxxv] can be consulted: Table 39. Uncertainty in structural parameters according to JCSS [lxxxv] Parameter Unit Distribution CoV [%] Concrete compression strength f C [N/mm²] Log-normal 15 Concrete tensile strength f t [N/mm²] Log-normal??? E-Modulus of concrete E C [N/mm²] Log-normal??? Relaxation factor K R [-] In a sensitivity analysis factors mainly responsible for the scatter for the time until crack initiation t crack were found in order of significance the expansion factor K E in combination with the volume for expansion of corrosion products in concrete pore structure V P, the E-Modulus of 123(169)

124 concrete E C, the corrosion penetration depth V corr and the concrete cover d c. More precise information in regard to these variables, e.g. from inspections, will reduce the variability of t crack. However, the largest degree of assumption and uncertainty is inherent in the expansion factor K E and the volume V P. In structure investigations K E may be quantified by chemical analysis of the corrosion products, but will in most cases not be conducted in practice. The volume V P is still a matter for future quantification. In a case study of corrosion initiation due to carbonation Gehlen and Banholzer [xcvii] assumed the mean value of µ(k E ) = 2-1 = 1, see (158). The standard deviation was set to (K E ) = 0,50µ. As distribution type was chosen a log-normal distribution. The volume V P was already incorporated into K E. The predicted time span between 0,125 and 2 year with an average of µ( tcrack ) = 0,62a and coefficient of variation CoV( tcrack ) = 60% until crack initiation seems quite realistic, see Table 38. For chloride induced corrosion no quantification of the expansion factor K E is yet available. However, as corrosion products due to chlorides usually are less expansive because oxygen supply is reduced due to the wet concrete values as used for carbonation seem to be on the safe side and the best choice available. If inspection data regarding crack initiation is available these can be used for model updating according to Bayesian methods, see chapter As input must be collected the percentage of cracked concrete cover along the re-bar length at inspection time t insp. It is evident that the relationship between section loss and formation of longitudinal splitting cracks is dependant on a number of factors including the method employed to condition test specimens. A corrosion penetration of 0.05 mm for general corrosion, which is the average value found in literature to induce corrosion, see Table 38, represents a reduction of less than 2,5% of cross sectional area for an 8 mm diameter bar, and less for larger bars (for comparison, UK production tolerances on reinforcement are 6.5% for 8 mm to 10 mm diameter reinforcement and 4.5% for sizes 12 and above [c]). Clearly, cracking will develop well before loss of bar section becomes significant. At least where general corrosion is concerned, it can safely be concluded that longitudinal cracking will precede significant loss of bar section. Modelling Crack Growth: Rodriguez [xciv] also derived relationships between crack width and corrosion penetration as corrosion progressed, Figure 65, which shows a mean surface crack width of 1 mm to be associated with an attack penetration of around 0.2mm (this would appear to correspond to a volume of corrosion products of 2.5 times the corrosion penetration). 124(169)

125 Figure 65. Relationship between surface crack width and corrosion [xciv] A uniform metal loss of 0.2mm around the circumference of 8, 10 and 25 mm diameter bars represents cross sectional area losses of 9,8, 7,8 and 3,2% respectively. Cover to bar diameter varied between 2 and 4 in these tests. It may also be inferred from the paper that concrete cover did not spall even where cracks reached 2 mm in width. Cabrera & Ghodussi [ci] independently developed expressions for the relationship between crack width and corrosion, based on different parameters. Predictions of the two sets of expressions are broadly consistent despite significant differences in conditioning. Others report crack widths in excess of 0.6mm without spalling. The data of Rodriguez was used during the DuraCrete project [xi] to develop a model for the growth of cracks. Cracks of width w = 0,05 mm were considered as visible cracks during experimental work, see also regression line in Figure 65. In DuraCrete it was considered that cracking propagation mainly depends on the corrosion penetration and the casting position of the reinforcement bar (top or bottom). In order to be line with the model for crack initiation of Gehlen and Banholzer detailed in the prior section, which serves to calculate the time until a crack of width w = 0,005 mm is developed, the DuraCrete model is adapted as follows: w 0,05 (p(x) p(x )) pos 0 (163) w crack width [mm] parameter controlling propagation of crack growth [-] p(x) attack penetration according to chapter 9 [mm] p(x 0 ) attack penetration necessary to produce a crack of width w = 0,005 mm [mm] calculated according chapter 9 (Models on Propagation of Corrosion) The factor is an empirical coefficient reflection influence of casting position. The more porous concrete near the top of a pour allows more dispersion of oxides from corrosion (so it is not simply the Volumetric expansion that is important, but also the ability of the corrosion products to disperse). It must however be stated that quantification of this regression parameter is very contradictory. This is because mean values for of 8.6 and 10.4 (95% confidence values of 10.0 and 12.5) are stated for the case of top and bottom cast concrete surfaces. These values obviously don t fit with the data shown in Figure 65. Models for crack growth must be considered as matter of debate. In this context should be kept in mind that, as was already concluded for the initiation 125(169)

126 time of cracking, the time until a crack width is reached which may be regarded as critical until spalling will occur (0,3 to 1,0 mm) is rather short compared to initiation phase. Highly sophisticated modeling of crack growth vs. time thus does not seem to be of importance either. Effect of Longitudinal Cracking on Residual Capacity: Longitudinal cracking leads to loss of resistance of cover concrete. Bond resistance is also affected, and will be considered separately in chapter According to proposals developed in the DuraCrete [viii] project, the area of concrete considered in calculations should be reduced by the concrete cover thickness, depending on the corrosion penetration p(t) and the ratios of tension and compression reinforcement. r w p(t) attack penetration [mm] r 2 Index 1 Index 2 flexure zone compression zone h d A 2 degree of reinforcement: 1 = A 1 /(bd) [%] A 1 2 = A 2 /(bd) [%] S spacing of shear bars [mm] r 1 V sd design shear [N/mm²] b V cd shear capacity [N/mm²] Figure 66. Details of beam section In flexure: a) The effective depth should be reduced from d to d-r 2 if: - ductile failure : ( 1 < 1.0%) a) 2 < 0.5% and p(t) > 0.4mm or b) 2 > 0.5% and p(t) > 0.2mm - brittle failure : ( 1 >1.0%?) (limit value is still a matter of debate) a) 2 > 0.5% and p(t) > 0.2mm (risk of spalling induced by corrosion of compression/shear reinforcement) b) 2 > 0.5%, V sd /V cd > 2 and p(t) > 0.1mm (risk of spalling induced by both shear stress and corrosion of compression/shear reinforcement) b) The section width should be reduced from b to b-2r w if: 126(169)

127 In shear: 1 > 1.5%, V sd /V cd >3 and p(t) > 0.2mm (risk of spalling induced by both shear stress and corrosion of compression/shear reinforcement) An estimation of residual ultimate shear force may be obtained by means of the standard method established in EuroCode 2, with the following modifications: a) The effective depth should be reduced from d to d-r 2 if: - V sd /V cd < 2 or a) s > 0.6d and P(t) > 0.2mm b) 2 > 0.5% and P(t) > 0.2mm - V sd /V cd > 2 a) 2 < 0.5% and P(t) > 0.2mm or b) 2 > 0.5% and P(t) > 0.1mm b) The section width should be reduced from b to b-2r w, if: - V sd /V cd > 2 or a) s > 0.6d and P(t) >0.4mm b) s<0.6d and P(t) >0.3mm Similar rules for concrete section loss are presented for columns. In addition, an additional load eccentricity should be added in order to determine the design moment. The magnitude of the additional eccentricity equal to the cover thickness should be taken in both directions (conservatively) Bond Modelling of Bond Loss: Bond is necessary to anchor reinforcement and to ensure composite interaction between reinforcement and concrete. Bond may conveniently be regarded as a shear stress over the surface of a bar, even if this represents a considerable simplification of the real behavior of ribbed bars. Although the factors which influence bond strength are generally agreed, opinions 127(169)

128 differ markedly on the magnitude of their effects and the mechanisms through which they take effect. Friction is the major component of strength plain round bars. With ribbed bars, bond depends principally on the bearing, or mechanical interlock, between ribs rolled on the surface of the bar and the surrounding concrete. Bond action of ribbed bars generates bursting forces which tend to split the surrounding concrete in the same manner as expansive products of corrosion. In many practical circumstances bond failure load is limited by the resistance provided by concrete cover and confining reinforcement to these bursting forces. Corrosion could be expected to affect bond strength in the following ways: Increases in the diameter of a corroding bar at first increases radial stresses between bar and concrete and hence increases the frictional component of bond. Further corrosion will lead to development of longitudinal cracking and a reduction in friction and in the resistance to the bursting forces generated by bond action of ribbed bars. Corrosion products at the bar/concrete interface affect friction at the interface. Some suggest that a firmly adherent layer of rust may contribute to an enhancement in strength at early stages of corrosion [lxxxiv]. Cabrera and Ghodussi suggest that at more advanced stages, weak and friable material between bar and concrete will be at least partially responsible for reductions in strength [lxxiv]. Cairns & Du (see chapter ) have produced data that contradicts this suggestion, however. Corrosion may reduce the height of the ribs of a deformed bar above the bar core. This is unlikely to be significant except at advanced stages of corrosion, however. Disengagement of ribs and concrete. The layer of corrosion products formed by oxidation of the steel may force the concrete away from the bar and reduce the effective bearing area of the ribs. Research into the influence of corrosion on bond has used a wide variety of bond specimens and bar types, and it is therefore not surprising that the magnitudes of the bond strengths reported and the effect of corrosion on those bond strengths differ widely. Furthermore, there have been considerable variations in conditioning of specimens for corrosion studies, and this has been proven to influence residual bond strength [xc]. Despite wide variations in test specimens and in conditioning techniques, the general trends reported are the same in almost all studies, as illustrated in Figure (169)

129 Bond Strength European Community. Fifth Framework Program: GROWTH 100% Longitudinal cracking Corrosion Figure 67. Variation in bond strength with corrosion (Schematic)The same pattern is observed in tests on plain and ribbed surface bars. Initially, bond strength is increased by small amounts of corrosion, but with further increases, bond starts to reduce. It appears, however, that bond strength does not reduce below the as new value prior to development of externally visible longitudinal cover cracks. For purposes of assessment of residual strength of concrete structures suffering from general corrosion, bond can be assumed to be sound in the absence of visible corrosion induced cracking. Once cracking develops, appreciable loss of bond strength may develop, particularly if no confining reinforcement is present. Residual strength decreases with increasing corrosion, and reductions of over 50 % are reported. Table provides a comparison of bond strength loss measured by various investigators at fairly advanced levels of corrosion. Table 40. Investigators Summary of tests on bond strength of corroded reinforcement all with a corrosion penetration of P = 0.25mm (interpolated where necessary) Cover/ bar Ratio Corrosion rate Links? Crack Width Section Loss Residual Bond Strength [-] [ma/cm 2 ] [mm] Al-Sulaimani et al [lxxxiv] N N N Large 3 Volts N Cabrera & Ghodussi [lxxiv] Large 3 Volts Y Large 3 Volts Y Clark & Saifullah [lxxvi] N Clark & Saifullah [xc] N N N Rodriguez et al. [cii] N Y Y Almusallam et al [xcv] N Coronelli [lxxxiii] Y Stanish [ciii] N [%] [%] 129(169)

130 The comparison has been estimated for a nominal corrosion penetration (thickness of material lost averaged over the bar surface, and equivalent to the reduction in bar radius) of 0.25mm and represent conditions well beyond the corrosion levels required to crack the concrete cover. In Figure 65, for example, a corrosion penetration of 0.25mm corresponds to a surface crack width of w = 0.8mm-1.5mm. Some values given in Table 40 have been obtained by interpolation between original results in order to obtain a more consistent basis for comparison. Residual bond strengths quoted by the various investigators could hardly vary more widely, with values from 0% (complete loss of bond strength) to 110% (a modest gain in strength) reported. The majority of results were obtained using specimens without confining reinforcement. Al- Sulaimani et al [lxxxiv] report strength losses exceeding 70%, as does Rodriguez et al [cii]. Cabrera & Ghodussi [lxxiv] report a reduction of only 35%, not dissimilar to that reported by Clark & Saifullah [lxxvi], although these authors have also pointed out that results are markedly influenced by corrosion rate [xc]. Lesser reductions are reported in specimens provided with links. Rodriguez et al [lxxxi], for example, found strength losses to be reduced by half to a third where links were provided. Berra et al [civ] alone report a continuing increase in bond strength with increasing corrosion to 8% section loss, equivalent to 0.3mm penetration, despite extensive longitudinal cracking. This is probably because stirrups, being at some distance outside the anchored bar, were particularly well arranged to maintain confinement in these specimens. There appear to be inconsistencies between reductions reported in these studies, and apart from the presence of confining reinforcement, no clear pattern of influencing parameters emerges. However, in the majority of cases the rate of reduction in bond attributable to corrosion clearly exceeds the corresponding rate of reduction in tensile strength of the bar. In what is probably the most extensive study undertaken to date, Rodriguez, Ortega, Casal and Diez developed empirical expressions for residual bond strength of corroded bars [xciv, cii, cv]. The experimental work was mainly based on tests carried out with cubic specimens reinforced with four bars, one in each corner, reproducing part of a beam subjected to constant shear force. These tests allowed bond strength values representative of the splitting failure modes considered in design Codes of Practice to be developed. They will, however, underestimate failure strengths where bars are well confined by high cover or large amounts of transverse reinforcement. Tests were conducted with and without stirrups, and used 16 mm and 10 mm diameter bars. Corrosion was accelerated by impressed current, current densities in the range /cm 2 -/cm 2. Neither the concrete quality nor the cover size/bar diameter ratio influenced residual bond strength when cover was cracked by reinforcement corrosion. A statistical analysis was carried out with these results and expressions obtained to predict the characteristic value of residual bond strength. If the ratio tr of the transverse reinforcement area at anchorage length (considering the reduction due to corrosion) versus the area of the main bars is higher than 0.25 (minimum value established in EC2), the bond strength f b (in N/mm²) can be predicted as follows: f= p(t) b (164) 130(169)

131 p(t) attack penetration (bar radius reduction) [mm] On the contrary, if tr is lower than 0.25, f b can be estimated by: f =10.04+( ( b /0.25)) (1.14+p(t)) tr (165) It is well known that external pressure, as occurs at support regions, for example, enhances the confinement of the bars. Consequently it improves bond strength, and its positive effect is considered in EC2 when calculating ultimate bond stresses in sound ribbed bars. In order to explore this bond enhancement in corroded bars, tests were carried out on beams designed to fail at anchorage of main tension bars. A similar expression to that of EC2 was obtained from the experimental results to predict the characteristic value of the residual bond strength f b : f =( P(t))/( f) b (166) f external pressure at anchorage [N/mm²] This expression can be used in the assessment of the bar anchorage at the support zone, independently of the amount of stirrups and their level of corrosion. This fact was verified in beam tests where bars anchored at support zones did not slip although heavy deterioration had been produced with significant stirrup corrosion and concrete cracking. (164) to (166) is applicable once longitudinal cover cracks develop, and are not applicable to small amounts of corrosion. Although the experimental values of the attack penetration p(t) ranged from 0.04 to 0.5 mm, the authors believe extrapolation up to p(t) = 1.0 mm is reasonable (although bond strengths in (164) actually become negative at corrosion penetrations greater than 0.4mm if no links are present). This proposal gives bond strength values for each attack penetration, taking account of the actual residual stirrup section at the anchorage length. The expressions can be used to demonstrate a more rapid reduction in bond strength where links are not provided, Figure 68. Residual Bond Strength [N/mm²] No stirrups - Rodriguez et al 20 25% Stirrups - Rodriguez et al No stirrups - Clark&Saifullah 0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 Corrosion Penetration [mm] Figure 68. Effect of links on residual bond strength of 16 mm diameter bar According to the investigators, these expressions can also be applied to the evaluation of composite interaction at intermediate parts of the bar. In these cases, the estimation of the tr 131(169)

132 value has to be made by replacing the number of stirrups within the anchorage length by 200/s, where s is the stirrup spacing in mm. Clark and Saifullah [xc] have also suggested semi-empirical expressions for the ratio of residual to original bond strength based on their tests on 8 mm diameter ribbed bars, although it was noted that residual bond strength was dependent on current intensity. Tests were conducted on beam end specimens similar to those used by Rodriguez, but 8 mm diameter bars were used and links were not provided. Averaging the two sets of coefficients for current intensities within the range used by Rodriguez et al, leads to: f /f = X corr control (167) f corr /f control ratio of bond strength of corroded specimen and non-corroded control specimen [-] X weight loss due to corrosion [%] It is evident that (164) predicts a much more rapid loss of bond in the absence of links than (167) does, Figure 68. The difference in strength reductions reported in the two studies demonstrates the inherent difficulty in reaching reliable expressions for residual capacity when the mechanism controlling loss of strength is not fully understood. Effect of Bond Loss on Residual Capacity: A reduction in bond may affect element strength in two ways, Figure 61: 1) the stress that can be developed in reinforcement may be limited by a reduction in anchorage capacity at laps and points of bar curtailment (including end anchorages). This could influence flexural and shear strength of beams and slabs as well as axial strength of columns and walls. 2) partial or complete loss of composite interaction between reinforcement and concrete over the affected length and beyond may occur due to marked reductions in bond stiffness. The plane strain assumptions normally made in section analysis/design would then no longer hold, and the pattern of strains in a member would be altered. Structural behavior of a beam will tend to move away from purely flexural action towards a tied arch form of action (provided that end anchorage is maintained) [cvi/, cvii]. 3) a combination of (1) and (2) where the loss of plane section behavior mentioned in (2) could increase the force to be anchored at points of bar curtailment. 132(169)

133 Table 41. Investigators Summary of tests on strength of beams and slabs with corroded reinforcement Cross Sect. Lost [%] Thickness Lost [mm] Long. Crack Width [mm] Links Details of End Anchorage Local Bond Stress [N/mm²] Residual Strength Okada et al [cviii] Y End hook Tachibana et al [cix] N 15 d b straight Al Sulaimani et al Y 12 d b straight [lxxxiv] Cabrera [lxxiv] Series Y None Series Y None Y 12.5/15 d b straight Rodriguez et al [cii, cv, cx, cxi] Y End hook 2.1 Av. 99 Kawamura et al [cxii] N End hook 2.1 Av Y Lapped joint N/A N Lapped joint N/A 25 Daly [cxiii] Y 12 d b straight Almusallam et al [xcv] N 8.5 d b straight [%] The largest reductions, reported by Kawamura and by Daly, arose from bond/anchorage failure. In general, however, strength loss measured on structural elements is less than might be feared given the relatively large values measured in bond tests at similar levels of deterioration in similarly reinforced specimens. The loss of element strength reported is greater than the average loss of cross section, probably attributable to a reduction in apparent yield strength as a result of uneven corrosion along the bars and to delamination of concrete cover. However, it is also apparent that many of the beam specimens tested would have been insensitive to loss of bond within the span [cvi], and end anchorage would have been enhanced by lateral pressure at simple supports. Many contained links which would have helped to maintain splitting resistance of cover concrete after longitudinal cracks developed, and structural elements without links might have shown greater susceptibility to bond loss. In the majority of laboratory tests reinforcement was not lapped or curtailed within the span, and there appears a strong possibility that residual strength in real structures will be strongly affected by reinforcement details. Findings thus tend to show that loss of anchorage capacity is more likely to be significant than loss of local bond. There is little evidence to suggest that conventional calculation procedures for flexural and shear strength are unsafe, provided allowance is made for reductions in cross sectional area. Nonetheless, there is limited evidence that loss of local bond may influence behavior of corrosion damaged structures, particularly where plain round bars are used for main flexural reinforcement or in the absence of confining reinforcement to maintain residual bond strength, and tied arch action may come into play in such circumstances. Obviously tied arch action can only develop where ends of bars are adequately anchored. The difficulties inherent in analysis of results of physical tests on deteriorated specimens should be noted, as the effect of a change in bond characteristics on member behavior cannot be entirely 133(169)

134 separated from the effects of section loss of reinforcement and of spalling of concrete. No information is available on the effect of corrosion on anchorage capacity of hooks or bends. Figure 69 compares the reductions in bond force arising from corrosion with the reduction in bar yield strength and section loss. The reduction in bar strength has been calculated using a value = in (154). The reduction in bond force has been calculated using (166) to account for a reduction in bond strength in combination with a reduced circumference of the re-bar due to corrosion. Note that (164) and (165) both indicate a more rapid loss in bond with corrosion. (164) shows the same rate of reduction as (166). Still, Figure 69 shows the reduction in bond to be more rapid than the reduction in yield strength. Residual Force [%] Yield Force Bond Force 0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 Corrosion Penetration [mm] Figure 69. Comparison of residual bond and yield strengths of 16 mm bar 11 Semi-Probabilistic Model on Alkali-Aggregate-Reaction 11.1 Introduction An extensive user manual for assessing the residual service life of concrete structures affected by AAR was developed in the EC innovation program project CONTECVET [cxiv]. Here the interested reader finds detailed information on: Mechanism and major influences upon AAR Procedure for general and detailed assessment Diagnosis methods Effects of AAR on load carrying capacity 134(169)

135 According to CONTECVET there are no reliable analytical or numerical methods for predicting the future expansion of AAR affected structures. Therefore one of the following methods may be used with care: Monitoring the expansion of moist cores from the affected structure Monitoring movement of the affected structure component Use known expansion behavior of a similar concrete under similar exposure 11.2 Predictions using Core Tests The mechanical properties of concrete and the future unrestrained expansion of concrete in a member affected by ASR can be determined from cores. The obtained potential for expansion must be corrected for restraint. The drawbacks to this approach are that cores are normally taken at right angles to the direction of restraint and that cores expand during and after coring. Hence, core tests should begin as soon as possible after sampling. During expansion monitoring cores may expand because of: Removal of restraint (which usually is not the restraint in the regarded direction, see above) Expansion is not yet completed Additional uptake of water The following conclusions were drawn: Expansion of cores stored at 20 and 38 C may over-estimate the expansion Expansion is mainly due to removal of restraint and the uptake of additional water From the previews conclusions follows that measurement of core expansion can result in a pessimistic view of the adverse effects of ASR 11.3 Predictions from Monitoring of Movement of Affected Members In CONTECVET [cxiv] monitoring is regarded as the most effective method of determining expansion rates and possible future expansion. The drawback is the considerable duration of measurements necessary until an extrapolation may be performed. The simplest method for monitoring is to place chains of monitoring pins along the chosen direction of an affected member (with a recommended spacing of 200 mm). The movement should be monitored at least twice a year. The obtained data may be extrapolated. Caution should be applied to the extent of extrapolation Predictions with known Expansion Behavior of Similar Concrete If the expansion behavior of a concrete with similar mix composition and constituents is known, these values may be used correcting for the effect of temperature and restraint (for which no 135(169)

136 quantitative values are provided in CONTECVET [cxiv]). Alternatively, if the age at which cracks first appeared is known, then an indication of the possible expansion behavior can be estimated by interpolation from a database of expansion data and then correct for the effect of restraint. 12 Full-Probabilistic Model on Alkali-Aggregate-Reaction The principal conclusion regarding probabilistic models as they are used for durability design towards alkali aggregate reaction (AAR) is that no credible predictive mathematical model exists until now and that avoidance is almost universally accepted as the best philosophy. The AAR is governed by the interaction of numerous effects [viii]: (a) Components cement type (equivalent alkali content, proportions of Na and K alkalis, fineness) additions/ cement replacements as there are fly-ash, blast-furnace slag, silica-fume (content, alkali content) aggregates (reactivity, proportion of fine and coarse fractions, salt impurities, alkali content, porosity, etc.) - admixtures (b) Mix proportions (c) Environment moisture availability temperature external chloride sources alkali concentration effects (wet-dry cycles, wick action) (d) geometry of structure (e) restraints reinforcement (amount, position) structure configuration Preventative measures intend to minimize the probability of destructive expansion. Nevertheless, since existing structures might be submitted to an attack of AAR, this damage mechanism has to be treated in respect of a service life prediction. Probabilistic techniques may be applied in order to enable the designer to: 136(169)

137 calculate the probability of failure compare relative merits of different preventative approaches A petrographic examination is commonly used in order to detect known reactive mineral phases to categorize aggregates. Application of a Bayesian approach is proposed to establish the reliability of the petrographers, [xiii]. Factors may be introduced to take account of the experience of the petrographer, the nature of the aggregate, etc. Furthermore the proportion of reactive components will be governed by natural scatter which has to be quantified. It has been accepted that limiting the alkali content of the cement can be an effective measure to avoid AAR. A limit of 0,6 [% Na 2 O equ ] has been adopted world-wide and has been shown to be appropriate in most cases, though with exceptions. A further factor is the moisture content of the concrete. A higher alkali content is necessary to initiate a deleterious expansion in drier concretes. Threshold values for the relative humidity may be defined below which AAR will not occur. These range between 75 to 90% RH, [xi]. AAR products initially form almost instantaneously, but expansion and the associated external cracking does not occur until sufficient moisture form the exposure environment has penetrated into the concrete, which can be considered to be the initiation period. In [cxv] it is stated that the time until damage initiation, is governed by the moisture transport in the concrete. The time for the development of a subsequent damage will then be governed by factors as the alkali content, reinforcement arrangement, temperature, etc. But due to a lack of data from real structures the concept is not yet applicable. Particularly the actual time to initiation of damage is seldom recorded and a limit state for damages due to AAR has to be defined yet. In considering alkali limits, the influence of alkali from sources other than the cement must be covered. External alkali from seawater, de-icing salts, etc. will impair the AAR effects, but the extent is yet unknown. The prediction of the potential consequences of AAR in new and existing constructions requires a wide range of structural effects to be considered as well: overall expansion of structural members differential movement between structural members global and local movement within structural members effect of stress condition on expansion reinforcement contribution in reducing expansion reduced compressive and tensile strength as well as elastic modulus of concrete 137(169)

138 13 Frost Attack 13.1 Semi-Probabilistic Model on Internal Frost Damage The limit state function of the initiation phase of the internal frost process can be given as follows [viii]: p (t) p S(t) S int ernal damage cr (168) p probability [-] S cr critical degree of water saturation S(t) degree of water saturation Table 42. Critical degree of saturation for selected w/c-ratios w/c = 0,30 w/c = 0,45 w/c = 0,70 0,97 0,96 0,93 (statistical data is not available) The above stated (168) is based on the premise that concrete will not be damaged by frost action if the capillary saturation S cap remains below a critical value of saturation S cr. The initiation phase is thus considered to be the time until the critical degree of saturation is reached. Methods for the measurement of the degree of saturation are provided in the appendix of D3.1 [i]. The capillary saturation degree depends on the material and the environmental conditions. One approach to account for environmental conditions is to perform capillary rise tests in the laboratory and apply correction factors to compensate for the difference between absorption behavior in the test and the exposure environment. Nevertheless, it is a complicated task to predict the development with time of the actual degree of saturation in a given structure. A simple model has been identified in [viii]: S(t) = S 0 + h(t) (169) S 0 initial degree of saturation [-] h(t) time dependent moisture ingress function [-] The function for the time dependent moisture ingress can be determined by laboratory capillary suction tests, which will be described in the appendix of D3.1 [i]. The maximum value of the degree of saturation within a given time period can be given as: S S max S k max c t S b t k max (170) maximum value of saturation degree within a given time period break point in the graph of the degree of saturation vs. the square root of time, being reached in a relatively short period b, c regression parameters obtained from capillary suction tests length of the longest wetting period of the structure within the considered period t max In order to determine t max three different environments have to be distinguished: 138(169)

139 1. An environment in which the drying of the concrete is negligible. For this case the longest period of wetting is equal to the age of the structure. 2. Drying brings the degree of saturation below the break point S k. The longest period of wetting is equal to the duration of rain events, determined by meteorological data. 3. An environment leading to an degree of saturation being intermittently above/ below the break point for certain periods. Here, an equivalent period of wetting has to be determined. The simplest approach is to set the longest period of wetting equal to kt, with t being the construction age. Due to the lack of data for the water ingress in existing structures the model is subjected to a high uncertainty, which can be accounted for by introducing a model uncertainty m. The model uncertainty can be estimated on the basis of simultaneous observations of the degree of saturation of a test specimen and the degree of saturation of a given structure made of the same concrete. The introduction of m leads to: p (t) p ms S int ernal damage max cr (171) m S Max model uncertainty (at present data is not available) maximum degree of saturation The output is the probability that internal damage occurs within a given period of time Full-Probabilistic Model on Internal Frost Damage Until now there are no full-probabilistic models known to the author Semi-Probabilistic Model on Frost induced Scaling A structure is said to fail, when the amount of scaled concrete has reached a given limit. The limit can be expressed as the loss of a given weight of concrete per unit surface area. The failure probability as a function of time is: p (t) p s(t) s scalling failure cr (172) s(t) s cr weight of scaled concrete as a function of time [g/cm²] limit for scaling [g/cm²] The model assumes that the amount of scaled concrete of a construction in-situ can be correlated with the amount of scaling measured by accelerated tests: s(n) = ms test (n) (173) n equivalent cycle number [-] m model uncertainty [-] s test scaling as a function of the number of freeze-thaw cycles in the test [g/cm²] n number of freeze-thaw cycles [-] 139(169)

140 The fact that a given structure in-situ is subjected to a number of cycles with variation of the minimum temperature, gave rise to define the parameter n, as an equivalent number of cycles: N T n i1 T 2 i 2 ref (174) N T i number of freeze-thaw cycles where the water content in the surface layer of the concrete is high enough for damages to occur [-] lowest temperature in a cycle [K] It is assumed that the number of cycles where the degree of saturation is harmful, can be determined as: N(t)=km(t) (175) k describes the environment (can be assumed to 1) [-] m(t) total number of cycles [-] The failure probability can now be formulated as: b p (t) p s(t) s p man(t) s scalling failure cr cr (176) a, b constants determined in experiments b<1 retarded scaling (poor cover concrete) b=1 linear process, homogenous concrete b>1 accelerated 13.4 Full-Probabilistic Model on Frost induced Scaling As for the internal frost damage there until now, no full-probabilistic models known to the author. 14 Parameter Study for Environmental Classification 14.1 General Procedure Aim of the performed parameter study was the definition of boundaries of classes for environmental data. Once these classes are defined environmental data can be mapped. Benefit for the user is a reduction of work during the process of collecting data as input to degradation models. For the mapping of environmental data the general procedure is as follows: 1. collect daily data of the last 10 years from weather stations to calculate mean values 2. classify each weather station 3. draw isolines of the class boundaries by interpolating classes of weather stations 4. for the areas within isolines the data of all weather stations must be combined to calculate the mean value and standard deviation using an appropriate distribution type 140(169)

141 The result is a map with classified areas. For each area distribution type, mean value and boundary limits are stated. For the meaningful classification of environmental parameters a study of these can be performed. The boundaries of five classes (0 to 4) need to be determined by dividing the maximum of the regarded damage measure (e.g. corrosion penetration depth) into 5 equal sections. In class 4 the severest extent of damage is to be expected. In class 0 no damage at all will occur within the time scale. To do so the entire process usually consisting of the initiation and propagation period has to be modeled. This is necessary because some parameters may have reverse influence on the duration of either phase. For instance, with rising relative humidity the time until initiation will increase, because the carbonation process is retarded. Nevertheless, rising relative humidity leads to an increase of the electrical resistivity and thus to an increase in the corrosion rate during the propagation phase. Hence, a pessimum of relative humidity RH must exist for which the service life time of a reinforced concrete element tends to a minimum Classification for Carbonation induced Corrosion Procedure The study of parameters given in Table 43 was performed distinguishing two qualities of concrete, both produced with CEM I cement: - good: low w/c-ratio (0,45); high concrete cover (50 mm); 7 days curing - bad: high w/c-ratio (0,60); low concrete cover (15 mm); 1 day curing Table 43. Environmental parameters included in service life models for carbonation induced corrosion Carbonation induced Corrosion Initiation Propagation k RH (RH); w(tow); C S k R, T (T); k R,RH (RH), ToW The study revealed, as should be expected, that the average time until depassivation of "good concrete" is far beyond the scale of commonly requested service lives. The decisive parameter showed to be the concrete cover. Thus, the classification was only performed for "bad concrete". The result of the calculations for the corrosion due to carbonation is the corrosion penetration depth vs. the regarded parameter (RH, ToW, T, C S ) for the age of 30 and 100 a years Input Data for Parameter Study For the study of one environmental parameter all other environmental data must be kept constant on an average level (European or national), as can be seen from the following tables. The time of wetness (days with rain above 2,5 mm) was set to 0 as surfaces exposed to rain usually will not suffer from carbonation induced corrosion, unless the concrete cover is very low. 141(169)

142 Table 44. Input data for parameter study on carbonation induced corrosion (initiation phase) No. Input Sub-Input Unit D-Type Mean StD Limits Good Bad Good Bad Min Max 1 d cover [mm] Beta RH [%] Weibull (max) 75 1) (40-100) 2) k RH RH ref [%] Const g RH [-] Const. 2,5 - - f RH [-] Const. 5,0 - - a c [-] const. 3, k c b c [-] ND -0,567 0,024 - t c [-] ND k t [-] ND 1,25 0,35 - [m 5 (skgco 5 2 )] 1,010 t ([mm 5 ND 0, (akgco 2 )]) (315,5) (48) - 6 C S [kgco 2 /m³]10-4 ND 8,2 1) (6,2-20) 2) 1,0-7 T [a] Const. 30 or ToW [-] Const. 0 1) (0 to 100) 2) - - b w [-] ND 0,446 0,163-8 W p splash [-] Const t 0 [a] Const. 0,0767 (equals 28d) - - a w [-] const. 0, [m 5 (skgco 9 R 2 )] ,1 13,4 1,67 5,21 ACC,o ([mm 5 ND (akgco 2 )]) (982) ) (4243) (149) (465) - D-Type: StD: 1) 2) 3) 4) distribution type standard deviation value chosen as constant for the study of other environmental parameters range of parameter study CEM I; w/b = 0,40 CEM I; w/b = 0,60 142(169)

143 Table 45. Input data for parameter study on carbonation induced corrosion process (propagation phase) No. Input Sub- Input Unit D-Type Mean StD Moments Good Bad Good Bad Min Max 1 [-] const k 0 [µmm /a] LogN F Cl [-] sln 2,63 3,51 1,09-4 F Galv [-] const. 1, F O2 [-] const. 1,0 - - RH [%] Weibull 75 1) max (40-100) k RH [-] const. 3,16 2,05-6 (t) D-Type: StD: 1) 2) 3) ToW [-] const. 0-1 (0 to 1) - T [K] Beta 283 (273 to 293) b T [K] ND k c [-] const. 1,0 - - k t [-] const. 1,0 - - k R,Cl [-] const. 1,0 - - n [-] ND 0,23 0,04 - t hydr [a] const t 0 [a] const. 0, [m] ND ,4 6 - distribution type standard deviation value chosen as constant for the study of other environmental parameters range of parameter study CEM I; w/b = 0,40 CEM I; w/b = 0,60 0 1) Classification of Relative Humidity RH A rise in relative humidity slows down the carbonation process but accelerates the subsequent corrosion once initiated. As a measure the corrosion penetration depth was regarded. The study of the effect revealed the following: A maximum of corrosion penetration depth can be observed. On the left side of the maximum corrosion is the limiting process. At the right the carbonation is the dominating factor. The relative humidity for which a maximum of corrosion penetration depth is observed depends on the ratio of initiation and propagation time and hence on the regarded service life. 143(169)

144 A change in corrosion rate due to a change in temperature or concrete porosity (not due to a change in relative humidity) alter the maximum value of corrosion penetration depth, but does not shift the pessimum of the relative humidity. With rising regarded service life the pessimum of relative humidity is shifted towards larger values (80% after 30a; 88% after 100a), as the corrosion process is given more weight in the study. 350 Penetration Depth p Corr [µm] t=30a;tow=0%;t=10 C t=100a;tow=0%;t=10 C t=100a;tow=0%;t=5 C t=100a;tow=5%;t=10 C 0,2 p corr,max Relative Humidity [%] Figure 70. Corrosion penetration depth of reinforcement vs. relative humidity at age of 30 and 100 years and variation of temperature (T) and time of wetness (Tow) For the matter of classification a period of 100 years was regarded. In Europe the yearly average relative humidity, calculated from hourly values, lies in between 60% (Spain, Madrid) and 88% (Germany, Fichtelgebirge). In this study the range of 60 to 92% (largest value for which depassivation will still occur within 100 years) was classified. The boundaries of five classes (0 to 4) were determined by dividing the maximum penetration depth into 5 equal sections as shown in Figure 70. In class 4 the severest, in class 0 the lowest extent of corrosion damage is to be expected. The difference in relative humidity by one class equals 20% of the maximum of penetration depth at 88% RH. 350 Penetration Depth p Corr [µm] & Relative Humidity [%] Figure 71. European classification of average annual relative humidity regarding carbonation induced corrosion, regarding 100 years of service life, ToW = 0; T = 10 C 144(169)

145 Table 46. 1) Classification of average annual relative humidity regarding carbonation induced corrosion Class (0) Domain [%] <60 1) or >93 1) >71-77 >77-81 or >90-91,5 >81-90 Beyond European range The same procedure can be adopted on a national level Classification of the Time of Wetness ToW Likewise as is the relative humidity (RH), the time of wetness (ToW) is a parameter with inverse influence on the initiation (carbonation) phase and the propagation of corrosion. An increase of ToW retards the carbonation process severely, but reduces the concrete resistivity causing an increase in corrosion rate. The study of the effect revealed the following: There is no pessimum of the time of wetness for which a maximum in penetration depth can be observed. The largest penetration depth will be obtained for ToW = 0, because carbonation is the dominating process. The dependence of penetration depth upon ToW is very sensible to changes in the relative humidity. For an average relative humidity of 75% on a European scale corrosion will only occur within a period of t = 100 years in a horizontal structure up to a value of ToW = 6,5%. For vertical surfaces the probability of a surfacing being splashed by driving rain must be taken into account. Penetration Depth p Corr [µm] t=30a;rh=75%;t=10 C t=100a;rh=75%;t=10 C t=100a;rh=75%;t=5 C t=100a;rh=70%;t=10 C Time of Wetness ToW [%] Figure 72. Corrosion penetration depth of reinforcement vs. Time of Wetness (ToW) at age of 30 and 100 years and variation of temperature (T) and relative humidity (RH) 145(169)

146 Penetration Depth p Corr [µm] Time of Wetness ToW [%] Figure 73. European classification of average annual time of wetness regarding carbonation induced corrosion Table 47. Classification of average annual time of wetness (ToW) regarding carbonation induced corrosion Class Domain [%] >6,6 >5,5-6,6 >4,0-5,5 >2,0-4,0 0-2, Classification of Carbon Dioxide Concentration C S Although the carbon dioxide concentration is a decisive environmental input parameter a classification seems not reasonable as it does not change considerably on a macro-environmental scale. Instead it can be considered to be quiet constant in the range of 350 to 380 ppm over Europe. These values may be exceeded in areas with high emissions of combustion gases especially within such buildings as tunnels. Mapping of the CO 2 -concentration is hence not reasonable. More important for this aspect are models on meso- and micro level, which means models for the determination of the CO 2 -content in the vicinity of a building and the regarded concrete surface Classification of Temperature T The effect of changing temperatures is only included in the model for the progress of corrosion whereas the carbonation process is considered to be independent of the temperature. A rise in temperature causes a decrease in concrete resistivity and thus an increase in corrosion rate, which is modeled by the exponential approach of Arrhenius. As can be seen from the parameter study, the effect of other parameters in the models is very low on the classification of the temperature, since the curve of penetration depth vs. temperature is only shifted more or less parallel without changing the gradient of the curve to a large extent. For the classification of the temperature relative humidity was set to RH = 75%, time of wetness was set to ToW = 0% and the considered service life is T 100 a. 146(169)

147 For the classification on a European scale the range of the annual temperature of T = 0 to 20 C were considered as relevant. Penetration Depth p Corr [µm] t=30a;rh=75%;tow=0% t=100a;rh=75%;tow=0% t=100a;rh=60%;tow=0% t=100a;rh=88%;tow=0% t=100a;rh=75%;tow=5% Temperatur T [ C] Figure 74. Corrosion penetration depth of reinforcement vs. temperature (T) at age of 30 and 100 years under variation of time of wetness (ToW) and relative humidity (RH) 80 Penetration Depth p Corr [µm] Temperatur T [ C] Figure 75. European classification of average annual temperature regarding carbonation induced corrosion Table 48. Classification of average annual temperature regarding carbonation induced corrosion Class Domain [ C] >0-6,4 >6,4-11,6 >11,6-16,0 >16,0-20,0 The class 0 is not defined as corrosion will always occur if other environmental parameters are set to default values. 147(169)

148 14.3 Classification for Chloride induced Corrosion Procedure Table 49. Environmental parameters included in service life models for chloride induced corrosion Carbonation induced Corrosion Initiation Propagation k T (T); C S,X ; X k R, T (T); k R,RH (RH), ToW The study of parameters given Table 49 was performed distinguishing two qualities of concrete: good: blast furnace slag cement (BFSC)t; w/c = 0,40; concrete cover 60 mm bad: OPC, w/c = 0,60; concrete cover 45 mm In the parameter study on carbonation induced corrosion a simple spreadsheet with mean values of the model parameters was programmed including the initiation phase (carbonation of concrete) and the propagation phase (corrosion of reinforcement). The study may also be conducted using software which enables full-probabilistic parameter studies as will be demonstrated in the following section. To do so a limit state criterion must be set. Here the loss of Q Max = 10% cross section area of a bar with = 12 mm was chosen (for which concrete cover will in most cases already be cracked for a long time). The choice of the limit state criterion does influence the result of the classification. If a larger value for the section loss is chosen, more weight is given to the propagation phase. A lower value for the limit state criterion gives more weight to the initiation phase. As 10% cross sectional loss will usually have considerable impact on the residual strength (most important bond strength, see chapter ) a value beyond this limit is not considered as reasonable in a management process, as immediate action will most likely have to be taken. With a value of 10% we thus investigate the whole range of the corrosion process managed by a Life Cycle Management System Input Data for Parameter Study All input parameters are quantified according to the model given in chapter 7. As chloride source was chosen de-icing salt, which is dependent on the site of the structure. The typical case for which a durability design may be applied is chosen, i.e. a structure close to the street edge (horizontal distance a = 1,0 m; height above street level h = 0,0 m). 148(169)

149 Table 50. Input data for parameter study on chloride induced corrosion (initiation phase) No. Input Sub- Input Unit D-Type Mean StD Limits Good Bad Good Bad Min Max D RCM,t=28d [10-12 m²/s] Log-N 1,7 9,2 0,88 4, D RCM (t) D RCM,t= [10-12 m²/s] 0,3 4,8 0,22 3, n 2 [-] 1,624 0,964 0,438 0, k w/b [-] Log-N 0,81 2,46 0,12 0, C x [wt.-%/cem] Log-N 1,53 1,60 1,15 1, k RH [-] D 0,9 0, b T [K] ND k T T [K] 8 (273 to 293) 5 n 1 [-] Beta 0,55 0,55 0,24 0, X [mm] Beta 9,03 9,03 9,03 9, C Crit [wt.-%/cem] Beta 0,48 0,48 0,15 0,15 0,2 2,0 8 C ini [wt.-%/cem] Log-N 0,108 0,108 0,057 0, d cover [mm] Beta D-Type: distribution type StD: standard deviation 1) value chosen as constant for the study of other environmental parameters 2) range of parameter study Good quality: CEM III; w/b = 0,40 Bad quality: CEM I; w/b = 0,60 Table 51. Input data for parameter study on chloride induced corrosion process (propagation phase) No. Input Sub-Input Unit D-Type Mean StD Moments Good Bad Good Bad Min Max 1 [-] Log-N. 9,28 4,04-2 k 0 [µmm /a] LogN F Cl [-] sln 2,63 3,51 1,09-4 F Galv [-] const. 1, F O2 [-] const. 1, k r,rh [-] D D-Type: (t) 149(169) 283 (273 to 293) 2) k T T [K] Beta b T [K] Log-N k c [-] const. 1,0 - - k t [-] const. 1,0 - - k R,Cl [-] ND 0,72 0,11 - t hydr [a] const t 0 [a] const. 0, ,Ref,t=28d [m] Log-N ,Ref,t= [m] Log-N t hyd [a] Log-N 1,5 3) 0,5 0,8 3) 0,3 - k w/b [-] D 1,12 0, Q max [-] D 0, t [a] D distribution type

150 StD: 1) 2) 3) standard deviation value chosen as constant for the study of other environmental parameters range of parameter study value from measurements after around 1,5 years (hydration not yet completed; there approach on safe side) Good quality: CEM III; w/b = 0,40 Bad quality: CEM I; w/b = 0, Classification of Temperature T The effect of the temperature upon the chloride induced corrosion is twofold: an increase in temperature increases the apparent diffusion coefficient in an exponential manner and hence leading to a more ingress of chlorides the resistivity of concrete is reduced, which causes a more rapid corrosion process The most severest corrosion problems are thus to be expected in warm climates. As stated before in chapter 9.1 the time until depassivation t ini can not be solved for directly in the proposed model on chloride ingress. A solution to this problem for the desired parameter study is to: 1. calculated and plot the probability of depassivation p depassivation (t = 100a, T [K]) in dependence of the temperature T [K] 2. determine the functional relationship for p depassivation (T) 3. multiply the probability of depassivation for p depassivation (T) with the model for section loss at the t = 100a: P(t 100a,T) V t V (100 t ) V 100p (t 100,T) corr prop corr ini corr depassivation (177) P penetration depth [mm] pitting factor [-] t prop duration of propagation phase [s] t age of structure [s] t ini time until initiation of corrosion [s] p depassivation (t = 100a, T) probability of depassivation at t = 100a [-] as a function of temperature As expected for bad quality concrete with a low concrete cover rather high probabilities of depassivation were calculated in the considered temperature domain, which means that the upper tail of the cumulative probability (probability distribution function) is looked at,. For good quality concrete with high concrete cover the opposite is the case, where we look at the bottom tail of the cumulative probability. 150(169)

151 probability of depassivation [-] 0,050 0,040 0,030 0,020 0,010 Model - Good Concrete Fit - Good Concrete probability of depassivation [-] 1,0 0,8 0,6 0,4 0,2 Probabilistic Model - Bad Concrete Fit Bad Concrete 0, Temperature T [K] 0, Temperature T [K] Figure 76. Cumulative probability of depassivation vs. temperature of environment for good quality (left) and bad quality (right) concrete after t = 100 years The quality of the concrete has a major impact on the result of the parameter study, as good quality concrete Figure 77. Cumulative probability for exceeding 10% section loss vs. temperature of environment for good quality (left) and bad quality (right) concrete after t = 100 years and resulting classes The example above shows how sensitive such parameter analysis are with respect to the chosen boundary conditions, especially concrete composition and concrete cover. It is proposed to apply the average of the boundaries for classes as given for the two extremes of Figure 77: Table 52: Classification of average annual temperature regarding chloride induced corrosion Class Domain [ C] ,5 9, >13 15 Modelling with a Markov Chain Approach 15.1 Introduction A management system for concrete structures may be applied on the object or the network level. For the object level, the deterioration processes should be modeled as precise as possible, as these calculations serve as the basis for decisions on future MR&R actions. Semi-probabilistic or full-probabilistic models can be applied. 151(169)

152 On the network level the performance of a whole set of objects or component groups has to be regarded. The so called Markov Chain approach has proven to be suitable for this purpose Principal of the Markov Chain Instead of continuous functions for which input parameters are defined by a statistical distribution, the Markov Chain uses a condition state (CS) distribution according to a discrete set of n predefined condition states i. Generally the number n of states used for the Markov chain is not restricted, but the consumption of computation time rises in a potential manner for an increase of condition states. An uneven number of states should be used in order to have a medium condition state and outer extremes. In LIFECON n = 5 states from i = 0 to 4 where chosen, see also [i, vii]. The damage index 0 represents the best and 4 the poorest condition. In general service life is the age at which the damage index 3 is reached. Table 53. Interpretation of condition states Condition states i State definition 0 Initial state, no degradation 1 1/3 limit state 2 2/3 limit state 3 limit state 4 post limit state The changes of the condition distribution within a duty cycle (normally one year) are predicted by multiplying the condition distribution vector q T (t) by a transition probability matrix P. The general form of a degradation matrix P is given in Table 54. For a structure that was at state i in the beginning, the probability of dropping to the state i+1 during the duty cycle is given by the matrix element p i, i+1. As it is impossible that the condition state of a structure is improved without repair actions the elements in a degradation matrix below the diagonal line are 0. The sum of elements in each row of a transition probability matrix must be 1. At the lower right corner of the matrix the value of the probability element is always 1 as the structures in the highest possible condition state is considered to always stay at the same condition state. Table 54. Transition probability matrix P for n = 5 conditions state i from 0 to 4 State p 00 p 01 p 02 p 03 p p 11 p 12 p 13 p p 22 p 23 p p 33 p The condition state distribution for each year, is a vector with n-dimensions, q T (t) = (q 0, q 1, q 2, q 3, q 4 ), with n being the number of considered condition states i. At the network level the components q i represent the percentages of structures at each condition state from all the 152(169)

153 population. At the project level q i is equal to the portion (surface area, etc.) of a structure component which is in the condition i to i+1: q(t)=p(icsi1) i (178) q i portion of a structure component or network which is in the condition i to i+1 p probability [-] CS current condition state The condition state distribution of year t is obtained by multiplying the condition state distribution of the previous year (t-1) with the transition matrix P: T T q (t)=q (t-1) p (179) Changes after n years are predicted by multiplying the initial damage index distribution, q T (t 0 ), by the transition matrix n times in row, which is conveniently done using spreadsheet tools as e.g. MS-EXCEL. More detailed descriptions of the Markov Chain Method and its application within the LIFECON framework are given in [vii] Procedure for Calibration of the Transition Probability Matrix The practical problem in applying the Markov Chain Approach is of course how to determine the transition probability matrices. As stated above each cell of the transition probability matrix expresses the probability that a regarded component or even the whole network of structures degrades from state i to the next state i+1 within the chosen time interval (usually 1 year). The full-probabilistic models described in the earlier sections can be used to calibrate these transition probabilities p i,i+1. The procedure to do so is explained in the following section step by step using the example of the case study on chloride induced corrosion of chapter 8. Step 1: First of all the condition states must be defined. For the present example chloride induced corrosion (state 3) is regarded as limit state. Table 55. Example for Condition States of Chloride induced Corrosion Condition state State definition Example of chloride induced corrosion 0 Initial state, no degradation No chloride ingress yet (coating is functioning) 1 1/3 limit state Chloride threshold depth 1/3 of concrete cover 2 2/3 limit state Chloride threshold depth reached 2/3 of concrete cover 3 limit state Chloride threshold depth concrete cover 4 post limit state Corrosion induced cracking The probability that a certain predefined condition state (i) is exceeded must be calculated for each time step, for which the author used the software package STRUREL [xix]: p(cs i) (180) p probability [-] 153(169)

154 CS current condition state i regarded state (0, 1, 2, 3, 4) Step 2: From the probability of exceeding a limit state the components of the condition vector can be calculated as follows: q (t)=p(i CS i 1) p(cs i) p(cs i 1) i (181) p probability [-] CS current condition state Figure 78. Calculated curves for probability of exceedance of different condition states vs. time (the difference between each line is the probability that the component is in between the two considered states) Please note that the probability of exceeding state 0, i.e. the state in which concrete is not loaded with chlorides, is p(cs 0) = 1 =const., because the concrete in the example is not coated and chlorides may reach the concrete surface from the beginning of the service life. If a coating would be present the degradation of the coating would have to be modeled as well, for which no models with physical data are available to the author. Currently such protection measures may be modeled by simple assumptions on the average service life of these measures, e.g. 5 t service life coating 15 years. Step 3: A starting solution for the probability transition matrix must be stated as shown in top right of Table 56. Only the cells on the diagonal (top left to bottom right) are variables. The cells at the right to these (p i,i+1 ) are automatically calculated to remain 1 as the sum of each line: p 1p i,i1 Table 56. i,i (182) Probabilities p(state i condition state i+1)(bottom left) for the first 20 years and example for spread sheet to determine the probability transition matrix for the Markov Chain 154(169)

155 Step 4: The multiplication of the transition matrix P with the condition vector at the previous time step results in the condition vector for each time step, see lines bottom right of Table 56. Usually the starting point for the optimization of the matrix P is the age t = 0. For the current example as the reference time t = 1 year was used, as deviations of the resulting probability matrix P from the real behavior would be considerable and this period is still of minor importance compared to the entire service life period. Therefore the line of year t = 1 was set equal to the one obtained in step 3. Step 5: Once the components of the condition vector q i = p(i CS i+1) are established (see bottom left in ) these can be compared to those obtained by the Markov Chain approach. The target is to minimize the squared deviation by optimizing the transition probabilities p i,i in the diagonal of the probability transition matrix This optimization is readily achieved using spread-sheets with optimizing tools as e.g. MS-EXCEL using the SOLVER option. The probabilities p i,i+1 are automatically calculated as the sum in each line must be equal to 1! The average of the condition state distribution at each year, CS(t), is obtained by multiplying the scale vector, r by the condition state vector q T (vector multiplication): T CS(t) = q(t) r (q,q,q,q,q ) (183) 155(169)

156 Figure 79 shows that the fitted Markov Chain represents the given problem quite well. The result of the transition probability matrix indicates that probabilities p,.,i+q of changing from one state to next within 1 years time are rather low. The severest jump in condition is obtained between t = 0 to 1 year because no coating is applied and chlorides enter the concrete for the first time. This is once again the reason why this time step was neglected in the optimization of the transiting matrix P, see above in step 4. Probability p [-] 1,0 0,8 0,6 0,4 State 0 to 1 State 1 to 2 State 2 to 3 State 3 to 4 State >4 Fit State 0 to 1 Fit State 1 to 2 Fit State 2 to 3 Fit State 3 to 4 Fit State >4 0,2 0, Age of structure [a] Figure 79. Probabilities p(state i condition state i+1) from full-probabilistic model and according to fitted Markov Chain Right: Average Condition State of case study pillar On the network level numerous sets of transition probability matrices of components in different condition and surface area must be grouped. This is achieved by summing up all weighted matrixes according to the ratio of the surface area of a single component and the total surface area of all components. 16 Conclusions Models and the corresponding default input data which can be used for durability design with respect to carbonation and chloride induced corrosion are provided on a full-probabilistic level. To apply these commercial software for reliability calculations is required. These models can be improved by Bayesian updating once measurements on the real input parameters at a specific structure becomes available. Full-probabilistic models have been simplified to a semi-probabilistic level, where the various input parameters of full-probabilistic models are merged into two variables (resistance R and stress S). This way reliability evaluations can be conducted by manual calculations without sophisticated software programs. However, semi-probabilistic require calibration data from structure investigations. There is ample visual evidence around about us that concrete structures continue to function adequately despite extensive visual signs of corrosion. Most service life models do not go beyond first cracking and thus consider only a part of the period during which a structure may perform its required functions in an adequate manner. There are, however, significant inconsistencies in the influences derived by individual studies of residual strength of corrosion damaged structures. The relatively short timescale of laboratory test programs in relation to the normal service life of structures requires that accelerated conditioning be used. It is evident that some of the methods used have distorted results, and that 156(169)

157 these results should not be directly applied in practice. Despite the inconsistencies, there is evidence to show that: 1. Reinforced concrete structures may retain a substantial portion of their original strength despite extensive visual signs of deterioration on the surface of the member. 2 In the absence of visual evidence of damage on the surface of a member, residual structural strength is not impaired by carbonation related damage. 3 In chloride contaminated structures, with the possible exception of rapid pitting corrosion, there is no loss of residual structural strength prior to onset of longitudinal cover cracking. (Rapid pitting corrosion sites are readily detectable by half cell potential survey.) 4 Several aspects of residual strength will be strongly dependent on expansiveness of corrosion products, but empirical models are derived for weight loss or corrosion penetration, not crack width, and thus are not robust. 5 Models for residual strength assessment are generally empirical, and as such must be treated with caution outside the range of parameters for which they were obtained. 6 A comparison of strength loss by the various mechanisms identified in Figure 61 suggests that for full scale members the greatest danger to structural integrity will come from matters related to anchorage/curtailment/detailing of reinforcement and reductions in rotation capacity/ductility as a result of non-uniform corrosion of reinforcement. 7 Confining reinforcement plays an important role in maintaining bond/anchorage strength. 8 There are no deterioration models that include effects of cover cracking on corrosion rate. Running a structure to exhaustion, followed by replacement and demolition, may well be a rational strategy, and its evaluation should be embraced within LIFECON. At the present time models at these late stages of corrosion damage are scarce or non-existent, and require further development before implementation through LIFECON. Models on frost damage (internal and scaling) are not existing to be applied for durability design purposes. The same applies to alkali-aggregate-reaction. For these two mechanism avoidance of damage is currently the best design strategy. Structures being in the under service life stage can be investigated (monitored) to obtain response data for future predictions of deterioration development if occurring. Techniques to do so are available and outlined in the report. The Markov Chain approach is a powerful tool for modeling the consequences of repair and maintenance methods. As every model the Markov Chain requires input data. Existing durability design models can be used to calibrate this input data as has been demonstrated. 17 Proposal for further development The effect of protective measures for concrete as coatings on the ingress of agents has been well studied. The service life of such measures is an important research topic for the future. Currently assumptions on the service life are mainly based on personal experience. Such knowledge can be 157(169)

158 incorporated into models as is done in the Markov Chain Approach [vii]. Models with a sound physical and chemical bases for the prediction of the time dependent deterioration mechanisms of protective coatings are still lacking. As outlined above, the probability of corrosion initiation is nowadays already predictable though the precision of these models, especially in the case of chloride induced depassivation still remains a matter of debate. It should be reckoned that there is no sense in improving the accuracy of predictions on chloride ingress if the chloride threshold level is still subject to a high level of uncertainty. From the perspective of the author there is still further well planned research necessary to clearly link the dependency between the concrete specific chloride threshold values and the environmental exposure conditions. Nevertheless it must also be kept in mind that the steel-concrete interface is after all considered as the overwhelming influence on the threshold level, which is to a large extent depend on the workmanship and curing conditions. An appropriate characterization and more important a prediction of this key parameter before hand seems currently out of reach. Having these shortcomings in mind the benefit of structure investigations including monitoring techniques should be realized: even though a model may deviate considerably from the real behavior at first a continuous model updating will in the longrun lead to rather precise predictions. At this point owner organizations must change their policy from currently mere visual inspection to more specific sampling as the cost for such investigations will be compensated by the achieved knowledge on the best moment for intervention. The propagation of the corrosion process in concrete is currently modeled in an over simplistic way. A galvanic element may be modeled in a simple way by an equivalent electrical circuit, in which anode and cathode are connected by a series of electrical resistances, of which the electrical resistance of the reinforcement is negligible low. R e R a R c U R St 0 Anode Cathode Figure 80. Equivalent circuit model for a galvanic element The driving force of a galvanic element is the corrosion voltage, being the difference in electrochemical potential E 0 between cathode and anode. If anodic and cathodic areas are very close to each other (general corrosion) a separate measurement of the corrosion current is not possible. The total corrosion current is thus the sum of the galvanic element current and the general corrosion process, which leads to: 158(169)

159 I corr ra A a U rc e k A c e I general (184) r a, r c anodic and cathodic polarization resistance related to surface area [m²] A a, A c anodic and cathodic surface areas l [m²] e electrolytic resistivity of concrete [m] k e geometry factor for electrolytic resistivity taking account of way the [m/m²] electrical current flows within the concrete volume between anode and cathode I general contribution of general corrosion to total corrosion current [A/cm²] Unfortunately most of the above mentioned parameters have not yet been sufficiently quantified in a systematic way with respect to concrete composition and environmental conditions. This gave way to a simplified approach using the oftentimes observed inverse relationship between electrolytic resistivity and corrosion current as was used here in the report. A systematic determination of the above stated corrosion parameters in dependence of concrete composition and environmental conditions is a highly important topic for future research projects, which can hardly be covered by single institutions. The same applies to the structural consequences of reinforcement corrosion as there are cover cracking, crack growth, the hereby induced loss of bond and the overall bearing capacity. The shortcomings regarding the mechanisms of frost and alkali-silica-reaction have already been concluded in the previous chapter. More systematized research work is highly desirable in these fields. 18 Acknowledgements The author thanks Prof. John Cairns from Heriot-Watt University for contributing an excellent literature review on the structural consequences of reinforcement corrosion. Special gratitude shall be expressed to Dr. Christoph Gehlen and Gesa Pabsch (Consulting Office Prof. Peter Schießl, Munich). They provided data and background information on the case studies for carbonation induced corrosion and have always been very competent and interested partners in discussions in the field of reliability analysis and deterioration modeling. Moreover it was the doctoral thesis of Christoph Gehlen which was to a large extent the starting point for this report. Major parts of the here presented results on chloride ingress in the road environment are part of a research project of the author "Durability Design of Reinforced Concrete Structures" (Dauerhaftigkeitsbemessung von Stahlbetonkonstruktionen: DBV/AiF No. 225/ 12525) focusing on corrosion of reinforcement induced by de-icing salts. The project was financed by the German AiF (Arbeitsgemeinschaft industrieller Forschungsvereinigungen "Otto von Guericke" e.v.) and supervised by the DBV (Deutscher Beton- und Bautechnik-Verein E.V.). 159(169)

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