Crack formation in structural slabs on underwater concrete

Transcription

1 Graduation Thesis Faculty of Civil Engineering Delft University of Technology Crack formation in structural slabs on underwater concrete W.H. van der Woerdt Graduation Committee: Prof. dr. ir. J.C. Walraven (TU Delft) Dr. ir. C. van der Veen (TU Delft) Ir. S. Pasterkamp (TU Delft) Ir. W.J. Bouwmeester (BAM Infraconsult/TU Delft) Ing. C. Huisman (BAM Infraconsult) i

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3 FOREWORD This report is the MSc graduation thesis of W.H. van der Woerdt at the faculty of Civil Engineering, department of concrete structures at TU Delft, the Netherlands. The research was performed in cooperation with BAM Infraconsult in Gouda. The report has been written to serve as a theoretical background and practical advice to those involved in the design of structural slabs on underwater concrete. Readers that are mainly interested in newly developed hand calculation methods for the stresses in structural slabs on underwater concrete can read sections 4.3, 4.6, 4.7 and 6.2. For the reasoning behind the practical advices, 5.4 can be viewed. Special thanks go out to those that have assisted in writing this thesis. First of all the graduation committee (see cover page) for the professional advices and support during the research. Also the interviews held with experts on structural slab on underwater concrete in different fields have been very helpful for a better understanding of today s building practice. An last but not least, many thanks go to the people who were willing to read en comment the report in the final stage. Gouda, 19 August 2010, W.H. van der Woerdt iii

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5 SUMMARY Structural slabs on underwater concrete are widely applied in the construction of tunnels, parking garages, rail- and road construction. Over the years many problems have been reported with aquiferous crack formation in structural slabs on underwater concrete. Aquiferous trough crack formation threatens the durability of structural slabs on underwater concrete. Through cracks can be the result of restrained deformation. Temperature- and shrinkage strains that are restrained, cause stresses in the structural slabs. Stresses from restrained deformation can cause through crack formation. During the hardening process and due to climate influences, the structural slab is affected by temperature- and shrinkage loads and cracks can form. In the design of structural slabs on underwater concrete, much attention was given to the calculation of stresses and calculation of reinforcement, but still aquiferous crack formation cannot be prevented. Over the years many discussion on the effect of an intermediate layer of sand between the structural slab and the underwater concrete has taken place amongst experts. Nowadays two sides exist; one in favour and the other against an intermediate layer of sand. Both sides are convinced that their alternative outperforms the other. No theoretical bases, but many uncertainties, exist about the magnitude of the stresses in structural slabs on underwater concrete. This research aims to create more insight in the stresses in hardened concrete that cause the forming of cracks in structural slabs on underwater concrete. The results should be used to develop a practical advice for handling of the problem of crack formation in structural slabs on underwater concrete. To obtain the goals of the research first the current state of the technology is examined in a literature study. To determine the magnitude of the stresses and to analyze the influence factors on the stresses a Finite Element model has been developed. The results of these models were used to come to a practical advice. A thermal model was built to calculate temperature loads. Based on long term temperature measurements in a structural slab on underwater concrete, the model has been calibrated. Temperature loads on any given structural slab on underwater concrete can now be calculated accurately. The temperature load in structural slabs on underwater concrete can vary between 3 C and 17 C. The largest influence factor on temperature load is the month of casting. The geometry of the structure can also have significant influence on the temperature load. v

6 A 3-D Finite Element structural model was designed to research the influence factors on restraint. This has gained more insight in the influence factor on the degree of restraint and the shear forces in the piles. It is now possible to calculate the degree of restraint of any structural variant of structural slabs on underwater concrete. The degree of restraint varies between 15% and 80%. The restraint is influenced to a large extent by the structural variant. The theoretical restraint can only be reduced by applying an intermediate layer of sand. With an intermediate layer of sand a possibility exists that the piles fail in shear. For practical use the complicated models have been transformed into simple calculation methods. Based on the results of the model, hand calculation methods have been developed for easy use in the building industry. Also measures to reduce stresses in the structural slab have been obtained. The efficiency of the measures is estimated by comparing the reduction of stresses to the cost of the measures. Based on the efficiency of the measures the following practical advices can be given: Only by the application of an intermediate layer of sand a reduction in the degree of restraint can be expected Shear forces in the piles can exceed the shear strength The thickness of the underwater concrete should be kept as low as possible Application of Gewi piles is an effective measure to reduce stresses in the structural slab Sections of more than 20 meter should not be applied with an intermediate layer of sand Extra reinforcement should not be applied as solution to the problem of crack formation When cracks occur, injection is a relatively cheap, but not always reliable, repair method With the methods described in this research, stress calculation in structural slabs on underwater concrete can be done accurately by using FEM software. Also a quick estimation of the probability of crack formation can be made by newly developed had calculation methods. An advice is given for measures to handle crack formation. The new developments in this report have therefore clarified many uncertainties. The research increased the insight in the influence factors on crack formation in structural slabs on underwater concrete significantly and developed an easy calculation method for practical use. vi

7 TABLE OF CONTENTS Foreword... iii Summary... v Table of contents... vii 1 Introduction Analysis of the problem of crack formation Description of structural slabs on underwater concrete Building method Structural variants Crack formation in concrete structures The problem of crack formation Causes of through crack formation Restrained deformation Analysis of previous research Research on crack width Research on Schiphol tunnel Research on early-age cracking Research on crack formation in structural slabs on underwater concrete Conclusions from previous research Practical solutions to the problem of crack formation Cooling of concrete Extra reinforcement An intermediate layer of sand Injection of cracks Concluding remarks Problem definition and methods Models for determination of stresses vii

8 3.1 Model 0: stress calculation Model 1: ambient temperature Theory on heat flow Theory on heat balance Calibration of the model Magnitude of the ambient temperature Model 2a: temperature load, theory Theory on temperature distribution Theory on temperature load Model 2b: temperature load, modelling Description of the long term thermal model Results of the long term thermal model Model 3: theoretical degree of restraint Restraint deformation in structural slabs on underwater concrete Theory on degree of restraint Magnitude of the theoretical degree of restraint Model 4: relaxation factors Other models Shrinkage Strength development Early-age thermal stresses Concluding remarks Models for calculation of influence factors Description of the thermal model on influence factors Results of the thermal model on influence factors Height of the structural slab Height of the underwater concrete Height of the intermediate layer View factor Calculation method for the thermal load Description of the structural model on influence factors Theoretical restraint with an intermediate layer of sand Shear deformation and stress Properties of the model Results of the structural model on influence factors Number of piles in the grid Pile type Height of the structural slab viii

9 4.5.4 Height of the intermediate layer Shear forces in the piles Calculation method for the degree of restraint Concluding remarks From research to practice The probability of crack formation Theory of calculation Values for the probability and safety factor Calculation example Measures for crack handling Cost of measures for crack handling Implications of the measures Costs of measures based on implications Calculation example Efficiency of measures for crack handling Measure for reduction of theoretical restraint and temperature load Measures for reduction with an intermediate layer of sand Measures used in practice Conclusions and calculation method Conclusions Calculation method Recommendations Literature Appendix 1: Appendix 2: Appendix 3: Appendix 4: Appendix 5: Appendix 6: Appendix 7: Appendix 8: Appendix 9: Appendix 10: View factor Calibration of the model Structural properties of Gewi+ Results of thermal model Results of structural model Hand calculation Calculation method Eurocode Probabilistic calculations Cost calculation method Temperature data ix

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11 1 INTRODUCTION Since the 1960 s in the Netherlands underwater concrete is mostly used for building below groundwater level. The underwater concrete is a temporary structure and serves as a horizontal closure of the cofferdam. On top of the underwater concrete, the structural slab can be built in a dry environment. Structural slabs on underwater concrete are widely applied in the construction of tunnels, parking garages, rail- and road construction. The structural slab has to be watertight to guarantee durability. Other problems arise when a sealing layer is applied on the structural slab. For example when tarmac is applied, leaking water through the structural slab can also cause bumps in the road and repair will be necessary. Water can only enter the structural slab through cracks and crack formation in structural slabs on underwater concrete is frequently a problem. The surface of the underwater concrete varies in height, because the slab is cast under water. An intermediate layer has to be applied to smoothen the surface before construction of the structural slab. Since the introduction of structural slabs on underwater concrete the intermediate layer material was always sand. Besides smoothening of the surface, sand also offers the possibility to drain water leaking from the underwater concrete. However, a sand layer can result in high shear forces on the foundation piles. In the early 1990 s the technique for construction of underwater concrete slabs had improved and a sand layer was no longer necessary to drain water. In some projects the sand layer was replaced by concrete. For a concrete intermediate layer less excavation is needed and also shear forces in the piles are lower. The advantages of a concrete intermediate layer created a new method in construction of structural slabs on underwater concrete. The problem of crack formation Over the years many problems have been reported with aquiferous crack formation in structural slabs on underwater concrete. Groundwater can enter the structure by through cracks in the structural slabs. Through cracks can be the result of restrained deformation. Temperature- and shrinkage strains that are restrained, cause stresses in the structural slabs. Stresses from restrained deformation can cause through crack formation. During the hardening process and due to climate influences, the structural slab is affected by temperature- and shrinkage loads and cracks can form. When cracks are aquiferous, they become visible at the surface. However, the 11

12 surface can be dirty and the groundwater pressure is lowered during construction. This makes visibility of cracks low. It is therefore often uncertain whether through cracks have been formed during hardening or due to climate influences. Research has been done on crack formation in structural slabs on underwater concrete. With the rise of the construction method of the concrete intermediate layer Den Boef (1996) found the mechanism of restrained deformation to be responsible for through crack formation. Later CUR commission VC71 tried to formulate a practical advice for handling of through crack formation. Because of a lack of practical data, VC71 was unable to succeed. In practice many solutions are tried to solve the problem of crack formation. In the design of structural slabs on underwater concrete, much attention was given to the calculation of stresses and calculation of reinforcement, but still aquiferous crack formation cannot be prevented. Over the years many discussion on the effect of an intermediate layer of sand has taken place amongst experts. Nowadays two sides exist; one in favour and the other against an intermediate layer layer of sand. Both sides are convinced that their alternative outperforms the other. The truth is that no theoretical bases, but many uncertainties, exist about the magnitude of the stresses in structural slabs on underwater concrete. Aim of the research This research aims to create more insight in the forming of cracks in structural slabs on underwater concrete. The results should be used to come to a practical advice for prevention of crack formation. The main question is: What is the influence of different factors on the stresses that can cause through crack formation in structural slabs on underwater concrete and can a practical advice be given for the handling and prevention of through crack formation in structural slabs on underwater concrete? To answer this question, first the current state of the technology is examined. A literature study combined with interviews with experts resulted in a clear view on the problem. The results of the literature study have determined the focus of the research. A model has been developed to calculate the stresses. The magnitude of the influence factors on stresses is determined in separate models. The results of all models are combined to calculate the stresses in structural slabs on underwater concrete. To come to a practical advice, the results of the model for stress calculation are used to determine the probability of crack formation. For prevention of crack formation measures have been found. The effect of the measures is determined in the reduction of the probability of crack formation and the cost of the measures. To widen the scope of this research, the construction principle of structural slabs on underwater concrete is analyzed. The results are therefore valid for any form of application of structural slabs on underwater concrete. Structure of the report In chapter 2 the problem of crack formation is analyzed. The properties of through crack formation, the results from previous research and the handling of crack formation in current 12

13 practice is explained. Based on this analysis the final problem description and the focus of this research are presented in section 2.5. The models needed for stress calculation are described in chapter 3. This chapter starts with the model for stress calculation. Every section covers a model that determines the magnitude of one of the influence factors on the stresses. For the temperature load and the degree of restraint of deformation, several influence factors are identified. In chapter 4 the modelling of the influence factors on temperature load and degree of restraint are explained. A description of the different structural variants for both models and the results of the modelling complete this chapter. A step-wise calculation method is given to be able to calculate the stresses in structural slabs on underwater concrete. In chapter 5 the step is made from the results of the research to the practice. Based on the stresses a calculation method for probability of crack formation is given, including an example. A cost calculation method with example is also presented here. The conclusions and the total calculation method for the probability of crack formation are presented in chapter 6. The conclusions from literature research and models result in practical advices that are the first part of the conclusions. The second part is a step-wise approach for calculation of the probability of crack formation based on the geometry and structural variant. The method of cost calculation of measures for prevention of crack formation is summarized here. Recommendations on future research finalize the report in chapter 7. 13

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15 2 ANALYSIS OF THE PROBLEM OF CRACK FORMATION Structural slabs on underwater concrete are applied in the construction of tunnels, parking garages, rail- and road construction below surface level. Crack formation is frequently a problem in these structures. For this research, not the application, but the principle of structural slabs on underwater concrete is researched. Different structural alternatives exist for structural slabs on underwater concrete. In this chapter the results of a literature study and interviews are presented. In section 2.1 the building method and common structural variants are shown. Section 2.2 covers the causes of crack formation. To define the scope of the problem and the current state of technology, sections 3 and 4 analyze the theoretical research and the practical solutions that exist to counteract the problem of crack formation. The chapter finalizes with the conclusion from the literature study and the research questions and methods for this research. 2.1 Description of structural slabs on underwater concrete In this section the building method and different variants of structural slabs on underwater concrete are presented Building method When building below groundwater level, in the Netherlands mostly underwater concrete is used. Construction starts by drilling the sheet piling and excavating the cofferdam. In the cofferdam the water remains and the underwater concrete is cast below the groundwater level at the bottom of the cofferdam. The underwater concrete serves as a temporary structure as a horizontal closure of the cofferdam. On top of the underwater concrete, the structural slab can be built in a dry environment. This is illustrated in Figure 1. The underwater concrete is executed under the water level, which makes it complicated to create a perfect level floor. Typically the underwater concrete has variations in height at the top of around 10 cm in height, Figure 2. Therefore, the floor is levelled out by an intermediate layer, which can consist of sand, gravel or concrete. On top of the underwater concrete and intermediate layer the final structural slab is built. The building method is illustrated in Figure 1. 15

16 Figure 1: building method of structural slab on underwater concrete: top left) placement of vertical closure of cofferdam, top middle) excavation of cofferdam, top right) placement of the tension piles, bottom left) casting of underwater concrete as temporary horizontal closure of cofferdam, bottom middle) pumping groundwater, bottom right) placement of structural slab (and potentially walls and roof) as final structure. (Betoniek: ) Figure 2: tolerances for an underwater concrete slab(cur 2001:9) Structural variants A structural slab on underwater concrete can be worked out structurally in numerous ways. The design of structural slabs on underwater concrete is dependent on the groundwater pressures. The pressure on the slabs defines the height of the slabs and the need for tension or compression 16

17 piles. Some structural variants that can be applied are shown in Figure 3. The differences between the variants can be: Type of tension piles In the figure, four different types of tension piles are shown: through prefab piles (bottom left), Gewi piles (bottom right), cut-off piles (top right) or rebars (top left). The prefab and Gewi piles are most common in construction of structural slabs on underwater concrete. The other variants are more laborious, but are sometimes applied because it is believed that it reduces the crack formation in the structural slab. Material for intermediate layer With reference to Figure 3, the intermediate layer can consist of: concrete (top left, bottom right), sand (top right, bottom left) or gravel. An intermediate layer of sand or gravel can drain water leaking through the underwater concrete, which can be advantageous during casting of the structural slab. It is also believed that an intermediate layer of sand reduces friction between structural slab and underwater concrete and thereby reduces crack formation in the structural slab. Height of structural slab and underwater concrete Not shown in the picture is that for specific projects the height of the structural slab and underwater concrete is not always the same. The geometry of the slabs is determined by the groundwater pressure, which increases with increasing depth of construction. The underwater concrete can have a height of about 1 m or even more. In parking garages, mostly thinner structural slabs are applied, around 400 mm, where in civil structures a structural slab of 800 mm is common. Figure 3: different ways of construction of structural slabs on underwater concrete (Gajaard 2007:81) 17

18 2.2 Crack formation in concrete structures Crack formation in structural slabs on underwater concrete is frequently a problem. In this section the problem of crack formation and its causes are explained The problem of crack formation The properties of reinforced concrete make it very likely that small cracks form in concrete structures and mostly this is no problem. For water retaining structures, matters are slightly different. When crack width becomes larger than approximately 0.08 mm water is able to leak into the structure. In the context of this research, crack formation is a problem when cracks become aquiferous. Groundwater that can enter the structural slab through cracks, can threaten the durability of the structural slab. Flowing water can cause corrosion to form on the reinforcement. When a sealing layer of for example tarmac is applied on the structural slab formation of blisters between the structural slab and the tarmac is possible. This causes bumps in the road and repair is necessary. Aquiferous crack formation can only occur when cracks are through. Also water can only flow when cracks are through. Only through cracks are harmful for the water tightness of the structure. The structure is said to be watertight when: The structure does not contain cracks The structure contains cracks, but no through cracks. The height of the compression zone is: - h x > 50mm - h x > 2* maximum grains size of aggregate This means that loads that cause bending can never be the cause of through crack formation, since a compression zone exists. There is also a possibility of self-healing. Self healing means that cracks that occur will close over time. Several processes can cause self healing, but also some boundary conditions are needed. Self healing will be explained later Causes of through crack formation The forming of cracks in concrete can have numerous causes. Through crack formation however can only have a limited amount of causes. Errors during construction can create leakage paths or weak spots in the concrete. In these places crack formation might be initiated, but erroneous execution cannot be the sole reason of through crack formation. For the same reasons, aftertreatment does not solve the problem of through crack formation, although it can reduce surface cracks. 18

19 For through crack formation in structural slabs on underwater concrete two main causes can be pointed out: Early-age thermal cracking can cause cracks in concrete during the hardening process. Mainly this is caused by thermal effects, initiated by the exothermal reaction of the concrete mixture. Also different shrinkage effects can cause early age cracking. Cracks in hardened concrete can be caused by fluctuations in the ambient temperature. Changes in temperature of the structural slab will cause strains in the slab. When strains are restrained, stresses build up and these can be the cause of crack formation. Restrained strains resulting from drying shrinkage can cause cracks in the same way. When analyzing these two causes, it must be concluded that the principle is the same. The reason for cracking is that deformation of the concrete, either by shrinkage or by thermal effects, is unable to take place. Both in young and hardened concrete thermal strains are obstructed. This is called restrained deformation. During hardening the structural slab will be exposed to temperature loads from the chemical reaction in the concreter mixture. After casting, the temperature of the structural slab will decrease in winter, which creates a temperature load. As a result of temperature variations, the structural slab will deform, which is to some extent restrained by the underwater concrete and the foundation piles. The restrained deformation causes stresses in the concrete which can cause crack formation. Restrained deformation and the loads that cause restrained deformation are important to quantify and much research has been done in this field Restrained deformation To understand restrained deformation, first unrestrained deformation is viewed. A temperature change in a material causes it to deform. In the case of temperature loads ΔT, the strain in the material is described by: L t c T [1] L Where ε T = thermal strain L = length of the slab α c = thermal expansion coefficient Figure 4 shows a statically determined beam that is free to shrink in the top picture. When the beam is clamped at both ends, shrinkage of the beam is restrained at the far end, shown in the bottom picture. The beam will now execute a force, which creates a reaction force of the clamping, resulting in tensile stresses in the beam. 19

20 Figure 4: free deformation versus restrained deformation; developing of forces (Breugel, Veen et al. 1998:1) A decrease in temperature of the structural slab causes shrinkage of the structural slab. When shrinkage is restraint, tensile stresses build up, which causes the forming of cracks once the stresses exceed the tensile strength. Thermal strains are transformed into thermal stresses by Hooke s law: E t t c [2] σ t = thermal stress E c = modulus of elasticity of concrete Restrained deformation in structural slabs on underwater concrete As stated above, thermal stresses can only develop when parts of the structure restrain deformation of the structural slab. In Figure 5 it can be seen how the structural slab is restrained by other parts of the structure. Restraint can be causes in two ways: End restraint (a) Axial deformation is restrained at the end of the structure. The piles, which are embedded in the underwater concrete, restrain the sections of the structural slab between the piles at it s ends. Edge restraint (b) Axial deformation is restrained at the side of the structure. The underwater concrete restrains the structural slab at it s side (bottom). This restraint is less when adopting an intermediate layer of sand (A). It is assumed that an intermediate layer of sand (A) does not restrain deformation of the structural slab. If the piles in A would have infinite stiffness, deformation in axial direction of the structural slab would be impossible, unless the underwater concrete would be deformed. The force exerted by the structural slab on the piles is transferred to the underwater concrete, which 20

21 will deform, but also restrain the deformation of the structural slab. In reality, the piles possess a shear stiffness, which makes some extra deformation possible to a certain extent. Part B of the figure shows a structural slab on underwater concrete with an intermediate layer of concrete and Gewi piles. The structural slab and underwater concrete are now a monolithic construction. The underwater concrete therefore undergoes the same deformation as the structural slab and will therefore restrain the deformation of the structural slab. Figure 5: end restraint (a) and edge restraint (b) and a comparison with the building practice (right) Because the underwater concrete, prefab piles and Gewi piles have an axial and shear stiffness, deformation of the structural slab will never be restrained completely. The stresses in the structural slab by restrained deformation are therefore: E R T E R [3] t t c c c Where R is the degree of restraint, varying from 0 to 1, or from 0 to 100%. 2.3 Analysis of previous research Previous research has tried to find a solution to the problem of crack formation in structural slabs on underwater concrete. In this section the main results are presented. Former researches on crack width in concrete structures, a practical casein Schiphol and early-age thermal cracking are viewed. The last research is one with the same objective as this one: obtaining a practical advice for handling of crack formation in structural slabs on underwater concrete Research on crack width Van Breugel (1998) states that a structure is also watertight when the structure contains through cracks, but crack width is smaller than the criterion for self healing. Self healing is the ability of the concrete to close narrow cracks over time. 21

22 Self healing in concrete structures depends on several boundary conditions (Breugel 2003). For practical use, self healing is related to the crack width. The most well known criterion for self healing was formulated by Lohmeyer. He related the crack width where self healing of the cracks is probable to the ratio of water height en structural height. The relationship is given by the purple line in Figure 6. Figure 6: representation of Lohmeyer's relation for the criterion of self healing (Breugel 2003:88) The criterion of self healing is sometimes used in the design phase of structural slabs on underwater concrete. The crack width can be calculated from the amount of reinforcement in a structure. To limit crack width to the criterion for self healing, extra reinforcement can be applied. This can result in very high reinforcement percentages, typically 1% in thick slabs. Narrow cracks do not always have to threaten the water tightness of the structural slab. The boundary conditions for self healing are uncertain and hard to achieve. So, even when the criterion of Lohmeyer is met, a water tight structural slab is not guaranteed. In practice, designing reinforcement to minimize crack width has proven to be difficult Research on Schiphol tunnel In 1996 a thesis on crack formation in structural slabs on underwater concrete has been made (Den Boef). In this thesis the causes of through crack formation were analyzed by analyzing a practical project in Schiphol, the Netherlands. This was a project where the structural slabs was applied on underwater concrete without an intermediate layer of sand. Den Boef developed a practical calculation method to calculate the restraint in structural slabs on underwater concrete with an intermediate layer of concrete. The restraint is dependent on the height and stiffness ratios of the structural slab and underwater concrete. Most important result of his research was that through crack formation in structural slab on underwater concrete can only be the result of restrained deformation. Analysis of different mechanisms of crack formation excluded external loads as a cause of through crack formation. 22

23 Temperature (deg. Celsius) Research on early-age cracking The developing material properties of young concrete have been the topic of many researches in the past. The exothermal reaction of the concrete mixture creates a temperature load in the young concrete, see Figure 7. After the maximum temperature is reached, the concrete starts to cool and shrink. Because the concrete possesses some stiffness, but considerably less than the underwater concrete, the deformation will be restrained. This results in early-age thermal stresses. Early age stresses can also be caused by shrinkage during the hardening process. 80 Temperature Monitoring - 27 Apr Time after casting (hours) Center of structural slab Figure 7: heat development in young concrete at different heights of the floor: 1 = bottom; 2 = middle; 3 = top Although the process of hardening is not yet fully understood, calculation methods exist for early-age stresses in concrete. CIRIA (Bamforth 2007) developed some hand calculation methods for early age stresses. Nowadays hardening calculations are performed using computer software packages. In the Netherlands the packages FEMMASSE (HEAT) and FeC 3 S are most common. In general, the early age stresses are predictable, but accuracy is not yet perfect. Therefore probabilistic calculation of early age stresses is performed. Values for both tensile stresses and tensile strength are assumed to be normally distributed. This means that cracks can occur when the average tensile stress is lower than the average tensile strength. For given stress/strength ratios the probability of crack formation is calculated. Also for the characteristic values of the stress and strength, a safety factor can be calculated. The same reasoning is adopted in chapter 5.1 on the value of the probability of crack formation. 23

24 Probabilistic calculation resulted in a design rule for early-age crack formation. To prevent crack formation in young concrete the tensile stresses should not exceed 0.5* tensile strength: 0 0,5 f ctm [4] Keeping in mind the criterion of [4], calculation of the early-age thermal stresses can be performed. For the calculation the geometrical properties of the structural slab on underwater concrete are known. The height of the structural slab influences heat development; thicker structural slabs will be more vulnerable to early-age thermal cracking. With the aid of computer software it can be said that the forming of cracks can be predicted with reasonable accuracy. When crack formation is likely to occur, the mixture can be adjusted. Very common is also cooling of the concrete during hardening to reduce early age thermal stresses. It can be said that much research has been done in the field of early age thermal cracking. With the aid of computer software packages and cooling it is possible to control early-age thermal cracking Research on crack formation in structural slabs on underwater concrete In 2003 a commission of CUR, VC71 (CUR 2007; Galjaard 2007), was given the task to research crack formation in structural slabs on underwater concrete. The aim of the research was to create a calculation method for the probability of crack formation in structural slabs on underwater concrete. Simple hand calculation should result in probability of crack formation in hardening and hardened structural slabs on underwater concrete. In order to find out what causes crack formation, VC71 came up with numerous possible causes of crack formation in both hardening and hardened concrete. It was assumed that the structural variant influences the probability of crack formation. Therefore a stocktaking of all factors that could possibly influence the crack formation was done. Analysis of practical cases could not point out which of the possible causes were deciding for crack formation. Still no conclusion was drawn on the most influential causes of crack formation in structural slabs on underwater concrete. Numerical calculation was also performed by VC71 (Schlangen 2004). The aim was to calculate the temperature load on structural slabs on underwater concrete and the degree of restraint. Because of the lack of temperature measurements, it was not possible to calculate the temperature load. No conclusions were drawn on the magnitude of the annual temperature load. The most important conclusion was that the temperature load caused by annual fluctuation of the ambient temperature is one of the main causes of crack formation. For the modelling of restrained deformation, models did perform well. Some possible causes of crack formation were excluded. The results of this part of the numerical situation have served as input for this research. 24

25 VC71 developed no calculation method or practical advice could be given. Although the results excluded some factors to have an influence on crack formation, the aim of the research was not reached. No possible solutions to the problem of crack formation in structural slabs on underwater concrete were given Conclusions from previous research Structural slabs on underwater concrete have been the topic of some researches. However, in current practice it is not certain what the influence factors on crack formation are. Nor is there a theoretical basis for solutions to the problem of crack formation. The following can be concluded from previous research: There is a possibility that narrow cracks self heal over time but the boundary conditions are uncertain When designing on crack width, self healing is still uncertain Crack formation in structural slabs on underwater concrete is caused by restrained deformation Based on stiffness and height the slabs, the theoretical restraint can be calculated Early-age thermal cracking can be calculated with reasonable accuracy Stresses in hardening concrete should not exceed 0.5 * tensile strength to avoid earlyage cracking The annual ambient temperature fluctuations influence crack formation The magnitude of the annual temperature load is uncertain No certainty can be given on the influence factors on crack formation 2.4 Practical solutions to the problem of crack formation In practice some solutions to the problem of crack formation have been thought of. These are: calculation of early-age stresses and cooling, extra reinforcement, an intermediate layer of sand and injection of cracks Cooling of concrete In section it was stated that research on early-age thermal cracking has lead to methods of calculation of early-age stresses. When stresses are below 0.5*tensile strength, crack formation is unlikely to occur. In practice, a system of cooling pipes can be embedded in the concrete. The cooling of concrete reduces temperature rise from the exothermal concrete mixture reaction. Thereby it reduces 25

26 early-age thermal stresses and thus the probability of early-age thermal cracking. In practice the results of cooling are good. The general consensus is that cooling will help to reduce early-age thermal cracking. There are however some disadvantages to cooling. First of all, cooling can only reduce the probability of early-age thermal cracking. These cracks are visible in within the first 10 days after casting. With cooling, early-age thermal cracking can very well be prevented. After hardening, the annual fluctuations of the ambient temperature cause temperature loads on the structural slab. These temperature loads can also cause restrained deformations and therefore crack formation. Cases are reported in which early-age thermal cracking was prevented by cooling, but cracks did occur during winter. Secondly, cooling is an expensive measure. Because cracks occur in the winter after casting, cooling does not solve the entire problem of crack formation. It is therefore sometimes believed that expenses on cooling can be saved, because cracks will form anyway. Cooling of concrete does not solve the entire problem of crack formation in structural slabs on underwater concrete. However, cooling does reduce the probability on early-age thermal cracking. When cracks have formed in the hardening concrete, this does not solve itself in a later stage. Therefore, the prevention of early-age thermal cracking should be a goal in itself and should be viewed separate from crack formation by annual temperature fluctuations Extra reinforcement For the engineer, the geometrical properties of the structural slab are determined by external loads as groundwater pressure and traffic load. The restrained deformation that causes crack formation is calculated separately. The only tool for the engineer is to add reinforcement to limit crack width. In section it can be seen that calculation on self healing has some uncertainties. This conclusion is adopted, but in this subsection the calculation method of the engineer is viewed in greater detail. Calculation of temperature load The impact of the temperature fluctuations on the specific case of structural slabs on underwater concrete has never been thoroughly researched. The temperature load can therefore only be estimated from comparable structures. Eurocode (NEN-EN ) gives calculation methods for summer and winter temperatures of structural elements (article 5.3) and temperature profiles of bridges (article 6). CIRIA (Bamforth 2007) states that slabs will have an annual temperature fluctuation of 20 C when cast in summer and 10 C when cast in winter. Both calculation methods can only result in rough estimations for the temperature loads in structural slabs on underwater concrete. For calculation of temperature loads on structural slabs on underwater concrete two basic outlines of the calculation method exist: 1) the first philosophy is that the structural slab is 26

27 Temperature (degrees) subjected to an annual temperature change and that the temperature of the underwater concrete is constant, 2) another method gives minimum temperatures for slabs below surface level. The level of the structural slab and the underwater concrete differ and so does the minimum annual temperature. The difference between these temperatures and a pre-specified (estimated) reference temperature is the temperature load. Both approaches are however flawed and below it is explained why. Figure 8 shows temperature measurements at different heights of the structural slab and underwater concrete, performed on an actual structure in Abcoude Based on this temperature measurement it can immediately be concluded that the temperature of the underwater concrete (purple line) is not constant. The first method of calculation of temperature loads is therefore inaccurate Jul-04 4-Aug Aug Sep-04 3-Oct Oct Nov-04 SS top SS middle INT UWC middle Figure 8: Temperature measurements for various heights in structural slabs on underwater concrete. Abcoude 2004 Figure 9 shows a calculation of the average annual temperatures of the structural slab and underwater concrete, based on the measurement. From this figure it can be seen that the average ambient temperature is closely related to the average temperature of the structural slab. However, calculation with the average temperature excludes extremes and therefore underestimates the temperature load. The temperature load can be seen as a change in temperature between casting (reference) and some extreme. Temperature changes can be calculated from a reference temperature, but this temperature should have a close relation to the month of casting. 27

28 Temperature (degrees) Average temperature (degrees) 20,0 15,0 10,0 5,0 0,0 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC T AVG SS T AVG UWC T AVG KNMI Figure 9: Average monthly temperatures of the structural slab, underwater concrete and ambient temperature. In Figure 10 the average temperatures over 1 year are shown for both structural slab and underwater concrete. It can be seen that temperature effects in the underwater concrete are somewhat delayed. The maximum annual temperature of the structural slab (1) is reached some weeks before the maximum temperature of the underwater concrete (2). When calculating the temperature load from the temperature differences between structural slab and underwater concrete (method 2), comparing the extremes of both slabs does not result in the actual temperature load. The maximum difference occurs in this case at the time when the structural slab reached maximum temperature. Lines 3 and 4 indicate the time at which moment the minimum temperatures of the structural slab (3) and the underwater concrete (4) are reached Time (days) Temp UWC avg Temp SS avg Figure 10: analysis of annual temperature difference between structural slab and undewater concrete; dots indicate max (red) and min (blue) values of the annual temperature. Lines indicate max difference in temperature between the slabs 28

29 From the above it should be clear that a new way of temperature load calculation should be developed. In chapter 3.3 the philosophy of temperature load calculation that is used in this research is explained. Calculation of degree of restraint The degree of restraint is very uncertain and this can best be seen by looking at examples in literature. Eurocode presents different factors of restraint. As discussed in section these are end- and edge restraint. Figure 11 shows the restraint factors in a particular case. The values for restraint include relaxation. It can be seen that the factor for restraint and relaxation combined is maximum 0.5. At some distance from the restraining member, the edge restraint goes to zero, but end restraint stays 0.5. The restraint is not specifically mentioned for the case of structural slabs on underwater concrete. Figure 11: Factors for the degree of restraint according to Eurocode NEN-EN ; ANNEX L CIRIA (Bamforth 2007) takes a closer look into several sources. Figure 12 shows difference in degree of restraint for several sources. Apart from the difference per source, not one of the cases specifically mentions structural slabs on underwater concrete. Both examples show that the degree of restraint is far from certain. Besides that, also the CIRIA argues the methods of crack width calculation from Eurocode. Without going into more detail it can be stated that calculation of crack width itself is uncertain ànd the degree of restraint is uncertain. 29

30 Figure 12: Restraint values according to different sources (Bamforth 2007:63) The role of early-age stresses In section it was stated that early-age thermal cracking can nowadays be prevented. Calculation methods exist to make sure that in practice the stresses do not exceed 0.5*f ctm. For engineering purposes it is assumed that stress relaxation reduces the influence of early-age stresses to zero in hardened concrete. German researchers have argued the fact that early-age stresses disappear by stress relaxation (Rostasy, Laube et al. 2006). In their research, stress measurements have been performed on a structural slab on underwater concrete in a tunnel in Berlin. The conclusion was that months after casting the tensile stresses from hardening are still present. For calculation of stresses in structural slabs on underwater concrete it should be born in mind that the first winter after casting is deciding for restrained deformation. The annual temperature load can be highest in any winter, but relaxation of early-age thermal stresses is least in the first winter. In current design methods this is not taken into account. The assumption that early-age stresses disappear seems not to be valid An intermediate layer of sand In the early days of structural slabs on underwater concrete an intermediate layer of sand was always applied to drain water leaking from the underwater concrete. In the early 1990 s, the techniques of constructing structural slabs on underwater concrete had improved to such an extent that the need for an intermediate layer for drainage was no longer there. Also the discussion was going on about the shear forces in the piles. With an intermediate layer the shear forces in the piles are high and without an intermediate layer shear forces are close to zero. From 30

31 this point on discussion amongst experts started on the effect of an intermediate layer of sand. By now experts are either in favour or against an intermediate layer. Both sides are convinced that they are right. The main arguments in favour of an intermediate layer of sand are: The degree of restraint is less with an intermediate layer Drainage of leaking water is still necessary to assure good quality When cracks occur, one wide crack will form, which is easy for repair The main arguments against an intermediate layer are: The piles will fail in shear with an intermediate layer Restraint is not reduced; cracks form also with an intermediate layer Cracks are wider with an intermediate layer; more reinforcement is needed to limit crack width An intermediate layer is more expensive The main reason to support construction with or without an intermediate layer is the success of past projects. When someone has constructed a project without an intermediate layer and no cracks were found, he or she is convinced of this construction method. Of course, this also works the other way around. Both sides are however convinced that their right, but no theoretical basis exists Injection of cracks When cracks occur, repair can be performed by injection of the cracks. This is a simple and effective measure to overcome formed cracks. Injection is also fairly affordable. When crack width is small, which can be the case when much reinforcement is applied, injection becomes more laborious and more expensive. When cracks are very narrow, but just enough to become aquiferous, injection can even be impossible. Some project managers think of the possibility to take no measures in crack prevention, but inject afterwards. In this was an economical optimum is reached they believe. It must be noted that, even though economics of a project is very important, the problem of crack formation is not solely an economic optimization. When choosing to accept cracks and taken repair costs for granted, some other issues start to play a role. First of all, repaired cracks can reopen; the cause of crack formation, temperature load, isn t affected by injecting cracks. Injection is a very precise job, in which errors can be made. Also, once cracks have been repaired, new cracks can be formed in another cold period. The cold period can come in any time, which could be in the second winter when for example tarmac can already be applied. This raises more problems for repair than just injection. It can thus be said 31

32 that technical problems are also to be considered when opting for economical solutions for crack formation. There is also the problem of performance of the contractor. When a structural slab on underwater concrete is delivered with cracks, this will not add to the professional image of the contractor. Even though the structure may be perfectly safe and durable, cracks in concrete do worry the project owner. To avoid bad publicity it can therefore be best to spend some money on crack prevention, rather than repair Concluding remarks Some project managers argue to do nothing against crack formation, because it is inevitable. Instead, they argue, let cracks form and inject afterwards; this will be the cheaper solution. Projects are known where weak spots have been created in the structural slab, to control the number of cracks and be able to repair them easily (Mortier and Tuunter 2002). Whether cracks form seems to be a random event and thorough calculation seems to have only little influence. The conclusions from practical measures are: Prevention of early-age thermal cracking is possible with cooling of hardening concrete The criterion for self healing does not guarantee a watertight floor when designing on critical crack width Calculation of stresses from restrained deformation is uncertain, which makes calculation of crack width uncertain The temperature load caused by annual fluctuations of the ambient temperature is uncertain. The degree of restraint for structural variants is uncertain The relaxation of early-age stresses is uncertain Practical arguments exist in favor and against an intermediate layer of sand; much discussion amongst experts exist. There is equally less theoretical basis in favor or against an intermediate layer of sand Injection of cracks can be a good solution, but the decision should not be based on economical criteria only. Many uncertainties exist in the design of structural slabs on underwater concrete. Many arguments exist in favor or against design methods and structural variant. A theoretical basis is lacking so far. It is therefore time for objective arguments in the discussion on crack formation in structural slabs on underwater concrete. This research aims to gain more insight in the influence factors on the stresses that follow from restrained deformation. 32

33 2.5 Problem definition and methods Given the uncertainties that followed from literature study and are described above, the main question of this research is: What is the influence of different factors on the stresses that can cause through crack formation in structural slabs on underwater concrete and can a practical advice be given for the handling and prevention of through crack formation in structural slabs on underwater concrete? The research focuses on only the stresses in the hardened concrete. It is assumed that early-age thermal stresses can be calculated using computer software and prevented by cooling of the structural slab. To answer the main question, the report takes several steps to support the final answer. The sub questions are: 1. How can the stresses be calculated? 2. What is the influence of different factors on the magnitude of the stresses? a. What is the magnitude of the temperature load? b. What is the degree of restraint? c. What is the magnitude of relaxation? d. What is the magnitude of shrinkage? e. What is the development of strength of hardened concrete? 3. What is the influence of different factors on temperature load? 4. What is the influence of different factors on the degree of restraint? 5. What is the order of magnitude of the shear stresses in the piles? 6. Which practical measures can be used to reduce the stresses? 7. What is the probability of crack formation for given stresses? 8. What are the costs of measures to reduce the probability of crack formation? 9. What practical advice can be given? To answer these questions several methods have been used. The method of stress calculation and the influence factors were obtained from literature, mainly Eurocode. The factors for which uncertainty is large, temperature load and restraint, Finite Element Method (FEM) modelling is performed using ANSYS (Macrovision Corporation 2003). In these models a representation of the structural slab on underwater concrete is made and used for analysis of the influence factors on temperature load and restraint. Modelling of temperature load The thermal model calculates temperatures in the structural slab and underwater concrete. Inputs are the ambient temperatures, retrieved from historical data of the KNMI. The model was calibrated based on long term temperature measurement in Abcoude, The KNMI data are 33

34 hourly temperature and radiation values from which the annual fluctuations in the structural slab and underwater concrete can be calculated. Based on the long term temperature measurement and historical data of KNMI the magnitude of the temperature load is calculated. A reference case is established with the geometry that is common in practice. For the reference case of 20 years ( ) of temperature data are modelled. In this way an average temperature load and its extremes have been estimated. To determine the influence of the structural variant on temperature load thermal modelling of the influence factors is performed. Input for the model on influence factors is one year of temperature data, which has values corresponding to the long term average. In this way the values of the annual temperature load for different geometries can be compared to the reference case. The difference in temperature load from the reference case determines the relative influence of the geometry. Modelling of the degree of restraint For the restraint theoretical calculation models exist. A 2-D structural model is first performed to check the results of the model according to the theory. The theoretical restraint serves as a basis for the calculation of the influence factors on restraint. In a 3-D calculation model the influence factors on restraint are calculated. This concerns only a possible reduction in restraint by application of an intermediate layer of sand. Sand is assumed to have zero stiffness. Reduction in restraint is expected because the structural slab is more free to deform. The reduction in restraint with respect to the theoretical restraint determines the influence of the structural variant. The influence of different factors is measured in a reduction percentage from the theoretical restraint. Practical advice For practical use of the methods and results from this research, the probability of crack formation has been estimated. The probability of crack formation is calculated based in the ratio of tensile stresses and strength. Different practical measures are found, based on their ability to lower stresses in the structural slab. The cost of reduction measures, together with the possible reduction in the probability of crack formation determines the efficiency of the measures. Based on the efficiency of the measures a practical advice was obtained. 34

35 3 MODELS FOR DETERMINATION OF STRESSES Stresses in structural slabs on underwater concrete caused by restrained deformation have many influence factors. In this chapter models are developed to analyze all influence factors. Models can be theoretical, based on literature, or computer models. All influences are combined in the model for stress calculation, this is called model 0. Model 0 is presented in section 3.1. For the thermal load several models are needed (model 1, 2a, 2b) and these are discussed in sections 3.2 to 3.4. Model 3 determines the theoretical degree of restraint in 3.5. Relaxation and other models for the influence factors on stresses are given in 3.6 and 3.7. Concluding remarks give an overview of the models in section Model 0: stress calculation The previous chapter explained how restrained deformation of temperature loads causes stresses in the structural slab. The stresses are composed of early-age thermal stresses and stresses caused by annual temperature fluctuations: t 0 t [5] Where σ(t) σ 0 σ t = stresses in the structural slab at time t = early age thermal stresses = stresses caused by annual temperature fluctuations Also stress relaxation and shrinkage play an important role in the determination of the magnitude of stresses. A graphical representation of all influence factors on stresses in structural slabs on underwater concrete is given in Figure 13. The input for stress calculation follows from models described in this chapter. For all factors of the figure, the magnitude is defined and stresses can be calculated. For all influence factors on stresses models have been composed for calculation. The results of the models serve as an input for the stress calculation model. 35

36 stresses in structural slabs on underwater concrete relaxation early-age streses relaxation thermal strain shrinkage strain modulus of elasticity degree of restraint Figure 13: schematical representation of stress calculation The equation format for the stresses is given by Van Breugel (1998): 0 0 i c 0 t t, t t, t T t, t E( t) R [6] Where: ψ(t,t 0 ) = relaxation factor for early-age thermal stresses ψ(t,t i ) = relaxation factor for stresses caused by annual temperature fluctuations α c = coefficient of thermal expansion (10*10-6 K -1 ) ΔT = temperature load caused by annual temperature fluctuations ε(t,t 0 ) = shrinkage; both drying and autogenous shrinkage E = modulus of elasticity R = degree of restraint Equation [6] determines the magnitude of the stresses. The input of equation [6] follows from the models created in this research. The influence factors are calculated in this chapter as: Temperature load in model 1 and 2 in sections 3.2 till 3.4 Degree of restraint in model 3 in section 3.5 Relaxation in model 4 in section 3.6 Shrinkage, E-modulus and early-age stresses in other models in section 3.7 Relaxation and shrinkage are dependent on the time at which the load is considered, t, and the age of the concrete at loading, t 0 or t i. The difference between t 0 and t i is explained in section

37 3.2 Model 1: ambient temperature The ambient temperature is influence by many factors. An introduction on heat flow and heat balance should give a better understanding of the determination of the ambient temperature Theory on heat flow In Figure 14 the heat flow through a structure consisting of different materials is visualized. It is indicated that a heat flow is caused by a temperature difference on both sides of the structure. The heat flow through the structure is constant (q 1 =q 2 =q 3 ). Figure 14: heat flow through a medium (Cauberg, Van der Spoel et al. 2004:4) In structural slabs on underwater concrete, the temperature T 1 can be seen as the ambient temperature. T 3 is then the temperature of the soil. The layers 1 and 2 are structural slab and underwater concrete respectively and the intermediate layer can be added between the two. The heat flow in structural slabs on underwater concrete is visualized in Figure 15. When the thermal properties of the concrete, intermediate layer and soil are known, the heat flow through the structure can be calculated. The following equation holds for constant heat flow through a material (Figure 14): q dt T T T T [7] dx d1 d2 Where λ = conduction coefficient of concrete (W/mK) 37

38 Figure 15: heat flow through structural slabs on underwater concrete Fourier found a differential equation that describes the heat flow in a medium. For time varying temperature loads, simplified to a 1-dimensional heat flow, Fourier s equation is: 2 T T c 2 x [8] Where, for structural slabs on underwater concrete: T/ τ = heat generation over time T/ x = heat flow through the material q = heat flow through the slabs (W/m 2 ) c = heat capacity of the concrete (J/kgK) ρ = density of the concrete (kg/m 3 ) λ = conduction coefficient of concrete (W/mK) Time varying loads are best calculated using computer software, which use equation [8] as a basis for calculation. The ambient temperature (see Figure 15) is a time varying load and will be calculated using models. 38

39 3.2.2 Theory on heat balance From climate data of the Royal Netherlands Meteorological Institute (KNMI), the ambient temperature can be calculated. The temperature of the surface, T 0, is unequal to the ambient temperature. The ambient temperature does influence the surface temperature, but also radiation plays a role. Radiation can be solar radiation, but also radiation from the surface to the sky. The surface temperature is equal to the ambient temperature + radiation. The heat balance of a structure looks like the left part of Figure 16. The heat flow in the material is q i and is constant through the structure. The surface temperature determines the amount of heat flowing into the material. Figure 16: graphical representation of the heat balance (left) brought back to temperature load T SAT (Cauberg, Van der Spoel et al. 2004:13) In the heat balance of Figure 16 the reflected solar radiation r z q z, does not add heat to the structure. Therefore, with reference to lectures on building physics (Cauberg, Van der Spoel et al. 2004), in equation form the heat balance can be written as: a q q q T q [9] 4 z z c i 0 0 atm a z q z q c q i q atm ε 0 σ T 0 = absorption coefficient of concrete * solar radiation = convective heat flow = heat flow inside concrete of structural slab = downwelling atmospheric radiation = emission coefficient = Stephan Boltzman constant = structural slab surface temperature For q atm empirical relations are known: 39

40 atm 4 e q T a b p [10] Where: T e p = outside air temperature = measure for humidity a, b = empirical constants Rewriting the heat flow q c in terms of temperature difference yields: c c 0 e q T T [11] Introducing the heat transfer coefficients α c and α s results in: T T a b p T T T a b p [12] e s 0 e e 1 After linearization of fourth order terms [9] becomes: a q T T q T T T a b p [13] z z c e i s e e α c and α s can be combined in a total heat transfer coefficient α e, yielding: a q T T q T a b p [14] z z e e i e Where: α e = transfer coefficient, dependant on wind speed The term T e4 1 a b p is the so called extra radiation to the sky, which is averaged for the Dutch climate as 100 W/m 2 (Cauberg, Van der Spoel et al. 2004:14). This is a rather coarse approximation, but has proved to work for this research. Further research should clarify whether the upwelling radiation should be adapted. Sol Air Temperature From the heat balance the Sol Air Temperature (SAT, see Figure 16) can be calculated. This is the equivalent air temperature where radiation is taken into account. Calculation of the SAT makes it possible to perform temperature modelling with only the SAT as input. The SAT is defined as: 40

41 T T q [15] e SAT 0 i Which makes [14]: T SAT aq z z 100 Te [16] e View factor The structural slab is located below surface level and will be shaded for part of the day. Solar radiation is therefore not always 100% of the incoming solar radiation. Radiation travels between surfaces with different temperatures. Part of the radiation from the structural slab is to the sheet piling which had about the same temperature as the structural slab. Only a part of all that is visible, is the sky. This is indicated in Figure 17. The sky is the only surface that has a different temperature than the surface of the structural slab. Radiation therefore only takes place between the structural slab and the sky. This is only part of the possible radiation. The view factor φ accounts for this part of the total radiation. The view factor is applied in physics to calculate the influence of radiating surfaces on one another. In Figure 17 φ A is the view angle at point A. The view factor is: A 180 [17] Figure 17: view factor; from point A only part of what one can 'see' is the sky For two opposed rectangles (Figure 18) for example the structural slab and the open part of the cofferdam, the view factor is calculated by the graph of Figure 18. In Appendix 1 the calculation for the view factor is described. Calibration showed that the view factor corresponding to the measurements is 0.3. More shallow and wide structural slabs on underwater concrete have higher view factor. For structural slabs on underwater concrete it is assumed that for the view factor it holds: 0.2 φ 0.8. (Appendix 1) 41

42 Figure 18: view factor calculation from graph for two identical opposed squares; for example structural slab and sky (Van der Spoel 2009) Ambient temperature The ambient temperature, T amb is a combination of the SAT and the view factor: aq z z 100 Tamb Te [18] e From historical KNMI data, the outside air temperature T e and the intensity of the solar radiation, q z can be retrieved. KNMI measures these data every hour. T amb is further defined by the constants a z, φ and α e. Theoretical values for these constants can be calculated. For this research, measurement data from a structural slab on underwater concrete constructed in Abcoude are available. The actual values for the constants determining T amb, can be determined with calibration to the values of the measurement in Abcoude Calibration of the model For the calibration of the model, one long term temperature measurement over the height of a structural slab on underwater concrete was available. The measurement was taken from July 2004 November 2004 on a site in Abcoude, the Netherlands, see Figure

43 Temperature (degrees) Jul-04 4-Aug Aug Sep-04 3-Oct Oct Nov-04 SS top SS middle INT UWC middle Figure 19: temperature measurement in a structural slab on underwater concrete in Abcoude 2004 These measurements have been reproduced by a 2-D Finite Element thermal model. The methods are described in appendix 2. Because in Abcoude the intermediate layer was made of concrete, an estimation had to be made of the material properties of an intermediate layer of sand. It is assumed that an intermediate layer of sand has the same thermal properties as the soil. Calibration of the material properties and the properties of T amb results in the values for the constants as presented in Table 1 and Table 2: Table 1: thermal material properties of different layers used in the thermal model Parameter Concrete Concrete Sand SS UWC and INT INT and soil c (W/mK) λ (J/kgK) 2,6 2,0 1,25 ρ (kg/m 3 ) Table 2: properties of the ambient temperature in the thermal model Parameter Value a (-) 0.9 α e (W/m 2 K) 17,2 φ (-) Magnitude of the ambient temperature The ambient temperature is described in the previous sections. The relations and values for different constants fully determine T amb. KNMI data can be used to determine the values of T amb. 43

44 Temperature (degrees) Figure 20 shows typical values for the hourly values of the T amb. T amb varies roughly between -20 C and 50 C, for a view factor of SAT Time (days) Figure 20: Sol Air Temperature for march march Model 2a: temperature load, theory The ambient temperature leads to a temperature distribution in the concrete. This distribution causes a temperature load, which serves as the input for stress calculation (eq. [6]) Theory on temperature distribution Because of the temperature difference on both sides of the structure (ambient temperature and soil temperature) the heat flow causes temperature differences in the concrete. Because the ambient conditions are time dependant the temperature distribution will vary over time. The temperature distribution in a structure is described as a temperature difference from a specified reference temperature and can be divided in three parts (Breugel, Veen et al. 1998): Average temperature difference Temperature gradient Eigen-temperature difference The different distributions are visualized in Figure 21. Below an explanation is given. 44

45 Figure 21: temperature distribution: ΔT=temperature load; ΔTgem=average temperature difference; ΔTb=temperature gradient; ΔT e =eigen-temperature (Breugel, Veen et al. 1998:32) Average temperature difference ΔT avg The average temperature difference is a uniform temperature difference, which causes uniform thermal strain. ΔT avg therefore causes only axial deformation of the structure. The influence of the average temperature difference is described in section Temperature gradient, ΔT b The gradient is a temperature difference between top and bottom of the structure. The temperature gradient ΔT b causes the structure to bend, because thermal strains over the height of the structure are unequal. A temperature gradient therefore causes only rotational deformation (see Figure 27 in section 3.5.1). Figure 22 shows three different temperature loads, where the temperature load is composed of and average load ΔT avg and a temperature gradient ΔT b. The temperature distributions are such that ΔT avg is the same for all three temperature loads. Also a critical temperature load ΔT critical is indicated (dotted line), which should not be exceeded. It can be seen that in both top (ΔT b positive) and middle picture (ΔT b negative) only part of the cross section exceeds the critical temperature load. In the bottom picture (ΔT b =0), the critical temperature load is reached in the entire cross section. This is therefore the deciding case. 45

46 Figure 22: three different temperature distributions with the same average temperature load; the uniform distribution (bottom) is critical Eigen-temperature difference ΔT e The sum of eigen-temperatures over the cross section is zero. Eigen-temperatures cause eigenstresses, which do not result in deformation and are levelled out within the cross section. For this research, eigen-temperature is not considered, since no deformation is caused by it Theory on temperature load It should now be evident that for the temperature distribution that causes stresses, only the average temperature difference ΔT avg is most important. A difference in average temperature of a structure causes uniform thermal strains and therefore axial deformation. When axial deformation is restrained, stresses will develop. The temperature load is defined as only the average temperature difference, measured from a starting point. The stresses that develop from a temperature load depend on the degree to which deformation is restrained. 46

47 The underwater concrete restrains the deformation of the structural slab because changes in ambient temperature affect the underwater concrete less. The annual fluctuations in ambient temperature cause lower ΔT avg in the underwater concrete than in the structural slab. Figure 23 shows a structural slab on underwater concrete with axial deformations caused by a temperature load in dotted lines. Figure 23: deformation of the structural slab on underwater concrete by different temperature loads The structural slab is deformed by a load ΔT avg = ΔT 1 and the underwater concrete deforms by temperature loads ΔT avg = ΔT 2. Deformations are Δx 1 and Δx 2 respectively. When ΔT 1 = ΔT 2, Δx 1 = Δx 2 ; deformation of the structural slab is the same as the deformation of the underwater concrete. This is the same as a situation of free deformation. One could also say that there is no temperature load that can be restrained. In other words: when ΔT 1 = ΔT 2, the temperature load on the structural slab is 0. When ΔT 2 = 0. no deformation in the underwater concrete takes place and therefore all of the deformation Δx 1 of the structural slab can be restrained. In this case, one could say that the load on the structural slab that can be restrained is ΔT 1. In general, only the difference in temperature load on the structural slab and underwater concrete is the actual temperature load on the structural slab. T T T 1 2 T T T SS UWC [19] To know what the temperature difference is, two parameters must be known: What is the initial temperature condition? What is the final temperature condition? This means that for both the structural slab and the underwater concrete, the starting and final conditions should be defined. To this end [19] can be rewritten as:,,,, T T T T T T T SS UWC SS final SS start UWC final UWC start 47

48 And the next step is:,,,, T T T T T T T [20] SS final UWC final SS start UWC start final start The starting condition, ΔT start is the temperature difference between the structural slab and the underwater concrete at the moment of casting. Therefore the starting temperature difference is called ΔT cast and is dependent on the month of casting. The final condition is the moment at which the temperature difference is largest. This is at a certain moment in winter where the structural slab is much colder than the underwater concrete. The minimum temperatures in winter cause the largest temperature difference between the structural slab and underwater concrete and therefore the final condition is called ΔT min. ΔT min is the value of the maximum temperature difference in winter. The temperature load that causes tensile stresses in the structural slab is now defined as: T T T [21] min cast Now that the method of calculation of the temperature load is known, the value of the temperature load can be determined. 3.4 Model 2b: temperature load, modelling Now that the theory behind the temperature load is explained, the magnitude has to be calculated. For the modelling of the temperature load a Finite Element model is made. The model in this section calculates the temperature load for a reference case. In chapter 4 the influence of the geometry on the temperature load is calculated in a separate model Description of the long term thermal model Goal of the model This thermal model is used to accurately determine the magnitude of the temperature load for a reference case. Based on 20 years of data from the Royal Netherlands Meteorological Institute (KNMI) the long term average values of ΔT min and ΔT cast are calculated. Also the values of the temperature gradient are estimated. The long term thermal model results in representative values of the temperature load for the reference case. Build up of the model For the thermal model, 1-D heat conduction is assumed caused by a temperature difference between the ambient temperature and the soil. The FEM model is only 1 m wide, since this 48

49 reduces the number of elements and therefore calculation time. The geometry in the model consists of the following layers: Structural slab Underwater concrete Intermediate layer of sand Soil: depth 10 m The soil influences the temperature distribution considerably and can therefore not be neglected. Below 10 meter depth the soil temperature can be assumed constant. From tests that it has followed that the material properties of the intermediate layer did not affect the temperature distribution to a large extent. The influence of the piles is negligible and these are therefore not included in the thermal model. The reference case for the temperature load has the following geometrical properties: Height of the structural slab 800 mm Height of the underwater concrete 1000 mm Height of the intermediate layer 200 mm View factor NODAL SOLUTION A representation STEP=1 of the model is shown in Figure 24, where the width of the model 14:21:59 is enlarged. SUB =6 TIME=1 TEMP RSYS=0 SMN =9 SMX =20 (AVG) MX AUG MN Figure 24: temperature distribution in a structural slab on underwater concrete with 10 m soil. Colours indicate equal temperature blue is cold, red is warm. The temperature variations in the soils are less severe, but non-zero Boundary conditions The material properties of the model are calibrated to follow the measurements performed in Abcoude. Also the view factor is estimated by calibration of the surface temperatures calculated 49

50 from data of the KNMI. Appendix 2 describes the entire process of calibration. The material properties and properties of the thermal load are presented in Table 3 and Table 4. Table 3: thermal material properties of different layers used in the thermal model Parameter Concrete Concrete Sand SS UWC and INT INT and soil c (W/mK) λ (J/kgK) 2,6 2,0 1,25 ρ (kg/m 3 ) Table 4: properties of the temperature load T amb in the thermal model Parameter Value a (-) 0.9 α e (W/m 2 K) 17,2 φ (-) 0.3 The model is calibrated for the measurements at Abcoude. The model is therefore based on this single measurement only, which makes verification based on new measurements necessary to confirm the reliability of the results. Input for the model The input for the long term model is 20 years of KNMI data. These data are hourly ambient temperature values and solar radiation. From these values the ambient temperature was calculated and this was input in the FE model. With 20 years of data long term characteristic values can be obtained for the temperature load. Realistic initial conditions are obtained by starting running the model from March of the starting year until April of the following year. The first March is not included in the results. In this way the nodal temperatures are able to respond to the ambient conditions and initial conditions match the actual values. This makes the results more reliable. Output of the model Hourly nodal temperatures are obtained as a result of the ambient temperature variation that served as input for the model. The nodal temperatures are analyzed to result in hourly values of ΔT avg and ΔT b. The hourly values of ΔT avg are then analyzed to result in monthly average values over 20 years and annual minima. From these average values ΔT min and ΔT cast can be calculated. For ΔT b average and extreme values have been calculated for every month over the last 20 years. 50

51 3.4.2 Results of the long term thermal model The thermal model is run with an input of 20 years of ambient temperatures from KNMI data. In Table 5 the minimum and maximum values for ΔT b are shown for every month, averaged over the analyzed 20 years. The gradient is both positive and negative every month and this is caused by daily temperature fluctuations. This implies that there is a point where the gradient is 0 every day. This point is most critical for the crack formation, as explained before. The temperature gradient is therefore irrelevant for the temperature load and is not considered in this research. Table 5: monthly min and max values of the temperature gradient caused by daily variations JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Max 3,6 4,7 7, ,9 12,2 11, ,6 4,0 2,7 3,1 Min -7,8-6,8-5,6-5,6-5,2-4,6-4,2-5,5-6,3-7,5-7,4-7,9 The average values of ΔT cast for every month in the analyzed 20 years resulted in Table 6. A negative ΔT cast means that during that month the average temperature of the structural slab is lower than the average temperature of the underwater concrete. Table 6: temperature load for the reference case in C Month JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC ΔT cast -2,3-1, ,6 3,0 3,2 3,4 2, ,6-2,7-3,2 To determine ΔT min for each of the 20 years the maximum temperature difference in winter is calculated. The average value of the maximum temperature differences per year is ΔT min. For the reference case, ΔT min is: -7,4 C. This means that on average, the temperature of the structural slab is 7,4 C lower than that of the underwater concrete at some moment in winter. With ΔT cast and ΔT min known, the temperature load can be calculated using [21]: T T T min cast Table 7 shows the numerical values for the temperature load and Figure 25 shows the same values in a graph. The total temperature load for the reference case when casting in January is thus 5.1 C. This value is the input for the stress calculation for this particular case. 51

52 Temperature load (degrees) Table 7: temperature load for the reference case in C Month JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC ΔT 5,1 6,0 7,7 9, ,7 7,5 5,8 4,7 4,2 14,0 12,0 10,0 8,0 6,0 4,0 2,0 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Reference Case Figure 25: temperature load for the reference case dependent on the month of casting It can be seen that the month of casting has a large influence on the temperature load. The difference in temperature load can be large when changing the month of casting. As expected the temperature load is lower for casting in winter for casting in summer. The difference between casting in winter and summer can be up to 7 C, but is also dependent on the geometry of the construction. Practical use of the long term thermal model The long term thermal model can be used to accurately calculate the temperature in structural slabs on underwater concrete for any given geometry. Historical temperature measurements can be retrieved from KNMI for any measuring station in the Netherlands. With these local data, modelling can be done for a specific project on a specific location with specific geometry. The result will in any case be an accurate representation of the temperature load on the structural slab on underwater concrete. In this research, the aim is to create practical methods. Practical methods require easy calculation. Therefore the influence factors on the temperature load are researched. In this way a hand calculation method will be obtained. 52

53 3.5 Model 3: theoretical degree of restraint In section the basic principles of restraint are explained. In this section, the restraint, applied to structural slabs on underwater concrete is further analyzed. The degree of restraint serves as an input in the model for stress calculation Restraint deformation in structural slabs on underwater concrete From section 3.3, is should be remembered that the temperature distribution determines the way in which a structure deforms. An average temperature load ΔT avg causes axial deformation and a temperature gradient ΔT b causes rotational deformation. To clarify this, the figures below show free and restrained deformation of the structural slab on underwater concrete. In the figures deformation at the left end is restrained and at the right and free. The colors indicate equal deformation; red indicated (close to) zero deformation. Figure 26 shows unrestrained axial deformation caused by only ΔT avg. Figure 27 shows unrestrained rotational deformation, caused by only ΔT b. The other figures show how this deformation is restrained by the underwater concrete, the intermediate layer and the piles. The part of the deformation that is restrained determined the magnitude of the stresses. Figure 28 shows restraint deformation with an intermediate layer of concrete and piles. It can be seen that at the structural slab deforms only at the end of the slab. Both rotation and 1 NODAL SOLUTION translation are restrained by the piles and underwater concrete. Figure 29 shows restrained axial STEP=1 SUB deformation =1 with an intermediate layer of sand and piles. Shear deformation in the piles allow TIME=1 UX the structural (AVG) slab to undergo larger deformation than the underwater concrete. The restraint is RSYS=0 DMX less than = in Figure 28. SMN = AUG :09:02 MN Y Z X MX Figure 26: free translational deformation of the structural slab due to temperature load E E E E E E E E

54 STEP=1 SUB =1 TIME=1 UX (AVG) RSYS=0 DMX = SMN = SMX =.293E-03 AUG :09:35 MN MX 1 NODAL SOLUTION STEP=1 SUB =1 TIME=1 Y Z X UX (AVG) RSYS=0 DMX =.596E-03 SMN =-.591E-03 Figure 27: free rotation of the structural slab due to temperature load AUG :03:31 MX MN E E E E-03 NODAL SOLUTION E E E-04 AUG.293E STEP=1 13:35:07 SUB =1 Y PLOT NO. 1 TIME=1 UX (AVG) Z X RSYS=0 DMX =.715E-03 SMN Figure =-.715E-03 28: Restraint deformations by piles, intermediate layer of concrete and underwater concrete: the structural slab is unable to deform, except for the free end MX -.591E E E E E E E E E-04 0 Y MN Z X Figure 29: Restraint deformation by piles, intermediate layer of sand and underwater concrete: some shear deformation is able to occur, but shear deformation is more at the free end Theory on degree of restraint For simple multi layered structures it is possible to calculate deformation and restraint by hand E E E E E E E E E-04 0 These calculation methods only apply for systems which deform as monolithic structures. A structural slab on underwater concrete having an intermediate layer of concrete can be seen as a monolithic structure. The method for calculation of the deformation of a multi-layered structure is described in Figure

55 Figure 30: calculation method in four steps for multi-layered monolithic structures (Breugel, Veen et al. 1998:184) A structural slab on underwater concrete can be seen as a multi layered system. The piles then have infinite stiffness and no shear deformation occurs. The calculation method is most suitable for structural variants with an intermediate layer of concrete, but can be used as a basis for calculation for an intermediate layer of sand too. This is further clarified in chapter 4 and below the calculation method is explained. The following steps are taken in calculating multi-layered systems: 1. One layer, layer k, is shortened; thermal strains are caused by a temperature load ΔT: ε t = α c ΔT (a). This layer is in reality the structural slab. 2. The shortening is restrained by the other layers (underwater concrete and intermediate layer) and a reaction force N* is created (b and c). N* has a value of ε t E k A k. 3. Taking into account the internal equilibrium in the structure, the force can be replaced by a force, N*, and a moment, M*=N*e, in the neutral axis (d). Parameter e is the distance between the point of application of the original load and the neutral axis. 4. When the equivalent normal force and bending moment are known, the ratio of stiffness of the individual layers is used to calculate the deformation in terms of rotation and translation. The rotation of the structural slab is almost completely restrained by the underwater concrete and especially the tension piles (see also appendix 5). When it is assumed that no rotation occurs, the axial force in a layer k is a part of the total force N*: N EA k * k N [22] EA s 55

56 Where EA s is the stiffness of the total structure. The above implicates that the deformation that does take place is EA k /EA s * unrestrained deformation. The restraint part of the deformation is then: R EA 1 k EA s unrestrained deformation [23] Which, for the case of structural slab on underwater concrete results in: R EA EA EA SS UWC INT 1 EA EA EA EA EA EA SS UWC INT SS UWC INT [24] Where the stiffness of the intermediate layer is assumed to be zero for a layer of sand. The theoretical restraint that can be calculated with [24] was verified in a 2-D structural model. In appendix 5 the results of the 2-D model can be found. The theoretical restraint can be used as a reference in calculation of the restraint. For structural slab on underwater concrete with an intermediate layer of concrete, the theoretical restraint is the actual restraint. For structure with an intermediate layer of sand, a reduction can be applied depending on the structural variant. To estimate the reduction depending on the structural variant, the influence factors are modelled in chapter Magnitude of the theoretical degree of restraint The theoretical restrain can be calculated by: R EA EA UWC INT EA EA EA SS UWC INT A graphical representation is given in Figure

57 Degree of restraint (-) 1,00 0,80 0,60 0,40 uwc 800 uwc 1000 uwc ,20 0, Heigth of structural slab (mm) Figure 31: indication of the degree of restraint for monolithic behavior of structural slabs on underwater concrete. In this case an intermediate layer of sand is used ands a structural slab of C28/35 with an underwater concrete slab of C20/25. The quantitative influence of the intermediate layer of sand cannot be determined in a 2-D model. The piles in a 2-D model are represented by a line with infinite thickness rather than a point in space with a finite area and volume. Therefore a 3-D model gives a better representation of the behaviour and influence of the piles. 3-D FEM modelling is performed to quantify the influences of an intermediate layer of sand, see chapter Model 4: relaxation factors Relaxation is one of the influence factors on the stresses. The relaxation factors calculated below serve as an input in the model on stresses. The values for relaxation can be obtained from Eurocode (NEN-EN : art. 3.1 and annex B). Relaxation can have a significant influence on stresses. Before going into more detail, first recall equation [6]: 0 0 i c 0 t t, t t, t T t, t E( t) R Relaxation of the early-age thermal stresses is different from relaxation of the annual temperature load. This is because relaxation is calculated at a certain point in time and depends on the age of the concrete at the moment when loading started. In [6] it can be seen that relaxation depends on the time at the moment considered (t) and the age at loading (t 0 or t i ). The time at the moment considered depends on the time of casting and can also be called the time at temperature load. The time at temperature load is the time 57

58 between the end of hardening of the concrete (28 days) and the moment when the temperature load is calculated in winter. The age at loading is the age of the concrete at the time when the load is initiated. Both t and t 0 (or t i ) are explained below. Time at temperature load The age of the concrete at the temperature load, depends on the month of casting. The age is the time between casting and time when the critical temperature load ΔT is present on the structural slab. This moment when the critical temperature load is present is when ΔT min occurs in winter. For the calculation of the stresses the first December after casting is used as the critical moment. Appendix 10 shows the month in which ΔT min occurs in red figures. The age of the concrete at the moment of calculation of stresses, t, is the time between the month of casting and the first December. Age at loading As can be seen in [6] the age at loading, t 0 or t i, is different for early-age and annual stresses. It is assumed that both stresses are completely separated. It is assumed that early age thermal stresses are subjected to relaxation at an age of the concrete of 28 days; t 0 = 28 days. This is visualized by the thick blue line of Figure 33. When casting in March, stress relaxation runs from March till December and the value of the relaxation coefficient ψ(t,t 0 ) for casting in March is lowest. For the annual temperature load it is assumed that stress relaxation only begins when tensile stresses become larger than the value at 28 days (σ 0 ). The age at loading t i is therefore the period between casting and the moment when tensile stresses are higher than σ 0. The age at loading can thus be larger than 28 days. When after casting temperature of the structural slab rises, compressive stresses originate in the structural slab, Figure 32. When casting in spring; during summer compressive stresses build up in the structural slab, only to be replaced by tensile stresses when the structural slab cools down in autumn. When ΔT cast is back at the level of the month of casting then this is the point loading starts. Table 7 shows that for casting in March this is in September. The age at loading t i for these cases is therefore not t = 28 days (Figure 32). When casting in March, the period between March and September does not count for stress relaxation. The lowest value of the relaxation factor ψ(t,t i ) is therefore found for casting in July. Figure 33 illustrated the difference between ψ(t,t 0 ) and ψ(t,t i ). For casting in winter it is assumed that the temperature load, the difference between ΔT cast and ΔT min, is at best realized in 7 days. Therefore t-t 0 (and t-t i ) has a minimum of 7 days, allowing for some stress relaxation. This is why the relaxation factor is never higher than 0.8. This makes relaxation values more realistic since temperature loading is a slowly developing phenomenon. 58

59 Relaxation factor Figure 32: determination of the age at loading t I for relaxation calculation; loading start when tensile stresses exceed σ 0 Considering all of the above, the relaxation factors ψ(t,t 0 ) and ψ(t-t i ) are presented in and Figure 33. 0,90 0,80 0,70 0,60 0,50 MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB PSI,0 PSI,I Figure 33: relaxation factor for early-age ψ 0 and annual temperature stresses ψ i Relaxation is mostly dependant on time and can therefore be approximated for every possible combination of heights of structural slab and underwater concrete by the values in Table 8. 59

60 Table 8: values of the relaxation coefficient related to the season of casting Casting (t,t 0 ) (t,t i ) Winter Spring Summer Autumn From the table it can be seen that relaxation can reduce the stresses by 20-40%. 3.7 Other models The values for the models in this section are based on literature. It includes shrinkage, strength development and the early-age thermal stresses Shrinkage Shrinkage consists of drying and autogenous shrinkage. Autogenous shrinkage strains develop mainly during the early hardening stage of the concrete, but should be taken into account in the early stage of hardened concrete. Drying shrinkage is for a large part dependent on the relative humidity. Drying shrinkage is influenced by geometrical properties of the structure, time of start of shrinkage and time at the moment considered. The time when shrinkage is considered is also dependant on the month of casting. The time between start of shrinkage and moment considered is the time between month of casting and December. In winter, shrinkage is assumed to be 0. Calculation of shrinkage strain is performed according to Eurocode (NEN-EN : art. 3.1 and annex B). Shrinkage is highly dependent on the height of the structural slab. The table below therefore presents values of shrinkage per season of casting divided in height of the structural slab. Table 9: values for the shrinkage in microstrain related to the season of casting Casting H SS 400 H SS 800 H SS 1200 Winter Spring Summer Autumn

61 Increase of parameter value (%) The values in Table 9 are only used as an indication of the strain created by shrinkage. For more accurate calculation of shrinkage per month Eurocode should be used. Since the coefficient of thermal expansion is 10*10-6, shrinkage adds maximum an equivalent of 2-5 C to the temperature load Strength development After 28 days the concrete is said to be hardened, but strength develops after that. Depending on the concrete mixture, strength and therefore the E-modulus and the tensile strength increase. Appendix 7 shows calculation methods conform Eurocode (NEN-EN : art. 3.1). Figure 34 shows that the tensile strength develops in a faster rate than the E modulus. This implies that the stresses develop more slowly than the tensile strength. Stresses therefore can be higher because of the development of E-modulus, but compared to the tensile strength, stresses are lower E-modulus Tensile strength Time after t = 28 days (months) Figure 34: development of E-modulus, which has influence on tensile stresses, and tensile strength in the months after the theoretical hardening phase Table 10 gives indicative values for the increase in tensile strength for the season of casting. Table 10: increase in E-modulus and tensile strength in % Casting E f ctm Winter 0 0 Spring 5 12 Summer 4 10 Autumn

62 When taking the strength development into account, the effective reduction in the annual temperature stresses can be up to 7% Early-age thermal stresses The tensile stresses are assumed to be: 0 0,5 f ctm [25] The tensile stresses are influenced by relaxation, but can certainly not be ignored in stress calculation in hardened concrete (Rostasy, Krauss et al. 2007). It is not an option to let the early age thermal stresses exceed half of the tensile strength. This would lead to higher probabilities of crack formation during hardening. Crack formation therefore will occur in the young concrete when stresses exceed 0.5 f ctm. This implicates that even when stresses due to annual temperature change are expected to be low, early age stresses should be dealt with separately. 3.8 Concluding remarks In the beginning of this chapter, it was stated that the stresses can be calculated by simple relations, which can be represented by Figure 35. In this chapter all values have been defines and in the next chapter the influence factors on thermal load en degree of restraint are further analyzed. stresses in structural slabs on underwater concrete relaxation early-age streses relaxation thermal strain shrinkage strain modulus of elasticity degree of restraint Figure 35: influence factors in stress calculation 62

63 The most uncertain factors were on beforehand the thermal strains developed under the influence of the ambient temperature and the degree of restraint dependent on structural variant. So far the following is obtained: For the thermal load a reference case is determined in section The influence factors on the thermal load are the topics of chapter 4. The significance of the influence factors will be determined as the relative influence on the temperature load in C. For the degree of restraint a reference case is determined in section The influence factors on the restraint are the topics of chapter 4. The significance of the influence factors will be determined as reduction in restraint compared to the reference case in %. For the other influences on the stresses in the structural slab, the following is determined: Relaxation factors are different for early-age stresses and annual thermal strains. Calculation is done using Eurocode and the magnitude of the relaxation factors is presented in section 3.6. Shrinkage strains are a combination of autogenous and drying shrinkage and are calculated using Eurocode. The method and indicative values are presented in section Strength development after 28-days is also calculated using Eurocode. The relative influence on stresses is presented in the graph of section Early age thermal stresses contribute significantly to the total stresses. The stresses should not exceed 0.5 f ctm during hardening to prevent early-age thermal cracking. Section elaborates on early age stresses. 63

64 64

65 4 MODELS FOR CALCULATION OF INFLUENCE FACTORS In the previous chapter, the temperature load for the reference case (section 3.4.2) and the theoretical restraint (section 3.5.3) have been calculated. The influence factors on temperature load (sections 4.1 to 4.3) and degree of restraint (4.4 to 4.6) are calculated in this chapter. Calculation models are given as preliminary conclusions: for the thermal model in 4.3, for the restraint in 4.6. In 4.7 all models from chapter 3 and 4 are combined in one step-wise calculation method for the stresses. 4.1 Description of the thermal model on influence factors Based on 20 years of climate data from KNMI the temperature load for the reference case was calculated based on the month of casting. The temperature load for the reference case is: Month JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC ΔT 5,1 6,0 7,7 9, ,7 7,5 5,8 4,7 4,2 In this chapter the influence factors on the temperature load are determined. The model is the same as the long term model, but input is different. The build up and boundary conditions are the same. Differences in geometry from the reference case generate different temperature loads. The influence of geometry on the temperature load will be determined as the difference from the reference case. 65

66 Goal of the model The thermal model is used to gain insight in different influence factors of the thermal load, ΔT. The influence factors are: Height of the structural slab Height of the underwater concrete Height of the intermediate layer View factor For these factors, the influence on the temperature load should be determined in C. Input for the model The input for the model on influence factors is the ambient temperature for March 2008 April This year s temperature data are closest to the average temperatures of the analyzed 20 years. Only one year is needed since only the relative influence of the factors on the temperature load is researched. Realistic initial conditions are obtained by running the model from March of the starting year until April of the following year. The first March is excluded from the model. In this way the nodal temperatures are able to respond to the ambient conditions and initial conditions match the actual values. This makes the results more reliable. Output of the model The influence factors are combined in numerous cases (see Figure 36). For each case, the model is run, and hourly nodal temperatures are produced as a result of the ambient temperature variation. The nodal temperatures are analyzed to result in hourly values of ΔT avg. The average monthly values are compared to that of the reference case and the variation in temperature load determines the influence of the factors. The relative influence is determined as the maximum variation from the reference case in C. 66

67 Height of structural slab Height of underwater concrete Height of intermediate layer View factor 0,4 0,5 0,2 0,3 0,6 0,7 0,8 Figure 36: Variants in the thermal model. The reference case is indicated within the squares 67

68 Temperature load (degrees) 4.2 Results of the thermal model on influence factors The influence of the geometry of the structural slab on underwater concrete on the temperature load is researched. The influence factors are: the heights of structural slab, intermediate layer and underwater concrete and the view factor Height of the structural slab The height of the structural slab influences the temperature load to some extent. Figure 37 shows the temperature load for different heights of the structural slab. Appendix 4 shows the influences on ΔT min and ΔT cast separately. The values of the other factors are: H uwc = 1000 mm H int = 200 mm φ = ,0 12,0 10,0 8,0 6,0 4,0 2,0 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC ss 400 ss 800 ss 1200 Figure 37: influence of the height of the structural slab on temperature load The following is observed: A higher structural slab decreases ΔT The influence of h ss is larger for smaller height The maximum difference is 2 C For smaller height of the structural slab the relative influence of daily variations is larger, which makes the average temperature in the structural slab more dependent on (solar) radiation. This 68

69 Temperature load (degrees) makes the reference temperatures higher, but the minimum temperature lower. The temperature load is higher for smaller heights of the structural slab Height of the underwater concrete The underwater concrete has some influence on the temperature load. However, both the variation in height and the influence of the variation are smaller for underwater concrete than for the structural slab. Figure 38 shows the temperature load for different heights of the underwater concrete. Appendix 4 shows the influences on ΔT min and ΔT cast. The values of the other factors are: H ss = 900 mm H int = 200 mm φ = ,0 12,0 10,0 8,0 6,0 4,0 2,0 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC uwc 800 uwc 1000 uwc 1200 Figure 38: influence of the height of the underwater concrete on temperature load The following is observed: A higher underwater concrete slab increases ΔT The influence is more significant in summer The maximum difference is 2 C In summer, the structural slab is heated by solar radiation, which makes the temperature difference larger. When solar radiation is absent, the influence of the height of the underwater concrete is negligible. 69

70 Temperature load (degrees) Height of the intermediate layer The intermediate layer works as an insulation layer for the underwater concrete slab. A variation in height therefore causes temperature fluctuations in underwater concrete to reduce. This increases temperature difference in summer (ΔT cast ) and decreases temperature in winter (ΔT min ). Figure 39 shows the influence of a higher intermediate layer. The values of the other factors are: H ss = 900 mm H uwc = 1000 mm φ = JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC int 200 int 400 Figure 39: influence of the height of the intermediate layer on temperature load The following is observed: A higher intermediate layer increases ΔT The influence is more significant in summer The maximum difference is 2 C In appendix 4 the influence of the intermediate layer can be seen in the graph for ΔT cast. It can be seen that ΔT cast is warmer in summer and colder in winter by increasing the intermediate layer height. 70

71 Temperature load (degrees) View factor The view factor influences the amount of radiation on the surface of the structural slab. A shallower and wider structural slab has a larger view factor and will therefore be exposed to more radiation. This increases the temperature load on the structural slab. Figure 40 shows the temperature load for different view factors. Appendix 4 provides more details on the influences on ΔT min and ΔT cast. The values of the other factors are: H ss = 900 mm H uwc = 1000 mm H int = 200 mm 14,0 12,0 10,0 8,0 6,0 4,0 2,0 JAN FEB MRT APR MEI JUN JUL AUG SEP OKT NOV DEC view 0,2 view 0,4 view 0,6 view 0,8 Figure 40: influence of the view factor on temperature load The following is observed: A higher view factor increases ΔT The influence is more significant in summer The maximum difference is 2 C The effect of the view factor is, by its definition, only on the radiation, which is visible in the graph. It shows that the solar radiation in summer can cause large temperature differences between structural slab and underwater concrete. 71

72 Temperature load (degrees) 4.3 Calculation method for the thermal load In the previous section it could be seen that the geometry of the structural slab on underwater concrete can influence the temperature load by several C. All positive and negative cases combined yield the minimum and maximum temperature load on the structure, see Figure 41. It can be seen that the temperature load varies between: o o 3 C T 17 C For the minimum case the values of the influence factors are: H ss = 1200 mm H uwc = 800 mm H int = 200 mm ϕ = 0.2 For the maximum case the values of the influence factors are: H ss = 400 mm H uwc = 1200 mm H int = 400 mm ϕ = ,0 15,0 12,0 9,0 6,0 3,0 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC reference minimum maximum Figure 41: difference in temperature load from the reference case Hand calculation methods can be developed from the results of the model on influence factors. The influence factors are displayed in Table 11. The values of the parameters that can differ from the reference case are displayed. Also the influence when changing a parameter is indicated. The influence of the factors is measured in C. 72

73 Table 11: Influence factors on temperature load with respect to the reference value; the table has to be read starting from the reference value. The parameter value can be higher or lower and the corresponding correction is displayed next to the new parameter value. Min value = the minimal value of the parameter; Max value = maximum value of the parameter; Correction Reference ( C) = difference in value of the parameter Influence factor Correction Min Reference Max Correction Reference Value Value Value Reference Height of the structural slab Height of the underwater concrete Height of the intermediate layer View factor Calculation of the temperature load for a given structural variant and given month of casting is performed in the following steps: Look up the reference value of ΔT for the month of casting in Table 7 in section When parameters differ from the reference case, look up the correction from the reference value in ΔT in Table 11. Values that are in between reference and extreme value (for example a view factor of 0.5) can be calculated using linear interpolation. Add/subtract the correction in ΔT from the reference value. 4.4 Description of the structural model on influence factors The 2-D structural model (section 3.5) already showed that the theoretical restraint can be calculated for structural slabs on underwater concrete. Based on height and stiffness ratios of the layers, the theoretical restraint can be calculated. A reduction in restraint can be expected only when an intermediate layer of sand is applied. First a recap of the theoretical restraint is given. The influence factors that determine the reduction in restraint for an intermediate layer of sand are the topic of this section. Because reduction in restraint is the consequence of shear deformation in the piles, this is also addressed Theoretical restraint with an intermediate layer of sand A graphical representation of the theoretical restraint for structural slabs on underwater concrete with an intermediate layer of sand is given in Figure 42. The influence of height of 73

74 Degree of restraint (-) structural slab and underwater concrete are shown for the theoretical restraint. The stiffness of the intermediate layer is assumed 0. The theoretical restraint for structural slabs on underwater concrete with an intermediate layer of sand is then: R EAUWC EA SS UWC [26] 1,00 0,80 0,60 0,40 0,20 0, Heigth of structural slab (mm) uwc 800 uwc 1000 uwc 1200 Figure 42: degree of restraint for monolithic behavior of structural slabs on underwater concrete for an intermediate layer of sand A reduction in restraint with respect to the theoretical model can be achieved by changing the structural variant. The structural model calculates the influence of the different factors on restraint. The relative influence is measured as a percentage of reduction of the theoretical restraint Shear deformation and stress A severe reduction in restraint values can be expected by applying an intermediate layer of sand. In Appendix 5 a table with results of the 3-D model is given. It can be seen that shear deformation of the piles allow for extra deformation of the structural slab. The effect of the intermediate layer of sand is therefore that shear deformation of the piles is possible. The shear deformation lowers the restraint. For some of the cases the shear deformation is a significant part of the total deformation, see Appendix 5. Shear deformation is beneficial for the reduction of restraint, but results in shear stresses in the piles. No detailed calculations are performed in this research on the shear forces. However, simple structural mechanics can give an idea of the order of magnitude of the shear stresses. Below 74

75 simple relations are presented, and many literature exists for the derivations (for example: Simone 2009). When it is assumed that the piles deform in pure shear, the shear stresses are: G d [27] Where: τ = shear stress in N/mm 2 G = shear modulus Δ = shear deformation d = height of the intermediate layer The structural model produces displacements in x-direction. The shear deformation is the difference in deformation between the structural slab and the underwater concrete. With this model the order of magnitude of the shear stresses in the piles can be determined. The results of the shear stresses in the piles are presented at the end of the results of the model on influence factors Properties of the model Goal of the model The structural model is used to gain more insight in the influence factors of the degree of restraint. The influence factors on the degree of restraint are: Number of piles in the grid Type of pile Height of the structural slab Height of the intermediate layer The structural model should also determine the order of magnitude of the shear forces in the tension piles. Note: Tests with the structural model show that variation of the center-to-center distance of the piles alone does not seem to effect the stresses in the floor, when keeping the number of piles the same (and thereby increasing the length of the slab). The number of piles in the grid does somehow influence the restraint and will be subject of investigation. Build up of the model The hatched part in Figure 43 is the part that is investigated. In this case it shows three piles in the grid that is analyzed. The analyzed part of the structural slab is the length of the slab and is 75

76 halved because of symmetry. Restraint deformations in the length of the section are analyzed, because this is the critical direction and therefore not the entire width is considered. The number of piles in the grid in the structural model is visible in Figure 43. The number of piles in the model should be doubled to yield the number of piles in a section. Assuming pile center-tocenter distance of 3 m, 3 piles in the grid of the model means a section length of 3 * 3 * 2 = 18 m. Figure 43: top view of a section of a structural slab on underwater concrete. The hatched part is one of the critical parts and is analyzed in the models The layers in the structural model are: Structural slab with variable height Underwater concrete with variable height Intermediate layer with variable height and material Prefab-, Gewi or Gewi+ piles with corresponding properties Note: For the type of piles only Gewi and prefab piles are tested, while also cut-off piles and rebars exist as optional variants. Cut-off piles have very little (if any) advantage over prefab pile: the reinforcement bonds with the concrete of the structural slab, the pile has a rough surface and is partly embedded in the structural slab. Furthermore, the surface roughness used in calculation (ref NEN 6702), results in no advantage compared to prefab piles. Cut-off piles are therefore not taken into account. Rebars is rather uncommon and very labour intensive and is also not taken into account. Applied with an intermediate layer of concrete, the same reasoning holds as for the cut-off piles. Rebars with an intermediate layer of sand is seldom applied because of corrosion issues. 76

77 1 AREAS TYPE NUM AUG :07:56 Boundary conditions The restraint is also influenced by the structural boundary conditions of the structural model. Figure 44 shows the 2-D representation of the model of a cross section over the piles. Y Z X Figure 44: representation of the structural model. Colours indicate different materials The boundary conditions for both models are: Deformation in x direction is 0 at the symmetry axis of the slab (x=0). This is the middle part of a section, where deformation is impossible Deformation in y direction is 0 at the pile feet (y=0). These boundary conditions imply that the soil does not counteract the deformation of the piles/anchors. Also rotation is restraint by close to 100% The material properties of the different layers are presented in Table 12. Table 12: Material properties for the structural model; sand has no stiffness and Gewi+ is a corrosion resistant Gewi pile Layer Material E-modulus (N/mm 2 ) Geometry Structural slab Concrete Variable height Underwater concrete Concrete Variable height Intermediate layer Concrete Variable height Intermediate layer Sand -- Variable height Prefab pile Concrete x 400 mm Gewi pile Steel ,5 Gewi + pile Concrete/Steel

78 Input for the model For the 3-D model only translational deformation is analyzed. The temperature load is therefore only an average temperature difference: ΔT avg = -10 C The ANSYS model produces nodal displacements, which are used as input for the MS Excel spreadsheet calculations. Output of the model The model produces nodal displacements, of which only the displacements in x direction, u x, are considered. The nodal displacements are analyzed in MS Excel. The final result of the model is a degree of restraint of every variant. The 3-D model outputs restraint values for different structural variants (see Figure 45), all having an intermediate layer of sand. These values are compared to the situation of monolithic deformation. The reduction in restraint for different variants is the output of the model. The influence of different factors is expressed in a percentage of reduction in restraint. 78

79 Type of pile Prefab Gewi+ Gewi Height of structural slab Height of intermediate layer Number of piles in grid Figure 45: Variants in the structural model. The values within the squares produce the highest restraint. 79

80 4.5 Results of the structural model on influence factors In this section all influence factors on restraint are analyzed and it can be seen that severe reduction in restraint can be achieved by applying an intermediate layer of sand. However, also shear forces in the piles are introduced by the intermediate layer Number of piles in the grid The number of piles in the grid is represented in every graph in this subsection. It can be seen that the lowest number of piles in the model (3) gives lowest restraint values. It was stated before that the center-to-center distance of the piles does not influence the degree of restraint. More piles in the section restrain deformation to a larger extent. From the figures in this section, it can be seen that in some cases also with many piles in the grid (7), a reduction in restraint can be achieved. In all cases a reduction in the number of piles in the grid from 7 to 3 gives a reduction in restraint of about 30%. As explained earlier in this chapter, the number of piles in the model is equal to the number of piles in half of the section. For easy calculation, the reduction in percentage for the number of piles in the grid of the length of one entire section is given in Table 13, based on Figure 46. Based on a center-to-center distance of 3 meter, the reduction in restraint for the length of a section is given in Table 14. Table 13: reduction in restraint for number of piles in the length of a section Nr. of piles Reduction 30% 15% 10% 5% 0% Table 14: reduction in restraint for the length of a section; 3 m center-to-center distance between piles is assumed. Length of section Reduction 30% 15% 10% 5% 0% It is best to apply no more than 6 piles in the length of the section. With a center-to-center distance of 3 meter, section length can best be around: 6 * 3 = 18 meter. 80

81 Restraint reduction (%) Pile type The pile type can have a very significant influence on the restraint. This is shown in Figure 46. The values of the influence factors for the cases presented in this graph are: Pile types = Prefab, Gewi, Gewi+ H ss = 800 mm Nr. of piles = 3, 4, 5, 6, 7 H int = 200 mm Number of piles in grid Prefab GEWI GEWI + Figure 46: Reduction in restraint for prefab, Gewi and Gewi piles with corrosion protection The following is observed: A severe reduction in restraint can be achieved for all types of piles The reduction in restraint is much lower for prefab piles The corrosion protection adds a significant amount to the restraint The difference in restraint between Gewi+ piles and prefab piles is 30-40% As expected, the stiffer and larger prefab piles restrain deformation by a larger extent than the Gewi pile. However, another way of corrosion protection could reduce the restraint even more. The difference between Gewi+ piles and prefab piles is 30-40%. Replacing prefab by Gewi piles is therefore assumed to reduce restraint by about 30%. For the Gewi piles, the reduction in restraint can be up to 90%. The restraint is then only 0.05 or 5%, which makes crack formation very unlikely. To reduce the stresses, application of Gewi piles instead of prefab piles seems to be very efficient. 81

82 Restraint reduction (%) Height of the structural slab The influence of the height of the structural slab is not very large, but should not be neglected. Figure 47 shows the influence of the height of the structural slab for prefab and Gewi (dotted line) piles. The values of the influence factors for the cases presented in this graph are: Pile types = Prefab, Gewi H ss = mm Nr. of piles = 3, 5, 7 H int = 200 mm Number of piles in grid SS 400 G SS 800 G SS 1200 G SS 400 P SS 800 P SS 1200 P Figure 47: reduction in restraint for different heights of the structural slab The following is observed: A thicker structural slab reduces restraint more The reduction is similar for Gewi piles and prefab piles The reduction in restraint is 0 for many prefab piles in the grid The influence of the height of the structural slab is relatively small. Furthermore, a higher structural slab produces a smaller temperature load. In this case the same temperature load is assumed for all height of the structural slab. In reality the temperature depends on the height of the structural slab and the difference in restraint will therefore disappear. For practical purposes reduction from the theoretical restraint for a thicker structural slab should not be expected. 82

83 Restraint reduction (%) Height of the intermediate layer The height of the intermediate layer can be increased to enlarge deformation. In Figure 48 it can be seen that increasing the height of the intermediate layer indeed increases the reduction in restraint. The values of the influence factors for the cases presented in this graph are: Pile types = Prefab, Gewi H ss = 800 mm Nr. of piles = 3, 5, 7 H int = mm Number of piles in grid GEWI INT 200 GEWI INT 400 PREFAB INT 200 PREFAB INT 400 Figure 48: reduction in restraint for different heights of the intermediate layer The following is observed: A thicker intermediate layer reduces the restraint The reduction in restraint is larger for Gewi piles The reduction in restraint by a thicker intermediate layer is about 15% From the figure is can be seen that for Gewi piles with an intermediate layer of 400 mm the reduction in restraint is almost 100%. This means a state of free deformation is reached. Since deformation is only several mm, this could very well be possible. When applying a higher intermediate layer with prefab piles care should be taken since still a severe restraint is present. The temperature load also increases by a higher intermediate layer. 83

84 Tau (N/mm2) Shear forces in the piles Application of an intermediate layer of sand is the only way to reduce restraint, because shear deformation in the piles is possible. Shear deformation reduces the degree of restraint, but also brings shear stresses in the pile. This is a discussion point between the experts in favour and against an intermediate layer of sand. In the figures below (Figure 49 and Figure 50) it can be seen that the shear stresses can exceed the shear strength. The values of the influence factors for the cases presented in these graphs are: Pile types = Prefab, Gewi H ss = 800 mm Nr. of piles = 3, 5, 7 H int = mm Number of piles in grid GEWI INT 200 GEWI INT 400 shear strength Figure 49: Influence of height of intermediate layer on shear forces in Gewi piles The following is observed: Shear stress can be well above shear strength A higher intermediate layer reduces the shear stresses Less piles in the grid reduce shear stresses The ratio of shear stresses and shear strength is better for Gewi piles A higher intermediate layer can reduce shear forces and at the same time reduce the restraint. However, in the previous chapter it was seen that also temperature loads rise considerably by increasing intermediate layer height. 84

85 Tau (N/mm2) Number of piles in grid PREFAB INT 200 PREFAB INT 400 shear strength Figure 50: Influence of height of intermediate layer on shear forces in prefab piles One of the strongest arguments against an intermediate layer of sand is that the piles fail in shear. These results show that shear stresses can exceed shear strength. The results also show that Gewi piles perform better (shear failure at 435 N/mm2) than prefab piles (shear failure at < 10 N/mm2). This is interesting, since many engineers believe that an intermediate layer should be applied with prefab piles. However, recent research (Sterken, Vambersky et al. 2007) has shown that shear strength of concrete dowels can be much higher than previously expected. It is also shown that the more flexible Gewi pile is less likely to fail in shear. When more flexible corrosion protection can be thought of, this might increase durability of the Gewi pile. One of the opportunities in this field is the very ductile Engineering Cementitious Composites, or ECC. Other forms of corrosion protection might be interesting to research. The conclusion from this subsection is that more research is needed on shear forces in the piles. Detailed research can show whether or not the piles will be able to withstand the shear forces. If the piles are able to cope with the shear forces, an intermediate layer of sand is a very good solution for reduction of stresses in structural slabs on underwater concrete. 4.6 Calculation method for the degree of restraint The 3-D structural model can be used to accurately calculate the degree of restraint for any given structural variant. When the material properties of all elements in the structural variant are input in the 3-D structural model, the restraint can be calculated. The deformation given in the structural model should therefore be compared to a situation of free deformation. The result will be an accurate representation of the degree of restraint for any given structural variant. 85

86 In this research, the aim is to create practical methods. The results for the influence factors in the structural model will be used to create easy hand calculation methods. With the results from this section, a hand calculation method for the degree of restraint in structural slabs on underwater concrete with an intermediate layer of sand is developed. The theoretical restraint can be calculated with [26]: R EAUWC EA SS UWC For the following structural variants a reduction in the theoretical restraint can be expected. The value of the reduction is also given: Number of piles in the length of a section Table 15 Replacing prefab by Gewi piles 30 % Increasing height of intermediate layer 15 % Table 15: reduction in restraint for number of piles in the length of a section Nr. of piles Reduction 30% 15% 10% 5% 0% Calculation of the restraint for a given structural variant with an intermediate layer of sand is performed in the following steps: Calculate the theoretical restraint with [26] Check if the structure has some of influence factors that cause reduction in restraint Multiply the restraint by (100% - reduction) With this method, the restraint will vary between the following extremes: 15% R 80% The restraint can be even lower, when other ways of corrosion protection in Gewi piles are adopted. The analysis of the restraint and its influence factors is given in section

87 4.7 Concluding remarks In this chapter, the influence factors on temperature load and degree of restraint have been analyzed. The following qualitative conclusions can be drawn: The geometry of structural slabs on underwater concrete can influence the temperature load The height of different layers influence the temperature load by several C An intermediate layer of sand gives way to reduction of the degree of restraint by shear deformation of the piles Replacing prefab by Gewi piles, reducing the number of piles in the grid and increasing the height of the intermediate layer can reduce the restraint Shear stresses in the piles can be higher than shear strength Based on the calculation methods from sections 4.3 and 4.6 and the results from chapter 3 a calculation method for the stresses can be developed. This is a step-wise approach to calculate the stresses from the geometrical properties of the structural slab on underwater concrete and the structural variant. The calculation method is shown in the next 4 pages. With this new calculation method it is now possible to make a very quick and reliable estimation of the stresses in structural slabs on underwater concrete. 87

88 Step 1: Properties of the structural slab on underwater concrete Month of casting Filling layer material: Concrete or Sand Pile type: Prefab or Gewi Nr. of piles in length of section Strength class of structural slab Strength class of underwater concrete Strength class of intermediate layer Height of structural slab Height of underwater concrete Height of intermediate layer Step 2: Calculation of the temperature load What is the month of casting? Section Temperature load for reference case Are there differences from the reference case? YES NO Step 3 Section 4.3 Temperature load 88

89 Step 3: Calculation of the degree of restraint Section Theoretical degree of restraint NO Is an intermediate layer of sand applied? Step 4 YES Are Gewi piles used? YES NO No reduction 30% reduction in restraint How many piles in the length of the section? Section 4.6 Is the height of the intermediate layer 400 mm? YES NO No reduction 15% reduction in restraint Final degree of restraint 89

90 Step 4: Calculation of other infleunce factors on stresses Section What is the season of casting? Section 3.7 Relaxation factors What is the height of the structural slab? Section Shrinkage value Section E-modulus and tensile strength 90

91 Step 5: Calculation of stresses Input factors from steps 2, 3 and 4 Section 3.1 Final stresses 91

92 92

93 5 FROM RESEARCH TO PRACTICE It is now possible to calculate stresses using simple hand calculation methods, see section 4.7. To asses whether stresses are acceptable, the probability of crack formation can be calculated (5.1). Also a safety factor can be calculated. Measures to reduce stresses are presented in 5.2. The cost of the measures (5.3) compared to the reduction in stresses determine the efficiency of measures in The probability of crack formation First the theory of calculating the probability of crack formation is explained. The values of the probability and a calculation example determine the probability and safety factor for crack formation. Both are based on the ratio of tensile stresses and strength Theory of calculation The average values of the temperature loads and restraint have been calculated, in the previous chapters. The previous section outlined the most important calculation methods. But what is really important to know is what the probability of crack formation is and what the safety factor is for crack formation. It is assumed that the tensile stresses calculated with [6] are normally distributed. The same is assumed for the tensile strength. Crack formation is initiated when the tensile stress exceeds the tensile strength, as indicated before. Since both are normally distributed (Figure 51), the average tensile stress can be smaller than the average tensile strength, but still cracks can be formed. 93

94 Figure 51: graphical representation of the probability of crack formation tensile stresses and tensile strength ar both normally distributed (Breugel, Veen et al. 1998:174) The probability of crack formation is then defined as the probability that tensile stresses exceed the tensile strength, or: P F P f [28] cr ct ctm Since both the tensile stresses and the tensile strength are normally distributed, so is the difference function between both: z = f ct - σ ct. When z < 0 crack formation will occur. For the difference function the following holds: z f ct ct ct z s z ct s z s f s Ratio z 2 2 [29] The ratio defines how many times the standard deviation the difference function is to be exceeded before crack formation is initiated. With this ratio the probability of crack formation can be looked up in the table of Appendix 8. The standard deviation of the strength and stresses is not easily calculated, since a lot of influence factors are at stake. The standard deviation is therefore estimated as a percentage of the average value of the parameter. When an accurate determination of the parameter is possible, the standard deviation will reduce. For the strength a standard deviation of 10% of the average value is estimated (Breugel, Veen et al. 1998). Since only hardened concrete is analyzed with slowly developing stresses, this seems reasonable. The tensile stresses contain inaccuracies. The value of restraint is determined in a theoretical way and the thermal load is based on only one temperature measurement. In Appendix 9 it can 94

95 be seen that the standard deviation of the temperature load is at most around 20% of the average value. Considering this, a value of 20% is assumed for the standard deviation of the thermal stresses from the average value. Safety factor In civil engineering, safety factors are used to be able to judge the structural safety. Aquiferous crack formation in structural slabs on underwater concrete does not directly harm the safety of the structure, but threatens the durability. The loading conditions are within the serviceability limit state (SLS). The safety factor is defines as the ratio of the characteristic values of strength and stresses: f ctc;0,05 ctc;0,95 [30] The characteristic value for the tensile strength is the value of the strength which is reached by at least 95 % of all structures. The characteristic value for the tensile stress is the value of the stress which is reached by at most 5 % of loads on the structure Values for the probability and safety factor With the above Table 16 can be obtained. It calculates the probability of crack formation and the safety factor for given stress/strength ratio. The probability of crack formation is looked up in the table of Appendix 8 for the corresponding ratio μ(z)/s(z). Table 16: calculation values for the probability of crack formation and the safety factor for different stresses relative to the tensile strength; stresses and strengths normally distributed Parameters f ct Unit σ ct /f ct Average value 2,8 N/mm 2 1,4 1,68 1,96 2,24 2,52 standard deviation 0.28 N/mm Characteristic value 2,34 N/mm 2 1,86 2,23 2,60 2,98 3,35 μ (z) N/mm 2 1,4 1, s(z) N/mm μ (z)/s(z) -- 3,54 2,56 1,74 1, P(cracks) % ,09 14,46 31,21 Safety factor (γ) -- 1,26 1,

96 Probability crack formation (%) In the SLS a safety factor of 1.0 is sufficient. In Table 16 it can be seen that this implies that a crack free floor can be obtained only when: 0,6 ct fct [31] The tensile strength should be determined for the moment of calculation of the temperature load, in winter. This means that the tensile strength is higher than the 28-days value. The probability of crack formation related to the stress/strength ratio is showed graphically in Figure P(cracks) ,5 0,6 0,7 0,8 0,9 1 Ratio stress/strength Figure 52: the probability of crack formation related to the ratio of stresses and strength, both normally distributed To gain more insight in calculation of the probability of crack formation, in the next section a calculation example is given Calculation example In Table 17 several cases have been identified. Calculations of all values are performed using the step wise approach of chapter 4.7. For accurate calculation of the shrinkage and strength development Eurocode is used (Appendix 7). Case 1 is the reference case. The properties of case 1 are: 96

97 Month of casting May Height of structural slab 1000 mm Height of underwater concrete 1000 mm Height of intermediate layer 200 mm Material of intermediate layer sand Early-age stresses 0.5 f ctm Strength class structural slab C28/35 Strength class underwater concrete C20/25 Relative humidity 80% Differences in boundary conditions per case are: 1. Reference case 2. Same as 1, cast in October 3. Same as 1, thin underwater concrete 4. Same as 1, thick structural slab 5. Same as 1, view factor high 6. Same as 1, reduction of R by 30% For case 6, the 30% reduction in restraint can be obtained by for example replacing prefab piles by Gewi piles or by reduction of the number of piles in the grid. Table 17: the probability of crack formation and safety factor for fictive cases; the influence of different factors can be seen Variable Case1 Case2 Case 3 Case4 Case5 Case6 H ss H uwc View factor Month May October May May May May (t.t 0 ) (t.t 1 ) (t.t 0 ) E R f ctm t f ct P(cracks) 14% 0.5% 4% 0.5% 14% 0.5% γ

98 The following can be observed from the example: Very standard cases, such as case 1, are likely to contain cracks Small adjustments can reduce the probability of crack formation It is very well possible to adjust the geometry or the structural variant and successfully reduce the probability of crack formation Since the structural safety is not directly threatened by the formation of small cracks, some cracks can be allowed for economical optimization. The input for this economical optimization is the probability of crack formation. This is why the cost of reduction measures for the stresses are also examined. First, the measures that can be taken are viewed. 5.2 Measures for crack handling The only possibility to reduce the probability of crack formation is to reduce the stresses in the structural slab. From the results for the influence factors in chapter 4, measures can be thought of to reduce the temperature load and the degree of restraint and therewith the stresses in the structural slab. The geometry of the construction will be determined based on the external loads. Based on this geometry adaptations can be made on the design to reduce the probability of crack formation. These measures can be divided in measures to reduce the theoretical restraint and measures to reduce restraint when an intermediate layer of sand is applied. Measures to reduce the theoretical restraint and temperature load: 1. Increase height of the structural slab 2. Decrease height of underwater concrete slab 3. Replace intermediate layer of concrete by sand Measures to reduce restraint when applying an intermediate layer of sand: 4. Replacing prefab piles by Gewi piles 5. Reduction of number of piles in the grid 6. Increase height of intermediate layer To assess the efficiency of the measures, the reduction of the probability of crack formation should be compared to the cost of a measure. The effect on the reduction of the probability of crack formation can be retrieved from the calculation example of the previous chapter. Cost calculation of the measures is done in the next section. 98

99 5.3 Cost of measures for crack handling To determine the cost of measures it should be known what extra resources are needed. This is called the implications of the measures. The implications and cost are the basis of the calculation example in this section Implications of the measures Measures for crack handling already exist in practice. A comparison must be made of these measures to determine the best measures for the handling of cracks in structural slabs on underwater concrete. The above measures to reduce the probability of crack formation can therefore be expanded with the measures currently used in practice. Measures currently used in practice: 7. Increase amount of reinforcement 8. Injection of cracks The identified eight measures have implications on costs. Modifications of the structure can cause a need for more or other material, more excavation, longer sheet piling etc. Below for every measure the implications are described. The injection of cracks is separated, since this is somewhat more complicated. Nr. Implication 1. More concrete is needed, as well as excavation and longer sheet piling along the length of the slab. Increasing the height of the slab, reduces temperature load and restraint, but increases early age thermal stresses. 2. This saves cost, since less excavation and less length of the sheet piling is needed. It creates a decrease in both temperature load and restraint. 3. The concrete is replaced by sand, which reduces the theoretical restraint since the stiffness of sand is assumed zero. For the cost calculation it is assumed that some height has to be added to the intermediate layer when replacing concrete by sand. It is assumed that an intermediate layer of sand is 0.2 m thicker that an intermediate layer of concrete. This means more excavation, and longer sheet piling is needed. 4. Gewi piles are more expensive than prefab piles, but reduce restraint when applied with an intermediate layer of sand. Corrosion resistance can be needed, but that is not taken into account in cost calculation. 5. The number of piles can be reduced by casting in smaller sections. For a project of a certain length, this means more sections have to be made. This might result in longer construction time. The costs for smaller sections are not taken into account. 99

100 It is advised to use no more than 6 piles from in the length of one section (3 piles in the model, see Figure 43). This means floor section length should not exceed 20 m. 6. More sand is needed, as well as excavation and longer sheet piling along the length of the slab. A higher intermediate layer decreases the restraint, but increases the temperature load. 7. Reinforcement only reduces crack width and can overcome the problem of leakage through the structural slab when the criterion of Lohmeyer is met (section 2.3.1). However, aquiferous cracks are sometimes able to form despite an increase in reinforcement. Many narrow cracks are harder to repair than a small amount of wide cracks. This can significantly increase injection costs and time. 8. Repair of cracks For the formation of cracks and the repair method the following is assumed: 1. Cracks do not reopen once injected. 2. Every 10 m contains maximum one crack 3. The number of cracks per 10 m is P(cracks)*(length in m/10) 4. A crack develops over the full width of the slab Ads: 1. Cracks should be repaired in winter with an elastic material. In winter the cracks are largest and using an elastic material will give the smallest probability of reopening of cracks. Since the first winter is the critical period for crack formation, reopening of cracks should be possible (but is not certain) to avoid. 2. When a crack occurs, the tension in the concrete will decrease. When the tensile stresses are high, crack spacing can be less than 10 m. The crack spacing can be calculated, but this is not part of this research. 3. It is hard to assure this assumption is valid for all cases. But, since there is no certainty on beforehand, for estimation this assumption is made. 4. To counteract ad2 and ad3, this assumption overestimated the seriousness of the cracks. A crack over the full width is most probably an overestimation of the length. Because the length is the critical direction for crack formation, cracks will occur over the width of the slab. 100

101 5.3.2 Costs of measures based on implications The implications of the measures from the previous subsection can be translated into costs. The indication of cost of the measures presented above is: Concrete: 100 / m 3 This is both material and placement of the concrete. Sand: 40 / m 3 This is both delivery and placement of the sand Excavation: 35 / m 3 Extra excavation takes place at the deepest and therefore most expensive part of the cofferdam. Replacing prefab piles by Gewi: 400 / pile This is based on the price per m pile, which is 110 for Gewi and 90 for prefab. The average length of the pile is assumed 20 m. Longer sheet piling: 150 / m width/ m depth This is only material, extra drilling is negligible. Increase reinforcement: 1,5 / kg The assumption is made that slabs have a reinforcement percentage of 0.4%. It is assumed that this has to be at least 1,0% to limit crack width. Injection: 50 / m 1 These are costs for material and labour. The used material can make a difference. Narrow cracks can be hard to inject and therefore labour intensive. With the implications of the measures and the costs of the measures based on the implications known, a calculation example can be made. The method of cost calculation is also describes in appendix

102 5.3.3 Calculation example For a fictive project, the properties are given below. The probability of crack formation is assumed 20%. Given the calculation example of section this is a very high, if not unacceptable, probability of crack formation. H ss 1 m H uwc 1 m H int 0.2 m P(cracks) 20 % Width of slab 20 m Length of slab 30 m Area of slab 600 m 2 Nr. of piles width 7 - Nr. of piles length 10 - Total nr. of piles 70 - Reinforcement 0.4% 31,4 kg/m 3 Reinforcement 0.4% total kg Reinforcement 1% 78,5 kg/m 3 Reinforcement 1% total kg Length of the project 1000 m The costs for every single measure are as described in the cost estimation of Remember that measure 5, the number of piles in the grid, is assumed to have not cost implications. The result of cost calculation is shown in Table 18, sorted in ascending order of cost of the measure. Table 18: cost calculation for 1 section: C=concrete; S=sand; E=excavation; SP=sheet piling; Cost in Euros * 1000 Measure C S E SP Cost Project Increase reinforcement kg Replace prefab by Gewi 60 piles Increase height of SS 0.2 m Increase height of INT 0.2 m Injection 12 m Replace INT of concrete by sand 0.2 m ,2-40 Decrease height of UWC 0.2 m

103 Table 18 shows the cost estimated by certain measures for a section and a fictive project of 1000 m structural slabs on underwater concrete. The following can be observed from the table: Increasing reinforcement in the structural slab is by far the most expensive measure Gewi piles are much more expensive than prefab piles Increase of thickness of a layer is costly Injection is a relatively cheap solution if cracks appear The replacement of the intermediate layer by sand will not increase cost Decreasing the height of the underwater concrete saves considerable cost To examine the practical use of solutions, the cost should be compared to the reduction in probability of crack formation. This is the topic of the next section. 5.4 Efficiency of measures for crack handling Below the effectiveness of the measures is examined. The reduction in the probability of crack formation compared to the costs determines the efficiency of a measure Measure for reduction of theoretical restraint and temperature load Increase height of the structural slab Increasing the height of the structural slab has some influence on the probability of crack formation. It both lowers the temperature load and the degree of restraint. Still, the influence is not quite large. The measure costs quite a lot of money for just the concrete. Besides that, there is the potential extra cost in cooling measures for early-age crack prevention that come with a thicker structural slab. An increase in the height of the structural slab is not a preferred measure for reduction of crack formation because of the high cost and moderate efficiency. Decrease height of underwater concrete slab Minimizing the height of the underwater concrete reduces temperature, degree of restraint and cost. This implies that the underwater concrete slab should in any case be as thin as possible. Replace intermediate layer of concrete by sand Application of an intermediate layer of sand enables possibilities for restraint reduction, that are not available with an intermediate layer of concrete. The cost of an intermediate layer of sand are comparable to the cost of an intermediate layer of concrete. An intermediate layer of sand in itself reduces restraint by some amount, because the stiffness is zero. However, measures for restraint reduction can only be applied when a layer of sand is adopted. It should be born in mind that there is the possibility that piles fail in shear. 103

104 When it is assumed that piles are able to withstand shear forces, an intermediate layer of sand should always be applied to reduce restraint; only with an intermediate layer of sand the measures from can be applied Measures for reduction with an intermediate layer of sand The measures below do not influence the probability of crack formation in a construction with an intermediate layer of concrete. These are measures that can reduce the restraint when applying an intermediate layer of sand. Replacing prefab piles by Gewi piles Applying Gewi piles is very efficient for reduction of the restraint. Corrosion measures make the Gewi piles less flexible and therefore restraint rises. Also, Gewi piles seem to be able to cope with shear forces somewhat better than prefab piles. Cost of Gewi piles are however quite high. In this model the cost of corrosion measures have not been taken into account. When the probability of crack formation in an already designed construction is high, an investment in Gewi piles can be a good option. Reduction of number of piles in the grid Less piles in the grid means less restraint when an intermediate layer of sand is adopted. In practice, sections of 20 meter are very common and it is advised not to lengthen the sections and to apply no more than 6 piles in the length of the section. Increasing the length of a section increases the probability of crack formation. Increase height of intermediate layer Increasing the height of the intermediate layer seems not to expensive can reduce the restraint. However, it also increases the temperature load and the net effect of this measure is therefore small. Costs are moderate, but for very small effect not worth it. The major advantage of an increase in the height of the intermediate layer is that shear forces in the piles will reduce. When shear forces are expected to exceed the shear strength of the piles, this might be a valid reason to increase the height of the intermediate layer Measures used in practice Increase amount of reinforcement Adding reinforcement does not reduce the probability of crack formation. Reinforcement can only reduce crack width, so that crack width is below the criterion for self healing. As explained before, even then prevention of aquiferous crack formation is not guaranteed. When cracks occur the reinforcement causes many narrow cracks instead of a small amount of wide cracks. Injection of a lower amount of wider cracks is easier and cheaper. Extra reinforcement is by far the costliest measure. The high cost, low effectiveness and potential problems with injection make more reinforcement not advisable. 104

105 Injection of cracks Injection is very cheap and therefore a good option for when cracks do appear, but is no solution when cracks in structural slabs on underwater concrete are unwanted. The professional image of a project is harmed by cracks in the structural slab. Cracks can also appear when the structure is already in use, which makes the structure temporarily unavailable. Cracks can reappear; once a crack is injected it can open again. Purely economical design for crack formation is likely to result in accepting cracks and injecting them. Still other unwanted consequences of crack formation make that prevention is advisable over repair. 105

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107 6 CONCLUSIONS AND CALCULATION METHOD In this chapter the conclusions are supported by a calculation method. The aim of this report was to come to a practical advice. The conclusions of this report in terms of measures to be taken are part of the practical advice. The other part is the hand calculation method for the probability of crack formation. The calculation method can be used in practice to easily calculate the probability of crack formation, taking into account the influence factors. In this chapter the new insight in the influence factors and the practical advice are therefore combined. 6.1 Conclusions Stresses that cause through crack formation in structural slabs on underwater concrete are caused by restrained deformation of temperature loads. Literature research has given more insight in the scope of the problems and the focus that was needed for this research. Modelling of the temperature effects on structural slabs on underwater concrete has lead to more insight and easy calculation methods of the temperature load and the degree of restraint. More insight has been gained in the influence factors on the stresses. This resulted in a practical advice for the prevention of crack formation in structural slabs on underwater concrete. Much research has been done on early-age thermal cracking. This resulted in adequate calculation methods for early-age stresses. With the aid of computer software and cooling of concrete during construction, early-age thermal cracking can be prevented. The stresses must therefore not exceed 0.5*tensile strength. Early-age thermal loads must be viewed separately from annual temperature loads. While early-age thermal loads are predictable, a large uncertainty exists in the magnitude of the annual temperature load. Research by Den Boef (1996) already showed that aquiferous through crack formation in structural slabs on underwater concrete is caused by restrained deformation. Later the commission VC71 (CUR 2007) concluded that annual fluctuations of the ambient temperature are the main and most uncertain cause of crack formation. The design of structural slabs on underwater concrete can result in different structural variants. The approach of this commission showed that the structural variant is believed to have considerable influence on crack formation. Partly because of lacking long term temperature measurements in structural slabs on underwater 107

108 concrete, VC71 was unable to come up with a solution for the problem of crack formation in structural slabs on underwater concrete. In practice, restrained deformation is dealt with by applying extra reinforcement in the structural slab. Reinforcement however is only activated when the concrete cracks. Therefore reinforcement only limits crack width and does not prevent crack formation. When crack width is very small, even through cracks are not necessarily aquiferous. There is a possibility of self healing of cracks but the boundary conditions that are needed for self healing make this uncertain. Because of the lack of better ways to control crack formation in structural slabs on underwater concrete, extra reinforcement is still the most adopted solution. To calculate the amount of reinforcement, usually the design is made on the maximum allowable crack width. To calculate the crack width the stresses that are caused by restrained deformation must be known. These stresses are very uncertain. Both the temperature load and the degree to which deformation is restraint are uncertain. Also, early-age stresses are not taken into account in stress calculations in hardened concrete even though research has shown that these stresses can have significant influence (Rostasy, Laube et al. 2006). The uncertainty of the major influence factors on stresses makes the magnitude of the stresses very uncertain. It should therefore be no surprise that in many practical cases aquiferous cracks form in spite of thorough calculation and extra reinforcement. Some experts believe that adding an intermediate layer of sand reduces restraint and therefore reduces stresses that causes crack formation. Others however don t. Arguments in favour and against an intermediate layer of sand exist and much discussion goes on about this matter. An intermediate layer of sand is said to be more expensive and the piles can possibly fail in shear. Truth is that there is no theoretical basis either in favour or against an intermediate layer of sand. From the literature research it was concluded that more insight should be gained in the influence factors on aquiferous crack formation. The focus should lie on developing calculation methods for restraint deformation of annual temperature loads in hardened concrete. The influence of the structural variant on the stresses had to be clarified. A calculation method for the stresses should be developed and a practical advice should be given on the handling of crack formation in structural slabs on underwater concrete. A thermal model was built to calculate temperature loads. First the equivalent ambient temperature from KNMI measurement data served as the basis for calculation of the temperature load. A Finite Element Model has been created that can accurately determine the temperature load on structural slabs on underwater concrete. Based on long term temperature measurements in a structural slab on underwater concrete, the model has been calibrated. A reference case for the temperature load was established to be able to compare the influence of different factors. Temperature loads on any given structural slab on underwater concrete can now be calculated accurately. The calculations in the thermal model resulted in the magnitude of the temperature load, which can vary between 3 C and 17 C. The largest influence factor on temperature load is the 108

109 month of casting. A difference of up to 7 C can be made by casting in another month. The structural variant can also have significant influence on the temperature load. The thickness of the layers can make a difference of several degrees on the temperature load. A 3-D structural model was designed to research the influence factors on restraint. In the structural model different structural variants have been analyzed. This has gained more insight in the influence factor on the degree of restraint and the shear forces in the piles. It is now possible to calculate the degree of restraint of any variant of structural slabs on underwater concrete. From the structural model the degree of restraint is obtained, which varies between 15% and 80%. The restraint is influenced to a large extent by the structural variant. The theoretical restraint can only be reduced by applying an intermediate layer of sand. With an intermediate layer of sand a possibility exists that the piles fail in shear. Application of Gewi piles is most influential as a reduction in restraint. Minimizing the number of piles in the length of a section can reduce the restraint significantly. The height of the intermediate layer can reduce both restraint and the shear forces in the piles. It is beneficial that it is now possible to accurately determine stresses in structural slabs on underwater concrete. For any given structural variant the Finite Element models can determine the temperature load and the degree of restraint. For practical use the complicated models have been transformed into simple calculation methods. Based on the results of the model, hand calculation methods have been developed for easy use in the building industry. In section 6.2 the step-wise method is presented, which makes it possible to estimate the stresses very quickly. To assess practical measures, the probability of crack formation is introduced. The probability of crack formation is related to the ratio of stresses and tensile strength. Also a safety factor is determined based on characteristic values of the stresses and tensile strength. Based on these calculations it can be decided to take measures to reduce the probability of crack formation. The efficiency of the measures is estimated by comparing the reduction of stresses to the cost of the measures. Based on the efficiency of the measures the following practical advices can be given: Only by the application of an intermediate layer of sand a reduction in the degree of restraint can be expected. Shear forces in the piles can exceed the shear strength. The height of the underwater concrete should be kept as low as possible; this reduces the stresses in the structural slab and reduces costs. Application of Gewi piles is a very effective measure to reduce stresses in the structural slab and to reduce the shear stress/strength ratio in the piles. Replacing prefab by Gewi piles can be costly. Based on the need to lower the probability of crack formation a decision should be made if Gewi piles are worth investing in. Sections of more than 20 meter (6 piles in the length of a section) should not be applied with an intermediate layer of sand; the stresses will be higher in longer sections. Extra reinforcement should not be applied as solution for crack formation; prevention of cracks by adding reinforcement is very expensive and does not prevent crack formation. 109

110 When cracks do occur, injection is a relatively cheap, but not always reliable, solution to solve the problem. With the methods described in this research, stress calculation in structural slabs on underwater concrete can be done accurately by using FEM software. Also a quick estimation of the probability of crack formation can be made by newly developed had calculation methods. When the probability of crack formation is unacceptable, measures can be taken to lower the stresses. The efficiency of the measures is described in this research. Cost calculation can be used to compare the cost of crack prevention to injection. However, injection has other disadvantages and not only costs should be taken into account. The new developments in this report have therefore clarified many uncertainties. The research increased the insight in the influence factors on crack formation in structural slabs on underwater concrete significantly and developed an easy calculation method for practical use. 110

111 6.2 Calculation method In this section the hand calculation model for the probability of crack formation is presented. The probability of crack formation can be calculated from the geometry of the structural slab on underwater concrete and the structural variant. Step 1: Properties of the structural slab on underwater concrete Month of casting Filling layer material: Concrete or Sand Pile type: Prefab or Gewi Nr. of piles in length of section Strength class of structural slab Strength class of underwater concrete Strength class of intermediate layer Height of structural slab Height of underwater concrete Height of intermediate layer Step 2: Calculation of the temperature load What is the month of casting? Section Temperature load for reference case Are there differences from the reference case? YES NO Step 3 Section 4.3 Temperature load 111

112 Step 3: Calculation of the degree of restraint Section Theoretical degree of restraint NO Is an intermediate layer of sand applied? Step 4 YES Are Gewi piles used? YES NO No reduction 30% reduction in restraint How many piles in the length of the section? Section 4.6 Is the height of the intermediate layer 400 mm? YES NO No reduction 15% reduction in restraint Final degree of restraint 112

113 Step 4: Calculation of other infleunce factors on stresses Section What is the season of casting? Section 3.7 Relaxation factors What is the height of the structural slab? Section Shrinkage value Section E-modulus and tensile strength 113

114 Step 5: Calculation of stresses Input factors from steps 2, 3 and 4 Section 3.1 Final stresses σ ct 0,6 * f ctm? YES NO Step 6 Probability of crack formation is low, structure is satisfactory. Go to cost calculation 114