Load and Resistance Factor Geotechnical Design Code Development in Canada. by Gordon A. Fenton Dalhousie University, Halifax, Canada

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1 Load and Resistance Factor Geotechnical Design Code Development in Canada by Gordon A. Fenton Dalhousie University, Halifax, Canada 1

2 Overview 1. Past: Where we ve been allowable stress design partial (strength) vs. total resistance factors 2.Present: Where we are current implementation in NBCC and CHBDC 3.Future: Where we are going incorporating site/model understanding allowing for failure consequence how to get the factors? 2

3 Past: Where we ve been geotechnical design based on working (allowable) stress prior to and 1983 bridge foundation design codes adopt partial factor format from Danish practice partial factor format did not lead to design consistency with allowable stress approach, so not readily accepted by geotechnical engineers. total resistance factor format adopted in the bridge foundation design code in

4 WSD TOLRFD DEVELOPMENT OF A GEOTECHNICAL DESIGN CODE Working (or Allowable) Stress Design (WSD) was the basis of geotechnical design until 1979, Rˆ F Lˆ s Geotechnical design codes have since been migrating towards a Load and Resistance Factor Design (LRFD) approach embedded in a Limit States Design (LSD) framework, Ψϕ Rˆ η I γ Lˆ gu u i ui ui i i 4

5 WORKING STRESS DESIGN Factors of safety (F s ) based on experience and observed performance All uncertainty lumped into a single factor Many years of empirical experience (extensive database) Simple, deterministic Does not lend itself to the estimation of failure probability thus difficult to get a sense for probability of failure F s is not quantitatively meaningful 5

6 LOAD AND RESISTANCE FACTOR DESIGN RATIONALE account for load and resistance uncertainties separately introduce reliability-based design benefits into geotechnical designs, e.g. increased construction economies for low failure consequence(low risk) problems, increased investigation effort, etc. harmonize with structural codes 6

7 Load and Resistance Factor Design replaces single factor-of-safety with a set of partial safety factors (load and resistance factors) acting on individual components of resistance and load (Taylor, 1948, Freudenthal, 1951, 1956, Hansen, 1953, 1956) Load and resistance factors are derived to account for; variability in load and material properties variability in construction model error (approximations in design relationships) failure consequences 7

8 Load and Resistance Factor Design load factors, γ i > 1, account for variability in loads resistance factor, ϕ < 1, accounts for variability in soil properties, variability in construction, and model error consequence factor, Ψ, accounts for failure consequences ΨϕRˆ γ Lˆ (LRFD) i i 8

9 Load and Resistance Factor Design Two common resistance factor implementations: 1) total resistance factor: a single resistance factor applied to the final computed soil resistance (as shown in previous slide) 2) partial resistance factors: multiple resistance factors applied to components of soil strength separately, e.g. to tan(φ ), c, etc. Also known as factored strength. 9

10 Partial Resistance Factor Approach only explicitly considers uncertainties associated with material strength parameters (e.g. not with model error) often implemented with myriad partial factors in order to account for all sources of material uncertainty sense of real behaviour often lost may not capture true mechanism of failure when failure mechanism sensitive to changes in material strengths non-linearity issues: resistance based on partial resistance factors is not the same as total factored resistance based on unfactored material parameters 10

11 Total Resistance Factor Approach resistance computed as with the WSD approach better representation of actual failure mechanism resistance is factored once at the end very similar to traditional F s approach, except specifically applied to the resistance allows for a smoother transition from WSD to LRFD allows engineers to work with real numbers until the last step where the result is factored. consistent with structural codes, where each material has its own single resistance factor soil is an engineering material 11

12 Comparison of LRFD Codes The following table lists the load and resistance factors used in a variety of geotechnical design codes from around the world. Where the code suggests a range of values (dependent, for example, on investigation intensity), only the range is presented. To assess the relative conservatism of the various codes, the required area of a spread footing designed against bearing failure (ULS) using L ˆ,, c = 100, φ = 30 D = 3700 L ˆ L = 1000 is computed in the rightmost column. The codes are ranked from the most conservative (top) to the least conservative (bottom). 12

13 Code Values of Load and Resistance Factors Dead Load (shallow foundations) Live Load tan(φ ) c Bearing Sliding Area CFEM NCHRP NCHRP Denmark AASHTO B. Hansen AS CHBDC AS Eurocode7 Model Eurocode7 Model ANSI A

14 Present: Where we are 1. National Building Code of Canada (2010) specifies Limit States Design, but resistance factors do not appear in the code they appear in the User s Guide. Importance factors applied to (site specific) snow, wind, and seismic loads. 2. Canadian Highway Bridge Design Code (2006)specifies both Limit States Design and the required resistance factors. Importance factors applied to snow, wind, and seismic loads. 14

15 National Building Code of Canada User s Guide

16 Canadian Highway Bridge Design Code

17 Future: Where we re going Reliability-Based Design Goals: Account for uncertainty rationally and consistently Make use of PDFs of loads and resistances (at least mean and variance) Quantify probability of failure Achieve societally acceptable levels of risk for our engineered systems (where risk = failure consequence times failure probability) 17

18 RELIABILITY-BASED CODE OBJECTIVES You pay for a site investigation whether you have one or not (Institution of Civil Engineers, Inadequate Site Investigation, 1991) There is a desire in the Canadian geotechnical community to: provide a means to adjust design/construction economies based on level of site understanding take site investigation/modeling intensity into account in the design process provide rationale for increased investigation/modeling effort provide a means to adjust geotechnical system reliability based on potential failure consequences higher reliability for more important structures/systems regardless of loading type 18

19 RATIONALE FOR RELIABILITY-BASED FOUNDATION DESIGN Reliability-based design concepts allow quantification of reliability, allow designs to target a specified reliability level, reward better site investigationby permitting a higher factor to be used in design, thus permitting a more economical design while ensuring acceptable reliability, lead to harmonizationwith other structural codes by establishing a common conceptual framework to address reliability issues. 19

20 CONCEPTUAL OVERVIEW FOR RELIABILITY- BASED DESIGN the probability and consequence of failureare considered in determining resistance and consequence factors reliability-based resistance factors are applied to the resistance, at both ultimate and serviceability limit states and, eventually, under both static and seismic loading conditions cost-effective resistance and consequence factors depend on the degree of understandingof the site conditions and accuracy of the design model (resistance factors) the consequenceof not providing adequate geotechnical resistance to imposed loads (consequence factor) the overall goal is to save money, for specified tolerable riskand required performance, by considering the trade-off between initial design and construction costs and long-term costs, including cost of failure. 20

21 FLOATING RESISTANCE FACTOR TABLE (CONCEPTUAL) HIGH Consequence DEFAULT VALUE 0.8 LOW Consequence LOW Uncertainty HIGH Uncertainty 21

22 RELIABILITY-BASED DESIGN CODE DEVELOPMENT Basic idea is to split traditional into 1. Load factors from load section of code, 2. Resistance factors, ϕgu and ϕgs : capture resistance uncertainty Depend on level of site and prediction model understanding Propose three degrees of site understanding: high, typical, and low Consider SLS and ULS resistance factors separately (different target Ψ maximum acceptable failure probability) F s 3. Consequence factor, : captures system importance (failure consequence) Propose three consequence levels: high, typical, and low High: β= 3.7 (p f = 1/10,000) at ULS, β= 3.1 (p f = 1/1000) at SLS Typical: β= 3.5 (p f = 1/5,000) at ULS, β= 2.9 (p f = 1/500) at SLS Low: β= 3.1 (p f = 1/1,000) at ULS, β= 2.3 (p f = 1/100) at SLS 22

23 LOAD AND RESISTANCE FACTOR DESIGN Ultimate Limit State (ULS) Factored ultimate geotechnical resistance effect of factored ULS loads where Ψ ϕ gu Rˆu γ ui Lˆui Ψϕ Rˆ = consequence factor, = ultimate geotechnical resistance factor, = ultimate characteristic geotechnical resistance, = i thuls load factor, γ Lˆ gu u ui ui i = i thload effect for a given ULS. 23

24 LOAD AND RESISTANCE FACTOR DESIGN Serviceability Limit State (SLS) Factored serviceability geotechnical resistance effect of factored SLS loads where Ψ ϕ gs Rˆs γ si Lˆsi Ψϕ Rˆ = consequence factor, gs s si si i = serviceability geotechnical resistance factor, = serviceability characteristic geotechnical resistance, = i th SLS load factor, and γ Lˆ = i th load effect for a given SLS. 24

25 DEGREE OF SITE AND PREDICTION MODEL UNDERSTANDING Site and prediction model understanding includes; understanding of the groundand the geotechnical properties throughout the site, the type and degree of confidence about the numerical prediction modelsto be used to estimate serviceability and ultimate geotechnical resistances, and observational (monitoring) methods for confirmation. 25

26 DEGREE OF SITE AND PREDICTION MODEL UNDERSTANDING Motivation: Differentiating between levels of site understanding allows for design economies the greater the level of understanding, the lower the risk of failure and the greater the economy of the final design should be. Allows the designer to show proof (thus justifying higher design phase costs) that increased understanding (e.g. increased site investigation) leads to construction savings and lower total project costs. 26

27 DEGREE OF SITE AND PREDICTION MODEL UNDERSTANDING Three levels of site understanding are proposed in the next CHBDC: High understanding: Extensive project-specific investigation procedures and/or knowledge is combined with prediction models of demonstrated (or proven) quality to achieve a high level of confidence with performance predictions. Typical understanding: Usual project-specific investigation procedures and/or knowledge is combined with conventional prediction models to achieve a typical level of confidence with performance predictions. Low understanding: Understanding of the ground properties and behaviour are based on limited representative information (e.g. previous experience, extrapolation from nearby and/or similar sites, etc.) combined with conventional prediction models to achieve a lower level of confidence with the performance predictions. 27

28 ULS GEOTECHNICAL RESISTANCE FACTORS (STATIC LOADING) ϕ gu Limit State Degree of Understanding Low Typical High Shallow Foundations Bearing resistance Passive resistance Horizontal resistance (sliding) Ground Anchors Static analysis tension Static test tension Deep Foundations Piles Static analysis Compression Tension Static test Compression Tension Dynamic analysis compression Dynamic test compression (field measurement and analysis) Horizontal passive resistance (for illustration only factors are not finalized) 28

29 SLS GEOTECHNICAL RESISTANCE FACTORS (STATIC LOADING) ϕ gs Limit State Degree of Understanding Low Medium High Shallow Foundations Settlement Embankments Settlement Lateral displacements Deep Foundations Piles Settlement Lateral displacements Retaining Systems Settlement Horizontal Deformation Anchors Displacement (for illustration only factors are not finalized) 29

30 CONSEQUENCE FACTOR Motivation: Different structures will have different consequences of failure. For example, the failure of an expressway bridge has far higher consequences (life threat, economic, etc.) than does the failure of a low volume rural bridge. The target maximum acceptable failure probability of a structure with high failure consequenceshould be significantly lower than that for a structure with low failure consequence. Rational assessment on the basis of failure probability and consequence of failure will allow for more realistic allocation of infrastructure budgets. 30

31 CONSEQUENCE FACTOR Geotechnical systems can be assigned consequence levels associated with exceeding various limit states; High consequence structure is designed to be essential to post-disaster recovery (e.g. hospital or bridge lifeline), and/or has large societal and/or economic impacts, Typical consequence structure is designed for typical failure consequences, e.g. the usual office building, bridge, etc. This is the default consequence level. Low consequence failure of the structure poses little threat to human safety, e.g. storage utilities, very low traffic volume bridges, temporary structures. 31

32 CONSEQUENCE FACTOR TABLE Consequence Level Reliability Index, β (SLS in parentheses) Example Consequence Factor, Ψ High 3.7 (3.1) Typical 3.5 (2.8) Low 3.1 (2.3) Lifelines, Emergency Highway bridges Secondary bridges (for illustration only factors are not finalized) 32

33 SUMMARY OF PHILOSOPHICAL CHANGES introduced three levels of site understanding high, typical (default), and low through the resistance factor resistance factors vary with site understanding higher for better understanding this approach allows for greater economies in the tradeoff between design/investigation effort and overall construction costs introduced three levels of failure consequence high, typical (default), and low through the consequence factor consequence factor, which modifies the factored resistance, varies with consequence level lower for higher consequences this also allows for greater economies in the tradeoff between target reliability and construction costs 33

34 Determination of Resistance Factors Level III: Fully Probabilistic Analysis The Random Finite Element Method (RFEM) The Random Finite Element Method involves a combination of Random Field Theory (e.g. Fenton and Vanmarcke 1990) with the Finite Element Method (e.g. Smith and Griffiths 2004) The method takes into account the mean, standard deviation and spatial correlation length of the input ground parameters as well as for random loading. The method takes full account of the statistical nature of local averaging of ground properties over the finite elements. The method is applied in a Monte-Carlo framework. 34

35 RFEM The Random Finite Element Method (RFEM) offers many advantages over conventional probabilistic analysis tool especially for nonlinear analyses. -reduced model error: no a priori judgment relating to the shape or location of the failure surface. The FE analysis seeks out the critical mechanism. -a worst case spatial correlation has been clearly identified for most geotechnical problems which leads to the highest probability of failure. We don t need to know the correlation length. -allows for the investigation of the affect of site understanding on design and code development. 35

36 Shallow Foundation Bearing Capacity Degree of Site Understanding 36

37 Shallow Foundation Bearing Capacity 37

38 RESISTANCE FACTORS FOR BEARING CAPACITY Resistance factors can be estimated theoretically; o for various failure consequence levels (e.g. low, p m = 0.01, or high, p m = ) o for various levels of site understanding. Note the worst case correlation length. 38

39 Earth Pressure Analysis Consider a frictional soil where we map tanφ onto the mesh (c =0) Active Pressure Typical realizations of the Monte-Carlo simulations. Light zones are low strength and dark zones are high strength 39

40 Earth Pressure Analysis Now sample the soil and predict force on the wall using traditional methods. Design the factored wall resistance against sliding to be ϕ Rˆ = F P gu u s a H H 2 H 2 Single soil sample at a depth of H/2 and H/2 away from the wall 40

41 Earth Pressure Analysis Estimated probability that the actual active force on wall exceeds the factored design resistance for a) friction angle and unit weight independent, and b) friction angle and unit weight strongly correlated 41

42 Shallow Foundation Settlement 42

43 Shallow Foundation Settlement 43

44 Shallow Foundation Settlement Various sampling schemes to predict foundation settlement 44

45 Shallow Foundation Settlement 45

46 Deep Foundations 46

47 Deep Foundations Failure probability as a function of 1. site understanding, r 2. residual variability, v c 47

48 Deep Foundation Resistance Factors 48

49 Consequence Factors for Bearing Capacity Fig. 1 Sampling layout Table 1 Parameters considered Parameters Values Considered Coefficient of variation, V c 0.1, 0.2, 0.3, 0.5 Correlation length, θ(m) 0.1, 1.0, 2.0, 3.0, 6.0, 10.0, 50.0 Sampling distance, r (m) 0.0, 4.5, 9.0 Resistancefactor, ϕ gu 0.4, 0.5, 0.65 Consequence factor, ψ u 0.80,0.85, 0.90, 0.95, 1.00, 1.05, 1.10, 1.15, 1.20 D = averaging domain under the footing Q = sampling region H = depth to bedrock Soil cohesion, c, is assumed to be lognormally distributed with mean µ c =100 kn/m 2, friction angle with mean µ c =20 o 49 September 21, 2009

50 Consequence Factors for Bearing Capacity Fig. 2 Failure probability plot Fig. 3 Failure probability-consequence factor plot Target p f September 21, 2009

51 Consequence Factors for Bearing Capacity Fig. 4 Resistance factor plot φ gu =0.5 Fig. 5 High failure consequence plot Fig. 6 Low failure consequence plot ψ u =0.95 ψ u =1.15 September 51 21, 2009

52 Consequence Factors for Bearing Capacity Source Consequence Level Low Medium High Recommended AASHTO (2007) AS (2004) Eurocode I (Gulvanessian et al., 2002) NBCC (2005, snow and wind loads) NBCC (2005, earthquake loads) September 21, 2009

53 How to Use Theoretical Results 53

54 SUMMARY o Geotechnical design codes are migrating towards LRFD/LSD to allow; harmonization with structural codes quantification of reliability o Soil and rock are typicallysite specific andhighly (spatially) variable. The development of LRFD in geotechnical engineering is a significant challenge. o Reliability-based design codes are currently largely developed through calibration with WSD. o Design codes should allow for varying degrees of site understanding and take failure consequence into account. o Sophisticated probabilistic tools exist to assess risk and develop required resistance and consequence factors (e.g. RFEM). o Much work is still required, but efforts are ongoing world-wide. 54

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