Selection of Characteristic Values for Rock and Soil Properties using Bayesian Statistics

1. Joint TC205/TC304 Working Group Selection of Characteristic Values for Rock and Soil Properties using Bayesian Statistics and Prior Knowledge Lead discusser: Yu Wang June 2017 Discussers (alphabetical order): Marcos Arroyo, Zijun Cao, Jianye Ching, Tim Länsivaara, Trevor Orr, Kok-Kwang Phoon, Hansruedi Schneider, Brian Simpson

2. Outline of the Report Introduction Definition of characteristic value Bayesian methods Sources and quantification of prior knowledge Software Application examples Concluding Remarks

3. Definition of Characteristic Value • Semi-probabilistic design format ISO2394:2015 • Consequence class categorizations • Design situations • Design equations • Design values = characteristic value/partial factor Eurocode 7 • Definition of characteristic value • Clause 2.4.5.2 (2) “characteristic value of a geotechnical parameter shall be selected as a cautious estimate of the value affecting the occurrence of the limit state.” Probabilistic Mechanical

4. Comparison of Three Possible Definitions • CVI=5% fractileof f (Probabilistic aspect) • CVII=5% fractile of mean value of f from n measurements (Probabilistic aspect considering statistical uncertainty) • CVIII=5% fractile of spatial average of f along the pile depth D (Probabilistic & mechanical aspects) f’~Normal (35, 5 ) SEXP with SOF = 1m 10 measured data at the interval of 1m CVIII(D=20): 33.2 Spatial average of f for D = 20m CVII(n=10): 32.4 Mean value of f for n =10 Quantification of geotechnical parameter uncertainty is essential CVIII(D=5): 31.5 Spatial average of ffor D = 5m CVI: 26.8 f 

5. Geotechnical Site Characterization CHALLENGES PROCEDURE INFORMATION I: Desk-study Prior knowledge Limited site-specific data (e.g., geological maps, geotechnical reports, engineering experience and judgment, etc.) II: Site reconnaissance III: In-situ investigation Site observation data IV: Laboratory testing (e.g., data from test boring, in-situ testing and/or laboratory testing) Information updating process V: Interpretation of site observation data Multi-sources information Transformation model (e.g., empirical regression) VI: Inferring geotechnical properties and underground strata Updated knowledge How to combine them Systematically?

6. Bayesian Framework for Geotechnical Site Characterization • Bayesian approach combines systematically information from different sources for uncertainty quantification

7. Bayesian Framework • Likelihood Function • Probability model MP of XD with model parameters Θp (e.g., random variable, random field) • Transformation model, XD = fT(XM; εT) • Prior Distribution • Non-informative – e.g., joint uniform distribution • Informative – subjective probability assessment framework (Cao et al., 2016) • Posterior Distribution Markov Chain Monte Carlo simulation Equivalent samples of XD

8. BEST EXCEL Add-In (Bayesian Equivalent Sample Toolkit) https://sites.google.com/site/yuwangcityu/best/1 • User-defined model • 12 Build-in model

9. Application Example A clay site of US National Geotechnical Experimentation Sites at Texas A&M University DATA = 5 SPT data Stiff Clay Stiff Clay Uniform PRIOR with m ∈[5MPa, 15MPa] s ∈[0.5MPa, 13.5MPa] (Phoon and Kulhawy 1999a and 1999b) 42 Pressuremeter test data (Briaud 2000) (Briaud 2000)

10. Application Example 5 SPT data & Prior knowledge 42 Pressuremeter test data 5% 3.9MPa

11. Concluding Remarks • Definition and selection of characteristic values of geotechnical parameters are discussed • Development and practical implementation of Bayesian methods for geotechnical site characterization • Bayesian equivalent sample algorithm • Quantification of prior knowledge • User-friendly software in EXCEL • BEST is applicable to direct and indirect measurements • Random field modeling of inherent spatial variability is not covered in this report

12. Thank you!