Lead discusser: Yu Wang 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 Thanks Prof. Phoon for the introduction. It is my pleasure to … Discussers (alphabetical order): Marcos Arroyo, Zijun Cao, Jianye Ching, Tim Länsivaara, Trevor Orr, Kok-Kwang Phoon, Hansruedi Schneider, Brian Simpson

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

Definition of Characteristic Value Semi-probabilistic design format ISO2394:2015 Consequence class categorizations Design situations Design equations Design values = characteristic value/partial factor Definition of characteristic value Eurocode 7 Clause 2.4.5.2 (2) … intrinsically linked to…, and it is used to produce designs values for verifying the design equation for a given design situation and structure category. The difficulties in defining characteristic values of geotechnical parameters arise from the a wide range of design situations and the fact geotechnical failure modes may not be well-defined, so are design equations. In Eurocode 7 “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

Comparison of Three Possible Definitions CVI=5% fractile of 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) CVI: 26.8 CVIII(D=5): 31.5 CVII(n=10): 32.4 CVIII(D=20): 33.2 f Mean value of f for n =10 Spatial average of f for D = 5m Spatial average of f for D = 20m f’~Normal (35, 5 ) SEXP with SOF = 1m 10 measured data at the interval of 1m Quantification of geotechnical parameter uncertainty is essential 

Geotechnical Site Characterization PROCEDURE INFORMATION CHALLENGES 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?

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

Bayesian Framework Likelihood Function Prior Distribution 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

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

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)

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

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

Thank you!