1. 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

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
Definition of characteristic value
Eurocode 7
Clause (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

4. 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 

5. 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?

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

7. 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

8. BEST EXCEL Add-In (Bayesian Equivalent Sample Toolkit)
12 Build-in model
User-defined 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. 42 Pressuremeter test data
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!