Georisk2017, Denver, CO, USA, 4-6 June 2017
Bayesian Method: A Natural Tool for
Processing Geotechnical Information
Lead discusser: Jie Zhang
Discussers (alphabetical order):
Philip Boothroyd, Michele Calvello, Malcolm Eddleston, Antonio
Canavate Grimal, Papaioannou Iason, Zhe Luo, Shadi Najjar,
Adrian Rodriguez-Marek, Daniel Straub, Marco Uzielli, Yu Wang
Introduction
In geotechnical engineering, it is a common for
engineers to consider information from multiple
sources
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•
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How to combine
information?
Regional experience
Engineering judgement
Direct or indirect laboratory data
Field test data
Performance of existing systems
Such information are often combined based on
engineering judgement and personal experience
Could be subjective and confusing
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Bayesian equation
From a mathematical perspective, the Bayesian method is a natural
tool for information combination
Updated
Prior
P(x|d) = P(d|x)P(x) / P(d)
Observed information
x: uncertain geotchnical quantities
d: observed data
P(x): prior probabibility density functon of x
P(d|x): the probability to observe d givn x, i.e., likelihood function
Computational techniques
 Conjugate prior
• Analytical solution; applicable to problems in special conditions (e.g., Ang & Tang 2007)
 Direct integration method
• Applicable when the number of random variables is small (e.g., Gelman et al. 2013)
 Markov Chain Monte Carlo (MCMC) simulation
• Applicable when the number of random variables is large (e.g., Ching et al. 2009)
 System identification (SI) method
• Applicable when the observed performance is used to update the geotechnical model
parameters (e.g., Tarantola 2005; Wu et al. 2007)
 Other methods
• e.g., Honjo et al. 1994; Gilbert 1998; Ghanem & Spanos, 1991, Sudret 2008, Cañavate et
al. 2015; Straub and Papaioannou 2015
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Example 1 - Updating pile capacity at a site with load test results (Zhang
2004)
Engineering background: Proof load test
piles are widely used to verify design
assumptions
Challenge: it is difficult to assess the
reliability of a design based on a few pile
load test
Bayesian solution
• Prior knowledge: regional experience
about the model uncertainty of a design
method
• Observed data: site-specific load test
• Outcome: site-specific distribution of
the model bias factor and hence the
reliability of the piles
Reliability index for single piles designed with
a FOS = 2 and verified by several proof tests
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Example 2 – Back analysis of slope failure (Hasan & Najjar 2013)
Background: When slope failure is
Bayesian solution
observed, back analysis is often performed
• Prior: laboratory test data are used as prior
to assess the shear strength parameters
distribution
• Observed data: slope failure
Challenge: given FOS (c, f, ru) = 1, there
might be numerous solutions.
• Outcome: updated distribution of c, f, and ru
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Example 3: Back-Analysis of the undrained strength of liquefied
soil (Gangrade et al. 2015)
Background: a key parameter controlling
the extent of lateral movements is the
undrained strength of the liquefied
ground, c’.
Challenges: censored observations, i.e.,
liquefied cases indicates FOS < 1, and
non-liquefied cases indicates FOS >1
Bayesian solution
• Prior knowledge: information from the
literature (Olson & Stark 1992)
• Observed data: liquefied and nonliquefied cases
• Outcome: distribution of the undrained
shear strength c’
Most likely value of c’
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Example 4: Reliability analysis of shallow foundation (Papaioannou
&Straub 2017)
 Bayesian solution
 Background: soil properties are
• Prior knowledge: regional experience
spatially variable.
• Observed data: direct shear tests of soil probes,
 Challenge: The spatial variability is
taken at different depths in the area of the
often difficult to characterize with
foundation are performed
limited data.
• Outcome: updated random field
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Example 5: Identification of underground soil stratification (Wang
et al. 2014)
Background: It is often required to
identify the soil strata based on in-situ
test data, i.e., CPT.
Challenge: : Often needs substantial
engineering judgement
Bayesian solution:
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Bayesian model selection technique
Prior knowledge: uniform distribution
Likelihood data: observed water content
Outcome: soil strata
Bayesian Identification of soil strata in the
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London Clay Formation
Other examples
Embankments
• e.g., Honjo et al. (1994), Calle et al. (2005), Wu et al. (2007), Schweckendiek et al. (2011), Huang
et al. (2014), Kelly & Huang (2015)
Tunnels
• e.g., Lee & Kim (1999); Cho et al. (2006); Camos et al. (2016)
Piles
• e.g., Baecher & Rackwitz (1982), Goh et al. (2005), Kerstens (2006), Ching et al. (2008), Najjar &
Gilbert (2009), Park et al. (2011, 2012), Huang et al. (2014), Abdallah et al. (2015a,b)
Deep excavations
• e.g., Miranda et al. (1999); Juang et al. (2012); Wang et al. (2014); Canavate-Grimal et al. (2015)
Soil liquefaction
• e.g., Cetin et al. (2004), Moss et al. (2006), Ku et al. (2012); Boulanger & Idriss (2012), Zhang et
al. (2016)
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Possible application in relation to Eurocode 7 (1)
Clause 7.6.2.2 Ultimate compressive resistance from static load tests
Clause 7.6.3.2 Ultimate tensile resistance from pile load tests
• Pile foundation example
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Possible application in relation to Eurocode 7 (2)
• Clause 2.7 Observational method
• When prediction of geotechnical behaviour is difficult, it can be
appropriate to apply the approach known as "the observational
method", in which the design is reviewed during construction
• Slope back analysis example
• Liquefaction back analysis example
• Examples in deep excavations and embankments
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Possible application in relation to Eurocode 7 (3)
Clause 2.4.3 Ground properties
• Properties of soil and rock masses, as quantified for design calculations by
geotechnical parameters, shall be obtained from test results, either directly or
through correlation, theory or empiricism, and from other relevant data.
• Shallow foundation example
• Soil strata identification example
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Other applications
 Quality control (e.g., Zhang et al. 2006;
Gilbert et al. 2017 )
 Decision making (e.g., Tang et al. 1994,
Schweckendiek & Vrouwenvelder 2015,
Najjar et al. 2016 )
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Challenges & recommendations for future work
Most engineers are not fully aware of the benefits of Bayesian methods
• Researchers are encouraged to illustrate the benefits of Bayesian methods to the working
professional (e.g., Georisk2017 Bayesian keynote by Dr. Baecher)
Most geotechnical engineers have no training in Bayesian statistics
• Incorporate the Bayesian analysis in the civil engineering reliability courses
• Organize short courses for professionals (e.g., Georisk2017 Bayesian short course by Dr.
Baecher and Dr. Schweckendiek)
May involve quite some computational techniques
• Easy to use tools or procedures for implementation (Two Bayesian tutorial papers are now
available: Straub & Papaioannou 2015, Juang & Zhang 2017)
How to specify the prior information could sometimes be challenging
• Derive the prior information in a more objective and more defendable way (e.g., the
Bayesian equivalent sample method by Dr. Wang & Dr. Cao, and the work by Dr. Ching & Dr.
Phoon to derive prior distribution from global database)
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Thank you!
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Prior distribution: constructed
based on empirical equations
reported in the literature
Multiple variables are updated
simultaneously
Easy to use; can be implemented
in Excel