1. Discussers (alphabetical order):
International Society for Soil Mechanics and Geotechnical Engineering
TC205 (Safety and serviceability in geotechnical design)
TC304 (Engineering practice of risk assessment and management)
Incorporating Spatial Variability into Geotechnical Reliability-based Design
Lead discusser:
Dian-Qing Li
Thanks … for the introduction. Because the lead discusser, Dr. Li has another presentation in the session in honor of Prof. Wilson Tang, I will present this report on the behalf him. …
Discussers (alphabetical order):
Zi-Jun Cao, Jianye Ching, Satyanarayana Murty Dasaka, Jinsong Huang, Mark Jaksa, Shin-ichi Nishimura, Armin Stuedlein, Giovanna Vessia
JOINT TC205/TC304 WORKING GROUP ON “DISSCUSSION OF STATISTICAL/RELIABILITY METHODS FOR EUROCODES”

2. Spatial variability of geotechnical properties
Introduction
Modeling
Illustrative examples
Characterization
Summary
Spatial variability of geotechnical properties
Characterization
t(z), trend function
σ, standard deviation
λ, scale of fluctuation
ρ, correlation function l
Modeling
Modeling
Geotechnical …, and their properties .. Previous studies have demonstrated that ….Rational treatment of
Rigorous and explicit modeling using random field generation techniques (R-method)
Approximate modeling using spatial average technique (A-method)

3. Applicable to simulation-based full-probabilistic RBD methods
Introduction
Modeling
Illustrative examples
Characterization
Summary
Rigorous modeling by random field simulation
R-method directly simulates random fields of geotechnical design parameters (e.g. effective stress friction, ϕ’) based on their statistical information derived from site investigation without considering influence zones and/or critical slip surfaces that affect responses
Sub-Layer 1:
f′(z1)
Sub-Layer 2:
f′(z2)
···
Sub-Layer i:
f′(zi) d B D
1-D spatial variability
Applicable to simulation-based full-probabilistic RBD methods

4. Introduction
Modeling
Illustrative examples
Characterization
Summary
Approximate modeling by spatial average technique
A-method uses random field theory to calculate statistics of spatial averages of geotechnical design parameters (e.g. effective stress friction, ϕ’) within influence zones and/or along critical slip surfaces affecting responses of geotechnical structures B D
Statistically Homogenous Soil Layer, f′(z) La Lb
Influence zone for side resistance Qside
Influence zone for tip resistance Qtip
Applicable to both full-probabilistic and semi-probabilistic RBD methods

5. Variance reduction factor
Introduction
Modeling
Illustrative examples
Characterization
Summary
Variance reduction factor

6. Drilled Shaft Example R-method A-method Results comparison
Introduction
Modeling
Illustrative examples
Characterization
Summary
Drilled Shaft Example
R-method
A-method
F50
F50
Design compression load
F50 = 800 kN
Allowable displacement
ya = 25 mm
γ = 20 kN/m3
μφ’ = 32°
σφ’ = 5.44°
λ = 0.2~1000 m
Results comparison

7. Sheet Pile Wall Example R-method A-method
Introduction
Modeling
Illustrative examples
Characterization
Summary
Sheet Pile Wall Example
R-method
A-method
Results comparison γ
(kN/m3) φ’
(°) q
(kPa) μ 20 39
8.02 σ
3.9
1.2
λ = 0.2~1000 m

8. Slope Example R-method A-method Results comparison Introduction
Modeling
Illustrative examples
Characterization
Summary
Slope Example
R-method
A-method
Results comparison γ
(kN/m3) φ’
(°) c’
(kPa) u
(m) μ
19.1
27.1 10 σ
2.21
1.72
0.34
λ = 2~5000 m

9. “Worst case” definition Characteristic length
Introduction
Modeling
Illustrative examples
Characterization
Summary
Challenges in characterization of ISV
t(z), σ and λ are site specific
Vary in a wide range l
Need a large amount of data
Demarcation between t(z) and w(z): D>50λ
λ: D > 20λ & sampling interval < λ/2
σ: D > 4λ (Ching et al. 2015, 2017)
Worst-case SOF, depending on
Geotechnical structure behavior
Random field modeling
Study
Problem type
“Worst case” definition
Characteristic length
Worst-case SOF
Fenton et al. (2003)
Bearing capacity of a footing on c-f soil
Mean bearing capacity is minimal
Footing width (B)
1B
Fenton et al. (2005)
Active lateral force for a retaining wall
Under-design probability is maximal
Wall height (H)
0.5~1H
Hu and Ching (2015)
Mean active lateral force is maximal
0.2H

10. Introduction
Introduction
Modeling
Illustrative examples
Characterization
Summary
Major procedures for modeling spatial variability in geotechnical RBD & challenges in probabilistic characterization of spatial variability
Using the A-method with the exact form of variance reduction function agree well with those obtained using R-method provided that reasonable influence zone or critical slip surfaces are considered in the analysis
Using approximate variance reduction function in A-method may lead to either conservative or un-conservative reliability estimates and design results. When the length of influence zone is close to λ, the approximate variance reduction function shall be used with caution.
Major assumptions in this report: failure mechanisms were prescribed prior to the analysis and only 1-D spatial variability was taken into account

11. Thank you ! Georisk 2017, Denver, U.S. This work was supported by
Wuhan University
Georisk 2017, Denver, U.S.
Thank you !
This work was supported by
the National Key Research and Development Program of China
& the National Natural Science Foundation of China