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”

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)

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

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

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

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

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

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

“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

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

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