Probabilistic failure envelopes of strip foundations on soils with non-stationary characteristics of undrained shear strength

Géotechnique ◽  
2021 ◽  
pp. 1-44
Author(s):  
Zhichao Shen ◽  
Qiujing Pan ◽  
Siau Chen Chian ◽  
Susan Gourvenec ◽  
Yinghui Tian

This paper investigates probabilistic failure envelopes of strip foundations on spatially variable soils with profiles of undrained shear strength su linearly increasing with depth using the lower bound random finite element limit analysis. The spatially variable su is characterised by a non-stationary random field with linearly increasing mean and constant coefficient of variation (COV) with depth. The deterministic uniaxial capacities and failure envelopes are firstly derived to validate numerical models and provide a reference for the subsequent probabilistic analysis. Results indicate that the random field parameters COVsu (COV of su) and Δ (dimensionless autocorrelation distance) have a considerable effect on the probabilistic normalised uniaxial capacities which alters the size of probabilistic failure envelopes. However, COVsu and Δ have an insignificant effect on the shape of probabilistic failure envelopes is observed in the V-H, V-M and H-M loading spaces, such that failure envelopes for different soil variabilities can be simply scaled by the uniaxial capacities. In contrast to COVsu and Δ, the soil strength heterogeneity index κ = μkB/μsu0 has the lowest effect on the probabilistic normalised uniaxial capacity factors but the highest effect on the shape of the probabilistic failure envelopes. A series of expressions are proposed to describe the shape of deterministic and probabilistic failure envelopes for strip foundations under combined vertical, horizontal and moment (V-H-M) loading.

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Mi Tian ◽  
Xiaotao Sheng

Applying random field theory involves two important issues: the statistical homogeneity (or stationarity) and determination of random field parameters and correlation function. However, the profiles of soil properties are typically assumed to be statistically homogeneous or stationary without rigorous statistical verification. It is also a challenging task to simultaneously determine random field parameters and the correlation function due to a limited amount of direct test data and various uncertainties (e.g., transformation uncertainties) arising during site investigation. This paper presents Bayesian approaches for probabilistic characterization of undrained shear strength using cone penetration test (CPT) data and prior information. Homogeneous soil units are first identified using CPT data and subsequently assessed for weak stationarity by the modified Bartlett test to reject the null hypothesis of stationarity. Then, Bayesian approaches are developed to determine the random field parameters and simultaneously select the most probable correlation function among a pool of candidate correlation functions within the identified statistically homogeneous layers. The proposed approaches are illustrated using CPT data at a clay site in Shanghai, China. It is shown that Bayesian approaches provide a rational tool for proper determination of random field model for probabilistic characterization of undrained shear strength with consideration of transformation uncertainty.


2020 ◽  
Vol 42 (2) ◽  
pp. 125-136
Author(s):  
Marcin Chwała

AbstractThis paper presents an efficient method and its usage for the three-dimensional random bearing capacity evaluation for square and rectangular footings. One of the objectives of the study is to deliver graphs that can be used to easily estimate the approximated values of coefficients of variations of undrained bearing capacity. The numerical calculations were based on the proposed method that connects three-dimensional failure mechanism, simulated annealing optimization scheme and spatial averaging. The random field is used for describing the spatial variability of undrained shear strength. The proposed approach is in accordance with a constant covariance matrix concept, that results in a highly efficient tool for estimating the probabilistic characteristics of bearing capacity. As a result, numerous three-dimensional simulations were performed to create the graphs. The considered covariance matrix is a result of Vanmarcke’s spatial averaging discretization of a random field in the dissipation regions to the single random variables. The matrix describes mutual correlation between each dissipation region (or between those random variables). However, in the presented approach, the matrix was obtained for the expected value of undrained shear strength and keep constant during Monte Carlo simulations. The graphs were established in dimensionless coordinates that vary in the observable in practice ranges of parameters (i.e., values of fluctuation scales, foundation sizes and shapes). Examples of usage were given in the study to illustrate the application possibility of the graphs. Moreover, the comparison with the approach that uses individually determined covariance matrix is shown.


2015 ◽  
Vol 31 (4) ◽  
pp. 381-390
Author(s):  
Y.-G. Hu ◽  
J. Ching

AbstractA new procedure for simulating the active lateral force (Pa) is proposed for clays with anisotropic spatially variable undrained shear strength (su). With the proposed procedure, the Pa samples can be simulated without the use of the random field finite element method (RFEM). It requires only simple algebraic calculations and chart checking. Two retaining wall examples with isotropic or anisotropic random field are used to demonstrate the effectiveness of the proposed procedure.


2017 ◽  
Vol 62 (2) ◽  
pp. 367-384
Author(s):  
Sebastian Olesiak

Abstract Soil strength parameters needed for the calculation of bearing capacity and stability are increasingly determined from field testing. This paper presents a method to determine the undrained shear strength cuWST of the soil, based on the Weight Sounding Test (WST). The innovative solution which allows for a significant reduction of equipment needed for geotechnical field investigation is presented. The proposed method is based on an additional measurement of the torque during testing. It then becomes possible to estimate the undrained shear strength, cuWST of the soil, using the correlation given in this paper. The research results presented in this paper were carried out on selected cohesive soils, Miocene clays from the Carpathian Foredeep.


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