Probabilistic modelling of auto-correlation characteristics of heterogeneous slopes

Abstract

Spatial variability of soil materials has long been recognised as an important factor influencing the reliability of geo-structures. This study stochastically investigates the influence of spatial variability of shear strength on the stability of heterogeneous slopes, focusing on the autocorrelation function, auto-correlation distance and cross-correlation between soil parameters. The finite element method is merged with the random field theory to probabilistically evaluate factor of safety and probability of failure via Monte-Carlo simulations. The simulation procedure is explained in detail with suggestions on improving efficiency of the Monte-Carlo process. A simple procedure to create cross-correlation between random variables, which allows direct comparison of the influence of each strength variable, is discussed. The results show that the auto-correlation distance and cross-correlation can significantly influence slope stability, while the choice of auto-correlation function only has a minor effect. An equation relating the probability of failure with the auto-correlation distance is suggested in light of the analyses performed in this work and other results from the literature.

Probabilistic Slope Stability Analysis: A Case Study

“…For a random sampling of soil parameters from a given statistical distribution, MC method is used. This method has been commonly used by other researchers for probabilistic slope stability analyses [3,4,7,13,14]. Since MC method requires long computational time, a series of MC LEM slope stability runs are conducted first, to determine how many samples (number of runs) are sufficient.…”

A general framework for coupled hydro-mechanical modelling of rainfall-induced instability in unsaturated slopes with multivariate random fields

“…where 𝜚 is the auto-correlation function, 𝜃 ℎ and 𝜃 𝑣 are the horizontal and vertical scales of fluctuation (also known as auto-correlation distances), respectively, and 𝜒 ℎ and 𝜒 𝑣 are the autocorrelation distances in horizontal and vertical directions, respectively. The auto-correlation distances are informally understood as the distance within which the values of a given soil property are significantly correlated [47]. Note that in this equation, major and minor autocorrelation distances can be chosen equal to each other (2.0 m), which leads to an 'isotropic' random field.…”

“…1, 50, 52]. The Gaussian autocorrelation function produces random fields with smoother transition and separation between regions of constant property values, compared to the widely-used Markov function [47].…”

Influence of Correlation Distance of Soil Parameters on Pile Foundation Failure Probability

“…In the random field model, the space mean-variance of soil parameters decreases with the increase of the average spatial range [11,12]. The minimum distance between any two points in the soil layer with parameters uncorrelated with each other is called the correlation distance of soil parameters [13][14][15]. Given the influence of the correlation distance, the spatial variability of foundation soil parameters can be better reflected [16,17].…”