Elsevier

Engineering Geology

Volume 168, 16 January 2014, Pages 120-128
Engineering Geology

Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method

https://doi.org/10.1016/j.enggeo.2013.11.006Get rights and content

Highlights

  • A non-intrusive stochastic finite element method is developed.

  • Slope reliability with spatially varying shear strength parameters is studied.

  • The proposed method is much more efficient than the LHS method.

  • Ignoring spatial variability may underestimate the probability of slope failure.

  • Variation of probability of slope failure highly depends on factor of safety.

Abstract

This paper proposes a non-intrusive stochastic finite element method for slope reliability analysis considering spatially variable shear strength parameters. The two-dimensional spatial variation in the shear strength parameters is modeled by cross-correlated non-Gaussian random fields, which are discretized by the Karhunen–Loève expansion. The procedure for a non-intrusive stochastic finite element method is presented. Two illustrative examples are investigated to demonstrate the capacity and validity of the proposed method. The proposed non-intrusive stochastic finite element method does not require the user to modify existing deterministic finite element codes, which provides a practical tool for analyzing slope reliability problems that require complex finite element analysis. It can also produce satisfactory results for low failure risk corresponding to most practical cases. The non-intrusive stochastic finite element method can efficiently evaluate the slope reliability considering spatially variable shear strength parameters, which is much more efficient than the Latin hypercube sampling (LHS) method. Ignoring spatial variability of shear strength parameters will result in unconservative estimates of the probability of slope failure if the coefficients of variation of the shear strength parameters exceed a critical value or the factor of slope safety is relatively low. The critical coefficient of variation of shear strength parameters increases with the factor of slope safety.

Introduction

In recent years, the spatial variability of soil properties has received considerable attention in slope stability analysis. Many investigators have contributed to this subject (e.g., Griffiths and Fenton, 2004, Cho, 2007, Low et al., 2007, Srivastava and Sivakumar Babu, 2009, Cho, 2010, Srivastava et al., 2010, Griffiths et al., 2011, Wang et al., 2011, Cho, 2012, Ji et al., 2012, Li et al., 2013c, Zhu and Zhang, 2013). For example, Griffiths and Fenton (2004) studied the effect of spatial variability of undrained shear strength on the probability of slope failure using random finite element method. Cho (2007) investigated the effect of spatially variable soil properties on the slope stability using direct Monte Carlo simulations (MCS). Low et al. (2007) proposed a practical EXCEL procedure to analyze slope reliability in the presence of spatially varying shear strength parameters. Srivastava and Sivakumar Babu (2009) quantified the spatial variability of soil parameters using field test data and evaluated the reliability of a spatially varying cohesive–frictional soil slope. Cho (2010) investigated the effect of spatial variability of shear strength parameters accounting for the correlation between cohesion and friction angle on the slope reliability. Srivastava et al. (2010) investigated the effect of spatial variability of permeability parameter on steady state seepage flow and slope stability. Griffiths et al. (2011) performed a probabilistic analysis to explore the influence of spatial variation in the shear strength parameters on the reliability of infinite slopes. Wang et al. (2011) developed a subset simulation-based reliability approach for slope stability analysis considering spatially variable undrained shear strength. Ji et al. (2012) adopted the First Order Reliability Method (FORM) coupled with a deterministic slope stability analysis to search the critical slip surface when the spatial variability in the shear strength parameters is considered.

In the majority of these studies, the traditional limit equilibrium method (LEM) is used to perform deterministic slope stability analyses. Then, the LEM is combined with random field theory for slope reliability analysis considering spatially variable soil properties. Thereafter, Monte Carlo Simulation is used to evaluate the probability of slope failure. A potential pitfall of the LEM is that some assumptions relating to the shape or location of the critical failure mechanism have to be made. Also, it does not account for the stress–strain behavior of the soil. Additionally, the spatial variability of soil properties cannot be considered realistically with the LEM-based methods, unless the shape of the slip surface is non-circular (Tabarroki et al., 2013). Fortunately, finite element based methods provide solutions to overcome the aforementioned shortcomings underlying the traditional LEM (Farias and Naylor, 1998, Griffiths and Fenton, 2004). As for the slope reliability evaluation, although the direct MCS is simple and suitable for evaluating the probability of slope failure in the presence of spatially variable shear strength parameters, the time and resources required for the MCS could be prohibitive because a substantial number of finite element model runs are needed to obtain reliability results with a sufficient accuracy. The resultant computational efforts are most pronounced at relatively small probability levels or when complex finite element analyses are needed for slope stability analysis. Traditional stochastic finite element methods require significant modification of existing deterministic numerical codes, and become nearly impossible for most engineers with no access to the source codes of commercial software packages (Ghanem and Spanos, 2003, Stefanou, 2009). Therefore, it is necessary to explore more efficient methods for slope reliability analysis, which considers spatially variable shear strength parameters and requires complex finite element analysis for determining the factor of safety.

The objective of this paper is to propose a non-intrusive stochastic finite element method for slope reliability analysis considering spatially variable shear strength parameters. To achieve this goal, this article is organized as follows. In Section 2, the two-dimensional (2-D) spatial variation of the shear strength parameters is modeled by cross-correlated non-Gaussian random fields, which are discretized by the Karhunen–Loève (KL) expansion. In Section 3, the procedure of a non-intrusive stochastic finite element method is presented. Two examples of slope reliability analysis are investigated to demonstrate the capacity and validity of the proposed method in Section 4.

Section snippets

Spatial variability of soil property

A Gaussian random field is completely defined by its mean μ(x), standard deviation σ(x), and autocorrelation function ρ(x1, x2). The autocorrelation function is an important physical quantity for characterizing the spatial correlation of soil properties (Vanmarcke, 2010). In this study, a squared exponential 2-D autocorrelation function is adopted with different autocorrelation distances in the horizontal and vertical directions as follows:ρx1y1x2y2=expx1x2lh2+y1y2lv2where (x1, y1) and (x2, y

Procedure of a non-intrusive stochastic finite element method

A procedure of slope reliability analysis using a non-intrusive stochastic finite element method is proposed in this section, as shown in Fig. 1. This procedure consists of nine steps as follows:

  • (1)

    Identify the spatially varying variables and determine their statistics such as means, coefficients of variation (COVs), distributions and cross-correlation coefficients among the variables associated with the slope reliability problem. Select an appropriate autocorrelation function and estimate the

Application to a saturated clay slope under undrained conditions (ϕu = 0)

In the first example, an undrained clay slope studied by Griffiths and Fenton (2004) and Cho (2010) is investigated. A typical finite element model of the considered slope is shown in Fig. 2. The majority of the elements are squares and the elements adjacent to the slope surface are degenerated into triangles. The types of elements are 4-node quadrilateral elements and 3-node triangular elements. In Fig. 2, the finite element mesh consists of 910 elements and 981 nodes. For illustrative

Conclusions

A non-intrusive stochastic finite element method has been proposed for slope reliability analysis considering spatial variability of shear strength parameters. The KL expansion is adopted to discretize the 2-D cross-correlated non-Gaussian random fields of spatially variable shear strength parameters. Two illustrative examples of slope reliability analysis are investigated to demonstrate the capacity and validity of the proposed method. Several conclusions are drawn from this study:

  • (1)

    The proposed

Acknowledgments

This work was supported by the National Science Fund for Distinguished Young Scholars (Project No. 51225903), the National Basic Research Program of China (973 Program) (Project No. 2011CB013506) and the National Natural Science Foundation of China (Project No. 51329901).

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