Coupled effects in stability analysis of pile–slope systems

Abstract

A numerical comparison of predictions by limit equilibrium analysis and 3D numerical analysis is presented for a slope–pile system. Special attention is given to the coupled analysis based on the explicit-finite-difference code, FLAC 3D. To this end, an internal routine (FISH) was developed to calculate a factor of safety for a pile-reinforced slope according to a shear strength reduction technique. Coupled analyses were performed for stabilizing piles in a slope, in which the pile response and slope stability are considered simultaneously and subsequently the factors of safety are compared to a solution for a homogeneous slope using an uncoupled analysis (limit equilibrium analysis). Based on a limited parametric study, it is shown that the factor of safety for the slope is less conservative for a coupled analysis than for an uncoupled analysis and thus represents a definitely larger safety factor when the piles are installed in the middle of the slopes and the pile heads are restrained.

Introduction

The stabilization of slopes by placing passive piles is one of the innovative slope reinforcement techniques in recent years. There are numerous empirical and numerical methods for designing stabilizing piles. They can generally be classified into two different types: (1) pressure/displacement-based methods [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]; (2) finite element/finite difference methods [11], [12], [13], [14], [15].

The first type of method is based on the analysis of passive piles subjected to lateral soil pressure or lateral soil movements. Generally, the lateral soil pressure on piles in a row is estimated based on a method proposed by Ito and Matsui [3]. This model is developed for rigid piles with infinite length and is assumed that the soil is rigid and perfectly plastic. Thus, this model may not represent the behavior of actual piles in the field: this model does not take into account the actual behavior of finite flexible piles, soil arching and soft soil, etc. [8], [23] On the other hand, the corresponding lateral soil movements are estimated using either measured inclinometer data or from an analytical result using the finite element approach, empirical correlations or based on similar case histories [9], [14]. However, a major problem with the displacement-based methods is the estimation of free soil displacements, because lateral soil displacements are notoriously difficult to estimate accurately. Moreover, the first method for pile-reinforced slopes often uses limit equilibrium, where soil–pile interaction is not clearly considered and thereby has some degree of weakness in representing the real pile–slope system.

The second type of method has been used to investigate the pile–slope system, which is analyzed as a continuous elastic or elasto-plastic medium using either finite-element or finite-difference formulations. This method provides coupled solutions in which the pile response and slope stability are considered simultaneously and thus, the critical surface invariably changes due to the addition of piles, even though it is computationally expensive and requires extensive training because of the three-dimensional and nonlinear nature of the problem.

For slopes, the factor of safety F is traditionally defined as the ratio of the actual soil shear strength to the minimum shear strength required to prevent failure [16]. As Duncan [17] points out, F is the factor by which the soil shear strength must be divided to bring the slope to the verge of failure. Since it is defined as a shear strength reduction factor, an obvious way of computing F with a finite element or finite difference program is simply to reduce the soil shear strength until collapse occurs. The resulting factor of safety is the ratio of the soil’s actual shear strength to the reduced shear strength at failure. This ‘shear strength reduction technique’ was used as early as 1975 by Zienkiewicz et al. [18], and has been applied by Naylor [19], Donald and Giam [20], Matsui and San [21], Ugai and Leshchinsky [22], Cai and Ugai [23] and You et al. [24], etc.

The shear strength reduction technique is used in this study. It has a number of advantages over the method of slices for slope stability analysis. Most importantly, the critical failure surface is found automatically. Application of the technique has been limited in the past due to a long computational run-time. But with the increasing speed of the desktop computer, the technique is becoming a reasonable alternative to the method of slices, and is being used increasingly in engineering practice.

In this study, factors of safety obtained with the shear strength reduction technique were investigated for the one-row pile groups on the stability of the homogeneous slope. The case of an uncoupled analysis using limit equilibrium analysis and subsequently the response of coupled analysis based on the shear strength reduction method were performed to illustrate the changes of critical surface invariably due to addition of piles on the pile–slope stability problem. The coupled effects were tested against other case studies on the pile–slope stability problem (see Fig. 1, Fig. 2).