Advances in Civil Engineering

Volume 2019, Article ID 6268079, 11 pages

https://doi.org/10.1155/2019/6268079

## Risk Assessment of Slope Failure Using Assumption of Maximum Area of Sliding Mass and Factor of Safety Equal to Unit

^{1}School of Civil Engineering, Qingdao University of Technology, Qingdao, China^{2}Cooperative Innovation Center of Engineering Construction and Safety in Shandong Blue Economic Zone, Qingdao, China

Correspondence should be addressed to Liang Li; nc.ude.tuq@gnailil

Received 24 February 2019; Accepted 27 March 2019; Published 15 April 2019

Academic Editor: Jian Ji

Copyright © 2019 Xuesong Chu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper aims to develop an effective tool for quantifying the risk of slope failure and identifying the sources of failure risk by combining the limit equilibrium method and the assumption of maximum area of sliding mass with factor of safety = 1. The assumption adopted in this study is firstly validated through the results from the homogeneous slope model, the laboratory experiment, and the smoothed particle hydrodynamics (SPH) program, respectively. Secondly, the proposed method is implemented through the quantification of slope failure risk and the identification of failure sources for a homogeneous slope and a cohesive slope. The conventional method which quantifies the failure risk based on the slip surface with minimum factor of safety (FS) is also performed to enable the comparison with the proposed method. The comparative study has demonstrated that the conventional method tends to underestimate the failure risk due to the negligence of the whole failure process as compared with the proposed method. The failure risk has a tendency to increase as vertical spatial variability of friction angle and *S*_{u} grow less significant for both proposed method and conventional method. However, the failure sources identified by the conventional method are more likely to decrease as the vertical spatial variability of *S*_{u} becomes less significant for cohesive slope, whereas the proposed method is able to find a nearly constant number of failure sources by considering the whole process of slope failure. As a result, it is worthwhile to point out that attention is highly recommended to be focused on the failure sources when the spatial variability is less significant, even if it is not considered during the risk mitigation and reinforcing works.

#### 1. Introduction

Risk assessment of slope failure accounting for both failure probability and the consequences plays a vital role in slope design and risk mitigation [1, 2]. Much attention has been focused on the issue of quantitative risk assessment of slope failure [3–11]. The failure probability and the consequence were evaluated based on the critical slip surface with the minimum factor of safety (FS) in most of the previous research [12–29]. Although the area (volume for 3D case) of sliding mass corresponding to the critical slip surface with the minimum FS can serve as an index to quantify the consequence of a slope failure, current studies have shown that the critical slip surface with minimum FS is only an initial location of a slope failure, and it cannot represent the whole process of a slope failure, including not only the initiation stage but also the propagation and the evolution stages [8]. Therefore, the use of critical slip surface to determine the consequence is a simple tool, and further studies should be conducted. To properly address this issue, numerical simulations of slope failure using appropriate algorithms have been conducted using material point method (MPM) [30], smoothed particle hydrodynamics (SPH) [31–34], and discrete element method (DEM) [35].

Although the numerical simulations can model the whole process of a slope failure and determine the subsequent consequence, the demanding computational effort involved makes it an unacceptable approach, especially when the Monte Carlo simulation (MCS) is adopted to perform the risk assessment of slope failure where a large number of numerical simulations are inevitable.

To achieve a balance between the computational efficiency and accuracy of calculated results, an alternative tool combining the simplicity of limit equilibrium method (LEM) and the assumption of maximum area of sliding mass (MASM) for slope failure is developed in the current study. As will be demonstrated in the later sections, the proposed method is an effective and efficient tool for the risk assessment of slope failure. The paper starts with the validation of MASM assumption based on respective experimental and homogeneous slope models, followed by the brief review of framework for risk assessment of slope failure by MCS. Then, the proposed methodology is illustrated through three slope stability examples. Finally, conclusions are drawn, and discussions are made to provide insights into geotechnical reliability analysis.

#### 2. Validation of Assumption of MASM and Its Use in Determination of Consequence

##### 2.1. Validation Based on Homogeneous Slope Model

A simplified homogeneous slope model with slope height *H* = 5 m and slope angle *α* = 45° is adopted to validate the assumption of MASM. The soil of slope has a cohesion *c* = 0 and friction angle *φ* = 30°. The critical slip surface with the minimum FS for this slope model is determined by SLOPE/W (LEM) and FLAC (FDM), respectively. The minimum respective FS values calculated by LEM (based on Morgenstern–Price method) and FDM are 0.58, and it is identical to that calculated by using equation (1), that is, FS = tan 30°/tan 45° = 0.58:where is the factor of safety, is the friction angle, and is the slope angle of the simplified slope model. Figure 1 plots the critical slip surface obtained by LEM and the contour of shear strain rate obtained by FDM. It can be noticed from Figure 1 that the critical slip surface by LEM is nearly parallel to the slope surface line. The area of sliding mass encompassed by the critical slip surface and the slope surface line is 0.34 m^{2}. Although the same FS is obtained, FDM indicates a different critical slip surface which is located at the upper part of the slope surface compared with that by LEM, as shown in Figure 1(b). The difference in the critical slip surface may be attributed to inherent assumptions between LEM and FDM, and detailed explanations are not provided herein. As noted in [33], the critical slip surface indicates only the initial location of slope failure and provides limited information for the whole process of slope failure. It can be intuitively appreciated that the slope is still instable after the removal of the critical slip surface obtained by LEM (i.e., the extreme case when the 0.34 m^{2} sliding mass slides away). A new critical slip surface will be obtained based on the updated slope geometry. This process will be repeated several times until the updated geometry has a slope angle of 30° (at that time, the FS calculated using equation (1) is equal to 1.0). The simplified final slip surface with FS = 1 as shown in Figure 1 by dashed blue line has an area of sliding mass = 9.15 m^{2}. Significant difference in the area of sliding mass between the critical slip surface and the simplified final slip surface is observed, and the choice of the slip surface must be properly dealt with before the consequence of a slope failure is rationally quantified.