Journal of Computational Engineering

Volume 2015, Article ID 895142, 10 pages

http://dx.doi.org/10.1155/2015/895142

## Slope Stability Analysis of Earth-Rockfill Dams Using *MGA* and *UST*

Department of Hydraulic Engineering, School of Civil Engineering, Tongji University, Shanghai 200092, China

Received 8 January 2015; Revised 21 March 2015; Accepted 24 May 2015

Academic Editor: Kostas J. Spyrou

Copyright © 2015 Li Nansheng 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

The nonlinear *Unified Strength Theory* (*UST*), which takes into account the effect of intermediate stress and nonlinear behavior on geotechnical strength, is applied in slope stability analysis of *earth-rockfill dams* (*ERD*) in this paper. The biggest drawback for general determination of slip surface is that it must presuppose the shape of slip surface and is unable to identify the critical noncircular slip surface more accurately. This paper proposes an optimal analytic model of slope stability analysis of *ERD* and employs *modified genetic algorithm* (*MGA*) to search for the slip surface on the basis of shear failure criteria of the nonlinear *UST* without prior assumption of the shape of slip surface. The application of *MGA* dependent on Matlab toolbox to the slope stability analysis of *ERD* shows that *MGA* can consequently overcome the weakness of easily falling into local optimal solutions brought by general optimal algorithms.

#### 1. Introduction

The material model of geotechnical strength plays a very important role in the problems of slope stability of* ERD*. Many researchers [1–4] have made a large amount of research work about the effect of applied loads and groundwater on slope stability of* ERD*, but it is still open for further research on the slope stability of* ERD* because of the complexity of the soil materials. The parameters of geotechnical strength in Slices Method based on the rigid body limiting equilibrium theory are ones related to the failure criterion of linear shear strength, just like in* Mohr-Coulomb* failure criterion that is widely applied in geotechnical engineering.* Mohr-Coulomb* failure criterion is the lower limit of a linear convex function and does not consider the effect of intermediate stress on the geotechnical strength, so the numerical results trend to more safety. However, the intrinsic complexity of the mechanical property of geotechnical materials results in that there are almost few strength criteria which can accurately describe the nonlinear fractural characteristics of soils and even the same with linear failure criteria. Some researches [5–7] have shown that the failure of geotechnical materials with nonlinear destruction is just one special case of failure criteria under linear damage and the intermediate stress effect which can enhance the slope safety factors to some degree. The major determinants causing the dams to be broken include applied forces, seepage, and earthquake. As known to all, the strength parameters of the soil play an indispensable role in the slope stability analysis of* ERD*. Many experts [1–4] have done a lot of studies on the effects produced by external loads and underground water on the slope stability; however there are still many works to be done in the field of strength theory of geotechnical material. By so far, a few hundred or more of yielding and failure criteria [8–11] have been proposed, whose applications in the geotechnical engineering have to be seriously restricted because there is not a general failure formula that is appropriate for all kinds of materials and different mechanical status. In 1991 Professor* Yu* [11] proposed the* UST* on the basis of all existing strength theories, by combining the double shear strength theory with the single shear strength theory into only one formula.* UST* is thought as the high generalization of all kinds of existing strength theories, but* UST* is only asymptotic approximation for the most of the nonlinear issues.

The Slices Method, based on the rigid body limiting equilibrium theory, should suppose the shape of slip surface in advance, so the greatest weakness is that it is difficult to cast about for the slip surface quickly and accurately corresponding to the minimum safety coefficients of slip surfaces. The geometrical configuration of the slip surfaces is assumed as in circular arc for the most of the searching algorithms, but we must take an arbitrary shape of slip surfaces for heterogeneous soil materials and discrepant distribution of pore pressure in soils. In the determination of minimum safety factor and its corresponding arbitrary slip surfaces, it might be the best choice to use the optimization methods to arrive at satisfactory results when the objective function is convex and the searching domains are irregular. But for the objective function with multipeak in the complicated searching domains, the general optimization methods often get into local optimal solutions for complex geotechnical structures and heterogeneous soil layers. On the basis of biology immune principles, a novel optimization algorithm [12–14] is proposed for solving many optimal solutions to multimodal functions. Since the late 1980s, the slope stability analysis begins to enter the period when the numerical theory develops flourishingly and finite element method becomes one method of spatial discretization which is the most widely applied; most popular methods of slope stability analysis include Shear Strength Reduction [15, 16] and Gravity Increase Method. When the Shear Strength Reduction Method is used for slope stability analysis and the mechanical states of soils are very close to limiting equilibrium, it is difficult to converge and to solve governing equations in numerical calculation.* Genetic Algorithm* (*GA*) is a global optimization algorithm, so it can overcome the shortcomings of the ordinary optimization methods that fall easily into local optimum.

How to ascertain the most critical slip surfaces faster and more accurately can be regarded as a difficult affair in the slope stability analysis of* ERD*, upon which this paper tries to apply the multivariable nonlinear optimal theory in slope stability analysis which is built on* Matlab* platform and then simulate the critical slip surfaces of* ERD* slope to find its minimum safety coefficient. For* GA* is a sort of global optimization method and can avoid simply getting into local minima, the paper will analyze slope stability by way of* GA*. How* UST* can be applied in the stability analysis of slops still makes few progresses, so this paper will try to put the linear and nonlinear* UST* applied to the stability analysis of* ERD* and compare various strength criteria to the influence of the slope stability of* ERD*. One of the difficulties of the slope stability analysis of* ERD* is how to determine the most critical slip surfaces more accurately and faster, although there have been some valuable achievements made by researchers in China, but what the most appropriate methods are still has not confirmed. Based on* Matlab* platform we try to apply the nonlinear optimization theory with multivariable to the stability analysis of* ERD* and to determine the minimum safety factor of slope stability in simulation of the critical slip surfaces of* ERD*.

#### 2. Linear and Nonlinear* UST*

Taking a unique mechanical model as the theoretic basis, Professor* Yu* puts forward an* UST* unifying all sorts of the linear and nonlinear strength theories into one. The linear and nonlinear* UST* proposed by Professor* Yu* can be summarized as [11] follows.

Ifthenalso ifthen we take following formula:in whichwhere , , and are the first, second, and third principal stresses, respectively, is the ratio of the tension with compression strength, is the factor concerned with the normal stress effect, is related coefficient to the intermediate principal stress, is nonlinear coefficient reflecting failure criteria, is cohesion, and is the inner friction angle.

When the coefficients of twins shear strength , , , and take some specific values,* UST* can be converted into existing major yield and strength criteria such as* Mohr-Coulomb* criterion as shown in Table 1. So we might think that the linear and nonlinear* UST* more comprehensively reflect the strength conditions of the practical problems of geotechnical engineering.