Elsevier

Computers and Geotechnics

Volume 70, October 2015, Pages 1-17
Computers and Geotechnics

Technical Communication
Three-dimensional slope stability assessment of two-layered undrained clay

https://doi.org/10.1016/j.compgeo.2015.07.011Get rights and content

Abstract

This paper uses the finite element upper and lower bound limit analysis methods to investigate the three-dimensional (3D) slope stability of two-layered undrained clay slopes. The solutions obtained from the slope stability analyses are bracketed to within ±10% or better. For comparison purposes, results from two-dimensional (2D) analyses based on the numerical limit analysis methods and the conventional limit equilibrium method (LEM) are also discussed. This study shows that 3D boundary of a slope can have significant effects on the slope stability. In addition, the results are presented in the form of stability charts which can be convenient tools for practicing engineers.

Introduction

Geotechnical engineering problems such as trench stability [1], [2], tunnelling [3], [4] and slope stability [5], [6] have been investigated for years. Slope stability is generally influenced by the slope’s physical properties, the strength parameters of the soil and the slope geometry while a slope’s profile is affected by its construction approach. In general, a slope can be classified as a cut slope, natural slope or fill slope based on the method of construction. Duncan et␣al. [7] shows that slopes with two-layered of undrained clay are commonly encountered in the construction of embankments or levees.

Slope stability has traditionally been analysed considering plane strain condition. However, various investigators have pointed out that the stability of a slope can be influenced by the 3D boundary of the slope. In the study by Cavounidis [8], it was shown that the factors of safety (F) from three-dimensional (3D) analyses are higher than those from two-dimensional (2D) analyses. Additionally, Gens et␣al. [9] indicated that a 2D back analysis will overestimate the mobilized shear strength and thus lead to an unsafe prediction. As such, many 3D slope stability analysis methods have been developed in recent years. However, many of the methods were extended from the existing 2D limit equilibrium method (LEM). In addition, most 3D assessments utilizing limit analysis methods have been based on the upper bound method alone [10], [11], [12], [13]. This is due to the inherent difficulty in manually constructing the statically admissible stress fields for lower bound limit analysis.

Although many methods have been developed for slope stability assessment, only a few sets of slope stability charts have been produced to date [9], [13], [14], [15], [16], [17], [18], [19], [20]. Furthermore, only some of those charts have considered 3D boundary effects. The conventional limit equilibrium analysis is the most popular approach to assess slope stability and thus the earliest slope stability charts have been proposed based on the LEM [9], [14], [21], [22]. Gens et␣al. [9] and Taylor [22] both investigated slopes with undrained clay. In particular, Gens et␣al. [9] proposed the first set of 3D slope stability charts. In recent years, stability charts have also been developed using limit analysis method. Michalowski [19], Viratjandr and Michalowski [23] and Kumar and Samui [15] performed their study based on a 2D analysis while Michalowski [13] considered 3D effects in his study. Their studies only used the upper bound limit analysis which is not conservative, therefore rigorous solutions have not been widely applied to slope designs.

Unfortunately, stability charts for fill slopes are limited. Therefore, this study aims to investigate the 3D stability of fill slopes using both the upper and lower bound finite element limit analysis methods developed by Lyamin and Sloan [24], [25] and Krabbenhoft et␣al. [26]. The obtained results will be presented in the form of comprehensive and convenient chart solutions that can be used by practicing engineers. These charts are particularly useful for quick first assessments of slopes. It should be noted that 3D boundary effects on slope stability will be investigated thoroughly in this paper. In addition to the stability charts, the 3D failure mechanism will also be discussed. In this study, the fill slopes are made up two layer of undrained clay.

Section snippets

Previous studies

Although many LEM based 3D analysis methods have been developed in the past, most of them are extended from the existing 2D methods [27], [28], [29]. Thus, the inherent limitations of LEM still exist within the formulations. As previously mentioned, several LEM based stability charts have been developed to date [9], [14], [21], [22]. In particular, Gens et␣al. [9] considered 3D effects in their study of undrained clay slope stability and presented their results in the form of stability charts.

Problem definition

Fig.␣1 shows the typical 2D and 3D slope geometry and boundary conditions for the problem considered in this study. The fill materials and foundation which have been divided into Region 1 and Region 2 will have an undrained strength of cu. The cohesive strength in the fill materials (Region 1) will be assigned as cu1 while the cohesive strength in the pre-existing soil (Region 2) is assigned cu2. The strength difference between both layers are considered using cu1/cu2 ratios which range from

Results and discussion

Due to similar obtained trends in the stability charts for various slope inclinations and L/H ratios, the stability charts in Fig.␣3, Fig.␣4, Fig.␣5 only present the solutions for β = 15°, 45° and 75° with L/H = 1, 3 and 5. For simplicity and demonstration purposes, only lower bound numerical solutions from the 3D analyses are shown (the full results, including upper bound results, can be found in the tables in Appendix A). Also they are more conservative and thus the results can be utilized in

Assumed application examples

A case study will be used to demonstrate the convenience of using the stability charts, consisting of a fill slope with the following parameters: cu1/cu2 = 4.5, a soil unit weight of γ = 18 kN/m3, a depth factor of d/H = 2, and a fill material cohesion of cu1 = 50 kN/m2.

Conclusions

This study uses the finite element upper and lower bound limit analysis methods to investigate the stability of slopes specifically for two-layered undrained clay slopes. The results obtained are bracketed to within ±10% or better. In fact, this study has shown that as slope 3D boundary (L/H) increases, the stability number increases which leads to a slope with higher risk. Furthermore, cu1/cu2 ratio is also found to have an effect on the stability number. When cu1/cu2  1.25, the stability of

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