Extension of Spencer’s Circular Model to Stability Analysis of Landslides with Multicircular Slip Surfaces

Yanhao Zheng,Tao Wen,Qinwen Tan,Yingming Yang,Zhiqiang Fan,Huiming Tang

doi:10.1155/2020/1298912

Abstract

This paper presents a new limit equilibrium method based on analysis of landslides with multicircular slip surfaces in the Three Gorges Reservoir area, China. An important innovation of this method is that the rigid sliding mass is divided into numerous interrelated Spencer’s circles sharing the same factor of stability, so that each of them possesses a real centre of rotation and an independent inclination of interslice forces. The analysis is accomplished by iterations to satisfy both force and moment equilibrium for each circle. Two real cases were then adopted to verify the effectiveness of the method in the analysis of both slope stability and the design forces on piles. Factors influencing the performance of the method were also investigated, which reveal that the concavity of the local slip surface near the slope toe has a major impact. The importance of the proximity between the actual and the fitted sliding surfaces was highlighted for ensuring accuracy of the method when extended to the real cases.

Highlights

Limit equilibrium methods of slices (LEMS) to assess slope stability have been prevalent for decades [1, 2]. e earliest slices model was based on a circular slip-surface because some evidence from slope failures in Sweden suggested that the failure surface is often circular in longitudinal section [3,4,5]
Distance from the slice to the slope toe.2 (m) and the Morgenstern & Price (M&P) methods), the design driving force (DDF) on pile.2 and pile.4 shows lower values when compared with those on other piles. is may be attributed to the gentler local sliding surfaces that are around these two piles and supports Tan et al.’s standpoint that a gently inclined position of the sliding surface is more suitable for installing stabilising piles [23], from which the extension of the new method for studying the DDF is proved to be feasible
The entire slip-surface is divided into several interrelated Spencer’s circles, so as to ensure that each of them has a real rotation centre and an independent inclination of interslice forces. Both real cases and conceptual slopes were adopted to verify the effectiveness of the new method, from which the new method is found to be acceptable for both stability analysis and design driving forces analysis

Summary

Introduction

Limit equilibrium methods of slices (LEMS) to assess slope stability have been prevalent for decades [1, 2]. e earliest slices model was based on a circular slip-surface because some evidence from slope failures in Sweden suggested that the failure surface is often circular in longitudinal section [3,4,5]. E novelty of this method is accomplished by dividing the rigid sliding mass into numerous interrelated Spencer’s circles sharing the same FoS, so that each of them possesses a real centre of rotation and an independent inclination of interslice forces. Qi is still derived from equation (2) or (3), but the variable F in the equations should be replaced by Fs. In order to determine the value of N2, force and moment equilibrium equations for each circle (2∼n) should be established in turn in the same way as. Ree indexes, the FoS, the normal stresses on slice bases, and the interslice forces calculated by the above methods for each case, are compared in Table 4 and Figure 11, respectively. Friction angle(°) Cohesion (kPa) E-modulus (MPa) Poisson’s ratio Unit weight (kg/m3)

Methods

Discussion

A: Common point of NM-1 B: Common point of NM-2 C

Conclusion