Determination of Mohr–Coulomb Parameters from Nonlinear Strength Criteria for 3D Slopes

Di Wu,Juan Zhang,Yue Qiu,Yuke Wang,Yukuai Wan

doi:10.1155/2019/6927654

Abstract

Many experimental data have illustrated that the strength envelops for soils are not linear. Nevertheless, the linear Mohr–Coulomb (MC) strength parameters are widely applied for the conventional method, software codes, and engineering standards in the slope design practice. Hence, this paper developed the 3D limit analysis for the stability of soil slopes with the nonlinear strength criterion. Based on a numerical optimization procedure written in Matlab software codes, the equivalent MC parameters (the equivalent friction angle and the equivalent cohesion) from the nonlinear strength envelopes were derived with respect to the least upper-bound solutions. Further investigations were made to assess the influences of nonlinear strength parameters and slope geometries on the equivalent MC parameters. The presented results indicate that the equivalent MC parameters are closely related to the nonlinear strength parameters. As the inclination angle increases, the equivalent friction angle becomes bigger, but the equivalent cohesion becomes smaller. Besides, 3D effects on the equivalent MC parameters were found to be slight. The presented approach for the determination of MC strength parameters is analytical and rigorous, and the approximate MC strength parameters in the provided design tables can be alternative references for practical use.

Highlights

Strength criterion is critical for all types of materials in the area of slope stability analysis
The strengths of soils and rocks are universally presented by the linear Mohr–Coulomb (MC) failure envelope, which represents the shear strength by two MC strength parameters: the friction angle and the cohesion
These presented investigations have been made for slopes in rock masses satisfying the Hoek-Brown criteria and the slope stability analysis have been generally conducted in the condition of plain strain

Summary

Introduction

Strength criterion is critical for all types of materials in the area of slope stability analysis. [11]; Li et al [12]; Shen & Karakus [13]; Gao et al [14, 15]; Zhao et al [16]; Xu & Yang [17]) These nonlinear failure criteria are not presented in forms of MC strength parameters and they cannot be directly used in practice for slope design. Yang & Yin [28] employed the tangential technique into the limit analysis method to evaluate the equivalent MC parameters for rock slopes with the Hoek-Brown strength envelope. Reviewing the literature, these presented investigations have been made for slopes in rock masses satisfying the Hoek-Brown criteria and the slope stability analysis have been generally conducted in the condition of plain strain. The influences of nonlinear parameters and slope geometries (the slope inclination and 3D effect) on the equivalent MC parameters have been further investigated in this paper

Estimation of MC Parameters for 3D Soil Slopes

H H x R a y x e

Numerical Results and Analyses

Example Problems

Conclusions