# Generalized three-dimensional slope-stability analysis

Dov Leshchinsky, Ching Chuan Huang

Research output: Contribution to journalArticle

60 Citations (Scopus)

### Abstract

A 3-D slope-stability-analysis method, explicitly satisfying all limiting-equilibrium equations, is presented. To make the problem statically determinate, the variational approach, rather than intuition in 3-D, is used. In this approach, the normal stress over the user's specified slip surface, which satisfies global limiting equilibrium and produces the minimum factor of safety for the critical surface, is sought and obtained mathematically. A simple numerical scheme to attain the safety factor is detailed and all the algorithms needed to assemble a computer program are given. Upon discretization of the surface by n rectangular elements, n simultaneous linear equations are solved for n discrete normal stresses. It is also necessary to solve three nonlinear equations for the factor of safety, Fs, and the coordinate of the center of rotation (xc, zc). It was observed that for a selected potential slip surface there may be many possible combinations of (n + 2) roots, all giving essentially the same Fs. The presented example problem demonstrates the importance of 3-D back-analysis if one is to configure in-situ soil strength.

Original language English 1748-1764 17 Journal of Geotechnical Engineering 118 11 https://doi.org/10.1061/(ASCE)0733-9410(1992)118:11(1748) Published - 1992 Nov

### Fingerprint

Slope stability
Dimensional stability
slope stability
stability analysis
safety
back analysis
soil strength
Safety factor
Linear equations
Nonlinear equations
Computer program listings
Soils
software

### All Science Journal Classification (ASJC) codes

• Environmental Science(all)
• Earth and Planetary Sciences(all)

### Cite this

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title = "Generalized three-dimensional slope-stability analysis",
abstract = "A 3-D slope-stability-analysis method, explicitly satisfying all limiting-equilibrium equations, is presented. To make the problem statically determinate, the variational approach, rather than intuition in 3-D, is used. In this approach, the normal stress over the user's specified slip surface, which satisfies global limiting equilibrium and produces the minimum factor of safety for the critical surface, is sought and obtained mathematically. A simple numerical scheme to attain the safety factor is detailed and all the algorithms needed to assemble a computer program are given. Upon discretization of the surface by n rectangular elements, n simultaneous linear equations are solved for n discrete normal stresses. It is also necessary to solve three nonlinear equations for the factor of safety, Fs, and the coordinate of the center of rotation (xc, zc). It was observed that for a selected potential slip surface there may be many possible combinations of (n + 2) roots, all giving essentially the same Fs. The presented example problem demonstrates the importance of 3-D back-analysis if one is to configure in-situ soil strength.",
author = "Dov Leshchinsky and Huang, {Ching Chuan}",
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Generalized three-dimensional slope-stability analysis. / Leshchinsky, Dov; Huang, Ching Chuan.

In: Journal of Geotechnical Engineering, Vol. 118, No. 11, 11.1992, p. 1748-1764.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Generalized three-dimensional slope-stability analysis

AU - Leshchinsky, Dov

AU - Huang, Ching Chuan

PY - 1992/11

Y1 - 1992/11

N2 - A 3-D slope-stability-analysis method, explicitly satisfying all limiting-equilibrium equations, is presented. To make the problem statically determinate, the variational approach, rather than intuition in 3-D, is used. In this approach, the normal stress over the user's specified slip surface, which satisfies global limiting equilibrium and produces the minimum factor of safety for the critical surface, is sought and obtained mathematically. A simple numerical scheme to attain the safety factor is detailed and all the algorithms needed to assemble a computer program are given. Upon discretization of the surface by n rectangular elements, n simultaneous linear equations are solved for n discrete normal stresses. It is also necessary to solve three nonlinear equations for the factor of safety, Fs, and the coordinate of the center of rotation (xc, zc). It was observed that for a selected potential slip surface there may be many possible combinations of (n + 2) roots, all giving essentially the same Fs. The presented example problem demonstrates the importance of 3-D back-analysis if one is to configure in-situ soil strength.

AB - A 3-D slope-stability-analysis method, explicitly satisfying all limiting-equilibrium equations, is presented. To make the problem statically determinate, the variational approach, rather than intuition in 3-D, is used. In this approach, the normal stress over the user's specified slip surface, which satisfies global limiting equilibrium and produces the minimum factor of safety for the critical surface, is sought and obtained mathematically. A simple numerical scheme to attain the safety factor is detailed and all the algorithms needed to assemble a computer program are given. Upon discretization of the surface by n rectangular elements, n simultaneous linear equations are solved for n discrete normal stresses. It is also necessary to solve three nonlinear equations for the factor of safety, Fs, and the coordinate of the center of rotation (xc, zc). It was observed that for a selected potential slip surface there may be many possible combinations of (n + 2) roots, all giving essentially the same Fs. The presented example problem demonstrates the importance of 3-D back-analysis if one is to configure in-situ soil strength.

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