This paper describes recent advances in stability analysis that combine the limit theorems of classical plasticity with finite elements to give rigorous upper and lower bounds on the failure load. These methods, known as finite-element limit analysis, do not require assumptions to be made about the mode of failure, and use only simple strength parameters that are familiar to geotechnical engineers. The bounding properties of the solutions are invaluable in practice, and enable accurate limit loads to be obtained through the use of an exact error estimate and automatic adaptive meshing procedures. The methods are very general, and can deal with heterogeneous soil profiles, anisotropic strength characteristics, fissured soils, discontinuities, complicated boundary conditions, and complex loading in both two and three dimensions. A new development, which incorporates pore water pressures in finite-element limit analysis, is also described. Following a brief outline of the new techniques, stability solutions ...

Geotechnical stability analysis

The formulation of limit analysis by means of the finite element method leads to an optimization problem with a large number of variables and constraints. Here we present a method for obtaining strict lower bound solutions using second-order cone programming (SOCP), for which efficient primal-dual interior-point algorithms have recently been developed. Following a review of previous work, we provide a brief introduction to SOCP and describe how lower bound limit analysis can be formulated in this way. Some methods for exploiting the data structure of the problem are also described, including an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage. The benefits of employing SOCP are then illustrated with numerical examples. Through the use of an effective algorithm/software, very large optimization problems with up to 700 000 variables are solved in minutes on a desktop machine. The numerical examples concern plane strain conditions and the Mohr–Coulomb criterion, however we show that SOCP can also be applied to any other problem of lower bound limit analysis involving a yield function with a conic quadratic form (notable examples being the Drucker–Prager criterion in 2D or 3D, and Nielsen's criterion for plates). Copyright © 2005 John Wiley & Sons, Ltd.

Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming

Soil anchors are commonly used as foundation systems for structures requiring uplift resistance, such as transmission towers, or for structures requiring lateral resistance, such as sheet pile walls. To date, the design of these anchors has been largely based on empiricism. This paper applies numerical limit analysis to rigorously evaluate the stability of vertical and horizontal strip anchors in undrained clay. Rigorous bounds on the ultimate pull–out capacity are obtained by using two numerical procedures that are based on finite element formulations of the upper and lower bound theorems of limit analysis. These formulations follow standard procedure by assuming a rigid perfectly plastic clay model with a Tresca yield criterion, and generate large linear programming problems. By obtaining both upper and lower bound estimates of the pull–out capacity, the true pull–out resistance can be bracketed from above and below. Results are presented in the familiar form of break–out factors based on various soil s...

Stability of plate anchors in undrained clay

Landslides are caused by a failure of the mechanical balance within hillslopes This balance is governed by two coupled physical processes: hydrological or subsurface flow and stress The stabilizing strength of hillslope materials depends on effective stress, which is diminished by rainfall This book presents a cutting-edge quantitative approach to understanding hydro-mechanical processes across variably saturated hillslope environments and to the study and prediction of rainfall-induced landslides Topics covered include historic synthesis of hillslope geomorphology and hydrology, total and effective stress distributions, critical reviews of shear strength of hillslope materials and different bases for stability analysis Exercises and homework problems are provided for students to engage with the theory in practice This is an invaluable resource for graduate students and researchers in hydrology, geomorphology, engineering geology, geotechnical engineering and geomechanics and for professionals in the fields of civil and environmental engineering and natural hazard analysis

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Hillslope Hydrology and Stability

Slope stability prediction for circular mode failure using gradient boosting machine approach based on an updated database of case histories

This paper compares conventional limit-equilibrium results with rigorous upper and lower bound solutions for the stability of simple earth slopes. The bounding solutions presented in this paper are obtained by using two newly developed numerical procedures that are based on finite-element formulations of the bound theorems of limit analysis and linear programming techniques. Although limit-equilibrium analysis is used widely in practice for estimating the stability of slopes, its use may sometimes lead to significant errors as both kinematic and static admissibility are violated in the method. Because there are no exact solutions available against which the results of limit-equilibrium analysis can be checked, the present bounding solutions can be used to benchmark the results of limit-equilibrium analysis. In addition, the lower bound solutions obtained also can be applied directly in practice because they are inherently conservative. purely cohesive and cohesive-frictional soils. These numerical procedures are based on finite-element formulations of the bound theorems of limit analysis and the best lower and upper bound solutions are obtained, respectively, by optimizing stat­ ically admissible stress fields and kinematically admissible ve­ locity fields using linear programming techniques. Over the years, many limit-equilibrium computer codes have been developed to locate the most critical failure surface by using various search strategies. In this study, the limit-equi­ librium results are obtained from the well-known slope stabil­ ity computer code STABL with the option of Bishop's sim­ plified method (Kim et al. 1997).

J. M. Kim

Papers

Limit Analysis versus Limit Equilibrium for Slope Stability

Closure of "Limit Analysis Versus Limit Equilibrium for Slope Stability"