Finite element versus limit equilibrium stability analyses for surface excavations

Abstract

Limit equilibrium methods are widely and routinely used in practice. In several codes, limit equilibrium methods are recommended to evaluate the stability of a lateral support systems, such as soil-nails and anchors, to an acceptable defined factor of safety. For decades, limit equilibrium methods have been used successfully in providing an acceptable margin of safety against failure (movements, which can be significantly more complex, is not considered). However, due to the advances in computational power offered by personal computers, finite element modelling has become increasingly accessible. Since the idea immerged of using a strength reduction factor in finite element displacement analyses, an increase in the use thereof to calculate the factor of safety has been observed. However, the use of finite elements has often led to misinterpretation of the results. Several authors have cautioned engineers to the complexities involved in using finite element analyses to model geotechnical problems. Studies have been conducted comparing the use of finite elements to other methods. However, most of these studies consider only slope problems. Few studies have been conducted for lateral support systems. Several codes of practice use the numerical quantity of ‘factor of safety’ to define the suitability of geotechnical design. Whether finite element- or limit equilibrium methods are used, the accurate calculation of the factor of safety remains paramount to quantifying the stability of a geotechnical structure. The aim of this research is to compare limit equilibrium and finite element methods in evaluating the stability, in terms of factor of safety, of soil-nailed and anchored lateral support systems in surface excavations. This was done by using four methods of analysis to calculate the factor of safety. Two traditional limit equilibrium methods were used (trail wedge and method of slices). The newer, finite element strength reduction technique was used. Finally, a hybrid method which combines a finite element analysis with limit equilibrium slip surface analysis was used. These methods of analysis were applied to three different geometries. A uniform slope without any reinforcing was analysed. This was followed by the analysis of an 8.5m soil-nail supported face and a 17m face supported by anchors. A parametric study was conducted for the soil-nailed and anchored excavations. Material properties (friction angle, cohesion etc.), modelling parameters (boundary distances, mesh resolution etc.) and engineering design variables (reinforcement capacity etc.) were varied in order to observe the influence on the factor of safety. It is concluded that limit equilibrium methods, such as a trial wedge method and the method of slices, compare well with each other throughout the analyses. Using a combination of finite elements with a slip surface analysis compares poorly with the other methods. By using the finite element strength reduction technique, an optimised failure mechanism is found. The finite element strength reduction technique compares well with limit equilibrium methods if the following two conditions are met: • The same failure mechanism is evaluated for both methods; and • the capacity of reinforcement is consistently specified in both methods.