INTRODUCTION For slopes, the factor of safety F is traditionally de®ned as the ratio of the actual soil shear strength to the minimum shear strength required to prevent failure (Bishop, 1955). As Duncan (1996) points out, F is the factor by which the soil shear strength must be divided to bring the slope to the verge of failure. Since it is de®ned as a shear strength reduction factor, an obvious way of computing F with a ®nite element or ®nite difference program is simply to reduce the soil shear strength until collapse occurs. The resulting factor of safety is the ratio of the soil's actual shear strength to the reduced shear strength at failure. This `shear strength reduction technique' was used as early as 1975 by Zienkiewicz et al. (1975), and has since been applied by Naylor (1982), Donald & Giam (1988), Matsui & San (1992), Ugai (1989), Ugai & Leshchinsky (1995) and others. The shear strength reduction technique has a number of advantages over the method of slices for slope stability analysis. Most importantly, the critical failure surface is found automatically. Application of the technique has been limited in the past due to the long computer run times required. But with the increasing speed of desktop computers, the technique is becoming a reasonable alternative to the method of slices, and is being used increasingly in engineering practice. However, there has been little investigation of the accuracy of the technique. In this paper, factors of safety obtained with the shear strength reduction technique are compared to limit analysis solutions for a homogeneous embankment.

Slope stability analysis by strength reduction

With reference to practical engineering problems it is shown that considerable differences may be encountered between the results from associated and those from nonassociated plasticity theories. Next, the need for a non-associated plasticity theory is demonstrated by considering test results for sand, concrete and rock. Elementary material parameters are discussed such as Young's modulus and Poisson's ratio for the description of the elastic properties; and a cohesion and a friction angle for the determination of the strength. The salient difference from associated plasticity theory concerns the introduction of a dilatancy angle which controls the inelastic (plastic) volume changes. This dilatancy angle is not only a suitable parameter for the description of soils, but also appears to be useful for concrete and rock. Basically, the paper consists of three parts as we consider three types of models of increasing complexity. The first model is a perfectly-plastic model, which employs the five aforementioned parameters. It is based on test data rather than on Drucker's hypothesis of material stability. The consequences thereof are examined. The second model is a straightforward extension of the first model by augmenting it with friction hardening and cohesion softening. This novel idea is introduced to account for the degradation of the cohesion of cemented granular materials with increasing inelastic deformation. The model is employed in an analysis which shows that plastic deformations tend to localize in thin shear bands, which may occur even before peak strength is reached. Finally, a review is given of concepts for modelling hysteresis and strain accumulation in cyclic loading. The concept of a bounding surface in addition to a yield surface is discussed and is adapted for use in a sophisticated model for loose and cemented granular materials under cyclic loading.

/pdf/non-associated-plasticity-for-soils-concrete-and-rock-1k1jstx009.pdf

Non-Associated Plasticity for Soils, Concrete and Rock

Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods

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

Slope stability analysis is one of the oldest applications in geotechnical engineering, yet it remains one of the most active areas of study in both research and practice. The vast majority of slope stability analyses are performed in two dimensions under the assumption of plane strain conditions. Even when two-dimensional (2D) conditions are not appropriate, three-dimensional (3D) analysis is rarely performed. There are a number of reasons for this. The majority of work on this subject strongly suggests that the 2D factor of safety is conservative (i.e. lower than the ‘true’ 3D factor of safety). Even when 3D may be justified on geometric grounds, the available methods, being often based on extrapolations of 2D ‘methods of slices’ to 3D ‘methods of columns’, are complex, involve numerous assumptions, and are not readily modified to account for realistic boundary conditions in the third dimension such as sloping abutments. The power and versatility of the elasto-plastic finite element approach to slope st...

Three-dimensional slope stability analysis by elasto-plastic finite elements

The visco-plastic model is established as a realistic general description of soil behaviour as well as a computationally convenient fiction for solving any properly formulated plasticity problem. T...

Associated and non-associated visco-plasticity and plasticity in soil mechanics

The solution of two-dimensional transient seepage problems under the influence of both electrokinetic and hydrodynamic forces is found using the finite element method. The governing differential equations account for both the time-dependent consolidation and the time-dependent storage of electricity of the soil media. Solutions to problems are primarily presented as the movement of the phreatic surface with time, but pore water velocities, hydraulic, and electric potentials at the nodes are also calculated in the program. A practical problem, where electroosmosis was used because normal dewatering methods have proven ineffective, was analyzed using the numerical model. The results obtained compared favorably with measurements made in the field. The main advantage of the numerical model is that the electrode configuration can easily be changed to enable the most efficient arrangement to be determined.

Numerical analysis of electro-osmotic flow in soils

Discussion: Associated and non-associated visco-plasticity and plasticity in soil mechanics

The solution of two-dimensional ground-water flow in soils of low hydraulic conductivity under the influence of both electrokinetic and hydrodynamic forces is found using the finite element method. The example investigated deals with a confined aquifer in which there is a recharging as well as a discharging well present. The results demonstrate the effect of the application of the electro-osmosis phenomenon. The formulation is general and permits the analysis of not only arbitrary shaped boundaries but also different electrode configurations.

Applications of Electro-Osmosis to Ground-Water Flow Problems

In many respects the offshore foundation problem is similar to conventional footing situations and some of the studies are equally applicable to both. However, in one respect the situation is not parallel with on load shore. This is manifest in cyclic horizontal loads due to wave action. Such relatively slow load cycling is seldom encountered elsewhere and under certain circumstances, as will be demonstrated, can lead to progressive deformation. Such progressive deformation is well-known in structural engineering whenever plasticity occurs, but has not been studied to any extent in the area of soil plasticity. Attention is focused on this important problem.

Chris Humpheson

Papers

Associated and non-associated visco-plasticity and plasticity in soil mechanics

Numerical analysis of electro-osmotic flow in soils

Discussion: Associated and non-associated visco-plasticity and plasticity in soil mechanics

Applications of Electro-Osmosis to Ground-Water Flow Problems

Numerical Analysis for Foundations of Offshore Structures With Special Reference to Progressive By Deformation