This paper describes a new technique for computing lower bound limit loads in anisotropic media under conditions of plane strain. Although limit analysis has been applied extensively to homogenous and isotropic soils, as well as soils with a variation of cohesion with direction, it is well recognised that natural soil deposits also exhibit a variation of friction angle with direction. A finite element formulation or the lower round theorem is presented which allows for the variation of soil strength with direction. In order to achieve this, the conventional Mohr-Coulomb yield criterion used. An example is given to illustrate the capability of the proposed numerical procedure.


In their natural state most soils are somewhat anisotropic. Due to the mode of deposition and subsequent loading of soil masses, measurements have shown that the particles tend to adopt a preferred orientation. It is this preferred particle orientation which results in a variation of soil properties as the angle of the major principal stresses varies during shear deformation. While the measurement of this inherent anisotropy is difficult, its effects have been shown via laboratory tests on samples cut at different angles. While existing data would seem to suggest that the variation of cohesion (undrained shear strength) with orientation due to soil anisotropy is more significant than the effects of friction angle, the effect of friction angle variation should not be ignored. Arthur and Menzies (1972) and Arthur and Phillips (1975) measured inherent anisotropy in prepared sand samples using a consolidated-drained shear test. They noted that a slightly higher friction angle (typically ill the order of 2–3 degrees) occurs when the direction of the major principle stress coincides with the direction of sand deposition as compared to when the major principal stress is perpendicular to the direction of deposition.

This content is only available via PDF.
You can access this article if you purchase or spend a download.