Application of Limit Analysis to Non-Linear and Non-Associative Yield Conditions

Limit analysis is a widely used method for determining the collapse load of soil constructions. Conventional limit analysis theory assumes that the soil is plastic with a linear failure criterion and follows the associative flow rule. However, a linear failure criterion is often an idealisation of an actual non-linear response for which available analytical techniques are limited. The associative flow rule always overestimates the volumetric strains along shearing planes for frictional soils, potentially leading to unsafe failure loads and unrealistic failure mechanisms. Therefore, both non-linear and non-associative yield conditions require further consideration within the framework of limit analysis. Within the framework of the numerical limit analysis procedure DLO (Discontinuity Layout Optimization), a multi-tangent technique is developed to conduct non-linear analysis of continuum geotechnical problems. A new fully general solution procedure for generating upper bound multi-wedge rigid block mechanisms for continuum soils with a non-linear power-law failure criterion is then presented. This approach utilises a curved interface that obeys the nonlinear yield function flow rule along its full length. The ability of the proposed non-linear upper bound solution to predict the shear and normal stresses at every point along the failure surface is discussed, and the obtained variational solutions are verified by those from the proposed DLO non-linear approach. The issue of non-associativity is investigated in the context of discrete rigid block limit analysis. New methods to obtain non-associative solutions are developed by separately quantifying dilation and shearing friction for frictional materials: (1) permutation method; (2) rapid direct method. The proposed non-associative procedures are applied to the determination of the load factors of rock slopes. The permutation method is able to determine the full range of physically possible non-associative results, but is time-consuming. In contrast, the rapid direct method is fast and was shown able to generate results similar to experimental and analytical results in the literature.