Introduction of Plastic Block Method in the Upper Bound Limit Analysis of Soil Stability Problems

In this paper, a new method, called the Plastic Block method, was introduced to improve the current rigid block solutions in framework of rigorous limit analysis method. It is a combination of rigid block limit analysis and finite-element limit analysis methods used in the upper bound limit analysis solutions of stability problems in soil mechanics. The method is similar to the first one in terms of speed of solution process and consideration of a collapse mechanism as a priority, and also is similar to the second one in terms of capability of considering plastic deformability of the blocks in calculation of internal dissipation of energy (besides that of velocity discontinuities between them). Comparison of the results obtained by the proposed method, using a few number of blocks (in case of the classical bearing capacity problem of shallow foundations selected to illustrate capability of the method), showed the better (smaller) upper bound not only in comparison with the well-known rigid block solutions, but also in comparison with some cases of finite-element limit analysis solutions obtained by the models including a large number of elements.

Automated summary

A new method called the Plastic Block method was introduced in this paper to improve the current rigid block solutions, combining rigid block limit analysis and finite-element methods for stability problems in soil mechanics. This method prioritizes speed and collapse mechanism while considering the plastic deformability of the blocks in energy dissipation calculations. The results show better upper bounds compared to rigid block solutions and some cases of finite-element analysis solutions.