Rigorous plasticity solutions for the bearing capacity of two-layered clays

This paper applies numerical limit analysis to evaluate the undrained bearing capacity of a rigid surface footing resting on a two-layer clay deposit. Rigorous bounds on the ultimate bearing capacity are obtained by employing finite elements in conjunction with the upper and lower bound limit theorems of classical plasticity. Both methods assume a perfectly plastic soil model with a Tresca yield criterion and generate large linear programming problems. The solution to the lower bound linear programming problem is obtained by modelling a statically admissible stress field, whereas the upper bound problem is solved through modelling a kinematically admissible velocity field. Results from the limit theorems typically bracket the true collapse load to within approximately 12%, and have been presented in the form of bearing capacity factors based on various layer properties and geometries. A comparison is made between existing limit analysis, empirical and semi-empirical solutions. This indicates that the latter can overestimate or underestimate the bearing capacity by as much as 20% for certain problem geometries