Collapse loads for rectangular foundations by three-dimensional upper bound limit analysis using radial point interpolation method

A three-dimensional kinematic limit analysis approach based on the radial point interpolation method (RPIM) has been used to compute collapse loads for rectangular foundations. The analysis is based on the Mohr-Coulomb yield criterion and the associated flow rule. It is understood that the internal plastic power dissipation function and flow rule constraints can be expressed entirely in terms of plastic strain rates without involving stresses. The optimization problem has been solved on basis of the semidefinite programming (SDP) by using highly efficient primal-dual interior point solver MOSEK in MATLAB. The results have been presented in terms of the variation of the shape factors with changes in the aspect ratio (L/B) of the footing for different values of soil internal friction angle (phi). Computations have revealed that the shape factors, s(c) and s(q), due to effects of cohesion and surcharge increase continuously with (1) decrease in L/B and (2) increase in phi. On the other hand, the shape factor s(gamma), due to the effect of soil unit weight, increases very marginally with an increase in L/B up to (1) phi = 25 degrees for a rough footing and (2) phi = 35 degrees for a smooth footing. Thereafter, for greater values of phi, the variation of s(gamma) with L/B has been found to be quite similar to that of the factors s(c) and s(q). The variations of (1) nodal velocity patterns, (2) plastic power dissipation, and (3) maximum plastic shear strain rates have also been examined to interpret the associated failure mechanism.