Numerical limit analysis solutions for the bearing capacity factor Nγ

Numerical limit analyses are applied to evaluate the self-weight bearing capacity factor for a rigid surface footing with a smooth or rough interface. To isolate the effect of the self-weight on the bearing capacity, the soil is modeled as a cohesionless frictional Mohr-Coulomb material. Assuming an associated flow rule, the true collapse load is bracketed to within 3.42% by computing rigorous lower and upper bound solutions using recently developed limit analysis methods [Lyamin and Sloan, 2002a. Upper bound limit analysis using linear finite elements and non-linear programming. International Journal for Numerical and Analytical Methods in Geomechanics 26 (2), 181; Lyamin and Sloan, 2002b. Lower bound limit analysis using linear finite elements and non-linear programming. International Journal for Numerical Methods in Engineering 55 (5), 573]. With these sharp bounds, the average bearing capacity factor provides an excellent estimate of the exact bearing capacity factor that can be used with confidence for design purposes. The numerical formulations of both the upper and the lower bound theorems are obtained by means of finite elements and solved using efficient non-linear mathematical programming schemes. The solutions, presented in the form of graphs, are compared against existing semi-empirical expressions and numerical solutions. An approximate analytical expression for Nγ is suggested at the end of the paper.