Finite Element Limit Analysis of Bearing Capacity Problem

Foundations are designed to take loads from the superstructure and convey it to the soil underneath. The foundation system has to be designed with a certain safety factor, so the foundation can withstand the applied load(s) without failure in the ground. Various solutions for the bearing capacity problem have been developed using statics. The main goal of these methods is to find the maximum magnitude of external loads that soil mass can take without failure. This type of analysis is called limit equilibrium methods and is comprised of two bounds, upper bound which tries to reach the exact solution from above and the other one is called lower bound which tries to reach the answer from below. Using limit analysis solutions and statics, solutions have been developed for solving problems in geotechnical engineering. These solutions are used in standard geotechnical engineering practice. The solution for undrained analysis and weightless soil for a shallow, strip footing without embedment, is derived and it is well known to be the exact solution. When it comes to the effect of weight of soil, the effect of footing shape and embedment on the bearing capacity, the hand-derived formulas assume a priori statements in solving the problems, and then derive a solution which is not necessarily correct. A new type of numerical analysis, namely numerical limit analysis has been developed, which uses finite element discretization to approximate the problem and solve it to obtain the upper and lower limit to the exerted load(s). In this work, this tool will be used to run simulations to check the validity of the current methods, and develop factors and expressions for the effect of soil weight, as well as developing depth, inclination, and shape factors. This thesis is proposing a new expression for bearing capacity factor Nγ under inclined loading. This new expression is compared to some of the experimental works by some other researchers. Furthermore, it proposes a new shape factor, depth factor, and strength anisotropy factor for bearing capacity of undrained soils. Moreover, a macro model is proposed for a special case of a shallow foundation with suction beneath the footing