Ultimate Bearing Capacity of Shallow Footings on Non-Homogeneous Soil Foundations

In this paper, a method for solving the ultimate bearing capacity of shallow footings on non-homogeneous foundations is developed. The method is based on the limit equilibrium principle and a variational technique is utilized. Layered deposits of soil with cohesion varied non-uniformly with its depth are considered. Pseudostatic equilibrium equations for the footing-foundation system are formulated where the Coulomb's criterion Is applied to the rupture surface. The effect of earthquake on the soil foundation is taken into account by using a pseudostatic acceleration coefficient. Then, the Lagrange's undetermined multiplier method is used to construct the functional of the actual problem. The Euler's equations, and the variational boundary conditions including the condition of transversality at the end point and the reflection conditions at joint points between two soil layers, are found by minimizing the applied vertical load in the constructed functional. They are accompanied by the geometric boundary conditions. After solving this boundary value problem, the critical type of the rupture surface and stress distributions along the surface can be determined, and the limit loads can be easily estimated.The discrete Brown's arithmatic is employed to solve the non-linear implicit equation set for predicting the ultimate bearing capacity of non-homogeneous soil foundation and for determining the ralated critical parameters. The effects of footing and layered soil property parameters on the bearing capacity are systematically studied. These parameters are soil cohesions and their variation in the layer, internal friction angles, embedment of footings, layer thickness, pseudostatic seismic acceleration coefficient, ground water level, etc. The combinations of these parameters are also considered. The computational results by this method are compared with those by other authors and with published experimental results. Finally, a simple formula for prediction of bearing capacity is suggested.