Soil inertia effects on the bearing capacity of rectangular foundations on cohesive soils

Two kinematic mechanisms are presented, which provide an upper bound of the ultimate bearing capacity of shallow rectangular foundations resting on cohesive soil, modeled by the Tresca strength criterion. The soil-foundation interface is described by the same criterion. The foundation is subjected to an inclined/eccentric load. The horizontal component of the body force in the soil is also taken into account to discuss the effects of the soil inertia on the bearing capacity. A multi-dimensional minimization algorithm allows one to find the geometric parameters corresponding to the best upper bound solutions for different load conditions. The shape effects are discussed and the solutions are compared both with previous theoretical upper bound solutions and with experimentally based formulas, in use in engineering geotechnical practice. Finally, the detrimental effects of the soil inertia on the ultimate bearing capacity of the foundation are analysed, as a function of the shape ratio and the design safety factor.