Two- and three-dimensional bearing capacity of footings in sand

Bearing capacity calculations are an important part of the design of foundations. Many of the terms in the bearing capacity equation, as it is used today in practice, are empirical. Shape factors could not be derived in the past because three-dimensional bearing capacity computations could not be performed with any degree of accuracy. Likewise, depth factors could not be determined because rigorous analyses of foundations embedded in the ground were not possible. In this paper, the bearing capacity of strip, square, circular and rectangular foundations in sand are determined for frictional soils following an associated flow rule using finite-element limit analysis. The results of the analyses are used to propose values of the shape and depth factors for calculation of the bearing capacity of foundations in sands using the traditional bearing capacity equation. The traditional bearing capacity equation is based on the assumption that effects of shape and depth can be considered separately for soil self-weight and surcharge (embedment) terms. This assumption is not realistic, so a different form of the bearing capacity equation is also proposed that does not rely on it.