Size Effects in Problems of Footings on Sand within Micro-Polar Hypoplasticity

Numerical FE investigations of size effects in problems of footings on sand were performed. Micro-polar hypoplastic constitutive model was used to describe a mechanical behaviour of a cohesionless granular material during a monotonic deformation path. The FE analyses were carried out with three different footing widths. In deterministic calculations, a uniform distribution of initial void ratio was used. In statistical calculations, initial void ratios took the form of random spatial fields described by a truncated Gaussian random distribution. In order to reduce the number of stochastic realizations without sacrificing the accuracy of the calculations, a stratified sampling method was applied. The numerical results were compared with corresponding laboratory tests by Tatsuoka et al (1997). The numerical results show that the bearing capacity of footings decreases with increasing specimen size. If the initial void ratio is stochastically distributed, the mean bearing capacity of footings may be larger than the deterministic value. The statistical size effect is smaller than the deterministic one.