Discussion on size effect of footing in ultimate bearing capacity of sandy soil using rigid plastic finite element method

Currently, many formulas are used to calculate the ultimate bearing capacity. However, these formulas have disadvantages when being applied in practice since they can only be applied for calculating simple footing shapes and uniform grounds. Most formulas do not take into account the size effect of the footing on the ultimate bearing capacity, except for the formula by the Architectural Institute of Japan. The advantage of using the finite element method (FEM) is its applicability to non-uniform grounds, for example, multi-layered and improved grounds, and to complicated footing shapes under three-dimensional conditions. FEM greatly improves the accuracy in estimating the ultimate bearing capacity. The objective of this study is to propose a rigid plastic constitutive equation using the non-linear shear strength property against the confining pressure. The constitutive equation was built based on experiments for the non-linear shear strength property against the confining pressure reported by Tatsuoka and other researchers. The results from tests on Toyoura sand and various other kinds of sand indicated that, although the internal friction angle differs among sandy soils, the normalized internal friction angle decreases with an increase in the normalized first stress invariant for various sands despite dispersion in the data. This property always holds irrespective of the reference value of the confining pressure in the normalization of the internal friction angle. The applicability of the proposed rigid plastic equation was proved by comparing it to the ultimate bearing capacity formula by the Architectural Institute of Japan, which is an experimental formula that takes into account the size effect of the footing. The results of rigid plastic finite element method (RPFEM) with the proposed constitutive equation were found to be similar to those obtained with the Architectural Institute of Japan's formula. It is clear that RPFEM, with the use of the non-linear shear strength against the confining pressure, provides good estimations of the ultimate bearing capacity of the footing by taking account of the size effect of the footing.