Modified ultimate bearing capacity formula of strip footing on sandy soils considering strength non-linearity depending on stress level

Most of the contemporary ultimate bearing capacity (UBC) formulas assume a linear yield function in shear stress-normal stress space. However, experimental investigations have corroborated the non-linearity in the failure envelopes of sandy soils. This study focused on the assessment of the stress level effect on the UBC of surface strip footings ascribed to the soil unit weight (γ), footing size (B), and uniform surcharge load (q). The rigid plastic finite element method (RPFEM) was employed for the analysis. The analysis method was validated against the centrifuge test results from the published references in the case of various sandy soils with different relative densities. The RPFEM, using the mean confining stress dependence property of Toyoura sand, is utilized in non-linear finite element analysis of model sandy soil. The normalized ground failure domains in the case of the non-linear shear strength model are gleaned smaller than those in the case of the linear shear strength one. The numerical results are compared with the guidelines of the Architectural Institute of Japan (AIJ) and the Japan Road Association (JRA). The modification coefficients are ascertained for the frictional bearing capacity factor (N_γ) and surcharge bearing capacity factor (N_q), and a modified UBC formula is proposed. The performance of the proposed UBC formula is examined against the analysis results and various prevailing UBC guidelines.