Seismic combined bearing capacity of strip footings on partially saturated soils using lower bound theorem of finite element limit analysis and second-order cone programming

Abstract

The seismic bearing capacity of strip footings resting on unsaturated soils subjected to combined loading is investigated in this study using a combination of lower bound limit analysis and finite element discretization. Second-order cone programming (SOCP) is used in this instance to simulate the nonlinear form of the universal perfectly-plastic Mohr-Coulomb yield criterion during the stress field optimization process. Under no-flow and steady-state infiltration/evaporation flow conditions, the significant influence of matric suction induced below the surface footing is accounted for using the suction stress concept. The load eccentricity and inclination applied to the footing and pseudo-static forces exerted simultaneously to the footing (superstructure) and underlying soil are all incorporated into the equilibrium equations, resulting in combinations of limit moment (M), and vertical (V), and shear (H) forces, under the influence of seismic loading. The results demonstrate that the matric suction induced within the porous structure of the underlying soil stratum increases the capacity of the surface footing to withstand various combinations of eccentric and inclined loadings under seismic excitation. Moreover, at a given hydraulic condition, the failure envelopes of obliquely/eccentrically loaded shallow foundations shrink significantly with the increase in the seismic intensity; the process which is more highlighted in sand (no-suction and all flow conditions). As the flow state in the unsaturated clay changes from infiltration to evaporation, the failure envelopes are observed to enlarge. In addition, as the load inclination angle reaches the soil-footing interface friction angle, the ultimate horizontal bearing capacity of the foundation resting on sand (no-suction) drops to zero; however, there still exists a residual shear resistance in the underlying clay layer or unsaturated sand, posing non-zero horizontal bearing capacity even at extremely high angles of inclination. Last but not least, the influence of earthquake horizontal loading on the bearing capacity envelopes of a shallow footing resting on a sand deposit was corroborated to be more pronounced than on a cohesive soil deposit. Indeed, the intrinsic (residual) cohesion, normally found in cohesive soils, was realized to contribute significantly to suppress the detrimental effect of earthquake horizontal loading.