Bearing Capacity of Strip Footing Placed on Reinforced Cohesionless Soil Slope Using Conic Programming

Abstract

By using lower bound finite element limit analysis technique with the combination of conic programming, the present study computes the bearing capacity of strip footing placed on the edge of a reinforced cohesionless soil slope and also subjected to a surcharge load. The bearing capacity factors (i) N_q associated with overburden pressure and (ii) N_γ associated with soil unit weight are computed by varying footing setback distance (b), soil friction angle (ϕ), and placement depth of reinforcement layer (d). The bearing capacity factors of the strip footing placed on the reinforced slope are found to be higher than that obtained for a strip footing situated on the unreinforced slope. The efficacy of the reinforcement layer is expressed in terms of dimensionless factors, η_q and η_γ which are the ratio of N_q and N_γ values obtained for the reinforced slope to the unreinforced slope. However, the maximum effectiveness of the reinforcement layer (η_q-max and η_γ-max) is achieved when it is placed at an optimum distance (d_cr) from the footing base. The magnitude of the efficiency factors increases if the reinforcement layer is embedded in a soil having higher soil friction angle and it is also found that the increment is more in case of η_γ-max. In contrast, the effectiveness of reinforcement is found to be maximum when footing is placed at the slope edge. The use of conic programming is found to be effective as the computational time reduces in comparison to linear programming during the computation of N_q and N_γ.