Bearing capacity of shallow strip foundations on reinforced soil subjected to combined loading using upper bound theorem of finite element limit analysis and second-order cone programming

Bearing capacity of shallow strip foundations placed over both unreinforced and reinforced granular soils and subjected to combined loading is calculated by implementation of upper bound finite element limit analysis in conjunction with second-order cone programming technique. The soil mass is considered to be a granular medium reinforced with the inclusion of horizontal single and double layers of geogrid elements. To represent the impact of tensile resistance of reinforcement elements, an axillary variable is utilized to simulate the plastic energy dissipation of reinforcing elements without the application of any stress variables. General loading conditions are considered to profile the expansion of the failure envelopes in the V-H and V-M spaces for shallow strip foundations resting on reinforced soils. Results of this study are compared and validated against three different cases including the bearing capacity of shallow strip foundations subjected to vertical loading in the case of perfectly smooth and fully rough interfaces, limit load of shallow strip foundations subjected to combined loading, and vertical bearing capacity of shallow strip footings over a soil deposit reinforced with a single-layer of geosynthetic. Consistency of the results with those reported in the literature demonstrates the efficiency of proposed extended finite element upper bound formulations. The results are reported in the form of an efficiency factor which can be multiplied by the vertical bearing capacity of the shallow strip footing over unreinforced soil to find the ultimate bearing capacity of the reinforced foundation. The results show that the load inclination angle and eccentricity have significant impacts on the limit load and the optimum embedment depths of the reinforcement layer. It is further noted that the effect of reinforcement layer(s) in the improvement of bearing capacity in the V-M space is more pronounced than in the V-H space. The efficiency of reinforcement elements inclusion in improving the expanse of safe loading domain in the V-H and V-M spaces enhances with an increase in the soil internal friction angle.