A rigorous numerical formulation for upper bound analysis of reinforced soils using second order cone programming

Abstract

A rigorous upper bound formulation is established for reinforced soils considering both the tensile rupture of the reinforcement and the relative slippage of the reinforcement-soil interface. To represent its finite tensile strength and negligible compressive strength, a novel strategy is proposed to calculate the plastic dissipation rate of the reinforcement without the incorporation of stress variables. Plastic dissipation rates of the soil, the reinforcement and their interfaces are obtained using only kinematic variables and all flow rules are expressed in terms of linear constraints and second order cones. The solution domain is then discretized using linear strain elements for the soil and constant strain elements for the reinforcement and the interface. Numerical examples are given to show the accuracy of the present formulation. The effect of design parameters such as the tensile strength, the length and the location of the reinforcement is discussed.