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.

考虑到钢筋的拉伸断裂和钢筋-土界面的相对滑移，为加筋土建立了严格的上限公式。为了表示其有限的抗拉强度和可忽略的抗压强度，提出了一种新的策略来计算钢筋的塑性耗散率，而无需引入应力变量。土壤、钢筋及其界面的塑性耗散率仅使用运动学变量获得，所有流动规则均以线性约束和二阶锥体表示。然后使用土壤的线性应变单元和钢筋和界面的恒应变单元离散解域。给出了数值例子以显示本公式的准确性。