A lower-bound formulation for unsaturated soils

A lower-bound formulation is proposed for consistent stability analysis of saturated and unsaturated soils with the suction stress-based effective stress employed to represent the shearing strength variation caused by matric suction. All constraints are expressed in terms of the effective stress. The body and surface forces induced by the suction stress are established and their effect on the equilibrium of unsaturated soils is studied in detail. Numerical solutions of the formulation are obtained by utilising linear triangular finite elements in combination with the second-order cone programming. Some numerical tests are given, and the lower-bound solutions are compared with the experimental data, the field measurements and the results of other methods. Close agreement is seen in all cases and the bounding property of the upper- and lower-bound formulations is guaranteed. The impact of the suction stress and the hydraulic state on the stability of some unsaturated earth structures is discussed.