Three-dimensional upper bound analysis of slopes subjected to water infiltration using Mohr-Coulomb criterion with tension cut-off

The classical Mohr-Coulomb criterion, widely used in geotechnical engineering, has been found to overestimate the tensile strength of materials such as clays and rocks. This overestimation leads to significant errors, particularly when structures are subjected to horizontal force components like seepage forces under water infiltration. To address this issue, tension cut-off or tensile cracks have been incorporated into the analytical upper bound limit analysis of slopes, yielding different conclusions. This paper proposes a rigorous three-dimensional numerical formulation for the upper bound analysis of slopes composed of Mohr-Coulomb materials with tension cut-off. The nonlinear strength envelope is represented by three semi-definite cones, and the resulting mathematical programming problem is solved using the optimization toolbox Mosek. Two- and three-dimensional numerical tests demonstrate the high numerical efficiency of the proposed method. The results show that, when full tension cut-off is considered, no energy is required for the formation of tension cracks at the slope's crest. The influence of factors such as tensile strength, water infiltration, and preexisting cracks is analyzed in detail.