Extended three-dimensional analysis of cracked slopes using upper-bound limit method

The existence of cracks will reduce the stability of a slope and the three-dimensional effect is more significant when its width is limited. Therefore, it is necessary to evaluate the stability of cracked slopes. In order to study the three-dimensional stability of cracked slopes, based on the upper-bound theorem of limit analysis, a vertical tensile crack is introduced into the three-dimensional failure mechanism, and the mechanism parameters are introduced to extend the three-dimensional failure mode of slopes, including face failure and base failure. The energy balance equation is established, and the upper bounds of stability number of cracked slopes are obtained by the optimization algorithm. The stability charts of cracked slopes are established based on the g-line graphical method to read the factor of safety conveniently. The influences of slope width-to-height ratio, slope angle and internal friction angle of soils on the failure mechanism of cracked slopes and the crack depth and location are analyzed. The results show that for the specific slope geometry and soil parameters, there is a minimum slope width B/H^*. When the slope width is less than B/H^*, the failure surface passes above the slope toe, and the influences of the crack on the upper surface of the slope can be ignored. When the internal friction angle φ is less than 5°, the failure surface passes below the slope toe; for the cracked slope, only when φ=1°, failure surface passes below the slope. As the width of the slope increases, the crack depth gradually increases, and the crack location gradually moves away from the slope crest, while the crack depth of the slope with inclination 75° increases first and then decreases.