Upper-Bound Limit Analysis of Rock Slope Stability with Tensile Strength Cutoff Based on the Optimization Strategy of Dividing the Tension Zone and Shear Zone

Abstract

The contribution of tensile cracks to the stability of cracked slopes is important. The tensile characteristics of tensile cracks have a significant influence on the stability of rock slopes. Therefore, in this paper, based on the upper-bound limit analysis method and modified M–C failure criterion, an improved failure mode of multislider of rock slopes is established by assuming that the first m − 1 sliders are shear failures and the other n − m + 1 sliders are tensile failures. The superior division of the tension zone and shear zone is realized through the optimized solution and the corresponding value of m. The influences of each parameter on the stability coefficient, failure region, tension zone, and shear zone are emphatically explored. The results show that the accuracy and superiority of the improved failure mode is verified by comparative analysis. The stability coefficient γH/c decreases nonlinearly with an increase in slope angle β and increases nonlinearly with an increase in dimensionless parameter u (the maximum increase in γH/c is up to 37.2%). The critical height of the slope, the whole failure region, and the ground failure length decrease sharply with an increase in β and increase nonlinearly with an increase in u (the critical height increases up to 20%). The critical height of the slope and the whole failure region increase nonlinearly with an increase in the internal friction angle φ. In addition, the ground overload weakens the effect of tensile strength, while seismic force strengthens this effect, but neither is conducive to rock slope stability. In addition, u is beneficial to slope stability, and the tensile characteristics are more significant for steep rock slopes with a small φ. In practical engineering, the energy dissipation and tensile strength characteristics of rock masses should be considered in the process of crack development, especially in the stability evaluation, reinforcement, and protection of high and steep slopes with frequent earthquakes.