First sliding area analysis of expansive soil slope based on the upper and lower bound solutions

Expansive soil landslides are prone to frequent disasters due to the expansion, cracking, and over-consolidation characteristics of expansive soil. However, traditional analysis methods cannot adequately reflect the progressive failure characteristic of expansive soil slopes, and effectively estimate the first sliding area. To better understand the disaster characteristics of expansive soil slopes and quantify the phased disaster scale, based on the change of the tangential force direction at the bottom of some soil strips caused by water swelling of expansive soil, the upper and lower bound solutions of the first sliding area of slope are analyzed. The sliding trend critical point of expansive soil slope is strictly derived using the Morgenstern-price static equilibrium analysis method. A case study is used to illustrate the calculation and analyze the influence of shear strength on the upper solution and lower solutions. The results show that partial and progressive failure may still occur on expansive soil slope under the influence of expansion although they are determined to be stable by classical analysis methods. The upper bound solution of the first slip area is less affected by the effective shear strength, while the influence of residual shear strength on the lower bound solution is particularly significant. The upper bound solution and its change rate decrease with the increase of effective cohesion and effective internal friction angle, while the lower bound solution and its change rate increase with the increase of residual internal friction angle and residual cohesion. In addition, the stability of expansive soil slope can be determined based on the relationship between the upper and lower limit solutions. This study provides the basic information for evaluating disaster scales and designing prevention and control measures for expansive soil landslides.