Retrogressive failure pattern and retrogression distance in sensitive clays induced by river erosion

The failure patterns and retrogression distances in sensitive clays induced by river erosion are two significant factors of concern in landslide risk assessment. For the former, empirical criteria, based on past events and numerical results, can hardly produce a unified guideline and explain their complex mechanism. For the latter, the capacity of the river cross section is rarely considered in existing studies, even though the failed soil would deposit on the riverbed and further affect upslope failure extension. The present study proposes an analytical method to quantitatively assess the failure patterns and retrogression distance by combining the shear band propagation method (SBP) with limit analysis on active block failure. A closed-form active earth pressure (CAEP) and the shape function of the failure surface are proposed with the variational calculus method (VCM), providing a tool to understand the transformation mechanism of the failure patterns. The criteria for initiation failure positions and stages are formulated following the competition results between the induced minimum slope-parallel force by foot unloading and the proposed CAEP. Further, the terminal retrogression distance is given considering two possible river cross sections. The proposed CAEP solution is validated against Buss's solution and further applied to a parametric study on the failure patterns. Finally, three practical cases are analyzed with the proposed method, and the predictions are shown to agree well with the field observations.