Analytical Solutions for General Two-Wedge Stability

Abstract

A force-based limit equilibrium analysis is presented for the stability of a general two-dimensional, two-wedge sliding mass of soil, including a vertical or nonvertical wedge interface. The analysis is conducted using three failure planes and can accommodate variable conditions for wedge geometry, pore pressure, shear strength parameters, reinforcement, applied loads, and pseudostatic seismic coefficients. A constant factor of safety is assumed for each failure plane and reinforcement element, although this assumption can be relaxed through selection of strength parameters. The factor of safety is obtained analytically and requires solution for the roots of a polynomial equation. Verification checks show exact agreement with existing solutions for simplified conditions, including Mononobe–Okabe dynamic active force. Numeric examples are provided to demonstrate the method and illustrate the importance of several parameters for stability of a landfill bottom liner system and reinforced soil retaining wall. The analytical solutions take compact form, provide insight for the two-wedge method, and offer good capability to tailor conditions for applications that can be suitably characterized by wedge failure.