Analytical Solutions for Three-Wedge Stability with Vertical Wedge Interfaces

A force-based limit equilibrium analysis is presented for the stability of a two-dimensional, three-wedge sliding mass of soil with vertical interfaces between the wedges. The analysis is conducted using five 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 the 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. A numerical example is provided to demonstrate the method and illustrate the importance of several parameters for stability of an earth slope. The analytical solutions take compact form, provide insight for the three-wedge method, and offer good capability to tailor conditions for applications that can be suitably characterized by wedge failure.