Location of critical three-dimensional non-spherical failure surface by NURBS functions and ellipsoid with applications to highway slopes

At present, location of critical three-dimensional failure surfaces is mainly limited to spherical shape due to the various difficulties in performing global optimization for general non-spherical failure surface. Non-spherical failure surface is however the most general and critical shape that should be considered in slope stability analysis. This paper introduces a practical way in using NURBS surface and ellipsoidal surface to simulate a three-dimensional sliding surface. Numerical examples have indicated that the present proposal is effective in application and the critical failure surfaces as determined for 2 specially designed problems are also reasonable. The authors have also applied the optimization search to a curved highway slope and have obtained the relation between curvature of slope and the minimum factors of safety of slope.