To investigate the variation of the factor of safety with angle of dilatancy, a method using both associated and non-associated flow rules is presented in this paper. An averaged value of the factor of safety obtained for different values of the angle of dilatancy using the proposed method is suggested and calculated. The variation of the factor of safety with angle of dilatancy for a range of the strength parameters is obtained and compared with those using the conventional limit equilibrium method.
The slice method based on the limit equilibrium theorem, which is widely applied to the problems of slope stability, has been investigated by a number of researchers (Bishop, 1955; Morgenstern and Price, 1965; Spencer, 1967; Sarma, 1979, 1987; Fredlund and Krahn, 1977; Chen and Morgenstern, 1983). The main differences between these limit equilibrium methods are the assumptions made about the position and inclination of interslice forces. In order to reduce the influence of the assumptions made in limit equilibrium methods on the factor of safety, the methods of limit analysis based on the rigid plasticity theory were developed by Chen (1975), Michalowski (1995) and Donald and Chen (1997). These methods based on the upper bound theorem of limit analysis are generally referred to as the upper bound methods, which give an upper bound solution to the real value of the factor of safety. However, the upper bound method for slope stability analysis relies on the associated flow rule, which may overestimate the volumetric strain of soil as verified by the experiment finding (Lade 1992). To better simulate the true deformation properties of soil, the non-associated flow rule should be used. The influence of the non-associated flow rule on the factor of safety using the proposed method is investigated.