Effects of nonlinearly of strength envelopes on stability analysis of 2-D and 3-D slopes are investigated. Combining the nonlinear strength law with Janbu's method and a minimization process based on dynamic programming makes it possible to determine the minimum factor of safety and critical slip surface for 2-D slopes. The factor of safety equation of a 3-D simplified Janbu method is derived in terms of the same nonlinear strength envelope. In the 3-D case the search procedure is based on dynamic programming and random number generation. Results of some example problems show that a linear approximation of the nonlinear strength envelope leads, under certain conditions, to a significant overestimation of safety factors for both 2-D and 3-D slopes.
Limit equilibrium methods have been extensively used to evaluate the stability of slopes in engineering practice. In these methods, the factor of safety is commonly defined as a reduction factor on strength, and this factor is an index measuring the relative stability of different potential slip surfaces in a given slope. It is obvious from this definition that the calculated factor of safety is affected by the way which shear strength of soil is evaluated. It has been shown by numerous experimental studies, however, that strength envelopes of many soils exhibit significant nonlinearity, for example, stiff London clay (Atkinson & Farrar 1985), soft clays (Lefebvre, 1981), compacted rock fill (Charles & Soares 1984a). The nonlinearity of strength envelopes can appear over a wide range of normal stresses but it is manifested particularly at low stress levels. Incorporating the above nonlinear strength law into the well known 2-D Janbu method, and using a minimization technique developed by Baker (1980) makes it possible to find the minimum factor of safety in 2-D problems.