On stability of slopes in clays with linearly increasing strength: Discussion

Abstract

The author has computed stability numbers for the 4 = 0 analysis of slopes excavated in clay with undrained strength that increases linearly with depth. For his analysis, he assumed that the minimum factor of safety always occurs on a slip surface that passes through the toe of the slope. He states that is so because the shear strength of the soil increases with depth according to c = co + aoz and, hence, any consideration of deep-seated failure surfaces is made unnecessary. However, this assumption is not correct, since the critical slip surface in the author's model clay slope is not always contained within the slope itself, but in many instances passes beyond the toe. The assumption is correct only for the special case of zero strength (co = 0) at the ground surface, which is the case for which Gibson and Morgenstern (1962) obtained their solutions. The results given in the note are therefore in error. The writers have recomputed some results to obtain correct stability numbers. The author had earlier formulated a complete solution for the stability on any circular surface (~o~~ul~ 1984), from which formulation considerations of deep-seated slip surfaces are complicated by the introduction of an independent variable n additional to the two angles a and A. A considerable simplification can be effected, however, by observance of the principle of the midpoint circle (Brand and Shen 1984), which applies to all slip surfaces, i.e. those that originate in the horizontal surface beyond the toe of the slope. This often-forgotten principle dictates that the centre of a critical base slip surface must lie vertically above the midpoint of the slope, a fact which enables the variable n to be related to the angles a and A, so that the stability analysis is still dependent only on the two variables a and A. The derivation of the relationship between n, a, and A is illustrated in Fig. 1, from which the chord length of the slip surface is given by C = 2R sin a