Circular and Logarithmic Spiral Slip Surfaces

A method of analysis of embankment stability is described which applies equally to slip surfaces having a cross section either in the form of a circular arc or a logarithmic spiral arc. The method is applied to the solution of a number of stability problems in which the slope of the embankment and the soil properties vary over a wide range. The solutions to critical cases are obtained for both types of slip surface and the values of the over-all factor of safety, F, are compared. It is shown that, of the two shapes, the circular arc gives the lower value for the factor of safety. It is also shown that the shape of the logarithmic spiral is not determined by the value of the angle of shearing resistance of the soil. The factor of safety against shearing on vertical planes, F_v, has also been investigated for each of the critical cases, and it was found that, in every case, values of FDv exceeded the corresponding value of F.