Variational method for determining slope instability based on the strength reduction method

The strength reduction method (SRM) is widely used in calculating the factor of safety (FOS) of a slope, and the key of this method is to select the appropriate instability criterion. At present, the commonly used instability criteria include displacement mutation, plastic zone penetration, calculation program nonconvergence, and energy mutation. To avoid human error in these criteria and find a unified mechanical explanation for slope instability, a new criterion, the variational criterion, is proposed in this paper. With this criterion, the slope stability is determined by identifying the positive or negative of the variational value. This criterion avoids the human error of other criteria and provides a unified and definite index for judging slope instability. The FOSs of two-dimensional and three-dimensional slopes calculated by this criterion are compared with those calculated by other criteria and classical papers, which verifies that this criterion is applicable and accurate. The effect of the mesh size on the accuracy of the results is analyzed, and the newly proposed criterion is applied to a variety of common slopes. It is further demonstrated that the proposed criterion is not an accident of numerical calculation and some examples but is universally applicable and accurate.

Automated summary

A new criterion, the variational criterion, is proposed in this study to avoid human error in instability criteria and provide a unified and definite index for judging slope instability.