Unity of three types of energy catastrophe criteria for slope failure

The research on the failure criterion for the strength reduction method (SRM) is a hot issue in the field of slope stability analysis. Three types of commonly used failure criteria, namely, the marked displacement mutation criterion, the plastic zone penetration criterion and the calculation program nonconvergence criterion are considered in correspondence with three types of energy catastrophe criteria, namely, the energy catastrophe criterion for gravity potential loss, the catastrophe criterion of dissipated energy increment and the catastrophe criterion of kinetic energy increment, respectively. To unify the three types of energy catastrophe criteria, a new failure criterion-variational value criterion for the SRM was proposed based on the principle of minimum potential energy. The calculation formulas of the second-order variational value of the total potential energy of a numerical model were derived. A method for applying variation was found. A variational value calculation procedure was written. Then, the process of judging the stability or instability of the model based on the positive or negative of the variational value was given. The unity of the variational value criterion and the three types of energy catastrophe criteria was verified through a typical slope example. The generality of the unity of the variational value criterion and the three types of energy catastrophe criteria was discussed by changing the typical parameters of the numerical model, such as mesh density, slope angle and slope height. It is shown that the results calculated by the variational value criterion are close to those calculated by the three types of energy catastrophe criteria, with the relative error of less than 5%. The variational value criterion unifies the three types of energy catastrophe criteria, and provides a mechanical explanation for the unity of the three types of energy catastrophe criteria.