Advantages of second-order work as a rational safety factor and stability analysis of a reinforced rock slope

Abstract

Landslides can be considered as a static–dynamic transition with the sudden release of kinetic energy. The sharp vanishing of the second-order work is also linked to this phenomenon. In this study, the relation between the second-order work and the kinetic energy is reviewed, and five advantages of the normalized global second-order work (D2Wn) as a factor of safety (FOS) are proposed and discussed, comparing this FOS with the one based on the strength reduction method. The D2Wn is considered in the explicit algorithm of the finite difference method, and its mesh-independence is numerically checked by a series of triaxial compression tests. By simulating the excavations of a reinforced rock slope, the stability analyses are performed using the D2Wn and the traditional FOS. The D2Wn is proven completely independent of the convergence criterion and more sensitive to the global failure. Finally, a recently developed energy-absorbing cable is considered for supporting the studied rock slope. Its supporting effect is compared with that of traditional cables.