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

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 ((DWn)-W-2) as a factor of safety (FOS) are proposed and discussed, comparing this FOS with the one based on the strength reduction method. The (DWn)-W-2 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 (DWn)-W-2 and the traditional FOS. The (DWn)-W-2 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.