Discrete modelling jointed rock slopes using mathematical programming methods

In this paper, a mathematical programming based discontinuum approach is developed for modelling jointed rock slopes. The formulation naturally leads to a standard second-order cone program, which can be solved using efficient optimisation solvers, and a purely static method is derived that does not require artificial damping parameters. Notably, the approach provides somewhat of a unification of two distinct discontinuum approaches: the soft-particle model and the hard-particle model. A series of numerical examples are conducted to validate the proposed approach. The soft-particle model is more versatile than the hard-particle model while the hard-particle model is more efficient.