Hypoplastic constitutive equation based on nonlinear tensor functions possesses a failure surface but no yield surface. In this paper, we consider the numerical integration and FE implementation of a simple hypoplastic constitutive equation. The accuracy of several integration methods, including implicit and explicit methods, is examined by performing a set of triaxial compression tests. Adaptive explicit schemes show the best performance. In addition, the stress drift away from the failure surface is corrected with a predictor-corrector scheme, which is verified by two boundary value problems, i.e. rigid footing tests and slope stability.

This study uses an incompressible smoothed-particle hydrodynamics (ISPH) model to investigate the run-out and deposit morphology of granular materials flowing down cut slopes. The primary aim is to study the influence of various factors on the run-out and to summarise a quantitative relationship for direct use in landslide hazard management. In the model, the granular materials are modelled as a rigid perfectly plastic material with a Coulomb yield surface. The coupled continuity equation and momentum equation are solved by a semi-implicit algorithm. The model is first validated and its results are carefully compared with various controlled experiments regarding granular flows. The model reproduces the flows and correctly predicts the deposition profiles under various conditions. Then, the computational results are used to study the run-out and mobility of landslides. For granular columns collapsing onto a flat surface, a normalised run-out and a new scaling relationship are proposed, which are supported by numerous measured and numerical results. A similar relationship for the run-out of granular rectangles on steep slopes has also been explored. It is found that the normalised run-out is mainly determined by the slope angle and the normalised drop height. Furthermore, three types of idealised cut-slope landslides are simulated to study the influence of the initial landslide shape on the run-out. It is found that the normalised run-out of these idealised cut-slope landslides is smaller than that of granular rectangles on slopes of the same angles and drop heights. The difference between the run-outs is found to be mainly determined by the proportion of the whole mass that initially lies above a predictable discontinuity plane.