A B-spline material point method for deformation failure mechanism of soft–hard interbedded rock

Geological hazards related to soft–hard interbedded rock are frequent in rock engineering. The material point method (MPM) is a mesh-free numerical approach specifically designed for analyzing large deformations. Notably, significant grid-crossing errors frequently arise when material points traverse the underlying grid. To investigate the failure mechanism of soft–hard interbedded rock, an enhanced MPM incorporating B-spline basis functions and Voronoi polygon discretization is developed and subsequently validated through comparisons with uniaxial compression test data and other numerical methods. The numerical results of soft–hard interbedded rock specimens associated with different soft layer dips (SLD) and confining pressures indicate that the SLD has a great effect on compressive strength and crack extension at low confining pressure. Rocks from SLD-30° to SLD-75° correspond to the “sliding failure along discontinuities” failure mode and have lower compressive strength than rocks with other SLD angles. It is also demonstrated that the propagation of cracks leads to a significant alteration in the internal stress state of the rock, and that stress concentrations at the crack tip exacerbate the development of failure surface. Furthermore, the failure mode of soft–hard interbedded rock can be categorized into four types: (1) sliding failure across multiple discontinuities, (2) tensile fracture across multiple discontinuities, (3) sliding failure along discontinuities, (4) tensile-split along discontinuities.