Analysis of critical excavation depth for a jointed rock slope using a face-to-face discrete element method

The critical excavation depth of a jointed rock slope is an important problem in rock engineering. This paper studies the critical excavation depth for two idealized jointed rock slopes by employing a face-to-face discrete element method (DEM). The DEM is based on the discontinuity analysis which can consider anisotropic and discontinuous deformations due to joints and their orientations. It uses four lump-points at each surface of rock blocks to describe their interactions. The relationship between the critical excavation depth D-s and the natural slope angle alpha, the joint inclination angle theta as well as the strength parameters of the joints c(r) ,phi(r) is analyzed, and the critical excavation depth obtained with this DEM and the limit equilibrium method (LEM) is compared. Furthermore, effects of joints on the failure modes are compared between DEM simulations and experimental observations. It is found that the DEM predicts a lower critical excavation depth than the LEM if the joint structures in the rock mass are not ignored.

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.