No abstract

A full set of solutions for the stability of homogeneous c, φ slopes with cracks has been obtained by the kinematic method of limit analysis, providing rigorous upper bounds to the true collapse values for any value of engineering interest of φ, the inclination of the slope, and the depth and location of cracks. Previous stability analyses of slopes with cracks are based mainly on limit equilibrium methods, which are not rigorous, and are limited in their capacity for analysis, since they usually require the user to assume a crack depth and location in the slope. Conversely, numerical methods (e.g. finite-element method) struggle to deal with the presence of cracks in the slope, because of the discontinuities introduced in both the static and kinematic fields by the presence of cracks. In this paper, solutions are provided in a general form considering cases of both dry and water-filled cracks. Critical failure mechanisms are determined for cracks of known depth but unspecified location, cracks of known location but unknown depth, and cracks of unspecified location and depth. The upper bounds are achieved by assuming a rigid rotational mechanism (logarithmic spiral failure line). It is also shown that the values obtained provide a significant improvement on the currently available upper bounds based on planar failure mechanisms, providing a reduction in the stability factor of up to 85%. Charts of solutions are presented in dimensionless form for ease of use by practitioners.

This paper investigates the characteristics of dynamic rock fragmentation and its influence on the postfailure fragment trajectory. A series of numerical simulations by discrete element method (DEM) were performed for a simple rock block and slope geometry, where a particle agglomerate of prismatic shape is released along a sliding plane and subsequently collides onto a flat horizontal plane at a sharp kink point. The rock block is modeled as an assembly of bonded spherical particles with fragmentation arising from bond breakages. Bond strength and stiffness were calibrated against available experimental data. We analyzed how dynamic fragmentation occurs at impact, together with the generated fragment size distributions and consequently their runout for different slope topographies. It emerges that after impact, the vertical momentum of the granular system decreases sharply to nil, while the horizontal momentum increases suddenly and then decreases. The sudden boost of horizontal momentum can effectively facilitate the transport of fragments along the bottom floor. The rock fragmentation intensity is associated with the input energy and increases quickly with the slope angle. Gentle slopes normally lead to long spreading distance and large fragments, while steep slopes lead to high momentum boosts and impact forces, with efficient rock fragmentation and fine deposits. The fragment size decreases, while the fracture stress and fragment number both increase with the impact loading strain rate, supporting the experimental observations. The fragment size distributions can be well fitted by the Weibull's distribution function.

SUMMARYIn this paper, the application of the distinct element method (DEM) to frictional cohesive (c, ) geomaterials is described. A new contact bond model based on the Mohr-Coulomb failure criterion has been implemented in PFC2D. According to this model, the bond strength can be clearly divided into two distinct micromechanical contributions: an intergranular friction angle and a cohesive bond force. A parametric analysis, based on several biaxial tests, has been run to validate the proposed model and to calibrate the micromechanical parameters. Simple relationships between the macromechanical strength parameters (c, ) and the corresponding micromechanical quantities have been obtained so that they can be used to model boundary value problems with the DEM without need of further calibration.As an example application, the evolution of natural cliffs subject to weathering has been studied. Different weathering scenarios have been considered for an initially vertical cliff. Firstly, the case of uniform weathering has been studied. Although unrealistic, this case has been considered in order to validate the DEM approach by comparison against analytical predictions available from limit analysis. Secondly, nonuniform weathering has been studied. The results obtained clearly show that with the DEM it is possible to realistically model boundary value problems of bonded geomaterials, which would be overwhelmingly difficult to do with other numerical techniques.