6.1 Continuum modeling

Continuum modeling is best suited for the analysis of slopes that are comprised of massive, intact rock, weak rocks, and soil-like or heavily fractured rock masses. Figure1 shows the discritiesed view of slope by continuum code using phase2 software. Continuum codes assume that material is continuous throughout the body. Discontinuities are treated as special cases by introducing interfaces between continuum bodies. This model cannot handle many intersecting joints. It can typically simulate less then 10 non-intersecting discontinuities. The fundamental importance to continuum models and deformable blocks in discrete element models is representation of the rock mass behaviour. Discrete fractures such as faults and bedding planes can be incorporated in most continuum models. However, these models cannot be used to simulate highly fracture rock mass. Finite difference, finite element and boundary element methods are based on this modeling theory. In this method, the problem domain is discretized into a set of sub-domains or elements. The solution procedure may be based on numerical approximations of the governing equations. Two-dimensional continuum codes assume plane strain conditions, which are frequently not valid in inhomogeneous rock slopes with varying structure, lithology and topography.

Complex behaviour of slope can be modeled using continuum codes. Groundwater, pore pressures and dynamic interaction can also be simulated.  It requires input properties such as constitutive model (e.g. elastic, elasto-plastic, creep etc.), groundwater characteristics, shear strength of surfaces and in situ stress state (figure 2 & 3). During modeling, effects of boundary, mesh aspect ratios, symmetry, hardware memory restrictions are important factors. Figure1 shows the discritiesed view of mne dump slope in 3D by continuum method. Some softwares based on continuum modeling like Phase2 (rocscience), FLAC2D, FLAC3D (Itasca 1997) and VISAGE  (VIPS,  2001), PLAXIS () are well suited for slope stability problems.

Figure 1: Finite-element model showing descritised slope.

Figure 2: Finite-element mesh of a rock slope having a coal seam.

Figure 3: Simulation of rain water infiltration by Finite-element method.

Figure 4: simulation of mine waste dump by FLAC based on finite difference method