Mathematical Physics - Volume II - Numerical Methods

6.5 Discrete Element Methods

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experimental results. In particular, there is a marked disparity in strength in the presence of lateral confinement. Potyondy and Cundall [128] also considered in detail the effect of particle size (given by the minimum diameter of 2 R min as the defining length scale) on the properties of the material macro-properties. They demonstrated that the discrete-element size is not only an independent parameter of the model that controls the DEM resolution but also an essential part of the material characterization coupled with the macro-properties of tensile strength and fracture toughness. Elastic constants are rather independent of the discrete-element size due to the scaling of the stiffness of the parallel bond as a function of particle size. The unconfined compressive strength seems to show a similar trend of model objectivity. On the other hand, the splitting tensile strength in the Brazilian test ("Brazilian strength") shows a clear dependence on particle size as well as fracture toughness in the first mode (opening). This observation, that the discrete-element size, which controls the model resolution, cannot be chosen arbitrarily because it is coupled with the fracture toughness of the material (expressed by the critical stress intensity factor; K Ic ), is not surprising because the very definition of the stress intensity factor implies an internal length scale. Moon and co-authors [140] developed a general procedure for calculating the fracture toughness of random packing of grains of unequal sizes.

Figure 6.21: 3DEC simulation of collapse of jointed rock masses around an underground excavation due to seismic loading. Field (a) of the maximum principal stress and (b) velocity magnitudes in two planes with given color interpreters. (Courtesy of Dr. Branko Damjanac.)