A BEM Formulation Of Free Hexagons Based On
Dynamic Equilibrium
Author(s)
P. Procházka
Abstract
In this paper, a time dependent (dynamical equilibrium) free hexagon DEM is
formulated and solved. The main application is found in geomechanics, namely
in bumps occurrence in deep mines. The time factor is included in a natural way
in the model of discrete elements created by the boundary element method. One
of the most important phenomena is the velocity of excavation. In the deep
mines the method of depositing packs and its mechanical properties are also
decisive. Their mutual coupling can principally influence the safety against
bumps. For a correct understanding of the behavior of the rock aggregate (coal
seam vs. overburden), the nucleation of cracks finally leading to bumps has to be
treated as time dependent, while so far it was observed only from statical
equilibrium. According to new experiments and results from accessible
literature, a dynamical effect has to be included in thr formulation.
Contact problems leading to bumps occurrence in deep mines have been
solved in many of the papers of the present author for the static case. Either
Lagrangian multipliers or penalty formulation were used. The new formulation
has to be submitted in terms of a penalty, which if high enough (bond effect of
adjacent elements) suppresses the influence of time. By including the interface
properties with the lumped inertia mass of the elements, complex nucleation can
be studied and the information on possible rock bursts is improved. From some
examples it was shown in the static case that the behavior at the face of longwall
mining is close to that near the crack tip, and the differences in material
properties of coal and overburden are also not negligible. These factors are also
expected to be important in the case of dynamic problems. Some examples show
the application of the procedure proposed.
Keywords: discrete element method, boundary element method, dynamical
equilibrium.
Keywords
discrete element method, boundary element method, dynamical
equilibrium.
Related Book
Other papers in this volume
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