Page 187 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

178 8 Spontaneous Crack Generation Problems in Large-Scale Geological Systems

Schrefler 1998) or the finite difference method, are used to simulate the whole
geological system (Potyondy and Cundall 2004, Suiker and Fleck 2004, Fleck and
Willis 2004). In this approach, the continuous deformation range of a system is
simulated using the continuum-mechanics-based method, and the discontinuous
deformation range of the system is simulated using the block-mechanics-based par-
ticle simulation method. Since large element sizes can be used to simulate the con-
tinuous deformation range for a quasi-static geological system, the third approach
is computationally more efficient than the first and second approaches in dealing
with large systems. However, the computational difficulty associated with the third
approach is that an adaptive interface between the continuous deformation range
and the discontinuous deformation range must be appropriately developed. This
means that if the discontinuous deformation range is obvious apriori for some kind
of geological problem, then the third approach is computationally very efficient.
Otherwise, the efficiency of using the third approach might be greatly reduced due
to the ambiguity in defining interfaces between the continuous and the discontinu-
ous deformation ranges. For this reason, the first and second approaches are com-
monly used to simulate large-scale geological systems using the particle simulation
method.
Because of the wide use of both the first and the second approaches, the fol-
lowing scientific questions are inevitably posed: Are two particle simulation results
obtained from both the first and the second approaches consistent with each other
for the same geological problem? If the two particle simulation results are consis-
tent, then what is the intrinsic relationship between the two similar particle mod-
els used in the first approach and the second approach? To the best knowledge
of the authors, these questions remain unanswered. Therefore, we will develop an
upscale theory associated with the particle simulation of two-dimensional quasi-
static geological systems at different length-scales to clearly answer these two sci-
entific questions. The present upscale theory is of significant theoretical value in
the particle simulation of two-dimensional systems, at least from the following
two points of view. (1) If the mechanical response of a particle model of a small
length-scale is used to investigate indirectly that of a large length-scale, then the
present upscale theory provides the necessary conditions that the particle model
of the small length-scale needs to satisfy so that similarity between the mechani-
cal responses of the two different length-scale particle models can be maintained.
(2) If a particle model of a large length-scale is used to investigate directly the
mechanical response of the model, then the present upscale theory can be used
to determine the necessary particle-scale mechanical properties from the macro-
scopic mechanical properties that are obtained from either a laboratory test or an
in-situ measurement. Because the particle simulation method has been used to solve
many kinds of scientific and engineering problems, the present upscale theory can
be directly used to extend the application range of the particle simulation results
for geometrically-similar problems without a need to conduct another particle sim-
ulation. This means that the present upscale theory compliments existing particle
simulation method, and is applicable for practical applications in many scientific
and engineering fields.