Page 186 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

8 Spontaneous Crack Generation Problems in Large-Scale Geological Systems 177

sions (Saltzer and Pollard 1992, Antonellini and Pollard 1995, Donze et al. 1996,
Scott 1996, Strayer and Huddleston 1997, Camborde et al. 2000, Iwashita and Oda
2000, Burbidge and Braun 2002, Strayer and Suppe 2002, Finch et al. 2003, 2004,
Imber et al. 2004, Zhao et al. 2007b, c, d, Zhao et al. 2008g). Although the particle
simulation method has been successfully used to solve these large-scale geologi-
cal problems, little work, if any, has been reported on using the particle simulation
method to deal with spontaneous crack generation problems in the upper crust of
the Earth. Nevertheless, the particle simulation method has been developed to sim-
ulate microscopic crack generation in small-scale laboratory specimens and mining
sites (Itasca Consulting Group, inc. 1999, Potyondy and Cundall 2004). Since both
the time-scale and the length-scale are quite different between laboratory speci-
mens and geological systems, it is necessary to deal with an upscale issue when the
particle simulation method is applied to solve spontaneous crack generation prob-
lems in the upper crust of the Earth. Due to the relative slowness of some geolog-
ical processes, many geological systems can be treated as quasi-static ones (that
is, inertia is neglected), at least from the mathematical point of view. Because the
mechanical response of a quasi-static system is theoretically independent of time,
the time-scale issue can be eliminated in the particle simulation of a quasi-static
system. For this reason, this chapter is restricted to deal with the particle simulation
of spontaneous crack generation problems within large-scale quasi-static geological
systems.
It is however computationally prohibitive to simulate a whole geological system
using real physical particles of a microscopic length-scale, even though with modern
computer capability. To overcome this difficulty, the following three approaches are
often used in dealing with the particle simulation of geological length-scale prob-
lems. In the first approach, a geological length-scale problem, which is usually of
a kilometer-scale, is scaled down to a similar problem of a small length-scale (i.e.
a meter-scale or a centimeter-scale) and then particles of small length-scale (e.g. a
microscopic length-scale) are used to simulate this small length-scale geological
problem (e.g. Antonellini and Pollard 1995, Imber et al. 2004, Schopfer et al. 2006).
In the second approach, the geological length-scale problem is directly simulated
using particles with a relative large length-scale (e.g. Strayer and Huddleston 1997,
Burbidge and Braun 2002, Strayer and Suppe 2002, Finch et al. 2003, 2004). In
this case, the particles used in the simulation can be considered as the representa-
tion of a large rock block. Although detailed microscopic deformation cannot be
simulated using the second approach, the macroscopic deformation pattern can be
reasonably simulated in this approach (e.g. Strayer and Huddleston 1997, Burbidge
and Braun 2002, Strayer and Suppe 2002, Finch et al. 2003, 2004). This implies
that if the macroscopic deformation process of a geological length-scale system is
of interest, then the second approach can produce useful simulation results. This
is particularly true for understanding the controlling process of ore body forma-
tion and mineralization, in which the macroscopic length-scale geological struc-
tures are always of special interest. In the third approach, the combined use of both
a block-mechanics-based particle simulation method and a continuum-mechanics-
based method, such as the finite element method (Zienkiewicz 1977, Lewis and