Page 184 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

Chapter 8
The Particle Simulation Method for Dealing

with Spontaneous Crack Generation Problems
in Large-Scale Geological Systems

Cracking and fracturing are one class of major failure mechanisms in brittle and
semi-brittle materials. Crustal materials of the Earth can be largely considered as
brittle rocks, and so cracking and fracturing phenomena are ubiquitous. Cracks cre-
ated within the Earth’s crust often provide a very useful channel for mineral-bearing
fluids to flow, particularly from the deep crust into the shallow crust of the Earth.
If other conditions such as fluid chemistry, mineralogy, temperature and pressure
are appropriate, ore body formation and mineralization can take place as a result of
such fluid flow. Because of the ever-increasing demand for mineral resources in the
contemporary world, exploration for new mineral resources has become one of the
highest priorities for many industrial countries. For this reason, extensive studies
(Garven and Freeze 1984, Yeh and Tripathi 1989, 1991, Steefel and Lasaga 1994,
Raffensperger and Garven 1995, Zhao et al. 1997a, Schafer et al. 1998a, b, Zhao et
al. 1998a, Xu et al. 1999, Zhao et al. 2000b, Schaubs and Zhao 2002, Zhao et al.
2002a, 2003e, 2005a) have been conducted to understand the detailed physical and
chemical processes that control ore body formation and mineralization within the
upper crust of the Earth. Thus, the numerical simulation of spontaneous crack gen-
eration in brittle rocks within the upper crust of the Earth has become an important
research topic in the field of computational geoscience.
The numerical simulation of crack initiation has existed from the inception
and development of numerical fracture mechanics. This was the direct outcome
of combining conventional fracture mechanics with numerical methods such as
the finite element and the boundary element methods. Due to the increased capa-
bility of numerical fracture mechanics for considering complicated geometry and
boundary conditions, it significantly extends the applicability of conventional frac-
ture mechanics to a wide range of practical problems in civil and geotechnical
engineering fields. In the study of numerical simulation of crack initiation and
evolution, it is usually assumed that a crack initiates when the value of a local
principal stress attains the tensile strength of the brittle material. Once a crack is
initiated, propagation of the crack, including the propagation direction and incre-
mental growing length of the crack, can be determined by crack propagation the-
ories established in fracture mechanics. Although there are at least three kinds
of mixed-mode crack propagation theories available, namely a theory based on

C. Zhao et al., Fundamentals of Computational Geoscience, 175
Lecture Notes in Earth Sciences 122, DOI 10.1007/978-3-540-89743-9 8,
C Springer-Verlag Berlin Heidelberg 2009