Page 234 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

Summary Statements 225

magma solidification problem with a moving boundary between the rock and
intruded magma has been transformed into a new problem without the moving
boundary but with the proposed mass sources and physically equivalent heat
sources. The major advantage in using the proposed equivalent source algo-
rithm is that a fixed mesh of finite elements with a variable integration time-
step can be employed to simulate the consequences and effects of the intruded
magma solidification using the conventional finite element method. The related
results from a benchmark magma solidification problem have demonstrated the
correctness and usefulness of the proposed equivalent source algorithm.
(8) To extend the application range of the particle simulation method from a labo-
ratory scale to a large scale such as a geological scale, we need to deal with an
upscale issue associated with simulating spontaneous crack generation prob-
lems in large-scale quasi-static systems. Toward this direction, three impor-
tant simulation issues, which may affect the quality of the particle simulation
results of a quasi-static system, have been addressed. The first simulation issue
is how to determine the particle-scale mechanical properties of a particle from
the measured macroscopic mechanical properties of rocks. The second sim-
ulation issue is that fictitious time, rather than physical time, is used in the
particle simulation of a quasi-static problem. The third simulation issue is that
the conventional loading procedure used in the particle simulation method is
conceptually inaccurate, at least from the force propagation point of view. A
new loading procedure and an upscale theory have been presented to solve the
conceptual problems arising from the first and third simulation issues. The pro-
posed loading procedure is comprised of two main types of periods, a loading
period and a frozen period. Using the proposed loading procedure and upscale
theory, the parameter selection problem stemming from the first issue can be
solved. Since the second issue is an inherent one, it is strongly recommended
that a particle-size sensitivity analysis of at least two different models, which
have the same geometry but different smallest particle sizes, be carried out
to confirm the particle simulation result of a large-scale quasi-static system.
The related simulation results have demonstrated the usefulness and correct-
ness of the proposed loading procedure and upscale theory for dealing with
spontaneous crack generation problems in large-scale quasi-static geological
systems.
(9) This is the end of this monograph, but just the beginning of the computational
geoscience world in the sense that more and more complicated and complex
geoscience problems need to be solved from now on. During writing this mono-
graph, there was the most disastrous earthquake occurring in Wenchuan, China.
Unfortunately, both the time and location for the occurrence of this earthquake
cannot be predicted by the present day’s knowledge of geoscientists. While we
express our deep condolence to those who lost their precious lives during this
earthquake, we really hope that with the further development of computational
geoscience, we can understand all the dynamic processes and mechanisms that
control the occurrence of earthquakes better, so that we could accurately predict
it in such a way as predicting weather today.