Page 229 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

220 8 Spontaneous Crack Generation Problems in Large-Scale Geological Systems

the underlying fault in rigid basement blocks are considered to investigate the effect
of the dip angle of the underlying fault on spontaneous crack generation patterns
in crustal brittle rocks. Figure 8.21 shows the related numerical simulation results
of crack generation and deformation patterns in the computational model due to
three different dip angles of the underlying fault. The results shown in this fig-
ure are obtained when the vertical displacement of the left-hand-side basement is
about 30% of the whole thickness of the computational model. It is observed from
these simulation results that there are some remarkable differences in the crack gen-
eration and deformation patterns due to these three different dip angles, implying
that the dip angle of the underlying fault has a significant influence on spontaneous
crack generation patterns in crustal brittle rocks. The major reason for causing such
remarkable differences in the simulation results is that for the same amount of ver-
tical displacement of the left-hand-side basement, the corresponding horizontal dis-
placement of the left-hand-side basement is significant different for the three differ-
ent dip angles of the underlying fault. For example, when the vertical displacement
of the left-hand-side basement is about 30% of the whole thickness of the com-
putational model, the corresponding horizontal displacement of the left-hand-side
basement is about 51.97, 30 and 17.32% of the whole thickness of the computa-
tional model in the case of the dip angle being 30 ,45 and 60 respectively. Due to
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◦
◦
the significant difference in the horizontal displacement of the left-hand-side base-
ment, the crack pattern in the computational model of θ = 30 is more diffuse than
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◦
that in the computational model of θ = 60 . In the case of θ = 60 , a macroscopic
◦
crack (i.e. a new fault) is formed in the slip direction of the underlying fault and also
passes the tip point of the left-hand-side basement. However, in the cases of θ = 30 ◦
◦
and θ = 45 , the dip angle of the resulting new fault in the computational model is
steeper than that of the underlying fault in the rigid basement blocks. In addition,
it is noted that in the case of θ = 45 , there is a large crack within the hanging-
◦
wall of the computational model. This crack penetrates into about 40% of the whole
thickness of the computational model. This phenomenon further demonstrates that
the dip angle of the underlying fault has a significant effect on spontaneous crack
generation patterns in crustal brittle rocks.