Page 217 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

208 8 Spontaneous Crack Generation Problems in Large-Scale Geological Systems

the laboratory experiments of rocks (Jaeger and Cook 1976). Since higher confining
stress can effectively prevent the lateral expansive axial stain of a test sample from
occurring at the critical stage, the value of the volumetric strain in the case of the
confining stress being 10 MPa is almost double the value of the volumetric strain in
the case of the confining stress being 0.1 MPa. This indicates that an increase in the
confining stress can result in an increase in the compressive volumetric strain at the
critical stage of the test sample. Clearly, the curves of volumetric strain versus axial
strain (as shown in Fig. 8.11) are identical in the elastic response ranges of both the
meter-scale and the kilometer-scale samples, while they are very similar in the post-
failure response ranges of the two samples of different length-scales. It is noted that
in the case of the confining stress being 0.1 MPa, there is a considerable discrepancy
between the maximum values of the volumetric strain in the post-failure response
ranges of the two samples of different length-scales. Nevertheless, this discrepancy
is significantly reduced in the case of the confining stress being increased to 10 MPa.
This further demonstrates that the proposed upscale theory is appropriate and use-
ful for establishing an intrinsic relationship between two similar particle systems of
different length-scales.
Next, we investigate the effect of the normal bond strength of particles on the
mechanical responses of both the meter-scale and the kilometer-scale samples. In
this case, the confining stress is taken as 10 MPa, while the unit shear bond strength
of particles is 100 MPa for both the test samples. Three different values of the unit
normal bond strengths of particles, namely NB = 0.1 MPa, 1 MPa and 10 MPa (as
shown in Figs. 8.12 and 8.13), are used in the particle simulation of the two similar
test samples.
Figure 8.12 shows the effect of the normal bond strength on the curves of devia-
toric stress versus axial strain, while Fig. 8.13 shows the effect of the normal bond
strength on the curves of volumetric strain (i.e. the dilation) versus axial strain for
both the meter-scale and the kilometer-scale samples. Due to the geometrical simi-
larity between these two samples, the simulation results from the meter-scale sample
are very similar to those from the kilometer-scale sample, especially in the elastic
response ranges of the two similar samples. It is also noted that the normal bond
strength of particles has a significant effect on both the stress-strain and the dilation-
strain curves of the two similar samples. The general trend is that the maximum fail-
ure stress of a particle sample increases with an increase in the normal bond strength
of the particles used in the particle sample.
Similarly, the effect of the shear bond strength on the mechanical response of the
two similar samples is examined by considering three different values of the unit
shear bond strengths, namely SB = 1, 10 and 100 MPa (as shown in Figs. 8.14 and
8.15). In this situation, both the confining stress and the unit normal bond strength
are kept as two different constants, which are equal to 10 and 1 MPa in the particle
simulation. Figures 8.14 and 8.15 show the effect of the shear bond strength of
particles on the stress-strain and dilation-strain curves for both the meter-scale and
the kilometer-scale samples respectively. In addition to a clear similarity between
the simulation results obtained from the two similar particle samples of different
length-scales, it is interesting to note that in the case of SB = 100 MPa, both the