Page 221 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

212 8 Spontaneous Crack Generation Problems in Large-Scale Geological Systems

2.00E–02
SB = 100MPa
SB = 10MPa
1.00E–02
SB = 1MPa
0.00E+00
0.00 0.04 0.08 0.12
Volumetric Strain –2.00E–02
–1.00E–02

–3.00E–02

–4.00E–02

–5.00E–02
–6.00E–02
Axial Strain
2
(A) 1× m sample
4.00E–02

SB = 100MPa
2.00E–02 SB = 10MPa
SB = 1MPa
Volumetric Strain –2.00E–02 0.00 0.04 0.08 0.12
0.00E+00

–4.00E–02

–6.00E–02
Axial Strain
2
(B) 1× km sample
Fig. 8.15 Effects of shear bond strength on the curve of volumetric strain versus axial strain

and 30.477 m, resulting in an average radius of 25.397 m. The porosities of both
the meter-scale and the kilometer-scale particle models are 0.17, while the density
3
and friction coefficient of the particle material are 2500 kg/m and 0.5 respectively.
Because the geometrical similarity ratio (i.e. 1/1000) of the two particle models
is equal to the corresponding particle diameter similarity ratio, the first similarity
criterion of the upscale theory is satisfied between these two similar particle mod-
els. Since the same value of the contact stiffness is used in both the meter-scale