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62 Applied Petroleum Geomechanics

120
Mudstone
Differen al stress (MPa) 80
Sandy mudstone
100
Fine-grain sandstone
60
40

20
0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Strain (%)
Figure 2.20 Complete stressestrain curves for sandstone, sandy mudstone, and
mudstone in Eastern China’s Permian formations under the triaxial compression tests
(confining stress s 3 ¼ 10 MPa).

(i.e., stiff), and the initial part of the complete stressestrain curve of the rock
will be steep. However, for a low Young’s modulus (soft) rock it is more
deformable, and the initial part of the complete stressestrain curve will be
gentle (Hudson and Harrison, 1997). Fig. 2.20 shows three complete
stressestrain curves of the triaxial compressive tests for fine-grained sand-
stone, sandy mudstone, and mudstone in the Permian formations in
Huainan, China (Meng et al., 2006). The differential stress in the figure
represents the difference of the axial and the confining stresses, i.e., s 1 s 3 .
Fig. 2.20 indicates that different rocks have different Young’s moduli: the
sandstone has a much greater peak compressive strength and larger Young’s
modulus than those in mudstones.
In triaxial compression tests, Young’s moduli may be different at
different confining stresses. Triaxial test results show that Young’s moduli
could be very different even for the rocks cored in the same formation at a
similar depth. Fig. 2.21 demonstrates that Young’s modulus increases as the
confining stress increases (Meng et al., 2006). When the confining stress is
small (e.g., S3 ¼ 0 and 5 MPa in Fig. 2.21), the difference of Young’s
moduli is large. Laboratory test results reported by Niandou et al. (1997)
have a similar phenomenon. Triaxial compression tests indicate that
Young’s modulus is dependent on the confining pressure (stress) and they
have a nonlinear relationship even for the same rock. This nonlinear
relationship can be expressed as the following form:
2
E s ¼ b 2 s þ b 1 s 3 þ b 0 (2.49)
3