Underground Construction - January 2019 - 38

CIGMAT Report
Hence, Mohr-Coulomb failure model does not satisfy the upper limit
condition for the shear strength tolerance of the materials.

The Vipulanandan failure model (Equation 6 and Figure 12) showed
the limestone coefficient of determination (R2) and root mean square
of error (RMSE) were 0.94 and 3.4 MPa, respectively, as summarized in
Table 6. The yield stress ( ) and tensile strength ( t) was 2.6 MPa and
3.2 MPa, respectively, and model parameters C and D for limestone were
1.26 and 0.01 MPa-1, respectively, per Table 3.
In the final analysis, the new Vipulanandan failure model (Equation
8) better predicted the experimental results compared to the Mohr-Coulomb model, and also quantified the maximum shear strength tolerance
( max.) for sandstone, shale and limestone as 410 MPa, 103 MPa and 102
MPa, respectively, as summarized in Table 3.
Figure 9: Vipulanandan failure model compared to Mohr-Coulomb model

Hence, the Vipulanandan model (Equation 6) has a limit on the maximum shear stress the rocks will tolerate at relatively high normal stress.
Shear stress-normal stress relationships were predicted using the Vipulanandan failure model and compared with the Mohr-Coulomb failure
model, as shown in Figure 9.
For sandstone, the shear-stress behavior of the 22 data collected from
the literature was modeled. Using the Mohr-Coulomb failure model
(Equation 3 and Figure 9), the coefficient of determination (R2) and root
mean square of error (RMSE) were 0.89 and 29.6 MPa, respectively, as
summarized in Table 3. The yield stress ( ), angle of internal friction ( )
and tensile strength ( t ) of the sandstone rock were 27 MPa, 48o and
24.2 MPa, respectively (Table 3).
With the Vipulanandan failure model (Equation 6 and Figure 10), the
coefficient of determination (R2) and root mean square of error (RMSE)
for sandstone were 0.98 and 14.1 MPa, respectively, as summarized in
Table 6. The yield stress ( ) and tensile strength ( t ) were 29 MPa and
7.8 MPa, respectively, and model parameters C and D for sandstone were
0.25 and 0.026 MPa-1, respectively, as summarized in Table 6.
The shear-stress behavior of shale used the 29 data collected from the
literature. Modeled using the Mohr-Coulomb failure (Equation 3 and
Figure 10), the coefficient of determination (R2) and root mean square
of error (RMSE) were 0.95 and 5.20 MPa, respectively, as summarized
in Table 6. The yield stress ( ), angle of internal friction ( ) and tensile
strength ( t ) of the shale rock were 2.5 MPa, 25o and 6.5 MPa, respectively (Table 3).
Using the Vipulanandan failure model (Equation 6 and Figure 11), the
coefficient of determination (R2) and root mean square of error (RMSE)
were 0.95 and 3.4 MPa respectively, as summarized in Table 6. The yield
stress ( ) and tensile strength ( t ) of the shale was 3 MPa and 3.9 MPa,
respectively, and the model parameters C and D for shale were 1.34 and
0.01 MPa-1, respectively, as summarized in Table 3.
For limestone, shear-stress behavior of the 40 data collected from
the literature, according to the Mohr-Coulomb failure model (Equation
3 and Figure 11) produced coefficient of determination (R2) and root
mean square of error (RMSE) of 0.97 and 3.3 MPa, respectively (Table
6). The yield stress ( ), angle of internal friction ( ) and tensile strength
( t ) of the limestone were 2.7 MPa, 28o and 5 MPa, respectively, per
Table 3.

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JANUARY 2019 | UConOnline.com

Figure 10: Vipulanandan failure model compared to Mohr-Coulomb model for sandstone

Figure 11: Vipulanandan failure model compared to Mohr-Coulomb model for shale rock
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Underground Construction - January 2019

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