Crack Damage Parameters and Dilatancy of Artificially Jointed Granite Samples Under Triaxial Compression

Abstract

A database of post-peak triaxial test results was created for artificially jointed planes introduced in cylindrical compression samples of a Blanco Mera granite. Aside from examining the artificial jointing effect on major rock and rock mass parameters such as stiffness, peak strength and residual strength, other strength parameters related to brittle cracking and post-yield dilatancy were analyzed. Crack initiation and crack damage values for both the intact and artificially jointed samples were determined, and these damage envelopes were found to be notably impacted by the presence of jointing. The data suggest that with increased density of jointing, the samples transition from a combined matrix damage and joint slip yielding mechanism to yield dominated by joint slip. Additionally, post-yield dilation data were analyzed in the context of a mobilized dilation angle model, and the peak dilation angle was found to decrease significantly when there were joints in the samples. These dilatancy results are consistent with hypotheses in the literature on rock mass dilatancy.

Appendix: Equations of the W–D Dilation Model

Walton and Diederichs (2015a) proposed a mobilized dilation angle which is piecewise with respect to plastic shear strain (γ^p), but continuous with respect to confining stress (σ₃):

$$\psi (\sigma_{3} ,\gamma^{\text{p}} ) = \left\{ {\begin{array}{*{20}l} {\frac{{\alpha \cdot \gamma^{\text{p}} \cdot \psi_{\text{peak}} }}{{e^{((\alpha - 1)/\alpha )} \cdot \gamma_{\text{m}} }} \,{\text{when}}\, \gamma^{\text{p}} < \gamma_{\text{m}} \cdot e^{((\alpha - 1)/\alpha )} } \\ {\psi_{\text{peak}} \cdot \left( {\alpha \cdot { \ln }\left( {\frac{{\gamma^{\text{p}} }}{{\gamma_{\text{m}} }}} \right) + 1} \right)\, {\text{when}} \,\gamma_{\text{m}} \cdot e^{((\alpha - 1)/\alpha )} \le \gamma^{\text{p}} < \gamma_{\text{m}} } \\ {\psi_{\text{peak}} \cdot e^{{( - (\gamma^{\text{p}} - \gamma_{\text{m}} )/\gamma^{*} )}}\, {\text{when}} \,\gamma^{\text{p}} \ge \gamma_{\text{m}} } \\ \end{array} } \right.$$

(11)

where

$$\alpha = \alpha_{o} + \alpha^{\prime } \cdot \sigma_{3}$$

(12)

$$\gamma^{*} = \left\{ {\begin{array}{*{20}l} {\gamma_{0} \,{\text{when}}\, \sigma_{3} = 0} \\ {\gamma^{\prime }\, {\text{when }}\,\sigma_{3} \ne 0} \\ \end{array} } \right.$$

(13)

and

$$\psi_{\text{peak}} (\sigma_{3} ) = \left\{ {\begin{array}{*{20}l} {\frac{{\phi_{\text{peak}} }}{{1 + log_{10} ({\text{UCS}})}} \cdot { \log }_{10} \left( {\frac{\text{UCS}}{{\sigma_{3} + 0.1}}} \right) ({\text{sedimentary rocks}})} \\ {\left\{ {\begin{array}{*{20}l} {\phi_{\text{peak}} \cdot \left( {1 - \frac{{\beta^{\prime } }}{{e^{{ - ((1 - \beta_{0} - \beta^{\prime } )/\beta^{\prime } )}} }}\sigma_{3} } \right) \,{\text{when}}\, \sigma_{3} < e^{{ - ((1 - \beta_{0} - \beta^{\prime } )/\beta^{\prime } )}} } \\ {\phi_{\text{peak}} \cdot \left( {\beta_{0} - \beta^{\prime } { \ln }(\sigma_{3} )} \right)\, {\text{when}}\, \sigma_{3} > e^{{ - ((1 - \beta_{0} - \beta^{\prime } )/\beta^{\prime } )}} } \\ \end{array} ({\text{crystalline rocks}})} \right.} \\ \end{array} } \right.$$

(14)

where UCS is the uniaxial compressive strength of the rock in MPa (σ₃ is also expressed in MPa).

The dilation angle model for $\gamma^{\text{p}} \ge \gamma_{\text{m}}$ is similar to that proposed by Alejano and Alonso (2005), and the peak dilation angle function for sedimentary rocks is identical.

As shown in Eq. (14), the confining stress dependency is primarily controlled by the influence of the $\beta^{\prime }$ and $\beta_{0}$ parameters on the peak dilation angle. While any of the four model parameters that describe the plastic shear strain dependency of the dilation angle in Eq. (11) ($\alpha$, $\gamma_{\text{m}}$, $\psi_{\text{peak}}$, $\gamma^{*}$), such as through the relationships in Eqs. (12) and (13), in practice, $\alpha$, $\gamma_{\text{m}}$, and $\gamma^{*}$ can often be considered as constants (Walton et al. 2014a, 2016).