Table 1 List of symbols used in this article.
Notation | |||
|---|---|---|---|
\(D\) | Damage factor | \(u\) | Radial displacement |
\(E_{0}\) | Intact rock deformation modulus | \(\varphi\) | Dilation angle |
\(v\) | Poison’s ratio of the rock mass | \(\rho\) | Normalized radii |
\(GSI_{p}^{u}\) | Peak geological strength index in the undamaged zone | \(\rho^{d}\) | Normalized damage radii |
\(GSI_{r}^{u}\) | Residual geological strength index in the undamaged zone | \(\Delta \varepsilon_{r}^{e}\) | Radial elastic strain increment |
\(GSI_{p}^{d}\) | Peak geological strength index in the damaged zone | \(\Delta \varepsilon_{\theta }^{e}\) | Tangential elastic strain increment |
\(GSI_{r}^{d}\) | Residual geological strength index in the damaged zone | \(\Delta \varepsilon_{r}^{p}\) | Radial plastic strain increment |
\(R_{d}\) | Damage radius | \(\Delta \varepsilon_{\theta }^{p}\) | Tangential plastic strain increment |
\(R_{p}\) | Plastic radius | \(\varepsilon_{\theta }^{p}\) | Tangential plastic strain |
\(R_{s}\) | Residual radius | \(\varepsilon_{r}^{p}\) | Radial elastic strain |
\(b\) | Radius of tunnel | \(\varepsilon_{r}\) | Radial strain |
\(k\) | Coefficient of dilation | \(\varepsilon_{\theta }\) | Tangential strain |
\(p_{i}\) | Internal supporting pressure | \(\sigma_{c}\) | Uniaxial compressive strength |
\(p_{ic}\) | Critical supporting pressure | \(\sigma_{0}\) | Hydrostatic stress |
\(\omega_{p}^{u}\) | Peak parameter in the undamaged zone | \(\sigma_{r}\) | Radial stress |
\(\omega_{r}^{u}\) | Residual parameter in the undamaged zone | \(\sigma_{\theta }\) | Circumferential stress |
\(\omega_{p}^{d}\) | Peak parameter in the damaged zone | \(\eta^{p}\) | Softening parameter |
\(\omega_{r}^{d}\) | Residual parameter in the damaged zone | \(\eta^{p*}\) | Critical deviatoric plastic strain |
