## 3 Rock Strength and Creep Constitutive Model Based on the Hoek-Brown Failure Criterion  
The classic rock mass failure criterion considers rock as a continuous homogeneous medium, which greatly simplifies the reality. A constitutive model for the rock mass with multiple structural planes was developed via superimposition of the constitutive equations of the rock mass with a single joint, which cannot accurately capture the complex mechanical characteristics of the tiny fissures and multiple groups of structural planes in the rock mass [31; 32]. Hence, the semi-empirical semi-theoretical approach was used to characterize the laminated rock mass in engineering practice. In 1980, [PERSON] and [PERSON] derived the correlation expression among the limiting principal stresses for the failure of rock (mass) (namely, the Hoek-Brown failure criterion) via a trial-and-error process, based on the statistical analysis of massive data from rock triaxial tests and field testing of rock mass, and the Griffith theory. Then, [PERSON] further proposed the generalized Hoek-Brown empirical failure criterion. The Hoek-Brown empirical failure criterion can reflect the effects of various factors of the rock mass--such as the rock strength, the number of structural planes, and the in situ stress--on the rock mass strength, and overcome the disadvantages of the conventional theoretical equation. The generalized Hoek-Brown failure criterion can be expressed as below:  
\[\sigma_{r}=\sigma_{3}+\sigma_{c}\left(m_{\rm b}\frac{\sigma_{3}}{\sigma_{c}}+ s\right)^{a} \tag{1}\]  
where \(\sigma_{r}\) is the maximum principal stress when the rock fails, namely, the rock strength; \(\sigma_{3}\) is the minimum principal stress when the rock fails; \(\sigma_{c}\) is the uniaxial compressive strength of the intact rock; \(m_{\rm b}\), \(s\), and \(a\) are all empirical parameters; \(m_{\rm b}\) represents the hardness of the rock, with a value of 0.0000001-25 (0.0000001 for severely-disturbed rock and 25 for intact hard rock); \(s\) represents the broken degree of the rock mass, with a value of 0-1 (zero for completely broken rock and one for intact rock); \(a\) is related to the rock mass quality. For rock mass with good quality, its strength characteristics are mainly controlled by the rock particle strength, due to the tight packing of rock particles. The restricted Hoek-Brown empirical failure criterion is more applicable to this case and \(a\) = 0.5. On the contrary, for rock mass with poor quality, the packing of fragments in the rock mass is loosened by shearing or weathering, which results in loss of the tensile strength of the rock mass (zero cohesion). Under such circumstances, if there is no confinement, the rock mass will collapse and \(a\) should be assigned to other values. The expressions of the parameters in Equation (1) are listed below:  
\[m_{\rm b}=m_{\rm i}\exp\left(\frac{GSI-100}{28-14D}\right) \tag{2}\]  
\[s=\exp\left(\frac{GSI-100}{9-3D}\right) \tag{3}\]  
\[a=\frac{1}{2}+\frac{1}{6}\left(\rm e^{-GSI/15}-\rm e^{-20/3}\right) \tag{4}\]  
\[0<\sigma_{3}<\frac{\sigma_{c}}{4} \tag{5}\]  
where \(D\) is the disturbance factor (zero for the undisturbed rock mass, and one for completely disturbed rock mass). \(m_{\rm i}\) indicates the values of constants for intact rock, which can be determined by laboratory testing (uniaxial compression test and conventional triaxial compression test). Based on laboratory data and engineering experience, [PERSON] et al. [33; 34] developed a comprehensive and detailed \(m_{\rm i}\) value table that was able to cover a variety of rocks; the \(m_{\rm i}\) index of intact phyllite in this paper refers to this \(m_{\rm i}\) value table.