# Deep Soft Rock Tunnel Perimeter Rock Control Technology and Research
## 2 Roadway Surrounding Rock Control Technology
### Analysis of Deformation of Broken Surrounding Rock in Deep Roadway
Since both the magnitude and direction of the creep rate of the surrounding rock are different, Equation (1) can be rewritten as follows:  
\[v=K\frac{\partial\delta_{r}}{\partial x}\ v=K\frac{\partial\delta_{r}}{\partial y} \tag{2}\]  
Due to the different nature of the roadway enclosure, Equation (2) can be rewritten as follows:  
\[v_{x}=K_{x}\frac{\partial\delta_{r}}{\partial x}\ v_{y}=K_{y}\frac{\partial \delta_{r}}{\partial y} \tag{3}\]  
If the creep phenomenon of the surrounding rock is regarded as a slow flow of a viscous medium, the movement of the surrounding rock should satisfy the following continuity equation:  
\[\frac{\partial v_{x}}{\partial x}+\frac{\partial v_{y}}{\partial y}=0 \tag{4}\]  
Substituting Equation (3) into Equation (4) gives the following:  
\[\frac{\partial}{\partial x}\left(K_{x}\frac{\partial\delta_{r}}{\partial x} \right)+\frac{\partial}{\partial y}\left(K_{y}\frac{\partial\delta_{r}}{ \partial y}\right)=0 \tag{5}\]  
where \(K_{x}\) and \(K_{y}\) are the rock creep coefficients in the corresponding axial directions, respectively. Equation (5) can be referred to as the differential equation for creep of the roadway perimeter. This equation is valid for a certain range of R-domains beyond the roadway perimeter. Obviously, as long as Equation (1) and Equation (5) hold, the boundary conditions of the enclosing rock in the R-domain are known, as follows:  
\[\delta(x,y)|r_{1},r_{2}=\Sigma\delta_{r}(x,y)|(x,y)\in r_{1},r_{2} \tag{6}\]  
or  
\[K_{m}\frac{\partial\delta}{\partial n}|r_{1}=\pm q(x,y)|(x,y) \tag{7}\]  
where \(r_{1}\) and \(r_{2}\) are the inner and outer boundaries of the roadway enclosure, respectively. \(K_{m}\frac{\partial\delta}{\partial n}\) is the perimeter rock creep per unit length around the roadway. \(\delta(x,y)\) is the stress distribution function on the R-domain boundary of the tunnel envelope. \(\delta_{r}(x,y)\) is the stress distribution function of the surrounding rock in the R domain. \(q(x,y)\) is the creep in the surrounding rock per unit length of the roadway boundary. From the differential equation solution method, it can be seen that if the rock on the outer boundary of the \(R\) domain does not move, i.e., \(K_{m}\frac{\partial\delta}{\partial n}=0\), and the stress distribution function on the inner boundary is known, or the amount of perimeter rock creep per unit length on the inner boundary is known, then the solution of the equation is unique; on the contrary, the artificial control of the amount of perimeter rock creep on the roadway can be adjusted to adjust the support load, the size of the deformation, and the direction of the support, so as to achieve the purpose of preventing the bracket and the support system from undergoing deformation and damage. Therefore, allowing the surrounding rock to creep within a certain range and releasing a certain amount of pressure not only provides better bearing capacity and resistance to deformation in the surrounding rock, but also allows for a better response to the effects of mining pressure.