# Research on Control Technology of Large-Section Water-Bearing Broken Surrounding Rock Roadway
## 2 Engineering Summary and Analysis of Surrounding Rock Failure Characteristics
### Theoretical Model Establishment and Analysis of Roadway  
Before analyzing the elastic-plastic distribution of the surrounding rock in a roadway influenced by pore water pressure, the following assumptions must be established: (1) the roadway excavation creates both a broken zone and an elastic zone; (2) the roadway is located at a depth greater than 20 times its radius; (3) the surrounding rock is considered an isotropic, homogeneous medium, with the original rock stress being equal in all directions; (4) the roadway cross-section is circular, its length is infinite, the properties of the surrounding rock are uniform, and the problem can be treated as a plane strain scenario; (5) groundwater flow adheres to [PERSON]'s law; (6) the seepage volume force in the mechanical model is represented by pore water pressure. The theoretical model is established under the assumption that the radius of the deeply buried circular roadway is \(R_{0}\), the radius of the broken zone is \(R_{p}\), the radius of the pore water pressure is \(R_{s}\), and \(r\) is the radial distance of any point in the surrounding rock. When \(r\geq R_{s}\), the pore water pressure is \(p_{w}\), and the pore water pressure within \(R_{s}\) is represented as \(P_{s}\), which varies with r. Additionally, \(p_{0}\) represents the original rock stress. The theoretical geometric model is illustrated in Figure 3. This scenario is classified as an axisymmetric seepage problem, and the equation for the seepage pore water pressure field is derived from seepage theory, as follows:  
\[p_{s}=\left\{ \begin{array}{ll}p_{w}&r\geq R_{s}\\ p_{w}\frac{\ln(r/R_{s})}{\ln(R_{s}/R_{0})}&R_{0}\leq r<R_{s}\end{array} \right. \tag{1}\]  
Figure 3: Roadway mechanics model. In the roadway model, it is not only affected by the stress of the original rock but also by the seepage volume force. The known seepage differential equation and its boundary conditions are as follows:  
\[\left. \begin{array}{c}\frac{\partial^{2}H}{\partial r^{2}}+\frac{1}{r}\frac{ \partial H}{\partial r}=0\\ H(r)=h_{0},r=R_{0}\\ H(r)=h_{w},r=\delta R_{0}\end{array} \right\} \tag{2}\]  
From the above equation, the water pressure can be expressed as follows:  
\[H(r)=\frac{h_{0}\cdot\ln(\omega R_{0}/r)+h_{w}\cdot\ln(r/R_{0})}{\ln(\omega)} \tag{3}\]  
The water pressure is converted into a seepage volume force acting inside the model, and its expression can be changed into the following:  
\[F_{r}=\frac{\eta(h_{0}-h_{w})}{r\ln(\omega)}\cdot\xi_{w} \tag{4}\]  
Therefore, the equilibrium differential equation under the action of osmotic body force is as follows:  
\[\frac{d\sigma_{r}}{dr}+\frac{\sigma_{r}-\sigma_{\theta}}{r}+F_{r}=0 \tag{5}\]  
In the equation, \(h_{0}\) is the surface water head of roadway-surrounding rock, \(h_{w}\) is the water head of the distant water surface, \(\xi_{w}\) is the weight of water, and \(\omega\) is the multiple of the equivalent radius of the roadway. In the early stage of roadway excavation, the water head \(h_{0}\) on the inner surface of roadway-surrounding rock is set to be 0. At this time, the water head potential energy difference is generated between the inner surface of surrounding rock and the complete rock mass, and the original balance of seepage volume force is broken. Then, the groundwater produces a certain pore water pressure acting on the outer surface of roadway-surrounding rock. Here, the water-bearing surrounding rock is regarded as a two-phase medium, and Equation (5) can be transformed into the following:  
\[\frac{d\sigma_{r}}{dr}+\frac{\sigma_{r}-\sigma_{\theta}}{r}-\frac{\eta dp_{s} }{dr}=0 \tag{6}\]  
In the formula, \(\eta\) is the effective pore pressure coefficient, and \(\eta=1\) when fully permeable and \(\eta=0\) when impervious; that is, the value range of the coefficient is \(0\leq\eta\leq 1\).