# Deep Soft Rock Tunnel Perimeter Rock Control Technology and Research
## 4 Roadway Support Program Design
### Design of Permanent Support Parameters  
The permanent support is in the form of anchor rods + anchor cables.  
(1) The formula for calculating the total length of the anchor is as follows:  
\[L=L_{1}+L_{2}+L_{3} \tag{8}\]  
where \(L\) is the total length of anchor. \(L_{1}\) is the sum of the pure exposed length (take 0.06 m), the thickness of the nut (take 0.05 m), and the thickness of the tray (take 0.008 m). \(L_{2}\) is the effective length (height of crushing belt). \(L_{3}\) is the depth of anchor into the formation (take 0.8 m). Equation (9) is as follows:  
\[L_{2}=R_{0}\sqrt{\frac{rZ}{rZsin\varphi+Cos\varphi}}-h \tag{9}\]  
where \(R_{0}\) is the total length of anchor (take 2.75 m) and is the bulk weight of the rock (take 16.5 kN/m\({}^{3}\)). \(Z\) is the depth of the center of the roadway from the surface (take 580 m), and is the angle of friction within the rock mass (take 47.2\({}^{\circ}\)). \(C\) is the cohesive force (take 2350 kN/m\({}^{2}\)) that takes 2.75 m.  
Figure 14: Numerical simulation of the horizontal deformation.  
After calculation, the value of \(L\) is 1.12 m. The actual anchor of the working face is 2.4 m long, which is larger than the calculated value, and the length of the anchors used in the design meets the calculation requirements.  
The spacing between rows of anchors is calculated as follows.  
According to the suspension theory, the anchor anchoring force should be able to bear the weight of the rock body suspended by the anchor, i.e., as follows:  
\[a^{2}<Q/KrL_{2} \tag{10}\]  
where \(Q\) is the anchor bar anchoring force (take 100 kN/root). \(K\) is the safety factor (take 2) and is the row spacing between anchors.  
After calculating the inter-row spacing of the anchors, \(a\) = 3.8 m, so the spacing of anchors was designed to be 0.8 m, and the row spacing was 0.8 m, which was less than 3.8 m to meet the calculation results.  
The formula for calculating the total length of the anchor cable is as follows:  
\[L=L_{a}+L_{b}+L_{c}+L_{d} \tag{11}\]  
where \(L\) is the total length of anchor cable. \(L_{a}\) is the length of the anchor ropes going deeper into more stable rock formations. \(L_{b}\) is the thickness of the unstable rock formation requiring suspension (take 3 m). \(L_{c}\) is the thickness of the pallets and anchorage (take 0.15 m). \(L_{d}\) is the exposed tension length (take 0.3 m).  
The length of the anchor cable going deeper into the more stable rock formation is determined by the following formula:  
\[L_{a}\geq K\times\frac{d_{1}f_{a}}{4f_{c}} \tag{12}\]  
where \(K\) is the safety factor (take 2). \(d_{1}\) is the anchor diameter (take 28.6 mm). \(f_{a}\) is the anchor cable tensile strength (take 1860 N/mm\({}^{2}\)). \(f_{c}\) is the adhesion strength of the anchor cable to the anchoring agent (take 10 N/mm\({}^{2}\)).  
The calculated length of anchor cable should be greater than or equal to 6.11 m. The length of anchor cable selected in the actual project is 7.3 m. The length of anchor cable selected in the design meets the calculation requirements.  
Suspension theory was used to calculate the row spacing between anchor cables using the following formula:  
\[a_{c}=nF_{2}/[BHr-2F_{2}sin\theta/L_{1}] \tag{13}\]  
where \(a_{c}\) is the row spacing between anchor cables. \(B\) is the maximum width of the roadway (take 5.5 m). \(H\) is the height of roadway fall (take 4.05 m). \(L_{1}\) is the top anchor row spacing (take 0.8 m). \(F_{1}\) is the top anchor anchoring force (take 100 kN). \(F_{2}\) is the anchor cable bearing capacity (take 594 kN). \(n\) is the number of anchor rows (take 1). \(\theta\) is the angle of angle anchors to the roof of the roadway (take 70\({}^{\circ}\)).  
After calculation, the distance between the rows of anchor cables is 2.7 m, while the distance between the rows of anchor cables is designed to be 1.6 m, which is less than 2.7 m and meets the support requirements.