## 3 Analysis of Mechanical Mechanism of Concrete Retaining Wall
### Comparative Analysis of Safe Thickness of Concrete Retaining Wall  
At present, in engineering practice, the traditional empirical formula [29] or Kalmykov formula [1] is generally adopted to determine the construction thickness of concrete retaining walls. The specific forms of the two methods are as follows:  
(1) The traditional empirical formula is:  
\[B=K_{0}\sqrt{\frac{Qh_{\pi}}{2h_{3}[\sigma]}} \tag{15}\]  
where \(B\) is the thickness of the concrete retaining wall, \(K_{0}\) is the safety coefficient (generally the value is 1-2), \(Q\) is the total load acting on the concrete retaining wall, \(Q=P.S.\), \(P\) is the final grouting pressure, \(S\) is the area of concrete retaining wall, \(h\) is the width of the concrete retaining wall, and \(h_{3}\) is the height of the concrete retaining wall.  
(2) The Kalmykov formula is:  
\[B=\frac{pr}{[\sigma]}+0.3r \tag{16}\]  
where \(B\) is the thickness of the concrete retaining wall, \(P\) is the final grouting pressure, \([\sigma]\) is the allowable compressive strength of the concrete, and \(r\) is the equivalent radius of the tunnel face.  
The above two formulas were compared and analyzed with the theoretical formulas obtained in this article. According to the basic parameters of the calculation example, the relationship between the obtained final grouting pressure and the safe thickness of the concrete retaining wall is shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Tunnel Buried** & **Groundwater** & **Concrete Retaining** & **Concrete Retaining** & **Concrete Tensile** & **Concrete Compressive** \\
**Depth/m** & **Level/m** & **Wall Length/m** & **Wall Height/m** & **Strength/m** & **Strength/MPa** \\ \hline
10 & 5 & 8 & 6 & 1.43 & 14.3 \\ Groundwater bulk & Stratum bulk & Floating bulk & Cohesion force/kPa & Internal friction angle of sand/\({}^{\circ}\) & - \\ density/MPa & density/kN/m\({}^{3}\) & density/kN/m\({}^{3}\) & 0 & 30 & - \\
9.8 & 18 & 9.5 & 0 & 30 & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Calculation parameters of the example.  
Due to the poor self-stabilization ability considered in this paper, the traditional empirical formula ignores the formation stress behind the concrete retaining wall and the groundwater pressure. Then, as can be seen on the graph, the curve starts from the origin, and when the safety coefficient \(K_{0}\) is one or two, there is a big difference. Therefore, in actual engineering, the value of the safety coefficient is crucial. When the value is small, the effect cannot be achieved; the cost increases when the value is large.
2. In the Kalmykov formula, there is a linear relationship between the final grouting pressure and the thickness of the concrete retaining wall. When the final grouting pressure is low, the thickness of the concrete retaining wall obtained by the Kalmykov formula is greater than that obtained by other formulas. With an increase of the final grouting pressure, the increase of the thickness of the concrete retaining wall is slight. The applicability of the Kalmykov formula is poor when the final grouting pressure is either small or large.
3. The relationships between the final grouting pressure and the thickness of the concrete retaining wall obtained by the traditional empirical formula and the theoretical formula are similar in this paper. The curve forms show a trend that is first fast and then slow, and the curve of the final grouting pressure and the thickness of the concrete retaining wall in the theoretical formula obtained in this paper is sandwiched between the curves obtained when the safety coefficient \(K_{0}\) of the traditional empirical formula is one or two. As such, there is a particular connection between the method in this paper and the traditional empirical formula.