# Calculation Method of Loose Pressure in Surrounding Rock Mass
## 1 Introduction  
Owing to rapid economic development, logistics, and the vehicle industry, the construction of tunnels with large-span and extra-large-span sections has boomed in recent years and serves as the optimum scheme to improve road capacity and meet the existing travel demand. Compared to a single-hole project with a small span, an extra-large-span-section tunnel consists of a much larger span, a lower high-span ratio, and a greater construction risk. There are no corresponding design codes and construction standards for these projects. Although some construction experience has been obtained, theoretical research is relatively lacking. To guarantee the rationality of the supporting structure design for super-span tunnels, the first problem to be solved is to clarify the method of predicting the loose pressure in the surrounding rock mass. At present, the empirical formulas commonly used for the loose pressure are divided into three categories: the equivalent thickness of the crown, statistics of collapse law, and surrounding rock classification, as shown in Figure 1. The equivalent thickness of the crown takes the gravity of the rock and soil mass above the vault as the primary influence for the loose pressure in the surrounding rock. Typical methods include [PERSON]'s theory [1], the Bierbaumer theory [2], the Terzaghi theory [3], and [PERSON]'s theory [4]. The statistics of collapse law method is based on practical engineering and is the leading engineering practice used in design codes in China [5, 6, 7, 8]. The correlations are relatively simple and consider the influence of the surrounding rock classification. The surrounding rock classification method derives the surrounding rock loose pressure from the RQD, Q, and RMR systems [9; 10; 11; 12]. The correlations and applicable conditions of various calculation methods are presented in Table 1.  
There are two deficiencies of the above-mentioned empirical formulas: (1) the calculations are derived or statistically obtained under the conditions of a small-span tunnel, and (2) the influencing factors are significantly different. The above two deficiencies restrict the applications of empirical formulas for loose pressure in the extra-large-span cross-section tunnels. \begin{table}
\begin{tabular}{c c c c} \hline \hline
\begin{tabular}{c} Neglects the effect \\ of height \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Different correlations for calculation methods. Figure 1: Empirical formula classification. In addition to the empirical formulas, the upper bound theorem of limit analysis with a strictly theoretical basis has also been used recently to calculate the loose pressure in the surrounding rock mass. It focuses on the ultimate failure state of the rock-soil mass without considering the elastic-plastic deformation process. In addition, this method is not restricted by the span. Some scholars have published papers on the surrounding rock pressure of soil tunnels. [PERSON] et al. [13] discussed the stability of a shallow circular tunnel in a cohesionless soil through the upper bound theorem of limit analysis together with results of tests performed in sand soil. [PERSON] et al. [14] deduced the upper boundary stability solutions for a shallow tunnel excavation at three different positions under undrained conditions and proposed a new stability evaluation method. In order to analyze the stability of an excavation face, [PERSON] et al. [15; 16] established the spatial discretization three-dimensional calculation method based on the limit analysis method, and the results of the calculation approached the real situation. Based on the Hoek-Brown failure criterion, [PERSON] et al. [17] presented an upper bound solution for the collapse shape for a circular tunnel considered the influence of different geological conditions and pore water pressure. [PERSON] et al.