1. Introduction
In recent years, the development of tunnel engineering in China has been improving, and it is inevitable that tunnel engineering will cause biased tunnels due to the contradiction between route selection and topographical conditions [
1,
2,
3]. Shallow bias tunnels typically occur at the entrance and exit of the tunnel. The tunnel support structure is subjected to asymmetric surrounding rock pressure, which will lead to asymmetric deformation and can easily cause cracks and other hazards (i.e., landsides, collapse, instability of the initial liner, and cracked linings) [
4,
5]. These hazards occur not only due to improper operation during construction, but also because there is no accurate judgment of the bias degree during the tunnel design phase.
At present, the research on bias tunnels mainly focuses on four research methods: field monitoring, numerical simulation, model tests, and theoretical calculation. Many studies use a combination of two or more methods. In terms of field monitoring, Xia et al. [
6] analyzed the deformation and stress properties of surrounding rocks and supporting system based on the field data. Xue et al. [
7] found that the piles on both sides of the umbrella arch were subject to large bending moments and axial force through the monitoring data of the umbrella arch. Wang et al. [
8] proposed that the deformation behavior of the surrounding rock mass was controlled by unsymmetrical loadings during the process of construction.
As for the theoretical analysis, Zhang et al. [
9] calculated the stability coefficient and the supporting force of shallow bias tunnels based on the principle of virtual power from the viewpoint of energy. Yang et al. [
10] investigated the load model of bilateral tunnels and calculated the stresses of three tunnels and analyzed the distribution characteristics of a single tunnel. According to the principle of virtual power, the upper bound solution for the surrounding rock pressure of a shallow unsymmetrical loading tunnel was derived and verified using an example [
11]. Based on the nonlinear failure criterion and the upper bound theorem, Yang et al. [
12] proposed a modified tangential technique method to derive the expression of supporting pressure acting on a shallow tunnel.
Xiao et al. [
13] found that a pipe roof at the entrance could effectively reduce the stresses and asymmetric loading between the tunnel support elements and enhance the tunnel safety during construction. Guo et al. [
14] found the thickness limits of large-span bias tunnels under different slopes based on different soil thickness research and three kinds of slope effects through the analysis of finite element numerical simulation results. Yang et al. [
15] performed a numerical simulation of soft rock tunnel excavation in large sections and investigated the stress and displacement of surrounding rock and the plastic area distribution and size. Xiao et al. [
16] found that the main reasons for cracking in the secondary lining were the increasing overburden depth and the stress concentration at the spring level as well as an increase in the horizontal deformation in the secondary lining.
However, there are certain problems in the research addressing the degree to which the tunnel bears pressure. Most previous studies took the ratio of the stress values at the same horizontal height on both sides of the tunnel to the unsymmetrical degree [
17]. At the same time, this stress ratio only represents the asymmetry of the corresponding points of the tunnel but not the degree of bias of the whole tunnel.
In this paper, we relied on the typical shallow unsymmetrical-loaded tunnel section of Huitougou (HTG) Tunnel to monitor various stress values and to calculate the stress ratio of the corresponding monitoring points. We propose a new unsymmetrical coefficient (UC). We established a numerical calculation model to calculate the UC to compare and verify with the monitoring results. In addition, we investigated the influence of the terrain factors, surrounding rock quality, and lining factors on the UC.
4. Single Factor Analysis
In this paper, it was necessary to study the variation law of the improved UC when the influencing factors changed, because the UC was exceedingly different from previous instances. In previous studies [
24,
25], many scholars explored the influence of various factors on biased tunnels. This paper summarizes these factors into three main categories, including topographic factors, surrounding rock properties, and construction. The topographic factors were the slope angle of the ground and the thickness of the cover layer. The surrounding rock properties mainly included the bulk density, elastic modulus, Poisson′s ratio, cohesion, and internal friction angle. The construction factors were mainly divided into two categories. One category is the design factors, such as the size and location of the tunnel, the choice of construction methods and steps, and the choice of design parameters of support measures. The other is technical problems that may arise during construction.
4.1. Influence of Topographic Factors
We examined the variation law of the tunnel UC when the slope angle range was 5–45°, and the thickness of the cover layer varied between 5 and 25 m.
4.1.1. Impact of Slope Angle
The curve shape of the UC as a function of the slope angle is parabolic, which is plotted in
Figure 12. When the thickness of the overburden layer remains unchanged with the increase in the slope angle of the terrain, the tunnel UC first increases rapidly and then slowly increases. This is not an imagined linear change but a parabolic change. This shows that the existence of tunnel lining can limit the growth of the tunnel UC.
4.1.2. Influence of the Cover Thickness
As shown in
Figure 13, the curve of the UC with the thickness of the cover layer changes approximately linearly. The UC decreases as the thickness of the cover layer increases. The curve in the figure is linearly fitted to obtain the relationship between the UC and the thickness of the cover layer. According to this relationship, under the initial slope angle, when the cover layer reaches 73 m, the UC is 1.
4.2. Effects of the Surrounding Rock Properties
4.2.1. Single Property of the Surrounding Rock
The physical and mechanical properties of the surrounding rocks directly affect the stability after tunnel excavation. Therefore, it is indispensable to examine the influence of the surrounding rock properties on the tunnel displacement coefficient. Generally, the tunnel bias section only occurs at the entrance of the tunnel, and the surrounding rock level at the entrance is mostly V or even VI. The range of the physical and mechanical properties of Class V surrounding rocks is shown in
Table 8 according to the Specifications for the Design of Highway Tunnels. The change law of the tunnel UC was tested when the five important physical and mechanical properties (the elastic modulus E, Poisson′s ratio μ, bulk density γ, cohesion c, and internal friction angle φ) changed.
The changes of the tunnel UC when the physical and mechanical parameters of the surrounding rock of the tunnel are changed individually are plotted in
Figure 14. As shown in
Figure 14a, the tunnel UC and the deformation modulus are roughly negatively linearly related. When the deformation modulus increases, the tunnel UC becomes smaller.
As shown in
Figure 14b, the relationship curve between Poisson’s ratio and the tunnel UC is roughly parabolic, and as the Poisson’s ratio increases, the UC decreases. When the parameter selection range changes, the UC changes very little.
As shown in
Figure 14c, the relationship between the cohesion and tunnel UC is roughly parabolic. As the cohesion increases, the UC first increases and then decreases.
As shown in
Figure 14d, the relationship between the internal friction angle and the UC is positively linear, and the UC increases with the increase in the internal friction angle. This may be due to the limitation of the value interval, as the tunnel UC changes little.
As shown in
Figure 14e, the relationship between the bulk density and UC is negatively linear. As the bulk density increases, the UC decreases. The reduction is very small, which is related to the range of the bulk density.
4.2.2. Effect of Rock Quality
The study in the previous section only analyzed the changes in the tunnel UC when the individual physical and mechanical indicators of the rock mass changed. The most important aspect in this engineering is the change of rock mass, and the change of rock mass is typically not the change of a factor. When the quality of the rock mass is higher, this typically indicates a larger deformation modulus, larger bulk density, larger cohesion, and internal friction angle, as well as a smaller Poisson′s ratio. The opposite is true when the rock mass is low in quality.
According to the range of physical and mechanical properties of the Grade V surrounding rock in
Table 7, the quality of Grade V surrounding rock is divided into three grades: high quality, medium quality, and low quality. High quality takes the optimal value of the value range, low quality takes the opposite, and medium quality takes the average of the best value and the worst value. The specific values are listed in
Table 9.
The tunnel UC under three different surrounding rock quality conditions is shown in
Figure 15. As the tunnel surrounding rock quality changes from low to high, the tunnel UC first increases and then decreases significantly, which is not the negative linear relationship that we originally expected. The main reason is that the deformation modulus and cohesive force in the physical and mechanical parameters of the rock mass mechanics have a greater influence on the UC. Going from low to high rock mass, the modulus of deformation and cohesion also increase, but the influence on the UC is different. The superimposition of the two effects shows the relationship curve in
Figure 15.