Study on the Influence of Tectonic Stress on Stability of Horseshoe-Shaped Tunnels

While the tunnel is in the high tectonic stress environment and surrounding rock of tunnel has the characteristics of soft texture and stronger expansion, the preference of tunnel shape is horseshoe. An elastic-plastic model is analyzed by complex function theory in accordance with the deformation characteristics of a horseshoe-shaped tunnel in an engineering site. ,e numerical model of the tunnel is built by FLAC3D, and the influence of the magnitude and direction of structural stress on the horseshoeshaped tunnel is studied in detail. Finally, the security support of the tunnel is discussed. Results show that the stress concentration phenomenon is easily focused on the left, right, and bottom sides of the tunnel; these places should therefore be the focus of attention of tunnel stability analysis. ,e magnitude and direction of tectonic stress greatly affect the stability of the horseshoeshaped tunnel. Similarly, the magnitude of tectonic stress can significantly affect the deformation state of the tunnel.,e direction of tectonic stress mainly reflects the orientation of the tunnel. In addition, the orientation of the tunnel should be arranged along the maximum direction of principal stress.


Introduction
With the continuous development of economic construction, science, and technology, the development of underground space has increasingly broadened, even to the Earth's deep interior [1]. In the environment of high ground stress and high geothermal heat, rocks undergo brittle-duct or brittle-plastic transformation, and the horseshoe-shaped section is widely used in deep tunnels. e horseshoe-shaped tunnel is used in engineering sites, where the surrounding rock is soft, the top and side pressures are high, and the bottom is under pressure due to its superior loading capacity [2][3][4][5][6].
In some cases in the literature, the straight wall arch section is used instead of the horseshoe section mainly because of the blindness and difficulty of modeling a horseshoe-shaped tunnel. To explain the meaning of the horseshoe-shaped tunnel, Li et al. [7] and Sun et al. [8] used the lateral pressure coefficient for a thorough analysis of the field of tunnel stability. e damage section of the horseshoe-shaped tunnel starts with the meso-unit tensile. en, the macroscopic tensile failure occurs along the direction of the maximum principal stress. Islam and Shinjo [9] used the boundary element method (BEM) to analyze the stress characteristics and deformation around the faults. e horizontal and vertical stresses influence the faults, and higher stresses are concentrated near the ends of the two faults. Sun et al. [8] investigated the floor heave and failure by the combined analyses of the acquired infrared images, video photographs, and straining field variations. e horizontal stress had a great effect on the floor heave failure, and the rock mass failure was accompanied with abnormal temperature change. Hui [10] considered dynamic testing as an impact factor behind the stability of horseshoe-shaped tunnels and studied the dynamic response of lateral blasting effect on horseshoe shape. In summary, studies on the stability of horseshoe-shaped tunnel are rare, and the magnitude and direction of tectonic stress are two important factors affecting the stability of such tunnels. Liu et al. [11] studied the rock burst in tunnel under dry and saturated conditions and investigated the influence of water contents on rock burst in tunnel. Water softened rocks and reduced their mechanical properties, and the tunnel model in the saturated state exhibited a lower dynamic failure rate, leading to quicker static failure. Hao et al. [12,13] studied the fracture behavior and crack propagation features of coal to evaluate the dynamic failure of coal and considered the effects of the static axial prestress and loading rate on the dynamic tensile strength and crack propagation characteristics of BD coal specimens. e AE cumulative energy is more suitable for determining crack strength and damage strength of coal reservoirs.
e horseshoe-shaped section support can be divided into two sides. One side is the original tunnel (not the horseshoe-shaped tunnel), which supports the horseshoeshaped section in the process of lining. is research accounts for the vast majority. e other side is the original tunnel (also the horseshoe-shaped tunnel), which continues to support the horseshoe-shaped section [14,15]. An experiment on a 40-degree inclined crack horseshoe penetrated tunnel by Peng et al. [16] revealed that the tunnel deformation and failure are asymmetric. ABAQUS can be used to study the excavation and support of horseshoeshaped tunnels [17]. e results showed a hyperbolic function relationship between concrete support and time. FLAC3D and ANSYS were used to simulate the effect of bolt support on a horseshoe-shaped tunnel [17][18][19].
e perspective of horseshoe-type tunnel support is mainly single, whereas according to the complex stress distribution characteristics of the deep tunnel, the single-support method is no longer suitable for deep tunnels [20]. erefore, the stability of horseshoe-shaped tunnel needs further studies from the aspects of magnitude and direction of tectonic stress. e research on the stability and support of circular tunnel, elliptical tunnel, and straight wall arched tunnel has been comprehensively conducted. e analysis and research on the horseshoe-shaped tunnel has yet to be further strengthened. In this study, the horseshoe-shaped tunnel was investigated by elastic-plastic mechanism. e stability of the horseshoe-shaped tunnel is discussed from the perspective of stress magnitude and direction.  Table 1.

Stability Analysis of Horseshoe-Shaped Tunnel
Meanwhile, the six sets of parameter values in Table 2 are imported into the software Surfer. is software can plot the contour map of stress and strain ( Figure 1). As shown in Figure 1, the stress and displacement concentration appeared in the two sections of the tunnel and the bottom area of the vault. ese areas can be analyzed intensively in the follow-up study. e relative distribution of stress in this area is ensured to be uniform in the discussion of the supporting effect.

Selection of Model Dimension.
Saint-Venant's principle suggests that the stress in an object caused by a load distributed over a small area (or volume) of an elastomer is substantially only slightly further from the load-applying zone, which is related to the resultant force load and resultant moment [21][22][23][24]. e area affected by the excavation of underground cavern is generally 2 to 4 times larger than that of the cavity radius. e specific size of the model can be reasonably set according to the size of the horseshoe section. e size is 10 cm from the left wall to the left boundary, 10 cm from the right wall to the right boundary, 10 cm from the upper boundary to the top of the vault, and 10 cm from the lower boundary to the highest point of the arch. e radius of the horseshoe lane excavated is 2 m.

Boundary Condition Setting.
e boundary setting of the two sides and the bottom of the model is fixed, whereas the upper section is free. Compared with the tectonic stress environment, the self-weight of the model is relatively small. us, the gradient of the self-weight is ignored, and the upper boundary is loaded with the uniform overload methods. e concrete model and its mesh distribution are shown in Figure 2.

Selection of Calculation Parameters.
e mechanical parameters of the surrounding rock around the tunnel are shown in Table 2.

Selection of the Constitutive Model.
e mechanical motion of common soils and rocks (such as slope stability and underground excavation) generally adopts the Mohr-Coulomb model, which is suitable for the analysis of granular materials under monotonic loading force [25][26][27].

Influence of the Magnitude of Tectonic Stress on the Stability of Tunnel.
e influence of the magnitude of tectonic stress on the stability of the tunnel can be mainly reflected from the two aspects of the displacement of the tunnel and the stress distribution of the tunnel. e lateral pressure coefficient is λ � 2.
e horizontal and vertical displacements of the tunnel as well as the horizontal stress and vertical stress images are recorded and discussed. e calculation data are shown in Table 3.
As shown in Figure 3, the horseshoe-shaped tunnel stress concentration mainly occurs at the joint of the four arches, and the stress concentration area at the junction of the bottom arch and the side arch is significantly larger than that of the top arch and the side arch. e stress concentration area also appears as a large displacement, which is worthwhile in the support. If the tectonic stress increases, then the stress concentration area becomes closer to the center of the tunnel, and the stress value increases accordingly. e displacement of the two sides is evidently increased, and the joints of the four stress concentrations are enhanced.
is analysis suggests that the stress concentration at the joint of the four arches of the horseshoe-shaped tunnel is evident, thereby easily leading to instability. ese four key points should be emphasized in the subsequent support simulation process to support the force resistance stress of the surrounding rock. In addition, different degrees of deformation are produced in the side wall and roof and floor, which cannot be ignored during the support process.

Influence of Tectonic Stress Direction on Tunnel Stability.
e full-plane strain problem is based on the analysis of plane strain problems on surface shear and one-way compressive stress [28][29][30]. In the engineering field, the actual stress state of the tunnel is a three-dimensional stress, and its stress state is shown in Figure 4, where σ 1 represents the maximum horizontal stress. For studying the influence of tectonic stress direction on tunnel stability, the maximum horizontal stress and the vertical angle α of the tunnel are changed. us, the effects can be analyzed according to the tunnel displacement and stress distribution images of the tunnel.
e coordinates of the third-order tensor (three stresses) are transformed by the transition matrix, given that the coordinate system of the tunnel model and the known ground stress are not in the same coordinate system. e coordinate system in the tunnel is called the new coordinate system P, and the ground stress coordinate system is called the original coordinate system O [31]. e coordinate transformation of the third-order tensor is as follows: where O is the third-order tensor of the original coordinate system, P is the third-order tensor of the new coordinate system, and L is the transition matrix. e third-order tensor of the new coordinate system is solved as follows: p � p xx p xy p xz p yx p yy p yz p zx p zy p zz In the simulation, the stress and displacement of the tunnel are analyzed at 30°, 45°, 60°, and 90°. Specific material parameters and stress parameters of the numerical simulation are shown in Table 4. e relevant parameters of the calculation model are also given in the table.
e total displacement of multiple measuring points on one line is calculated in accordance with the written Fish language to accurately evaluate the displacement data. e horizontal displacement and vertical displacement at five angles are acquired by   Figure 5.
As shown in Figure 5, the overall change trend in the top and bottom of the tunnel and side wall is the same, and the displacement is increased. e differences are that the displacement of the top plate and side wall is negative deformation (corresponding to the falling of the top plate and squeezing in the side wall, respectively), whereas the bottom plate appears to be positively deformed (corresponding to the bulging of the floor of the tunnel). When the angle between the tunnel axial and maximum horizontal stress             Advances in Materials Science and Engineering increases from 0°to 90°, the displacement of the top plate is the largest, followed by the side wall, and the bottom plate is the smallest. is finding is mainly related to the geometrical dimensions of the model and the model arrangement of the four arches. e result shows that when the tunnel axial is parallel to the maximum horizontal stress, the tunnel displacement of the key points is the smallest, which is beneficial to the stability of the surrounding rock. When the tunnel axial is perpendicular to the maximum horizontal stress, the tunnel displacement of the two sides and the top and bottom plates is the largest [32,33]. e literature proves that when the angle between the tunnel axial and maximum horizontal stress ranges from 25°to 30°, the effect on stability of the tunnel is not evident [34].

Discussion
From above studies, the stress concentrations are easily caused in the place of the left, right, top, and bottom sides of tunnel. Some serious damages were happened in underground tunnels, and these destructions mainly occurred in left, right, and top sides of tunnel ( Figure 6).
Shotcrete support is a support method based on the selfstability of the surrounding rock, and its main principle is embodied in four aspects, namely, support, filling, isolation, and conversion. e aim of support is to prevent the surrounding rock weathering, falling off, and form the surrounding rock as a whole. e timely injection of the initial support during excavation support is good for the subsequent installation of the anchor and the anchor cable. e anchoring depth is set to be large to anchor the lower part of the unstable rock layer to the upper stable rock layer. Prestress anchorage cable reinforcement support plays an important role in highstress tunnel support. It can also exert prestressing, which can be applied to implement active support.
us, the focused monitoring areas should be actualized along the left, right, top, and bottom sides of the tunnel. In view of the complex geo-stress environment faced by deep tunnels, the three methods of combined support should be considered.

Conclusions
(1) Stress concentration easily occurs at the left, right, and bottom sides of a horseshoe-shaped tunnel. ese areas can thus be highlighted in the analysis of stability, and the uniform distribution of stress and strain in these areas is defined as the supporting effect.
(2) e impact of the direction of tectonic stress on the tunnel is mainly reflected by the selection of tunnel

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.