Keywords

1 Introduction

As China's major projects like the “Belt and Road Initiative” continue to advance, tunnel construction faces unprecedented challenges in dealing with geological diversity and complexity [1]. Particularly in layered rock masses, the presence of jointed rock bodies can lead to complex bedding plane dislocation and anisotropy, which, if not properly addressed, may cause tunnel collapse and instability [2]. Small-clearance tunnels, due to their flexibility in terrain and route selection, are widely used in both short tunnels and the entrance sections of long tunnels. Although current research has covered the failure modes and mechanical properties of layered rock masses, as well as the impacts of construction responses in small-clearance tunnels, studies using the Discrete Element Method (DEM) to analyze the effects of structural planes on the stability of rock walls in small-clearance tunnels are still limited. This study aims to address this gap by exploring the impact of rock layer dip angles on rock wall stability in small-clearance tunnels, thus providing theoretical support for similar projects.

The utilization of DEM is particularly advantageous for this study due to its ability to simulate the complex behaviors of discontinuities and jointed rock masses, essential for understanding the stability challenges in small-clearance tunnel environments. This approach offers a more comprehensive understanding of the structural plane impacts on tunnel stability, making a significant contribution to the field.

2 Establishment of the Numerical Model

This study employed the classic Discrete Element software UDEC to construct plane strain models of shallow-buried small-clearance tunnels with different rock layer dip angles β, both with and without support measures such as shotcrete. To eliminate boundary effects [3], the model dimensions were set at 100 m \(\times \) 80 m, with displacement constraints applied to the left, right, and bottom boundaries, and the top boundary simulating the natural ground surface without constraints. The model features a tunnel buried at a depth of 20 m, with a net distance between the left and right tunnels of 0.5 times the tunnel span, and a rock layer thickness of 1.5 m. The schematic diagram of the calculation model is shown in Fig. 1.

The choice of UDEC is grounded in its proficiency for simulating the non-continuity and complex behaviors of rock mass, particularly beneficial for studying stress redistribution and failure processes in small-clearance tunnels.

Fig. 1.
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Schematic diagram of the calculation model

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Due to the difficulty in obtaining joint interface parameters through experiments, this study relied on rock mass parameters and geological conditions from field surveys, referencing the methods of Weiyuan Zhou [4] and B Sainsbury [5] for selecting structural plane parameters. The physical and mechanical parameters are as follows, with both the surrounding rock and rock layers modeled using the Mohr-Coulomb criterion, and the initial support modeled using an elastic criterion. The table of physical and mechanical parameters is shown in Table 1:

Table 1. Physical and Mechanical Parameters
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3 Results Analysis

3.1 Displacement Analysis

Since the deformation of the central rock wall mainly causes horizontal convergence of the tunnel, this study focuses on the displacement in the thickness direction (i.e., the X-direction in the model) of the central rock wall as a reference to analyze the deformation distribution characteristics under different rock layer dip angles. The displacement cloud diagrams for 0°, 45°, and 90° scenarios are shown in Fig. 2.

Fig. 2.
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Deformation cloud diagram in the thickness direction of the central rock wall

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Figure 2 illustrates that variations in rock layer dip angle significantly influence the deformation distribution of central rock walls in small-clearance tunnels. Without support, at a 0° dip angle, maximum displacements of 2.78 mm occur symmetrically near the arch waist on both sides of the wall. With increasing angles, displacement peaks shift following the excavation-formed sharply angled rock blocks. For example, at 60°, the left side shows -17 mm displacement near the right arch foot, and the right side 15 mm near the left arch shoulder. At 90°, the rock mass above the tunnel collapses, causing the central rock wall to bend and bulge longitudinally, with an 83 mm peak displacement at the arch waist. With shotcrete support, deformation patterns resemble those without support but are less pronounced due to the support's restraining effect. This effect is more significant at high dip angles due to the axial force exerted by the rock mass above the tunnel.

Horizontal displacements at the arch shoulder, waist, and foot on both tunnel sides were monitored, producing deformation curves (Fig. 3). These curves reveal that without support, deformation at the three positions fluctuates with the dip angle: initially increasing, then decreasing, and finally increasing again. The most notable increase occurs between 50° and 55°, peaking at 118 mm at the arch waist. With shotcrete support, deformation follows a similar pattern but peaks around 55°. These findings align with the Coulomb criterion, suggesting that the central rock wall's deformation is mainly affected by structural plane slip failure.

Fig. 3.
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Deformation curves of the central rock wall with changes in dip angle

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3.2 Analysis of the Plastic Zone Range

The shape and development trend of the plastic zone are key factors in assessing the stability of the central rock wall. Figure 4 demonstrates significant differences in the plastic zones under unsupported and supported conditions. In small-clearance tunnels, the plastic zones primarily appear around the central rock wall and the lateral arch waist of the tunnel. In the unsupported condition, the plastic zone penetrates through the central rock wall, while shotcrete reinforcement inhibits the development of the plastic zone, preventing penetration. Simultaneously, irrespective of shotcrete application, the distribution of the plastic zones in the surrounding rock noticeably shifts following the dip angle of the rock layers: initially, at a 0° dip angle, the plastic zones appear at the tunnel arch waist. As the dip angle increases, the plastic zones gradually incline in the direction of the increasing dip angle, with the left side of the central rock wall shifting towards the arch foot, and the right side towards the arch shoulder. At a 90° angle, the plastic zones again present a symmetrical distribution.

Fig. 4.
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Distribution of plastic zones under different rock dip angles

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In summary, without support, the plastic zones penetrate the center of the central rock wall, indicating that the wall is subjected to extreme stress, posing a direct threat to the stability of the tunnel. After reinforcement, the plastic zones are confined to a smaller area and do not cross the central rock wall, signifying the significant effectiveness of shotcrete reinforcement in preventing the development of plastic zones. Further analysis shows that as the rock layer dip angle increases, the plastic zones exhibit a characteristic inclination along the direction of the dip angle, consistent with theoretical analyses of the influence of rock layer angles on shear stress distribution.

3.3 Analysis of Stress on Structural Planes

The stress distribution on structural planes is crucial for predicting rock mass behavior. Changes in stress on these planes, especially sudden changes at certain critical angles, provide early warning signs of potential slip surfaces. This study analyzed the patterns of normal and shear stress changes on three structural planes in the central rock wall area as the rock layer dip angle varies. As shown in Fig. 5, in the unsupported condition, the normal stress on structural planes generally decreases with an increasing dip angle, while shear stress is zero at a 0° angle, then generally increases and then decreases with increasing dip angle, returning to zero at 90°. Notably, at around 55°, both normal and shear stresses on the structural planes undergo a sudden decrease. Under shotcrete reinforcement, the trends in normal and shear stresses on structural planes are generally similar to those in the unsupported condition, but do not show a sudden decrease around 55°.

Fig. 5.
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Variation curve of plane stress with dip angle of rock formation

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The results indicate that when rock layers are horizontal or vertical, central rock walls do not undergo slip failure along structural planes; deformation primarily occurs through structural plane tension or rock mass shear failure. When rock layers are at certain angles, the central rock walls tend to slide along structural planes, particularly at around 55°. If support is not timely applied, the central rock walls are at risk of slip failure.

4 Conclusion

This paper investigates the mechanics of deformation and slip failure in the central rock walls of small-clearance tunnels through numerical simulation, leading to the following conclusions:

When the rock layer structure interfaces with the tunnel profile to form sharp-angled rock blocks, large deformations occur in these sharp-angled areas. As the dip angle of the rock layer increases, the deformation of the central rock wall first increases and then decreases. The range of dip angles at which the maximum deformation occurs is consistent with the range of angles at which slip failure occurs along structural planes.

In the absence of support, the plastic zone spans the entire central rock wall. When support is applied promptly after excavation, the extent of the plastic zone is significantly reduced. As the dip angle of the rock layer increases, the plastic zone gradually shifts in the direction of the increasing angle.

The stability of the central rock wall is primarily influenced by the rock layer structural planes. As the dip angle of the rock layer increases, the shear stress on the structural planes first increases and then decreases. When the rock layer dip angle is in a specific range, the central rock wall tends to slip.

Importantly, these insights are crucial for designing and maintaining small-clearance tunnels, particularly in managing rock layer angles and construction support. This research also guides future tunnel mechanics studies in complex geological settings.