Keywords

1 Introduction

Due to the small spacing between the two tunnels of the small clear distance, the construction of the rear tunnel have adverse effects on the existing lining and the stress-strain state of the surrounding rock of the first tunnel, seriously endangering the construction safety of the first tunnel. For tunnels excavated by the bench cut method, the invert closure distance has a great impact on the deformation and pressure of the surrounding rock.

Jin Xiaoguang et al. [1] analyzed the construction mechanical behavior of side wall heading and two-bench method, double wall heading method, and double hole and two-bench method by numerical simulation. Jiang Kun et al. [2] relied on the Kuiqi large-section and small clear distance tunnel project to reveal the influence of different construction methods on the settlement of the tunnel arch through numerical simulation. Yan Qixiang et al. [3, 4] used elastic-plastic numerical calculation methods to analyze the stress and deformation characteristics of the middle rock column in small clear distance tunnels. Li Yunpeng et al. [5] calculated the reasonable clear distance by numerical simulation under different levels of surrounding rock. Sun Zhigang [6] conducted a study on the excavation steps of the front and rear tunnels of small clear distance overlapping tunnels through three-dimensional numerical simulation. Wang Kang [7] relied on a large -section and small clear distance tunnel to reveal the influence of excavation sequence on the stability of surrounding rock through numerical simulation. Zhang Dingli et al. [8] established an analytical formula for the stress state of the intermediate rock wall in small clear distance tunnels using the bipolar coordinate method. Li et al. [9] analyzed the viscoelastic plastic deformation during the excavation process of the small spacing tunnel by benches method through numerical simulation. Chen et al. [10] revealed the distribution of seepage field and its impact on structural mechanical properties of small clean tunnels in water-rich areas through seepage model experiments. Li et al. [11] revealed the mechanical response laws of the construction process of large-span and small clear distance tunnels through model experiments and numerical simulations. Song et al. [12] compared the effects of different excavation methods and clearance on the stress characteristics and displacement of tunnel support through numerical simulation. Yao et al. [13] analyzed the deformation patterns and stress characteristics of small spacing tunnels under different levels of surrounding rock through numerical simulation. Tang et al. [14] established numerical simulation models of two-bench method, core soil method, and side wall heading method for a small clear distance highway tunnel. Su et al. [15] analyzed the plastic zone and internal forces of shallow buried small clear distance loess tunnels through numerical simulation.

Many scholars analyzed the stress and deformation effects of different excavation methods on small spacing tunnels through numerical simulation, model experiments, and other methods. However, few scholars studied the excavation methods and safe construction spacing of large cross-section and small clear distance underwater tunnels suitable for weak surrounding rock conditions. Therefore, this study combines the Rongjiang Tunnel Project with finite difference numerical simulation software to calculate the stress and displacement under different excavation intervals using three construction methods, namely the three step method, CD method, and CRD method, and reveal their evolution laws. It is of great significance for guiding the safe construction of large cross-section and small clear distance underwater tunnels in weak surrounding rocks.

2 General Situation of the Project

Rongjiang Tunnel’s length of the main line is 2.412 km. The main works include the cross-river tunnel and the entrance/exit ram. The minimum distance from the tunnel cross-section is only 8.0m. The surrounding rock in this tunnel section has poor self-stabilizing ability, with an overlying layer of weathered rock less than 1 times the tunnel diameter. The landward segment of the tunnel is located near Chaoyang Road, requiring stringent control of settlement caused by construction activities. Excavating a small clearance tunnel in weak surrounding rock can have a significant impact on the surrounding environment. Implementing appropriate reinforcement measures and determining a reasonable excavation method and construction spacing are crucial for controlling settlement during the construction process.

3 Overview of Numerical Computational Models

In this paper, the finite difference software FLAC3D is used for three-dimensional numerical simulation calculations.

3.1 Assumptions for Numerical Simulations

Due to the complexity of engineering practices and the non-uniform nature of geological strata, it is impossible to fully encompass the actual conditions of the project in the model during model setup and numerical calculations. The following assumptions are made under the premise of meeting the needs of the project:

The soil and rock layers are assumed to have a homogeneous layered distribution. The surrounding rock is considered to be isotropic and a continuous elastic-plastic material. The weakening effects of groundwater on the surrounding rock and support structures are not taken into account. When simulating soil and rock material, only self-gravitational stresses are taken into account and tectonic stresses are ignored.

3.2 Model Dimensions

According to Saint Venant's principle, in order to minimize the influence of the model boundaries on the model calculation error, the length on both sides of the model is taken as 7 times the diameter of the tunnel, and the overburden layer was taken to be the most unfavorable conditions, and The thickness of the soil above the tunnel is 9.0m, which takes into account the layering effect of the soil. The numerical model established in this study has the following dimensions as shown in Fig. 1.

Fig. 1.
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Three-dimensional numerical model

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4 The Simulation of Construction Methods and Safe Spacing for the Rongjiang Tunnel

Based on the results of on-site investigation, the surrounding rock of the tunnel in the land section is class V. This tunnel is a super small clearance and large cross-section tunnel. The commonly used construction methods for excavation of tunnels with super small clearance and large cross-section in soft rock include the three-bench method, CD method, and CRD method. This paper analyzes the minimum spacing between tunnels under different excavation methods using these three methods. The excavation step distance and tunnel step distance for the three excavation methods are shown in Fig. 2.

Fig. 2.
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Excavation steps for different excavation methods

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4.1 Material Properties and Boundary Conditions

The soil layer above the tunnel is mainly composed of soft soil layers such as sand layers, and is generally described using the Mohr-Coulomb constitutive model. While the tunnel is located in the hard weathered rock, which is generally described by D-P constitutive model (Table 1).

Table 1. Physical and mechanical parameters of rock and soil strata
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For the advanced small conduit grouting support of the tunnel, a single layer of φ42 × 4 mm advance grouting pipes with a length of 4.5 m is used. The circumferential spacing is 0.4 m, the outer insertion angle ranges from 5° to 15°, and the longitudinal spacing is 4 m. A total of 46 pipes are used in a single ring. To simulate the advanced support, a numerical model is constructed using beam elements to represent the corresponding pipes, as shown in Fig. 3. The reinforcement area of the pipes is determined by calculating the pipe's range, and the strength of the soil within the reinforcement area is increased to simulate the implementation of advance support measures.

Fig. 3.
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Advance small conduit support

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For the initial support, anchor rods and shotcrete support are used. The shotcrete thickness is 30 cm, and 6.0 m long hollow anchor rods are arranged within a 120° range of the arch crown, with a longitudinal spacing of 1 m and a circumferential spacing of 0.6 m.There are a total of 26 anchor rods in one ring. Cable elements are used in the modeling to represent the corresponding anchor bolts, as shown in Fig. 4.

Fig. 4.
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Bolting support

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The soil strength within the reinforcement area is increased to simulate the reinforcement measures. Existing research suggests that the soil strength in the advance reinforcement area is generally increased by a factor of 1.2, while the soil strength in the grouting area can be increased by a factor of 1.5. Rongjiang Tunnel’s pre-reinforcement project in the mined land section of the tunnel adopts a high-pressure jet grouting method. This means grouting and pre-reinforcing from the tunnel roof to the ground surface. In the model calculations, it is assumed that the reinforcement area is located above the tunnel roof. When simulating the temporary invert arch support in the CD method and CRD method, Shell elements included in FLAC3D are used to represent the temporary support, as shown in Fig. 5.

Fig. 5.
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Temporary support

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The physical and mechanical properties of the support measures used in the model are shown in Table 2.

Table 2. Support parameters
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4.2 Simulation

In the numerical simulation, the three-bench method of excavation was carried out according to the following steps:

Assign the properties of the advanced support material, excavating the upper bench of the first tunnel step by step, with a depth of 2 m each time, and assign the properties of the initial support material at the corresponding position, and assign the anchor strengths to the anchors, and then run the calculations;

After excavating the upper bench of the former tunnel for 8 m, the middle bench will be excavated at the same time, and after excavating the upper bench for 10 m, start excavating the later tunnel. At this time, the excavation distance between the two tunnels will be 10 m.

After 16 m of excavation for the upper bench of the former tunnel and 8 m for the middle bench, start excavating the lower bench. At this time, the excavation of the upper, middle and lower benches is the same, each time excavation is 2 m. After 18 m of excavation for the middle bench of the former tunnel, start excavating the middle bench of the later tunnel, and after 18 m of excavation for the lower bench of the former tunnel, start excavating the lower bench of the later tunnel. The upper and lower benches of the two tunnels keep the same speed, and the excavation work is completed after 5 steps of cyclic excavation, analyzing the surface settlement and the deformation of the initial support and other indicators, and changing the spacing between the former and later tunnels to 20 m, 30 m and 40 m, comparing the control indicators, and determining the reasonable spacing between the tunnels.

The excavation steps of CD and CRD methods are basically similar to those of the three-step method and will not be repeated here. The ultimate relative displacements of the initial support shall meet the provisions in Table 3. The maximum deformation of the initial support at the vault should not exceed 0.08%H ~ 0.16%H. The height of the crossing tunnel on Rongjiang Road 4 is H = 8.6 m, which means that the deformation of the initial support at the top of the arch must not exceed 14 mm.

Table 3. Limit relative displacement of initial support with width 7 m < B ≤ 12 m.
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The deformation of the structure was simulated using the three-bench method (10 m between the former and later tunnels) and is shown in Fig. 6. In Fig. 6, after the tunnel was excavated by the three-bench method, the deformation was that the top of the arch was sinking and the bottom of the arch was bulging to a certain extent, and as the excavation proceeded, the value of the top of the arch sinking and the value of the bottom of the arch bulging increased, and the size of the surface settlement and the range of the settlement increased as well.

Fig. 6.
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Deformation by using three-bench method

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Comparing the surface settlement data and vault settlement data under different excavation spacing. The monitoring statements of corresponding cross sections were compiled, and the changes of maximum surface settlement and vault settlement with the depth of excavation on the upper bench of the three-bench method under the excavation spacing of 10 m, 20 m, 30 m, and 40 m were plotted, as shown in Fig. 7.

Fig. 7.
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Deformation of ground and vault during excavation by three-bench method

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In Fig. 7, when the excavation distance between the first and the second tunnels are 10 m, 20 m, 30 m and 40 m, the maximum surface settlement are 14.3 mm, 13.1 mm, 12.2 mm and 11.7 mm, and the maximum vault settlement are 18.5 mm, 15.2 mm, 14.6 mm and 13.7 mm, respectively. As the excavation distance between the two tunnels increases, the maximum settlement of the vault and the maximum surface settlement decreases, and the excavation distance between the two tunnels is greater than 40 m, which still does not meet the requirements of the construction specification, and it is necessary to increase the excavation distance between the two tunnels.

The deformation of the structure was simulated using the CD method of excavation (10 m between the former and later tunnels) and the results are shown in Fig. 8.

Fig. 8.
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Deformation by using CD method

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In order to compare the surface settlement and vault settlement data under different excavation spacing. The monitoring statements of corresponding sections were compiled, and the maximum surface settlement and vault settlement with the excavation depth of the upper-left part of the CD method were plotted under the excavation spacing of 10 m, 20 m, 30 m, and 40 m, as shown in Fig. 9.

Fig. 9.
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Deformation of ground and vault during excavation by CD method

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In Fig. 9, with the increase of excavation spacing between the former and later tunnels, the maximum arch settlement and surface settlement gradually decrease. When the excavation spacing between the two tunnels is 20 m, 30 m, and 40 m, the maximum arch settlement are 15.1 mm, 14.3 mm, and 13.6 mm, and the maximum surface settlement are 11.4 mm, 10.4 mm, and 9.7 mm, in that order. The settlement control value can be satisfied when the excavation distance between the former and the later tunnels is 40 m. The excavation spacing between the former and later tunnels must be at least three times the diameter of the tunnel in order to meet the construction specification. It was also demonstrated that the CD method was more effective in controlling the deformation of the tunnel and the ground settlement deformation than the three-bench excavation method.

The deformation of the structure was simulated using the CRD method of excavation, as shown in Fig. 10.

Fig. 10.
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Deformation by using CRD method

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Fig. 11.
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Deformation of ground and vault during excavation by CRD method

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Comparing with the surface settlement data and arch settlement data under different excavation spacing, the monitoring statements of the corresponding sections were compiled, and the changes of the maximum surface settlement and the maximum arch settlement with the depth of the upper left part of the CRD excavation under the excavation spacing of 10 m, 20 m, 30 m, and 40 m were plotted, in Fig. 11.

In Fig. 11, with the increase of the excavation distance between the two tunnels, the maximum value of the arch settlement and the maximum surface settlement decrease gradually. When the excavation distance between the two tunnels are 20 m, 30 m and 40 m, the maximum arch settlement are 14.1 mm, 13.5 mm and 12.7 mm, and the maximum surface settlement are 9.7 mm, 9.1 mm and 8.2 mm in the order of the excavation distance between the two tunnels. When the excavation distance between the two tunnels is ≥30 m, the settlement control requirement can be met. If the CRD method is used on site, the excavation spacing between the former and later tunnels must be at least two times the diameter of the tunnels in order to meet the construction specification. In terms of the deformation of initial support and displacement control of surrounding rock, CRD method > CD method > three-bench method.

5 Conclusion

Through the study of the construction mechanical behavior of the mined land section of the Rongjiang Fourth Road river-crossing tunnel with different excavation spacing of the former and later tunnels using the three-bench method, CD method and CRD method, and the analysis of the surface settlement and vault displacement during the construction process with the aid of three-dimensional numerical simulation, the following conclusions were drawn:

  1. (1)

    When the three-bench excavation method is used, the deformation of the tunnel and surface settlement cannot meet the construction requirements. When the excavation distance is 40 m, the maximum settlement value of the vault is 13.7 mm and the maximum settlement value of the surface is 11.7 mm, which cannot meet the requirements of the construction specification.

  2. (2)

    Adopting the CD method of excavation can meet the construction specification when the excavation distance between two tunnels is greater than or equal to 40 m. Adopting the CRD method of excavation can meet the construction specification when the excavation distance between two tunnels is greater than or equal to 30 m.

  3. (3)

    In terms of the control effect of initial support deformation and perimeter rock displacement, CRD method > CD method > three-bench method.

  4. (4)

    Considering the factors of safety, economy and construction efficiency, it is recommended to use CD method of excavation for this project, and the spacing of tunnel excavation is controlled to be 40 m.