Keywords

1 Introduction

To alleviate the increasingly congested urban surface traffic conditions, the development and utilization of urban underground space have become a current trend, giving rise to underground interchange tunnel projects [1, 2]. This inevitably raises the issue of constructing new tunnels in close proximity to existing ones. The original stress and deformation fields around the existing tunnels will undergo significant changes due to the excavation of the neighboring new tunnels [3]. The research aims to assess the extent of the impact on existing tunnels during the construction of new tunnels, and based on the impact zones, formulate relevant control measures.

Currently, there have been some achievements in the research on impact zoning for tunnel proximity construction. Internationally, the Japan Railway Technical Research Institute [4] has systematically elaborated on tunnel proximity projects and proposed criteria for tunnel proximity levels. In China, Wenge Qiu [5] has further delved into proximity and introduced proximity zone guidelines. Wenhao Fan [6] conducted a study on the impact zones when a new double-line shield tunnel passes beneath an existing tunnel, using displacement criteria. Xianguo Wu [7] conducted a proximity study based on the increment of stress in existing tunnels, considering different tunnel spacing ratios and burial depth ratios under various conditions. Charle [8] through a series of three-dimensional centrifugal tests, the response of an existing tunnel in sandy soil to the excavation of a new tunnel perpendicular to it is studied. Kim et al. [9] carried out a series of tunnel–tunnel interaction tests using a 1g model in clay. They found that the section of the existing tunnel directly above the new tunnel was vertically compressed due to the large jacking force induced by the installation of the liner of the new tunnel.

In the aforementioned studies, tunnel impact zones are typically divided using a single discernment criterion. In this paper, based on the Xinsen Avenue Tunnel Project in Chongqing Gaoxin District, we propose a composite discernment criterion involving additional displacement and additional stress in the existing tunnel. This criterion is employed to study the impact zones when a new twin-arch tunnel passes over an existing tunnel.

2 The Mechanical Principles of Tunnel Proximity Construction

Tunnel excavation leads to stress redistribution within a certain range, and in cases of underground projects involving proximity construction, multiple stress alterations occur, making structural loading more intricate.

2.1 Initial Stress State

Before tunnel excavation, the rock mass is in a balanced and stable state of stress. In the numerical simulations in this paper, the initial stress state only takes into account the self-weight stress field. The expressions for the vertical stress at a depth of h are as follows:

$$\sigma_{z} = \lambda_{1} h_{1} + \gamma_{2} h_{2} + \cdots + \gamma_{n} h_{n} = \mathop \sum \limits_{i = 1}^{n} \lambda_{i} h_{i}$$
(1)

In the equation, λ represents the bulk density of the rock or soil, and h stands for the thickness of the overlying rock or soil.

2.2 The Secondary Stress State After Tunnel Excavation

In the excavation of a circular tunnel with a radius of a, the elastic secondary stress state around the tunnel can be expressed as follows:

Radial Stress:

$$\sigma_{r} = \frac{{\sigma_{y} }}{2}[(1 - \alpha^{2} )(1 + \lambda ) + (1 - 4\alpha^{2} + 3\alpha^{4} ) \times (1 - \lambda )\cos 2\phi ]$$
(2)

Tangential Stress:

$$\sigma_{t} = \frac{{\sigma_{y} }}{2}[(1 + \alpha^{2} )(1 + \lambda ) - (1 + 3\alpha^{4} ) \times (1 - \lambda )\cos 2\phi ]$$
(3)

In the equations: \(\alpha = a/r\), a represents the tunnel radius, and r represents the radial distance to the tunnel center; \(\lambda = \sigma_{X} /\sigma_{y}\), \(\sigma_{y}\) represents the initial stress, and \(\phi\) denotes the friction angle within the surrounding rock.

3 Leveraging Project Overview

Based on the Xinsen Avenue Tunnel Project in Chongqing Gaoxin District. The new twin-arch tunnel passes over the existing Gaoteng Avenue Tunnel in an area where the geological formations consist mainly of moderately weathered mudstone with interbedded sandstone, and the surrounding rock grade is ranging from IV to V. The overburden thickness ranges from 16.6 to 25.6 m, the tunnel height is 12.2 m, the width is 16.5 m, and the tunnel excavation cross-sectional area is approximately 400 square meters. The hidden excavation section of the Xinsen Avenue Tunnel starts at station K1 + 100 and extends to K1 + 255, with a length of 155 m. The clear distance between the crowns of the Xinsen Avenue Tunnel and the Gaoteng Avenue Tunnel is only 6 m. Taking into account various factors, the decision was made to employ the dual-side-wall pilot tunnel method for the construction of the new twin-arch tunnel. The site construction drawing is shown in Fig. 1.

Fig. 1
A photograph of 2 large, semi-circular tunnels supported by frames being constructed into the side of a hill. 4 construction in hardhats working on the site. The area is surrounded by wooden planks, metal rods, and other materials. There is a forest over the hill in the background.

A practical view of the Xinsen avenue tunnel entrance construction

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4 Establishing the Numerical Model

4.1 Basic Assumptions

In this study, numerical simulations are conducted using Midas GTS NX, based on the following basic assumptions: (1) The geological materials are homogeneous and isotropic, and the ground surface is horizontal. (2) The existing tunnel is treated as a homogeneous solid, with initial structural loading considered only for the self-weight of the soil. (3) Since the tunnel deformation mainly occurs during the initial support construction phase, and the secondary lining is primarily for safety reserves, it is not simulated.

4.2 Model Dimensions and Parameter Settings

A three-dimensional elasto-plastic constitutive model is established, using the Mohr–Coulomb criterion as the plastic failure criterion. The soil is simulated using 3D solid elements, while the initial shotcrete is simulated using 2D plate elements. To eliminate boundary effects, the dimensions of the foundational model in this paper are set as 180 m*160 m*100 m, as depicted in Fig. 2. Material parameters and model calculation conditions are shown in Tables 1 and 2.

Fig. 2
A diagram of a grid-based cuboid has a length, width, and height of 180, 160, and 100 meters, respectively. At the center, 2 tubes labeled new twin-arch tunnel attached parallel to each other cross over 2 tubes labeled existing tunnels.

Numerical calculation model

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Table 1 Model parameters
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Table 2 Calculation conditions of the model
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4.3 Criteria for Impact Zoning.

This paper chooses a composite criterion based on additional stress and displacement as the basis for determining the impact zones when the new double-line shield tunnel passes beneath the existing tunnel. Currently, there is no unified standard in China for defining impact zones in the case of a new tunnel being in proximity to an existing tunnel. Therefore, on the basis of references [10, 11], a composite criterion considering the rate of additional stress change and additional displacement in the existing tunnel is used as the basis for determining the impact zones. The maximum range of influence for both criteria is considered, and the areas affected by the construction of the new tunnel are divided into zones. It is defined here that an additional stress change rate of 15% and 5% in the existing tunnel caused by the construction of the new tunnel is used as thresholds for strong, weak, and no impact zones. The rate of additional stress change can be expressed as:

$$\omega = \left| {\frac{{\sigma_{1} - \sigma_{2} }}{{\sigma_{1} }}} \right| \times 100{\text{\% }}$$
(4)

In the equation, \(\sigma_{1}\) represents the initial stress value of the existing tunnel structure before the excavation of the new tunnel, and \(\sigma_{2}\) is the maximum stress value in the existing tunnel structure after the excavation of the new tunnel.

5 Longitudinal Impact Zoning of New Tunnel Overcrossing Construction on the Existing Tunnel

5.1 Longitudinal Impact Zoning of New Tunnel Construction on the Existing Tunnel Under Different Vertical Clear Distances

Four different calculation scenarios (0.5D, 1D, 2D, 4D) were defined based on the ratio of the clear distance between the two tunnels to the diameter of the existing tunnel (H/D). The study examined the relationship between the deformation of the existing tunnel and the vertical clear distance between the two tunnels during the construction of the new tunnel. Maximum additional displacement values and the maximum rate of additional stress change were extracted for various locations in the existing tunnel, including the crown, left and right sidewalls, and the bottom, as shown in Figs. 3 and 4.

Fig. 3
4 line graphs plot settlement amount versus distance from the crossover section. The titles are as follows. a, Arch crown. b, Left sidewall. c, Right sidewall. d, Arch bottom. All graphs has 4 curves for 0.5 D, 1 D, 2 D, and 3 D. All curves peak between negative 40 and 40 distance.

Additional vertical displacement of existing tunnels with different clearances

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Fig. 4
A line graph of the maximum stress rate of change versus distance from the monitoring surface plots 4 curves for 0.5 D, 1 D, 2 D, and 4 D. All curves peak between negative 40 and 40 distance.

Maximum rate of change of stress in existing tunnels with different clearances

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From Fig. 3, it can be observed that when the new double-arch tunnel is constructed above the existing tunnel, the existing tunnel exhibits an overall uplift deformation. The maximum vertical displacement occurs at the overlap section between the new and existing tunnels. Additionally, the additional displacement at various locations decreases as the vertical net distance between the new and existing tunnels increases.

Figure 4 shows that as the spacing increases, the maximum stress change rate of the existing tunnel gradually changes from an "M" shape to an inverted "V" shape, eventually becoming almost a horizontal straight line. The variation pattern of the maximum stress change rate of the existing tunnel is roughly similar to the pattern of additional displacement change in the existing tunnel.

Based on the above zoning criteria, the longitudinal impact partition diagram of the existing tunnel under different vertical net distances can be obtained, as shown in Fig. 5.

Fig. 5
4 schematic of a square with 2 parallel new tunnels and a tunnel centerline has a horizontal existing tunnel in the center titled H slash D = 0.5, 1, 2, and 4, respectively. The existing tunnel is divided into 1 strong and 2 weak impact zones. An upward arrow is labeled excavation direction.

Vertical impact zoning of existing tunnels with different vertical clear distances

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From Fig. 5, it is evident that the impact zone of the existing tunnel, due to the construction of the new tunnel crossing over it, changes significantly with variations in the net distance between the two tunnels. When the net distance between the new and existing tunnels is 0.5D, the longitudinal impact zone of the existing tunnel (strong impact zone + weak impact zone) is the largest. However, when the distance between the two tunnels increases to 4D, the existing tunnel is entirely within the no-impact zone.

5.2 Different Surrounding Rock Grade's Impact on the Longitudinal Impact Zones of the Existing Tunnel During New Tunnel Construction

Using the finite element software Midas GTS, maintaining a constant vertical overlap angle and net distance between upper and lower crossing tunnels at 90° and 1D, respectively, the rock mass levels are sequentially changed to III, IV, and V. This analysis investigates the impact of new double-arch tunnel construction on the mechanical properties of the surrounding rock and support structures of the existing tunnel for different rock mass levels. The results are presented in Figs. 6 and 7.

Fig. 6
4 line graphs of settlement value versus distance from cross-section distance plots 3 bell-shaped curves for level 3, level 4, and level 5 of arch crown, arch bottom, left sidewall, and right sidewall. All curves peak between negative 40 and 40 meters distance.

Additional vertical displacement of existing tunnels under different surrounding rock grades

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Fig. 7
A line graph of the stress change rate versus the distance from the cross-section plots 3 curves for level 3, level 4, and level 5. All curves peak between negative 40 and 40 meters distance. Level 5 has the highest peak followed by levels 4 and 3.

Maximum rate of change of stress in existing tunnels under different surrounding rock grades

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From Figs. 6 and 7, it can be observed that with a decrease in the surrounding rock grade, the vertical additional displacement increments and additional stress change rate generated in the lining of the existing tunnel due to the construction of the new tunnel gradually increase. For different surrounding rock grades, the maximum vertical displacement increments and additional stress change rate at each monitoring location occur in the overlapping sections of the upper and lower tunnels. The vertical displacement increments and additional stress change rate in the surrounding rock of the existing tunnel gradually decrease as you move away from the intersection point.

Based on the above zoning principles, different longitudinal impact zones of the existing tunnel under different surrounding rock grades can be determined, as shown in Fig. 8.

Fig. 8
4 schematic of 4 square has 2 parallel new tunnels and a tunnel centerline with a horizontal existing tunnel in the center titled grade 3, 4, and 5 surrounding rock, respectively. The existing tunnel is divided into 1 strong and 2 weak impact zones. An upward arrow is labeled excavation direction.

Vertical impact zoning of existing tunnels with different rock grades

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From Fig. 8, it can be observed that with the same net distance and crossing angle between the new and existing tunnels, as the surrounding rock grade increases, the longitudinal impact range of the new double-arch tunnel construction on the existing tunnel gradually decreases. Under Grade III surrounding rock conditions, the range of the unaffected zone in the existing tunnel is 119.6 m, the range of the weakly affected zone is 12 m, and the range of the strongly affected zone is 28.4 m. Under Grade IV surrounding rock conditions, the range of the unaffected zone in the existing tunnel is 110.6 m, the range of the weakly affected zone is 12 m, and the range of the strongly affected zone is 37.4 m. Under Grade VI surrounding rock conditions, the range of the unaffected zone in the existing tunnel is 98.6 m, the range of the weakly affected zone is 15 m, and the range of the strongly affected zone is 46.4 m.

6 Transverse Impact Zoning of New Tunnel Crossing Construction on Existing Tunnel

By changing the orientation angle between the new and existing tunnels, a two-dimensional model is established to simulate the impact of new tunnel overcrossing and undercrossing construction on the existing tunnel. Simultaneously, the relative spacing between the new and existing tunnels is altered. Five groups of relative net distances are selected from close to far (0.5D, 1D, 2D, 3D, 4D), and nine sets of relative angles are chosen (0°, -30°, -45°, -60°, -90°, 30°, 45°, 60°, 90°). The model dimensions are 240 m in the horizontal direction and 200 m in the vertical direction. Material parameters are consistent with those mentioned earlier. The layout for the parallel adjacent condition of the two tunnels is shown in Fig. 9.

Fig. 9
A schematic of a vertical line labeled 90 degrees at the top and negative 90 degrees at the bottom is made of new tunnels. The center has an existing tunnel that radiates 7 lines from negative 60 to 60 degrees at increments of 15 degrees. The 0-degree line is made of new tunnels.

Two tunnels parallel close working condition

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Based on the above scenarios, numerical simulations were conducted using the finite element software Midas GTS. The maximum vertical displacement and stress change values of the existing tunnel were extracted and obtained, with results shown in Figs. 10 and 11.

Fig. 10
A line graph of maximum vertical displacement versus crossing angle plots 5 decreasing trend curves for 0.5 D, 1 D, 2 D, 3 D, 4 D, and 5 D.

Maximum vertical displacement of the existing tunnel

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Fig. 11
A line graph of the maximum stress change rate versus the relative angle plots 5 fluctuating increasing trend curves for 0.5 D, 1 D, 2 D, 3 D, 4 D, and 5 D.

Maximum rate of change of stress in existing tunnels with different clearances

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Based on the simulation results shown in Figs. 10 and 11, the influence boundary values based on the additional displacement criteria and the additional stress criteria were obtained using linear interpolation. The maximum value between the two was used as the standard for dividing the influence zones for the composite criteria. The final result is the impact zone map for the new tunnel adjacent to the existing tunnel, as shown in Fig. 12.

Fig. 12
A spider chart plots 1 strong and 2 weak impact zones. The strong impact zone is at the center with the values 0.9, 1.1, 1.3, 1.6, 1.8, 1.9, and 2.5 D. The strong impact zone is surrounded by the first weak impact zone that has the values 1.7, 1.8, 2.3, 2.7, 3.3, 3.5, and 3.6 D.

Lateral impact zone map of the new tunnel adjacent to the existing tunnel

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From the lateral impact zone map in Fig. 12, it is clear that the impact range of the new tunnel's upward construction is generally smaller than the impact range of the new tunnel's downward construction.

7 Conclusion

  1. (1)

    When the vertical clearance of the interchange tunnel is less than 2D, the overlapping section of the existing tunnel is in the strong impact zone of the new tunnel construction. When the vertical clearance increases from 2 to 4D, the original weak impact zone of the existing tunnel becomes an unaffected zone. Changing the rock grade can lead to the presence of strong, weak, or unaffected zones within the existing tunnel. As a result, the influence of the vertical clearance factor is more pronounced than that of the rock grade factor.

  2. (2)

    Regarding the lateral influence of new tunnel construction on existing tunnels: the maximum impact range for parallel upward crossing is 2.7D, and for parallel downward crossing, it is 3.6D, while horizontal parallel construction has the smallest impact range of only 1.8D. This shows that the impact range for parallel downward crossing is greater than that for parallel upward crossing. When the new and existing tunnels are in a horizontally parallel relationship, their impact range is the smallest.

  3. (3)

    This study considered the impact of factors such as vertical clearance, crossing angle, and rock grade, but did not encompass factors such as tunnel support parameters and excavation methods. Further research is needed in the future.