Since the safety and stability of the original tunnel structure are easily affected by the adjacent foundation pit excavation, it is strongly necessary to study the deformation evolution of tunnels during the adjacent foundation pit excavation. With regard to the two cases that tunnel is adjacently located at the right and bottom of foundation pit, the influence of different supporting methods, including pile support, bolt support, pile-bolt support, and shotcrete-bolt support, on the tunnel stability was investigated on the basis of the whole excavation process numerical simulation of deep foundation pit for determining the best foundation pit supporting beneficial to the stability of adjacent tunnel. The results indicate that both one-step excavation and multistep excavation have great influences on the displacement of adjacent tunnels, wherein the influences on the tunnel located at the right of foundation pit are greater than those at the bottom of foundation pit. Multistep excavation is recommended for the foundation pit adjacent to shallow tunnel. In the case of the tunnel located on the bottom of the foundation pit, the maximum stress generated around the tunnel is small, the maximum stress area is limited, and the displacement of tunnel monitoring points is also small. For the tunnel located at the right of the foundation pit, the pile-bolt supporting can effectively limit the displacement of soil between the tunnel and the foundation pit, reduce the maximum stress and the maximum stress distribution area, and effectively control the tunnel displacement.

Currently, the foundation pit excavation near existing tunnel has become a common occurrence with the rapid development of urban rail transit and underground space utilization. In the process of excavation, both the retaining structure and soil deform towards the pit [13]. With the advance of excavation depth, the displacement of soil outside the pit increases along with the increase of the deformation of the retaining structure and gradually transfers outward [4], thus causing the deformation of the surrounding underground tunnel to change with the construction process [57]. Since the excavation of adjacent subway tunnel will affect the safety and stability of the original tunnel structure [8] (see Figure 1), it is necessary to study the deformation of adjacent tunnel in the excavation process [3, 9]. In recent years, many scholars have made relevant research and discussion on this problem. Shi et al. [10] numerically studied the deformation of adjacent subway tunnel caused by foundation pit excavation. Finite element software is used by Zheng et al. [11] to study the influence of excavation depth, horizontal displacement of retaining structure, and relative position of tunnel and foundation pit on existing tunnel deformation. Doležalová [12] used finite element method to calculate and analyze the stress deformation of the underlying tunnel caused by foundation pit excavation and evaluated the control effect of relevant control measures. Jiangwei et al. [13] carried out centrifugal model tests on the influence of foundation pit excavation on the underlying tunnel in sandy and soft clay strata. Liu et al. [14] used numerical simulation to predict the long-term deformation response of adjacent tunnels under the action of foundation pit excavation in silty clay region. Liang et al. [15] derived the analytical solution of adjacent tunnel deformation under the action of foundation pit excavation by introducing the correction coefficient and considering the tunnel buried depth effect and shear effect.

Previous researches mainly focus on the deformation stability of tunnel after excavation of foundation pit [1618]. However, there are few researches on how to choose reasonable excavation and supporting methods of foundation pit to reduce the influence on tunnel structure. Therefore, based on the engineering case, this paper simulates the whole process of deep foundation pit excavation through numerical analysis. Regarding the two cases that tunnel is adjacently located at the right and bottom of foundation pit, the influence of different supporting methods on the tunnel stability was investigated to obtain the optimal foundation pit supporting.

Taking the excavation of a certain foundation pit as an example, the original geomorphic unit of the site is river alluvial terrace, and the soil calculation parameters can be obtained according to the site investigation report, as shown in Table 1.

There is a tunnel with a diameter of 6 m that passes through the whole site along the length direction of the site. At present, shotcrete-bolt supporting is widely used in tunnel support, and the change of axial force of bolt can reflect the stability of tunnel [1922]. In order to accurately analyze the influence of foundation pit excavation on the stability of adjacent tunnels, it is necessary to conduct statistical analysis on the change of axial force of bolt. The anchor rod is fixed at one end of the pull rod (anchor segment) in the stable stratum, and the other end is connected with the engineering structure to bear the thrust force imposed on the structure due to earth pressure and water pressure, so as to maintain the stability of the structure or rock and soil body by using the anchor force of the stratum. The numerical simulation method is widely used in geotechnical engineering [2326]; in this paper, FLAC3D is used to establish a numerical calculation model [27, 28], as shown in Figure 2. The left and right sides of the model are constrained by the normal boundary conditions, and the model bottom is constrained by the displacements in all directions [29]. The tunnel is located at the right and bottom of the foundation pit, and the support form is shotcrete-bolt supporting, in which the bolt is fully grouting bolt and concrete spraying is carried out after the layout of bolt. The calculation parameters of tunnel bolt, mortar, and shotcrete are shown in Tables 2 and 3. Due to the friction between bolt element and soil, each bolt element generates axial force, and the overall axial force of bolt can be obtained by superposition of the axial force of each bolt element. The bolt used has 7 nodes and 6 units, which are numbered from 1 to 6, respectively. No. 1 unit is the closest to the edge of the tunnel, and No. 6 unit is the furthest away from the edge of the tunnel, as shown in Figure 3.

3.1. Influence of Excavation Method on Bolt Axial Force

In order to study the influence of excavation method, namely, one-step excavation and multistep excavation, on the stress change of adjacent existing tunnel bolt, the excavation model with the scale of 20m×10m is employed. Without considering foundation pit supporting, one-step excavation of 10 m is carried out first, and both the bolt axial forces on the top and left of the tunnel were, respectively, recorded in the cases that the tunnel is located on the bottom of foundation pit with the distances of 6 m, 10 m, 16 m, 22 m, and 28 m, as well as the cases of the tunnel located at the right of foundation pit with the distances of 6 m, 8 m, 14 m, 20 m, and 26 m. By contrast, the multistep excavation depth of the foundation pit is still 10 m, divided into 5 steps, and the bolt axial forces are also recorded. Subsequently, the monitoring data for different excavation methods is compared. For simplicity, the data curve is noted in the form of “excavation method” + “the position of tunnel from foundation pit.” For example, “one-step + 6m-bottom” means the recorded bolt axial force of the tunnel in the case that the tunnel is 6 m located on the bottom of foundation pit.

For the tunnel located on bottom of the foundation pit after excavation, the soil stress at the bottom of the pit is released, and the pressure at the top of the tunnel is reduced. The tunnel is subjected to an upward additional stress, which causes the vertical uplift of the tunnel. The horizontal stress of the tunnel is basically balanced, and the horizontal displacement is small. It can be seen from Figure 4 that in all cases that the tunnel is located on the bottom of foundation pit except for the case of tunnel 6 m located on the bottom of foundation pit where there are slight deviations, the bolt axial force curves completely coincide for both excavation methods, which means the excavation method has no influence on the axial force of top bolt. Similar conclusions can be drawn from Figure 5, except for the case of tunnel 10 m located on the bottom of foundation pit where the axial force of bolt on the left of the tunnel corresponding to multistep excavation is greater than that of one-step excavation.

For the tunnel located at the right of foundation pit after excavation, the soil stress is released, and the retaining structure deforms towards the pit. As a result, the horizontal lateral pressure of the tunnel near the pit decreases, and the tunnel is subjected to a horizontal additional force, causing horizontal displacements towards the pit. Figure 6 elaborates that in all cases that the tunnel is located at the right of the foundation pit after excavation, the bolt axial force curves show significant agreements for the two different excavation methods, further proving the excavation method will not affect the axial force of top bolt. In comparison, the curves in Figure 7 demonstrate that only in the cases of tunnel located at the right of foundation pit with the distances of 14 m, 20 m, and 26 m, the left bolt is insusceptible by excavation method. For other cases in this study, there are separations of the axial force curves of left bolt. Specifically, the curve corresponding to the multistep excavation is greater than that of one-step excavation for the tunnel 6 m located at the right of the foundation pit. The opposite conclusion appears in the case that the tunnel is 8 m located at the right of the foundation pit. Therefore, for unsupported foundation pit with right-located adjacent tunnel, multistep excavation is recommended when the distance is relatively close, otherwise, one-step excavation is better.

3.2. Influence of Supporting Method on Tunnel Stability

Through calculation, the foundation pit with the scale of 28m×14m will be destroyed without supporting, as shown in Figure 8, where the foundation pit has been damaged in a wide range.

Taking the foundation pit model in Figure 8 as the research object, the foundation pit with four supporting forms of pile supporting, bolt supporting, pile-bolt supporting, and shotcrete-bolt supporting is, respectively, simulated. The related parameters of each supporting are presented in Tables 24. The variation of stress and displacement of tunnel 6 m located on the bottom of the foundation pit under different supporting conditions is presented.

The schematic diagrams of different supporting forms of foundation pit, namely, pile supporting, bolt supporting, pile-bolt supporting, and shotcrete-bolt supporting, are shown in Figure 9.

In order to study the influence of foundation pit supporting method and excavation method on the deformation of adjacent existing tunnels, the excavation simulation of the foundation pit is carried out by 7-step excavation, 2 m for each step. The displacement of adjacent tunnel roof in each step is recorded under different supporting conditions, as shown in Figures 10 and 11. Figure 10 shows that in the case that the tunnel is located on the bottom of the foundation pit, the vertical displacement of the tunnel roof changes linearly with the excavation step when the foundation pit is supported by piles, bolts, or piled bolts. However, it only linearly increases in the first five steps, and then, the increasing rate decreases if the shotcrete-bolt supporting is adopted. Therefore, using shotcrete-bolt to support the foundation pit is beneficial to the stability of the underlying tunnel.

As for the tunnel located at the right of the foundation pit, comparing to other supporting method in this study, the lateral horizontal displacement of tunnel is obviously larger if pile is adopted to retain foundation pit [3032], as shown in Figure 11. Note that the slope of displacement curve slightly increases with the excavation step for bolt supporting and shotcrete-bolt supporting, while it obviously slows down in the last two steps for pile-bolt supporting. Besides, after the foundation pit excavation is completed, the lateral horizontal displacement of the tunnel is minimum when the pile-bolt supporting is adopted. To sum up, pile-bolt supporting shows the least influences on the stability of tunnel which is located at the right of the foundation pit.

In the following, the displacement of adjacent existing tunnel monitoring points under the condition of one-step excavation and multistep excavation with various pit supporting is compared, as presented in Tables 5 and 6. Regardless of the tunnel location, the displacement produced by multistep excavation is less than that produced by one-step excavation, and it is also applicable to any type of foundation pit supporting. From the difference of tunnel displacement under two excavation conditions, it can be seen that the influence of excavation method on bottom-located tunnel displacement is much less than that of tunnel at the right of foundation pit.

  • (1)

    The excavation method of foundation pit, namely, one-step excavation and multistep excavation, has a great influence on the displacement of adjacent tunnels, wherein the influence on the tunnel located at the right of the foundation pit is greater than that underlying the foundation pit. In addition, the multistep excavation is suggested for the foundation pit adjacent with shallow buried tunnel

  • (2)

    For the tunnel underlying the foundation pit, the maximum stress around the tunnel is small, the maximum stress area is limited, and the displacement of tunnel monitoring point is also small if shotcrete-bolt supporting is employed. So it is suitable to use shotcrete-bolt supporting when there is a tunnel underlying the foundation pit

  • (3)

    In the case that the tunnel is located at the right of the foundation pit, the pile-bolt supporting can effectively limit the displacement of soil between tunnel and foundation pit and reduce the maximum stress value and the maximum stress distribution area. Thus, it is better to adopt piled bolt to support foundation pit at the right of which there exist a tunnel

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

On behalf of all authors, the corresponding author states that there is no conflict of interest.

This paper is supported by the CRSRI Open Research Program (CKWV2017512/KY), Science and Technology Hunan Civil Air Defense Research Project (HNRFKJ-2021-07), Water Conservancy Science and Technology Major Project of Hunan Province (XSKJ2019081-10), Scientific Research Project of Education Department of Hunan Province (18C1513), and Project (2021) of Study on Flood Disaster Prevention Model of Nanning Rail Transit. The authors wish to acknowledge these supports.

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