Influence Law of Foundation Pit Excavation on Stress of Surrounding Tunnel Bolt

Abstract

Due to the existence of a tunnel next to the foundation pit, the soil surrounding the foundation pit deforms into the foundation pit due to the excavation unloading during the process of foundation pit excavation, which causes the deformation of the tunnel. The supporting structure of the tunnel can ensure the deformation stability of the tunnel, so it is necessary to study the stress of the tunnel bolt supporting structure caused by the excavation of the foundation pit. In this paper, the numerical simulation method was adopted to study the influence of the distance between the foundation pit and tunnel and the width and depth of foundation pit excavation on the stress of the tunnel bolt, and the following results were obtained: (1) When the distance between the tunnel and the foundation pit changes, the axial force of the bolt changes accordingly. The axial force of the left bolt first increases and then decreases, and the largest axial force is located in the middle of the bolt. (2) With the increase in the excavation width of the foundation pit, the stress of the left bolt does not change much. For the left bolt, with the increase in excavation depth, the stress of the left bolt does not increase monotonically but shows a trend of increasing first and then decreasing. When the excavation depth exceeds a certain value, the influence of excavation depth on lateral soil displacement gradually decreases. With the increase in excavation depth, the axial force of the top bolt decreases first and then increases.

1. Introduction

Given that many underground space projects are built in cities, the foundation pit excavation of surface engineering is often adjacent to existing tunnels [1]. With increasing excavation depth, due to the excavation unloading effect, the grouting on the foundation pit wall moves to the interior of the foundation pit [2,3], thus causing the deformation or differential deformation of the surrounding underground tunnels to change with the construction process [4], as shown in Figure 1. Therefore, it is necessary to study the influence law of the foundation pit excavation on the deformation stability of existing tunnels [5].

At present, by focusing on the influence of excavation on nearby subway tunnels, some research has been conducted, but most results are according to practical engineering experience [6,7]. Based on the field data, the semi-empirical and the semi-theoretical formula, the qualitative analysis of underground engineering was implemented [8]. Wu and Shen [9] proposed a new longitudinal structural model to consider the shearing dislocation between rings. Quantitative analysis and calculation are limited, and the simulation calculation of the construction process of the foundation pit cannot be carried out. For example, Kouretzis [10] found that the displacement of the side wall of the foundation pit, the deformation of the retaining structure of the foundation pit, and the settlement of the backfill soil of the foundation pit would lead to the horizontal displacement of the underground pipeline. Jiang et al. [11] believed that the proximity of the foundation pit to the tunnel changes the transfer of surrounding rock displacement, which is mainly manifested as transverse deformation. Pei et al. [12] found that the excavation of the foundation pit had an obvious influence on the adjacent tunnel, especially the horizontal displacement. Blackburn and Finno [13] studied the influence of rigid and flexible supporting foundation pits on the structural safety of neighboring buildings through the engineering case of adjacent building cracking by foundation pit excavation and explored the cracking causes and prevention measures. On the other hand, with the development of numerical calculation [14,15,16,17], many scholars compiled numerical simulation software to study the interaction between foundation pit excavation and adjacent tunnels [18,19]. Dolezalova [20] used a numerical simulation method to simulate the excavation process of the foundation pit above the tunnel, and the results were basically consistent with the field-measured data. Finno and Bryson [21] studied the size effect and space effect of foundation pit excavation by numerical simulation. Bryson and Zapata-Medina [22] used Plaxis 3D software to establish a three-dimensional numerical calculation model to simulate the excavation effect of a deep foundation pit of a building, which was compared with the two-dimensional model. Lo and Ramsay [23] took the construction of the foundation pit adjacent to the Toronto subway as the background, simulated and predicted the additional displacement of the underground subway tunnel caused by different construction schemes. Based on the foundation pit project of Shanghai Agile Square, Li [24] established a three-dimensional finite element model with FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) and analyzed the effect of excavation with different reinforcement methods on reducing the vertical displacement of the subway below. Huang et al. [25] used PLAXIS to analyze the influence of four different working conditions on the tunnel deformation based on the open excavation foundation pit. Song et al. [26] employed MIDAS/GTS to simulate the deformation characteristics of shield tunnel under different construction stages and pit-tunnel location relations.

In summary, theoretical or numerical analysis methods have been widely used to study the effect of foundation pit excavation on adjacent subway tunnels [27,28,29]. However, the geological conditions surrounding the excavation are complex, and the research on the impact of deep foundation pit excavation on adjacent subway tunnels is not systematic and perfect, especially for supporting tunnels. In this study, with a specific engineering case as the background, the whole process of deep foundation pit excavation was simulated by numerical analysis. The axial stress characteristics of a bolt in an adjacent subway tunnel under the influence of foundation pit excavation were discussed, and the research findings can be applied as a reference for similar projects.

2. Numerical Calculation Model

The study in this paper was mainly implemented by FLAC3D, developed by ITASCA [30]. Based on the finite difference method, it can describe the three-dimensional constitutive model of the soil and engineering materials. According to the mechanical characteristics of the simulation and calculation analysis, the material elastic–plastic change or flow process is accurately simulated in FLAC3D, which is widely used in the calculation and analysis of tunnel, slope, mine, chamber, and other geotechnical engineering [31]. Specific solution flow and modeling steps were presented in detail by Yin and Lin [32]. By taking the excavation of a certain foundation pit as an example, the original geomorphic unit of the site is an alluvial river terrace, and the soil calculation parameters can be obtained according to the site survey report [3,33], which is presented in Table 1. It should be pointed out that, in the excavation problem, soil deformation is also affected by soil water content or soil suction [34]; however, it was ignored in this paper. The interaction between the tunnel and the foundation pit was the focus of this paper.

Along the length direction of the site, a 6 m inner diameter tunnel passes through the whole site. A bolt is currently widely used in tunnel engineering; when the tunnel deforms, the bolt also deforms and produces support stress [35]. Therefore, the deformation stability of the tunnel can be reflected by monitoring the stress change in the bolt [36,37]. The numerical calculation model was established, as shown in Figure 2a, and the Mohr–Coulomb criterion was assigned to the model [38]. In modeling, the mesh around the tunnel was encrypted because the tunnel was the focus of the investigation. The model contains 8056 grids with 16,486 nodes. The left and right sides of the model are constrained by the normal boundary conditions, and the bottom of the model is constrained by the displacements in three directions. The diameter of the tunnel is 6 m, and the depth is 6 m.

Due to the existence of a tunnel next to the foundation pit, the soil surrounding the foundation pit deforms into the foundation pit due to the excavation unloading during the process of foundation pit excavation, which causes the deformation of the tunnel. The supporting structure of the tunnel can ensure the deformation stability of the tunnel, so it is necessary to study the stress of the tunnel bolt supporting structure caused by the excavation of the foundation pit. Concrete spraying is carried out after the bolt layout. The calculation parameters of tunnel bolt, mortar, and shotcrete are shown in Table 2 and Table 3 [3,33]. The bolt used seven nodes and six elements, which are numbered from 1 to 6. The no. 1 element is closest to the edge of the tunnel, and the No. 6 element is furthest away from the edge of the tunnel [3,33], as shown in Figure 2.

3. Sensitivity Analysis of Influencing Factors on the Axial Force of Rock Bolt

3.1. Distance between Foundation Pit and Tunnel

The following scheme was set as the calculation standard: the depth of the excavation was 15 m, the excavation width was 20 m, and the distance between the tunnel and the excavation was 5 m. When discussing the influence of the distance between the foundation pit and tunnel (denoted as “D_ft”) on the anchor bolt axial force, the distance between the foundation pit and tunnel was set as 3, 5, 7, 9, 11, 13, and 15 m, respectively. The left bolt (denoted as “left bolt”) and the top bolt (denoted as “top bolt”) of the tunnel were selected as the monitoring objects to record the changes in the bolt axial force during the construction process.

When there is a tunnel next to the foundation pit, the tunnel is reinforced with a bolt. After the foundation pit is excavated, the soil around the foundation pit tends to move into the foundation pit. At this time, the soil on the left side of the tunnel also tends to move into the foundation pit, as shown in Figure 3 (Taking D_ft = 5 m, for instance). After the excavation of the foundation pit, the soil around the tunnel is negative and moves into the foundation pit. At this time, as shown in Figure 4, the bolt on the left is gradually stretched and bears tensile stress, showing a positive value. Moreover, the horizontal displacement at the top of the right side of the foundation pit is the largest. However, the soil around the tunnel within 1–2 times the diameter of the tunnel is affected. It can be seen from the distribution of bolt axial force that along the direction of bolt length, the distribution of axial force is not uniform but shows a trend of increasing first and then decreasing.

When the distance between the tunnel and the foundation pit changes, the axial force of the bolt changes accordingly. The stress of the left bolt was recorded, as shown in Figure 5, and it has the same trend as the work by Xu, Liu [3], so the results of this paper can be verified. It can be seen from the figure that the axial force of the left bolt is positive; that is, the bolt is in a tension state, and along the bolt length direction, the axial force first increases and then decreases, and the largest axial force is located in the middle of the bolt. When the D_ft is 3 m, the axial force of the bolt is the maximum, and with the increase in the D_ft, the axial force of the bolt decreases gradually. This is because the larger the D_ft is, the larger the distance between the foundation pit and the tunnel is, and the smaller the impact of foundation pit excavation is, that is, the smaller the deformation of the soil around the tunnel is, and therefore the smaller the corresponding bolt axial force is, shown in Figure 6.

In addition, in order to further study the influence of D_ft on the bolt at the top of the tunnel, the axial force of the bolt at the top under different D_ft conditions was recorded, as shown in Figure 7. It can be seen that the stress distribution of the top bolt is similar to that of the left bolt, and the axial force increases first and then decreases along the bolt length direction, and the maximum axial force of the bolt occurs in the middle of the bolt. When the foundation pit is not excavated, the anchor rod bears the tensile force, but with the excavation of the foundation pit, the anchor rod is squeezed due to the rebound effect of excavation [39,40], which leads to the decrease in the tensile force. However, with the increase in D_ft, the springback effect caused by foundation pit excavation decreases, so the stress on the bolt continues to increase. In addition, in the process of uniform change in D_ft, the bolt axial force shows non-uniform characteristics. When the D_ft is greater than 9 m, the change in bolt axial force is small. This indicates that when the D_ft is greater than 9 m, the excavation effect of the tunnel can be neglected. Therefore, in the actual construction, in order to reduce the impact of foundation pit excavation on the tunnel, it is suggested that the distance between the two should be controlled beyond 9 m.

3.2. Width of Foundation Pit

In order to analyze the influence of the excavation width of the foundation pit on the tunnel bolt, the excavation width of the foundation pit was changed to 5–30 m, and the axial forces of the left and top bolts of the tunnel were recorded under different excavation widths, as shown in Figure 8 and Figure 9. It can be seen from the figure that the top and left bolts showed the same trend of change. Along the bolt length, the axial force increases first and then decreases. However, with the increase in the excavation width of the foundation pit, the stress of the left bolt does not change much. This is because foundation pit excavation causes the soil to move horizontally inside the pit, and the width of foundation pit excavation does not affect the horizontal displacement of soil. In addition, by comparing the stress of the top bolt and the left bolt, it can be seen that the stress of the left bolt is much larger than that of the top bolt. This is because there is foundation pit excavation on the left side of the tunnel, so the soil deformation is mainly caused by horizontal displacement, and the stress of the left bolt is correspondingly larger. In addition, due to the rebound effect of soil excavation, the axial force of the tunnel roof bolt is also small.

3.3. Depth of Foundation Pit

In order to analyze the influence of the excavation depth of the foundation pit on the tunnel bolt, the excavation depth of the foundation pit was changed to 5–30 m. Since the excavation depth has a great influence on the rebound of soil, the load borne by the bolt at the top of the tunnel changes greatly. Therefore, the axial forces of the top bolts and left bolts of the tunnel were recorded under different excavation depths, as shown in Figure 10 and Figure 11. It can be seen from the figure that the influence law of excavation depth on anchor bolt axial force is the same as that of excavation width and D_ft. For the left bolt, with the increase in excavation depth, the stress of the left bolt does not increase monotonically but shows a trend of increasing first and then decreasing. This is because when the excavation depth of the foundation pit changes, the dimension of the interface on the right side of the foundation pit closest to the tunnel changes so that the horizontal displacement of soil into the foundation pit also changes, as shown in Figure 12. However, when the excavation depth exceeds a certain value, the influence of excavation depth on lateral soil displacement gradually decreases. When the excavation depth reaches 15 m, it has the greatest influence on the axial force. Moreover, when the excavation depth exceeds 15 m, the axial force borne by the bolt element closest to the tunnel boundary does not change with the excavation depth.

Figure 13 shows the vertical displacement of soil caused by foundation pit excavation. It can be seen that the soil springback effect caused by foundation pit excavation is relatively obvious, and the vertical springback effect of soil has little influence on the axial force of the left bolt but has a great influence on the axial force of the top bolt. This is because, after tunnel excavation, the soil at the top moves downward due to unloading. At this time, the anchor rod interacts with the soil and bears axial tensile force. With the increase in excavation depth, the axial force of the top bolt decreases first and then increases. This is because when the excavation depth of the foundation pit is small, the springback effect has a great influence on the displacement of the tunnel roof. At this time, the axial force of the bolt decreases due to the springback effect of the soil. When the excavation depth is large, the influence is relatively small because the excavation face is far away from the tunnel. Therefore, with the increase in the excavation depth, the axial force of the bolt also increases.

4. Conclusions

• (1). When the distance between the tunnel and the foundation pit changes, the axial force of the bolt changes accordingly. The axial force of the left bolt first increases and then decreases, and the largest axial force is located in the middle of the bolt. When the Dft is 3 m, the axial force of the bolt is the maximum, and with the increase in the Dft, the axial force of the bolt decreases gradually;

• (2). The stress distribution of the top bolt is similar to that of the left bolt. With the increase in Dft, the springback effect caused by foundation pit excavation decreases, so the stress on the bolt continues to increase. When the Dft is greater than one certain, the change in bolt axial force is small. This indicates that when the Dft is greater than that certain value, the excavation effect of the tunnel can be neglected;

• (3). With the increase in the excavation width of the foundation pit, the stress of the left bolt does not change much. This is because foundation pit excavation causes the soil to move horizontally inside the pit, and the width of foundation pit excavation does not affect the horizontal displacement of soil;

• (4). For the left bolt, with the increase in excavation depth, the stress of the left bolt does not increase monotonically but shows a trend of increasing first and then decreasing. When the excavation depth exceeds a certain value, the influence of excavation depth on lateral soil displacement gradually decreases. With the increase in excavation depth, the axial force of the top bolt decreases first and then increases.

Author Contributions

Data curation, S.H., J.L., R.Z., C.G. and H.L.; Formal analysis, S.H. and T.Z.; Funding acquisition, X.J., S.S. and H.L.; Investigation, T.Z. and Y.Z.; Methodology, Y.Z., X.J. and Z.W.; Project administration, S.S.; Software, H.L.; Writing—original draft, S.H.; Writing—review & editing, S.H., C.G. and H.L. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

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

Acknowledgments

This paper received its funding from Science and Technology Hunan Civil Air Defense Research Project (HNRFKJ-2021-07); Project (2021) of Study on Flood Disaster Prevention Model of Nanning Rail Transit; Projects (42277175) supported by the National Natural Science Foundation of China; Hunan provincial key research and development Program (2022SK2082). The authors wish to acknowledge this support.

Conflicts of Interest

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

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Tunnel support structure cracking caused by surrounding foundation pit excavation.

Figure 2. Numerical simulation model. (a) Numerical model; (b) bolt monitoring position.

Figure 3. Displacement of soil after excavation of foundation pit. (a) Horizontal displacement; (b) vertical displacement.

Figure 4. Axial force distribution of anchor bolt after excavation.

Figure 5. Axial force of left bolt with different distance between foundation pit and tunnel. (a) axial force of bolt along direction of bolt length; (b) axial force of bolt with different Dft.

Figure 6. Soil displacement caused by excavation with different distances between foundation pit and tunnel. (a) Dft = 3 m; (b) Dft = 7 m; (c) Dft = 11 m; (d) Dft = 15 m.

Figure 7. Axial force of top bolt in the tunnel at one side of foundation pit. (a) Axial force of bolt along direction of bolt length; (b) axial force of bolt with different Dft.

Figure 8. Axial force of left bolt with different width of foundation pit. (a) axial force of bolt along direction of bolt length; (b) axial force of bolt with different width of foundation pit.

Figure 9. Axial force of top bolt with different width of foundation pit. (a) axial force of bolt along direction of bolt length; (b) axial force of bolt with different width of foundation pit.

Figure 10. Axial force of left bolt with different depth of foundation pit. (a) axial force of bolt along direction of bolt length; (b) axial force of bolt with different depth of foundation pit.

Figure 11. (a) Axial force of bolt along direction of bolt length; (b) axial force of bolt with different depth of foundation pit; axial force of top bolt with different depth of foundation pit.

Figure 12. Influence of excavation depth on horizontal displacement of soil. (a) Five-meter depth; (b) 10 m depth; (c) 15 m depth; (d) 20 m depth; (e) 25 m depth; (f) 30 m depth.

Figure 12. Influence of excavation depth on horizontal displacement of soil. (a) Five-meter depth; (b) 10 m depth; (c) 15 m depth; (d) 20 m depth; (e) 25 m depth; (f) 30 m depth.

Figure 12. Influence of excavation depth on horizontal displacement of soil. (a) Five-meter depth; (b) 10 m depth; (c) 15 m depth; (d) 20 m depth; (e) 25 m depth; (f) 30 m depth.

Figure 13. Influence of excavation depth on vertical displacement of soil. (a) Five-meter depth; (b) 10 m depth; (c) 15 m depth; (d) 20 m depth; (e) 25 m depth; (f) 30 m depth.

Figure 13. Influence of excavation depth on vertical displacement of soil. (a) Five-meter depth; (b) 10 m depth; (c) 15 m depth; (d) 20 m depth; (e) 25 m depth; (f) 30 m depth.

Table 1

Calculation parameters of site soil.

Cohesion (kPa)	Internal Friction Angle (°)	Unit Weight (kN/m3)	Deformation Modulus (MPa)	Poisson Ratio
300.0	25.0	20.0	50.0	0.35

Table 2

Parameters of bolt.

Bolt Diameter	Bolt Area	Slurry Diameter	Slurry Perimeter	Tensile Strength of Bolt	Prestressing of Bolt
22 mm	3.50 cm2	100 mm	0.314 m	250 kN	60 kN
Bolt length	Slurry cohesion	Slurry friction	Slurry rigidity	Bolt number	Angle between bolts
3 m	20 kPa	25°	22.33 MN/m2	21	9°

Table 3

Shotcrete calculation parameters.

Grade Type	Unit Weight	Deformation Modulus	Poisson Ratio	Thickness
C20	25 kN/m3	25.3 GPa	0.266	0.3 m

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