# Influence of Utility Tunnel on the Lower Part of the Existing Double-Track Shield Tunnel in Loess Soil

Authors: Min Yang; Hongru Li; Ning Li; Shun Yang
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

The interaction between the double-track shield tunnel and the integrated pipe gallery is complex, and there is still a lack of systematic research. Based on the numerical simulation of the Xi’an case, this paper studies the influence of the construction of the integrated pipe gallery on the deformation characteristics of the existing double-line subway tunnels with different buried depths and clear distances and finds the safe buried depth and clear distance of the tunnel. The results indicated that, in the loess area, the maximum deformation of the existing subway has a linear and inverse relationship with the buried depth and spacing, respectively. Increasing the buried depth can reduce the impact of the upper construction disturbance more than increasing the clear distance ratio. Moreove, under the design conditions of constructing a utility tunnel by the open-cut method, when the buried depth of the tunnel is 4.5 D and the spacing is greater than 4.5 D, or the buried depth is 5.0 D and the spacing is greater than 2.5 D, the combination of subway tunnels can meet the deformation control standards.


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## Body

## 1. Introduction

Nowadays, cities are developing at a fast pace and more and more underground buildings are being built. The construction of underground structures will inevitably lead to the change of stress field and displacement field, which will greatly affect the stability of existing underground structures [1–5]. How to reduce the influence between the lines will be an urgent problem to be solved in the future underground building construction. Previous research is mostly focused on the interaction between tunnels and foundation or existing tunnels [6–12]. However, with the development of the utility tunnel, it is urgent to study the influence of the excavation of the utility tunnel on the stability of the existing subway.In order to improve the safety and maintainability of tunnels and pipelines, more and more researches on the interaction between tunnels and pipelines have been conducted [13–18]. However, most previous studies have chosen to simplify the duct-to-pipe interaction as a two-dimensional problem. These include several analytical solutions for estimating pipeline response to tunneling [13, 19–21]. Since these previous studies have simplified the tunnel–pipe interaction as a two-dimensional problem, it is impossible to determine this three-dimensional problem. In addition to the analysis solutions, a series of model tests and numerical simulations were performed to provide more information about the main mechanisms controlling the soil–pipe interaction caused by tunneling [18, 22–25].In previous studies, pipes and tunnels are usually set perpendicular to each other. However, in reality, the pipe can intersect the tunnel at any angle [14, 17, 19, 20, 21, 23, 25, 26–28]. When the existing tunnel and integrated pipe gallery are parallel to each other up and down, the excavation of the integrated pipe gallery will affect the entire existing tunnel. This problem needs to be simulated using a three-dimensional model. Aiming at the parallel phenomenon of utility tunnel and subway tunnel, [29] established a three-dimensional model that studied the numerical simulation of the influence of shield tunnel three-dimensional dynamic construction process with different support pressures on the comprehensive pipe gallery in the loess area of Xi’an. However, there is no research on the impact of the excavation of the utility tunnel on the existing subway tunnels. Therefore, it is particularly important to simulate the influence of utility tunnel construction on shield tunnel by numerical method.Based on loess in the Xi’an, this paper establishes a numerical model to investigate the influences of pipe gallery tunnel excavation on the lower part of the existing tunnel. It simulates the construction of comprehensive pipe gallery by the open-cut method over an existing subway tunnel under different combinations of cover span and net distance ratios. It obtains the scope of influence of the excavation of the comprehensive pipe gallery on the tunnel, which provides reference for the design and construction of similar projects.


## 2. General Situation of Tunnel and Utility Tunnel

The Metro Line 2 (ML2) tunnel is a double-track tunnel with parallel left and right sides in Xi’an. The support method of existing tunnel is prefabricated C50 reinforced concrete segments with a width and thickness of 1.5 m and 300 mm, respectively. The outer diameter of segment is 6.0 m. The connection between segments adopts bent bolts.Combined with a utility tunnel project in Xi’an, it is planned to build the utility tunnel on the lower part of the existing tunnel that is located in ML2 in operation in Xi’an. The relative position of a section tunnel and the pipe gallery is shown in Figure1.Figure 1
Sketch of relative position of utility tunnel and metro tunnel (unit: m).D represents the diameter of the tunnel.It can be seen from the previously mentioned cross-section of the relative position between the pipe gallery and the tunnel that the comprehensive pipe gallery is composed of three storehouses, which is natural tank, comprehend tank, and power tank from left to right. Their widths are, respectively, 2.1 m, 3.3 m, and 2.3 m. Their heights are all 2.6 m. The sizes of the left and right hatches of the pipe gallery are not symmetrical, which is a typical unsymmetrical three-storehouse comprehensive pipe gallery. The structure of the utility tunnel is a rectangular structure surrounded by reinforced concrete roof, side wall, and floor. The side wall is called longitudinal structure, while the roof and floor are called horizontal members. The schematic diagram of cross section of pipe gallery is shown in Figure2.Figure 2
Schematic diagram of cross section of pipe gallery (unit: mm).The construction of the utility tunnel adopts cut-and-cover method. Its reinforcement form adopts slope and soil nail wall. The excavation is divided into five layers. The first and second excavation depths are 2.0 m. The third and fourth excavation depths are 1.5 m. The excavation depth of the last layer is 0.3 m. After the excavation, shotcrete with mesh of C20 concrete is applied in time, and then, soil nails are applied. The soil nails are made of HRB400 steel bars with a diameter of 14 mm, vertical spacing of 1.5 m, and longitudinal separation of 1.0 m. The thickness of sprayed concrete is 60 mm. The cushion is made of C15 concrete. The utility tunnel structure is made of C35 concrete. Since the left and right support and treatment of the utility tunnel are the same, only the left half of the utility tunnel is shown in Figure3.Figure 3
Schematic diagram of the left half of the utility tunnel (unit: mm).


## 3. Three-Dimensional Numerical Model

### 3.1. Numerical Scheme

The subway tunnel is an existing building, and a comprehensive pipe gallery will be built in the upper soil layer. For convenient description, introducing two concepts here, the cover span ratio (H/D) is the ratio of the overburden layer thickness (H) on the subway tunnel to the maximum span of the tunnel cross section, and the distance span ratio (I/D) is the net distance (I) between the two tunnels and the maximum span of the tunnel cross-section ratio for the two-lane tunnel. For the shield tunnel subway tunnel project, D is the outer diameter of the segment.In view of this actual situation, the model design conditions are combined according to the span ratio and the net ratio. The span ratio is 3, 3.5, 4, 4.5, and 5. The net ratio is 2.5, 3, 3.5, 4, 4.5, and 5. There are 26 working conditions in total. The specific working conditions are shown in Table1.Table 1
Model working condition statistics.
ConditionH/DI/D133233.5334434.553563.5373.53.583.5493.54.5103.5511431243.513441444.51545164.53174.53.5184.54194.54.5204.552152.522532353.524542554.52655


### 3.2. Material Model and Parameters

According to the soil properties, the soil layers within the buried depth of the tunnel section can be roughly divided into plain fill, neoloess, paleosol, and silty clay. The thickness of the soil layers is as follows: plain fill thickness is 3.0 m, neoloess thickness is 4.0 m, paleosol thickness is 3.0 m, and the remaining soil layers can be considered as silty clay. According to different test methods, compression modulus is recommended for one-dimensional compression in soil simulation analysis. In case of three-dimensional deformation, modulus of deformation is recommended. In case of elastic deformation or initial deformation, elastic modulus is used [24]. So, the deformation modulus is as one of the soil parameters. The parameters required for the numerical simulation were based on the relevant literature [30–35], as shown in Table 2. The corresponding structures of tunnel and utility tunnel are simplified as elastic models. The specific parameters are selected according to the “Code for Design of Concrete Structures” [36] and the “Code for Design of Building Foundations” [37]. The specific parameters are shown in Table 3.Table 2
Soil basic physical property index.
Soil layerγ (kN/m3)E0 (MPa)νβdλke0M①1-1 artificial fill18.14.30.2820.2430.99————②1-2 plain fill1740.3332.9467.57————③3-1-3 neoloess18.360.33——0.102060.009120.8660.77④3-2-2 paleosol18.980.31——0.076870.007820.7560.69⑤4-4 silty clay20.1130.3——0.065140.007820.640.77γ is the soil bulk density. E0 is the deformation modulus. ν is Poisson’s ratio. β is the internal friction angle. d is the cohesive strength. λ is the logarithm of plastic bulk modulus. k is the logarithm of bulk modulus of elasticity. e0 is the initial void ratio of soil. M is the slope of CSL line.Table 3
Parameters of structures of metro tunnel and utility tunnel.
NameBulk density (kN/m3)Elasticity modulus (MPa)Poisson’s ratioThickness (m)Shield463.842.10E + 050.300.04Segment252.84E + 040.200.3Grouting (early)230.90.30—Grouting (late)234000.2—Soil-nailed wall222.18E + 040.2Soil nailing78.52.00E + 050.3Cushion232.60E + 040.2Corridor253.15E + 040.2“—” means that the grouting layer completely fills the gap at the shield tail, without a fixed thickness.


### 3.3. FEM Model

The numerical simulation software ABAQUS is used to simulate each scheme. It takes the numerical model of scheme 1 as an example. A three-dimensional model is established to investigate the double-tube parallel tunnels underneath deformation due to the construction of utility tunnels. The detailed model of the finite element model is shown in Figure4. The model is 120 m in length, 90 m in width, and 50 m in depth. According to the actual geological conditions of Xi’an in China, the backfilling soil layer of pipe gallery is ①, and the stratum is ②∼⑤ from top to bottom. For the boundary conditions of the model, all four vertical sides restrain movement in the horizontal direction, the bottom boundary of the mesh restrains movement in the vertical and horizontal direction, and the top boundary is freedom to displace.Figure 4
Numerical model of engineering.The simplified treatment of the model is as follows:(1)
Finite element method of linear elastic model has been used to calculate each structure of the utility tunnel and the shield tunnel.(2)
The construction process of the utility tunnel is simulated without regard for the consolidation settlement of the backfill in the later period.(3)
Regarding the tunnel segment as a whole, the splicing seams of segment is not considered.(4)
The tunnel grouting process is simplified, and the synchronous grouting range is taken as the six-ring range of shield tail segment without regard for the midterm grouting layer strength. Each ring of segment is 1.5 m.(5)
The taper of shield machine and the friction between shield machine and soil are not considered in the simulation.The simulation process was divided into three stages: (i) ground stress equilibration under the gravity; (ii) excavation of the existing shield tunnels; (iii) excavation of the utility tunnel on the lower part of the existing double-track shield tunnel. This paper focuses on the effect of the third stage. After the completion of the first and second stages, the displacement of the soils and structures was reset to zero. Therefore, the calculation of the deformation of the existing tunnel is actually the incremental deformation caused by the excavation of the new utility tunnel.


### 3.4. Arrangement of Subway Tunnel Monitoring Points

Since the structure of the integrated pipe gallery is asymmetric, it is not only concerned with the deformation of a single tunnel. For better analysis, it is necessary to set monitoring points on both the left and right lines.The section of the monitoring point is selected as the 15th, 30th, and 45th ring of the tunnel. That is, the longitudinal length of the model tunnel is 22.5 m, 45 m, and 67.5 m. Eight monitoring points are arranged at the monitoring section of the tunnel. The point number gives the left and right lines of the 30-ring monitoring points, as shown in Figure5. The location of the monitoring points in the model is shown in Figure 6.Figure 5
Monitoring points arrangement of each monitoring cross-section. (a) The 30th ring monitoring point on the left line. (b) The 30th ring monitoring point on the right line.
(a)(b)Figure 6
Monitoring cross-section arrangement.


## 3.1. Numerical Scheme

The subway tunnel is an existing building, and a comprehensive pipe gallery will be built in the upper soil layer. For convenient description, introducing two concepts here, the cover span ratio (H/D) is the ratio of the overburden layer thickness (H) on the subway tunnel to the maximum span of the tunnel cross section, and the distance span ratio (I/D) is the net distance (I) between the two tunnels and the maximum span of the tunnel cross-section ratio for the two-lane tunnel. For the shield tunnel subway tunnel project, D is the outer diameter of the segment.In view of this actual situation, the model design conditions are combined according to the span ratio and the net ratio. The span ratio is 3, 3.5, 4, 4.5, and 5. The net ratio is 2.5, 3, 3.5, 4, 4.5, and 5. There are 26 working conditions in total. The specific working conditions are shown in Table1.Table 1
Model working condition statistics.
ConditionH/DI/D133233.5334434.553563.5373.53.583.5493.54.5103.5511431243.513441444.51545164.53174.53.5184.54194.54.5204.552152.522532353.524542554.52655


## 3.2. Material Model and Parameters

According to the soil properties, the soil layers within the buried depth of the tunnel section can be roughly divided into plain fill, neoloess, paleosol, and silty clay. The thickness of the soil layers is as follows: plain fill thickness is 3.0 m, neoloess thickness is 4.0 m, paleosol thickness is 3.0 m, and the remaining soil layers can be considered as silty clay. According to different test methods, compression modulus is recommended for one-dimensional compression in soil simulation analysis. In case of three-dimensional deformation, modulus of deformation is recommended. In case of elastic deformation or initial deformation, elastic modulus is used [24]. So, the deformation modulus is as one of the soil parameters. The parameters required for the numerical simulation were based on the relevant literature [30–35], as shown in Table 2. The corresponding structures of tunnel and utility tunnel are simplified as elastic models. The specific parameters are selected according to the “Code for Design of Concrete Structures” [36] and the “Code for Design of Building Foundations” [37]. The specific parameters are shown in Table 3.Table 2
Soil basic physical property index.
Soil layerγ (kN/m3)E0 (MPa)νβdλke0M①1-1 artificial fill18.14.30.2820.2430.99————②1-2 plain fill1740.3332.9467.57————③3-1-3 neoloess18.360.33——0.102060.009120.8660.77④3-2-2 paleosol18.980.31——0.076870.007820.7560.69⑤4-4 silty clay20.1130.3——0.065140.007820.640.77γ is the soil bulk density. E0 is the deformation modulus. ν is Poisson’s ratio. β is the internal friction angle. d is the cohesive strength. λ is the logarithm of plastic bulk modulus. k is the logarithm of bulk modulus of elasticity. e0 is the initial void ratio of soil. M is the slope of CSL line.Table 3
Parameters of structures of metro tunnel and utility tunnel.
NameBulk density (kN/m3)Elasticity modulus (MPa)Poisson’s ratioThickness (m)Shield463.842.10E + 050.300.04Segment252.84E + 040.200.3Grouting (early)230.90.30—Grouting (late)234000.2—Soil-nailed wall222.18E + 040.2Soil nailing78.52.00E + 050.3Cushion232.60E + 040.2Corridor253.15E + 040.2“—” means that the grouting layer completely fills the gap at the shield tail, without a fixed thickness.


## 3.3. FEM Model

The numerical simulation software ABAQUS is used to simulate each scheme. It takes the numerical model of scheme 1 as an example. A three-dimensional model is established to investigate the double-tube parallel tunnels underneath deformation due to the construction of utility tunnels. The detailed model of the finite element model is shown in Figure4. The model is 120 m in length, 90 m in width, and 50 m in depth. According to the actual geological conditions of Xi’an in China, the backfilling soil layer of pipe gallery is ①, and the stratum is ②∼⑤ from top to bottom. For the boundary conditions of the model, all four vertical sides restrain movement in the horizontal direction, the bottom boundary of the mesh restrains movement in the vertical and horizontal direction, and the top boundary is freedom to displace.Figure 4
Numerical model of engineering.The simplified treatment of the model is as follows:(1)
Finite element method of linear elastic model has been used to calculate each structure of the utility tunnel and the shield tunnel.(2)
The construction process of the utility tunnel is simulated without regard for the consolidation settlement of the backfill in the later period.(3)
Regarding the tunnel segment as a whole, the splicing seams of segment is not considered.(4)
The tunnel grouting process is simplified, and the synchronous grouting range is taken as the six-ring range of shield tail segment without regard for the midterm grouting layer strength. Each ring of segment is 1.5 m.(5)
The taper of shield machine and the friction between shield machine and soil are not considered in the simulation.The simulation process was divided into three stages: (i) ground stress equilibration under the gravity; (ii) excavation of the existing shield tunnels; (iii) excavation of the utility tunnel on the lower part of the existing double-track shield tunnel. This paper focuses on the effect of the third stage. After the completion of the first and second stages, the displacement of the soils and structures was reset to zero. Therefore, the calculation of the deformation of the existing tunnel is actually the incremental deformation caused by the excavation of the new utility tunnel.


## 3.4. Arrangement of Subway Tunnel Monitoring Points

Since the structure of the integrated pipe gallery is asymmetric, it is not only concerned with the deformation of a single tunnel. For better analysis, it is necessary to set monitoring points on both the left and right lines.The section of the monitoring point is selected as the 15th, 30th, and 45th ring of the tunnel. That is, the longitudinal length of the model tunnel is 22.5 m, 45 m, and 67.5 m. Eight monitoring points are arranged at the monitoring section of the tunnel. The point number gives the left and right lines of the 30-ring monitoring points, as shown in Figure5. The location of the monitoring points in the model is shown in Figure 6.Figure 5
Monitoring points arrangement of each monitoring cross-section. (a) The 30th ring monitoring point on the left line. (b) The 30th ring monitoring point on the right line.
(a)(b)Figure 6
Monitoring cross-section arrangement.


## 4. Analysis of the Impact of Comprehensive Pipe Gallery Excavation on Existing Subway Tunnels

The relevant deformation standard of the subway tunnel of degree II level of magnitude of tunnel is the benchmark. For the subway tunnel structure deformation control standard, the maximum subsidence is −10 mm, the maximum uplift is 5 mm, and the maximum horizontal displacement is 4 mm.


### 4.1. Displacement Analysis of Existing Tunnel Monitoring Points in Each Working Condition

#### 4.1.1. Vertical Displacement Analysis of Monitoring Points

Due to the large amount of data, only the monitoring points of the 30-section monitoring section on the left line were selected for analysis in each case to save space. This article only gives the vertical displacement maps of the monitoring points under conditions 1, 5, 21, and 26, as shown in Figures7 and 8. Positive sign represents uplift, and negative sign represents subsidence in the Figures 7 and 8. Here, the load step is supplemented as follows. The excavation of the utility tunnel is divided into five layers. The corresponding load step of initial stress calculation is 0. The first, second, third, and fourth excavations correspond to load steps 1, 2, 3, 4, respectively. The cushion construction that is the fifth excavation corresponds to load step 5. The construction of pipe gallery corresponds to load step 6. The soil is backfilled to the top of the pipe gallery according to load step 7. After backfilling, it corresponds to load step 8.Figure 7
The vertical displacement of each monitoring points of each case whenH/D is 3. (a) Working condition 1 (I/D = 3) vertical displacement of monitoring point. (b) Working condition 5 (I/D = 5) vertical displacement of monitoring point.
(a)(b)Figure 8
The vertical displacement of each monitoring point of each case whenH/D is 5. (a) Working condition 21 (I/D = 2.5) vertical displacement of monitoring point. (b) Working condition 26 (I/D = 5) vertical displacement of monitoring point.
(a)(b)It can be seen from Figure7 that the maximum peak of uplift appears at the right spandrel (L30-RT-2), which is 10.89 mm in case 1. The minimum peak appears at the left spandrel (L30-LT-8), which is 7.25 mm in case 1. The maximum value of the final displacement appears at the right spandrel (L30-RB-4), which is 1.45 mm, and the minimum value of the final displacement appears at the left spandrel (L30-LT-8), which is 0.34 mm. In case 5, the maximum peak of uplift that is 7.33 mm appears at the right arch foot (L30-RB-4), the minimum value of uplift that is 3.85 mm appears at the left arch shoulder (L30-LT-8), the maximum value of the final displacement that is 1.03 mm appears at the right arch foot (L30-RB-4), and the minimum value of the final displacement that is −0.04 mm appears at the left arch shoulder (L30-LT-8). With the increase of the distance between the subway tunnel and the pipe gallery, the maximum peak point will move from the upper part of the tunnel near the construction to the lower part of the tunnel. Moreover, the positions of the minimum peak value and the minimum value of the final value remain unchanged.It can be seen from Figure8 that the maximum peak of uplift appears at the vault (L30-TO-1), which is 4.92 mm in case 21. The minimum peak appears at the arch bottom (L30-BO-5), which is 3.52 mm in case 21. The maximum value of the final displacement appears at the right arch foot (L30-RB-4), which is 0.57 mm. The minimum value of the final displacement appears at the left shoulder span (L30-LT-8), which is −0.09 mm in case 21. In case 26, the maximum peak of uplift that is 3.62 mm appears at the right arch foot (L30-RB-4), the minimum value of uplift that is 1.94 mm appears at the left arch shoulder (L30-LT-8), the maximum value of the final displacement that is 0.55 mm appears at the right arch foot (L30-RB-4), and the minimum value of the final displacement that is −0.29 mm appears at the left arch shoulder (L30-LT-8). With the increase of the distance between the subway tunnel and the pipe gallery, the maximum peak point will move from the upper part of the tunnel near the construction to the lower part of the tunnel. Moreover the positions of the minimum peak value and the minimum value of the final value remain unchanged.It can be seen from Figures7 and 8 that each working condition shows that the floating increment is positive in the off-load period, and each working condition shows that the floating increment is negative in the loading process. In the two stages, the floating increment value of each measuring point is different. In addition, as the distance between the tunnel and the integrated pipeline gallery increases under various working conditions, the impact of the construction disturbance on the subway tunnel will become less and less, which shows that the floating value is getting smaller and smaller. With the increase of the distance between the subway tunnel and the pipe gallery, the maximum peak point will move from the upper part of the tunnel near the construction to the lower part of the tunnel. Moreover, the positions of the minimum peak value and the minimum value of the final value remain unchanged.On all these counts, under the condition of keeping theH/D constant, the peak maximum point of the uplift will gradually move from the upper part of the tunnel near the construction to the lower part of the tunnel with the increase of I/D. However, with the increase of H/D, the maximum value of uplift peak does not move when I/D is kept constant.The maximum peak value of the vertical displacement, the minimum peak value of the vertical displacement, the maximum value of the final vertical displacement, and the minimum value of the final vertical displacement of each working condition are organized as shown in Table4.Table 4
Statistics of vertical displacement of each case.
ConditionThe maximum peak (mm)The minimum peak (mm)The maximum value of the final displacement (mm)The minimum value of the final displacement (mm)H/DI/D110.897.251.450.343329.916.291.340.2233.539.085.381.200.123448.204.611.120.0434.557.333.851.03−0.043568.976.151.260.223.5378.315.391.170.103.53.587.684.671.090.013.5497.034.011.01−0.063.54.5106.393.380.93−0.143.55117.255.140.940.1243126.794.580.930.0843.5136.334.020.880.0244145.853.430.81−0.1244.5155.452.940.80−0.1945165.784.190.750.024.53175.503.730.76−0.064.53.5185.163.240.69−0.184.54194.812.860.69−0.164.54.5204.462.440.66−0.224.55214.923.520.57−0.0952.5224.543.280.57−0.1353234.302.920.56−0.1853.5244.072.580.55−0.2354253.812.260.53−0.2454.5263.621.940.55−0.2955The maximum vertical displacement peak of working condition 1 is the largest (10.89 mm) in each working condition, and that of working condition 26 is the smallest (3.62 mm) in Table5. When H/D is constant, the maximum vertical displacement peak decreases with the increase of I/D. When H/D is constant, the minimum value of vertical displacement peak decreases with the increase of I/D. After the backfill of the pipe gallery is completed, the final vertical displacement in each working condition is small. In the actual project, if there is a safety problem in the existing tunnel during the excavation stage of the integrated pipe gallery, other measures will be taken to remedy it. The actual stratum conditions of the pipe gallery pouring and backfilling will not be the same as the simulation situation in this paper.Table 5
Statistics of lateral displacement of each case.
ConditionThe maximum peak (mm)The minimum peak (mm)The maximum value of the final displacement (mm)The minimum value of the final displacement (mm)H/DI/D14.742.380.980.443324.732.791.030.4733.534.633.131.070.503444.663.261.150.5334.554.483.311.160.543564.391.900.930.333.5374.372.270.970.383.53.584.352.601.020.443.5494.332.861.040.483.54.5104.303.001.100.493.55113.901.470.830.1643123.931.840.870.2643.5133.912.130.890.3244143.872.390.870.3744.5154.012.620.990.4145163.611.200.830.094.53173.691.540.870.174.53.5183.691.760.840.154.54193.702.070.910.304.54.5203.682.300.930.364.55213.180.630.71−0.0852.5223.330.970.790.0153233.411.270.820.0853.5243.401.480.790.0854253.451.750.850.1854.5263.501.960.910.2255Therefore, it is necessary to pay more attention to the maximum vertical displacement peak. According to the maximum vertical displacement peak of each working condition, linear regression is shown in Figure9.Figure 9
Variation of the maximum value of vertical deformation withH/D and I/D respectively. (a) Variation of the maximum vertical deformation of each working condition with I/D under different H/D. (b) Variation of the maximum vertical deformation of each working condition with H/D under different I/D.
(a)(b)It can be seen from Figure9 that H/D and I/D are highly correlated with the maximum vertical deformation respectively for R2 greater than 0.98. When the H/D is constant (Figure 9(a)), I/D has a linear relationship with the maximum vertical deformation. The larger the I/D, the smaller the maximum vertical deformation. As the H/D increases, the fitting line slope gradually becomes larger, and the influence of I/D on the maximum vertical deformation will be smaller. When I/D is constant (Figure 9(b)), H/D has a linear relationship with the maximum vertical deformation. The larger the H/D, the smaller the maximum vertical deformation. As I/D increases, the fitting line slope gradually becomes larger, and the influence of H/D on the maximum vertical deformation will be smaller. It can be seen from the two figures that the maximum vertical deformation is within the control range when H/D is 5. The two figures can show that the maximum vertical deformation is within the control range when H/D is 5 and I/D is variation. In addition, by the fitting line slope in the two figures, it can be found that H/D has a greater influence on the maximum vertical deformation than I/D. Increasing the buried depth can reduce the construction disturbance more than increasing the net distance.


#### 4.1.2. Analysis of Lateral Displacement of Monitoring Points in Various Working Conditions

Due to the large amount of data, only the monitoring points of the 30-section monitoring section on the left line were selected for analysis in each case to save space.Here, the maximum value of the peak value, minimum value of the peak value, maximum value of the final value, and minimum value of the final value of the lateral displacement of each working condition will be directly given. The statistics are shown in Table5.The maximum lateral displacement peak of working condition 1 is the largest (4.74 mm) in each working condition, and that of working condition 21 is the smallest (3.18 mm), as shown in Table6. The correlation between the maximum lateral displacement peak and I/D has a certain relationship with H/D. When the minimum lateral displacement peak of each working condition is fixed at H/D, it will increase with the increase of I/D. After the backfill of the pipe gallery is completed, the final vertical displacement in each working condition is small. After the backfill of the pipe gallery is completed, the final lateral displacement in each working condition is small. It is necessary to pay more attention to the maximum displacement peak. According to the maximum displacement peak of each working condition, linear regression is shown in Figure 10.Table 6
Statistics of circular additional pressure of each case.
ConditionThe maximum peak of the additional tension stresses (MPa)The maximum peak of the additional compression stress (MPa)The maximum value of the final additional tension stresses (MPa)The maximum value of the final additional compression stresses (MPa)H/DI/D13.32−2.720.501−0.5113323.15−2.710.491−0.47433.532.95−2.560.480−0.4163442.73−2.450.516−0.42934.552.45−2.240.506−0.4013562.73−2.060.379−0.3593.5372.65−2.130.375−0.3603.53.582.53−2.120.378−0.3603.5492.38−2.070.386−0.3663.54.5102.24−1.970.415−0.3503.55112.40−1.580.290−0.25943122.12−1.660.270−0.30543.5132.03−1.710.233−0.33244141.97−1.710.239−0.33044.5151.92−1.610.278−0.25345162.27−1.610.299−0.2764.53172.04−1.340.273−0.2494.53.5181.78−1.260.209−0.1804.54191.65−1.330.221−0.2434.54.5201.58−1.350.190−0.2644.55212.28−1.750.286−0.27952.5222.13−1.570.283−0.27553231.94−1.360.259−0.25153.5241.72−1.120.2.13−0.19754251.54−1.020.212−0.19154.5261.35−1.040.188−0.18755Figure 10
Variation of the maximum value of lateral deformation withH/D and I/D respectively. (a) Variation of the maximum vertical deformation of each working condition with I/D under different H/D. (b) Variation of the maximum vertical deformation of each working condition with H/D under different I/D.
(a)(b)In Figure10(a), when H/D is 4.0 and 4.5, R2 is 0.2341 and 0.478, respectively, which indicates that I/D has a little influence on the maximum lateral deformation. When H/D is 3.0, 3.5, and 5.0, R2 is 0.7928, 0.9934, and 0.8619, respectively, which indicates that I/D is linear with the maximum value of lateral deformation. When H/D is 3.0 and 3.5, the maximum lateral deformation decreases with the increase of I/D. When H/D is 5.0, the maximum transverse deformation increases with the increase of I/D. When I/D is constant (Figure 10(b)), H/D has a linear relationship with the maximum lateral deformation for R2 greater than 0.97. The greater the H/D is, the smaller the maximum lateral deformation is. Moreover, with the increase of I/D, the fitting line slope gradually becomes larger, which indicates that the influence of H/D on the maximum lateral deformation will be smaller. In addition, from the fitting line slope in the two figures, it can be found that H/D has a greater impact on the maximum lateral deformation than I/D. That is, increasing the buried depth can reduce construction disturbances more than increasing the clear distance.In summary, according to Figures9 and 10, when the buried depth of the tunnel is 4.5 D and the spacing is greater than 4.5 D, or the buried depth is 5.0 D and the spacing is greater than 2.5 D, the combination of subway tunnels can meet the deformation control standards.


### 4.2. Subsidiary Stress Analysis of Existing Tunnel

The monitoring points of the monitoring section of the 30th ring on the left line are selected for circumferential stress analysis. The statistics are shown in Table6.In Table6, the maximum peak of the additional tension stresses of working condition 1 is the largest among all working conditions (3.32 MPa), while that of working condition 26 is the smallest (1.35 MPa). When the value of H/D is constant, the maximum peak of the additional tension stresses decreases with the increase of I/D. The maximum peak of the additional compression stress of working condition 1 is the largest among all working conditions (−2.72 MPa), while that of working condition 25 is the smallest (−1.02 MPa). The correlation between the maximum peak of the additional compression stress of each working condition and the I/D has a certain relationship with H/D.After the completion of backfilling, the subsidiary stress absolute value of each working condition is within 0.51 MPa. In actual engineering, it is necessary to pay more attention to the tension of reinforced concrete segments. According to the maximum peak of the additional tension stresses of each working condition, linear regression is shown in Figure11.Figure 11
Variation of the maximum peak of additional tensile stress withH/D and I/D, respectively. (a) Variation of the maximum peak of additional tensile stress with I/D under different H/D. (b) Variation of the maximum peak of additional tensile stress with H/D under different I/D conditions.
(a)(b)H/D and I/D are highly correlated with the maximum peak of the additional tension stresses, respectively, for R2 greater than 0.85 in Figure 11. When the H/D is constant (Figure 11(a)), I/D has a linear relationship with the maximum peak of the additional tension stresses. The larger the I/D, the smaller the maximum peak of the additional tension stresses. When the I/D is constant (Figure 11(b)), H/D has a linear relationship with the maximum peak of the additional tension stresses. The larger the H/D, the smaller the maximum peak of the additional tension stresses. In addition, from the fitting line slope in the two figures, it can be found that H/D has a greater influence on the maximum peak of the additional tension stresses than I/D. Increasing the buried depth can reduce the construction disturbance more than increasing the net distance.


## 4.1. Displacement Analysis of Existing Tunnel Monitoring Points in Each Working Condition

### 4.1.1. Vertical Displacement Analysis of Monitoring Points

Due to the large amount of data, only the monitoring points of the 30-section monitoring section on the left line were selected for analysis in each case to save space. This article only gives the vertical displacement maps of the monitoring points under conditions 1, 5, 21, and 26, as shown in Figures7 and 8. Positive sign represents uplift, and negative sign represents subsidence in the Figures 7 and 8. Here, the load step is supplemented as follows. The excavation of the utility tunnel is divided into five layers. The corresponding load step of initial stress calculation is 0. The first, second, third, and fourth excavations correspond to load steps 1, 2, 3, 4, respectively. The cushion construction that is the fifth excavation corresponds to load step 5. The construction of pipe gallery corresponds to load step 6. The soil is backfilled to the top of the pipe gallery according to load step 7. After backfilling, it corresponds to load step 8.Figure 7
The vertical displacement of each monitoring points of each case whenH/D is 3. (a) Working condition 1 (I/D = 3) vertical displacement of monitoring point. (b) Working condition 5 (I/D = 5) vertical displacement of monitoring point.
(a)(b)Figure 8
The vertical displacement of each monitoring point of each case whenH/D is 5. (a) Working condition 21 (I/D = 2.5) vertical displacement of monitoring point. (b) Working condition 26 (I/D = 5) vertical displacement of monitoring point.
(a)(b)It can be seen from Figure7 that the maximum peak of uplift appears at the right spandrel (L30-RT-2), which is 10.89 mm in case 1. The minimum peak appears at the left spandrel (L30-LT-8), which is 7.25 mm in case 1. The maximum value of the final displacement appears at the right spandrel (L30-RB-4), which is 1.45 mm, and the minimum value of the final displacement appears at the left spandrel (L30-LT-8), which is 0.34 mm. In case 5, the maximum peak of uplift that is 7.33 mm appears at the right arch foot (L30-RB-4), the minimum value of uplift that is 3.85 mm appears at the left arch shoulder (L30-LT-8), the maximum value of the final displacement that is 1.03 mm appears at the right arch foot (L30-RB-4), and the minimum value of the final displacement that is −0.04 mm appears at the left arch shoulder (L30-LT-8). With the increase of the distance between the subway tunnel and the pipe gallery, the maximum peak point will move from the upper part of the tunnel near the construction to the lower part of the tunnel. Moreover, the positions of the minimum peak value and the minimum value of the final value remain unchanged.It can be seen from Figure8 that the maximum peak of uplift appears at the vault (L30-TO-1), which is 4.92 mm in case 21. The minimum peak appears at the arch bottom (L30-BO-5), which is 3.52 mm in case 21. The maximum value of the final displacement appears at the right arch foot (L30-RB-4), which is 0.57 mm. The minimum value of the final displacement appears at the left shoulder span (L30-LT-8), which is −0.09 mm in case 21. In case 26, the maximum peak of uplift that is 3.62 mm appears at the right arch foot (L30-RB-4), the minimum value of uplift that is 1.94 mm appears at the left arch shoulder (L30-LT-8), the maximum value of the final displacement that is 0.55 mm appears at the right arch foot (L30-RB-4), and the minimum value of the final displacement that is −0.29 mm appears at the left arch shoulder (L30-LT-8). With the increase of the distance between the subway tunnel and the pipe gallery, the maximum peak point will move from the upper part of the tunnel near the construction to the lower part of the tunnel. Moreover the positions of the minimum peak value and the minimum value of the final value remain unchanged.It can be seen from Figures7 and 8 that each working condition shows that the floating increment is positive in the off-load period, and each working condition shows that the floating increment is negative in the loading process. In the two stages, the floating increment value of each measuring point is different. In addition, as the distance between the tunnel and the integrated pipeline gallery increases under various working conditions, the impact of the construction disturbance on the subway tunnel will become less and less, which shows that the floating value is getting smaller and smaller. With the increase of the distance between the subway tunnel and the pipe gallery, the maximum peak point will move from the upper part of the tunnel near the construction to the lower part of the tunnel. Moreover, the positions of the minimum peak value and the minimum value of the final value remain unchanged.On all these counts, under the condition of keeping theH/D constant, the peak maximum point of the uplift will gradually move from the upper part of the tunnel near the construction to the lower part of the tunnel with the increase of I/D. However, with the increase of H/D, the maximum value of uplift peak does not move when I/D is kept constant.The maximum peak value of the vertical displacement, the minimum peak value of the vertical displacement, the maximum value of the final vertical displacement, and the minimum value of the final vertical displacement of each working condition are organized as shown in Table4.Table 4
Statistics of vertical displacement of each case.
ConditionThe maximum peak (mm)The minimum peak (mm)The maximum value of the final displacement (mm)The minimum value of the final displacement (mm)H/DI/D110.897.251.450.343329.916.291.340.2233.539.085.381.200.123448.204.611.120.0434.557.333.851.03−0.043568.976.151.260.223.5378.315.391.170.103.53.587.684.671.090.013.5497.034.011.01−0.063.54.5106.393.380.93−0.143.55117.255.140.940.1243126.794.580.930.0843.5136.334.020.880.0244145.853.430.81−0.1244.5155.452.940.80−0.1945165.784.190.750.024.53175.503.730.76−0.064.53.5185.163.240.69−0.184.54194.812.860.69−0.164.54.5204.462.440.66−0.224.55214.923.520.57−0.0952.5224.543.280.57−0.1353234.302.920.56−0.1853.5244.072.580.55−0.2354253.812.260.53−0.2454.5263.621.940.55−0.2955The maximum vertical displacement peak of working condition 1 is the largest (10.89 mm) in each working condition, and that of working condition 26 is the smallest (3.62 mm) in Table5. When H/D is constant, the maximum vertical displacement peak decreases with the increase of I/D. When H/D is constant, the minimum value of vertical displacement peak decreases with the increase of I/D. After the backfill of the pipe gallery is completed, the final vertical displacement in each working condition is small. In the actual project, if there is a safety problem in the existing tunnel during the excavation stage of the integrated pipe gallery, other measures will be taken to remedy it. The actual stratum conditions of the pipe gallery pouring and backfilling will not be the same as the simulation situation in this paper.Table 5
Statistics of lateral displacement of each case.
ConditionThe maximum peak (mm)The minimum peak (mm)The maximum value of the final displacement (mm)The minimum value of the final displacement (mm)H/DI/D14.742.380.980.443324.732.791.030.4733.534.633.131.070.503444.663.261.150.5334.554.483.311.160.543564.391.900.930.333.5374.372.270.970.383.53.584.352.601.020.443.5494.332.861.040.483.54.5104.303.001.100.493.55113.901.470.830.1643123.931.840.870.2643.5133.912.130.890.3244143.872.390.870.3744.5154.012.620.990.4145163.611.200.830.094.53173.691.540.870.174.53.5183.691.760.840.154.54193.702.070.910.304.54.5203.682.300.930.364.55213.180.630.71−0.0852.5223.330.970.790.0153233.411.270.820.0853.5243.401.480.790.0854253.451.750.850.1854.5263.501.960.910.2255Therefore, it is necessary to pay more attention to the maximum vertical displacement peak. According to the maximum vertical displacement peak of each working condition, linear regression is shown in Figure9.Figure 9
Variation of the maximum value of vertical deformation withH/D and I/D respectively. (a) Variation of the maximum vertical deformation of each working condition with I/D under different H/D. (b) Variation of the maximum vertical deformation of each working condition with H/D under different I/D.
(a)(b)It can be seen from Figure9 that H/D and I/D are highly correlated with the maximum vertical deformation respectively for R2 greater than 0.98. When the H/D is constant (Figure 9(a)), I/D has a linear relationship with the maximum vertical deformation. The larger the I/D, the smaller the maximum vertical deformation. As the H/D increases, the fitting line slope gradually becomes larger, and the influence of I/D on the maximum vertical deformation will be smaller. When I/D is constant (Figure 9(b)), H/D has a linear relationship with the maximum vertical deformation. The larger the H/D, the smaller the maximum vertical deformation. As I/D increases, the fitting line slope gradually becomes larger, and the influence of H/D on the maximum vertical deformation will be smaller. It can be seen from the two figures that the maximum vertical deformation is within the control range when H/D is 5. The two figures can show that the maximum vertical deformation is within the control range when H/D is 5 and I/D is variation. In addition, by the fitting line slope in the two figures, it can be found that H/D has a greater influence on the maximum vertical deformation than I/D. Increasing the buried depth can reduce the construction disturbance more than increasing the net distance.


### 4.1.2. Analysis of Lateral Displacement of Monitoring Points in Various Working Conditions

Due to the large amount of data, only the monitoring points of the 30-section monitoring section on the left line were selected for analysis in each case to save space.Here, the maximum value of the peak value, minimum value of the peak value, maximum value of the final value, and minimum value of the final value of the lateral displacement of each working condition will be directly given. The statistics are shown in Table5.The maximum lateral displacement peak of working condition 1 is the largest (4.74 mm) in each working condition, and that of working condition 21 is the smallest (3.18 mm), as shown in Table6. The correlation between the maximum lateral displacement peak and I/D has a certain relationship with H/D. When the minimum lateral displacement peak of each working condition is fixed at H/D, it will increase with the increase of I/D. After the backfill of the pipe gallery is completed, the final vertical displacement in each working condition is small. After the backfill of the pipe gallery is completed, the final lateral displacement in each working condition is small. It is necessary to pay more attention to the maximum displacement peak. According to the maximum displacement peak of each working condition, linear regression is shown in Figure 10.Table 6
Statistics of circular additional pressure of each case.
ConditionThe maximum peak of the additional tension stresses (MPa)The maximum peak of the additional compression stress (MPa)The maximum value of the final additional tension stresses (MPa)The maximum value of the final additional compression stresses (MPa)H/DI/D13.32−2.720.501−0.5113323.15−2.710.491−0.47433.532.95−2.560.480−0.4163442.73−2.450.516−0.42934.552.45−2.240.506−0.4013562.73−2.060.379−0.3593.5372.65−2.130.375−0.3603.53.582.53−2.120.378−0.3603.5492.38−2.070.386−0.3663.54.5102.24−1.970.415−0.3503.55112.40−1.580.290−0.25943122.12−1.660.270−0.30543.5132.03−1.710.233−0.33244141.97−1.710.239−0.33044.5151.92−1.610.278−0.25345162.27−1.610.299−0.2764.53172.04−1.340.273−0.2494.53.5181.78−1.260.209−0.1804.54191.65−1.330.221−0.2434.54.5201.58−1.350.190−0.2644.55212.28−1.750.286−0.27952.5222.13−1.570.283−0.27553231.94−1.360.259−0.25153.5241.72−1.120.2.13−0.19754251.54−1.020.212−0.19154.5261.35−1.040.188−0.18755Figure 10
Variation of the maximum value of lateral deformation withH/D and I/D respectively. (a) Variation of the maximum vertical deformation of each working condition with I/D under different H/D. (b) Variation of the maximum vertical deformation of each working condition with H/D under different I/D.
(a)(b)In Figure10(a), when H/D is 4.0 and 4.5, R2 is 0.2341 and 0.478, respectively, which indicates that I/D has a little influence on the maximum lateral deformation. When H/D is 3.0, 3.5, and 5.0, R2 is 0.7928, 0.9934, and 0.8619, respectively, which indicates that I/D is linear with the maximum value of lateral deformation. When H/D is 3.0 and 3.5, the maximum lateral deformation decreases with the increase of I/D. When H/D is 5.0, the maximum transverse deformation increases with the increase of I/D. When I/D is constant (Figure 10(b)), H/D has a linear relationship with the maximum lateral deformation for R2 greater than 0.97. The greater the H/D is, the smaller the maximum lateral deformation is. Moreover, with the increase of I/D, the fitting line slope gradually becomes larger, which indicates that the influence of H/D on the maximum lateral deformation will be smaller. In addition, from the fitting line slope in the two figures, it can be found that H/D has a greater impact on the maximum lateral deformation than I/D. That is, increasing the buried depth can reduce construction disturbances more than increasing the clear distance.In summary, according to Figures9 and 10, when the buried depth of the tunnel is 4.5 D and the spacing is greater than 4.5 D, or the buried depth is 5.0 D and the spacing is greater than 2.5 D, the combination of subway tunnels can meet the deformation control standards.


## 4.1.1. Vertical Displacement Analysis of Monitoring Points

Due to the large amount of data, only the monitoring points of the 30-section monitoring section on the left line were selected for analysis in each case to save space. This article only gives the vertical displacement maps of the monitoring points under conditions 1, 5, 21, and 26, as shown in Figures7 and 8. Positive sign represents uplift, and negative sign represents subsidence in the Figures 7 and 8. Here, the load step is supplemented as follows. The excavation of the utility tunnel is divided into five layers. The corresponding load step of initial stress calculation is 0. The first, second, third, and fourth excavations correspond to load steps 1, 2, 3, 4, respectively. The cushion construction that is the fifth excavation corresponds to load step 5. The construction of pipe gallery corresponds to load step 6. The soil is backfilled to the top of the pipe gallery according to load step 7. After backfilling, it corresponds to load step 8.Figure 7
The vertical displacement of each monitoring points of each case whenH/D is 3. (a) Working condition 1 (I/D = 3) vertical displacement of monitoring point. (b) Working condition 5 (I/D = 5) vertical displacement of monitoring point.
(a)(b)Figure 8
The vertical displacement of each monitoring point of each case whenH/D is 5. (a) Working condition 21 (I/D = 2.5) vertical displacement of monitoring point. (b) Working condition 26 (I/D = 5) vertical displacement of monitoring point.
(a)(b)It can be seen from Figure7 that the maximum peak of uplift appears at the right spandrel (L30-RT-2), which is 10.89 mm in case 1. The minimum peak appears at the left spandrel (L30-LT-8), which is 7.25 mm in case 1. The maximum value of the final displacement appears at the right spandrel (L30-RB-4), which is 1.45 mm, and the minimum value of the final displacement appears at the left spandrel (L30-LT-8), which is 0.34 mm. In case 5, the maximum peak of uplift that is 7.33 mm appears at the right arch foot (L30-RB-4), the minimum value of uplift that is 3.85 mm appears at the left arch shoulder (L30-LT-8), the maximum value of the final displacement that is 1.03 mm appears at the right arch foot (L30-RB-4), and the minimum value of the final displacement that is −0.04 mm appears at the left arch shoulder (L30-LT-8). With the increase of the distance between the subway tunnel and the pipe gallery, the maximum peak point will move from the upper part of the tunnel near the construction to the lower part of the tunnel. Moreover, the positions of the minimum peak value and the minimum value of the final value remain unchanged.It can be seen from Figure8 that the maximum peak of uplift appears at the vault (L30-TO-1), which is 4.92 mm in case 21. The minimum peak appears at the arch bottom (L30-BO-5), which is 3.52 mm in case 21. The maximum value of the final displacement appears at the right arch foot (L30-RB-4), which is 0.57 mm. The minimum value of the final displacement appears at the left shoulder span (L30-LT-8), which is −0.09 mm in case 21. In case 26, the maximum peak of uplift that is 3.62 mm appears at the right arch foot (L30-RB-4), the minimum value of uplift that is 1.94 mm appears at the left arch shoulder (L30-LT-8), the maximum value of the final displacement that is 0.55 mm appears at the right arch foot (L30-RB-4), and the minimum value of the final displacement that is −0.29 mm appears at the left arch shoulder (L30-LT-8). With the increase of the distance between the subway tunnel and the pipe gallery, the maximum peak point will move from the upper part of the tunnel near the construction to the lower part of the tunnel. Moreover the positions of the minimum peak value and the minimum value of the final value remain unchanged.It can be seen from Figures7 and 8 that each working condition shows that the floating increment is positive in the off-load period, and each working condition shows that the floating increment is negative in the loading process. In the two stages, the floating increment value of each measuring point is different. In addition, as the distance between the tunnel and the integrated pipeline gallery increases under various working conditions, the impact of the construction disturbance on the subway tunnel will become less and less, which shows that the floating value is getting smaller and smaller. With the increase of the distance between the subway tunnel and the pipe gallery, the maximum peak point will move from the upper part of the tunnel near the construction to the lower part of the tunnel. Moreover, the positions of the minimum peak value and the minimum value of the final value remain unchanged.On all these counts, under the condition of keeping theH/D constant, the peak maximum point of the uplift will gradually move from the upper part of the tunnel near the construction to the lower part of the tunnel with the increase of I/D. However, with the increase of H/D, the maximum value of uplift peak does not move when I/D is kept constant.The maximum peak value of the vertical displacement, the minimum peak value of the vertical displacement, the maximum value of the final vertical displacement, and the minimum value of the final vertical displacement of each working condition are organized as shown in Table4.Table 4
Statistics of vertical displacement of each case.
ConditionThe maximum peak (mm)The minimum peak (mm)The maximum value of the final displacement (mm)The minimum value of the final displacement (mm)H/DI/D110.897.251.450.343329.916.291.340.2233.539.085.381.200.123448.204.611.120.0434.557.333.851.03−0.043568.976.151.260.223.5378.315.391.170.103.53.587.684.671.090.013.5497.034.011.01−0.063.54.5106.393.380.93−0.143.55117.255.140.940.1243126.794.580.930.0843.5136.334.020.880.0244145.853.430.81−0.1244.5155.452.940.80−0.1945165.784.190.750.024.53175.503.730.76−0.064.53.5185.163.240.69−0.184.54194.812.860.69−0.164.54.5204.462.440.66−0.224.55214.923.520.57−0.0952.5224.543.280.57−0.1353234.302.920.56−0.1853.5244.072.580.55−0.2354253.812.260.53−0.2454.5263.621.940.55−0.2955The maximum vertical displacement peak of working condition 1 is the largest (10.89 mm) in each working condition, and that of working condition 26 is the smallest (3.62 mm) in Table5. When H/D is constant, the maximum vertical displacement peak decreases with the increase of I/D. When H/D is constant, the minimum value of vertical displacement peak decreases with the increase of I/D. After the backfill of the pipe gallery is completed, the final vertical displacement in each working condition is small. In the actual project, if there is a safety problem in the existing tunnel during the excavation stage of the integrated pipe gallery, other measures will be taken to remedy it. The actual stratum conditions of the pipe gallery pouring and backfilling will not be the same as the simulation situation in this paper.Table 5
Statistics of lateral displacement of each case.
ConditionThe maximum peak (mm)The minimum peak (mm)The maximum value of the final displacement (mm)The minimum value of the final displacement (mm)H/DI/D14.742.380.980.443324.732.791.030.4733.534.633.131.070.503444.663.261.150.5334.554.483.311.160.543564.391.900.930.333.5374.372.270.970.383.53.584.352.601.020.443.5494.332.861.040.483.54.5104.303.001.100.493.55113.901.470.830.1643123.931.840.870.2643.5133.912.130.890.3244143.872.390.870.3744.5154.012.620.990.4145163.611.200.830.094.53173.691.540.870.174.53.5183.691.760.840.154.54193.702.070.910.304.54.5203.682.300.930.364.55213.180.630.71−0.0852.5223.330.970.790.0153233.411.270.820.0853.5243.401.480.790.0854253.451.750.850.1854.5263.501.960.910.2255Therefore, it is necessary to pay more attention to the maximum vertical displacement peak. According to the maximum vertical displacement peak of each working condition, linear regression is shown in Figure9.Figure 9
Variation of the maximum value of vertical deformation withH/D and I/D respectively. (a) Variation of the maximum vertical deformation of each working condition with I/D under different H/D. (b) Variation of the maximum vertical deformation of each working condition with H/D under different I/D.
(a)(b)It can be seen from Figure9 that H/D and I/D are highly correlated with the maximum vertical deformation respectively for R2 greater than 0.98. When the H/D is constant (Figure 9(a)), I/D has a linear relationship with the maximum vertical deformation. The larger the I/D, the smaller the maximum vertical deformation. As the H/D increases, the fitting line slope gradually becomes larger, and the influence of I/D on the maximum vertical deformation will be smaller. When I/D is constant (Figure 9(b)), H/D has a linear relationship with the maximum vertical deformation. The larger the H/D, the smaller the maximum vertical deformation. As I/D increases, the fitting line slope gradually becomes larger, and the influence of H/D on the maximum vertical deformation will be smaller. It can be seen from the two figures that the maximum vertical deformation is within the control range when H/D is 5. The two figures can show that the maximum vertical deformation is within the control range when H/D is 5 and I/D is variation. In addition, by the fitting line slope in the two figures, it can be found that H/D has a greater influence on the maximum vertical deformation than I/D. Increasing the buried depth can reduce the construction disturbance more than increasing the net distance.


## 4.1.2. Analysis of Lateral Displacement of Monitoring Points in Various Working Conditions

Due to the large amount of data, only the monitoring points of the 30-section monitoring section on the left line were selected for analysis in each case to save space.Here, the maximum value of the peak value, minimum value of the peak value, maximum value of the final value, and minimum value of the final value of the lateral displacement of each working condition will be directly given. The statistics are shown in Table5.The maximum lateral displacement peak of working condition 1 is the largest (4.74 mm) in each working condition, and that of working condition 21 is the smallest (3.18 mm), as shown in Table6. The correlation between the maximum lateral displacement peak and I/D has a certain relationship with H/D. When the minimum lateral displacement peak of each working condition is fixed at H/D, it will increase with the increase of I/D. After the backfill of the pipe gallery is completed, the final vertical displacement in each working condition is small. After the backfill of the pipe gallery is completed, the final lateral displacement in each working condition is small. It is necessary to pay more attention to the maximum displacement peak. According to the maximum displacement peak of each working condition, linear regression is shown in Figure 10.Table 6
Statistics of circular additional pressure of each case.
ConditionThe maximum peak of the additional tension stresses (MPa)The maximum peak of the additional compression stress (MPa)The maximum value of the final additional tension stresses (MPa)The maximum value of the final additional compression stresses (MPa)H/DI/D13.32−2.720.501−0.5113323.15−2.710.491−0.47433.532.95−2.560.480−0.4163442.73−2.450.516−0.42934.552.45−2.240.506−0.4013562.73−2.060.379−0.3593.5372.65−2.130.375−0.3603.53.582.53−2.120.378−0.3603.5492.38−2.070.386−0.3663.54.5102.24−1.970.415−0.3503.55112.40−1.580.290−0.25943122.12−1.660.270−0.30543.5132.03−1.710.233−0.33244141.97−1.710.239−0.33044.5151.92−1.610.278−0.25345162.27−1.610.299−0.2764.53172.04−1.340.273−0.2494.53.5181.78−1.260.209−0.1804.54191.65−1.330.221−0.2434.54.5201.58−1.350.190−0.2644.55212.28−1.750.286−0.27952.5222.13−1.570.283−0.27553231.94−1.360.259−0.25153.5241.72−1.120.2.13−0.19754251.54−1.020.212−0.19154.5261.35−1.040.188−0.18755Figure 10
Variation of the maximum value of lateral deformation withH/D and I/D respectively. (a) Variation of the maximum vertical deformation of each working condition with I/D under different H/D. (b) Variation of the maximum vertical deformation of each working condition with H/D under different I/D.
(a)(b)In Figure10(a), when H/D is 4.0 and 4.5, R2 is 0.2341 and 0.478, respectively, which indicates that I/D has a little influence on the maximum lateral deformation. When H/D is 3.0, 3.5, and 5.0, R2 is 0.7928, 0.9934, and 0.8619, respectively, which indicates that I/D is linear with the maximum value of lateral deformation. When H/D is 3.0 and 3.5, the maximum lateral deformation decreases with the increase of I/D. When H/D is 5.0, the maximum transverse deformation increases with the increase of I/D. When I/D is constant (Figure 10(b)), H/D has a linear relationship with the maximum lateral deformation for R2 greater than 0.97. The greater the H/D is, the smaller the maximum lateral deformation is. Moreover, with the increase of I/D, the fitting line slope gradually becomes larger, which indicates that the influence of H/D on the maximum lateral deformation will be smaller. In addition, from the fitting line slope in the two figures, it can be found that H/D has a greater impact on the maximum lateral deformation than I/D. That is, increasing the buried depth can reduce construction disturbances more than increasing the clear distance.In summary, according to Figures9 and 10, when the buried depth of the tunnel is 4.5 D and the spacing is greater than 4.5 D, or the buried depth is 5.0 D and the spacing is greater than 2.5 D, the combination of subway tunnels can meet the deformation control standards.


## 4.2. Subsidiary Stress Analysis of Existing Tunnel

The monitoring points of the monitoring section of the 30th ring on the left line are selected for circumferential stress analysis. The statistics are shown in Table6.In Table6, the maximum peak of the additional tension stresses of working condition 1 is the largest among all working conditions (3.32 MPa), while that of working condition 26 is the smallest (1.35 MPa). When the value of H/D is constant, the maximum peak of the additional tension stresses decreases with the increase of I/D. The maximum peak of the additional compression stress of working condition 1 is the largest among all working conditions (−2.72 MPa), while that of working condition 25 is the smallest (−1.02 MPa). The correlation between the maximum peak of the additional compression stress of each working condition and the I/D has a certain relationship with H/D.After the completion of backfilling, the subsidiary stress absolute value of each working condition is within 0.51 MPa. In actual engineering, it is necessary to pay more attention to the tension of reinforced concrete segments. According to the maximum peak of the additional tension stresses of each working condition, linear regression is shown in Figure11.Figure 11
Variation of the maximum peak of additional tensile stress withH/D and I/D, respectively. (a) Variation of the maximum peak of additional tensile stress with I/D under different H/D. (b) Variation of the maximum peak of additional tensile stress with H/D under different I/D conditions.
(a)(b)H/D and I/D are highly correlated with the maximum peak of the additional tension stresses, respectively, for R2 greater than 0.85 in Figure 11. When the H/D is constant (Figure 11(a)), I/D has a linear relationship with the maximum peak of the additional tension stresses. The larger the I/D, the smaller the maximum peak of the additional tension stresses. When the I/D is constant (Figure 11(b)), H/D has a linear relationship with the maximum peak of the additional tension stresses. The larger the H/D, the smaller the maximum peak of the additional tension stresses. In addition, from the fitting line slope in the two figures, it can be found that H/D has a greater influence on the maximum peak of the additional tension stresses than I/D. Increasing the buried depth can reduce the construction disturbance more than increasing the net distance.


## 5. Conclusions

This paper investigates the influences of pipe gallery tunnel excavation undercrossing on the existing twin tunnels. It simulates the construction of comprehensive pipe gallery by the open-cut method over an existing subway tunnel under different combinations of cover span and net distance ratios. It analyzes the vertical displacement, lateral displacement, and additional stress of the segment during the construction process.(1)
The maximum peak of vertical displacement, lateral displacement, and additional stress of the pipe segments appear in the unloading stage of each working condition. The tunnel closer to the construction area in each working condition will be more disturbed. For the working condition withH/D = 3 and I/D = 3, the vertical displacement and lateral displacement have exceeded the deformation after being disturbed.(2)
The maximum vertical displacement has a linearly inverse relationship with the cover span and distance span ratios in each working condition. The maximum lateral displacement has a linearly inverse relationship with the cover span ratio. The maximum lateral displacement has different relativities with the distance span ratio under different cover span ratios. Increasing the buried depth can reduce construction disturbances more than increasing the clear distance. The maximum additional stresses have obvious linear inverse relationships with the cover span and distance span ratios.(3)
Under the design conditions of constructing a comprehensive pipe gallery by the open-cut method, when the buried depth of the tunnel is 4.5 D and the spacing is greater than 4.5 D, or the buried depth is 5.0 D and the spacing is greater than 2.5 D, the combination of subway tunnels can meet the deformation control standards. If it is necessary to build a comprehensive pipe gallery under a smaller cover span ratio or distance span ratio combination, other foundation pit excavation methods are required to ensure the safety of the subway tunnel.



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*Source: 9927245-2021-07-24.xml*