Study on the Mechanical Response of a Dense Pipeline Adjacent to the Shallow Tunnel

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Introduction
During the construction of urban subway systems, it is inevitable that the dense network of underground pipelines will be afected. Te subway construction may cause accidents such as excessive deformation, cracking, and even damage to underground pipelines, which seriously threaten their normal service life and use. Furthermore, damage to water supply and drainage pipelines can lead to an increase in groundwater in the surrounding soil of the tunnel, posing a threat to tunnel construction.
Te research methods for underground pipeline deformation mainly include theoretical calculations, numerical simulations, and model experiments. Based on the elastic foundation beam theory, Klar et al. [1][2][3][4] have derived a theoretical and analytical formula for calculating pipeline deformation caused by tunnel excavation [5]. Teoretical, analytical formulas of Klar and Vorster were revised through model experiments and discrete element tests [6]. Derived analytical formulas to accurately describe the stress and deformation of underground pipelines when subjected to arbitrary displacement load conditions [7]. Using the Pasternak foundation model, a two-stage analysis method was employed to establish the pipeline equilibrium diferential equation, efectively predicting pipeline displacement resulting from water leakage during tunnel construction [8].
To predict the deformation of the existing pipeline caused by shield machine excavation, the researchers simplifed the pipeline as an Euler-Bernoulli beam resting on a Pasternak foundation beam. Tey employed the fnite diference method (FDM) and established equations to accurately estimate the deformation of the pipeline [9]. Assuming that the deformation of the upper pipeline caused by tunnel excavation conforms to a Gaussian distribution, we      Advances in Materials Science and Engineering introduced the variational energy principle to investigate the deformation of the overlying pipeline under small clearances induced by tunnel excavation and obtained a more convenient calculation method for such deformation. With the aid of numerical simulation, Kshama et al. [10] Investigated the mobilization of uplift resistance in dense sand through fnite element analysis in this study [11]. Te impact of pipeline seepage on surface deformation during tunnel excavation is being investigated [12]. Based on the measured data, the impact of shallowly buried tunnel construction on the overlying pipeline is analyzed using superposition method. Large-scale grouting measures are implemented to mitigate pipeline deformation caused by tunneling activities [13]. Te impact of shield tunnel sewage pipes on stratum    Advances in Materials Science and Engineering  [14]. Te stress and deformation of grouted reinforced materials during tunnel excavation through the pipeline are analyzed comprehensively [15]. Te impact of deep foundation excavation on the displacement of underground pipelines is simulated, followed by an analysis of hazardous areas and a study of the combination of risk factors that pose the greatest threat. Te aforementioned studies have advanced research on the mechanisms underlying the impact of tunnel excavation on adjacent pipelines. However, these studies have primarily focused on single pipelines, and there is a lack of research on densely clustered pipelines. Terefore, this article relies on the concealed excavation of the Nanchang Metro station entrance and exit tunnels to establish a three-dimensional fnite element model for densely clustered pipelines passing underneath shallow-buried subway tunnels. By investigating the stress characteristics and deformation patterns of underground pipelines with varying depths, materials, and diameters when crossing densely clustered underground pipelines, a theoretical basis for pipeline protection has been established. Targeted pipeline protection measures have been proposed to provide a reference for the protection of similar underground pipelines in engineering projects based on the research fndings.

Project
Overview. Dengbu Station on Line 3 of the Nanchang Metro is located at the intersection of Yingbin Avenue and Yangguang Road, with the route running north to south along Yingbin Avenue. Yingbin Avenue has four lanes in each direction, with one non-motorized vehicle lane on each side, while Yangguang Road has four lanes in each direction. Multiple bus routes intersect in this area, and the concealed excavation section spans the main trafc roads, as shown in Figure 1 for the horizontal position. Te crosssectional form of the tunnel structure is a straight wall arch, with an excavation width of 8.3 m and an excavation height of 6 m. In order to guarantee construction safety and control surface and pipeline deformation, the CRD (cross diaphragm) method is used for tunnel construction, as shown in Figure 2.
Within the concealed excavation tunnel scope, the following pipelines are present from east to west in the overhead direction: DN500 concrete sewage pipe at a depth of 3.55 m, DN1500 concrete rainwater pipe at a depth of 3.27 m, DN800 cast iron pipe for water at a depth of 2.5 m, and a 300 × 300 mm PVC conduit with nine openings for low-voltage electrical cables (communication cable) buried at a depth of 2.38 m. DN500 concrete sewage pipe conduit and DN1500 concrete rainwater conduit were found to be distributed beneath the existing trafc evacuation roadways. Te thickness of the overburdened soil on the tunnel arch excavated by the cut-and-cover method was measured to be 4.275 m. Te deepest buried utility conduit was a sewage pipe located 3.55 m below the ground level, with a minimum clear distance of 0.725 m from the tunnel excavation. Te distribution of utility conduits within the construction impact zone is shown in Figure 3.

Geological Profle.
Within the exploration depth, the upper layers of the site's stratigraphy consist of artifcial fll (Qml) and Quaternary Holocene alluvial deposits (Q3al). In contrast, the lower layers comprise the Eocene Nanyu Formation (Exn) bedrock. Te stratigraphy is divided from top to bottom based on rock type and its engineering characteristics into the following layers: ①1 miscellaneous fll soil, ①2 plain fll soil, ③1 silty clay, ③3 medium sand, ③4 coarse sand, and ③5 grit sand, as illustrated in

Numerical Model Size.
Te shallow tunnel has a total length of 23.6 m. It contains a densely packed segment of utility conduits with an overburdened soil thickness of approximately 4.2 m, where the excavation in this section is 12.8 m. A computational model was developed based on engineering data for the densely packed utility conduits and tunnels. To reduce boundary efects, the overall model was established with a length of 30 m, height of 25 m, and thickness of 12.8 m. Te surrounding rock, tunnel support structure, and utility conduits were modeled using solid elements. Te lateral and bottom surfaces of the model were fxed, restricting the normal displacement of these fve surfaces. Meanwhile, the top surface represented the ground surface and was set as an open boundary. Based on the actual working conditions, the model is shown in Figure 5.

Parameter Selection of the Model.
Based on the site investigation report, material parameters necessary for numerical simulation were selected. Te numerical model classifed the soil layers into miscellaneous fll, plain fll, powder quality clay, and medium sand. Te specifc parameters for each soil layer are presented in Table 1. Considering the situation, a linear elastic constitutive model was adopted for the underground utility model. Te physical and mechanical parameters of the concrete sewage pipe, concrete rainwater pipe, PVC communication cable, and cast iron pipe for water are presented in Table 2. Advances in Materials Science and Engineering  PVC communication cable DN800 cast iron pipe for water DN1500 concrete rainwater pipe DN500 concrete sewage pipe

Advances in Materials Science and Engineering
Te surrounding rock in the computational model is assumed to be continuous and uniform. Considering the buried pipelines' actual geological conditions, three diferent sets of parameters for the surrounding rock were established. Te mechanical parameters for the surrounding rock are shown in Table 3.

Numerical Calculation Scheme.
Due to the factors affecting the deformation response of nearby dense pipelines during tunnel excavation, including the clear distance between the pipeline and the tunnel, the intersection angle, the surrounding rock parameter, and the construction method, each of these factors contains diferent levels of infuence. Based on the position diagram of the tunnel and pipelines in Figure 2 and the basic engineering information, a numerical calculation model was established to analyze various factors' infuence on nearby dense pipelines' mechanical properties. Te specifc calculation scheme is shown in Table 4. All working conditions do not consider additional grouting reinforcement measures. Te net distances between the pipelines and the tunnel are 1.895 m for PVC communication cable, 1.725 m for cast iron pipe for water, 0.725 m for sewage pipe, and 1.005 m Sedimentation value (mm) (d) Figure 11: Comparison between actual monitoring curve and calculation curve of settlement value of each pipeline: (a) PVC communication cable; (b) cast iron pipe for water; (c) concrete sewage pipe; (d) concrete rainwater pipe.      Advances in Materials Science and Engineering for rainwater pipe. Diferent excavation simulation methods are shown in Figure 6.

Setting Field Monitoring Points.
According to the requirement of vertical deformation monitoring, fve direct monitoring points are arranged equidistant on the PVC communication cable (GXC6-1∼5), and GXC6-3 is located directly above the central axis of the tunnel. Tree direct monitoring points (GXC5-1∼3) are arranged equidistant on the formation where the DN800 cast iron pipe for water is located, among which GXC5-2 is located directly above the central axis of the tunnel. Five direct monitoring points (GXC7-1∼5) are arranged equidistant on the formation where DN1500 concrete rainwater pipe is located, among which GXC7-3 is located directly above the central axis of the tunnel. Five direct monitoring points (GXC8-1∼5) are arranged equidistant on the ground where DN500 concrete sewage pipe is located, among which GXC8-3 is located right above the central axis of the tunnel, as shown in Figure 7. Construction site monitoring points are set, as shown in Figure 8. Tunnel structure construction is shown in Figure 9.

Selection of Numerical Simulation Monitoring Sites.
In the numerical simulation model, relevant characteristic points were selected to study the mechanical response characteristics of the pipeline, as shown in Figure 10. Te vertical direction in the fgure represents the tunnel, and the upper horizontal line represents the dense pipeline intersecting the tunnel at a 90-degree angle. Te midpoint of the lower section of each pipeline, located at the centerline of the tunnel, was designated as the point with an X-axis value of 0. X � 0, ± 2.5, ± 5, ± 7.5, ± 10 were selected on the pipeline as characteristic points for analysis, and all are located at the bottom of the pipeline. In the analysis of the mechanical response characteristics of the pipeline, the same feature points were selected as those when the crossing angle between the pipeline and the tunnel was 90°and when the crossing angles were 0°, 30°, and 60°.

Comparative Analysis of Measured Values.
Trough the comparison and analysis of the actual monitoring points of each pipeline in the project and the numerical calculation results, compared with the maximum sedimentation value of measured value, PVC communication cable has an error of 1.84 mm; DN800 cast iron pipe for water has an error of 0.88 mm; DN1500 concrete rainwater pipe has an error of 0.1 mm; and DN500 concrete sewage pipe has an error of 0.8 mm. As shown in Figure 11, the errors are all very small, indicating that the numerical model is reasonable.

Mechanical Properties of Surrounding Rock.
According to the actual excavation method of the engineering project, the CRD method was used for excavation simulation calculation. Based on the calculation, it is found that there is a signifcant stress concentration phenomenon at the crown and bottom of the tunnel, where the stress at the crown increases while at the bottom, due to the excavation of the surrounding rock and the subsequent compression from other directions, the direction of stress changes. In the numerical analysis, it was found that there was signifcant stress concentration at the arch crown and tunnel bottom. Te stress increased at the arch crown, while the stress direction changed at the arch bottom due to the squeezing from other directions after excavating the surrounding rock. Te vertical displacement path of the surrounding rock coincided with the stress path, resulting in settlement of the soil above the arch bottom and the uplift of the soil at the arch bottom, presenting a "bottom heave" phenomenon. Based on the simulation results shown in Figure 12(a), the concentrated stress at the tunnel crown increased by approximately 100 kPa compared to the surrounding soil after the tunnel excavation. Te concentrated stress at the tunnel invert was approximately 361 kPa. As for Figure 12(b), the maximum settlement of the tunnel crown occurred at the top of the right-side adit, which was approximately 11.9 mm, and the maximum uplift of the tunnel invert also occurred on the right side, which was approximately 12.8 mm.

Mechanical Characteristics of Individual Pipelines.
Pipeline deformation occurs because of soil loss caused by tunnel excavation. From the cloud diagram of the maximum principal stress of the pipeline, it can be concluded that the deformation of the pipeline is highly correlated with its maximum principal stress. Te distribution law of the minimum principal stress of the pipeline is basically the same as that of the principal stress, which indicates that the deformation of the pipeline is also related to the minimum principal stress to a certain extent. After the excavation of the tunnel is completed, the maximum Advances in Materials Science and Engineering 13 settlement value of each pipeline is as follows: that for PVC communication cable is 8.23 mm; that for DN800 cast iron pipe for water is 7.88 mm; that for DN1500 concrete rainwater pipe is 5.83 mm; and that for DN500 concrete sewage pipe is 10.18 mm. Cloud diagram of vertical displacement of dense pipelines after excavation is shown in Figure 13. Te maximum value of the maximum principal stress of each pipeline is as follows: that for PVC communication cable is 257.48 kPa; that for DN800 cast iron pipe for water is 26.62 MPa; that for DN1500 concrete rainwater pipe is 850.2 kPa; and that for DN500 concrete sewage pipe is 2.22 MPa. Cloud chart of maximum principal stress of dense pipelines after excavation is shown in Figure 14.
Te maximum absolute value of the minimum principal stress of each pipeline is as follows: that for PVC communication cable is 1.06 MPa; that for DN800 cast iron pipe for water is 28.77 MPa; that for DN1500 concrete rainwater pipe is 1.24 MPa; and that for DN500 concrete sewage pipe is 2.65 MPa. Cloud diagram of minimum principal stress of dense pipelines after excavation is shown in Figure 15

Dense Pipeline Is Afected by the Clear Distance of the
Tunnel. Based on the results of scenarios 1, 2, 3, and 4 in Table 4, the vertical displacement, maximum principal stress, and minimum principal stress of the dense pipeline were analyzed to determine the efect of tunnel clearance on the response characteristics of the dense pipeline. 14 Advances in Materials Science and Engineering Figure 16 shows the maximum vertical displacement of each pipeline feature point at diferent net distances of 0.05D, 0.1D, 0.15D, and 0.2D. Under the same rock mass conditions, intersection angle, and excavation method, the vertical displacement of the pipeline increases as the net distance decreases.  Figure 18 shows the maximum absolute value of the minimum principal stress for each pipeline characteristic point at diferent net distances of 0.05D, 0.1D, 0.15D, and 0.2D. Except for when the net distance is 0.05D, the response curves of the minimum principal stress for the water supply pipeline and other pipelines difer in shape. Tis is because the material of the water supply pipeline is cast iron, which has a higher stifness, resulting in a much smaller minimum principal stress than the top and unexcavated areas on both sides.

Efect of Cross Angle on Dense
Pipeline. Using the calculation results from cases 5, 6, 7, and 8 in Table 3, the vertical displacement, maximum principal stress, and minimum principal stress of the dense pipeline were analyzed to determine the response characteristics of the dense pipeline to the intersection angle between the pipeline and the tunnel.

Vertical Displacement Response Characteristics of Each
Pipeline Characteristic Point. Te maximum vertical displacement of each pipeline at diferent crossing angles (0°, 30°, 60°, and 90°) under various net distances is shown in Figure 19. Te maximum variation of vertical displacement for the communication cable ranging from 0°to 90°is 2.07 mm, while for the water supply pipeline, it is 4.28 mm. For the sewage pipeline, it is 3.59 mm, and for the rainwater pipeline, it is 3.59 mm. When the pipelines are parallel to the tunnel, their overall vertical displacement is approximately the same as the maximum vertical displacement. Under the same conditions of the surrounding rock, clear distance, and excavation method, the vertical displacement of the pipeline increases with decreasing crossing angle. In contrast, the crossing angle has a negligible efect on the maximum value of the vertical displacement but has a signifcant impact on the overall settlement of the pipelines. Figure 20 depicts the maximum principal stress curves of various pipeline characteristic points under diferent crossing angles and net clearances. Te communication cable is a fexible pipeline made of PVC material. Its maximum principal stress characteristic value exhibits a slightly diferent variation pattern from the maximum principal stress characteristic values of cast iron water pipes, concrete sewage pipes, and rainwater pipes, as the crossing angle varies. For all pipelines, the maximum principal stress response is the smallest at a crossing angle of 0°, whereas the communication cable exhibits the maximum principal stress response at a crossing angle of 30°, while other rigid pipelines exhibit the maximum principal stress response at a crossing angle of 90°. Under the same conditions of the surrounding rock, net clearance, and excavation method, for rigid pipelines, the maximum principal stress response increases with the increase of crossing angle. In contrast, for fexible pipelines, the maximum principal stress response decreases with the increase of the crossing angle (except at 0°). Figure 21 depicts the minimum principal stress curves of various pipeline characteristic points under diferent crossing angles and net clearances. Te rigid cast iron water pipe, which exhibits the maximum rigidity, shows a slightly diferent variation pattern in the minimum principal stress characteristic value as the crossing angle varies, compared to the minimum principal stress characteristic values of PVC communication cables, concrete sewage pipes, and rainwater pipes. For all pipelines, the minimum principal stress response remains stable at a relatively small value at a crossing angle of 0°, while the cast iron water pipe exhibits the minor minimum principal stress response at a crossing angle of 90°, and other rigid or fexible pipelines exhibit the most minor minimum principal stress response at a crossing angle of 0°. Under the same conditions of the surrounding rock, net clearance, and excavation method, for pipelines with relatively low rigidity or fexibility, the minimum principal stress response increases with the increase of crossing angle, while for pipelines with high rigidity, the minimum principal stress response decreases with the increase of crossing angle (except at 0°).

Infuence of Surrounding Rock Parameters on Dense
Pipeline. Te results of calculations for scenarios 9, 10, and 11 in Table 3 were selected to analyze the dense pipeline's vertical displacement, maximum principal stress, and minimum principal stress. Te objective was to determine the response characteristics of the dense pipeline concerning various parameters of the surrounding rock, including density, elastic modulus, Poisson's ratio, cohesion, and internal friction angle. Figure 22, the maximum vertical displacement curves of various pipeline characteristic points are presented under diferent parameter rock conditions (rock parameters: type 1 < type 2 < type 3). Diferent types of pipelines have diferent values of vertical displacement caused by the construction of the tunnel excavation, but as the strength of surrounding rock increases, these diferences will become smaller. Moreover, the asymmetrical settlement curve caused by the CRD method will gradually become symmetrical with the increase of rock parameters. Under the same net distance, cross angle, and excavation method conditions, the vertical displacement of the pipeline decreases with the increase of rock parameters. Figure 23 shows the maximum principal stress of various types of pipelines at diferent parameters of surrounding rock conditions (where the rock parameters are compared as type 1 < type 2 < type 3). Under the same clear distance, intersection angle, and excavation method conditions, the maximum principal stress of fexible pipelines increases as the surrounding rock parameters increase, while the maximum principal stress of rigid pipelines decreases as the surrounding rock parameters increase. Figure 24 shows the minimum principal stress curve of various pipeline characteristic points under diferent surrounding rock conditions, where the surrounding rock parameters are ranked as follows: type 1 < type 2 < type 3. Under the same conditions of net distance, crossing angle, and excavation method, the minimum principal stress of the pipeline decreases with an increase in the strength of the surrounding rock parameters.

Te Infuence of Construction Parameters on Dense
Pipeline. Te calculation results of working conditions 12, 13, and 14 in Table 3 were selected to analyze the vertical displacement, maximum principal stress, and minimum principal stress of the dense pipeline, and the response characteristics of diferent construction methods (CRD method, up and down step method, and full section method) to the dense pipeline were obtained.   Figure 26, under the same conditions of the surrounding rock, net distance, and crossing angle, the maximum principal stress of the pipeline increases with an increase in the disturbance of the soil by the construction method. Figure 27, the minimum principal stress response curve of the characteristic points of the water supply pipeline difers in form from those of other pipeline types. Tis is attributed to the fact that the water supply pipeline is made of a higher strength material, i.e., cast iron, which ofers more excellent resistance to the deformation of the surrounding rock compared to other lower strength pipelines. Consequently, the minimum principal stress at the bottom of the water supply pipeline is signifcantly smaller than that at the top and in the unexcavated areas on both sides. Under the same conditions of the surrounding rock, net distance, and crossing angle, the pipeline's minimum principal stress increases with the construction method's disturbance of the soil.

Conclusion
Based on the entrance and exit tunnel project of Dengbu Station of Nanchang Metro Line 3, this paper establishes a multi-condition numerical model with numerical calculation method by considering key infuencing factors such as the clear distance, intersection angle, surrounding rock parameter, and construction method. Te mechanical response of the dense pipeline adjacent to the dug tunnel was studied, and the infuence of key factors on the mechanical behavior of the pipeline was analyzed. Te results show the following: (1) When the CRD method was used to construct and grout the surrounding strata of the tunnel, the maximum settlement of the tunnel roof was located at the roof of the right guide tunnel, at approximately 11.9 mm. Te measured settlement values of characteristic points of each pipeline are consistent with the simulated values, and the maximum settlement value is located at the bottom of the rainwater pipe directly above the tunnel. Te error between the measured value and the simulated value is small, which refects that the numerical model is more reliable.
(2) Trough numerical simulation, the infuences of key factors such as the clear distance, intersection angle, surrounding rock parameter, and construction method on the mechanical properties of close neighbor dense pipeline are analyzed. When other factors are fxed, the vertical displacement of pipeline, the maximum principal stress, and the minimum principal stress all decrease with the increase of the clear distance, cross angle, and surrounding rock strength.
(3) Te vertical displacement, maximum principal stress, and minimum principal stress of the pipeline are arranged in descending order of magnitude for full-face, stepped method, and CRD methods, respectively. Te greater the soil disturbance caused by the construction method, the more adverse the impact on the pipeline.

Data Availability
Te datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.