Numerical Study on the Disturbance Effect of Short-Distance Parallel Shield Tunnelling Undercrossing Existing Tunnels

The construction of new tunnels poses a threat to the operational safety of closely existing tunnels, and the construction mode of parallel undercrossing over short distances has the most significant impact. In this study, a new double-line shield tunnel parallel undercrossing of existing tunnels in Hefei, China, is taken as an example. A three-dimensional (3D) numerical model using FLAC3D finite difference software was established. The dynamic construction of the new double-line shield tunnel undercrossing the existing subway tunnel over a short distance and in parallel was simulated. The pattern of existing tunnel settlement and change in lining stress caused by the shield tunnelling process were analyzed. The reliability of simulation was verified through field-monitoring data. Finally, based on the numerical model, the effects of change in stratum sensitivity on the settlement of existing tunnel, lining internal force, and surface settlement are discussed. The results show that during shield tunnelling, the maximum ground settlement is 3.9 mm, the maximum settlement at the arch waist of existing tunnel near the new tunnel is 7.75 mm, and the maximum vault settlement is 5.38 mm. The maximum stress of lining of existing tunnel before the excavation is 7.798 × 105 Pa. After the construction of double-line shield tunnel, the maximum stress of lining is 1.124 × 106 Pa, an increase of 44% than that before the construction. The surface settlement and tunnel settlement are sensitive to the weakening of soil layer strength, and lining stress is not affected by the weakening of soil layer strength. The field-monitoring results are consistent with the numerical simulation results, and the model calculation is reliable. This study plays an important role in ensuring construction safety and optimizing the construction risk control of a tunnel.


Introduction
In China, subway transportation has shown a leap forward in development, especially in some large cities. Subway lines have gradually developed into a network and three-dimensional (3D) form. e 3D construction is mainly reflected in the 3D intersection of tunnel space, easily causing disturbance and damage to existing tunnels [1]. According to the relative position relationship between a new tunnel and existing tunnel, the undercrossing construction is mainly divided into three modes: orthogonal, oblique, and parallel. According to relevant studies, the construction mode of close parallel undercrossing has the greatest effect on the disturbance of existing tunnels and the highest construction risk [2,3]. erefore, to ensure the safety and stability of an existing tunnel, it is necessary to conduct safety analysis before construction to develop a strict construction control scheme. e construction of an urban subway tunnel inevitably affects the existing structure around it (e.g., tunnels, pipes, and buildings). An undercrossing tunnel changes the balanced stress field and induces settlement, resulting in an additional load and bending moment on the existing structure and further threatening its normal operation [2,4]. Many empirical or semiempirical methods, physical model experiments, analytical methods, and numerical methods have been used to study the effect of adjacent tunnel construction on the existing structure. While the effect of adjacent tunnelling on existing buildings [5,6], roads [7], pipelines [8,9,10], or bridges [11] has been extensively studied using the aforementioned methods, the effects of undercrossing tunnelling on existing tunnels have been less studied [4].
Empirical or semiempirical methods have simple and practical characteristics, and they are widely used in practice. For example, based on monitoring data, Fang et al. [12] used an empirical method to study the settlement of a tunnel crossing two existing tunnels to solve the settlement problem of the existing tunnel. Chen et al. [13] studied the deformation and stress characteristics of an existing tunnel caused by a closed earth pressure balance (EPB) shield during an oblique crossing process. e Gauss distribution curve of displacement was used to simulate the settlement profile of existing tunnel. Physical model tests include scale model tests and centrifugal model tests. e tests truly reflect the field situations, but this method has high cost and a long test cycle.
rough large-scale model tests, Byun et al. [14] studied the surface characteristics and tunnel behavior of existing tunnels above and below newly excavated tunnels.
e results show that the existence of an upper tunnel significantly affects the stress flow produced by the longitudinal arching effect of lower tunnel excavation. e analytical method is to analyze the effect of mechanical behavior of tunnel construction by simplifying the constitutive behavior of soil (elastic or elastoplastic). For example, based on in situ monitoring data, Zhang and Huang [15] presented an analytical solution to calculate the deformation of existing subway tunnels induced by an EPB shield during above-overlapped and down-overlapped crossing tunnels with oblique angles. Liang et al. [2] proposed an analytical method to analyze the deformation of an existing tunnel caused by crossing over a new tunnel, and based on the Winkler foundation model, the interaction between tunnel and soil caused by unloading stress was analyzed. Numerical simulation methods such as finite element method (FEM) or finite difference method (FDM) not only consider the heterogeneity and nonlinear characteristics of soil but also truly describe the complex geometry and dynamic construction process. ese are the most economical methods widely used to study the interaction between new and existing tunnels. For example, Lin et al. [16] used a numerical simulation method to simulate the deformation characteristics of a new double tunnel obliquely crossing an existing tunnel. rough 3D numerical analysis, Ng et al. [17] studied the effects of ratio of breadth of an existing horseshoe-shaped tunnel to the diameter of new circular tunnels on the interaction of perpendicularly crossing tunnels in sand. Yin et al. [18] built a 3D finite element numerical model and analyzed the deformation of existing tunnels induced by the construction of new vertical undercrossing tunnels.
With the development of underground space and improvement in space utilization rates, the number of close parallel undercrossing projects will increase. However, in previous studies, the new tunnel construction mode of undercrossing mainly focused on orthogonal and oblique modes, while the construction mode of close parallel undercrossing was rarely studied. In fact, the effect of parallel undercrossing of new double-track tunnels on the disturbance of existing tunnels may be greater than that of orthogonal or oblique undercrossing. Parallel undercrossing has a long disturbance distance and space-time effect, which might lead to 3D changes in the settlement and deformation of existing tunnels and endanger the operational safety of existing tunnels. erefore, it is necessary to conduct more research on the disturbance mechanism of new double tunnels parallel undercrossing existing tunnels over a short distance. For studying parallel undercrossing, although a model test is the most effective method to reflect the real process, the implementation of a model test is complex, expensive, and time-consuming. e theoretical analysis method has many assumptions. Moreover, it is difficult to solve, or the deviation in analytical results is too large for complex stratum and construction conditions. In contrast, the numerical simulation method is a good alternative to accurately evaluate the construction response (Li et al. [19]).
In this study, combined with the case of Hefei subway tunnel project, a numerical method was used to evaluate the disturbance mechanism of existing tunnel and ground caused by the construction of parallel double tunnels undercrossing over a short distance. e purpose of this study is not only to analyze the effect of parallel undercrossing construction mode on the safety of existing tunnels but also to assist engineers in developing effective construction risk control measures. e study mainly includes the following three parts. First, FLAC 3D finite difference software was used to build a 3D numerical model of a new double-line shield tunnel undercrossing the existing tunnel over a short distance in a parallel mode, and the effect of shield tunnel construction process on surface settlement, existing tunnel settlement, and lining internal force was analyzed. Second, the validity of model was verified using field monitoring data. Finally, based on the numerical model, the effects of change in stratum sensitivity on the settlement of existing tunnel, lining internal force, and surface settlement are discussed. In the conclusion and discussion section, the numerical simulation results are combined to analyze the risk control measures of this project.

Case Overview.
is paper is based on the case study of Hefei subway project in China. e plan view and spatial location of the project are shown in Figure 1. Subway line 1 was completed and put into operation. Subway line 5 is a new metro line. Figure 1(a) shows a planned overlapping area between lines 1 and 5, and the length of overlapping area is approximately 120 m. Figure 1 Combined with the stratum conditions of the project, the grouting method and high-pressure jet mixing method were used to reinforce the stratum within 3 m from the surface to the underground of the project to improve the strength and impermeability of stratum. C35 grade concrete was used for the lining of existing metro tunnel line 1. To reduce the disturbance to the existing tunnel, high-strength concrete C50 was used to improve the lining stiffness of line 5.

Regional Stratigraphic Conditions.
e stratum distribution and properties from the top to the bottom of the project are described as follows: e site is covered with Quaternary Holocene artificial miscellaneous fill ①: it is composed of broken bricks and domestic garbage. It is loose and dry and distributed on the surface of site with a thickness of 0.5-5 m. e test results of physical and mechanical parameters of rock strata in the geological investigation are shown in Table 1, and the values of these parameters are also required for numerical simulation. In addition, the groundwater level in these strata is mainly supplied by atmospheric precipitation, and the buried depth of groundwater level is in the range of 1.5-10.5 m. erefore, the effect of groundwater on the stratum and tunnel construction should be considered during the simulation.

Numerical Simulation Scheme
e FEM, DEM, and FDM are the three main numerical methods to analyze geotechnical engineering problems. In addition, the discontinuity layout optimization numerical method has unique advantages in the study of tunnel structure stability [20,21], but this study does not involve this aspect. e FEM has obvious advantages in the analysis of geometry, linear solution, phase field model, and the efficiency of dealing with complex problems [22,23]. e DEM is very suitable for simulating the deformation and failure of discrete particle assemblies under quasistatic or dynamic conditions [24,25]. However, the FDM seems to be more effective in the solution of deformation problems of geotechnical engineering, which is also the reason for selecting the FDM in this study.

Constitutive Model and Parameters.
e constitutive model of soil is the Mohr-Coulomb model; the lining of shield tunnel used a solid linear elastic model; the soil after excavation used a null element simulation. e isotropic seepage model was used in seepage simulation, i.e., the seepage difference in different directions was not considered. During building the calculation model, the physical and mechanical parameters of the soil layer in Table 1 were selected. e cohesion values, internal friction angles, and elastic moduli of materials in the reinforcement area increased by 20% compared with the mechanical parameters of soil materials [26]. e lining parameters of shield tunnel were selected according to the actual values of parameters, and the mechanical parameters of lining are shown in Table 2. Before tunnel excavation, the pore water pressure is hydrostatic pressure. In the seepage model, the four sides and the bottom of the model are impermeable boundaries, and the groundwater level is an impermeable boundary. After tunnel excavation, the pore water pressure of tunnel wall was fixed to zero.

Simulation
Steps. In the construction scheme, the right line of line 5 was first excavated and pushed forward at an average speed of 5 rings per day. After the right line is connected, the left line of line 5 was excavated again to keep the shield driving speed unchanged. e shield excavation length of line 5 is 120 m. e actual amount of excavation in a day during construction is 5-6 rings. In the calculation model, the shield excavation was divided into 32 steps, and each step is 7.5 m. erefore, the excavation of right line and left line of line 5 includes 16 excavation steps. e tunnel lining was simulated by one-time construction, and the soil mass after excavation was simulated by a null element. In the simulation, it was assumed that the pressure exerted on the excavation face by slurry-pressure-balance shield machine varies linearly with elevation and ground density. e stress at the top of tunnel is usually equal to 50% of the total stress at the invert of tunnel. In the actual construction process, an additional thrust force of about 28 kPa was applied to the excavation face. In this study, the face pressure at the tunnel axis was set as 302 kPa.

Numerical Monitoring Layout.
To obtain the numerical simulation monitoring results, during the construction of line 5, combined with the field monitoring measurement scheme, a monitoring section was arranged every 15 m for the operation of tunnel line 1, and four settlement monitoring points were selected on the tunnel section. e starting position of excavation was selected as the settlement monitoring section for surface settlement. e monitoring layout is shown in Figure 1

Reliability Verification of Numerical Model.
During construction, it is difficult to obtain the monitoring data of two existing tunnels in operation at the same time. erefore, the left line of line 1 nearest to the construction line was selected for monitoring in this project. e main monitoring content is the crown settlement of left section line of line 1. e location of field monitoring point is basically the same as that of numerical simulation monitoring point.
After the right line of line 5 starts tunnelling construction, field monitoring was carried out for line 1. e monitoring process is divided into two time periods: the right line and the left line of line 5. e field monitoring data are shown in Figure 3.  Figure 4. By comparing with Figures 3 and 4, it was found that the development trend of maximum settlement curve of arch crown calculated using FLAC 3D is consistent with the change trend of field monitoring results. e comparative analysis results of the maximum settlement and error of the vault obtained from field monitoring and numerical simulation are shown in Table 3. e maximum error between the numerical solution of maximum vault settlement and maximum vault settlement of field monitoring is 6.67%, and the average error is 5.01%. is result shows that the numerical model has considerable reliability and rationality.

Advances in Civil Engineering
In addition, from the simulation cloud chart of vertical soil settlement, it was observed that the effect of existing tunnel (metro line 1) on the ground settlement has obvious sheltering effect; the soil settlement above the two sides of existing tunnel is obviously smaller than that of soil in the middle of existing tunnel. e vertical displacement of soil mass produced by the successive excavation sequence of newly built double-track tunnel (metro line 5) has superposition effect. erefore, it is necessary to pay special attention to the change and control of soil settlement in the middle of existing tunnel during the sequential excavation of new double-track tunnel.    Advances in Civil Engineering displacement control of tunnel is 20 mm, and the settlement value obtained from numerical simulation of tunnel lining of line 1 satisfies the requirements of code. However, it should be noted that the lining of line 1 shield tunnel is an assembled structure connected by bolts. Excessive differential settlement on both sides of tunnel lining will increase the internal force of tunnel structure, which might induce structural cracks, concrete crushing, and water leakage. Figure 9 shows the simulation results of lining stress of left and right lines of line 1.    Advances in Civil Engineering Figure 9(a) shows that the maximum stress inside the lining of line 1 is 7.798 × 10 5 Pa when line 5 is not constructed, and the maximum stress is near both sides of arch crown. Figure 9(b) shows that after the construction of right line of line 5, the maximum stress of lining of line 1 is 9.314 × 10 5 Pa, an increase of 19% than that before the construction. e maximum stress is located near both sides of arch crown, and the stress near the arch bottom of side near line 5 increased most significantly. As the stress increased by 80%, the maximum stress gradually moved toward the arch bottom of one side near line 5. Figure 9(c) shows that after the double-track construction of line 5, the maximum stress inside the lining of line 1 is 1.124 × 10 6 Pa, 44% higher than that before the construction, and the stress at the vault is 1.036 × 10 6 Pa, 32% higher than that before the construction. At this time, the maximum stress is near the vault bottom of line 5. Before and after the excavation, the stress position and change in stress size are obvious. It is necessary to strengthen the monitoring of lining stress to prevent damage to the existing subway tunnel lining.

Effect of Stratum Change on Disturbance Effect
In some cities in China, metro shield tunnels are built in relatively poor soil conditions and with thick soft soil stratum, such as Shanghai, Shenzhen, and Guangzhou. At the same time, most of these cities have developed subway networks. erefore, it is necessary to verify whether the above reinforcement measures can ensure the safety of tunnel construction in the case of worse soil conditions. To study the disturbance to the existing subway caused by the parallel undercrossing construction of new tunnel under the condition of a poor soil layer or deep soft soil layer, based on the numerical model constructed in Section 2 of this paper, the thickness of a miscellaneous fill soil layer was increased to reduce the strength of soil layer. Using the method of stratum strength weakening, the sensitivity changes in surface settlement, existing tunnel settlement, and lining stress due to soil strength weakening were studied, providing a theoretical reference for similar engineering construction and design. In this paper, the scheme of soil layer strength weakening involves a change to the soil layers ② and ③ in Table 1 into a miscellaneous fill, and the parameters are shown in Table 4. After the soil layer strength is weakened, the simulation results of surface settlement, existing tunnel settlement, and lining stress are shown in Figure 10. By comparing Figures 3  and 10(a), it was observed that after the soil strength is weakened, the maximum surface settlement increased to 17.8 mm, 356% higher than that before the soil strength is weakened. e surface settlement is sensitive to the weakening of soil layer strength.
By comparing Figures 4,10(b), and 10(c), it was observed that after the strength of soil layer is weakened, the tunnel settlement of line 1 increased significantly, and the maximum settlement appeared at the arch waist of line 1. e maximum settlement is 18.8 mm, and the maximum settlement increased by 142% than that before the weakening. e settlement difference between the left and right sides of arch waist of line 1 reached 10.2 mm, an increase of 59% than that before weakening. is shows that tunnel settlement is very sensitive to changes in soil strength. Figures 7 and 10(d) show that the effect of stratum weakening on lining stress is not significant, but the initial stress of lining is changed due to tunnel excavation. (1) In this case, during the construction of a parallel undercrossing of an existing tunnel, a large settlement exists at the position of existing tunnel arch waist, and the settlement difference between the two  sides of arch waist is large. erefore, it is necessary to strengthen the monitoring of position of existing tunnel arch waist to prevent excessive settlement or settlement difference. If necessary, the soil layer should be grouted and reinforced in advance.

Conclusions and Discussion
(2) During a parallel underpass construction, the stress of existing tunnel lining is significantly affected, and the maximum stress of lining increased by 80%. To protect the operational safety of existing tunnel, the stress of existing tunnel lining should be monitored to prevent structural cracks caused by the excessive stress change in the existing tunnel lining. (3) After the strength of soil layer is weakened, the settlement of existing tunnel increases significantly. For a short-distance parallel shield construction project in an area with poor stratum conditions and deep soft strata, it is necessary to reinforce the strata and strengthen the monitoring of surface settlement to prevent damage to the existing buildings. During shield tunnelling, simultaneous grouting is used to reduce the disturbance to existing tunnel and surface. (4) A 3D numerical model of shield tunnelling undercrossing the existing tunnel was developed in this study. e simulation results are highly consistent with the field monitoring data. is shows that the numerical model and related parameters are reasonable and reliable. is study provides valuable information for the safe implementation of a project.

Data Availability
All data are included in the paper.

Conflicts of Interest
e authors declare that there are no conflicts of interest.