Structural displacement and deformation of adjacent shield tunnel induced by foundation pit excavation

Excavating a foundation pit close to a tunnel will unavoidably impact the nearby soil, causing the tunnel to shift and deform. Examining the longitudinal displacement and convergence deformation of a nearby shield tunnel during foundation pit excavation is crucial for maintaining safe operations. Nevertheless, most of the current research primarily focuses on the effects of a single foundation pit excavation on existing tunnels. This study examines and analyzes the effects of multiple foundation pit excavations on the displacement and deformation of pre-existing tunnels, using a project at a subway station as a case study. By employing the PLAXIS three-dimensional finite element software, a large-scale computational model based on the HS model is established, and then five dangerous working conditions are selected for simulation analysis. The research findings delineate that: (i) The displacement of the tunnel is affected by various factors. These encompass the magnitude of the foundation pit excavation, the positioning of the foundation pit excavation in relation to the tunnel, and the closeness of the tunnel to the foundation pit. (ii) The deformation encountered by the tunnel is largely influenced by external loads, where the scale of the unloading load primarily determines the deformation characteristics of the tunnel.


Introduction
With the rapid growth of Chinese society and the deepening of urbanization, the number of urban populations in China is increasing rapidly, which poses a great challenge to the urban public transport space [1,2].With the swift expansion of the tunnel construction scope, the count of foundation pit excavation projects near these tunnels is also escalating daily.The digging of nearby foundation pits generally unloads the surrounding soil, modifying the stress condition of the subsurface terrain.This can trigger a series of damaging impacts on the pre-existing tunnels within the nearby influence radius.In case the alterations in displacement and deformation of the tunnel surpass the load-bearing capability of the segment structure, there could be problems such as segment cracking and water leakage, this could considerably jeopardize the secure functioning of the tunnel [3][4][5][6].
The primary methodologies employed in current research encompass field observation, model experimentation, theoretical examination, and numeric modelling.In terms of field measurement, Wei et al. [7] first analyzed the influence mechanism of foundation pit excavation above the tunnel on the deformation of the existing tunnel, and then used the measured data to compare with the theoretical analysis data to verify the reliability of the formula.However, there is a lack of research on lateral unloading.In the aspect of model test, Xiang et al. [8] measured the influence of loading, unloading and excavation on tunnel settlement and additional stress in soft clay by indoor model test; Wei et al. [9] further delved into the protective impact of the embedded isolation pile system on the pre-existing tunnel during the excavation of the adjacent foundation pit.Chen et al. [10] examined the impact of excavation on tunnels with varying overburden depths using centrifugal testing methods.Although the data obtained by field measurement and model test are more realistic than other methods, both have the disadvantages of long test period and high cost.
About theoretical analysis, current methods typically simplify the shield tunnel to be akin to a Winkler foundation-Euler-Bernoulli beam.The final calculations of tunnel deformation, brought about by unloading effects of foundation pit excavation above the shield tunnel, make use of the Mindlin solution.Yet, these calculations do not factor in the soil foundation parameters within the disturbed area that resist the uplift of the tunnel post-excavation.Similarly, there is a lack of in-depth analysis along the longitudinal direction of the tunnel.Thus, Liu et al. (2019) implemented the Vlasov foundation-Timoshenko beam computation model [11][12][13].
Regarding numerical simulations, Huang et al. [14] and Hu et al. [15] used varying 3D finite element analysis software to imitate the impact of the additional deformation and internal force on the tunnel beneath, caused by excavation of adjacent and above foundation pits.They compared the results with the field monitoring data; however, the failure mode of the tunnel structure was not analyzed; Zhang et al. [16] suggested a dual-phase analysis technique to investigate the impact of foundation pit excavation on the longitudinal stress and distortion of nearby tunnels.They compared the outcomes of theoretical analysis with numerical simulation results, aiming to decrease the computational load; Using FLAC3D, Lin et al. [17] calculated the variation in tunnel displacement under diverse foundation pit lengths, widths and relative positions between the tunnel and foundation pit.They determined the impact range of the foundation pit excavation on the tunnel.
In this study, the three-dimensional finite element software, PLAXIS, is utilized to examine the effects of foundation pit excavation at a subway station on neighboring subway tunnels.The tunnel displacement and deformation resulting from foundation pit excavation under five hazardous scenarios are computed and analyzed.

Engineering project
As illustrated in Figure 1, the external operations having an impact on subway functionality include: (1) the primary excavation pit of the new subway station, (2) the supporting excavation pit of the same new station (3) the excavation pit that encompasses the new subway and the existing subway's transfer hall.The transfer hall, a pivotal component in this project, is integrated with an existing subway line station and positioned directly atop the existing subway infrastructure.

Figure 1. Top view of engineering site
The new station's primary excavation pit (Zone 1) has a total length of approximately 170 meters.The standard section's width measures roughly 26.9 meters, while the shield end section has a width of around 31.4 meters.The excavation depths for the standard and shield end sections are 34.3 meters and 36.3 meters, respectively.A diaphragm wall, 1500 mm thick, acts as a divider between the minor mileage end well and the main pit.This primary pit is comprised of two separate pits.Station auxiliary foundation pit (Zone 2) contains a two-story underground structure, with a depth of approximately 15 meters.A continuous subterranean wall, 800 mm in thickness and 38 meters deep, surrounds the onsite construction.The transfer hall foundation pit (Zone 3) includes a basement level, with a pit depth of about 8.2 meters.To minimize interference with the subway tunnel, the foundation pit is divided into four distinct areas (I, II, III, IV) and consists of 6 separate pits (A, B, C, D, E, F), as indicated in Figure 2.
Using the three-axis mixing pile (SMW) method, the soil inside the foundation pit is strengthened.By utilizing the SMW method, it substantially improves the load-bearing capability and compression resistance of the soil strata.Simultaneously, to minimize disturbances to the existing tunnel, the highpressure jet grouting method (MJS) is applied for reinforcing the soil surrounding the tunnel.The MJS process injects cement slurry into the soil layer through a rotating high-pressure nozzle, blending it with the soil.Excess soil is discharged to form a continuous, overlapping cement reinforcement, as illustrated in Figure 3.

Shield segment
The pre-existing subway shield tunnel segment features a single-layer lining with an internal diameter of 5.5 meters.This segment has a thickness of 0.35 meters, a ring width of 1.2 meters, and is constructed using C50 concrete.The entire ring of the segment is divided into one capping block C1 (20°), two adjacent blocks A1 and A2 (67.5°), and three standard blocks S1, S2, and S3 (68.75°), as depicted in Figure 4.The two adjacent blocks are connected using two bolts, each having a diameter of 30 mm, a bolt hole diameter of 39 mm, and a bolt grade of 5.8.The segment uses a staggered joint assembly strategy, which enhances the stiffness of the ring's joint and restricts joint deformation.As a result, the ring can be approximately considered as having homogeneous stiffness.

Numerical calculation model
In order to precisely assess the influence of this project's construction on the current shield tunnel, the commercial finite element analysis tool, PLAXIS 3D, is employed for conducting an elastic-plastic evaluation using the continuous medium finite element approach.A simplified model of the project can be seen in Figure 5.A reasonable selection of the model size, considering the interaction range between the two tunnels, helps to minimize the influence of boundary conditions on the calculation results.The dimensions of the computational model are 300m (X direction) × 135m (Y direction) × 60m (Z direction), with the entire project's conditions established within the same model.

Constitutive model and working condition definition
Currently, there are three categories of soil constitutive models applied in calculation and analysis of foundation pit excavation: (1) Elastic model; (2) Elastic-plastic model; (3) Viscoelastic-plastic model.[18] For this project, a soil hardening model (HS model) is utilized for the soil material and the pilesoil interface.The HS model was established by T. Schanz et al., [19] based on the Duncan-Chang model.This model can capture not only the nonlinear characteristics of soil stress-strain relationship, but also the complex stress pathway of geotechnical engineering.[20] In contrast to the ideal elasticplastic model, the yield surface of the soil hardening model does not remain stationary in the principal stress space.Rather, it changes as plastic strain begins to develop.The HS model is a sophisticated tool capable of mimicking the behaviour of diverse soil types, ranging from soft to hard soils.It's commonly used in finite element simulations for projects such as foundation pit digging and shield tunnel propulsion.The simulation outcomes align closely with the real-world conditions, consequently contributing to extensive experience in finite element simulation calculations [21,22].Figure 6 illustrates the layout of the soil layers.Table 1 displays the parameters of the soil in the threedimensional model.The boundary of the model is formed according to typical limitations.The side boundary surfaces have horizontal restrictions (UX = 0 in the X direction, UY = 0 in the Y direction), while the base of the model has vertical restrictions (UZ = 0).Figure 7 demonstrates these boundary limitations.Meanwhile, Figure 8 shows the divided mesh.

Result analysis
Tables 2 and 3 present the variations in displacement of the existing subway under five different operational circumstances.In the context of horizontal deformation (Deformation), 'L' signifies westward movement, while 'R' represents eastward movement.For vertical displacement (TZ), '-' indicates settlement, and '+' denotes uplift.Our calculations reveal the following observations as illustrated in Table 2: Relevant to vertical movement, the initialization of working condition 1 on the left line instigates vertical settlement displacement in the tunnel, reaching a maximum of -7.6mm.Further excavation within the super incumbent foundation pit results in uplift, or what's known as vertical floating displacement of the tunnel, which reaches its peak of 8.10mm under working condition 3. Considering horizontal displacement, initiation of working condition 1 triggers significant deformation of the tunnel towards the side of the lateral foundation pit, where substantial excavations take place.During ongoing excavation in the super incumbent foundation pit, the horizontal deformation of the tunnel gradually recedes, persisting until the implementation of working condition 5.
In relation to vertical movement, the maximum settlement of the right line also takes place during working condition 1, with a peak settlement value of -8.10mm in Table 3.Even though subsequent excavation in the overlying foundation pit introduces floating displacement in the tunnel, the right line stays predominantly near the lateral foundation pit-the area with maximum excavation.Consequently, the tunnel exhibits a sustained propensity towards settlement.As for horizontal displacement, the right line is more susceptible to lateral foundation excavation than the left line, resulting in more pronounced deformation of the tunnel towards the excavation side of the foundation pit.

Conclusions
This study, set against the excavation of a foundation pit for a subway station, examines the impact of multiple foundation pit excavations on the displacement and deformation of existing tunnels.The conclusions drawn are as follows: (1) Numerous factors shape the displacement a tunnel undergoes, such as the volume of the adjacent foundation pit's excavation, the intrinsic spatial relationship between the excavation and the tunnel, as well as how close the tunnel is to the foundation pit.The impact on the displacement of a tunnel is much more pronounced when the amount of excavation in the foundation pit is significant in comparison to when it's relatively minimal.Excavation undertaken towards the side of the tunnel tends to cause the tunnel to settle, whereas excavation above the tunnel prompts an upward or 'floating' movement of the tunnel.Moreover, the nearer the foundation pit's location is to the tunnel, the greater the impact on the tunnel's displacement.
(2) Both the left and right tunnel lines exhibit horizontal deformations, and these deformations are directed towards the foundation pit with the most extensive excavation.This indicates that tunnel deformation predominantly responds to external load factors.Consequently, the volume of excavation, or namely the quantity of the unloaded load, is a decisive element influencing the manner in which tunnel deformation manifests.

Table 2 .
Left line displacement change table

Table 3 .
Right line displacement change table