Soil Displacement of Slurry Shield Tunnelling in Sandy Pebble Soil Based on Field Monitoring and Numerical Simulation

Abstract

Due to its inherent advantages, shield tunnelling has become the primary construction method for urban tunnels, such as high-speed railway and metro tunnels. However, there are numerous technical challenges to shield tunnelling in complex geological conditions. Under the disturbance induced by shield tunnelling, sandy pebble soil is highly susceptible to ground loss and disturbance, which may subsequently lead to the risk of surface collapse. In this paper, large-diameter slurry shield tunnelling in sandy pebble soil is the engineering background. A combination of field monitoring and numerical simulation is employed to analyze tunnelling parameters, surface settlement, and deep soil horizontal displacement. The patterns of ground disturbance induced by shield tunnelling in sandy pebble soil are explored. The findings reveal that slurry pressure, shield thrust, and cutterhead torque exhibit a strong correlation during shield tunnelling. In silty clay sections, surface settlement values fluctuate significantly, while in sandy pebble soil, the settlement remains relatively stable. The longitudinal horizontal displacement of deep soil is significantly greater than the transverse horizontal displacement. In order to improve the surface settlement troughs obtained by numerical simulation, a cross-anisotropic constitutive model is used to account for the anisotropy of the soil. A sensitivity analysis of the cross-anisotropy parameter α was performed, revealing that as α increases, the maximum vertical displacement of the ground surface gradually decreases, but the rate of decrease slows down and tends to level off. Conversely, as the cross-anisotropy parameter α decreases, the width of the settlement trough narrows, improving the settlement trough profile.

1. Introduction

When constructing subways and high-speed railways, tunnels are typically used to traverse urban areas. Due to its construction advantages, shield tunnelling is commonly selected as the preferred method for building these urban tunnels [1]. However, as more cities join the wave of subway and high-speed railway construction, the engineering geological conditions the tunnels must navigate through are becoming increasingly complex, presenting numerous engineering challenges that urgently need to be addressed [2,3]. In China, these challenges include the collapsible loess layer encountered during the construction of the Xi’an Metro [4,5,6]; the composite strata with varying hardness faced in the metro and high-speed rail projects in cities like Guangzhou, Shenzhen, and Qingdao [7,8,9]; the peat soils in Kunming; the highly abrasive cobble layers in the river-crossing metro projects in Wuhan and Nanjing; and the sandy pebble soils encountered in the metro and high-speed rail constructions in Beijing and Chengdu [10,11]. Sandy pebble soil can be considered an extremely heterogeneous and loose geotechnical system consisting of a mixture of coarse and fine particles [12]. When tunnelling through this type of soil with a shield machine, the disturbances induced can lead to rock mass deformation and ground settlement, making it difficult to control the settlement magnitude and rate. Sandy pebble soil layers are widespread in Southwest China and the North China Plain [13], characterized by large voids between particles, a lack of cohesion, and high sensitivity. In the Beijing area, the spaces between the sandy pebbles are filled with fine sand, clay, and other small particles, resulting in a dense structure with localized cementation. This gives the soil high overall strength, making cutting tools more prone to wear, complicating shield tunnelling, and increasing the likelihood of disturbances to the surrounding strata.

In shield tunnelling-induced ground disturbances, the magnitude and distribution patterns of ground deformation have consistently been a focus of interest among tunnel research scholars. Engineering practice indicates that even with the most advanced shield tunnelling techniques, ground disturbances during excavation are unavoidable. These disturbances lead to stress redistribution, which in turn induces ground settlement and can impact the normal functioning of surrounding buildings and structures. Accurately predicting ground settlement patterns and assessing their impacts is of significant engineering importance for the planning, design, and construction of shield tunnels.

Numerous scholars have conducted a series of studies related to shield tunnelling in sandy pebble soil. Taking the launching section of a tunnel in the Chengdu Metro as the engineering background, Yang [14] conducted a preliminary exploration of slurry shield construction techniques in sandy pebble soil and analyzed the adaptability of the cutterhead and the reasons for excessive ground settlement. Zhang and Chen [15] focused on the water-rich sandy pebble soil in Beijing, analyzing the structural characteristics of various types of shield machines. They investigated the relationships between shield types and soil permeability, clay content, and particle size distribution. Zhao et al. [16] conducted a study on the surface settlement patterns during large-diameter slurry shield tunnelling in sandy pebble soil, but they primarily focused on the impact of tunnelling parameters on slurry shield construction, without providing a systematic analysis of ground deformation. Xu et al. [17] conducted a study on micro-disturbances induced by shield tunnelling and the corresponding control methods in sandy pebble soil. Compared with silty clay layers, they found that shield tunnelling in sandy pebble soil causes greater settlement and more significant disturbances to the ground. Moeinossadat et al. [18] demonstrated that surface settlement in sandy pebble soil is closely related to various shield tunnelling parameters, with grouting filling rate and grouting pressure identified as the most influential factors. Liang and Bai [19] focused on ground deformation control during shield tunnelling in sandy pebble soil, in their study of the new Line 17 of the Beijing Metro, the tunnel of which crosses above a water conveyance tunnel. Through field monitoring and numerical simulation, they investigated the optimal tunnelling parameters, deformation patterns, and control methods for shield tunnelling in this complex geological condition. Li et al. [11] studied the water ingress mechanisms and impacts during shield tunnelling in sandy pebble soil. Du et al. [20] proposed a composite analysis method to simulate tunnel excavation in sandy pebble soil. Their multi-scale analytical approach offers high efficiency in simulating tunnel excavation in sandy pebble layers without compromising accuracy in loose material representation.

Research on the movement and deformation patterns induced by shield tunnelling is quite advanced, but most studies focus on earth pressure balance shields and soft clay layers. There is relatively limited research on the deformation patterns and control methods for slurry shield tunnelling in sandy pebble soils, and field measurement data for shield excavation in such conditions are particularly scarce. This study uses the Tsinghuayuan Tunnel of the Beijing–Zhangjiakou High-Speed Railway as a case background to explore and analyze the ground disturbance induced by large-diameter slurry shield tunnelling in sandy pebble soil through field tests and numerical simulations. A correlation analysis was conducted on the main tunnelling parameters during the excavation process of the shield in both silty clay and sandy pebble soil. Sensors were installed on-site to monitor surface settlement and deep soil horizontal displacement, providing a substantial amount of valuable field data, particularly for deep soil horizontal displacement. Three-dimensional numerical simulations were conducted to analyze the ground disturbance caused by shield tunnelling. Optimized simulations of the transverse settlement trough were performed, yielding more accurate inversion results.

This paper is organized as follows. The background of the research is introduced in Section 1, including the discussions of the engineering background and shield tunnelling in sandy pebble soil. A brief introduction of the settlement principle induced by tunnelling is presented in Section 2. The research project is described in Section 3, including project overview and geological conditions, which provides basic data for this research. Field monitoring including tunnelling parameters, surface settlement, and horizontal displacement of deep soil, is described in Section 4 to contextualize the soil displacement induced by shield tunnelling. A numerical simulation of shield tunneling-induced soil displacement, especially for the optimized simulations of the transverse settlement trough, is presented in Section 5. Finally, some concluding remarks are offered in Section 6. The results of this study are useful in analyzing shield tunnelling-induced ground disturbance in sandy pebble soil in China and globally and represent an original contribution to the field measurement and numerical simulation analysis of large-diameter slurry shield tunnelling in sandy pebble soil.

2. Brief Introduction of Settlement Induced by Tunnelling

Tunnel construction will cause the relaxation of in situ stress and lead to the movement of soil to the formed hole, leading to deformation of the surrounding strata and generating pressure on the lining. The typical green field surface settlement trough related to tunnel excavation is depicted in Figure 1. It should be noted here that the green field condition refers to the surface deformation caused by tunnel excavation only, without other factors. According to Mair and Taylor [21], the components of ground movements can be listed as follows:

(a)

Deformations of the ground towards the face caused by stress relief.

(b)

Radial ground movements caused by over-cutting and ploughing.

(c)

Tail void, i.e., the gap between the tail skin of the TBM (tunnel-boring machines) and the installed lining.

(d)

Deflection of the lining with the development of ground loading. Consolidation settlement due to the changes in water pressure in the ground to their long-term equilibrium values.

It is obvious from Figure 1 that tunnelling is a three-dimensional problem. It is therefore necessary to consider a three-dimensional effect for both analytical and numerical convenience.

There have been many studies on the disturbance and movements of surrounding strata induced by tunnel excavation. Peck [22] first proposed an empirical Gaussian distribution curve to describe this transverse settlement trough. It is described by the following error function (geometrical details of the parameters are shown in Figure 2):

$$S_v(x)=S_{v\max }·\exp \left(-{\displaystyle \frac{x^2}{2i^2}}\right)$$

(1)

where S_v is the vertical displacement; S_vmax is the maximum vertical soil settlement at the centerline of the tunnel; x is the horizontal offset from the tunnel centerline; and i is the horizontal distance from the centerline to the location of the inflexion point.

In the process of tunnel excavation, in addition to the horizontal distribution of surface settlement, the longitudinal distribution of surface settlement is also particularly important. Attewell and Woodam [23] and Attewell et al. [24] proposed an empirical formula based on the Peck formula, which uses the error accumulation function to characterize the longitudinal distribution of surface settlement above the tunnel centerline, as shown in Equation (2):

$${\delta }_{\mathrm{z}}={\displaystyle \frac{V_{\mathrm{s}}}{\sqrt{2\pi }i}}\exp {\displaystyle \frac{-x^2}{2i^2}}\left[\mathsf{\Phi }\left({\displaystyle \frac{y-y_i}{i}}\right)-\mathsf{\Phi }\left({\displaystyle \frac{y-y_f}{i}}\right)\right]$$

(2)

where V_s is the volume of the transverse settlement trough per unit distance during tunnel excavation; y_i is the starting point of tunnel excavation; y_f is the location of the tunnel excavation face; and $\mathsf{\Phi }$ is the standard normal function. Based on this, the empirical formula for surface settlement has been extended to three-dimensional situations.

3. Project Description

3.1. Project Overview

The Tsinghuayuan Tunnel of the Beijing–Zhangjiakou High-Speed Railway extends for a total length of 6020 m. Construction was carried out simultaneously using two slurry shield TBMs, each with an outer diameter of 12.64 m. The tunnel excavation is divided into two segments: 2#~1# Shield Section and 3#~2# Shield Section. It is located in the bustling urban area of Haidian District, Beijing, where buildings and structures are densely concentrated and highly complex. The construction also involved crossing multiple subway lines, municipal roads, and utility pipelines. The tunnel lining was assembled using a 6 + 2 + 1 segment arrangement, with an inner diameter of 11.1 m and an outer diameter of 12.2 m. The thickness of the segments is 0.55 m. The TBM is designed with a maximum excavation speed of 60 mm/min. The maximum thrust and torque are 160,850 kN and 26,118 kN·m, respectively.

3.2. Geological Conditions

The 3#~2# Shield Section was selected as the subject of this study, as shown in Figure 3. The geological conditions in this section are complex and variable: the launching shaft at 3# is relatively shallow, with the excavation cross-section consisting entirely of silty clay. As the depth of the overburden increases, the excavation cross-section gradually transitions to a sandy pebble soil composed of sand, silty clay, and pebble soil. The pebbly soil content is approximately 60%, characteristic of a typical soft upper layer and hard lower layer stratum. As observed in the geological profile in Figure 3, the launch section from DK18+200 to DK18+100 is primarily composed of silty clay. Beyond this segment, the excavation is predominantly in the sandy pebble soil. Within this section, the pebble-bearing stratum extends for 3700 m, with the tunnel-boring machine excavating entirely through the pebble stratum for a distance of 2400 m. The pebble stratum covers a significant proportion of the excavation, with pebbles measuring 2 cm to 6 cm in diameter accounting for over 60% of the material. The largest pebbles exceed 15 cm in diameter. A core sample from the pebble stratum is shown in Figure 4. Due to severe over-extraction of groundwater in the suburban areas of Beijing, the water table is in a state of negative balance, leading to a significant supply–demand conflict. Consequently, there is little to no groundwater in the soil layers being tunneled through. Therefore, the impact of groundwater is not considered in this study.

4. Field Monitoring

This section reports the ground disturbance caused by large-diameter slurry shield tunnelling based on field monitoring considering tunnelling parameters, surface settlement, and the horizontal displacement of the deep soil.

4.1. Monitoring Scheme

Referring to the plan and longitudinal section diagrams of the Tsinghuayuan Tunnel shield section, as well as the feasibility of field testing, an open area within the shield section was selected for the installation of field monitoring equipment. A series of typical monitoring cross-sections of the stratum were selected, as shown in Figure 5. The monitoring range extends from DK17+600 to DK17+700, with the arrangement of the monitoring cross-sections shown in Figure 6. Surface settlement monitoring points were placed every 10 m along the surface above the tunnel axis. Monitoring cross-sections of the transverse surface settlement trough were installed every 50 m, with 5 m spacing between the transverse monitoring points. Horizontal displacement monitoring points for the deep soil were arranged from DK17+680 to DK17+692, as shown in Figure 6c. The deep soil horizontal displacement monitoring equipment after installation is shown in Figure 7. The physical and mechanical indexes of each soil layer at the monitoring section DK17+650 are shown in

Table 1. Physico-mechanical parameters of soil layers for the monitoring section.

Strata Layer	Bulk Density (kN/m3)	Young’s Modulus (Mpa)	Poisson’s Ratio	Friction Angle (°)	Cohesion (kPa)
Pavement	25.0	1366.00	0.30
Silt	20.1	41.25	0.30	25.2	14.3
Silty clay 1	19.9	37.00	0.30	18.4	33.8
Pebble soil	20.2	226.00	0.28	45.0
Silty clay 2	20.0	38.00	0.30	19.6	36.0

.

4.2. Shield Tunnelling Parameters

The reasonable selection and control of tunnelling parameters are crucial for tunnelling efficiency, cutter wear management, cutterhead protection, and surface settlement control. To evaluate the tunnelling performance of the shield machine in the sandy pebble soil, the monitoring interval from ring 1 to ring 447 of the 3#~2# Shield Section was selected for statistical analysis. The main tunnelling parameters in the sandy pebble soil and silty clay strata—specifically, shield thrust, cutterhead torque, tunnelling speed, and slurry pressure—were analyzed. The time history of the variation in the key tunnelling parameters within the monitoring interval is shown in Figure 8.

Figure 8a shows the time history of the total thrust of the shield machine as it progresses during tunnelling. During the initial launching stage, the shield thrust fluctuated significantly within the first 70 rings, and then the fluctuation amplitude decreased. Under different geological conditions, the average total thrust of the shield increased from 33,632 kN in the silty clay section to 48,586 kN in the sandy pebble soil, representing a 44.46% increase. Since the shield operation remained generally stable, the significant change in total thrust can be primarily attributed to the variation in geological strata. In the sandy pebble soil, maintaining a stable shield tunnelling speed requires a higher thrust to overcome the resistance encountered during the excavation process.

Figure 8b shows the variation of the cutterhead torque with the progress of tunnelling under different geological conditions. The average cutterhead torque increased from 5.75 MN·m in the silty clay section to 8.42 MN·m in the sandy pebble soil, an increase of 46.43%. This increase is primarily due to changes in geological conditions rather than variations in the tunnelling process caused by operator actions. In the sandy pebble soil, the physical and mechanical properties of the strata become more complex, and the significant increase in pebble content raises the resistance that the tunnelling tools must overcome to break the surrounding rock. This results in a substantial increase in the torque required by the cutterhead during excavation.

The tunnelling speed and slurry pressure directly reflect the tunnelling efficiency of the shield. Figure 8c,d show the statistical time series of slurry pressure and tunnelling speed, respectively. The setting of slurry pressure is crucial for maintaining stable excavation at the tunnel face. As shown in Figure 8c, the slurry pressure typically ranges from 0.1 bar to 2.0 bar, which is approximately 12.5% to 23.6% of the peak slurry pressure. The slurry pressure in the silty clay is more stable compared to that in the sandy pebble soil. In the sandy pebble soil, the slurry pressure continuously increases. The trend of slurry pressure is steadily rising, which is closely related to the depth of cover and the variations in the soil layers at the tunnel face. Unlike slurry pressure, the average tunnelling speed decreases from 20.49 mm/min in the silty clay to 18.23 mm/min in the sandy pebble soil, representing a reduction of 11.03%. Reducing the tunnelling speed appropriately allows the cutter tools to fully break up the harder pebbles at the bottom, thereby effectively reducing the wear on the tools caused by large-sized pebbles.

A preliminary analysis of the shield tunnelling parameters was conducted using the correlation coefficient. Correlation is used to measure the degree to which two variables deviate from being independent of each other. The correlation coefficients among the four parameters of the slurry balance shield—slurry pressure, shield thrust, cutterhead torque, and tunnelling speed—are presented in

Table 2. Correlation coefficients between tunnelling parameters.

Parameters	Slurry Pressure	Shield Thrust	Cutterhead Torque	Tunnelling Speed
Slurry pressure	1.0000	0.7726	0.7057	0.1459
Shield thrust	0.7726	1.0000	0.7019	−0.2377
Cutterhead torque	0.7057	0.7019	1.0000	−0.0558
Tunnelling speed	0.1459	−0.2377	−0.0558	1.0000

.

4.3. Surface Settlement Monitoring

The surface settlement trough induced by tunnel excavation typically resembles a Gaussian curve [22], meaning that the maximum surface settlement generally occurs directly above the tunnel axis. Figure 9 presents the surface settlement monitoring data collected from the Tsinghuayuan Tunnel’s 3#~2# Shield Section. The transverse surface settlement trough follows a Gaussian normal curve, with the maximum settlement at the tunnel centerline and gradually diminishing on both sides. Due to ground reinforcement in the shield launching section, the settlement values are relatively small. In the normal tunnelling section, the maximum surface settlement values mostly range from 10 mm to 13 mm. Surface settlement is effectively controlled, with the maximum surface settlement value being approximately 24 mm.

4.4. Horizontal Displacement Monitoring of Deep Soil

Horizontal displacements at different depths in the soil surrounding the tunnel can be obtained by measuring the variation in the angle between the inclinometer axis and the vertical plumb line. When monitoring deep soil horizontal displacement, the bottom of the inclinometer casing is used as a fixed point, and the horizontal displacement of the soil is measured at 1 m vertical intervals using an inclinometer. To offset measurement errors, each inclinometer casing is measured twice in both the horizontal and vertical directions. The measurement frequency is determined based on the shield tunnelling and ring assembly progress. When the cutterhead of the shield machine is within 20 m of the monitoring section, data are recorded after the completion of each ring, continuing day and night without interruption. Once the shield cutterhead moves more than 20 m away from the monitoring section, the data measurement frequency is reduced.

As shown in Figure 10, the sign conventions for horizontal displacements are as follows: for the tunnel cross-section, displacements towards the axis of the tunnel are considered positive; for the longitudinal section, displacements in the direction of the shield tunnelling are considered positive. The horizontal relative displacements measured at the monitoring section relative to the inclinometer bottom are shown in Figure 11. The time history of the horizontal displacements in the deep soil during tunnelling is illustrated in Figure 12.

As shown in Figure 11a and Figure 12a, before the shield machine reaches the monitoring section, the displacement values fluctuate within a range of −1~1 mm. This suggests that the tunnelling process causes minimal transverse disturbance to the soil before the shield machine reaches the monitoring section. As the shield machine passes through the monitoring section, the transverse displacement gradually shifts to positive values, indicating that the soil tends to move towards the tunnel axis. Before and after the shield machine’s tail passes through the ring, the ground displacement increases significantly. This is due to the fact that the backfill grouting has not yet hardened during the passage of the shield tail through the monitoring section, leading to substantial ground loss. As the shield continues to advance, the transverse movement of the soil tends to stabilize. At this point, the impact of shield tunnelling on the ground diminishes, and subsequent displacements are primarily due to soil consolidation and deformation. The maximum transverse horizontal displacement of the deep soil occurs after the shield tail passes, with a value of approximately 3.8 mm.

As shown in Figure 11b and Figure 12b, there is a noticeable difference between the longitudinal and transverse displacements of the deep soil. Approximately 10 m before the shield reaches the monitoring section, the longitudinal displacement is negative, meaning that the displacement direction is opposite to the shield tunnelling direction. As the shield machine reaches the monitoring section, the longitudinal displacement values show a significant increasing trend, indicating that the soil is moving in the direction of the shield tail. The displacement peak, which is approximately 15 mm, occurs 3~5 m after the shield tail passes through the monitoring section.

The law of horizontal displacement of deep soil in the transverse direction is as follows: Before the shield arrives, the horizontal displacement of the deep soil is not obvious. When the shield passes through, the soil on both sides of the shield machine moves toward the tunnel. During the passage of the shield tail, the displacement of the soil will fluctuate greatly and reach the maximum value. As the shield continues tunnelling, the soil displacement gradually stabilizes.

The law of horizontal displacement of deep soil in the longitudinal direction is as follows: Before the shield arrives, the longitudinal displacement of the soil is not obvious. When the shield passes through, the soil will move opposite to the driving direction because of the extrusion effect of the shield tunnelling machine. When the shield body passes through, the soil accelerates its displacement opposite to the tunnelling direction. The longitudinal displacement of the soil reaches the maximum value after the shield passes. As the shield continues tunnelling, the longitudinal displacement of the soil falls back to a stable value.

In summary, the horizontal displacement of deep soil primarily occurs during the passage of the shield machine through the monitoring section and after the shield tail has passed. Factors such as shield attitude adjustments, cutterhead over-excavation, uneven slurry pressure, and irregular backfill grouting pressure can all lead to variations and discrepancies in deep soil deformation.

5. Numerical Simulation

5.1. Numerical Modeling

A three-dimensional numerical model of shield tunnel excavation was established based on the actual engineering conditions and excavation environment of the Tsinghuayuan Tunnel. The tunnelling section corresponds to the Tsinghuayuan Tunnel from DK17+600 to DK17+700, as illustrated in Figure 13. Due to the symmetry of the model, only half of the structure is shown in the figure. The X-axis represents the tunnel width direction (transverse), the Y-axis represents the direction opposite to the tunnel axis (longitudinal), and the Z-axis represents the tunnel depth direction. Considering Saint-Venant’s principle and the influence range of tunnel excavation, the model extends 140 m in the X direction, 155 m in the Y direction (with 100 m from y = 0 m to y = 100 m representing the tunnel excavation section, and 55 m from y = 100 m to y = 155 m representing the extended influence zone), and 80 m in the Z direction. A transverse monitoring section is set at the surface along y = 50 m, and a longitudinal monitoring section is set at the surface along x = 0 m. The shield tunnel axis is buried at a depth of 23.32 m, and the tunnel crown is buried at a depth of 17.0 m. The shield has an outer diameter of 12.64 m, with each tunnel segment ring having a width of 2.0 m. The segment’s inner diameter is 11.1 m, and the segment thickness is 0.55 m. The shield machine body is 14 m long, equivalent to the width of seven segment rings.

The Tsinghuayuan Tunnel project of the Beijing–Zhangjiakou High-Speed Railway falls under the category of high-speed railway tunnels. China has stringent requirements for the longitudinal gradient of these tunnels. The maximum longitudinal gradient of the Tsinghuayuan Tunnel is 30‰, which meets the requirements of the Railway Tunnel Design Code (TB10003-2016). For the shield section studied in this paper, the depth variation of the tunnel from DK17+600 to DK17+700 is only 1.2 m, resulting in a longitudinal gradient of 12‰. At the monitoring section DK17+650, compared to DK17+600 or DK17+700, the tunnel depth variation is only 0.6 m, which constitutes just 3.5% of the depth at the monitoring section (17 m). Such a depth variation has a minimal impact on surface settlement. Therefore, this study does not consider the effects of depth variation and longitudinal gradient on surface settlement caused by shield tunnelling.

The boundary conditions in the numerical model are set as follows: In the X-axis direction of the model, horizontal constraints in the x direction are applied at the boundary surfaces of x = −70 m and x = 70 m. In the Y-axis direction, horizontal constraints in the y direction are applied at the boundary surfaces of y = 0 m and y = 155 m. These horizontal constraints in both the X and Y directions are intended to account for the surrounding soil’s restraining effects. A vertical constraint in the Z direction is applied to the bottom boundary surface of the model (z = 0 m), while the top boundary surface of the model (z = 0 m) is set as a free boundary.

In the numerical model, all soil materials are discretized with eight-node linear brick integration elements (C3D8), as well as the shield, lining elements, and grouting layer. It should be noted that the focus of this study is on ground deformation induced by shield tunnelling. Therefore, detailed simulation of the segmental lining is not conducted and the interactions between segment blocks, as well as between rings, are not analyzed. The interactions between the soil and the shield, the soil and the grouting layer, and the grouting layer and the lining are all simulated using contact surfaces. The contact behavior is modeled using a tied constraint (Tie contact). In the elastic stage, the stress–strain relationship of the soil is modeled using a cross-anisotropic elastic model. For comparative analysis, an isotropic linear elastic model is used in the comparison model. In the plastic stage, the modified Mohr–Coulomb yield criterion is applied. In order to implement the 3D cross-anisotropic elastic model, the modified Mohr–Coulomb yield criterion for the plastic stage had to be custom programmed and developed through secondary development. Therefore, both the stress–strain relationships in the elastic and plastic stages were obtained through custom programming via UMAT secondary development. These were then utilized in ABAQUS 6.14 by invoking the UMAT subroutine for the calculations. The shield structure, concrete lining structure, and concrete grouting layer structure are all modeled using a linear elastic model.

The physical and mechanical parameters of the soil are provided in Table 1, while the physical and mechanical parameters of the lining segments, grouting layer, and shield are detailed in

Table 3. Physico-mechanical parameters of shield tunnel.

Specification	Reinforced Concrete Lining	Backfill Grouting		Shield Machine
Bulk density (kN/m3)	25	22		76
Young’s modulus (MPa)	35,500	I-level	36	210,000
		II-level	50
		III-level	60
Poisson’s ratio	0.25	0.25		0.2
Thickness (m)	0.55	0.22		0.22

. It is worth noting that the properties of cement, such as the Young’s modulus and Poisson’s ratio, change as the grouting material hardens. The strength of cement increases from 0.6 MPa to 1.2 MPa after initial setting, indicating that the Young’s modulus undergoes significant changes as the grout hardens, while the Poisson’s ratio remains relatively stable. Therefore, following the simulation methods referenced in the works of Thomas and Gunther [25], Lambrughi et al. [26], and Michael et al. [27], the Young’s modulus is divided into three stages to account for the hardening process of the grouting layer over time, as shown in Table 3. The meshing of the 3D numerical finite element model was conducted manually. Since the soil elements surrounding the tunnel are of primary interest, the mesh around the tunnel was refined, while the mesh elements for the soil further away from the tunnel were gradually coarsened. Ultimately, the entire 3D model consists of 303,030 nodes and 277,760 elements.

5.2. Model Verification

To verify the validity of the numerical simulation, a comparative analysis was first conducted between the field measurements and the numerical simulation results of the transverse and longitudinal surface settlement troughs, as shown in Figure 14 and Figure 15. Since the settlement troughs are symmetrical along the vertical plane of the tunnel axis, only half of the surface lateral settlement troughs are displayed in this paper. As shown in Figure 14, the shape of the surface lateral settlement troughs is generally consistent, resembling a Gaussian curve. The transverse settlement trough obtained from the field measurements is noticeably narrower and deeper compared to that predicted by the numerical simulation; this discrepancy can be unfavorable for tunnel design and construction. As shown in Figure 15, the shape of the surface longitudinal settlement trough is also generally consistent, matching the cumulative distribution function curve proposed by Attewell and Woodman [23]. This indicates that the numerical simulation conducted in this study is effective.

A comparative analysis was conducted between the field measurements and numerical simulations of the deep soil horizontal displacement, as shown in Figure 16. The shape of the deep soil horizontal displacement from both the numerical simulation and the field measurements is generally consistent, though the field measurements show greater variability. This greater fluctuation is related to other disturbance factors present during the monitoring process. The longitudinal horizontal displacements induced by tunnel excavation are significantly larger than the transverse horizontal displacements. This indicates that, after excavation, the soil moves more noticeably towards the newly created excavation face, and longitudinal unloading of the soil more readily triggers displacement and movement. Therefore, during tunnel excavation, it is crucial to enhance monitoring of longitudinal deep soil horizontal displacement. If necessary, reinforcement measures should be implemented to prevent accidents caused by excessive displacement.

Overall, the results obtained from the numerical model of tunnel excavation in this study align well with the field measurements and are consistent with the patterns of ground disturbance caused by tunnel excavation. Therefore, it can be concluded that the numerical simulation used in this study is reasonable and effective.

5.3. Analysis of Surface Settlement Trough Considering 3D Cross-Anisotropy

The longitudinal settlement trough above the tunnel axis, obtained from three-dimensional simulations based on the traditional isotropic Mohr–Coulomb yield criterion, shows the development trend as the shield tunnel excavation progresses, as illustrated by the curves in Figure 17. As the shield tunnel advances from y = 10 m to y = 100 m, the longitudinal settlement curves at different excavation stages are provided at 10 m excavation intervals. In the initial stages of excavation, the shape of the longitudinal settlement trough resembles a cumulative error curve, which is commonly used to estimate the longitudinal settlement caused by tunnel excavation [23,28]. As the shield tunnel excavation progresses to y = 70 m, this trend becomes less apparent. When the excavation reaches y = 80 m, the longitudinal settlement curve exhibits a reverse curvature. Due to the boundary effect of the model, the settlement at y = 0 m first increases and then decreases. The maximum settlement occurs when the shield excavation reaches y = 80 m. The overall trend of the longitudinal surface settlement trough is consistent with the results obtained by Franzius et al. [28], with the exception of slight differences in the soil heave value in front of the shield cutterhead. This further confirms the feasibility and reliability of the three-dimensional numerical model used in this study.

The surface settlement trough calculated using the traditional isotropic Mohr–Coulomb model differs from the field measurements, with the field-measured surface settlement trough being relatively narrower and deeper. To address this issue, an anisotropic constitutive model is used for the numerical simulations, specifically the three-dimensional cross-anisotropic elastoplastic constitutive model (CAM model). Considering that the cross-anisotropy of the soil in the elastic stage can also reflect soil anisotropy, this approach can partially address the issues with the results obtained from three-dimensional simulations using the traditional isotropic Mohr–Coulomb yield criterion.

Figure 18 presents the transverse surface settlement trough considering the cross-anisotropy of the soil in the elastic stage, along with a parametric analysis conducted for different values of the corresponding parameters. For the case of $\alpha =1.0$ in Figure 18, the cross-anisotropic elastic stiffness matrix degenerates into the traditional isotropic elastic stiffness matrix defined by Hooke’s law. The results obtained from the CAM model under this condition are consistent with those calculated using the traditional isotropic Mohr–Coulomb model. The maximum vertical settlement along the tunnel axis increases as the degree of cross-anisotropy increases, meaning it becomes larger as the α value decreases. Furthermore, the shape of the surface transverse settlement trough becomes narrower and deeper as the α value decreases. When $\alpha <0.63$, the surface transverse settlement trough exhibits a pronounced narrow and deep characteristic. When $\alpha >0.63$, the normalized settlement trough becomes even wider than the one calculated using the isotropic Mohr–Coulomb model. This indicates that using the CAM model, which accounts for cross-anisotropy in the elastic phase, to simulate shield tunnel excavation can significantly impact the maximum vertical displacement of the surface transverse settlement trough and the normalized trough width caused by the tunnel excavation.

The relationships between the cross-anisotropic parameter α and the maximum vertical displacement and between the cross-anisotropic parameter α and the settlement trough width, are illustrated in Figure 19 and Figure 20, respectively. The relevant data for the settlement trough width are presented in

Table 4. Settlement trough width i obtained from the cross-anisotropic numerical simulation.

Cross-Anisotropic Parameter, α	Width of Transverse Settlement, i	R2	Deviation of Maximum Vertical Displacement Obtained from Simulation from the Field Data (%)
1	12.87	0.99	1.03
0.95	12.63	0.99	0.99
0.89	12.41	0.99	0.96
0.84	12.16	0.99	0.92
0.77	11.89	0.99	0.88
0.71	11.56	0.99	0.82
0.63	11.2	0.99	0.77
0.55	10.77	0.99	0.7
0.45	10.23	0.99	0.61
0.32	9.38	0.99	0.48

. As the parameter α increases, the maximum vertical displacement of the ground surface gradually decreases, but the rate of decrease diminishes, becoming more gradual. The width of the settlement trough calculated from the transverse settlement trough data obtained through three-dimensional simulations using the Mohr–Coulomb yield criterion embedded in ABAQUS is 10.44 m, with a linear fit evaluation metric R² of 0.99. The settlement trough width values obtained from the three-dimensional numerical simulations using cross-anisotropy are consistently larger than those measured on-site.

Also shown in Figure 20 and Table 4, as the transverse isotropy parameter α decreases, the width of the settlement trough gradually decreases, thus improving the accuracy of the settlement trough predictions. Furthermore, as the parameter α decreases, the maximum vertical displacement increases, leading to a greater deviation from the field data. This discrepancy may be attributed to the fact that the cross-anisotropic stress–strain relationship proposed in this study is based on improvements in the elastic phase. In the elastic phase, the deformation of the soil influenced by anisotropy tends to be more pronounced. It can be seen from Table 4 that when the cross-anisotropic parameter α changes from 1 to 0.32, the width of the transverse settlement changes from 12.87 to 9.38 (a decrease of 27%), and the maximum vertical settlement variation changes from 1.03 to 0.48 (a decrease of 53.4%). There is a significant difference in the magnitude of changes between the two, with the maximum vertical settlement being greater than the width of the settlement trough, indicating that the maximum vertical settlement is more sensitive to changes in the cross-anisotropy.

By optimizing the constitutive model and numerical model, the deformation law obtained from numerical simulation is basically consistent with the on-site monitoring results, but there are still deviations. This is because numerical simulation cannot fully simulate the actual situation on-site, and there are certain simplifications and assumptions. It only considers and analyzes the important influencing factors, which inevitably leads to certain discrepancies.

In order to reduce the soil displacement caused by the excavation of shield tunnels, many possible measures have been proposed. Appropriate tunnelling parameters can be adopted and adjusted in real-time to avoid surface settlement and uplift caused by uneven pressure [29]. The posture of the shield tunneling machine can be controlled to avoid unnecessary correction operations, thereby reducing the risk of soil settlement [30]. Timely grouting behind the wall will prevent soil displacement caused by the gap at the tail of the shield [31]. Stronger monitoring and feedback of soil displacement and taking effective measures in a timely manner will achieve the goal of controlling settlement [32]. For shield tunneling under special geological conditions, it is necessary to reinforce the strata to ensure the smooth excavation of the shield machine and to control surface settlement.

6. Conclusions

In this paper, field measurements and 3D FE modeling were carried out to evaluate the strata disturbance induced by shield tunnelling. Tunnelling parameters, surface settlement, and horizontal displacement of deep soil were analyzed and the following conclusions were drawn:

(1)

The tunnelling parameters obtained from the shield machine were analyzed during tunnelling from silty clay to sandy cobble soil. The cutterhead rotational speed remained at a relatively stable level, while the tunnelling speed decreased slightly. However, due to the change in geological conditions, the thrust increased by a notable amount. In sandy pebble soils, the thrust increased by 44.46%. The force required for the shield machine to propel forward was larger than the thrust in silty clay, resulting in increased torque. When the shield excavation encounters adverse geological conditions, it simultaneously leads to significant changes in slurry pressure, shield thrust, and cutterhead torque. Moreover, these three parameters exhibit a strong correlation in their variations.

(2)

By installing monitoring equipment on-site to measure surface settlement and deep soil horizontal displacement, data were collected on surface settlement and deep soil horizontal displacement at typical monitoring sections during shield tunnelling. The field measurements indicate that surface settlement values fluctuate significantly in silty clay sections but remain relatively stable in sandy pebble soil. The horizontal displacement of deep soil primarily occurs during the passage of the shield machine through the monitoring section and after the tail void. The longitudinal horizontal displacement of deep soil is significantly greater than the transverse horizontal displacement. Attention should be primarily focused on longitudinal horizontal displacement, and protective measures should be implemented when necessary.

(3)

A three-dimensional finite element numerical simulation was conducted to analyze the surface settlement and horizontal displacement of the deep soil induced by shield tunnelling. The use of a cross-anisotropic constitutive model effectively accounts for the anisotropy of the soil, thereby providing corrections and improvements to the numerical simulation results for surface transverse settlement troughs caused by shield tunnel excavation. A sensitivity analysis of the cross-anisotropic parameter α revealed that as α increases, the maximum vertical displacement of the ground surface gradually decreases, but the rate of decrease slows down and tends to level off. Conversely, as the cross-anisotropic parameter α decreases, the width of the settlement trough narrows, improving the settlement trough profile.