Deformation Analysis of Wall-Pile-Anchor Retaining Structures During Shield Tunneling Considering Tunnel-Pit Spatial Interaction

Abstract

In recent years, the increasing complexity of shield tunneling environments has made it critical to control the deformation of adjacent excavation structures and surrounding soils. This study employs numerical simulation using MIDAS GTS/NX to comprehensively analyze the spatial interaction factors between shield tunnels and wall-pile-anchor-supported foundation pits. Structural parameters of the retaining system and tunneling conditions are also evaluated to identify the key factors influencing construction-induced deformation. The results show that the maximum settlement of the adjacent retaining wall occurs when the tunnel burial depth reaches 1.4L, where L is the height of the diaphragm wall. In addition, when the horizontal distance between the tunnel and the excavation is less than 0.75D (D being the tunnel diameter), significant settlement deformation is observed in the nearby support structures. A linear correlation is also identified between the variation in tunnel crown settlement and the excavation depth of the overlying pit during tunnel undercrossing. Furthermore, sensitivity analysis indicates that increasing the embedment depth of the diaphragm wall effectively reduces horizontal displacement at the wall base. Increasing the wall thickness decreases displacement in the upper section of the wall. Similarly, increasing pile diameter and anchor length and diameter, while reducing the inclination angle of anchors, are all effective in minimizing the lateral displacement of the support structure.

1. Introduction

In densely built urban environments, shield tunneling often faces severe spatial and temporal constraints. It is common for construction to occur close to existing tunnels, underground stations, commercial basements, pipelines, and surface buildings [1,2]. Excavation by shield machines induces soil disturbances and deformation in nearby structures, which, in extreme cases, may lead to ground fissuring and structural damage [3,4,5]. Therefore, understanding the deformation behavior of surrounding soils and adjacent infrastructure due to tunnel excavation and implementing effective control measures has become a critical topic in tunnel engineering [6].

When a shield tunnel crosses a foundation pit, the engineering challenge lies in ensuring both the safety of tunneling operations and the deformation control of nearby retaining structures [7,8]. Addressing this challenge requires two strategies: first, a comprehensive study on the interaction between tunneling and nearby excavations to guide practical engineering; second, the adoption of advanced or composite retaining systems to improve pit stability and reduce deformation risk [9].

Previous studies on the influence of shield tunneling near foundation pits have primarily focused on simplified support systems such as diaphragm walls or pile walls [10,11,12]. However, modern deep excavations are often subject to higher technical demands, particularly in permanent or sensitive construction zones [13,14]. These include strict limits on wall displacement, base heave, and surface settlement [15]. While several predictive methods have been proposed, for example, analytical solutions under homogeneous soil assumptions or elastic foundation beam models incorporating lining nonlinearity approaches, they may not capture complex geological or boundary conditions [16,17,18,19,20]. Simplified beam models, such as the Winkler or Pasternak type, often underestimate tunnel uplift, particularly when ground–structure interaction is significant [21,22,23].

Experimental studies using scaled physical models have also provided insights into deformation behavior when shield tunnels pass beneath retaining walls [24,25]. Tests in sandy soils have shown that when the tunnel face passes 1.7 times the tunnel diameter beyond the wall monitoring section, wall deformation tends to stabilize [26,27]. However, such tests are costly and their applicability under complex subsurface conditions remains limited. Numerical modeling, by contrast, offers flexibility, efficiency, and control over geological and structural parameters, making it a preferred method for such analyses [28]. For example, simulations using a small-strain hardening model have shown that the settlement of diaphragm walls increases rapidly when the angle between the wall base and tunnel invert exceeds 32° [29]. Other studies have used spring elements to simulate tunnel-soil interaction and examined stress and deformation responses in large diaphragm walls [30,31]. Three-dimensional simulations have also been developed to assess shield tunneling effects on nearby station structures, including retaining walls, slabs, and uplift piles [32]. Additionally, compared with a single support element, the composite wall–pile–anchor support system provides higher overall stiffness and deformation resistance in deep excavations and adjacent tunnel construction. The load-bearing mechanism of this system is characterized by the coordinated action of the retaining wall, foundation piles, and anchors. Previous studies have demonstrated that the system can significantly reduce the horizontal displacement at both the wall crest and the pile shaft, while the active tensile force of the anchors helps redistribute the bending moment in the wall and the shear force in the piles, thereby improving the overall structural performance [33,34]. Within the context of tunnel–excavation spatial interaction, the multi-component coupling effect of this composite system becomes particularly prominent, such as the retaining wall offering continuous soil-retaining capacity, the foundation piles enhancing both vertical and lateral load-bearing capacity, and the ground anchors controlling the upper excavation displacement while alleviating stress in the lower structural elements. Moreover, three-dimensional finite element studies have further shown that variations in the parameters of individual components can exert a significant influence on the deformation of adjacent tunnels and the stability of the excavation [35,36,37]. In summary, although many researchers have investigated tunnel–excavation interaction, most focus on worst-case deformation scenarios [38,39]. Studies addressing the mechanical behavior of composite wall-pile-anchor systems and their response to shield tunneling-induced secondary deformation remain limited [40,41,42].

In this study, a comprehensive numerical investigation is conducted to explore the spatial effects of shield tunneling adjacent to wall–pile–anchor–supported foundation pits. A series of 3D finite element models is established to evaluate different tunnel depths, horizontal clearances between the tunnel and pit, and excavation depths. The deformation behavior of both retaining and tunnel structures is analyzed. Moreover, a parametric sensitivity study is carried out to assess the influence of key design parameters such as wall embedment depth, wall thickness, pile diameter, and anchor properties on lateral deformation, thereby providing theoretical guidance for deformation control during shield tunnel construction.

2. Methodology

2.1. Fundamental Assumptions of the Model

Finite element modeling was conducted using MIDAS GTS/NX software (2024R1), with the following basic assumptions applied in the numerical simulation: The soil was assumed to be a homogeneous elastoplastic material, and each soil layer was uniformly distributed across the construction site. The diaphragm wall, piles, capping beam, anchors, and tunnel segments were modeled as linear elastic structures. To account for the influence of segmental joints during assembly [43], the strength of the tunnel segments was reduced by 15%. The initial stress field considered only the self-weight of the soil. The interface friction between the shield machine and the soil during tunneling was neglected. Groundwater pressure was included in the model, and the groundwater level was set to a stable confined water level at 10.8 m below the surface, based on the geotechnical investigation report. Seepage effects were not considered. Regarding the construction sequence, the excavation of the foundation pit was simulated first. After the deformation of the pit stabilized, the excavation of the shield tunnel was subsequently modeled. It should be noted that the simplified assumptions of neglecting seepage effects and interface friction may underestimate the deformation responses of the soil and the supporting structures in highly permeable strata or under high groundwater pressure conditions. However, in this project, the groundwater table is stable, the overlying soil exhibits low permeability, and the shield tunneling depth is relatively large. As a result, the instantaneous hydraulic gradient within the construction disturbance zone is limited, and the influence of this simplification on the computational results is expected to be minimal.

In the selection of the strain formulation for the simulation, the large-strain formulation can account for geometric nonlinearity under large deformations. However, under the millimeter-scale deformations considered in this study, its advantages are negligible. Since the deformation magnitude in the present working conditions is far smaller than the overall model dimensions, the small-strain formulation can maintain calculation accuracy while reducing computational complexity and convergence difficulty. Therefore, the small-strain formulation was adopted for strain measurement in the model calculations.

2.2. Finite Element Mesh and Boundary Conditions

In this study, the lateral influence zone of shield tunneling was defined as a range of 3D to 5D, where D represents the outer diameter of the shield. The vertical extent of the model extended 20 m below the tunnel invert. A foundation pit, significantly affected by tunneling and used for instrumentation, was modeled with dimensions of 48 m × 30 m × 10 m. The overall model size was set to 120 m in length, 120 m in width, and 50 m in height.

In the model, the soil and tunnel segments were represented using 3D hexahedral solid elements. The shield shell and diaphragm walls were modeled using 2D plate elements. The capping beam and piles were simulated with 1D beam elements, while anchors were represented by 1D embedded truss elements. As shown in Figure 1.

The coordinate system was defined such that the long side of the foundation pit aligned with the X-axis, the short side with the Y-axis, and the Z-axis was vertical. The model base was fully constrained in the X, Y, and Z directions. Normal displacement was restricted on the lateral boundaries, while the top surface was left free. All 1D elements in the model had their rotational degrees of freedom constrained. During tunneling, the grouting process was simulated by modifying the material properties of the soil in the designated grouting zone. In this model, the horizontal boundaries were placed at a distance of 3–5 times the tunnel diameter from the outer edge of the tunnel, and the bottom boundary was set 20 m below the tunnel invert to mitigate boundary constraint effects. Validation results showed that, under this arrangement, the variations in structural and soil deformations did not exceed 3%, ensuring that the computational results were not significantly affected by the boundary conditions.

A gravity load was applied to the entire model. As shield tunneling progressed, face pressure was applied at the excavation face. After each excavation step, lining segments were installed, followed by tail grouting where grouting pressure was applied and activated in the corresponding region. Based on tunnel depth, site conditions, and surface loads, the face pressure was set to 0.2 MPa, the grouting pressure to 0.3 MPa, and the stress release ratio during excavation was set at 25%. As shown in Figure 2.

During construction, surface water was drained through open channels, and groundwater remained relatively stable. The upper perched water table was minimal, so the groundwater level in the model was defined as a stable confined aquifer located 10.8 m below the ground surface.

2.3. Soil Constitutive Model and Material Parameters

(1)

Modified Mohr–Coulomb constitutive model

The constitutive model of soil describes the relationships among stress, strain, time, and strength, and is widely applied in numerical simulations of construction processes [44,45,46]. The geological strata in this study primarily consist of silty clay, silt, and silty sand. Under the disturbance of shield tunneling, the dominant deformation mechanisms are elastoplastic shear and partial rebound rather than long-term consolidation compression. This makes the applicability of the Cam-Clay model, which is commonly used for the consolidation analysis of saturated cohesive soils, relatively limited in this context. In addition, the parameters of the Cam-Clay model rely heavily on high-quality triaxial consolidation test data, which are difficult to obtain comprehensively under site investigation conditions. Considering both applicability and computational efficiency, and by comparison with advanced constitutive models such as the Hardening Soil and Hardening Soil with Small-Strain Stiffness (HS Small) models, the modified Mohr–Coulomb model offers clear advantages in terms of parameter accessibility, computational stability, and adaptability to large-deformation elastoplastic shear behavior. This is particularly suitable for engineering studies involving multi-condition three-dimensional finite element analyses, meeting the requirements of this research for investigating the spatial interaction mechanisms between shield tunneling and foundation pits [47,48,49]. For this reason, the modified Mohr–Coulomb model is adopted in this study.

(2)

Soil parameters

The required parameters for the modified Mohr–Coulomb model include soil unit weight, internal friction angle, cohesion, Poisson’s ratio, secant stiffness from triaxial tests ($E_{50}^{ref}$), tangent stiffness from oedometer tests ($E_{oed}^{ref}$), and the unloading-reloading modulus ($E_{ur}^{ref}$) [50].

The tangent stiffness $E_{oed}^{ref}$ is taken as the soil compression modulus. For $E_{50}^{ref}$, a value of $E_{50}^{ref}=2E_{oed}^{ref}$ is used for soft clay, while silty and sandy soils use $E_{50}^{ref}=E_{oed}^{ref}$. For the unloading-reloading modulus $E_{ur}^{ref}$, soft clay takes 4$E_{50}^{ref}$ and sand takes 3$E_{50}^{ref}$. The detailed geotechnical parameters are listed in

Table 1. Geotechnical properties of soil layers.

Layer Number and Soil Type	Unit Weight γ (kN/m)	Cohesion c (kPa)	Internal Friction Angle ϕk (°)	Compression Modulus Es(1–2) (MPa)	Poisson’s Ratio v
Miscellaneous fill	19.1	15	15	3.0	0.37
Silty clay	19.5	30	20	7.2	0.33
Silty clay	20	32	18	7.5	0.32
Silt	20.6	28	24	10.5	0.31
Silty sand	21.6	1	35	12	0.29
Silty clay	20.3	30	27	8	0.32
Silt	20.5	26	23	9.5	0.31

. To improve mesh quality in the finite element model, the layer thicknesses were rounded to the nearest integer based on average values, as shown in

Table 2. Assigned soil layer thicknesses in the numerical model.

Formation Name	The Thickness of Soil Layer in the Model (m)
Miscellaneous Fill	2
Silty Clay	3
Silty Clay	3
Silt	5
Silty sand	10
Silty Clay	17

.

(3)

Structural material parameters

The diaphragm wall, piles, and capping beams were modeled using C35 concrete, while the tunnel lining segments were made of C50 concrete. To account for the stiffness reduction due to staggered assembly of the segmental rings, a reduction factor of 0.85 was applied to the segment stiffness. Detailed material parameters used in the model are listed in

Table 3. Material properties for structural elements.

Structural Elements	Elastic Modulus E(MPa)	Density ρ (kg/m3)	Poisson’s Ratio μ
Shield shell	2.1 × 105	8 × 103	0.30
Tunnel segment	2.93 × 104	2.35 × 103	0.25
Ground anchor	2.0 × 105	7.7 × 103	0.2
Wall, pile, and tie beam	3.15 × 104	2.35 × 103	0.25

.

(4)

Monitoring point layout

The layout of monitoring points for the support structure deformation and ground surface settlement during shield tunneling is shown in Figure 3. Displacement monitoring points, including both horizontal and vertical directions, were installed along the top of the retaining wall and numbered K1 through K12. The spacing between monitoring points was 15 m along the short sides of the excavation and 12 m along the long sides.

3. Experimental Processes

(1)

Tunnel burial depth scenarios

During tunnel excavation, unloading of the surrounding soil can lead to settlement in adjacent strata, which in turn causes deformation of the retaining system composed of walls, piles, and anchors [51,52,53]. To investigate the influence of tunnel depth on the settlement behavior of this retaining system, several computational scenarios were developed based on practical engineering experience. Numerical simulations were conducted for tunnels at different depths adjacent to wall-pile-anchor-supported excavations, as summarized in

Table 4. Support schemes for excavations under various tunnel depths.

Scenarios	1	2	3	4	5	6
Tunnel burial depth (m)	10	12.5	15	17.5	20	22.5
Excavation depth of foundation pit (m)	10	10	10	10	10	10
Horizontal distance between tunnel and foundation pit (m)	0.5D	0.5D	0.5D	0.5D	0.5D	0.5D

.

(2)

Horizontal clearance between tunnel and excavation

To evaluate the impact of horizontal distance between the tunnel and the excavation on support settlement, two representative burial depths—17.5 m and 20 m—were selected, which correspond to cases with significant support deformation. Various tunnel-to-excavation horizontal clearances were set, and settlement at the base of the retaining system was computed under each condition. The layout of simulation scenarios is provided in

Table 5. Construction schemes with varying tunnel-to-excavation horizontal clearances.

Scenarios	1	2	3	4	5	6	7	8
Tunnel burial depth (m)	17.5	17.5	17.5	17.5	20	20	20	20
Excavation depth of foundation pit (m)	10	10	10	10	10	10	10	10
Horizontal distance between tunnel and foundation pit	0.5D	0.75D	1D	1.25D	0.5D	0.75D	1D	1.25D

.

(3)

Tunnel passing beneath retaining structures

To analyze the vertical deformation induced by shield tunneling beneath wall-pile-anchor-supported excavations, numerical simulations were performed for various tunnel-underpass depths. Special attention was paid to changes in tunnel crown settlement concerning the depth of the undercrossing. The simulation plans are presented in

Table 6. Simulation cases for tunnel passing beneath wall-pile-anchor excavation.

Scenarios	1	2	3	4	5
Excavation depth of pit above tunnel (m)	0	2.5	5	7.5	10
Tunnel burial depth (m)	15	15	15	15	15

, and the corresponding modeling configuration is shown in Figure 4.

4. Results and Discussion

4.1. Verification of Numerical Model Calculation Results

The numerical model results in this study were validated based on field monitoring data obtained during the shield tunnel construction process. The validation mainly involved a comparative analysis of the surface settlement at sections outside the excavation and the settlement at the top of the excavation retaining wall.

Field-measured ground settlement data for sections M1, M3, and M5, located outside the excavation (as shown in Figure 3), were obtained 28 days after the shield tunnel passed beneath the excavation. These data were compared with the numerical simulation results, as illustrated in Figure 5. It can be observed that the measured settlement directly above the tunnel centerline is slightly greater than the simulated value. The reasons can be attributed to two factors. First, shield construction deviated from the designed alignment, resulting in over-excavation, which increased ground loss and, consequently, ground settlement. Second, the excavation pressure of the earth pressure balance shield machine was lower than the design value, leading to additional ground settlement above the tunnel. Overall, the measured and simulated ground settlement profiles exhibit similar shapes.

In addition, settlement monitoring data at points K3 and K5, located at the crest of the excavation retaining wall near the tunnel, were compared with the simulation results, as shown in Figure 6. The figure indicates that the final measured settlement values at the wall crest deviate to some extent from the simulated results. This is primarily because the numerical model was developed under the assumption of homogeneous soil conditions, whereas in reality, non-uniform soil distribution and over-excavation during shield construction may have increased wall settlement. Nevertheless, the shapes of the measured and simulated settlement curves at the wall crest remain generally consistent.

The above comparisons demonstrate that the differences between the simulated and measured values of both ground surface settlement and settlement at the crest of the diaphragm wall are minor, confirming the scientific validity of the numerical model adopted in this study.

4.2. Influence of Tunnel Burial Depth on Settlement of Wall-Pile-Anchor Support System

Figure 7 presents the vertical deformation cloud maps of the wall–pile–anchor retaining system under various tunnel burial depths. As shown in the Figure 7, the settlement of the retaining structure increases initially with tunnel depth and then decreases. Settlement values at the base of the retaining wall, measured at monitoring points K3 to K7 for different tunnel depths, are listed in

Table 7. Base settlements of diaphragm wall under various tunnel depths.

Scenarios	1	2	3	4	5	6
Wall base settlement at K3 (mm)	6.2	5.8	8.6	12.8	15.2	11.4
Wall base settlement at K4 (mm)	5.9	6.1	9.2	13.2	16.0	12.4
Wall base settlement at K5 (mm)	6.0	6.3	9.6	13.7	16.5	12.8
Wall base settlement at K6 (mm)	6.3	6.6	9.9	14.1	17	13
Wall base settlement at K7 (mm)	6.8	6.8	10.1	14.4	17.2	12.9

. Taking point K3 as an example, when the tunnel depth increases from 10 m to 12.5 m, the settlement at the bottom of the adjacent diaphragm wall ranges between 6.0 mm and 6.8 mm, indicating minor variation. This is because shallow tunnel excavation causes limited disturbance to the soil beneath the wall, resulting in minimal settlement. When the tunnel depth increases from 15 m to 20 m, the wall base settlement rises from 8.6 mm to 15.2 mm. This increase is attributed to the tunnel depth exceeding the embedment depth of the diaphragm wall (14 m), thereby inducing significant soil movement beneath the wall and increasing its settlement. As the tunnel depth increases further from 20 m to 22.5 m, the wall base settlement decreases from 15.2 mm to 11.4 mm. At this stage, the deeper tunnel causes less ground loss and disturbance, and the greater vertical clearance between the tunnel and the retaining structure reduces its influence, resulting in less settlement at the wall base.

The relationship between wall base settlement and tunnel depth at various points is illustrated in Figure 8. According to the settlement trend, the impact of tunnel depth on the wall-pile-anchor retaining system can be divided into three stages: Stage I (h ≤ L): When the tunnel depth h does not exceed the diaphragm wall embedment depth L, wall settlement is minimal; Stage II (L < h ≤ 1.4L): Settlement increases with tunnel depth and reaches a maximum when h = 1.4L; and Stage III (h > 1.4L): Further increases in tunnel depth lead to a gradual reduction in wall settlement. In conclusion, when h ≤ L, the shield tunneling has a limited impact on the retaining system. However, shallow tunneling may pose higher risks such as ground collapse. Considering both safety and settlement control, a tunnel depth of h = 14 m is identified as an optimal design value.

4.3. Influence of Tunnel-to-Pit Horizontal Clearance on Support Structure Settlement

When the tunnel burial depth is 17.5 m, the settlement cloud maps of the retaining system under various tunnel-to-excavation horizontal clearances are shown in Figure 9. The corresponding wall-pile-anchor base settlement values at different distances are listed in

Table 8. Support wall base settlements for different clearances (tunnel depth = 17.5 m).

Scenarios	1	2	3	4
Wall base settlement at K3 (mm)	12.8	9.5	8.2	7.4
Wall base settlement at K4 (mm)	13.2	10.2	8.9	7.7
Wall base settlement at K5 (mm)	13.7	10.6	9.2	8.0
Wall base settlement at K6 (mm)	14.1	10.9	9.5	8.2
Wall base settlement at K7 (mm)	14.4	11.0	9.5	8.4

. As seen from Table 8, for monitoring point K3, when the horizontal clearance increases from 0.5D to 0.75D, the wall base settlement decreases from 12.8 mm to 9.5 mm, a reduction of 3.3 mm. This indicates a significant sensitivity of wall settlement to clearance in this range. When the clearance increases from 0.75D to 1D, the settlement decreases from 9.5 mm to 8.3 mm, a smaller difference of 1.2 mm. Further increasing the clearance from 1D to 1.25D results in a settlement decrease from 8.3 mm to 7.4 mm, with a difference of only 0.9 mm. Therefore, at a tunnel depth of 17.5 m, the wall base settlement becomes less sensitive to horizontal clearance changes within the range of 0.75D to 1.25D.

Figure 10 presents the settlement cloud maps for a tunnel depth of 20 m under different horizontal clearances. For monitoring point K3, when the clearance increases from 0.5D to 0.75D, the wall base settlement decreases from 15.2 mm to 10.7 mm, a reduction of 4.5 mm, indicating high sensitivity to clearance changes in this range. When the clearance increases from 0.75D to 1D, settlement reduces from 10.7 mm to 9.7 mm, a difference of 1.0 mm. As the clearance increases from 1D to 1.25D, settlement at the wall corner decreases from 9.7 mm to 8.9 mm, with a difference of only 0.8 mm. Therefore, at a tunnel depth of 20 m, the wall base settlement also shows limited variation when the clearance ranges from 0.75D to 1.25D. As shown in

Table 9. Support wall base settlements for different clearances (tunnel depth = 20 m).

Scenarios	5	6	7	8
Wall base settlement at K3 (mm)	15.2	10.7	9.7	8.9
Wall base settlement at K4 (mm)	16.0	11.6	10.4	9.6
Wall base settlement at K5 (mm)	16.5	12.1	10.9	10.0
Wall base settlement at K6 (mm)	17	12.3	11.1	10.2
Wall base settlement at K7 (mm)	17.2	12.4	11.2	10.3

.

Figure 11 illustrates the relationship between wall–pile–anchor base settlement and the horizontal clearance between the tunnel and the excavation for tunnel depths of 17.5 m and 20 m. It can be observed that the settlement of the retaining structure decreases as the horizontal clearance increases. When the clearance ranges from 0.5D to 0.75D, the wall base settlement decreases rapidly. However, when the clearance exceeds 0.75D, the rate of settlement reduction becomes more gradual. This indicates that the retaining system is significantly influenced by tunnel excavation when the horizontal clearance is less than 0.75D. Therefore, during shield tunneling, it is recommended to maintain a minimum horizontal clearance of 0.75D between the tunnel and the excavation to minimize adverse impacts on the retaining structure.

4.4. Vertical Deformation Induced by Tunnel Under Crossing Beneath Wall-Pile-Anchor Supported Excavations

Figure 12 presents vertical deformation cloud maps for cases in which the tunnel passes beneath foundation pits of different depths. When the tunnel does not pass beneath a pit, the maximum crown settlement reaches 11.5 mm. After the tunnel passes beneath the pit, the unloading of the overburden reduces the crown settlement significantly, with the minimum value reduced to 1.8 mm. This indicates a reduction of 9.7 mm in crown settlement due to the pit. Figure 13 shows the variation in tunnel crown settlement as a function of pit depth. As the excavation depth of the wall-pile-anchor system increases from 0 m to 10 m, the change in crown settlement during the underpass increases from 1 mm to 9.7 mm, showing a clear linear correlation. Therefore, when tunneling beneath deep excavations, appropriate control measures should be implemented to prevent excessive crown settlement, which may cause segment dislocation or structural instability.

4.5. Sensitivity Analysis of Structural Parameters in the Wall-Pile-Anchor System

4.5.1. Structural Parameters of the Diaphragm Wall

The flexural stiffness of a diaphragm wall is governed by both its embedded depth (i.e., fixity depth) and wall thickness [54,55]. Therefore, under otherwise identical conditions, this study investigates how variations in fixity depth and wall thickness affect the lateral displacement of the wall.

(1)

Embedded depth of diaphragm wall

A series of numerical models was developed with varying embedded depths to analyze their influence on lateral wall displacement. Figure 14 shows the horizontal displacement profiles at monitoring point K5 after initial excavation.

When the embedded depths were 4 m, 6 m, 8 m, and 10 m, the corresponding maximum lateral displacements were 3.45 mm, 3.19 mm, 2.94 mm, and 2.86 mm, respectively. These results indicate that increasing the fixity depth can effectively reduce wall displacement. However, once a certain depth is exceeded, the incremental reduction in displacement becomes marginal. Similarly, the lateral displacement at the wall base decreased from 2.20 mm to 1.48 mm as the fixity depth increased, further confirming that deeper embedment improves control over wall deformation.

(2)

Wall thickness of diaphragm wall

Using 2D plate elements, wall thickness was varied by modifying material properties to study its effect on lateral displacement under a combined support system. Thicknesses of 800 mm, 1000 mm, 1200 mm, and 1400 mm were modeled. Figure 15 presents the displacement curves at point K5 for each wall thickness.

The results demonstrate that increasing wall thickness enhances flexural stiffness, effectively reducing horizontal displacement. The maximum lateral displacements were 3.45 mm, 2.80 mm, 2.61 mm, and 2.47 mm for wall thicknesses of 800 mm, 1000 mm, 1200 mm, and 1400 mm, respectively, reductions of 18.8%, 7.5%, and 5.3%. Corresponding top-of-wall displacements were 3.31 mm, 2.63 mm, 2.12 mm, and 1.80 mm, with reductions of 20.5%, 19.4%, and 15.1%. Overall, increasing wall thickness from 800 mm to 1400 mm results in a 28.4% reduction in maximum displacement and a 45.6% decrease in top-of-wall displacement. These findings suggest that increasing wall thickness effectively constrains deformation and improves structural stiffness. Based on performance and economic efficiency, a wall thickness of 1000 mm is considered optimal for controlling lateral displacement in practical applications.

4.5.2. Structural Parameters of Piles

The mechanical behavior of piles with different cross-sectional sizes was further investigated by varying the pile diameter. Figure 16 and Figure 17 present the horizontal displacement curves in the X- and Y-directions, respectively, for piles with different diameters after completion of the excavation.

The results indicate that the deformation pattern of the piles remains “inward-convex” regardless of diameter. As the diameter increases, the flexural stiffness of the pile improves, leading to a gradual reduction in maximum horizontal displacement. For pile diameters of 0.6 m, 0.8 m, 1.0 m, and 1.2 m, the maximum horizontal displacements in the X-direction were 3.74 mm, 3.49 mm, 3.31 mm, and 3.18 mm, corresponding to reductions of 6.7%, 5.2%, and 3.9%, respectively. In the Y-direction, the maximum displacements were 2.36 mm, 2.22 mm, 2.12 mm, and 2.06 mm, with respective reductions of 5.9%, 4.5%, and 2.8%. These findings suggest that while increasing pile diameter enhances lateral stiffness, the marginal benefit diminishes with larger diameters. When the diameter reaches 1.0 m, an additional increase of 0.2 m results in a displacement reduction of less than 5%, indicating limited effectiveness in further controlling pile deformation.

4.5.3. Structural Parameters of Anchors

The influence of anchor parameters on excavation-induced deformation was investigated through numerical simulations. Different anchor lengths, diameters, and inclinations were evaluated by computing the lateral displacement of the retaining structure.

(1) 

Anchor length

Figure 18 illustrates the horizontal displacement of the diaphragm wall at monitoring point K5 for various anchor lengths after excavation. As anchor length increases, the lateral displacement of the wall decreases, particularly in the upper and middle sections, while changes near the base are less significant. When the anchor length is 12 m, the maximum wall displacement is 3.81 mm; when increased to 20 m, the displacement reduces to 3.20 mm. This indicates that longer anchors provide better control of lateral deformation. The enhanced performance is attributed to increased tensile capacity and greater interface area between the anchor and soil, which improves frictional resistance and overall anchorage efficiency [56,57,58].

(2) 

Anchor diameter

Figure 19 shows the lateral displacement of the support system using anchors with different diameters. The variation in anchor diameter does not affect the deformation pattern. The maximum horizontal displacement occurs at a depth of 5 m in the X-direction and 7 m in the Y-direction. When the anchor diameter increases from 18 mm to 25 mm, the maximum displacement decreases from 3.15 mm to 2.85 mm. This demonstrates that larger anchor diameters can help reduce horizontal displacement, primarily due to the increased contact surface between the anchor and surrounding soil, which improves frictional resistance and anchorage stability.

(3) 

Anchor Inclination

The angle between the anchor and the horizontal plane is defined as the anchor inclination. Figure 20 presents the horizontal displacement profiles for anchors with different inclinations. While changes in inclination do not alter the “inward-convex” deformation pattern of the diaphragm wall, they do influence displacement in the upper portion of the wall. When the inclination angles are 15°, 30°, and 45°, the maximum wall displacements are 3.45 mm, 3.68 mm, and 4.12 mm, respectively. The displacement increases by 6.7% when the inclination rises from 15° to 30%, and by 12.0% from 30° to 45%. These results indicate that greater anchor inclinations reduce the effectiveness of horizontal support, thereby increasing lateral displacement and potentially compromising the stability of the excavation support system.

5. Conclusions

Based on numerical simulations, this study investigates the spatial influence of shield tunneling adjacent to foundation pits supported by wall-pile-anchor systems. Through single-factor sensitivity analysis, the effects of key structural parameters on the horizontal displacement of the retaining system are clarified. The main conclusions are as follows:

(1) The influence of tunnel depth on the wall–pile–anchor system can be divided into three stages. In the first stage, when the tunnel burial depth h is less than the embedment depth L of the retaining structure (h < L), wall settlement remains relatively constant as h increases. In the second stage (L < h ≤ 1.4L), settlement increases with tunnel depth and reaches its maximum when h = 1.4L. In the third stage (h > 1.4L), wall settlement gradually decreases as the tunnel depth increases further.

(2) The spatial relationship between the shield tunnel and the wall–pile–anchor support system significantly affects the deformation behavior of both the tunnel and the retaining wall. As tunnel depth increases, wall settlement first increases and then decreases, reaching a peak when the tunnel depth equals 1.4L, where L is the diaphragm wall height. Horizontally, when the tunnel-to-pit clearance is less than 0.75D, the retaining wall experiences significant settlement due to tunneling. In cases where the tunnel passes beneath the excavation, crown settlement decreases, and the change in crown settlement is linearly correlated with pit depth.

(3) In the wall-pile-anchor system, increasing the embedment depth of the diaphragm wall effectively reduces horizontal displacement at the wall base. Increasing wall thickness reduces displacement at the top of the wall. When the embedment depth increases from 4 m to 10 m, the maximum wall displacement decreases by 17.1%, and the base displacement decreases by 32.7%. When the wall thickness increases from 800 mm to 1400 mm, the maximum displacement reduces by 28.4%, and the top displacement reduces by 45.6%.

(4) After excavation, pile deformation exhibits an inward-convex pattern, which remains unchanged with varying pile diameters. Large-diameter piles effectively reduce maximum horizontal displacement. However, when the pile diameter exceeds 1 m, further increases in diameter (e.g., by 0.2 m) reduce displacement by less than 5%, indicating limited improvement in deformation control.

(5) In the wall-pile-anchor system, increasing the length and diameter of anchors enhances the frictional resistance between the anchor and soil, thereby improving anchorage performance. However, increasing the inclination angle between the anchor and the horizontal plane leads to greater lateral displacement. An optimal inclination angle of 15° is recommended for minimizing displacement.