Evaluation Method of the Impact of Twin Shield Tunneling Construction on Elevated Bridges: Case Study

Abstract

In urban metro construction, shield tunneling often needs to pass through building and bridge pile foundations, potentially affecting the stability of existing structures. Therefore, accurately assessing the impact of shield tunneling on bridges and buildings is crucial. This study presents a comprehensive prediction method combining numerical simulation and empirical formulas, taking the underpass project of the Shijiazhuang–Wuhan High-Speed Railway Bridge by Zhengzhou Metro Line 5 as a case study. Three-dimensional numerical model calculations were performed using finite element software to analyze the displacement and stress changes of buildings and tunnel structures at different construction stages, revealing the deformation patterns of buildings adjacent to the tunnel during shield tunneling. In particular, the ground settlement caused by twin-tunnel excavation was compared with Peck’s empirical formula to verify the reliability of the numerical simulation. The results show that twin-tunnel excavation exacerbates the horizontal displacement, uplift, and settlement of the ground, with maximum deformation rates increasing by 7.10%, 20%, and 11.4%, respectively. Comparing the ground deformation results of Peck’s empirical formulas with numerical calculations revealed similar trends in the settlement curves, with a maximum deviation of 6.67%. It can be concluded that using Peck’s empirical formula to calculate ground deformation characteristics complements the limitations of numerical simulations, making the assessment results more reliable. The findings of this study demonstrate that integrating numerical simulation with empirical formulas significantly enhances the reliability of deformation predictions in complex tunneling scenarios. This research not only offers a comprehensive safety assessment method for shield tunneling construction but also provides valuable guidance for the design and construction of similar projects, serving as a theoretical reference for future engineering endeavors.

1. Introduction

Currently, many cities face severe transportation issues, with above-ground transportation space no longer meeting public needs. To alleviate surface traffic congestion and reduce environmental pollution, urban areas worldwide are actively developing and utilizing underground spaces. However, underground construction inevitably causes ground settlement and cracks [1,2]. When underground construction intersects with complex structures, it can impact other underground structures. Particularly, when construction occurs near existing structures, it can have unpredictable effects, potentially leading to severe structural damage [3,4].

Underground engineering often employs shield tunneling construction. Methods for predicting and analyzing ground settlement caused by shield tunneling and its impact on adjacent structures mainly include theoretical analysis, model testing, and numerical analysis [5,6]. Empirical formula methods utilize practical engineering experience from experts and scholars, along with extensive experimental data, to express settlement patterns in formulaic form. This facilitates the prediction of maximum surface settlement and settlement distribution above tunnels. Among these, Peck’s empirical formula is the most widely used, describing the surface settlement trough based on the normal distribution curve theory [7]. Sagaseta [8], based on the assumption of an incompressible elastic half-space, proposed the use of the source–sink method to predict surface settlement caused by tunnel construction. Subsequently, researchers have improved upon this method, deriving more complex formulas for calculating surface settlement [9,10]. As a critical component of metro construction, shield tunneling impacts not only surface settlement but also existing tunnels and other structures. Scholars have proposed various methods based on different models to analyze the deformation and response of existing metro tunnels due to new tunnel construction. These methods include the simplified two-stage method based on the Winkler foundation model [11,12] and the Timoshenko beam model analysis method, which considers shear deformation [13,14].

Theoretical methods rely more on idealized assumptions, and their calculation results have certain limitations. In contrast, model experiments can directly collect actual data of the model under specific conditions such as stress, strain, displacement, and so on. Nomoto et al. [15] conducted centrifuge model tests to study the variations in lining stress, lateral and longitudinal ground surface settlement during shield tunnel construction, as well as the changes in earth pressure around the tunnel. They derived experimental formulas to estimate ground surface settlement above the shield tunnel. Chapman et al. [16] used small-scale laboratory model tests to investigate ground deformation prediction for closely spaced multiple tunnels (especially parallel tunnels) in soft soil, proposing an improved Gaussian curve method to enhance prediction accuracy. Sun et al. [17] conducted model tests using transparent sand to study the internal soil deformation ahead of the tunnel boring machine. They successfully captured and calculated soil displacement using optical equipment and computer processing. Fang et al. [18] explored the effects of tunnel depth and ground volume loss on settlement through sand model tests and proposed a prediction equation based on the Gaussian curve. Miliziano et al. [19] studied the impact of the excavation of the Rome Metro Line C on the historic Carducci School building. Through numerical analysis, they predicted settlement, considering major tunneling characteristics such as advancement, pressure, design, and grouting.

Numerical calculations can complement and validate theoretical and experimental methods. For example, Rowe et al. [20] developed a three-dimensional elastoplastic finite element method to simulate the effects of tunnel construction on ground subsidence. They provided solution procedures and applicable constitutive models. They applied this method in practical engineering to calculate excavation displacements, emphasizing the importance of gap parameters in predicting ground deformations. Migliazza et al. [21] established a three-dimensional finite element model to simulate surface settlement caused by EPB-S shield tunneling in the alluvial sandy area of the Padana Plain. They compared actual monitoring data and empirical formulas to assess the impact of tunnel construction on surrounding structures. Sousa et al. [22] used 3D finite element analysis to simulate the construction sequence in detail, considering two different soil constitutive models. Their results, compared with observational data and plane strain finite element analysis, showed that only 3D finite element analysis incorporating more complex soil models could fully reflect field performance. Kivi et al. [23] employed 3D finite element analysis to study settlement control at a large-span underground station of the Tehran Metro. By introducing a central beam-column structure (CBC) to increase the stiffness of the support system, they reduced soil deformation and ground settlement. Xie et al. [24] used the three-dimensional finite difference method to simulate the excavation process of an EPB shield machine. Through parameter studies, they optimized construction parameters and conducted field measurements to validate the numerical model’s applicability to large-diameter tunnel construction. Their research also indicated that grouting pressure and quality are key factors in determining surface settlement.

The above studies provide significant insights into analyzing the stress and deformation of ground soil and buildings caused by tunnel excavation. Due to the highly complex geological conditions encountered when tunnels pass under buildings, and the varying structural forms, material properties, and functions of the buildings themselves, these interwoven factors increase the uncertainty in ensuring the safety of nearby structures during shield tunneling. Thus, safety assessment of shield tunneling is a primary concern for relevant authorities and engineering personnel. Currently, safety assessment of shield tunneling primarily relies on numerical simulation results, which makes the evaluation basis relatively singular and less reliable. Although theoretical analysis is accurate, it requires a high level of expertise and is difficult to implement. Physical model tests, on the other hand, are limited by their lengthy duration and high cost.

Therefore, taking the underpass project of the Shijiazhuang–Wuhan High-speed Railway Connection Bridge by Zhengzhou Metro Line 5 as an example, this study employs finite element software to carry out three-dimensional numerical model calculations. The changes in key parameters such as displacement and stress of existing buildings and tunnel structures at different construction stages are analyzed in detail, and the deformation patterns of buildings adjacent to the tunnel during shield tunneling are also carefully delved. Simultaneously, Peck’s empirical formula is used to calculate the ground deformation characteristics, verifying the reliability of the numerical simulation results and compensating for the shortcomings of single numerical simulation. This comprehensive assessment method not only enables a more comprehensive safety assessment and analysis of shield tunnel construction but also provides valuable references for the design and construction of similar projects.

2. Project Overview

2.1. Profile of the Project

Zhengzhou Metro Line 5 spans approximately 40.235 km entirely underground, comprising 32 stations, including 15 transfer stations. The average station spacing is 1.257 km, with a maximum of 1.857 km and a minimum of 0.648 km. The right track extends 1774.2 m from right CK18+060.600 to right CK19+834.800, and the left track spans 1775.89 m from left CK18+060.600 to left CK19+834.800, with a slight difference in length due to a 1.69 m chainage variation. The left track includes horizontal curves with radii of 1200 m, 800 m, and 1000 m, while the right track features curves with radii of 1500 m, 1000 m, and 1500 m.

This metro project utilizes shield tunneling from right CK18+920 to right CK19+030, passing beneath several high-speed railway link bridges. These bridges, listed from smallest to largest mileage, include the North Up Connection Bridge (NU), North Down Connection Bridge (ND), Southwest Down Connection Bridge (SW2), and Southwest Up Connection Bridge (SW1). Figure 1 illustrates their spatial relationship with the shield tunnel. All four bridges are passenger dedicated and designed for a speed of 160 km/h. The NU, ND, and SW1 bridges are simply supported beams. The SW2 bridge section being crossed is a four-span continuous beam.

The tunnel intersects the NU, ND, and SW2 bridges at oblique angles of 75°, 70°, and 106°, respectively, with the tunnel structure buried at a depth of approximately 14.5 m. The minimum horizontal clear distances between the section tunnel and the bridge piles are 5.51 m, 6.62 m, and 8.69 m, respectively. The section between Zhengbian Metro Station and Jingbei Second Metro Station (named as ZJ Section in this study) intersects the pile of the SWU connection bridge of the Shijiazhuang–Wuhan High-Speed Railway Connection Bridge at Right CK19+025.000, with an oblique angle of 88.2° and a tunnel depth of approximately 15.5 m. The minimum horizontal clear distance between the section tunnel and the high-speed rail pile is about 4.63 m. This study focuses on the safety evaluation of the shield tunnel passing under SW1, as shown in Figure 2. The method of crossing the bridge involves the section tunnel passing between adjacent spans, as shown in Figure 3. The overburden thickness of the section tunnel ranges from approximately 10 to 18 m, with a minimum gradient of 2‰ and a maximum gradient of 16.68‰.

2.2. Engineering Geological and Hydrogeological Conditions

The area is part of the Yellow River alluvial plain and dune landform, characterized by flat and open terrain with sparse vegetation. Based on the geological age, lithology, and engineering characteristics of the soil, the main lithology within the exploration depth of this site includes artificial fill, silt, silty clay, fine sand, and medium sand. The depth and thickness distribution of the soil layers are shown in Figure 3. The geological stratification of the site is described as follows:

Miscellaneous fill: Variegated in color and composition; loose; mainly consisting of municipal road pavement, cultivated soil, backfill, garbage, and plant roots, typically with a surface layer of cement pavement about 0.2–0.4 m thick. The layer thickness ranges from 0.40 to 6.00 m, with an average thickness of 2.30 m.

Silt: Yellow-brown to light gray; slightly wet to wet; slightly dense to medium dense; containing mica and small amounts of white shell fragments, with occasional clay clumps, low dry strength, and low plasticity. The layer thickness ranges from 1.80 to 4.20 m, with an average thickness of 2.52 m.

Clayey silt: Yellow-brown to light gray, plastic, uneven texture, non-glossy, smooth cut surface, containing iron rust spots and small amounts of iron–manganese spots. The layer thickness ranges from 0.30 to 4.50 m, with an average thickness of 2.13 m.

Fine sand: Brownish-yellow, slightly wet to wet, medium dense to dense, with occasional silt intercalations, primarily composed of quartz and feldspar, with small amounts of mica fragments. The layer thickness ranges from 1.00 to 3.50 m, with an average thickness of 2.25 m.

Medium sand: Brownish-yellow, wet to saturated, medium dense to dense, primarily composed of quartz and feldspar, with small amounts of mica fragments and occasional gravel. The layer thickness ranges from 1.90 to 5.90 m, with an average thickness of 3.77 m.

The groundwater at the site can be classified into perched water and phreatic water. During the investigation, perched water was mainly revealed at the Zhengbian Metro Station at a depth of 6.20 m and an elevation of 82.60 m. It is primarily replenished by rainfall infiltration and leaks from underground pipelines, with evaporation being the main discharge method. The hydrogeological conditions of the site have a minimal impact on the project.

3. Model and Parameters

3.1. Establish of the Numerical Model

In this study, the MIDAS/GTS NX finite element software was used to conduct three-dimensional (3D) numerical simulation and analysis of the shield tunnel crossing under the SW1 Bridge of the Shijiazhuang–Wuhan Passenger Railway Connection Bridge. Based on the spatial relationship between the shield tunnel of ZJ Section of Metro Line 5 with the SW1 Bridge, a 3D finite element calculation model was established, as shown in Figure 4. In order to analyze the impact of shield excavation on the bridge, the model considered three closely adjacent piers as well as two relatively distant piers and pile foundations, numbered from smallest to largest as 13#, 14#, 15#, 16#, and 17# (Figure 4b). The pile lengths of piers 15–17# are 50 m, while those of piers 13# and 14# are 52.5 m and 53.0 m, respectively. The heights of piers 14–17# are 13.2 m, whereas pier 13# has a height of 11.2 m. The model has an X-direction range of 200 m, a Z-direction range of 70 m, and a Y-direction range (shield excavation direction) of 50 m. Especially, the soil layer thickness along the Z-direction is shown in

Table 1. Parameters for the 3D numerical model calculation.

Formation Lithology	Unit Weight (kN/m3)	Characteristic Bearing Capacity (kPa)	Coefficient of Static Lateral Earth Pressure	Deformation Modulus (MPa)	Poisson’s Ratio	Friction Angle (°)	Cohesion (kPa)	Soil Thickness (m)
1-1 Mix filled soil (Q4ml)	18.0	-	-	3.8	0.30	-	-	2.2
2-32 Silt (Q4al)	18.9	110	0.42	3.93	0.35	25.0	21.9	1.6
2-33D Fine sand (Q4al)	19.4	120	0.38	4.66	0.35	23.1	14.7	5.5
2-35 Silt (Q4apl)	19.7	120	0.42	4.00	0.35	26.7	18.1	6.1
2-51c Fine sand (Q4apl)	20.2	135	0.38	0.00	0.35	33.6	25.3	4.1
2-52 Fine sand (Q4apl)	20.4	135	0.38	5.25	0.35	34.6	21.0	4.2
3-23 Clayey silt (Q3apl)	20.0	220	0.33	4.53	0.35	19.8	35.9	21.3
4-51 Fine sand (Q2apl)	20.0	220	0.38	24	0.32	30.0	18.0	25.0
Shield tunnel segments	25.0	-	-	27,600	0.20	--	--
Bridge pile foundation	25.0	-	-	34,500	0.20	--	--
Cap and pier	25.0	-	-	31,500	0.20	--	--
Isolation pile	25.0	-	-	31,500	0.20	--	--

. Consequently, the total dimensions are 200 m × 50 m × 70 m.

The surrounding rock is simulated using solid elements and follows the Mohr–Coulomb yield criterion. The bridge piers and caps are also simulated using solid elements with an elastic model. The shield tunnel segments are modeled using two-dimensional structural elements, while the bridge piles and isolation piles are modeled using one-dimensional structural elements. In this 3D computational model, the study area, including the shield excavation and surrounding soil, is divided into 445,076 solid elements and 1,780,304 nodes (as shown in Figure 4a). The caps, bridge piers, and pile foundations are divided into 24,216 structural elements and 96,864 nodes, with the specific division shown in Figure 4b.

The boundary conditions shown in Figure 4a are selected as follows: the planes at X = 0 m and X = 200 m restrict displacement in the X direction; the planes at Y = 0 m and Y = 50 m restrict displacement in the Y direction; and the plane at Z = –70 m restricts displacement in the Z direction. The loads on the pile foundations primarily include the self-weight of the bridge, piers, sleepers, tracks, and other ancillary facilities.

3.2. Parameter Selection

The physical and mechanical parameters of the surrounding rock strata, bridge pile foundations, caps, bridge piers, and shield tunnel segments in the simulation are shown in Table 1. Based on the geological age of the soil layers, the soil strata involved in the model are classified as follows: Quaternary mixed fill (Q4^ml), Quaternary alluvial and floodplain deposits (Q4^al), Late Pleistocene alluvial deposits (Q3^apl), and Middle Pleistocene alluvial deposits (Q2^apl), as shown in Table 1. It can be observed that there are two friction angles (°) are greater than 30°. In such cases, the dilation angle should be considered in the calculations [25,26]. However, in this study, the dilation angle was not considered, because after the calculations were completed, six different scenarios were set up with dilation angles ranging from 5° to 30°. A comparison between the models considering and not considering the dilation angle showed that the impact patterns of tunnel excavation on the bridge were consistent, with minimal differences in maximum deformation, all within 1%. Furthermore, due to practical constraints in the project, the site investigation did not provide actual measured values for the dilation angle of the site’s soil layers. Therefore, the dilation angle was not activated in this finite element simulation.

3.3. Simulation Process of Shield Tunnel Construction

The excavation construction steps for the shield tunnel section passing under the bridge include eight steps, and the left-line shield tunnel was excavated first, followed by the right-line shield tunnel. Figure 5 shows the relationship between the typical excavation steps of the shield tunnel and the position of the existing SW1 bridge. These eight typical construction steps are as follows:

(1)

Stage 1 (S1) involves excavating the left-line tunnel to the near edge below the SW1 cap;

(2)

Stage 2 (S2) involves excavating to the middle below the SW1 cap;

(3)

Stage 3 (S3) involves excavating to the far edge below the SW1 cap;

(4)

Stage 4 (S4) marks the complete passage of the left-line tunnel;

(5)

Stage 5 (S5) involves excavating the right-line tunnel to the near edge below the SW1 cap;

(6)

Stage 6 (S6) involves excavating to the middle below the SW1 cap;

(7)

Stage 7 (S7) involves excavating to the far edge below the SW1 cap;

(8)

Stage 8 (S8) marks the complete passage of both lines.

By analyzing the results of these eight typical construction steps, a detailed assessment can be made of the impact of the entire shield tunnel construction process on the safety of adjacent pile foundations and the upper bridge structure.

4. Results Analysis and Discussion

4.1. Ground Deformation Analysis during Shield Tunnel Excavation

Figure 6 shows the horizontal displacement cloud map of the soil during the entire excavation process of the shield tunnel. During the excavation of the single-line tunnel from S1 to S4, horizontal displacement mainly occurs on both sides of the tunnel, with the direction of soil displacement pointing towards the tunnel center. The maximum horizontal displacements are 8.74 mm, 8.87 mm, 8.95 mm, and 9.02 mm, respectively. As the excavation progresses, the horizontal displacement gradually increases. This is due to the shield machine’s gradual advancement and the continuous expansion of the excavation area, which increases the disturbance to the surrounding soil, leading to greater soil displacement. Additionally, the maximum horizontal displacement growth rates are 1.49%, 0.90%, and 0.78%, respectively. The growth rates indicate that the increase in maximum horizontal displacement is not uniform during the shield tunnel excavation. From S1 to S4, the growth rate is relatively low and shows a decreasing trend. This is because the initial advancement of the shield machine causes disturbance to the surrounding soil, and as the excavation progresses, the soil stress redistribution gradually stabilizes.

During the double-line excavation from S5 to S8, the maximum horizontal displacements are 9.39 mm, 9.43 mm, 9.47 mm, and 9.66 mm, respectively. Between S4 and S5, the growth rate suddenly increases to 4.10% due to the secondary disturbance caused by the excavation of the second tunnel, which further increases soil displacement around the already excavated first tunnel. Between S5 and S7, the maximum horizontal displacement growth rate remains small at 0.42%. However, from S7 to S8, the growth rate increases again to 2.01% due to the cumulative effect of the double-line tunnel excavation, resulting in further soil displacement.

Figure 7 shows the vertical displacement contour map of the soil during the entire shield tunnel excavation process. Due to stress release and soil rebound caused by tunnel excavation, the soil exhibits varying degrees of heaving and rebound in the vertical direction. The most significant heaving occurs in the area beneath the tunnel, where soil unloading rebound is most pronounced. The amount of heaving gradually decreases with increasing distance from the tunnel centerline. From S1 to S4, the tunnel excavation is single-line, and the maximum heaving remains relatively constant at 4.6 mm. From S5 to S8, the tunnel excavation is double-line, with maximum heaving of 5.23 mm, 5.43 mm, 5.50 mm, and 5.52 mm, respectively. The corresponding maximum heaving increase rates are 11.75%, 3.82%, 1.29%, and 0.36%. The greatest increase rate, 11.75%, occurs from S4 to S5, primarily due to the transition from single-line to double-line excavation, which significantly expands the area and extent of soil stress reduction, resulting in considerable heaving. From S5 to S8, although heaving continues to increase, the increase rate gradually decreases, indicating that the redistribution of soil stress is stabilizing.

In the areas above and alongside the tunnel, stress release and soil consolidation result in significant soil settlement. As the tunnel excavation progresses, the excavation area increases, leading to a greater extent and degree of stress release, which in turn results in increased soil settlement and a wider distribution of the settlement range. From S1 to S4, the maximum soil settlement is 9.36 mm, 9.38 mm, 9.39 mm, and 9.73 mm, respectively. From S1 to S3, the maximum soil settlement is similar, with a low growth rate, indicating relatively stable soil settlement during the initial stages of single-line tunnel excavation. From S3 to S4, the growth rate suddenly increases to 3.62% due to the completion of the tunnel excavation and the maximum stress release. Starting from S4, in the double-line tunnel excavation stage, the maximum deformation is 10.11 mm, 10.18 mm, 10.27 mm, and 10.84 mm, respectively. From S4 to S5, the growth rate reaches 3.90%, primarily because double-line excavation significantly alters the surrounding soil stress field, further exacerbating soil settlement. From S7 to S8, the growth rate reaches 5.55%, with the maximum soil settlement occurring when the double-line tunnel is fully excavated.

4.2. Analysis of Pile Foundation Settlement and Deformation Characteristics

4.2.1. Pile Cap Deformation Characteristics Analysis

The monitoring of the maximum horizontal deformation of the pile cap during shield tunnel excavation is shown in Figure 8a. The horizontal displacement of the pile cap exhibits a specific pattern throughout the excavation process. As the tunnel advances from the edge below the bridge pile cap (S1) to completely passing through (S4), the horizontal displacement of each pile cap gradually increases. This is primarily due to the stress release in the surrounding soil caused by tunnel excavation, which in turn induces horizontal displacement in the soil around the piles, leading to horizontal displacement of the pile cap. The increase in horizontal displacement of the pile cap becomes particularly pronounced with the excavation of the right tunnel (S5). This is due to the intense stress changes in the soil induced by the excavation of the twin tunnels and the interaction between the two tunnels, which exacerbates the horizontal displacement of the pile cap. Notably, Pier 15# is located between the two tunnels; it experiences the most significant mutual impact during the excavation of the twin tunnels. After the left tunnel completely passes through (S4), the displacement of the pile cap of Pier 15# reaches a relatively high value. However, with the excavation of the right tunnel (S5 to S7), the redistribution of soil stress between the twin tunnels causes the soil that had already displaced around the left tunnel to experience stress from the right tunnel excavation. This leads to a reverse displacement in the previously rightward-moving soil, eventually reaching a balanced state.

The maximum vertical displacement of the pile cap during shield tunnel excavation is shown in Figure 8b, as can be seen that it varies with different excavation stages. For all piers, in the initial stages of left tunnel excavation (S1 to S4), the vertical displacement of the pile cap increases as excavation progresses. This is due to the vertical displacement of the soil around the piles caused by tunnel excavation, which leads to vertical displacement of the pile cap. When the right tunnel excavation begins (S5), the vertical displacement of the pile caps of different piers continues to increase with the excavation stages. Particularly, for Piers 15# and 16#, located between the two tunnels, the vertical displacement of the pile caps becomes more pronounced after S5. This is because the stress changes in the soil due to twin tunnel excavation create a cumulative effect between the two tunnels, significantly increasing the vertical displacement of the pile caps. Additionally, the distance of the piers from the tunnel also affects the vertical displacement of the pile caps. Piers closer to the tunnel (e.g., Pier 14#) experience greater impact and, hence, greater vertical displacement of the pile caps, while piers farther from the tunnel (e.g., Piers 13# and 17#) experience less impact and smaller changes in vertical displacement of the pile caps.

4.2.2. Deformation Characteristics of Bored Piles

The horizontal displacement contour maps of the pile foundations at typical construction stages S4 and S8 are shown in Figure 9a,c. During the excavation of the left tunnel, the 14# pile foundation, which is close to the left tunnel, is affected by soil movement and stress redistribution caused by the excavation, resulting in horizontal displacement. As the left tunnel excavation is completed, the horizontal displacement of the pile foundation reaches its maximum value, with the 14# pile foundation exhibiting a maximum displacement of 1.78 mm. Additionally, the soil movement and stress changes are transmitted to farther pile foundations, causing noticeable horizontal displacement in the 15# pile foundation. In contrast, the 13# pile foundation, which is farther from the left tunnel, experiences less impact and minimal displacement. On the other hand, the excavation of the right tunnel similarly induces soil movement and stress changes. For the 15# pile foundation, located between the two tunnels, horizontal displacement further increases due to the influence of both the left and right tunnel excavations. The 16# pile foundation, being close to the right tunnel, also begins to exhibit significant horizontal displacement. Furthermore, the stress changes induced by the twin tunnel excavation create an asymmetrical distribution in the soil, leading to asymmetrical deformation of the pile foundations. Upon completion of the right tunnel excavation, the maximum deformation of the pile foundations is observed on the right side of the 14# and 15# pile foundations and the left side of the 16# pile foundation, with the maximum displacement reaching up to 2.98 mm.

The settlement displacement cloud diagrams for pile foundations at stages S4 and S8 during typical construction phases are shown in Figure 9b,d. Tunnel excavation causes unloading of the surrounding soil, resulting in stress redistribution and subsequent pile foundation settlement. After the completion of the left tunnel excavation, the 14# pile foundation, being in close proximity to the left tunnel, exhibits the maximum settlement displacement at the depth near the tunnel, reaching 1.29 mm. The 15# pile foundation, located on one side of the left tunnel, is also affected by the excavation, with a maximum settlement of 0.49 mm. Upon the complete excavation of both tunnels (S8), the settlement displacement of the 15# pile foundation becomes most pronounced, reaching 3.26 mm, demonstrating the cumulative effect of the excavation of both tunnels on the intermediate pile foundation. Similarly, due to the varying distances of the double tunnels from the pile foundations, the uneven stress changes in the soil caused by the excavation affect the pile foundations differently. The settlement deformation range of the 16# pile foundation is slightly larger than that of the 14# pile foundation.

4.3. Impact of Shield Tunnel Excavation on Existing Bridges

The horizontal and vertical displacement deformation cloud diagrams for the bridge deck and piers of the SW1 during shield tunnel excavation are shown in Figure 10. As the tunnel excavation progresses, the horizontal displacement of the bridge deck and piers gradually increases and the affected areas expand. During the excavation of the left line tunnel, Pier 14#, being closer to the left line tunnel, is the first to be impacted. From Stage 1 to Stage 4, the horizontal displacement of Pier 14#’s deck gradually increases, reaching a maximum of 1.038 mm. After the complete excavation of the left line tunnel (Stage 4), the deck displacement gradually decreases, while the piers below the deck exhibit more significant horizontal displacement, with a maximum of 1.39 mm. Pier 15#, located between the two tunnels, is less affected during the left line tunnel excavation. However, during the right line tunnel excavation, Pier 15#, being closer to the right line tunnel, begins to experience significant impact. At Stage 5, both the deck and piers of Pier 15# exhibit noticeable horizontal displacement, with a maximum of 1.67 mm. After the complete excavation of both tunnels (Stage 8), the range of impact broadens, and Pier 16# exhibits a maximum horizontal displacement of 2.01 mm. However, due to the excavation on both sides, the stress redistribution partially offsets, resulting in a relatively smaller final horizontal displacement for pier and deck numbered 15#.

During the shield tunnel excavation, the surrounding soil undergoes unloading, altering its stress state and causing settlement displacement in the nearby bridge. Particularly, when the tunnel excavation reaches beneath the bridge foundation, the unloading of the soil under the foundation results in soil compression and settlement, leading to bridge displacement. The settlement displacement cloud diagram shows that during the excavation of a single-line tunnel, the settlement displacement of the nearby bridge increases as the excavation progresses. In Stages 1 and 4, the settlement displacement of bridges closer to the tunnel (e.g., Pier 14# and its deck) is more pronounced compared to those farther away (e.g., Piers 15# and 16#), with a maximum settlement of 1.75 mm. During the excavation of the twin-line tunnel, the settlement displacement of the nearby bridge further increases with the excavation of the right-line tunnel, extending the range of displacement to the entire Pier 16 area. When both tunnels are fully excavated, the peak settlement displacement occurs in the Pier 15# area between the two tunnels, with a maximum settlement of 2.83 mm.

If the deformation caused by tunnel construction is excessive, it can affect the normal operation of the bridge. According to Article 5.3.3 of the “Basic Design Standards for Railway Bridges and Culverts” (TB10002.1-2005), the following limitations are set for displacement and stiffness of pier foundations: the post-construction settlement of open-deck bridges should not exceed 40 mm, and the difference in uniform settlement between adjacent piers should not exceed 20 mm. The calculation results of this study indicate that the impact of shield tunnel excavation on the bridge meets the regulatory requirements and complies with the operational standards.

5. Discussion

5.1. Empirical Formula of Surface Deformation

The transverse surface settlement trough caused by shield tunneling typically appears “bowl-shaped”. As the shield advances, the surface settlement trough gradually expands. The general surface settlement curve induced by tunnel excavation is shown in Figure 11. The impact of shield excavation varies in different soil layers. In cohesive soil layers, the settlement of the soil surrounding the shield is gradual, with a uniform settlement expansion rate. However, the local collapse of the sand causes abrupt changes in the settlement expansion in sandy soil layers.

It is generally believed that the surface settlement trough deformation due to shield tunneling conforms to Peck’s empirical formula [7]. The estimation formula for transverse settlement is given in Equation (1):

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

(1)

$$S_{\max }={\displaystyle \frac{\pi R^2\eta }{i\sqrt{2\pi }}}$$

(2)

$$i={\displaystyle \frac{z}{\sqrt{2\pi }\tan \left(45°-\phi /2\right)}}$$

(3)

where S_x is the surface settlement value at distance x from the tunnel center; S_max is the maximum surface settlement at the tunnel centerline; V_l is the volume loss per unit length due to construction; i is the width coefficient of the surface settlement trough in meters, Z = H + R, where H is the depth of cover and R is the structural radius.

Ma [27] considered that the impact on ground settlement might differ between the leading and trailing tunnels during excavation. To more accurately reflect the actual situation, different settlement parameters (i and η) were assigned to the leading and trailing tunnels, respectively. This method allows for the calculation of ground settlement values induced by the excavation of each tunnel. By applying the superposition principle, the total ground settlement value for the twin-tunnel excavation can be obtained by summing these two settlement values. The calculation formula is as follows:

$$S_x=S_{\max f}\exp \left[-{\displaystyle \frac{{\left(x-0.5L\right)}^2}{2{i_f}^2}}\right]+S_{\max h}\exp \left[-{\displaystyle \frac{{\left(x+0.5L\right)}^2}{2{i_h}^2}}\right]$$

(4)

where $S_{\max f}={\displaystyle \frac{\pi R^2{\eta }_f}{i_f\sqrt{2\pi }}};S_{\max h}={\displaystyle \frac{\pi R^2{\eta }_h}{i_h\sqrt{2\pi }}}$; i_f and i_h represent the width coefficients of the surface settlement trough for the leading and trailing tunnels, respectively; η_f and η_h represent the ground loss rates for the leading and trailing tunnels, respectively; and L represents the distance between the axes of the two tunnels.

5.2. Comparison and Analysis

To verify the accuracy and effectiveness of the numerical simulation study, a comparative analysis was conducted using both the single-line and twin-line Peck empirical formulas. The entire process, from the commencement of the left-line shield construction to the complete completion of the right-line construction, was divided into eight stages. In these eight stages, the first four stages essentially correspond to the shield construction of the left tunnel alone. During this period, the single-line Peck’s empirical formula was used to calculate settlement. When the right tunnel was fully completed at stage 8, the twin-line empirical formula was employed for settlement calculation. The calculation results are shown in Figure 12.

Figure 12a shows that the ground surface settlement curves predicted by empirical formulas and obtained by finite element simulations for single-line tunnel excavation both exhibit a single-peak characteristic. The trends are highly consistent, with the maximum settlement occurring at the tunnel centerline. The maximum surface settlement obtained by numerical simulation when the left tunnel line is completely excavated is 2.75 mm, while the empirical formula predicts a maximum settlement of 2.93 mm, a difference of only 0.18 mm, indicating good reliability of the numerical simulation.

In Figure 12b, the numerical simulation results show a double-peak characteristic in the settlement curve during tunnel excavation, with the two peaks appearing at the axes of the two tunnels. This conforms to the typical ground settlement feature induced by tunnel excavation. Between the two tunnels, the soil is compressed by both tunnels, making the soil in this area denser and thus reducing the settlement. Additionally, the numerical simulation results indicate that when both tunnel lines are fully excavated, the maximum settlement for the left tunnel is 3.25 mm, which is greater than the 2.75 mm settlement when the left tunnel is excavated alone. This is because the excavation of the right tunnel causes additional disturbance to the soil around the left tunnel, leading to increased settlement. The maximum settlement at the right tunnel axis reaches 3.75 mm due to the secondary disturbance, which causes further deformation of the already unstable soil, resulting in greater settlement at the right tunnel axis. In contrast, the empirical formula predicts a single-peak settlement curve, with the maximum settlement located at the right tunnel axis and a value of 3.50 mm, showing a discrepancy of −6.67% from the numerical results. This difference is due to the fact that the empirical formula is a fitting calculation model, and the curve is usually smooth. In this case, the close proximity of the two tunnels results in the inability of the formula to precisely reflect the two peak values. However, it can still be observed that the empirical formula curve is asymmetrical, with less settlement on the left side than on the right. This somewhat reflects the different ground settlements caused by the excavation of the left and right tunnels. Therefore, it has a certain reliability in predicting settlement deformation patterns and maximum settlement.

6. Conclusions

This study investigates the shield construction of Zhengzhou Metro Line 5, which passes beneath the Shijiazhuang–Wuhan High-Speed Railway Connection Bridge. The dynamic excavation process and its effects on ground deformation, nearby pile foundations, bridge piers, and the deck were analyzed based on using a 3D finite element model and Peck’s empirical formula. The specific conclusions and recommendations are as follows:

(1) During shield construction, the surrounding soil experiences horizontal displacement, heaving, and settlement. While above and beside the tunnel, it is primarily horizontal and settling, but beneath the tunnel, unloading rebound causes significant heaving. Deformation increases and then stabilizes during single-line tunnel excavation and intensifies to overall displacement due to secondary disturbances during double-line excavation.

(2) Horizontal and vertical displacements of pile caps, foundations, and bridge decks increase progressively with the excavation of single-line tunnels. Vertical displacements decrease with distance from the tunnel, while the horizontal displacements of structures at different locations exhibit varying patterns. Structures between the two tunnels experience soil compression and superposition effects during the double-tunnel excavation, leading to complex displacement patterns, with an initial increase followed by a decrease in horizontal displacement. Structures at other locations show a consistent increase in horizontal displacement.

(3) The results from Peck’s empirical formula and the finite element simulation are closely aligned, confirming the simulation’s reliability. Both methods indicate a single-peak settlement curve for single-line tunnel excavation, with the peak at the tunnel centerline. For double-line tunnel excavation, the right-line tunnel’s excavation increases the left-line tunnel’s settlement, with the maximum settlement occurring at the right-line tunnel axis. The simulation shows a double-peak curve, with peaks at the axes of both tunnels. Although the empirical formula predicts a single peak due to its tendency to produce a smooth curve, it cannot precisely capture the two distinct peaks. However, the empirical curve is asymmetrical, showing less settlement on the left side than on the right, and still reliably indicates the maximum settlement location.

The simulation results show that the impact of shield tunnel excavation on the overhead connection bridge meets all relevant standards. Both post-construction settlement and differential settlement between piers are within safety limits, ensuring the bridge’s normal operation.