Deformation Response of Underlying Twin Shield Tunnels Induced by Large Excavation in Soft Soils

Abstract

The potential deformation of underlying shield tunnels caused by extensive excavations in soft soil presents a significant practical concern. In this paper, the deformation of operating twin metro shield tunnels of Shenzhen Metro Line 2 caused by large upper excavation in soft soils is investigated. The field monitoring data vividly portrays the noteworthy tunnel deformations witnessed during the construction of excavation. A three-dimensional numerical model was established to analyze the deformation response of the underlying twin tunnels and surrounding soils. Various protective measures were explored to mitigate the potential impacts of the excavation on the tunnel deformation and structural stress, including sequential excavation, staggered excavation and soil improvement. The results indicate that the deformation of the underlying operating tunnel and surrounding soil’s deformation can be effectively alleviated by properly adjusting the excavation procedure. Compared to the sequential excavation procedure, the adoption of staggered excavation procedure can reduce the vertical deformation of the operating tunnel by at least 11.2% and maximum of 24.89% with the optimal procedure. Soil improvement is not recommended to alleviate tunnel deformation when the depth of the improvement zone is shallow. The outcomes of this study hold valuable insights for safeguarding metro tunnels beneath soft soil excavation.

1. Introduction

With the scarcity of land resources becoming more pronounced, there has been a growing emphasis on the development of underground spaces, especially within the thriving districts of several major cities. In the pursuit of fully optimizing land resources, excavation projects above pre-existing shield tunnels have become an inevitable course of action. The excavation-induced ground stress triggers soil displacement, subsequently leading to additional deformation in the underlying metro tunnel [1,2,3,4,5,6]. This excessive deformation can result in the separation and misalignment of segment connections, as well as warping and distortion of the track, impacting the smooth operation of subway trains. In more severe instances, the tunnel might suffer from water and sand seepage due to the pronounced deformation and segment expansion, thereby compromising subway operational safety [7,8,9]. Consequently, investigating the underlying tunnel’s deformation response resulting from excavation and devising appropriate protective measures assumes significant importance.

Many studies have explored the deformation of adjacent or underlying tunnels stemming from extensive excavations. The numerical simulation method has gained substantial prominence [8,10,11,12,13,14,15,16]. Hu et al. investigated the design and construction of the deep excavation near the Shanghai subway tunnel [12]. They effectively controlled the tunnel deformation through pumping consolidation, cement soil mixing piles, and adjusting excavation procedures. In a similar vein, Huang et al. conducted a FEM study on the deformation response of the tunnel caused by nearby deep excavation [13]. Their found indicates a substantial impact of the excavation on the underlying tunnel within an approximate range of five times the excavation width, as measured along the tunnel axis. Abbas et al. investigated the stress–deformation and stability challenges in Himalayan tunnels considering the impact of geological discontinuities, providing valuable insights into tunnel behavior in highly variable ground conditions [10]. Furthermore, field measurement methods [1,17], empirical or analytical analysis [18,19,20,21,22], and laboratory test methods [23,24] are also frequently used to investigate the deformation response of the underlying tunnel resulting from excavation. However, most of the current excavation studies adhere to sequential block-wise excavation procedures. As highlighted by Sun et al. [25] and Chen et al. [8], there is a notable space effect during the construction of large-scale excavations. It is unclear whether employing staggered excavation can help alleviate the deformation of operating tunnels in soft soils, which benefits to explain the space effect during the construction stage of excavation.

Although the above studies have greatly improved understanding of excavation-induced tunnel deformation, several research gaps remain. Existing work mainly focuses on deformation patterns under sequential excavation and lacks systematic discussion of the spatial effect produced by large-scale staggered excavation in soft soils. Moreover, few studies have combined field monitoring data with validated three-dimensional numerical models to quantitatively evaluate how staggered excavation and soil improvement jointly influence the deformation of underlying operational tunnels. Addressing these issues is crucial for developing more refined excavation and protection strategies in densely built urban areas.

In view of the increasing demand for large-scale excavations above existing metro lines in densely built urban areas, it is essential to examine representative engineering cases that capture the complex interaction between excavation activities and operating tunnels. Shenzhen, a rapidly developing city in southern China characterized by soft soil deposits and intensive underground construction, provides an ideal setting for such an investigation. The findings from this site can offer practical guidance for similar urban tunneling environments.

This study takes Shenzhen Metro Line 2 as a case to explore the deformation response of twin metro shield tunnels during large-scale deep excavation above and the associated protective measures. The effectiveness of staggered excavation, as well as the effect of soil improvement in alleviating deformation in operational tunnels is demonstrated by comparing the construction methods of the sequential excavation method. The following sections outline the structure of this paper. The paper begins by presenting the project’s context and the geological conditions at the construction site. The large deformation of the underlying twin tunnels caused by excavation is illustrated by the field monitoring data. Subsequently, the basic soil mechanical parameters for the HSS model at the construction site are derived from laboratory tests. Following this, a validated three-dimensional finite element model is established to assess tunnel displacements under sequential and staggered excavation procedure. The effectiveness of staggered excavation in alleviating the deformation of the underlying tunnel was confirmed by comparing it with the sequential excavation approach. By evaluating different staggered section’s widths and numbers, the optimal staggered excavation scheme is determined. Additionally, the paper explores the influence of soil improvement on tunnel deformation. This study offers valuable insights for safeguarding metro tunnels beneath excavations in soft soils.

2. Engineering Background

2.1. Project Description

Shenzhen Metro Line 2, initiated on 13 June 2007 and successfully completed on 28 June 2011, serves as the pivotal route connecting the eastern and western parts of Shenzhen. As shown in Figure 1 and Figure 2, the investigated segment encompasses two parallel shield tunnels extending from Hongshuwan station to World-Window station, forming a part of Shenzhen Metro Line 2. The gap between the two tunnels spans approximately 11.4 m. The burial depth of the tunnel crown varies from 16.9 m to 18.1 m. The excavation above these twin tunnels was executed through open-cut methods. The excavation’s extent covered approximately 120 m in length, with an excavation width of around 40 m and a final excavation depth averaged 12.5 m. To ensure the safety of Metro Line 2 twin tunnels and take advantage of the space effect during excavation, the excavation was carried out in a sloping manner, divided longitudinally and layered vertically, to minimize rebound and uplift of the underlying twin tunnels.

2.2. Geological Conditions

The survey report reveals that the original topography of the site resembled a coastal beach landscape, subsequently filled with a combination of rock and soil, eventually resulting in the present land configuration. Presently, the site stands as a level and open expanse. According to the survey report, there are no major fault zones traversing the designated area. The twin tunnels and the excavation were implemented within typical soft soil layers. Groundwater is evident in all boreholes on-site, with an average depth of 4.91 m. Figure 3 illustrates the subsurface soil layer profile. The shield tunnel primarily traverses clay (layer ③₁) and gravel sand (layer ③₂). The soil layers within the excavation zone are composed of fill (layer ①), muddy clay (layer ②), and clay (layer ③₁) from top to bottom. Marine sedimentary soft soils with characteristics such as high water content, sensitivity, permeability, and low strength are extensively distributed across the construction site. The mechanical properties of these soils are markedly compromised after being disturbed by neighboring construction activities. The excavation unavoidably introduces disturbances to the adjacent soil, consequently impacting the stability of the underlying twin tunnels.

3. Field Observation and Monitoring

The initial excavation occurred between 30 June 2019 and 15 August 2019, reaching a depth of 5.5 m. Following a two-month resting period of the excavation site, the tunnel experienced a maximum vertical displacement of approximately 1.75 mm before settling into a stable state. However, the original plan was discarded due to the limits of construction site. Consequently, the first change to the original plan involved partitioning the excavation area into 22 sections along the tunnel’s longitudinal axis. Between 20 October 2019 and 26 October 2019, an earthwork section measuring 22 m in length and 4 m in thickness adjacent to the sales office was excavated. Following this construction phase, field monitoring data indicated distinct levels of uplift deformation in the twin tunnels. Figure 4 shows the monitoring data detailing tunnel deformation at various positions after the excavation. The field monitoring location is described in Figure 4a. As seen in Figure 4b, the excavation prompted a notable uplift deformation in the tunnel, which progressively stabilized over a span of five days. The maximum deformation of the left line tunnel is 13.5 mm, with the corresponding locations at D19. Owing to the substantial uplift deformation of the twin tunnels, a second alteration of the scheme became imperative. The revised plan involves employing Larsen steel sheet piles to partition the excavation area into two sections along the tunnel’s longitudinal axis: a right-side section and a left-side section. Each of these sections is further divided into several subsections spaced at 4-meter intervals along the metro line’s length. The excavation is then executed using a staggered procedure, starting with the right-side section and followed by the left-side section.

4. Determination of Parameters in the HSS Model

Benz introduced the Hardening Soil Model with Small Strain Stiffness (HSS) [26], which accounts for the nonlinear correlation between shear stiffness and strain within the small strain range. The HSS model offers distinct advantages in capturing shear hardening, compression hardening, as well as loading and unloading effects in soils, rendering it particularly suitable for simulating excavations in soft soil regions [25,27,28,29,30]. Consequently, the HSS model is employed herein to characterize the constitutive model of soft soils. HSS model contains 13 mechanical parameters, which can be obtained through laboratory tests. Some main mechanical parameters of the HSS model and their corresponding experimental methods are listed in

Table 1. Main mechanical parameters of the HSS model and corresponding test methods.

Parameters	Test Method
c′ (kPa)	Triaxial consolidated drained (CD) shear test
${\phi }^{\mathrm{\prime }}$(°)
$E_{50}^{ref}$ (kPa)	Triaxial loading and unloading test
$E_{ur}^{ref}$ (kPa)
$R_f$
$E_{oed}^{ref}$ (kPa)	One-dimensional compression consolidation test
m

Note: c′ = effective cohesion of soil; ${\phi }^{\mathrm{\prime }}$ = effective friction angle of soil; $E_{50}^{ref}$ = secant stiffness in standard drained triaxial test; $E_{oed}^{ref}$ = tangent stiffness for primary oedometer loading; $E_{ur}^{ref}$ = unloading/reloading stiffness from drained triaxial test; m = power for stress-level dependency of stiffness.

. In combination with the field survey data, the muddy clay layer (②) and clay layer (③₁) were mainly sampled on the construction site. The determination of soil parameters and the results of laboratory tests are described in detail below. It is noteworthy that, for the sake of brevity, the following is only an example of a clay layer (③₁) to illustrate the test results and determination of soil mechanical parameters.

Firstly, four triaxial consolidated drained (CD) shear tests were conducted for the typical clay layer (③₁) in Shenzhen to obtain the effective stress strength index. The $q-{\epsilon }_{\alpha }$ curve, $p\prime -q\prime$ plane stress path, pore water pressure growth curve, and effective stress ratio curve are shown in Figure 5. It can be observed that the deviatoric stress of the clay gradually increases during the undrained shearing process and then tends to be stable. Figure 6 plots the stress envelope of the Mohr circle after post-processing the results of Figure 5. Through curve fitting, the values of cohesion and effective friction angle can be obtained as $c^{\prime }=14.93$ kPa and ${\phi }^{\prime }=25.78$°.

The $E_{oed}^{ref}$ and m in Table 1 can be determined by a one-dimensional compression consolidation test. The loading and unloading curves of the clay layer are shown in Figure 7. The compression coefficient $C_c$ and rebounding coefficient $C_s$ of clay can be obtained from the slope of the compression section and the slope of the unloading section. Specifically, the compressibility coefficient is $C_c$ = 0.058 and rebounding coefficient $C_s$ = 0.023. Based on this, the $p\prime -{\epsilon }_{\alpha }$ data of the clay was fitted, and the tangent slope of the fitting curve at the reference pressure $p^{ref}=100 \mathrm{k}\mathrm{P}\mathrm{a}$ is the $E_{oed}^{ref}$. The tangent modulus $E_{oed}$ under different consolidation pressures $p^{\prime }$ is normalized and plotted in logarithmic coordinates by $E_{oed}^{ref}$, and then m can be obtained. The relationship between $E_{oed}^{ref}$ and m is listed as follows:

$$E_{oed}=E_{oed}^{ref}{\left({\displaystyle \frac{c^{\prime }cos{\phi }^{\prime }-{\sigma }_3^{\prime }sin\phi \prime }{c^{\prime }cos\phi \prime -p^{ref}sin\phi \prime }}\right)}^m$$

(1)

The corresponding results are plotted in Figure 8a and Figure 8b, respectively. Through the fitting equation in Figure 8a, it can be obtained that the tangent stiffness for primary oedometer loading when $p^{\prime }=100 \mathrm{k}\mathrm{P}\mathrm{a}$ is $E_{oed}^{ref}=5.94 \mathrm{M}\mathrm{P}\mathrm{a}$. By fitting the data in Figure 8b, it can be obtained that $m=0.478$.

Finally, based on the triaxial loading and unloading test, the secant stiffness in the standard drained triaxial test $E_{50}^{ref}$, the unloading/reloading stiffness from drained triaxial test $E_{ur}^{ref}$ of the soil under the reference stress $p^{ref}=100 \mathrm{k}\mathrm{P}\mathrm{a}$, and the failure ratio $R_f$ can be obtained. Under the consolidation pressure of $p_0$ = 100 kPa, the results of the triaxial consolidated drained unloading/reloading test in the clay layer are shown in Figure 9. It can be seen from Figure 9a that the deviatoric stress increases first and then decreases with the increase in the axial strain, which shows the characteristics of shear hardening and shear softening, respectively. It can be obtained that under 100 kPa confining pressure, the failure ratio is $R_f=0.97$, and the corresponding stiffness is $E_{50}^{ref}=3.29 \mathrm{M}\mathrm{P}\mathrm{a}$, $E_{ur}^{ref}=29.76 \mathrm{M}\mathrm{P}\mathrm{a}$. All the main soil mechanical parameters of the HSS model listed in Table 1 were obtained through laboratory tests. The specific mechanical parameters of the muddy clay layer (②) is listed in Section 5.2, together with the numerical finite element model.

5. Numerical Analysis Details

5.1. Analysis Cases

In order to replicate the real construction sequence, the simulation also included the construction of the twin tunnels before excavation. It is noteworthy that the main objective of this study was to focus on the net effect of the upper excavation on the operating tunnel. The soil deformation caused by the construction of tunnel is not in our scope of consideration. Meanwhile, considering that the tunnel construction occurred 8 years prior to the current excavation, the pore water pressure caused by tunnel construction has largely dissipated. Hence, the simulation of tunnel construction was streamlined relative to the step-wise approach and the stress reduction method. The tunnel lining was first activated in the 3-D numerical model, and the soil elements in the tunnel were deactivated. The deformation of soil and structures caused by tunnel construction was reset to zero before proceeding to the subsequent calculation step. Then the excavation was simulated using a step-by-step approach. Interface elements were applied to retaining piles to simulate a waterproof curtain around the excavation. The excavated soil was assigned as “dry”, while the hydraulic boundary condition for the soil below the excavation face was set to “head”, with the water level set 0.5 m below the excavation face. The water condition outside the excavation area remained unchanged. The specific construction steps for several different cases involved in this study can be briefly summarized as follows.

For case 1, the simulation focuses on sequential excavation, providing a baseline against which the outcomes of subsequent staggered excavation scenarios are evaluated. The specific excavation steps in case 1 are to divide the excavation area into 22 blocks along the longitudinal direction of the metro line, followed by sequential excavation of each block, as shown in Figure 10. The aforementioned simulation also approximately mirrors the actual field conditions.

Furthermore, to investigate the difference between the staggered excavation and the sequential excavation procedure, a staggered excavation simulation, referred to as case 2, is conducted. As shown in Figure 11, Larsen steel sheet piles are used to divide the excavation into the left and right lines along the metro line. Then, the excavation area is then sectioned at 4 m intervals along the metro line’s longitudinal direction. Within this framework, two staggered sections are simultaneously excavated, starting with the right line and followed by the left line. The space between the two stagged sections is half the length of the excavation. Meanwhile, to examine the influence of the width of staggered sections on the deformation of the underlying twin tunnels, the width of the staggered sections is adjusted to 5 m in case 3 and 6 m in case 4. The excavation procedures in case 3 and case 4 mirrors that of case 2. Furthermore, to assess the effect of the number of staggered sections on the deformation of the underlying twin tunnels, case 5 follows the staggered section width of case 2 but excavates one section at a time. On the other hand, case 6 excavates three sections simultaneously, also based on the staggered section width of case 2. All excavation schemes employ sloping excavation, with a slope of 1:1.0 and a vertical excavation depth of 1 m each time.

Finally, to explore the effectiveness of soil improvement in alleviating the deformation of the underlying twin tunnels, case 7 involves soil improvement at the excavation bottom. Since the area within 3 m around the tunnel is the no-disturbance zone, combined with the construction site dimensions, the depth of the improved soil is determined to be within 1 m of the excavation bottom. The excavation procedure in case 7 is performed in the same manner as in case 2. The above-mentioned analysis cases are listed in

Table 2. Analysis cases.

Case	Staggered	Section’s Width (m)	Number of Sections Excavated Simultaneously	Soil Improvement
1	-	6	1	-
2	Simulated	4	2	-
3	Simulated	5	2	-
4	Simulated	6	2	-
5	Simulated	4	1	-
6	Simulated	4	3	-
7	Simulated	4	2	Simulated

.

5.2. Numerical Finite Element Model and Parameters

In this study, the finite element software Plaxis-3D V21 [31] was used to simulate the excavation process. To minimize the influence of model boundaries on calculation results, lateral boundaries were established at three points of the final excavation depth. As a result, the domain of the model is 140 × 80 × 40 m. The boundary conditions encompass a fixed base and lateral rollers on the side face. The mesh of the finite element model is illustrated in Figure 12, comprising approximately 330,000 10-node wedge elements and 480,000 nodes. The retaining piles, Larsen steel sheet piles, tunnel linings, and the bottom slab of the excavation were simulated using 6-node plate elements, assuming linear elastic behavior. The interface element is a joint element added to the plate to properly simulate the interaction between structure and soil. The interface strength and soil strength are interconnected through the selection of an appropriate interface strength reduction factor, denoted as $R_{inter}$, to simulate the interaction roughness between structure and soil. This study uses 0.67 for cohesive soil and 0.6 for non-cohesive soil based on the suggested value of technical specifications for excavation support. Meanwhile, the stiffness of the tunnel lining is reduced to 70% of its nominal value to account for construction joints, segmental connections, and early-age concrete creep, which reduce the effective stiffness compared to the theoretical value. This reduction only applies to Young’s modulus and does not alter the boundary conditions of the model [13,32,33].

In this study, different constitutive models were adopted for different soil and rock layers to capture their mechanical behavior more accurately. The Hardening Soil Small (HSS) model was used for the majority of soft soil layers, as these soils exhibit significant nonlinear and stress-dependent stiffness, which the HSS model can realistically simulate. In contrast, the Mohr–Coulomb (MC) model was applied to the fill layer and the four weathered granite strata. These materials are comparatively stiffer and display linear elastic–plastic behavior with well-defined cohesion and friction parameters, making the MC model sufficient to represent their mechanical response while reducing computational complexity.

Table 3. Soil parameters for HSS model and Mohr–Coulomb model.

Parameter (Units)	①	②	③1	③2	④	⑤1	⑤2	⑤3	⑤4
Constitutive Model	MC	HSS	HSS	MC	HSS	MC	MC	MC	MC
γ (kN/m3)	21	18.5	18	19	18.5	20	21	22.5	23.5
E′ (kPa)	10 × 103	-	-	28 × 103	-	65 × 103	130 × 103	500 × 103	600 × 103
$\nu$	0.35	-	-	0.28	-	0.3	0.25	0.22	0.2
${\nu }_{ur}$	-	0.2	0.2	-	0.2	-	-	-	-
c′ (kPa)	12	16.37	14.93	1	25	30	35	100	200
${\phi }^{\mathrm{\prime }}$ (°)	25	18.75	25.78	30	22	27	30	33	35
$E_{50}^{ref}$ (kPa)	-	2660	3290	-	14.67 × 103	-	-	-	-
$E_{oed}^{ref}$ (kPa)	-	2390	5940	-	15 × 103	-	-	-	-
$E_{ur}^{ref}$ (kPa)	-	12.13 × 103	29.76 × 103	-	110.1 × 103	-	-	-	-
m	-	0.515	0.478	-	0.8	-	-	-	-
Rf	-	0.79	0.97	-	0.91	-	-	-	-

Note: γ = volumetric weight of soil; E’ = effective Young’s modulus; $\nu$ = Poisson’s ratio for MC model; ${\nu }_{ur}$ = Poisson’s ratio of unloading/reloading; c′ = effective cohesion of soil; ${\phi }^{\mathrm{\prime }}$ = effective friction angle of soil; $E_{50}^{ref}$ = secant stiffness in standard drained triaxial test; $E_{oed}^{ref}$ = tangent stiffness for primary oedometer loading; $E_{ur}^{ref}$ = unloading/reloading stiffness from drained triaxial test; m = power for stress-level dependency of stiffness; Rf = failure ratio.

shows the soil characteristics utilized for numerical analysis using data gathered from laboratory tests or field investigations, whereas

Table 4. Parameters for retaining pile, tunnel lining, and Larsen steel sheet pile.

Parameter (Units)	Retaining Pile	Tunnel Lining	Larsen Steel Sheet Piles
d (m)	0.82	0.3	0.15
γ (kN/m3)	18	18	78
E1 (kN/m2)	3 × 107	6.47 × 106	2.06 × 108
E2 (kN/m2)	-	3.45 × 107	-
υ	0.15 ss	0.15	0.30

Note: d = thickness of plate element; γ = additional unit weight of plate; E1 = Young’s modulus in longitudinal direction for lining; E2 = Young’s modulus in circumferential direction for lining; and υ = Poisson’s ratio of concrete.

shows the mechanical properties of plate elements involved in the numerical model.

6. Results and Discussions

6.1. Numerical Model Validation

Before proceeding with the analysis, it is essential to validate the accuracy of the computational model and the reasonableness of input parameters. This validation can be accomplished by comparing the numerical results with field monitoring data. However, due to several modifications in the excavation procedure, it is challenging to faithfully replicate the original excavation sequence in its entirety. Hence, in this part, a partial reenactment of the initial excavation stages has been conducted. This detailed excavation process in this period is depicted in Figure 13. The tunnel deformation after this construction period is shown in Figure 14. It can be observed that the simulated value is relatively consistent with the monitored value. The tunnel deformation is relatively small outside the excavation area and gradually increases as it approaches the excavation area. The maximum deformation of the left tunnel obtained by numerical simulation is 5.55 mm, a 5.93% difference compared to the monitored 5.9 mm. Similarly, the maximum deformation of the right tunnel obtained by numerical simulation is 4.14 mm, which is only a 4.83% difference compared to the monitored 4.35 mm. It should be noted that both monitoring results and numerical results indicate that the floating deformation of the left tunnel is greater than that of the right tunnel, which is due to the shallower burial depth of the left tunnel. The chosen reduction factor is consistent with site-specific conditions, and the numerical results with 70% stiffness show good agreement with field monitoring data, confirming that the adjustment adequately captures the tunnel’s deformation behavior during excavation. As a result, it can be considered that the three-dimensional finite element numerical model established in this paper can reasonably reflect the deformation response of underlying twin tunnels induced by excavation.

In this study, the observed differences in deformation between the left and right tunnels are primarily attributed to the depth-dependent soil stress distribution and the interaction with the excavation above, rather than from asymmetric loading conditions. The numerical model assumes symmetric surrounding conditions and uniform external loading from buildings and other structures, meaning that any asymmetry in actual construction loads or adjacent buildings is not considered.

6.2. Effect of Staggered Excavation Procedure

It can be imagined that sequential excavation and staggered excavation have different effects on tunnel deformation. Hence, the effectiveness of the staggered procedure method in alleviating the deformation of the underlying twin tunnels caused by excavation is discussed, and the impact of the width and number of staggered sections on the vertical and horizontal displacement of the tunnel is investigated. Taking the right tunnel as an illustration, Figure 15 presents the horizontal and vertical displacement of the right tunnel after excavation in different staggered excavation scenarios. A comparison with sequential excavation in case 1 reveals that the implementation of staggered excavation effectively reduces both horizontal and vertical tunnel displacement. The width and number of staggered sections seem to have minimal impact on alleviating the horizontal displacement of the tunnel in varying staggered excavation cases. However, it can be observed from Figure 15b that the staggered excavation can significantly reduce the vertical deformation of the tunnel. This indicates a heightened sensitivity of vertical displacement to excavation-induced deformation in contrast to horizontal displacement. Compared to the sequential excavation procedure, adopting the staggered excavation procedure can reduce the vertical deformation of the operating tunnel by a minimum of 11.20%. From Figure 15b, it is evident that case 2 stands out as notably superior to the other staggered excavation schemes in alleviating the vertical tunnel displacement. Compared to alternative staggered excavation procedures, adopting case 2 leads to an additional 13.69% reduction in the vertical deformation of the operational tunnel. The total reduction is 24.89% compared to the sequential excavation procedure. To better illustrate the effectiveness of the staggered excavation method, Figure 16 presented the vertical displacement of the soil at the position of the foundation pit bottom along A-A′ line (Figure 1). The effect of the staggered excavation method on the vertical displacement of the excavation bottom is not obvious in the excavation area. However, the effectiveness in alleviating the soil deformation beyond the excavation area is obviously better compared to case 1. In addition, compared with other different cases of staggered excavation, case 2 is also better in alleviating the deformation of the excavation bottom.

Besides the displacement of the tunnel and excavation bottom, structural deformation is also a significant concern to engineers. Therefore, it is necessary to study the deformation response of the retaining piles to the different excavation schemes. Figure 17 presents the lateral deformation of the piles installed at the excavation bottom along A-A′ line. Figure 17a–c correspond to the left row of piles, the middle row of piles, and the right row of piles, respectively. It can be observed from Figure 17 that the lateral displacement of the three rows of piles is quite small. Specifically, the lateral displacement of the middle row of piles caused by case 1 is only −0.13 mm, marking the lowest value. In contrast, the maximum lateral displacement of the middle row of piles, caused by case 4, reaches 2.32 mm. This variation can be attributed to the fact that case 1 involves excavating the entire excavation in longitudinal blocks along the metro line, without dividing it into left and right sections. Consequently, in case 1, the middle row of piles demonstrates negligible lateral deformation. The distinct impact of different excavation schemes on structural deformation is a compelling indication of the evident space effect during the excavation process. Additionally, a noteworthy observation emerges: above the tunnel, pile deformation in case 1 is less than that observed in other schemes, whereas below the tunnel, this trend is reversed. Among the staggered excavation schemes, case 2 results in the least pile deformation. Given its capacity to effectively manage tunnel deformation, case 2 emerges as the optimal scheme among the various scenarios.

To further illustrate the deformation characteristics of the retaining piles under different construction schemes, a comparative summary of pile displacements is presented in

Table 5. Summary of displacement of piles in different simulation cases.

Case	Left Row of Piles	Middle Row of Piles	Right Row of Piles
1	−1.56 mm	0.13 mm	−1.53 mm
2	−1.44 mm	1.64 mm	−1.71 mm
3	−1.53 mm	1.56 mm	−1.84 mm
4	−1.95 mm	2.29 mm	−2.02 mm
5	−1.60 mm	1.70 mm	−1.83 mm
6	−1.92 mm	1.92 mm	−1.94 mm

. The table includes the maximum lateral displacements of the left, middle, and right rows of piles for six simulation cases, encompassing both sequential and staggered excavation schemes, as well as the cases with and without soil improvement. The comparison clearly shows that case 2 effectively reduces the lateral displacement of all pile rows among staggered excavation schemes.

6.3. Development of Tunnel Deformation

As previously explained, the excavation was executed through a step-by-step process, consequently resulting in varying degrees of influence on the underlying twin tunnels during distinct construction stages. To explore the deformation response of tunnels across these different stages, the construction process has been segmented into four discrete stages, visually represented in Figure 18. Among them, ‘Stage 1’ corresponds to the halfway completion of right line excavation, ‘Stage 2’ indicates full completion of right line excavation, ‘Stage 3’ indicates the halfway completion of left line excavation, and ‘Stage 4’ marks the completion of the excavation. As mentioned before, case 2 emerges as the optimal choice for the staggered excavation, demonstrating the most effective impact in alleviating the vertical displacement of the tunnel and the uplift at the excavation bottom. Hence, this discussion will exclusively focus on the evolution of tunnel deformation in case 2. Figure 19 and Figure 20 show the displacement of the right tunnel and left tunnel during different construction stages, respectively. The growth in the vertical and horizontal displacement of the right tunnel during stages 1 and 2 is significantly greater than during stages 3 and 4. Conversely, the left tunnel exhibits an opposing pattern compared to the right tunnel.

Table 6. Development of tunnel deformation at different construction stages.

Construction Stage	Left Tunnel		Right Tunnel
	Vertical Displacement	Increment	Vertical Displacement	Increment
Stage 1	1.75 mm	1.75 mm	6.27 mm	6.27 mm
Stage 2 (Right line completed)	2.19 mm	0.44 mm	10.06 mm	3.79 mm
Stage 3	5.43 mm	3.24 mm	10.40 mm	0.34 mm
Stage 4 (Left line completed)	8.62 mm	3.05 mm	10.71 mm	0.31 mm

summarizes the development of tunnel deformation during different construction stages. Evidently, the growth of the left tunnel deformation occurs primarily in stages 3 and 4 (corresponding to the excavation of the left line), whereas the growth of the right tunnel deformation occurs primarily in stages 1 and 2 (when the right line is excavated). It can be inferred that the excavation of the right line is primarily responsible for the displacement of the right tunnel, and the excavation of the left line has little effect on the displacement of the right tunnel. The left tunnel deformation follows a similar pattern to that of the right tunnel. The various growth patterns demonstrate the existence of space effect during excavation. Thus, making good use of the space effect during the excavation process can prove instrumental in alleviating the deformation of underlying tunnel.

To analyze the influence of excavation procedure on the structure, Figure 21 plots the development of bending moment in the Larsen steel sheet piles along A-A′ line at various construction stages. It is noteworthy that the maximum bending moment of Larsen steel sheet piles appears after the completion of the right line excavation (i.e., stage 2), rather than after the completion of the entire excavation (i.e., stage 4). As shown in Figure 20, the bending moment of the Larsen steel sheet piles gradually increases during stage 1 and stage 2 of excavation, culminating at a maximum value of 295.72 kN∙m. Subsequently, the bending moment starts diminishing during stages 3 and 4 of excavation, corresponding to the excavation of the left line. By stage 4, the bending moment in the steel sheet piles decreases to 178.80 kN∙m, approximately 40% less than the maximum bending moment during stage 2. This shift is primarily attributed to the decrease in lateral soil pressure behind the steel sheet pile from stage 3 onward, contributing to a reduction in the bending moment. This observation underscores that the influence of excavation sequence on the structure is not to be dismissed. Namely, adopting staggered excavation procedure can effectively alleviate the deformation of the underlying tunnel; however, it concurrently necessitates a corresponding enhancement in the mechanical load-bearing capacity of the structure.

6.4. Influence of Soil Improvement

To examine the influence of soil improvement on tunnel deformation, the soil at the excavation bottom was reinforced in case 7. Given that the area within 3 m of the tunnel is a no-disturbance zone, combined with the dimensions of the actual construction site, the scope of soil improvement is within 1 m of the excavation bottom. Figure 22 plots the vertical displacement of the left tunnel across various construction stages after soil improvement. The effect of soil improvement on stages 1 and 2 is obvious. Compared with case 2, the soil improvement has reduced the tunnel heave by about 5%. This implies that while soil improvement can indeed mitigate the vertical deformation of the underlying tunnel to a certain extent, the economic feasibility remains limited when the soil improvement zone is shallow.

Figure 23 plots the vertical displacement of soil at different positions along the A-A′ line in both cases 2 and 7. It can be observed that soil improvement plays an important role in alleviating the uplift at the excavation bottom. As depth (d) increases, the vertical displacement of the soil experiences a decline. The impact of excavation on soil vertical displacement remains negligible in positions distant from the excavation bottom (e.g., d > 2H). Meanwhile, Figure 24 depicts the evolution of bending moment in the Larsen steel sheet piles along A-A′ line during different excavation stages. Compared with case 2, soil improvement leads to an increase in the bending moment of the Larsen steel sheet piles. This is because soil improvement increases the stiffness of the surrounding soil, which enhances its ability to resist deformation and transfers larger loads to the supporting piles. Consequently, the mechanical load-bearing capacity requirements of the piles are elevated, which must be considered in the design of retaining structures.

7. Conclusions

Taking typical soft soils in Shenzhen as an example, this paper investigates a case study on the deformation response of underlying twin metro shield tunnels caused by large excavation. The mechanical soil parameters of the HSS model at the construction site are obtained through laboratory tests. A verified three-dimensional finite element model is established based on the HSS and MC constitutive models. The displacement of the underlying twin tunnels, the uplift of the excavation bottom, and the lateral displacement of the piles are investigated under different cases of staggered excavation schemes. In particular, the development of tunnel deformation under the optimal case of staggered excavation, as well as the effectiveness of soil improvement, are discussed in detail. The main conclusions obtained from this study can be summarized as follows:

(1) Significant deformation occurred in the operating tunnels during the excavation process, indicating that large-scale excavations in soft soils can pose severe risks to the structural integrity and operational safety of underlying tunnels. The comparison between field monitoring and numerical results confirmed that the adopted 3D finite element model based on the Hardening Soil Small (HSS) model can reliably capture the deformation behavior observed in practice.

(2) The excavation-induced deformation of underlying twin tunnels is strongly governed by the space effect. Vertical displacement is more sensitive to the excavation process than horizontal displacement. Compared with the conventional sequential excavation, the staggered excavation method can effectively mitigate tunnel deformation, reducing the maximum vertical displacement of the operating tunnel by up to 24.89% under the optimal staggered scheme.

(3) The optimal staggered excavation scheme divides the excavation area into several 4 m wide longitudinal sections, with two adjacent sections excavated in a staggered manner—first the right line, then the left. This configuration effectively alleviates the deformation of the underlying tunnels and improves the overall stress distribution in the surrounding soil. While soil improvement has limited benefits when the treated depth is shallow, the staggered excavation method provides a more effective control of tunnel deformation.

(4) The deformation control mechanism can be attributed to the redistribution of soil stress and the evolution of the plastic zone around the tunnel. The sequential excavation allows gradual stress release and limits abrupt unloading above the tunnel crown, thereby improving the overall stability of the tunnel–soil system.

(5) Effective utilization of the space effect during excavation can significantly mitigate the deformation of underlying tunnels. The study provides practical guidance for the design and construction of underlying tunnels beneath large-scale excavations. The findings offer a reference for the development of refined excavation schemes and deformation control measures in densely built urban areas.