Response Monitoring and Analysis in Deep Foundation Pit Excavation: A Case Study in Soft Soil at Subway Tunnel Intersections

Abstract

With the rapid development of urban rail transit and underground space development, the occurrence of excavation near existing tunnels is becoming more common. This excavation and unloading will inevitably cause soil deformation outside the pit and the tunnel buried therein. This paper presents an investigation into the entire excavation process and the deformation effects on the adjacent subway structure under complex construction environments, including soft soil foundations and adjacent subway intersections, based on measured data of pit construction. The horizontal and vertical displacements of deep soils in two pits were analyzed along with safety management measures to determine the horizontal displacement curve pattern and the lateral displacement development distribution law of deep soils. The analysis of subway deformation data shows that after excavation, the subway tunnel undergoes “lateral expansion” and “vertical compression” type deformation, accompanied by “in-pit” horizontal displacement and “settlement” vertical displacement. Furthermore, a correlation analysis reveals a clear linear relationship between pit deformation and subway structure deformation, which can be used as a prediction method for adjacent structure deformation. Finally, a comparative analysis of existing relevant influence zone models and tunnel deformation prediction formulas is carried out based on the monitoring. The results of this study have significant guiding implications for the excavation construction of soft soil foundations in the vicinity of subway crossings.

1. Introduction

The excavation process of deep foundation pits under soft soil conditions is a challenging and complex engineering task [1,2,3,4], which requires a high level of expertise and skill. There are established codes and standards in place to limit the impact of soft soil permeability on the excavation process. Now, one of the most significant risks associated with excavation under soft soil conditions is the potential impact on adjacent structures and infrastructure, especially when excavating in close proximity to an existing subway system [5,6,7,8]. In particular, the construction of a deep foundation pit can pose significant risks to the integrity of the subway infrastructure. To mitigate these risks, it is essential to conduct thorough measurements and analysis of the existing subway deformation before, during, and after the excavation process. This allows engineers and construction professionals to monitor the potential impact of the excavation on the subway system and take appropriate measures to mitigate any risks. In this study, we investigate a particularly complex foundation construction environment. Specifically, we examine the excavation of deep foundation pits on a soft soil foundation at the intersection of two tunnels. The foundation pits at two separate locations are excavated successively, presenting a challenging and intricate task.

Numerous studies have investigated the deformation of existing subway infrastructure during the excavation of nearby deep foundation pits. Through the statistical analysis of 42 engineering cases and 47 tunnels, it was observed that the excavation process causes significant deformation of the subway tunnel, which poses a threat of structural damage [9,10]. Notably, the monitoring results of the Zhengzhou East High-speed Railway Station [11] indicate that bilateral deep foundation pit excavation leads to stress redistribution and substantial deformation of the adjacent tunnel, and may even result in the cracking of the lining structure. Additionally, measured results from a new building project in Beijing demonstrate that the inner bracing + pile–anchor composite support structure offers better control over the deformation of adjacent stations and tracks [12].

The excavation of foundation pit projects is known to disturb the surrounding geotechnical body to varying degrees, resulting in what is called the engineering influence zone. According to the Zhejiang Code [13], no construction can take place within a 3 m radius adjacent to both sides of the metro project’s outer edge. The Technical Specification [14] provides a more detailed graded influence zone, which is divided into a strong influence zone (A), a significant influence zone (B), and a general influence zone (C) based on the proximity of construction activities outside the existing tunnel. Moreover, the Monitoring code [15] offers zoning recommendations for the environmental impact of pit excavation, which are divided into three zones based on the level of impact. However, this method fails to account for the impact of the encircling piles (walls) inserted below the bottom of the pit. It seems more suitable for traditional shallow pits that lack insertion depth. Similarly, relevant British codes provide a relatively simple range, specifying the excavation impact width of the pit and the impact depth, but they do not consider different excavation conditions, enclosure deformation patterns, deformation sizes, and different deformation control standards. To address this gap, researchers Zheng et al. [16] and Liu et al. [9,10] used the finite element method to parametrically analyze the effect of pit construction on the deformation law of existing tunnels outside the pit. They combined different code deformation control standards and divided the influence zone of existing tunnel deformation outside the pit under different enclosure structure deformation modes and maximum horizontal displacement conditions. By doing so, they sought to find a more suitable method for dividing influence zones and guiding engineering practice.

The prediction methods [17,18,19,20,21,22] for tunnel deformation caused by foundation pit excavation unloading can be broadly classified into three categories: empirical formula, theoretical analysis, and numerical simulation. While numerical simulation methods offer high accuracy, they require users with advanced technical expertise, especially in theoretical calculation models, due to the impact of several factors such as constitutive models and parameters, boundary conditions, and simulation process on the simulation results. In contrast, the empirical formula method is more practical, as it avoids complex theoretical formulas and assumptions made in theoretical analysis and numerical simulation methods. Wei et al. [23,24] conducted statistical analyses to determine significant factors influencing the horizontal displacement of the tunnel caused by excavation unloading. They established a power function relationship between the net distance and the maximum horizontal displacement of the tunnel. The excavation width of the pit was also considered to be indicative of the degree of stress release in the soil. On the other hand, Liu et al. [9] considered additional factors such as engineering geological conditions, pit excavation depth, horizontal spacing between the tunnel and pit, and the longitudinal width of the pit along the tunnel. A formula was developed to predict the maximum horizontal displacement of the lateral tunnel caused by pit excavation in different soil types, including specific formulas for chalky soil and silt strata. This project involves a more complex construction environment and construction measures than conventional projects, including soft soil foundations and adjacent subway intersections. The cost of theoretical and numerical analysis methods is deemed too high, and the applicability and accuracy of empirical methods cannot be fully justified. As a result, the analysis is based on the whole process construction monitoring approach.

This study investigates the excavation process of foundation pits under soft soil conditions around two subway tunnel intersections using actual measurement data. Horizontal and vertical displacements of deep soil in two pits, as well as the response of the neighboring existing subway structure, are studied. The relationship between tunnel displacement and foundation pit lateral displacement is then analyzed using the Pearson correlation coefficient. Finally, the influence zone model and tunnel deformation prediction formula are introduced to evaluate the excavation process of deep foundation pits at subway tunnel intersections.

2. Project Overview

The analyzed deep foundation pit project is situated in a soft soil area in Nanjing and employs sub-pit construction. The project consists of three plots, namely AD, B, and C, with a specific construction sequence for each plot: B1, C1 area → B2, C2 area → A1 + D1 area → A2 area → D2 area. Due to the vast scale and numerous working conditions, this paper provides a detailed analysis of the construction process for B2 and C2 pits located near the intersection of Line S3 and Line 7, as illustrated in Figure 1. The depths of the pit for B2 and C2 are 12.75 m and 16.15 m with two and three-story basements, respectively. The west side of pit B2 is supported by an 800 mm thick underground continuous wall, while the east and south sides are reinforced with 1000 mm thick underground continuous walls. In addition, two reinforced concrete supports and 850 mm diameter triaxial deep churning trench wall reinforcement piles provide further support. Similarly, the south side of pit C2 is fortified with a 1200 mm thick underground continuous wall, while the east and west sides are reinforced with 1000 mm thick underground continuous walls. Furthermore, 850 mm diameter tri-axial deep churning trench wall reinforcement piles were set to support the pit. To safeguard the subway structure, Trench—Cutting and Re-mixing Deep Wall Method (TRD method) piles with a depth of 34 m were installed on the south side of both B2 and C2 pits, with internal pipe piles approximately 20 m long.

The location profile of pit B2 in relation to the subway is depicted in Figure 2. To ensure the stability and safety of the subway structure, it is crucial to take into account the location of the foundation pit concerning the subway and its burial depth. By considering the net distance from the subway and the burial depth of each critical component, the construction team can devise an appropriate construction plan. The depth of burial for Line S3 is approximately 13.0 m, while the bottom of the station house is buried at a depth of about 18.1 m. The bottom of the subsidiary structure for Line 7 and the station house are buried at depths of approximately 9.6 m and 26.0 m, respectively. Pit B2 is located at a net distance of about 36.7 m from the Line S3 upline and about 51.7 m from the downline. Meantime, it is situated at a net distance of approximately 18.1 m and 28.1 m from the subsidiary structure and station house of Line 7. Similarly, pit C2 is situated at a net distance of about 40.3 m upline and 55.3 m downline of Line S3. The net distance to the station house of Line 7 is approximately 16.8 m. After the pit maintenance and pile foundation works, the pit dewatering works need to be carried out, and then the excavation and support construction of the soil layer. The greater the permeability coefficient of the soil layer within the dewatering depth leads to the more obvious permeability anisotropy. Additionally, within the same dewatering time, a greater degree of pore water pressure reduction will occur in the soil layer. At last, the lateral displacement of the supporting wall will be greater under the total pressure redistribution of the wall–soil interface. In this project, there is a deep silt layer below the excavation surface, which is highly permeable, so it is necessary to use an underground diaphragm wall to enter the strongly weathered rock to form a water curtain. The dewatering should be conducted about two weeks in advance, and dynamically adjusted to ensure that the water level in the pit is 1.0 m below the excavation surface during the excavation process. Additionally, the foundation pit excavation was carried out layer by layer, with the general working conditions summarized in

Table 1. Working conditions.

Pits	Conditions	Time	Main Description (Completion Details)
B2	1	13 October 2021	B2: The excavation of the first layer of soil and the pouring of the second inner support
	2	8 December 2021	B2: The excavation of the second layer of soil and the pouring of the bottom plate
	3	28 December 2021	B2: The removal of the second inner support
C2	1	2 November 2021	C2: The excavation of the first layer of soil and the pouring of the second inner support
	2	15 December 2021	C2: The excavation of the second layer of soil and the pouring of the third inner support
	3	8 February 2022	C2: The excavation of the third layer of soil and the pouring of the bottom plate
	4	10 March 2022	C2: The removal of the third inner support

.

In this study, we focus on analyzing the deep horizontal displacement of the enclosure structure of the foundation pit adjacent to the subway side. We examine its specific characteristics and potential impact on the surrounding soil and subway tunnel. The deep horizontal displacement monitoring points are also depicted in Figure 1. Additionally, we monitored the subway structure adjacent to the pit, focusing on parameters such as horizontal displacement, vertical displacement, horizontal convergence, and vertical convergence of the subway tunnel. The monitoring section is also schematically represented in Figure 1.

3. Measured Results of Foundation Pits and Subway Tunnel

3.1. Displacements of Foundation Pits

For the deep horizontal displacement of soil outside the enclosure structure, we present the horizontal displacement curves of typical measurement points in B2 and C2 pits with excavation conditions in Figure 3 and Figure 4, respectively. Positive values indicate the movement towards the pit. The results show that the deep horizontal displacement of the soil body increases gradually with the excavation of the pit, and the displacement curve presents a typical composite curve. There is a certain horizontal displacement at the top of the curve, and the whole presents a bow-shaped curve with narrow ends and wide middle moving toward the pit. This pattern is typical of deep soil deformation of deeper pits where large stiffness support has been set at the top of the initial stage.

Based on the composite curve, the deep horizontal displacement curve can be further subdivided into two patterns: “smooth bulge” as in Figure 3b and “sawtooth fluctuation” as in Figure 3c. The “smooth bulging shape” is a common displacement pattern, while the “sawtooth fluctuation shape” could be influenced by the neighboring subway structure (tunnel and station house) and the stiffness of the TRD pile on the south side of the foundation pit. These factors limit the deformation of the soil in the depth range, making the horizontal displacement of the soil appear unsmooth and abrupt. Moreover, we observe that the depth of the maximum lateral displacement point of the soil at each measurement point is near the excavation surface.

Figure 5 and Figure 6 display the graphs of the maximum horizontal displacement of the deep soil body on the south and east sides of pit B2, and on the south and west sides of pit C2, with varying working conditions. Positive values indicate movement toward the pit, where measured points B2 and C12 failed due to worker operation errors during the construction process. The results indicate that the excavation of the pit has a spatial effect, with greater lateral deformation occurring in the middle of the pit than in the corners. For the B2 pit, the maximum horizontal displacement peak occurred when the construction of condition 3 was completed, and the second support was removed, with the south side reaching 14.3 mm, significantly larger than the east side by 7.9 mm. This was not only due to the different forms of internal support on the south and east sides but also because the stiffer subway platform adjacent to the east side suppressed the development of soil deformation.

Regarding the C2 pit, the peak deformation also occurred when the construction was completed, and the third support was removed, with peak deformation on the south and west sides being 33.6 mm and 34.8 mm, respectively. These values were relatively close and significantly larger than those of the B2 pit. In summary, the excavation depth of the C2 pit is about 1.3 times greater than that of the B2 pit, and its deformation is more than twice as large. These results suggest that the deformation and danger level of the pit construction increase greatly with the excavation depth. Thus, close monitoring is necessary during deep foundation pit excavation construction to avoid the occurrence of safety accidents.

3.2. Displacements of Subway Tunnel

To aid in later discussions, Figure 7 depicts the dimensions, relative positions, and deformations of the pit and adjacent tunnel. The variables used in the figure are defined as follows: a represents the width of the pit along the lateral excavation direction of the tunnel, b represents the width of the pit along the longitudinal excavation direction of the tunnel, H_e represents the depth of the pit excavation, H_t’ represents the burial depth of the tunnel vault, H_t represents the burial depth of the tunnel center, L_t’ represents the horizontal distance of the tunnel vault waist from the pit, L_t represents the horizontal distance of the tunnel center from the pit, R represents the diameter of the tunnel, δ_hm represents the maximum deep horizontal displacement of the pit enclosure structure, ξ_hm represents the maximum horizontal displacement of the tunnel, ξ_vm represents the maximum vertical displacement of the tunnel, ω_hm represents the maximum horizontal convergence of the tunnel, and ω_vm represents the maximum vertical convergence of the tunnel.

3.2.1. Horizontal and Vertical Displacements

Figure 8 and Figure 9 show the horizontal and vertical displacement curves of Line S3 tunnel, respectively, with respect to the construction working condition of the B2 pit used as the time node. The numbers of the horizontal tunnel monitoring point rings are presented in Figure 1, where “S” and “X” represent the upline and downline, respectively. In addition to the working condition in Table 1, another working condition is added when the first support construction of the B2 pit is completed, but excavation has not yet begun. The figure includes the ranges of the foundation pit, tunnel pipeline, and subway platform to facilitate data analysis.

Before the excavation of the B2 pit, the upline and downline of the subway had already experienced some horizontal displacement toward the pit within the scope of the B2 pit, which was mainly due to the influence of construction activities such as the enclosure structure and waterfall. The construction measures before excavation caused the initial deformation of the adjacent subway. As the B2 pit was excavated, the horizontal displacement of the subway tunnel towards the pit increased significantly, especially between measurement rings 27 and 42. The horizontal displacement of both the upline and downline reached its maximum value when working condition 3 was completed and the first support was removed, resulting in ξ_hm values of 5.13 mm and 4.61 mm for the upline and downline, respectively. The displacement of the downline was slightly smaller since it was farther away from the pit and less influenced by it. The section of the subway platform from rings 7 to 19 was less influenced by the construction of the foundation pit because of its higher lateral stiffness and the horizontal displacement was around 2.50 mm.

Figure 9 shows that before the excavation of the B2 pit, a certain degree of tunnel settlement had already occurred due to construction disturbances such as the enclosure structure and waterfall in the early stage. With the excavation of the B2 pit, both the upline and downline of the subway showed a more obvious settlement trend, which was also concentrated in the range of the B2 pit. The settlement deformation reached its maximum peak during the construction of the B2 pit to working condition 3, with a peak value of ξ_vm of −8.22 mm for the upline and a peak value of ξ_vm of −7.63 mm for the downline. The subway tunnel settlement was significantly reduced and even tended to upward deflection due to the limitation of the platform pile foundation.

Tunnel conditions are classified into three categories based on the relationship between the burial depth of the tunnel vault H_t′ and the excavation depth of the pit H_e, using the elevation (H_e + R) as the boundary. Category 1 is characterized by H_t′ ≤ H_e, meaning that the (H_e + R) elevation is located below the bottom of the tunnel arch. Settlement displacement is expected in this case as the tunnel is mainly controlled by the settlement of the soil outside the pit. Category 2, on the other hand, is defined as H_e < H_t′ ≤ H_e + R, where the (H_e + R) elevation is located between the tunnel vault and the bottom of the arch. Settlement or uplift displacement may occur in this case as the tunnel is in the transition area between settlement and uplift of the soil outside the pit. Finally, Category 3 is H_t′ > H_e + R, where the (H_e + R) elevation is located above the tunnel vault. In this case, uplift displacement is expected as the tunnel is mainly controlled by the unloading rebound of the soil below the pit bottom.

Moreover, the horizontal distance L_t′ of the tunnel from the pit also affects the rumble or settlement displacement of the tunnel. The critical horizontal distance of the lateral tunnel affected by the excavation of the pit to produce rumble and settlement is H_e, where rumble occurs when L_t′ ≤ H_e and settlement occurs when H_e < L_t′. In the current project, the burial depth of the tunnel vault in the upper and lower lines is H_t′ = 10.69 m, which is smaller than the excavation depth of the pit H_e = 12.75 m. Meanwhile, the horizontal distances of L_t′ from the pit in the upline and downline are 35.4 m and 50.4 m, respectively, both of which are larger than H_e. Therefore, settlement displacement is expected to occur in both the upline and downline, as per the judgment method, further confirming the reasonableness of the method of judging tunnel uplift or settlement by the relative position of the pit and tunnel.

The excavation of the pit mainly affects the horizontal and vertical displacement of the subway structure by removing the soil in the pit, triggering the spatial movement of the pit enclosure and the surrounding strata. The removal of the support also weakens the retaining effect of the pit enclosure system, leading to an increase in lateral earth pressure in the adjacent tunnel and driving the continued growth of the horizontal and vertical displacement of the tunnel.

In recent years, several national and industry standards have been proposed to regulate the structural safety of urban rail transit, such as the technical code [14]. This specification recommends an early warning value of 10 mm and a control value of 20 mm for horizontal and vertical displacements of the tunnel. Moreover, the monitor code [15] proposes even more rigorous control standards, with a control value of 3–10 mm for tunnel structure settlement, 5 mm for tunnel structure uplift, and 3–5 mm for tunnel structure horizontal displacement. In this project, the deformation control values for horizontal and vertical displacements of the tunnel structure are set to 10 mm and −10 to 5 mm, respectively. These values correspond to specific safety levels as outlined in

Table 2. Classification of safety monitoring levels and corresponding management measures.

Warning Levels	Monitoring Ratio 1	Warning Status Description
Yellow warning	0.6 ≤ G < 0.8	Start the alarm and take measures such as encrypting monitoring points or increasing monitoring frequency.
Orange warning	0.8 ≤ G < 1.0	Suspend external operations and conduct process safety assessments.
Red warning	1.0 ≤ G	Activate the safety emergency plan.

¹ The monitoring ratio G is the ratio of the measured value of the monitoring project to the structural safety control index value.

. Based on the measured data, it is observed that the horizontal displacement of the tunnel structure in Line S3 subway remained within the normal range during the construction of the pit. However, the vertical displacement of the upper and lower lines has reached the orange and yellow warning levels, respectively. These results highlight the need for engineers to remain vigilant and provide timely feedback in the event of abnormalities.

3.2.2. Horizontal and Vertical Convergences

Figure 10 and Figure 11 depict the curves of horizontal and vertical convergence values of Line S3 tunnel with B2 pit excavation conditions, respectively, with positive values indicating diameter expansion and negative values representing diameter compression. The preliminary construction led to a certain degree of horizontal and vertical convergence deformation in the upline and downline tunnel sections before the pit excavation, with the horizontal direction indicating diameter expansion and the vertical direction showing diameter compression. As the B2 pit excavation commenced, the horizontal and vertical convergence deformation of both the upline and downline of the subway increased significantly, mainly concentrating on the influence of the B2 pit. Upon excavation to the completion of the bottom plate of working condition 3 and the removal of the first support, the tunnel’s horizontal and vertical convergence reached the maximum peak. The upline horizontal and vertical peaks were 7.4 mm and −5.4 mm, respectively, while the downline horizontal convergence value rapidly decreased to nearly 0 as it approached the location of the ring 30 subway platform, whereas the vertical convergence value was relatively less affected by the subway platform.

According to specification [14], this deformation control value for horizontal and vertical convergence of the tunnel is set to ±10 mm. The horizontal convergence values of the upper and lower lines of the subway tunnel have exceeded the yellow warning value, as shown in Table 2, and should be a cause for concern. From the above measurements, it can be concluded that the subway tunnel undergoes “horizontal expansion and vertical compression” type deformation, accompanied by “in-pit” horizontal displacement and “settlement” vertical displacement.

4. Discussion

4.1. Displacement Relationship between the Tunnel and Foundation Pit

Based on the analysis presented above, it is evident that the excavation and unloading of foundation pits can cause deformation in the enclosure structure and the surrounding soil, resulting in changes in the displacement of neighboring subway tunnels. To predict such deformation in the future using foundation pit monitoring data, this study adopts a statistical method to quantitatively analyze the relationship between the deep horizontal displacement of the enclosure structure and the horizontal and vertical displacement and convergence values of the underpass tunnel.

Figure 12 displays the scatter plot of measured data illustrating the relationship between the maximum horizontal displacement of the deep layer of the enclosure structure and the accumulated deformation of the corresponding measured points of the adjacent subway tunnel in the upline and downlines (horizontal and vertical displacements/convergence) at different moments during the excavation of the B2 pit. B11-S38 refers to the measured data of the deep horizontal displacement at the B11 measurement point corresponding to the S38 ring of the upline of the subway tunnel. The solid and dashed straight lines represent the fitted lines of the scatter point sets of the upline and downline, respectively. In order to quantitatively evaluate the correlation between the variables, the corresponding Pearson correlation coefficients are calculated and presented in

Table 3. Pearson correlation coefficients of different tunnel deformation parameters to the maximum horizontal displacement of deep foundation pit.

	Tunnel Horizontal Displacements	Tunnel Vertical Displacements	Tunnel Horizontal Convergences	Tunnel Vertical Convergences
Upline	0.701	0.918	0.913	0.913
Downline	0.601	0.699	0.73	0.73

.

The results reveal strong correlations between the maximum value of deep horizontal displacement of soil and the corresponding upline and downline horizontal displacement, vertical displacement, horizontal convergence, and vertical convergence values during the excavation of the B2 foundation pit, with corresponding Pearson correlation coefficients ranging between 0.6 and 1.0. Notably, the Pearson values for upline vertical displacement and horizontal convergence even exceed 0.9. Since the maximum horizontal displacement of the deep soil indicates the degree of change in the displacement field of the soil around the measurement point, it further confirms that the displacement and unloading effect of the surrounding soil resulting from pit excavation is the root cause of the deformation of the adjacent subway tunnel. Based on the lateral displacement trend of the pit, the subway deformation can be predicted using this direct correlation. Furthermore, the Pearson coefficients for the upline of the subway are larger than the corresponding downline coefficients, and the slopes of the fitted straight lines for the upline in Figure 12 are larger than the corresponding downline slopes. This observation indicates that the upline, which is closer to the B2 pit than the downline, develops deformation more rapidly due to the influence of pit excavation and is more sensitive to pit construction, and thus requires more attention.

4.2. Influence Zone of Tunnel Displacement

In this paper, the influence zone classification is adopted to evaluate the measured results. The coordinate values of three points are defined on the influence zone fold line: the influence zone width factor M, the depth factor N1, and the depth factor N2, as shown in Figure 13. The influence zone control values are set to 20 mm, 10 mm, and 5 mm. Using the calculation method in the literature [9,16], we obtain the corresponding influence zone parameters by interpolating the depth H_e (12.75 m in this project) of the pit and the maximum deep horizontal displacement δ_hm (14.3 mm in this project) of the enclosure structure, as shown in

Table 4. Predicted parameters for determining the deformation impact zone of adjacent foundation pit tunnels.

Method	Control Value 20 mm			Control Value 10 mm			Control Value 5 mm
	M	N1	N2	M	N1	N2	M	N1	N2
Liu [9]	0.08	0.38	0.37	0.97	1.41	2.04	1.77	1.66	3.24
Zheng [16]	0.58	1.50	1.55	1.10	1.66	2.00	2.10	2.00	2.50

. We then draw the corresponding influence zone fold lines and the location of the upper and lower lines of this project, as shown in Figure 14. The analysis results show that there is a certain difference in the range of influence areas between Liu [9] and Zheng [16]. Zheng influence zone results [16] are obtained under the premise of a fixed pit excavation depth (18 m) and with the maximum deformation of the pit enclosure structure set into three fixed values of 30 mm, 45 mm, and 60 mm based on the quality of deformation control. In contrast, Liu model [9] refines different pit excavation depths and enclosure structures and predicts the lateral tunnel deformation influence zone under lateral shift conditions, making it relatively more suitable for engineering reality. However, both influence zone models show that both the upline and downline of this project are located within the weak influence zone (Ⅳ) and are farther away from the 5 mm control line. Section 4.1 reveals that the actual ξ_hm values of the upline and downlines are 5.10 mm and 4.61 mm, respectively, which means that the upline should be located in the general influence zone (Ⅲ) and the lower line, although located within the weak influence zone (Ⅳ), should be close to the 5 mm control line. This indicates that the two influence zone models can predict tunnel deformation to a certain extent, but both tend to underestimate the actual deformation. The reason may be that the establishment of both models is based on certain assumptions, such as those derived from finite element models, which have certain limitations. In addition, the interaction between the two subway lines has also increased the actual tunnel deformation.

Two methods for predicting tunnel deformation caused by excavation unloading were used and compared with monitoring results in this study: the Wei method [24] and the Liu method [9]. The Wei method [24] considers the distance between the tunnel and the excavation pit, as well as the width of the pit excavation, as key factors affecting deformation uniformity, expressed as

$${\xi }_{hm}=2.993\times e^{0.1856\times \frac{b}{L_t’}}$$

(1)

The Liu method [9] considers engineering geological conditions, pit excavation depth, horizontal spacing between the tunnel and the pit, and the longitudinal width of the pit along the tunnel. The prediction equation obtained from the fitting is expressed as

$${\xi }_{hm}=2.11\times {10}^{-2}\times b\times \frac{H_e}{L_t’}+2.85$$

(2)

To validate these methods, relevant data from the project were used to substitute Equations (1) and (2), and compared with the actual measured results of 5.13 mm and 4.61 mm for the maximum horizontal displacement in the upline and downline in Section 4.1. The results are summarized in

Table 5. Results of tunnel horizontal displacement prediction formula.

Tunnels	Measured Results	Liu [9] Method		Wei [24] Method
		Prediction Results	Error (%)	Prediction Results	Error (%)
Upline	5.13	3.78	−26.3	5.69	10.9
Downline	4.61	3.50	−24.1	4.70	2.0

. It is found that the actual measurement results lie between the two predicted results, with the overall prediction of the Wei method [24] being better, while the Liu method slightly underestimates the deformation. This finding can provide a reference for predicting subway tunnel deformation in similar adjacent pits.

5. Conclusions

This paper investigates the deformation pattern of pit excavation under soft soil conditions in subway crossing areas and analyzes its impact on adjacent subway structures based on measured data from the pit construction. The horizontal displacement curve of the deep foundation pit enclosure structure outside the adjacent subway tunnel exhibits a typical “bow-shaped” composite curve pattern under the action of large stiffness internal support. It can be further subdivided into “smooth bulge” and “sawtooth fluctuation” under the influence of factors such as adjacent TRD piles and subway structures. Excavation of the foundation pit leads to a significant increase in deep horizontal displacement. The middle of the foundation pit experiences greater lateral displacement than the corners, and the lateral displacement reaches its peak when the first support is removed after the excavation of the foundation slab is completed, with the maximum lateral displacement point near the excavation surface.

The deformation of surrounding soil and the adjacent subway structure due to measures such as rain and the construction of the enclosure structure before excavation cannot be ignored. Soil removal and unloading after excavation causes a “lateral expansion and vertical compression” type deformation of the subway tunnel, accompanied by a “toward the pit” horizontal displacement and “settlement type” vertical displacement, with deformation concentrated in the influence range of the foundation pit. The deformation of the subway platform is less affected by the excavation of the foundation pit. An apparent linear relationship exists between the maximum value of deep horizontal displacement of the soil body and the corresponding horizontal displacement, vertical displacement, horizontal convergence, and vertical convergence values of the upline and downline of the subway tunnel. The development of subway deformation can be predicted through the lateral displacement trend of the foundation pit based on this correlation. The deformation mode, prediction methods and safety management measures can provide a reference for similar projects.

However, the existing correlation influence zone model tends to underestimate the tunnel deformation of this project, and further research is needed to refine the influence zone classification method for deep foundation pit projects. This can be achieved through more comprehensive and accurate field monitoring data, as well as more sophisticated numerical simulation models that better reflect actual deformation patterns and deformation control standards for different pit excavation conditions and enclosure structures. Furthermore, the Wei method is recommended for predicting tunnel deformation in similar adjacent pits due to excavation unloading. However, further research and validation are necessary to determine the suitability of these methods for different soil and geological conditions. Additionally, more refined construction monitoring measures are required in worse construction environments than in this article. At that time, additional support, including new equipment, manpower and research, can be supplied by local governments or the public.