Study on the structural response of surrounding buildings during tunnel excavation in urban areas

Abstract

This study, based on the Guanzhong Road tunnel project in the core urban area of Chongqing, systematically investigates the influence of tunnel excavation on adjacent building structures by establishing a tunnel-building interaction numerical model. A two-dimensional plane strain model was developed using MIDAS/GTS software, focusing on the response mechanisms of key factors such as horizontal spacing, soil layer parameters, and building height on building deformation. The research reveals that the horizontal spacing between the tunnel and the building significantly affects the settlement distribution characteristics. When the spacing is 15 m, the settlement difference between the head and tail of the building reaches 1.94 mm, and the established displacement prediction formula effectively characterizes the nonlinear relationship between horizontal distance and displacement. The elastic modulus of the soil plays a decisive role in deformation, with the maximum settlement in silty clay formation (E is 20 MPa) increasing by 572% compared to sandy mudstone formation (E is 60 MPa), reaching 15.9 mm. Increasing building height exacerbates settlement differences, with the settlement difference of a 30 m high-rise building (2.29 mm) increasing by 487% compared to a 12 m low-rise building (0.39 mm). The study proposes 35 m as the horizontal safety spacing threshold and recommends the Cross Diaphragm (CRD) method or the large pipe roof method for highly compressible formations to control the formation loss rate (<0.5%). The research findings provide a theoretical basis for risk assessment and construction method optimization in tunnel proximity construction in urban core areas.

Keywords

urban core area tunnel excavation buildings response patterns

Introduction

In urban core areas, tunnel excavation projects in close proximity to existing buildings are inevitable. The complexity and risks associated with such scenarios pose challenges to the safety and stability of tunnel engineering, while also potentially impacting the structural response of surrounding buildings. Therefore, an in-depth exploration of the influence of tunnel excavation in urban core areas on the structural loading of existing buildings is of paramount importance.

The safety and stability of existing structures adjacent to tunnel excavations in urban core areas are of paramount importance. In recent years, scholars both domestically and internationally have conducted extensive research on the impact of tunnel excavation on nearby structures, yielding significant findings. Zhang et al.¹ analyzed over 200 tunnel engineering cases using machine learning algorithms and found that building stiffness contributes up to 52% to surface settlement, with the stiffness effect exhibiting a nonlinear enhancement trend as the tunnel-building distance decreases, particularly when the tunnel depth is less than 30 m. Wang et al.² proposed a sensitivity analysis method based on random forests, systematically quantifying the interactive effects of building dimensions, relative position (horizontal distance of 5–25 m), and ground stiffness on deformation patterns. Their research indicates that when the tunnel-building distance is less than one tunnel diameter, building stiffness plays a dominant role in controlling settlement difference. Additionally, Liu et al.³ developed a 3D finite element-discrete element coupled model that incorporates soil damage evolution. By introducing contact mechanics criteria for initial cracks in masonry structures, they revealed how stress redistribution caused by tunnel excavation triggers chain-like damage propagation in existing buildings. Notably, when the tunnel-building distance is less than 15 m, material nonlinearity leads to an 18%–24% increase in the width of the settlement trough. Numerous scholars in China have also directed their attention towards this issue. Wang et al.,⁴ employing dynamic simulation analysis through finite element software, scrutinized the impact of variations in relative positioning (I, $θ$ ) on the deformation of newly constructed tunnels in urban core areas and adjacent buildings. Ding et al.⁵ utilizing numerical simulation techniques, examined the influence of tunnel construction in urban core areas on buildings with different types of surface foundations. Their findings pointed out that shallow foundation structures exhibit a stronger resistance to disturbances caused by tunnel excavation compared to pile foundation structures. Huang et al.⁶ integrated distributed fiber optic monitoring technology with 3D finite element inversion to reveal the spatiotemporal evolution of pile foundation settlement in super high-rise buildings during different shield advancement stages (0–30 m from the building). Their research demonstrated that when the shield cutterhead crossed the building’s projection boundary (approximately 15 m of advancement distance), the building’s tilt rate instantaneously increased to 0.15‰/ h, and the pile-soil stiffness ratio accounted for 62% of the total influencing factors in controlling the settlement pattern. Zhang et al.⁷ further proposed a deep learning-based optimization model for shield construction parameters. Through validation with 12 engineering cases in Shanghai’s soft soil region, they found that the synergistic control of advancement speed and synchronous grouting pressure could reduce building settlement difference by 18–34%. Additionally, Liu et al.⁸ established a nonlinear analysis framework considering the cumulative damage of masonry structures, successfully predicting the tilt mutation threshold (horizontal distance of 8 m) for the historical building group adjacent to the Fuzhou Metro tunnel. This provided a theoretical basis for revising the specifications for adjacent construction. Zhang et al.⁹ analyzed the dynamic response of frame structures to tunnel construction in soft soil areas using FLAC3D, finding that structural crack propagation occurs when the ground loss rate exceeds 0.8%. Liu et al.¹⁰ determined the sensitivity ranking of tunnel burial depth and span ratio to building inclination through orthogonal experiments, providing a basis for parameter optimization. For special geological conditions, Chen et al.¹¹ developed a tunnel-structure interaction model considering rheological effects, confirming the significant time-dependent behavior of building settlement in water-rich sand layers. In terms of construction method comparison, Huang et al.¹² compared the deformation control effects of the CRD method and the bench method in adjacent construction, proposing a critical horizontal spacing determination formula. Some scholars have also studied the impact of tunnel construction in the urban core on existing structures.^13–15 It is worth noting that intelligent prediction models have emerged as a new research direction. Wang et al.¹⁶ established a mapping relationship between shield parameters and surface settlement based on machine learning algorithms, improving prediction accuracy by 23% compared to traditional methods. Meanwhile, Li et al.¹⁷ employed distributed fiber optic monitoring technology to achieve real-time dynamic assessment of building deformation during tunnel construction. In terms of standard application, Zheng et al.¹⁸ revised the deformation control indicators in the “Technical Code for Structural Safety Protection of Urban Rail Transit” and proposed a graded early warning mechanism. Additionally, Yang et al.¹⁹ established a damage threshold database for different building types (frame, brick-concrete, and steel structures) through statistical analysis of case studies. The aforementioned studies collectively indicate that the building deformation of existing buildings in close proximity to tunnel excavation in urban core areas is a complex issue, entailing considerations of tunnel excavation methods, the relative positioning of tunnels and buildings, building stiffness, and building structure foundations.

Although previous studies have extensively discussed the stability of existing buildings during the tunnel excavation process, the novelty of this study lies in: (1) the establishment of a comprehensive mechanical analysis model that considers various key factors, such as different horizontal distances, soil properties, and building heights, to more holistically assess the impact of tunnel excavation on buildings; (2) the development of a formula to describe the relationship between tunnel excavation and the displacement of buildings at varying horizontal distances, which was validated against finite element simulation results, providing an accurate and practical tool for predicting the impact of tunnel excavation on buildings.

This study employs numerical simulation calculation methods to investigate the structural response of existing buildings in close proximity to tunnel excavation in urban core areas, exploring the stress and deformation patterns of existing buildings during tunnel excavation and establishing the relationships between different key parameters and building behavior. The research outcomes provide a theoretical basis for assessing the stress variations in existing building structures during tunnel excavation in urban core areas, aiding in structural safety assessments. This study is of significant importance in providing insights and references for ensuring the safety and stability of existing buildings during tunnel excavation in urban core areas.

Engineering context

The Guanxing Road project is situated in the western sector of the Guanyin Bridge commercial area in Jiangbei District. It extends from Jinyuan Road in the south, passing beneath Jianxin West Road, Guanhong Avenue, the Yaoziqiu area in the Diance Village, and Hongshi Road, and terminates at the boundary between Jiangbei District and Yubei District in the north. The road is classified as an urban secondary road with four lanes in each direction, designed for a speed of 40 km/h, spanning approximately 2 km in total length. For this study, a specific section of the Guanxing Road project, with pile numbers ranging from K0 + 0 to K1 + 520, covering a mainline length of 1520 m, was selected as the engineering background. This section primarily consists of a close-spacing, dual-tunnel, four-lane configuration. Predominantly, the buildings along this section are commercial and residential structures. The construction methods used for the sections of the mainline tunnel passing beneath existing buildings include the Cover and Dig method (CD method) and the Cross-Passing Diaphragm Wall method (CRD method). The internal standard profile of the tunnel is shown in Figure 1.

Figure 1.

Standard inner contour of the tunnel.

The depth of the tunnel has a significant impact on the settlement of surrounding buildings. In this study, the depth of the tunnel ranges from 30 m. The closest distance between the centerlines of the two tunnels and the centerlines of the surrounding buildings is 10 m, a critical parameter for assessing the influence of tunnel excavation on the buildings. The spatial relationship between the buildings and the tunnel is illustrated in Figure 2. During the numerical simulation, this study considers varying tunnel depths and distances from the tunnel to the buildings to comprehensively evaluate the impact of tunnel excavation on the settlement of surrounding structures.

Figure 2.

Diagram of the location of the building plan.

Finite element modeling

Basic functional relationships

In the model, the following fundamental functional relationships were employed to describe the behavior of soil and structural materials:

Constitutive Model: The Mohr–Coulomb failure criterion was used to describe the elastoplastic behavior of soil. This criterion takes into account the soil’s internal friction angle (ϕ) and cohesion (c), which are determined based on field and laboratory test data.

Stress-Strain Relationship: For structural materials, an elastoplastic model was adopted, which considers the material’s elastic modulus (E) and yield strength (fy).

Basic assumptions

The fundamental assumptions and explanations utilized in the model are as follows:

(1) The material follows the Modified M-C failure yield criterion, accounting for unloading and reloading stiffness hardening of the soil.

(2) Stress and strain within the materials and strata are assumed to vary within the elastic-plastic range during the loading process.

(3) The influence of groundwater is disregarded due to the site-specific hydrogeological conditions, where preliminary assessments indicated negligible groundwater impact on the soil-structure interaction during tunnel excavation.

Parameter selection

This paper employs the MIDAS/GTS software to establish a numerical model for calculating the deformation impact of tunnel construction on adjacent multi-story framed buildings. The common-node pile-soil connection assumes full bond, which may marginally overestimate pile-soil coordination. However, this simplification is justified for axial-load-dominated scenarios in stiff soils, as demonstrated by comparative trials. Future studies will incorporate interface elements to address cyclic or lateral loading conditions. In the model, all soil layers are calculated using the Mohr–Coulomb failure criterion, and the physical and mechanical parameters of each soil layer are presented in Table 1.

Table 1.

Values of parameters for rock and soil layer in modeling.

No.	Soil	Severe (kN/m³)	Cohesion (MPa)	Internal friction angle (°)	Elastic modulus (MPa)	Poisson’s ratio
1	Miscellaneous fill	17.5	0.022	25	35	0.3
2	Sandy mudstone	19.3	0.042	22	42	0.35

During the simulation process, the building in the model adopts a 4-bay, 6-story framed structure with pile foundations. The pile diameter is 1 m, and the pile length is 5 m. The beam-column system above the foundation of the building is simulated using beam elements, with beam sections of 0.6 m × 0.3 m rectangular sections, and column sections of 0.8 m × 0.8 m rectangular sections. A live load of 0.5 kPa is applied at the top level, with a floor load of 2.25 kPa per story. Additionally, considering the gravity of the walls, a load of 4.9 kPa is applied on each floor slab surface.²⁰ The constitutive relations are all elastic. The specific parameters for the diaphragm wall and adjacent buildings are shown in Table 2.

Table 2.

Parameter values of supporting structures and buildings in numerical modeling.

No.	Name	Material	Dimensions (mm)	Elastic modulus (E/MPa)
1	Lining	Concrete	220 (thickness)	23,000
2	Building plates	Concrete	150 (thickness)	30,000
3	Building columns	Concrete	800 × 800	30,000
4	Building piles	Concrete	1000 (diameter)	30,000
5	Building beams	Concrete	600 × 300	30,000

Finite element model

In this study, a numerical model was constructed using MIDAS/GTS software to analyze the deformation effects of tunnel construction on adjacent multi-story framed buildings. Given the research focus on the deformation patterns of buildings and the surrounding strata, the impact along the longitudinal direction of tunnel excavation was neglected, and a simplified two-dimensional plane strain model was established.

To mitigate the impact of boundary effects on the computational results, the model dimensions were set to 120 m × 60 m (refer to Figure 3). In the model, the thickness of the first soil layer is 10 m, and the thickness of the second soil layer is 50 m. The overall positional relationship between the building and the tunnel is shown in Figure 3. During the simulation of tunnel construction, the soil mass is divided into multiple sections, with different colors used to distinguish between various construction steps. The mesh size for both the tunnel and the building is 1 m, while the mesh size for the soil layers is 2 m.

Figure 3.

Schematic diagram of the model.

Boundary conditions and material parameters

(1) Boundary Conditions: The model coordinates were established in a Cartesian coordinate system, with the two-dimensional plane strain model set up on the XOY plane, where the Z-axis signifies the model’s depth direction. Within the XOY plane, the X-axis represents the horizontal direction, while the Y-axis signifies the vertical direction. Horizontal constraints are applied to both sides of the rock and soil materials within the model, with full constraints applied at the bottom and the top designated as a free surface.

(2) Material Parameters: The aim of this study is to investigate the impact of tunnel excavation on the existing structural elements. To maintain uniformity in the variation patterns beneath the soil layers, the finite element model is endowed with identical types of properties.

(3) In the model, it is assumed that the soil is homogeneous, meaning that the soil’s physical and mechanical properties are uniform in all directions. This assumption helps to reduce the complexity of the model, enabling more efficient calculations.

Settlement of building foundation

The allowable settlement standards for building foundations were determined based on the requirements of the engineering survey code and the specifications outlined in the Code for Building Deformation Measurement (JGJ7-2016). According to this code, the settlement limits for low, medium, and highly compressible soils are 20 mm, 40 mm, and 120 mm, respectively. Considering the elastic modulus E of the rock and soil mass as 10 MPa, categorizing it as highly compressible soil, the safety standard for building settlement was set at 120 mm.

To investigate building foundation settlement, each foundation was systematically numbered as illustrated in Figure 4. According to the numbering scheme in Figure 4, the first column (A1, B1, and C1) represents foundations closest to the tunnel, followed by the second column (A2, B2, and C2), with the third column (A3, B3, and C3) positioned relatively farther from the excavation zone. The spatial relationship between the building and tunnel configuration is visually presented in Figure 4.

Figure 4.

Relative position of the building to the tunnel.

The tunnel excavation was conducted using the CD method. A model was established based on the actual tunnel excavation progress, with a current advance of 3 m. The specific construction simulation process included the following steps: Firstly, the initial state of the site was considered, and displacements were reset to zero to ensure accurate initial conditions. Subsequently, the construction of the structure was carried out; then, the simulation of the initial lining construction of the tunnel took place, including the process of initial covering of the tunnel walls. Finally, the simulation of the secondary lining construction of the tunnel was conducted. Through this series of steps, a comprehensive simulation and analysis of each stage of the entire construction process was achieved, providing a deeper understanding of the site’s dynamic response and structural changes. Ultimately, the settlement values of the building foundations were obtained, as shown in Figure 5 and Table 3.

Figure 5.

Settlement values at various points of the building foundation.

Table 3.

Settlement values of the foundation of the building (mm).

First row of building foundations	No.	A1	A2	A3	A4	A5
First row of building foundations	Settlement values of the foundation points	2.268	2.068	1.826	1.504	1.183
Second row of building foundations	No.	B1	B2	B3	B4	B5
Second row of building foundations	Settlement values of the foundation points	2.277	2.076	1.834	1.510	1.188
Third row of building foundations	No.	C1	C2	C3	C4	C5
Third row of building foundations	Settlement values of the foundation points	2.304	2.099	1.850	1.521	1.186

Based on the monitoring data analysis from Figure 5 and Table 3, the settlement of the building after tunnel excavation exhibits distinct spatial distribution characteristics: in the transverse direction along the tunnel axis, the closer the foundation is to the tunnel section, the larger the settlement value (the maximum cumulative settlement in row C reaches 2.4 mm). As the distance from the tunnel increases, the settlement decreases in a gradient manner (the minimum settlement in row A is 1.8 mm), consistent with the typical pattern of surface settlement caused by ground loss. The settlement curves of the three foundation rows show highly consistent linear slopes (settlement increments of 0.2–0.4 mm between adjacent foundations), indicating good homogeneity in the longitudinal distribution of geological conditions and upper loads in the field area.

From the perspective of inter-row differences, the building foundation settlement exhibits a significant hierarchical pattern of row C exhibits higher values than row B, which in turn exceeds row A, with stable settlement gradient differences of 0.2–0.3 mm between rows. The maximum inter-row difference of 0.6 mm occurs at foundation position 5. This regular settlement distribution indicates that the soil disturbance induced by tunnel construction has predictable transmission characteristics in the horizontal direction, with its influence range and attenuation pattern demonstrating engineering controllability. According to the safety standard value derived earlier, the maximum calculated settlement value of the building foundation is 2.257 mm, which is far below the safety standard value of 120 mm. Therefore, the settlement of the building is within a reasonable range, indicating that the ground environment is safe and controllable.

Analysis of key parameters of deformation in existing buildings

Effect of horizontal spacing on building deformation

The analysis results indicate that the settlement values of buildings during tunnel construction remain within a reasonable range. However, to ensure the safety and stability of the construction process, it is necessary to further investigate the influence of sensitive parameters induced by tunnel construction on the deformation of adjacent existing buildings.

This study primarily focuses on the horizontal distance between the tunnel and the building. The horizontal distance L between the right tunnel and the building axis is selected as 0 m (between the two tunnels), 5 m, 10 m, 15 m, 20 m, 25 m, 30 m, and 35 m. The ground deformation caused by tunnel excavation at different distances from the building is calculated. According to Table 3, during tunnel construction, the maximum settlement of the building foundation occurs at the column closest to the tunnel centerline, while the minimum settlement appears at the column farthest from the tunnel centerline. Therefore, it is sufficient to consider the settlement values at the points closest to and farthest from the tunnel centerline in each row (Figure 6–8).

Figure 6.

Settlement values at different horizontal spacings for A1 and A5.

Figure 7.

Settlement values at different horizontal spacings for B1 and B5.

Figure 8.

Settlement values at different horizontal spacings for C1 and C5.

Due to the presence of buildings, the type of ground settlement curve is not axially symmetric, resulting in noticeable variations in ground settlement at building foundations.

From Figure 6–8, it can be concluded that when L is 0 m, the building is located between the two tunnels, and the settlement of the building foundation is relatively uniform, with a difference of less than 0.4 mm between the left and right settlement values in each row of the building, and the maximum settlement does not exceed 2.11 mm. When L is 10 m, the building axis coincides with the right tunnel axis, representing a case of the tunnel passing under the existing building. The maximum settlement is larger than that at L is 0 m. The excavation of the left tunnel causes unloading of the soil on the lower left side of the building, resulting in a settlement difference of 1.44 mm between the head and tail of the building foundation. When the right tunnel passes directly under the building’s central axis, the building experiences overall subsidence. Although the excavation of the left tunnel causes tilting, its impact on the existing building is relatively small. When L is 15 m, the settlement of the building caused by tunnel excavation is most pronounced, with a maximum value of 2.5 mm, and the existing building exhibits a tendency to tilt toward the tunnel excavation side, with the settlement difference between the head and tail of the building expanding to 1.94 mm. When L is 20 m, compared to L is 15 m, the overall settlement of the building decreases, but the settlement difference between the head and tail of the foundation increases to approximately 2.01 mm. When L is 25 m, both the settlement and the settlement difference between the head and tail of the building further decrease. As the horizontal spacing continues to increase, both the settlement and the settlement difference between the head and tail of the building show a decreasing trend.

Further insights from the figure indicate that between L is 0 m and L is 10 m, the building settlement is significant but relatively secure; however, between L is 15 m and L is 25 m, the substantial difference in settlement between the front and rear ends lowers the safety of the buildings. For L is 30 m to L is 35 m, the impact of tunnel construction on buildings is minimal, negligible at L ≥35 mm in terms of its effect on buildings.

In conclusion, the positional variation of buildings can significantly impact foundation settlement. In the context of a twin-tunnel scenario, when the edges of a building’s foundation align above a single tunnel, there is a significant difference in settlement between the front and rear ends of the building, indicating a higher risk. However, as the horizontal spacing further widens, the impact of tunnel excavation on buildings diminishes.

Based on finite element simulation data, mathematical formulas were fitted to describe the influence of tunnel excavation on surrounding buildings at varying horizontal distances. The results indicate that the impact of tunnel excavation on buildings at different horizontal distances can be effectively captured using a sine function, as shown in equation (1).

f (x) = \frac{2.47 \sin (0.05 x + 1.02) + 0.12 \sin (0.25 x + 3.09)}{1000}

(1)

where

f (x)

is the vertical displacement and

x

is the horizontal distance of the building from the tunnel centerline. Figure 9 illustrates the comparison between the fitted formula and the computed values from Midas-GTS, demonstrating the accuracy of this formula in describing the evolving impact of tunnel excavation on buildings. This provides valuable insights for pertinent engineering endeavors.

Figure 9.

Comparison of the fitting formula with the calculated values.

Impact of soil layer parameters on building deformation

Examining the deformation of buildings induced by tunnel excavation under different soil conditions, we specifically addressed the soil characteristics of Chongqing in this section. Three distinct soil types were selected for investigation within the model, as indicated by the variations in soil parameters outlined in Table 4. Taking into consideration the time effects associated with sand and clay during tunnel construction, varying stress release coefficients were employed to simulate the stress relief of different soil types. Consequently, post-tunnel excavation, stress levels did not immediately stabilize, but rather took some time to reach a state of equilibrium. Typically, in situations where stress and deformation have not yet stabilized, support structures play a pivotal role in constraint. The differing stress release rates in numerical software were utilized to represent varying instances of support intervention in practical engineering applications. For the analysis of soil variation, a fixed depth parameter of L is 10 m was considered. Settlement values of points in row C under different soil layer parameters, based on the maximum settlement point C1, are shown in Figure 10.

Table 4.

Soil parameters.

Soil type	Density (kN/m³)	Cohesion C ((MPa)	Friction angle φ (°)	Elastic modulus (MPa)	Poisson’s ratio µ
Silty clay	18.9	18	19	20	0.35
Sandy mudstone	23.4	5	31.6	60	0.30
Medium coarse sand	24.2	5	34.1	120	0.30

Figure 10.

Deformation patterns of foundations with different soil parameters.

According to the data in Figure 10, as the soil quality deteriorates, the maximum settlement of the building increases significantly. When E is 20 MPa (the soil layer is silty clay), the maximum settlement reaches 15.9 mm, and a large settlement difference of approximately 11.9 mm occurs beneath the building foundation. In this case, the building is prone to cracking, indicating that the concealed excavation method is not suitable for poor soil conditions. If construction conditions only permit the use of the concealed excavation method, for small to medium-sized sections in weak strata, the CRD, CD methods, or the large pipe roof method can be considered. It is important to note that the full-face excavation method should not be used.

Influence of varied building heights

In addition to the horizontal spacing between tunnels and existing structures and the soil parameters, the differing heights of existing buildings also impact the deformation of structures. To investigate the influence of varying building heights on the deformation patterns of existing structures under the excavation of twin tunnels, four height scenarios are considered: H is 12 m, H is 18 m, H is 24 m, H is 30 m. Analyzing the deformation patterns of existing structures caused by tunnel excavation under different building height conditions, a uniform model parameter of L is 10 m was adopted.

From Figure 11, it can be concluded that when the building height H is 30 m, the vertical deformation of the building reaches its maximum value of 2.75 mm, and the settlement difference between the head and tail of the building is also the largest, approximately 2.29 mm, indicating that the building may exhibit a tendency to tilt toward the tunnel side. When H is 12 m, the maximum settlement value is about 2.17 mm, and the settlement difference between the head and tail of the building foundation is approximately 0.39 mm, which is the smallest among all working conditions. Therefore, as the height of the building increases, the settlement of the building gradually increases, and the corresponding risk of damage also rises.

Figure 11.

Displacement of row at different building heights.

Conclusions

This study, integrating practical engineering considerations, investigates the deformation effects of tunnel excavation on adjacent buildings using numerical simulation techniques. It validates the stability of structures in practical engineering scenarios. Furthermore, an analysis of the response patterns of different key parameters on building deformation yields the following conclusions:

(1) The spatial position effect is significant: the horizontal spacing between the building and the tunnel is the core factor influencing the deformation distribution. When L is 0 m (the midpoint between the two tunnels), the settlement of the building exhibits a uniform distribution, with a maximum difference of only 0.4 mm. When L is 15 m (directly above a single tunnel), the settlement difference between the head and tail reaches 1.94 mm, forming a pronounced tilting trend. The established displacement prediction formula (Equation (1)), through the superposition of sine functions, effectively characterizes the nonlinear relationship between the horizontal distance and the displacement response (R² > 0.95).

(2) The sensitivity of the formation exhibits significant differences: the elastic modulus of the soil has a decisive influence on deformation. Under silty clay formation (E is 20 MPa), the maximum settlement reaches 15.9 mm, representing a 572% increase compared to sandy mudstone formation (E is 60 MPa). In this case, the settlement difference between the head and tail reaches 11.9 mm, far exceeding the safety standards for buildings. Research indicates that when the soil elastic modulus is below 30 MPa, special construction methods such as the CRD method or the large pipe roof method are required to control deformation.

(3) The coupling effect of building height is evident: increasing building height enhances the interaction between load and formation. The maximum settlement of a 30 m high-rise building (2.75 mm) increases by 26.7% compared to a 12 m low-rise building (2.17 mm), and the settlement difference between the head and tail increases from 0.39 mm to 2.29 mm. However, the horizontal displacement remains consistently less than 12% of the vertical displacement, indicating that the structure primarily bears asymmetric vertical loads.

(4) The engineering safety threshold is defined through multi-condition comparisons, with a horizontal spacing of 35 m identified as the boundary threshold. At this distance, the building settlement attenuates to 0.18 mm, and the settlement difference between the head and tail is less than 0.1 mm. For highly compressible formations (E less than 30 MPa), it is recommended to employ dynamic grouting compensation technology to control the formation loss rate within 0.5%. The 35 m safety spacing threshold has been validated for tunnels with an H of around 2.5D. For shallow tunnels (H less than 1.5D), spacing should be scaled proportionally to burial depth and soil stiffness.

The limitations of this study primarily lie in the simplification of spatial effects by the two-dimensional model and the discrepancy between the assumption of homogeneous soil and on-site conditions. Future research will develop a three-dimensional refined model, integrate BIM monitoring data, and consider the coupling effects of complex loads such as seismic motions to enhance the engineering applicability of the prediction model.

Footnotes

ORCID iD

Qi Liu

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the China Postdoctoral Science Foundation (No. 2023MD734186), the Chongqing Doctor Direct Online Fund (CSTB2023 NSCQ-MSX0208, CSTB2022NSCQ-MSX0518), Chongqing Technological Innovation and Application Development Project (CSTB2022TIAD-KPX0144), Chongqing Construction Science and Technology Plan Project: (Chengkezi 2023 No.1-1).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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