Analyzing the Impact of Deep Excavation on Retaining Structure Deformation Based on Element Tracking

Abstract

In the simulation of foundation pit excavation, the traditional element birth–death method commonly used tends to encounter issues such as uncoordinated deformation and changes in the constitutive model, affecting the accuracy of the prediction results. To address these issues, this study proposes the use of element tracking. By duplicating elements for temporary supports or structures requiring changes in material properties and appropriately activating or deactivating them at the right moments, the simulation of the foundation pit excavation process can be achieved more precisely. Using the construction process of the Tangxi Passenger Transport Station’s comprehensive transportation hub foundation pit as an example, this study applied the proposed simulation method and compared the results with actual measurements, demonstrating its effectiveness. This research offers a more accurate approach for simulating foundation pit excavation and provides a reference for similar numerical simulation problems.

1. Introduction

As the development and utilization of urban underground space continue to expand, metro stations, as crucial nodes in urban transportation networks, play a significant role in improving traffic conditions [1,2]. However, constructing metro stations often involves deep excavation projects, presenting complex engineering challenges and posing risks to the safety of surrounding buildings and underground facilities [3,4,5].

Various studies have explored methods to address these challenges. For instance, Zeng et al. [6] examined the use of transverse walls to limit the movement of fences during soil pit excavation, highlighting the importance of optimal spacing to minimize deformation. Ye et al. [7] conducted a case study on the safety of metro tunnels near foundation pits, emphasizing the role of excavation processes in tunnel deformation. Wang et al. [8] introduced a trenchless method using prefabricated subway stations, reducing greenhouse gas emissions by 10.5% compared to traditional methods. He et al. [9] proposed a probabilistic model using a Bayesian network to estimate failure probabilities during excavation, offering insights into risk management.

Real-time displacement monitoring and prediction of retaining structures is vital for the safety management of deep excavation projects [10]. Zhang et al. [11] proposed a method combining deep learning and machine vision to monitor structural displacement, while Lu et al. [12] developed a deep learning model to predict the displacement of super-high arch dams. Luo et al. [13] proposed a method for predicting the deformation field of deep foundation pits considering spatial effects, demonstrating its effectiveness and practicality through comparisons with existing engineering examples. Wu et al. [14] developed a hybrid machine learning framework to predict existing tunnel deformation from adjacent foundation pit construction, achieving high accuracy and identifying key influencing parameters. Cui et al. [15] improved a calculation method based on elastic foundation beam theory, showing that their method accurately resolves deformation and internal force issues in diaphragm walls with maximum errors of 4.5% and 1.3%, respectively. However, these methods primarily reflect the current state of structures without predicting future deformation and internal forces.

Numerical simulation plays a crucial role in predicting and controlling pit deformation, analyzing soil parameters, and assessing the impact on adjacent buildings [16,17,18]. Liu et al. [1] presented a case study on optimizing the design of a super-large foundation pit excavation under unsymmetrical loading in a water-rich floodplain, showing that numerical simulations and design modifications, such as partitioned excavation and additional horizontal struts, effectively mitigated excavation risks. Zhao et al. [19] investigated the deformation responses of foundation pit construction for an urban metro station in Xiamen, using on-site monitoring and numerical simulations to demonstrate that wall penetration ratios significantly affect deformation. They proposed a new articulated support structure to counteract these adverse effects. Cui et al. [20] analyzed the freezing-temperature field and frost heave deformation in deep foundation pits utilizing artificial ground freezing, providing design references for complex geological conditions through numerical simulations. Tanoli et al. [21] used a new small-strain elastoplastic constitutive model to analyze deep foundation pit excavation in soft clay, showing the model’s capability to describe mechanical properties and structural characteristics. Li et al. [22] enhanced the distinct lattice spring model (DLSM) to better predict soil plasticity and handle multistage construction through the birth–death particle method.

While these studies have made significant contributions, challenges remain. Describing the constitutive relationship of soil, assessing construction impacts, and integrating construction management information require further research. The birth–death element technique is widely used in finite element simulations of excavation, but it often leads to convergence difficulties due to abrupt changes in the model’s nonlinear characteristics.

This study proposes using element tracking in pit excavation simulation to improve the performance of the birth–death method. By replicating elements for temporary supports or structures needing material property adjustments and managing their activation and deactivation appropriately, the excavation process can be simulated more accurately. This approach was applied to the Tangxi Passenger Transport Station’s comprehensive transportation hub, with simulation results compared to real-world measurements, confirming its effectiveness. This research provides a more accurate technique for simulating foundation pit excavations and offers valuable insights for the design and construction of deep excavation projects like subway stations, ensuring engineering safety and reliability.

2. Methodologies

This section will firstly review the conventional birth–death element method in FEM analysis of structures and infer the schematic picture of the new element tracking method. The overall technical route map of this paper is shown in the Figure 1 below.

2.1. Birth–Death Element Method

In FEM software, the addition and removal of a structure can be described by activating and “killing” relevant elements. When “killing” elements, FEM software multiplies the stiffness of the killed element by a very small number and eliminates the mass of the killed element from the total mass matrix [23]. It also sets inactive loads such as pressure, heat flux, and thermal strain to zero, thus effectively “killing” the element.

However, the “element birth and death” method used for simulating foundation pit excavation has two major shortcomings:

1. Low simulation accuracy and inability to account for existing deformations of components: The commonly used element birth and death technique simulates underground structure construction by setting certain elements to an inactive state (“dead” state) and gradually activating them according to the construction progress to mimic soil excavation and concrete pouring. However, this method fails to consider the deformation of the already constructed structure. Activated elements remain in their initial positions, leading to an inaccurate reflection of the interactions and cumulative effects between structural components during the construction process, which results in inaccurate simulation outcomes, which is also called the element drift problem (Figure 2c).

2. Difficulty in changing the constitutive type of elements: Additionally, during the simulation of underground structure construction, scenarios often arise where soil is excavated, and structures are added. In such cases, changing the material parameters of elements (for instance, from soil material properties to concrete material properties) is a common simulation approach. However, this method is limited because it cannot change the constitutive model of the materials themselves (e.g., soil requires a Mohr–Coulomb model, while concrete needs a damage elastoplastic model), thus presenting significant limitations.

The conventional method for simulating the construction process through “element birth and death” requires predefining all elements during the modeling stage. Then, operations like “kill” or “activate” are performed on the elements at different time points to simulate actual steps such as “concrete pouring” and “setting up and removing temporary supports”. Element tracking implements the tracking of structure-following displacement by duplicating elements with shared nodes.

2.2. Element Tracking Method

Element tracking involves, on top of the aforementioned steps, making additional copies of elements that require precise positional control based on their dependent nodes. For example, if the set of elements representing a particular component is labeled A, a duplicate set labeled A’ with the same position and shared nodes is created. A and A’ share nodes but are independent elements. A is assigned the normal material properties, while A’ is given material properties with stiffness much lower than A. This allows the element to follow movements without affecting the structural deformation. During simulation, initially, A is kept “dead”, while A’ is “alive” to represent the state before the construction of the component. When it is time to construct the component, A is “activated” [24,25] and A’ is “killed” to simulate the addition of the component. If the component needs to be removed and will not be required later, both A and A’ can be deleted. However, if the component needs to be temporarily removed but will be needed again later, A can be “killed”, while A’ stays “active” until A needs to be reactivated and A’ “killed” again, as seen in Figure 2d.

Similarly, for elements B that require a change in material properties, a duplicate set B’ is made, where B is assigned material 1 and B’ is assigned material 2. Initially, B is kept “alive” and B’ “dead”. When a material property transition is needed, B’ is “activated”, while B is “killed”.

This paper attempts to use unit tracking technology to model the excavation process of foundation pits, addressing the aforementioned issues with minimal cost. Taking the excavation process of a foundation pit supported by a diaphragm wall and internal bracing system as an example, the following text explains the simulation process of foundation pit excavation based on element tracking.

Step 1: Model Establishment:

Establish the underground structure components based on the specific engineering design, including foundation soil (A), diaphragm wall (B), internal supports (C1, C2, C3), and underground concrete structures (using a three-story structure as an example, including D1, D2, D3).

Step 2: Element Duplication:

Duplicate the elements corresponding to the diaphragm wall, internal supports, and underground concrete structures: B’, C1’, C2’, C3’, D1’, D2’, D3’. The duplicated elements share nodes with the original elements, and their numbers are assigned as the original element number plus the total number of model elements plus one.

Step 3: Material Assignment:

Assign the Mohr–Coulomb constitutive model for soils to the primary element sets A, B, D1, D2, and D3. Assign the constitutive relationship of the internal supports to C1, C2, and C3. For the tracking element sets C1’, C2’, and C3’, temporary elastic constitutive models are assigned with an elastic modulus of 1/10,000 of the corresponding primary elements. Assign the elastoplastic damage constitutive model to the concrete structure elements B’, D1’, D2’, and D3’.

Step 4: Interaction Application:

Bind the end nodes of the internal supports to the side walls of the diaphragm wall to simulate the connection between the internal supports and the retaining structure.

Step 5: Element Initialization:

Activate the element sets A, B, D1, D2, and D3 to simulate the soil body. “Kill” elements C1, C2, and C3 to indicate that the internal supports have not yet been applied. Activate C1’, C2’, and C3’ to enable element tracking. “Kill” D1’, D2’, and D3’ to indicate that the concrete structure has not yet been constructed at the initial stage.

Step 6: Geostress Equilibrium:

Perform the geostress equilibrium operation on A, B, D1, D2, and D3. Since different materials are separated through element tracking, the geostress equilibrium can be accomplished using an automatic balancing method (e.g., the auto mode in the geostatic analysis step in ABAQUS 2022).

Step 7: Diaphragm Wall Construction Simulation:

“Kill” element set B, and then activate element set B’ to simulate the trenching and reinforced concrete pouring process of the diaphragm wall.

Step 8: Soil Excavation and Temporary Support Construction Simulation:

According to the construction plan, “kill” the soil above the C1 support within the excavation pit, and then activate element C1 and “kill” element C1’. Then, “kill” the soil above the C2 support within the excavation pit, activate element C2, and “kill” element C2’. “Kill” the soil above the C3 support within the excavation pit, activate element C3, and “kill” element C3’. Finally, “kill” the remaining soil elements to complete the excavation and temporary support installation.

Step 9: Structure Construction:

Sequentially activate D3 and “kill” D3’, activate D2 and “kill” D2’, and activate D1 and “kill” D1’.

3. Case Study

3.1. Project Overview

In this study, the excavation process of the Tangxi Passenger Transport Complex Transport Hub project is used as an example. The project is located below the Beijing–Guangzhou railway, oriented east–west, extending from the national railway red line in the west to the side wall of line 12 in the east. The pit is approximately 350 m long, with a standard width of 45.9 m, and a depth of about 11.4 m.

The station features a double-island four-track underground island platform station design, where the eastern and western parts of the platform facilitate T-shaped transfers with lines 12, 24, and 22, respectively. The station structure is made of cast-in-place concrete (partially using steel composite structures), with the top, middle, and bottom slabs together with the central columns and inner lining walls forming a closed frame. The design for the top, middle, and bottom slabs is based on a beam–slab system; the retaining structure and the main station structure utilize a composite structure. A schematic diagram of this can be seen in Figure 3.

3.2. Overview of the Pit

The pit employs a slope + diaphragm wall + internal bracing system, with the main perimeter structure using a 1000 mm thick underground continuous wall together with a horizontal internal bracing scheme. Open-cut and sequential construction methods are used within the range of axes 2–18 to 2–19 + 14.5 m, while the cover and dig sequential construction method is adopted from axis 2–19 + 14.5 m to axis 2–25. Based on the results of geological exploration, the stratum distribution from axis 2–19 + 14.5 m to axis 2–25 mainly includes four distinct soil layers:

a. Miscellaneous Fill

Description: This layer consists of heterogeneous materials, including construction debris, soil, and organic matter. It is typically associated with urban areas and can vary significantly in composition and compaction.

Properties: The density of this layer is 18.7 kN/m³, with a cohesion value of 12.00 kPa and an internal friction angle of 8.00°. The deformation modulus of this layer is approximately 12.7 MPa. The layer is characterized by its relatively low bearing capacity and high compressibility due to its mixed and loose nature.

b. Silt

Description: This fine-grained soil layer is predominantly composed of silt-sized particles, known for their smooth texture and low plasticity. It is often found in floodplain areas and can have significant capillary action.

Properties: The density is 15.9 kN/m³, with a cohesion value of 8.45 kPa and an internal friction angle of 4.03°. The deformation modulus is approximately 24.3 MPa. This layer has moderate permeability and can be susceptible to liquefaction under dynamic loading.

c. Silty Clay

Description: This layer is a mixture of silt and clay particles, leading to a plastic and a cohesive nature. It has a higher plasticity index compared to pure silt and can exhibit significant settlement characteristics.

Properties: The density is 18.9 kN/m³, with a cohesion value of 23.49 kPa and an internal friction angle of 11.27°. The deformation modulus is approximately 17.8 MPa. This layer has low permeability and relatively high compressibility.

d. Completely Weathered Carbonaceous Shale

Description: This layer represents the end product of weathering processes acting on carbonaceous shale. It contains softened rock fragments mixed with clay and silt, having lost much of its original structure.

Properties: The density is 18.7 kN/m³, with a cohesion value of 35.51 kPa and an internal friction angle of 20.88°. The deformation modulus is approximately 32.4 MPa. This material tends to be weak, with a high degree of weathering-induced fractures and reduced strength that is shown in

Table 1. Key physical and mechanical properties of the main soil layers.

Soil Layer	Soil Layer Name	Density/kN·m−3	Cohesion/kPa	Internal Friction Angle/(°)	Deformation Modulus/MPa
1	Miscellaneous Fill	18.7	12.00	8.00	12.7
2	Silt	15.9	8.45	4.03	24.3
3	Silty Clay	18.9	23.49	11.27	17.8
4	Completely Weathered Carbonaceous Shale	18.7	35.51	20.88	32.4

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3.3. Excavation Conditions

The first step is to carry out slope excavation down to −5.5 m. The second step involves the construction of the retaining structure, completing the construction of the underground continuous wall and vertical columns. The third step is the construction of the diaphragm wall crown beam and the first set of internal supports. In the fourth step, after the completion of the crown beam and internal support construction, excavation of the soil is carried out, first excavating down to a depth of −11.5 m, then conducting an analysis of monitoring data, followed by another round of excavation down to the bottom of the pit at −16.5 m and casting the structural base slab. The division of these conditions can be seen in

Table 2. Table of working condition contents.

Work Condition	Content
1	Slope excavation down to −5.5 m
2	Construction of the underground continuous wall and vertical columns
3	Construction of diaphragm wall crown beam and internal supports
4	Excavation of the pit down to −11.5 m depth
5	Excavation of the pit down to −16.5 m
6	Casting of the structural base slab

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3.4. Establishment of the Numerical Model for the Pit

A two-dimensional plane strain numerical analysis simulation of the pit excavation is carried out using finite element analysis software. The analysis employs the element tracking method in conjunction with the birth–death element (model change) approach for modeling and analysis of the pit-retaining structure and the excavation of soil. The element tracking method involves copying an identical element at the original nodes of the model, reassigning materials to the copied elements, and using the birth–death element feature to activate or deactivate elements in the respective analysis steps. This approach facilitates the replacement of the soil with the pit-retaining structure to simulate the construction process of the retaining structure, resulting in better model convergence.

The influence area of the surrounding soil is taken as approximately five times the depth of the pit, with the overall dimensions of the model being 92 m × 72 m (length × width). According to the geological survey report, the soil layers within the depth range of the diaphragm wall construction are all completely weathered carbonaceous shale, with parameters shown in Table 1. The contact element in FEM is utilized to model the relative displacement and force transmission between the soil, underground structures, and supports. The relative displacement between the soil and piles has little effect on the simulation results; so, they are directly bound using the embedded function in ABAQUS. The soil is modeled using an ideal elastoplastic constitutive model based on the Mohr-Coulomb yield criterion. Meshing is carried out using a sweeping method, with a density of approximately 5 elements per meter, and the model is established using the element copy method. The underground continuous wall and concrete supports are simulated using beam elements, with C30 concrete (elastic modulus, Poisson’s ratio, and density taken as 30 GPa, 0.167, and 24 kN/m³, respectively). The finite element model of the pit is shown in Figure 4, and the grid division is shown in Figure 5.

Using the element tracking method for simulating pit excavation, the main difficulty lies in the re-emergence and modification of the materials at the original element locations, during which the structure’s configuration is in a continuous state of change [26,27]. When an element re-emerges and its material properties are modified, its structural configuration should be coordinated with these changes, that is, it should satisfy the strain compatibility relationship. Therefore, in the geological stress equilibrium analysis step of this simulation process, all copy elements (retaining structure elements) and beam elements (supports) are deactivated, leaving all soil elements in an active state for geological stress equilibrium. In the analysis step for constructing the retaining structure, elements with material properties of soil where the retaining structure is located are deactivated, and the copy elements (retaining structure elements) are activated to form the pit support. Then, in the excavation analysis step, the excavated soil elements are deactivated using the birth–death element (model change) method to simulate soil excavation [28,29,30]. This method of simulation can reduce the contact between elements and effectively save computational time. Figure 6 shows the geological displacement scalar contour map, at which point the units of the retaining structure are in a deactivated state. Modeling in this manner can achieve precision while reducing the establishment of contact elements and computation time.

4. Analysis and Discussion

4.1. Monitoring Projects and Layout of Monitoring Points

Two monitoring items are set for the retaining structure: horizontal displacement at the top of the wall and vertical displacement at the top of the wall, with a total of 51 measuring points arranged. According to relevant standards, the depth of the pit excavation, and the surrounding environment, the safety level of the pit is considered grade one. Based on this, the alarm values for each monitoring item are set as shown in

Table 3. Monitoring alarm values.

Number	Monitoring Item	Rate of Change (mm/d)	Cumulative Value (mm)
1	Horizontal Displacement at the Top of the Wall	3	30
2	Vertical Displacement at the Top of the Wall	3	20

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The arrangement of the measuring points for each monitoring project is shown in Figure 7, in order from the top in a longitudinal direction. A section near the 2–22 axis is selected as the monitoring section JC, which passes through the monitoring points LS-8 and LS-15.

4.2. Analysis of the Monitoring Results of the Retaining Structure

4.2.1. Horizontal Displacement at the Top of the Wall

The cumulative horizontal displacement time curve of the top of the wall is shown in Figure 8, with the completion time of the underground continuous wall maintenance marked as day 0. According to the figure, the horizontal displacement at the top of the diaphragm wall first stabilizes, then rapidly increases, and finally tends towards a stable value. This is because the process of excavation unloading of the pit soil causes the retaining structure to experience internal and external pressure, resulting in horizontal displacement. This makes the horizontal displacement of the retaining structure inside the pit significantly increase, and this increasing trend continues until the excavation of the earthwork is completed. After the excavation of the pit is completed, and with the completion of the pouring of the base slab, the change in horizontal displacement gradually weakens and eventually stabilizes, as shown in the red circled area in Figure 8. During the excavation period, the monitoring points are all displaced towards the interior of the pit. However, the cumulative horizontal displacement at the monitoring points selected on the monitoring section did not exceed 30 mm, with a maximum value of 10.64 mm. Therefore, it can be concluded that the cumulative horizontal displacement at the top of the wall at the monitoring points inside the pit did not reach the alarm value and is within the normal range.

4.2.2. Vertical Displacement at the Top of the Wall

The vertical displacement–time curve at the top of the wall is shown in Figure 9. It can be observed that as the pit is excavated, the vertical displacement at the top of the wall at all monitoring points first increases, then decreases, and subsequently stabilizes at a certain value. During the 100 to 150 phases, the curve shows a turning point where the settlement gradually decreases. This could be due to two reasons: First, the excavation reaches its lowest point and the construction of the base slab is completed, leading the overall structure to stabilize, which reduces the degree of vertical deformation. Second, after the completion of the pit excavation, the foundation soil may experience a rebound deformation, similarly reducing the degree of vertical deformation [31]. Notably, around 120 days, the monitoring curve at measuring point LS-15 shows a bulge, which may be due to the uplift caused by the influence of gravity on the surrounding soil during the excavation process, resulting in a “rebound” of the vertical displacement at the top of the wall [32]. Throughout the entire excavation period, the maximum cumulative vertical displacement at the monitoring points selected on the monitoring section was 5.02 mm, which did not exceed the alarm value of 20 mm and is considered within the normal range.

4.3. Comparison and Analysis of Numerical Results and Monitoring Data

Since the pit excavation occurs at condition 4, and at condition 5 the pit is excavated to −16.5 m, this section analyzes the cumulative horizontal displacement at the top of the wall based on condition 5. Moreover, according to the selected monitoring section, the simulated data are distributed to the left diaphragm wall (coded as ZD and referred to LS-8) and the right diaphragm wall (coded as YD and referred to LS-15), respectively.

Figure 10 presents a schematic comparison of actual monitoring data and numerical simulation data and Figure 11 shows a contour diagram of the numerical simulation analysis for the horizontal displacement at the top of the wall, both of which are under the circumstances of condition 5. According to the diagram, when the excavation depth is within 5 m, the horizontal displacement at the top of the retaining structure ranges between 2 and 4 mm, indicating relatively minor displacement overall. As the excavation depth increases from 5 to 12 m, the horizontal displacement gradually rises, peaking at 10.64 mm at the LS-8 measurement point. Beyond an excavation depth of 12 m, the horizontal displacement at the top of the retaining structure starts to decrease with further depth increases. This decrease is attributed to minimal soil damage at the pit bottom and the restraining effect of the embedded underground continuous wall, which controls the development of deformation.

Overall, there is high consistency between the actual monitoring data and the numerical simulation analysis data. The cumulative horizontal displacement curve of the retaining structure’s top in this condition develops in an “arch” shape, with deformation being smaller at both ends and larger in the middle. This pattern is commonly seen in retaining structures that have a support system, with the first line of support being concrete supports, which closely corresponds to this project’s situation. This indicates that the numerical model established for this project closely matches the actual situation, although the numerical simulation values are generally smaller than the actual monitoring values. The maximum horizontal displacement in the actual monitoring data is 10.64 mm, while in the numerical simulation analysis, the maximum horizontal displacement is 7.88 mm, with a deviation of about 26%. This deviation is related to factors such as construction loads, vehicular loads, and groundwater.

5. Conclusions

The element tracking method proposed in this paper offers an improved approach to simulating foundation pit excavations. This method addresses limitations of traditional birth–death element techniques by allowing for more precise activation and deactivation of elements during different construction stages.

Both model simulations and actual monitoring data reveal similar deformation patterns of the retaining structure. This consistency indicates that using finite element analysis with the element tracking method for two-dimensional finite element simulation of pit excavation can effectively assist in assessing the safety of excavation retaining structures.

The numerical simulation analysis values are generally smaller than the actual monitoring values, with a deviation of about 26%. This discrepancy is attributable to the simulation not accounting for factors such as construction loads, vehicular loads, and groundwater. While providing a conservative bias in the calculation results, this also indicates areas for potential model refinement.

Regarding horizontal displacement at the top of the wall, the maximum value typically appears at 3/4 of the maximum excavation depth, forming an arch shape. This pattern likely results from minimal soil damage at the pit bottom and the restraining effect of the embedded underground continuous wall controlling deformation development.

Vertical displacement at the top of the wall shows an initial increase, followed by a decrease, and eventual stabilization. This pattern reflects the overall structure stabilizing after base slab pouring completion, reducing vertical deformation. Post-excavation rebound of foundation soil may further contribute to reduced vertical deformation.

Bulges observed in some displacement curves can be attributed to middle soil around the pit bulging upwards under its weight during excavation, leading to sudden reductions in settlement.

These findings demonstrate the effectiveness of the element tracking method in simulating complex excavation processes. However, future research should focus on incorporating additional factors such as groundwater effects and dynamic loads to further improve model accuracy. Extending this approach to three-dimensional simulation applications could provide more comprehensive insights into complex excavation projects.

The element tracking method presented in this study offers a tool for better understanding and predicting the complex behaviors of soil and structures during excavation processes. As urban development intensifies and underground space utilization increases, such advancements in modeling techniques will play a crucial role in enhancing the safety, efficiency, and sustainability of underground construction projects.