A Model Based on Neural Network to Predict Surface Settlement During Subway Station Construction: A Case Study of the Dongba-Zhongjie Station in Beijing, China

Abstract

Surface settlement prediction is crucial to assess the safety of subway station construction. To overcome challenges such as missing on-site settlement data and a limited number of monitoring points, this study proposes a composite prediction model that integrates finite element analysis, a time-series interval GA-BP neural network, and variational mode decomposition (VMD) techniques. Using the Dongba-zhongjie Station in Beijing Subway Line 3 as a case study, surface settlement predictions were made for both typical monitoring points and randomly selected feature points throughout the construction period, followed by validation. The experimental results show that the root mean square error (RMSE) of the finite element model is 15.77%, confirming the model’s effectiveness. As excavation progressed through the second underground floor and bottom plate, the settlement at the maximum settlement point began to rebound, and the structure tended to stabilize. At this stage, construction of the comprehensive utility tunnel above the station can proceed concurrently.

1. Introduction

In subway stations constructed using the Pile-Beam-Arch (PBA) method, predicting and controlling ground settlement is crucial to assess construction safety. However, due to cost constraints and the complexity of on-site construction processes, measured settlement data often suffer from issues such as time discontinuity and a limited number of measurement points. These limitations hinder the study of surface settlement patterns caused by tunnel pile construction. Currently, the main methods for predicting surface settlement include empirical formulae [1,2], influence function methods [3], theoretical models [4,5], and machine learning approaches [6,7]. Among these methods, the empirical formula approach is heavily based on the precision of geological parameters and demonstrates limited adaptability to complex strata, such as mixed polymetallic zones [8,9]. The Knothe function method often requires extensive field measurement data for parameter calibration, and exhibits significant prediction errors in asymmetric structures or three-dimensional spaces [10,11]. Although the finite element method (FEM) and the boundary element method (BEM) yield accurate models, both are computationally intensive, making real-time dynamic adjustments challenging [12,13].

In recent years, it has been demonstrated that neural networks are with significant advantages in geotechnical engineering due to their strong nonlinear mapping capabilities and adaptability. Since their introduction in the 1940s, artificial neural networks (ANNs) have undergone numerous technological advancements. Among these, the backpropagation (BP) neural network has become one of the most widely used models in geotechnical engineering due to its efficiency in training through the backpropagation algorithm [14,15]. Its key advantages include nonlinear modeling, dynamic learning capabilities, and multiparameter collaborative optimization. As a result, BP neural networks are widely applied in predicting the bearing capacity of pile foundations, estimating foundation pit displacements, and analyzing slope stability [16,17,18]. Furthermore, the time series analysis method identifies inherent patterns and trends in historical data through statistical analysis and is commonly used to forecast future trends. In geotechnical engineering, neural network-based prediction methods with consistent time intervals have become well-established [19,20]. Variational Mode Decomposition (VMD) is an adaptive signal processing technique that decomposes complex signals into multiple intrinsic mode functions (IMFs), each associated with a specific center frequency. By iteratively optimizing the bandwidth and center frequency of each mode within a variational framework, VMD effectively mitigates the issues of mode mixing and endpoint effects that are commonly encountered in traditional Empirical Mode Decomposition (EMD) [21,22,23]. VMD is increasingly being applied in geotechnical engineering to process nonlinear and nonstationary monitoring data, such as surface subsidence and vibration signals, thus enhancing prediction accuracy and model robustness [24,25]. In InSAR (Interferometric Synthetic Aperture Radar) or GNSS (Global Navigation Satellite System)-based settlement monitoring, VMD is widely used to decompose complex time series data and isolate the effects of various driving factors, including groundwater level fluctuations and construction loads, on settlement [26,27].

The Dongba-zhongjie Station project in Beijing Subway Line 3, constructed using the Pile-Beam-Arch (PBA) method, also involved the development of an underground utility tunnel directly above the station. In this case, a significant challenge is the severe lack of on-site monitoring data. To analyze the surface settlement patterns induced by the PBA construction and determine the optimal timing to initiate the utility tunnel, in the present report the finite element model and the time series interval GA-BP neural network model are developed. By integrating field measurements, finite element modeling, and neural network predictions, surface settlement predictions were carried out for the monitoring point and the randomly selected feature point throughout the overall construction cycle. Monitoring these feature points effectively addresses the issues of insufficient on-site monitoring and discontinuous data collection. Finally, it enables a comprehensive investigation of the station’s surface settlement patterns and provides guidance on the optimal timing for constructing the comprehensive pipe gallery above the subway station.The flowchart of this report is shown in Figure 1.

2. Project Review

2.1. Station Design

The western section of Beijing Subway Line 3 Phase I extends from Dongsi-shitiao Station in Dongcheng District to Dongfeng Station in Chaoyang District, running primarily in an east-west direction. Dongba-zhongjie Station, part of Line 3 phase I, is an underground island-platform station situated in the Dongba-zhongjie commercial district of Chaoyang District, Beijing. The main station structure consists of a two-story, straight-wall, triple-arch design, constructed using the PBA six-guide tunnel method and the reverse construction method.

To manage groundwater, an out-of-pit dewatering system is used. The station’s smaller mileage end connects to a section constructed using the mining method, while the larger mileage end transitions to a shield tunneling section, with mining method construction proposed at the station junction. The station includes three construction shafts and multiple cross passages. The first shaft is located at the smaller mileage end, while the second and third shafts are positioned at the station’s midsection; all shafts are constructed using the inverted wellbore method.

Dongba-zhongjie Station is a 10-m-deep underground island-platform station, with a total length of 192 m and a standard section width of 22.1 m. The standard section features a two-story, double-column, three-span underground structure. The station is built using the concealed excavation column method, with the soil cover thickness of approximately 9.5 m and the bottom plate burial depth of approximately 25.3 m.

2.2. Engineering and Hydrogeological Conditions

The maximum depth of the controlled exploration borehole surveyed at this station is 52.00 m. Based on sedimentary age, genetic type, lithology, and the physical and mechanical properties of the strata, the geological formations at the proposed station site are classified into ten distinct layers and sub-layers.

During the exploration periods (September 2012, July 2014, and April 2016), three groundwater layers were identified within the surveyed area, reaching a maximum depth of 52 m. These groundwater layers are classified as water table, interlayer water, and confined water. The site strata from top to bottom are the artificial fill, which includes filled soil and plain fill, and has a thickness of 1.1∼3.6 m but with poor engineering performance. Among these, the Quaternary sedimentary layers cover medium-high density silt, cohesive soil, medium-dense sand layers, mixed soil layers, organic clay, and gravel layers. The engineering geological and hydrogeological profiles of the standard cross-section are shown in Figure 2.

2.3. Surface Settlement Layout

The soil stability at the Dongba-zhongjie Station site is relatively poor, exhibiting significant deformation due to construction disturbances. In particular, when covering the soil above the station structure, continuous monitoring of deformation during subway station construction is crucial to ensure safety.

Surface settlement measurement points are primarily arranged along the roadway, with a longitudinal spacing of 10 m and a transverse spacing ranging from 3.3 to 5 m.

During station construction, the settlement of power, sewage, and rainwater pipes with a Level 1 risk rating must be controlled within 20 mm, the inclination rate within 0.005, and the displacement rate within 2 mm/day. For gas pipes and $\varphi$400 water supply pipes with a Level 2 risk rating, the settlement control value must be within 10 mm, the inclination rate within 0.002, and the displacement rate within 1 mm/day. For tertiary buildings, the settlement control value shall not exceed 30 mm, the differential settlement shall be limited to 10 mm, and the displacement rate shall remain within 2 mm/day.

3. Settlement Prediction in the Construction Process

3.1. Finite Element Modeling

The station was modeled using finite element software, with model dimensions of $120\times 36\times 80$ m [4,28]. The modified Mohr-Coulomb constitutive model was applied to the soils. In combination with the geological exploration report, a back-analysis was performed to determine the secant modulus, cohesion, and internal friction angle for the seven soil layers. The physical and mechanical properties of the soils are provided in

Table 1. Mechanical properties of soils.

Soils	Secant Modulus (MPa)	Cohesion (kPa)	Poisson’s Ratio	Unit Weight (kN·m−3)	Frictional Angle (°)	Distributed Depth (m)
AF	7	0	0.32	17.5	10	0∼3
SCC	15	25	0.3	19.5	9.2	3 ∼6
CS	33.3	21	0.25	21	31.9	6∼8.9
FSS	49.8	25	0.22	20.9	23.3	8.9∼15.6
SCC	30.6	41.5	0.22	20	45	15.6∼24.11
CS	36.3	60	0.23	18.6	16.2	24.11∼28.5
OC	55	0	0.25	20.5	33	28.5∼80

AF = Artificial fill, SCC = Silty clay—sandy clay, CS = Clayey silt, FSS = Fine sand-silty sand, OC = Organic clay.

. The other mechanical parameters for the supporting structure and key components of the station are presented in

Table 2. Other mechanical parameters in FE modeling.

Structures	Natural Gravity (kN·m−3)	Elastic Modulus (MPa)	Poisson’s Ratio	Element Type
PL	27	25,500	0.20	2D plate
SL	25	32,500	0.21	3D solid
CTB	25.5	33,500	0.25	3D solid
GR	22	80	0.25	3D solid
BC	23.5	20,000	0.20	3D solid
SP	25	27,000	0.24	1D beam
SPC	33	41,500	0.23	1D beam

PL = Primary lining, SL = Secondary lining, CTB = Crown and top beam, GR = Grouting reinforcement, BC = Backfilling concrete, SP = Side piling, SPC = Steel pipe column.

[29,30,31]. The computational mesh of finite elements is shown in Figure 3.

The measuring points selected are illustrated in Figure 4, where point DB-17-01 to point DB-17-07 represent the measurement stations of field-installed ground surface settlement. A comparative analysis of the relative errors between the simulations and field monitoring data is presented in

Table 3. Relative errors predicted for each construction stage.

	Excavation & Support of Pilot Tunnels	Construction of Pile Beam System	Second Lining Buckle Arch	Excavation of Main Structure	Average Error %
DB-17-01	48.11	32.04	12.58	17.65	27.59
DB-17-02	10.01	18.50	20.56	11.16	15.06
DB-17-03	20.39	8.78	10.85	8.06	12.02
DB-17-04	18.73	7.24	3.72	9.16	9.71
DB-17-05	6.42	6.84	3.14	8.33	6.18
DB-17-06	33.74	16.50	20.94	13.42	21.15
DB-17-07	13.19	26.60	20.34	14.51	18.66
Average error %	21.51	16.64	13.16	11.75	15.77

. The average error between the numerical simulations and field measurements is calculated to be 15.77%, with the DB-17-05 monitoring point exhibiting a significantly lower average error of 6.18%, demonstrating favorable model accuracy.

3.2. Neural Network Prediction Model with Equal Time Intervals

To address the issue of missing in-situ monitoring data, a GA-BP neural network model is developed using Matlab to supplement the data. In practical engineering, monitoring soil settlement and deformation due to pilot tunneling or soil excavation involves recording settlement values $x\left(t_1\right),x\left(t_2\right),\cdots ,x\left(t_n\right)$ at specific time intervals through a series of equidistant measurements. These values are then used as input for training a GA-BP neural network, which predicts future settlement values $x\left(t_{n+1}\right),x\left(t_{n+2}\right)\cdots$ at subsequent time intervals. The brief supplementary training parameters are as follows: in the genetic algorithm, the population size is set to 40, the crossover rate is set to 0.7, the mutation rate is set to 0.01, and the maximum number of generations is set to 50. In the neural networks, the number of input nodes is 4, the number of output nodes is 1, and the number of hidden layer is set to 1. The detailed process is outlined in

Table 4. Training samples based on neural networks with equal time intervals.

Serial Number	Training Samples					Target Value
1	$x\left(t_1\right)$	$x\left(t_2\right)$	$x\left(t_3\right)$	⋯	$x\left(t_m\right)$	$x\left(t_{m+1}\right)$
2	$x\left(t_2\right)$	$x\left(t_3\right)$	$x\left(t_4\right)$	⋯	$x\left(t_{m+1}\right)$	$x\left(t_{m+2}\right)$
3	$x\left(t_3\right)$	$x\left(t_4\right)$	$x\left(t_5\right)$	⋯	$x\left(t_{m+2}\right)$	$x\left(t_{m+3}\right)$
⋮	⋮	⋮	⋮	⋮	⋮	⋮
$m-n$	$x\left(t_{n-m}\right)$	$x\left(t_{n-m+1}\right)$	$x\left(t_{n-m+2}\right)$	⋯	$x\left(t_{n-1}\right)$	$x\left(t_n\right)$

. The in situ settlement monitoring point DB-17-05 was selected for prediction. The location of the proposed prediction point in three-dimensional models is shown in Figure 4. The moving window method was used to construct training samples, with a total of 29 sets of on-site monitoring data from 6 April 2020, to 7 May 2020, selected as training samples for the neural network model. Figure 5 and

Table 5. Prediction error of surface settlements.

Date	Monitor Value (mm)	Fitted Value (mm)	Absolute Error %	Relative Error %
4/6/2020	−8.8	-	-	-
4/7/2020	−8.65	-	-	-
4/8/2020	−8.81	-	-	-
4/9/2020	−9.44	-	-	-
4/10/2020	−9.46	−9.581579660	0.121579660	1.285197253
4/11/2020	−10.1	−9.718163306	0.381836694	3.780561327
4/12/2020	−9.52	−9.948770254	0.428770254	4.503889227
⋮	⋮	⋮	⋮	⋮
5/5/2020	−21.91	−21.89414359	0.015856407	0.072370641
5/6/2020	−21.85	−21.87490701	0.024907005	0.113990871
5/7/2020	−22.26	−22.29903578	0.039035778	0.175362883

presents a comparison between the neural network predicted values and the in-situ measured values. The maximum relative error between the predicted and actual monitoring values is 4.50%, while the relative error for the majority of data points is below 0.1%, demonstrating high prediction accuracy. This neural network model is suitable for predicting settlement and effectively addresses the issue of discontinuous in-situ monitoring data.

3.3. VMD Decomposition Model

To eliminate the interference of factors such as rainfall and human activities on surface settlement monitoring, variational mode decomposition (VMD) is used to decompose the settlement into three components: the trend term, the periodic term, and the random term. The displacement associated with the trend term represents surface settlement caused by station construction. The displacement of the periodic term corresponds to settlement caused by factors with periodic variations, such as rainfall. The displacement of the random term accounts for surface settlement caused by external factors, including human activities.

The VMD process for decomposing displacement data involves the following steps:

(1)

Formulation of the Variational Problem

The objective is to decompose the signal $f\left(t\right)$ into k modes $\left\{u_k\left(t\right)\right\}$, where each mode has a center frequency ${\omega }_k$ and the narrowest possible bandwidth. The corresponding optimization problem is defined as follows:

$$\underset{\left\{u_k\right\},\left\{{\omega }_k\right\}}{min}\left\{\sum _{k=1}^K{∥{\partial }_t\left[\left(\delta \left(t\right)+{\displaystyle \frac{j}{\pi t}}\right)\ast u_k\left(t\right)\right]e^{-j{\omega }_{k}t}∥}^2\right\}$$

(1)

where the corresponding constraint condition is:

$$\sum _{k=1}^K{u}_k\left(t\right)=f\left(t\right)$$

(2)

where $u_k\left(t\right)$ represents the kth modal component in the time domain; ${\omega }_k$ is the center frequency of the kth mode; ${\partial }_t$ denotes the time derivative; $\delta \left(t\right)$ is the Dirac delta function; j is the imaginary unit; ∗ represents convolution; $\left[\left(\delta \left(t\right)+j/\left(\pi t\right)\right)\ast u_k\left(t\right)\right]$ denotes the Hilbert transform of $u_k\left(t\right)$ to obtain an analytical signal; and $e^{-j{\omega }_{k}t}$ represents the demodulation of the analyzed signal to base band by shifting its center frequency to zero.

(2)

Expansion of the Lagrangian Function

To construct an augmented Lagrangian function $\mathcal{L}$, a Lagrange multiplier $\lambda \left(t\right)$ and a quadratic penalty term are introduced:

$$\begin{array}{cc}\hfill \mathcal{L}(\left\{u_k\right\},\left\{{\omega }_k\right\},\lambda )& =\alpha \sum _{k=1}^K{∥{\partial }_t\left[\left(\delta \left(t\right)+{\displaystyle \frac{j}{\pi t}}\right)\ast u_k\left(t\right)\right]e^{-j{\omega }_{k}t}∥}^2\hfill \\ \hfill & +{∥f\left(t\right)-\sum _{k=1}^K{u}_k\left(t\right)∥}^2+〈\lambda \left(t\right),f\left(t\right)-\sum _{k=1}^K{u}_k\left(t\right)〉\hfill \end{array}$$

(3)

where $\alpha$ is the regularization parameter that balances the trade-off between the bandwidth term and the reconstruction error. $\lambda \left(t\right)$ is the Lagrange multiplier in the time domain, which enforces the constraint conditions more strictly. $〈·,·〉$ represents the inner product operation, i.e., $\int \lambda \left(t\right)\left(f\left(t\right)-\sum u_k\left(t\right)\right)\mathrm{d}t$.

(3)

Alternating Direction Method of Multipliers (ADMM)

Variables are updated using frequency domain transformation and alternating optimization:

(a)

Updating the Mode $u_k$:

In the frequency domain, with ${\omega }_k$ and $\lambda \left(t\right)$ fixed, the following problem is solved:

$$U_k^{n+1}\left(\omega \right)={\displaystyle \frac{F\left(\omega \right)-{\sum }_{i\ne k}{U}_i\left(\omega \right)+\frac{\mathsf{\Lambda }\left(\omega \right)}{2}}{1+2\alpha {(\omega -{\omega }_k)}^2}}$$

(4)

where $U_k\left(\omega \right)$, $F\left(\omega \right)$, and $\mathsf{\Lambda }\left(t\right)$ are the Fourier transforms of $u_k\left(t\right)$, $f\left(t\right)$, and $\lambda \left(t\right)$, respectively, where $\alpha$ represents the strength of the bandwidth constraint.

(b)

Update the Center Frequency ${\omega }_k$:

The centroid of the spectrum is calculated as follows:

$${\omega }_k^{n+1}={\displaystyle \frac{{\int }_0^{\infty }\omega {\left|U_k\left(\omega \right)\right|}^{2}d\omega }{{\int }_0^{\infty }{\left|U_k\left(\omega \right)\right|}^{2}d\omega }}$$

(5)

This refers to using the spectral energy centroid of the mode as the new center frequency.

(c)

Update the Lagrange Multiplier ${\lambda }_t$:

$${\mathsf{\Lambda }}^{n+1}\left(\omega \right)={\mathsf{\Lambda }}^n\left(\omega \right)+\gamma \left(F\left(\omega \right)-\sum _{k=1}^K{U}_k^{n+1}\left(\omega \right)\right)$$

(6)

where $\gamma$ is the multiplier update step size, typically chosen such that $0<\gamma <1$.

(4)

Convergence Conditions

Iterate until the following condition is met:

$$\sum _{k=1}^K{\displaystyle \frac{\parallel U_k^{n+1}-U_k^n{\parallel }^2}{\parallel U_k^n{\parallel }^2}}<\epsilon$$

(7)

where $\epsilon$ is the preset tolerance.

The organization of on-site monitoring data is represented by the black data points in Figure 6. Clearly, there is a significant data gap, which hinders the VMD method from yielding reliable results. To overcome this issue, both finite element numerical simulations and GA-BP neural network prediction methods were applied comprehensively to predict ground subsidence at monitoring point DB-17-05. The results are presented in Figure 6.

As shown in Figure 6, data from 15 August 2021, to 12 April 2022 (a total of 241 days, which includes the main stages of PBA construction) were selected and processed using VMD to decompose the time series into trend, periodic, and random components. The decomposition results are presented in Figure 7 [29,30,31]. A detailed analysis was performed on the displacement attributed specifically to station construction activities, with the quantitative results summarized in

Table 6. Trend term displacement results.

Construction Stage	Surface Subsidence (mm)	Accumulated Surface Subsidence (mm)	Incr./Total	Cumulative Proportion
EPT	40.87	40.87	75.47%	75.47%
TAE	2.44	43.31	4.51%	79.98%
SLBA	6.32	49.63	11.68%	91.66%
EFBF	3.99	53.62	7.36%	99.02%
ESBF	0.53	54.15	0.98%	100%

EPT = Excavation of pilot tunnel, TAE = Top arch excavation, SLBA = Second lining buckle arch, EFBF = Excavation of the first basement floor, ESBF = Excavation of the second basement floor.

.

As shown in Table 6, the maximum surface settlement at point DB-17-05 is 54.15 mm. The settlement caused by pilot tunnel excavation accounts for 75.47% of the total settlement. The second-lining arch-closing stage follows, contributing 11.68% to the total surface settlement. After the completion of the second-lining arch-closing, the total contribution to surface settlement exceeds 90%. During the construction of the floor slab and the second basement level, a noticeable rebound phenomenon occurs in the surface settlement.

The data from the last 17 days (from 27 March 2022, to 12 April 2022) were fitted using a Fourier function, and the results are shown in Figure 8. The Fourier fitting is performed here to prove that the surface settlement has stabilized after the construction is completed. The reason for selecting 17 data points is that through trial calculations, 17 of them can obtain good fitting results. The coefficient of determination ($R^2$) reached 0.9702. The amplitudes $a_1$ and $b_1$ were −0.031 and −0.13, respectively. The fluctuation amplitude of surface settlement is less than 0.2 mm, which is significantly below the specified displacement rate control limit of 2 mm/day, indicating that the settlement has stabilized.

4. Prediction of Settlement for Random Feature Points in the Construction Process

Due to the extensive scope of construction, subway stations often have limited on-site monitoring points for settlement. This paper proposes a method to effectively predict settlement at unmonitored nodes. Random feature points (labeled DB-18-05) were selected to predict their settlement over the entire construction period. The location of the predicted point is shown in Figure 9, with the corresponding calculation results presented in Figure 10. The quantitative results summarized in

Table 7. Trend term displacement analysis results.

Construction Stage	Surface Settlement (mm)	Accumulated Surface Settlement (mm)	Incr./Total	Cumulative Proportion
EPT	30.22	30.22	73.27%	73.27%
TAE	1.70	31.92	4.12%	77.39%
SLBA	13.14	45.06	31.86%	109.25%
EFBF	−2.17	42.89	−5.25%	104%
ESBF	−1.65	41.24	4%	100%

EPT = Excavation of pilot tunnel, TAE = Top arch excavation, SLBA = Second lining buckle arch, EFBF = Excavation of the first basement floor, ESBF = Excavation of the second basement floor.

.

As shown in Figure 10, with ongoing construction, the displacement of the trend term continues to increase during the excavation of the guide tunnel, the top arch excavation, and the buckling of the second lining. The maximum surface settlement reached 45.06 mm. The total settlement ratio for land occupation during the excavation of guide tunnel was 73.27%, followed by the second lining arch stage, with a maximum settlement ratio of 13.14%.This is consistent with the conclusion drawn from many references [32,33,34] that surface settlement in PBA construction is mainly caused by two stages: the excavation of guide tunnels and arch construction, accounting for 70% to 80% of the total settlement value. After the completion of the second lining arch, the contribution to surface settlement had reached 109.25%. During the construction of the middle plate, negative first layer, bottom plate, and negative second layer, a significant rebound in surface settlement was observed, occurring earlier than at DB-17-05. This is because DB-18-05 is 12 m from DB-17-05, and the structure at DB-18-05 stabilizes more quickly. As a result, the stress is absorbed more rapidly by the steel pipe columns and edge piles, leading to earlier rebound in surface settlement.

Analysis of the settlement patterns at the characteristic points DB-17-05 and DB-18-05 reveals that during the excavation of the negative layer and middle plate, the structure began to stabilize, with DB-18-05 showing early signs of settlement rebound. Similarly, during the excavation of the negative second layer and bottom plate, the point of maximum settlement (DB-17-05) also began to exhibit noticeable settlement rebound. Based on the stability of the station structure and the surface settlement caused by construction, it is evident that the comprehensive pipe gallery above the station can be constructed simultaneously with the excavation of the negative second layer.

5. Conclusions

This work takes Dongba-zhongjie Station as a typical example to study the settlement by PBA subway station construction, using the finite element method combined with the equal-time-interval GA-BP neural network model. By integrating in-situ measured data, settlement predictions were made for monitoring points and randomly selected feature points over the entire construction period, followed by a detailed analysis of the results. The following conclusions were drawn:

(1)

The average error of the finite element simulation is 15.77%, and the correlation coefficient (R) of the neural network reaches $0.99$, demonstrating the strong predictive capability of the present model.

(2)

During the construction of Dongba-zhongjie Station, surface settlement is primarily caused by the excavation of the pilot tunnel and the arch closure of the secondary lining, which together account for more than 70% and 10%, respectively, of the total settlement. As excavation progresses through the first basement floor and the middle slab, the structure begins to stabilize. Upon excavation of the second basement floor and the bottom slab, settlement at the maximum settlement point begins to rebound. At this stage, the comprehensive utility tunnel above the station can be constructed simultaneously.

(3)

The prediction method proposed in this article effectively addresses the issues of insufficient in situ monitoring points and discontinuous monitoring data over time. It not only supplements nodes with on-site monitoring data but also predicts random feature points, which facilitates the analysis of surface subsidence patterns caused by similar projects.

Finally, it is noted that due to the limitations of the present report, specifically in-situ data sparsity and potential overfitting in neural networks, the generalizability of the findings to other subway construction projects in different geological conditions or urban environments should be further studied.