Groundwater Recovery and Associated Land Deformation Along Beijing–Tianjin HSR: Insights from PS-InSAR and Explainable AI

Abstract

With sub-millimeter deformation capture capability, InSAR technology has become an important tool for surface deformation monitoring. However, it is still limited by interferences like land subsidence and bridge deformation in long-term linear engineering monitoring, failing to accurately identify track deformation. Based on RadarSAT-2 and Sentinel-1A satellite data from 2013 to 2023, this study uses time-series InSAR technology (PS-InSAR) to accurately invert the track deformation information of the Beijing–Tianjin Intercity Railway (Beijing section) in the past decade. Key findings demonstrate (1) rigorous groundwater policies (extraction bans and artificial recharge) drove up to 48% regional subsidence mitigation in Chaoyang–Tongzhou, with synchronous track deformation exhibiting 0.6‰ spatial gradient; (2) critical differential subsidence identified at DK11–DK23, where maximum annual settlement decreased from 110 to 49.7 mm; (3) XGBoost-SHAP modeling revealed dynamic driver shifts: confined aquifer depletion dominated in 2015 (>60%), transitioned to delayed consolidation in 2018 (45%), and culminated in phreatic recovery–compressible layer coupling by 2022 (55%). External factors (tectonic/urban loads) played secondary roles. The rise in groundwater levels induces soil dilatancy, while the residual deformation in cohesive soils—exhibiting hysteresis relative to groundwater fluctuations—manifests as surface subsidence deceleration rather than rebound. This study provides a scientific basis for in-depth understanding of the differential subsidence mechanism along high-speed railways and disaster prevention and control.

1. Introduction

As an important transportation hub between Beijing and Tianjin, the Beijing–Tianjin Intercity Railway undertakes the dual mission of promoting regional economic integration and ensuring efficient personnel circulation. The Beijing section of the railway is 49.3 km long, with 42 km of viaducts, accounting for 87.6% of the total length [1,2]. It crosses the middle-lower reaches of the Yongding River alluvial–proluvial plain, where long-term excessive groundwater extraction has caused severe land subsidence. From 2003 to 2016, the Beijing section was affected by severe uneven subsidence, with the edges of the Dongbali–Dajiaoting and Taihu–Liyuan subsidence funnels gradually approaching the railway. The subsidence rate in the Chaoyang District section increased year by year, with the maximum rate reaching −110 mm/a at the center [3,4,5,6]. Differential land subsidence seriously impacts the railway structure. High-speed train operation and vibration exert pressure on the subgrade and bridges, causing deformation, affecting track smoothness, and reducing operational stability [7]. With the implementation of policies such as the South-to-North Water Diversion Project promoting groundwater extraction bans, restrictions, and recharge, as well as replacement of self-owned wells in urban areas, groundwater overexploitation in Beijing has improved [8,9,10,11,12]. Land subsidence patterns in the Beijing Plain are transitioning from single-phase subsidence to alternating subsidence-uplift regimes, with most areas exhibiting slowed or even reversed subsidence trends [13,14,15]. Numerous studies have focused on the impact of land subsidence on railways [16,17,18,19,20]. Unfortunately, there is little research on the effect of land subsidence mitigation on railway.

There are various subsidence monitoring methods, with GPS [21,22], GNSS, and leveling being the most common ones. These methods offer high measurement accuracy but have drawbacks such as long observation cycles, few sampling points, high costs, and the need for long-term maintenance of the measuring points. Multi-temporal Interferometric Synthetic Aperture Radar (MT-InSAR) technology, characterized by its high spatiotemporal resolution, non-contact measurement capability, data reusability, and all-weather monitoring advantages, has enabled routine and high-precision monitoring of linear infrastructure. This technique is increasingly applied to deformation monitoring of critical transport facilities. Zhang et al. [4] used multi-source remote sensing imagery and PS-InSAR to invert vertical deformation rates, comparing single-platform and multi-platform results. Zhou et al. [23] applied PS-InSAR to TerraSAR-X imagery, combining groundwater and fault zone data to explore the influence of groundwater extraction and dynamic/static loads on subsidence distribution. Lu et al. [2] processed multi-source remote sensing imagery with PS-InSAR data to analyze subsidence differences before and after the South-to-North Water Diversion. Chen et al. [5] proposed a minimum gradient difference fitting curve to fuse multi-source time-series data and used the maximum entropy model to analyze the relationship between subsidence and hydrogeological factors.

Land subsidence is a complex multi-factor process involving groundwater level changes, geological structures, soil compressibility, and human activities. Land subsidence has emerged as a critical research priority in sustainable water resources management worldwide [24,25]. Contemporary studies demonstrate that subsidence dynamics are governed by complex interactions between anthropogenic activities and geological predispositions [26,27,28]. Extensive hydrogeological investigations employing spatiotemporal correlation analyses have established that groundwater depletion-induced aquifer compaction constitutes the predominant anthropogenic driver of subsidence phenomena [29,30,31]. This causal relationship has been consistently observed across diverse hydrogeological settings [32,33]. From a geotechnical perspective, the stratigraphic architecture, particularly the distribution of compressible units, fundamentally controls both the initiation and spatial heterogeneity of subsidence patterns [25]. Notably, alluvial plains exhibit maximum subsidence rates in their mid-to-lower reaches where thick, high-plasticity clay sequences predominate [34], while deltaic and coastal plains demonstrate enhanced vulnerability due to their unconsolidated marine deposits [13]. Furthermore, neotectonic activity, as evidenced by fault-zone-associated differential subsidence, significantly influences the spatial configuration of subsidence bowls [35].

Traditional prediction models (e.g., statistical regression or physical–mechanical models) often struggle to capture these nonlinear, high-dimensional relationships, limiting prediction accuracy [36,37]. In recent years, machine learning has offered new approaches in geosciences [38,39,40,41,42,43,44,45]. XGBoost (eXtreme Gradient Boosting), an efficient ensemble learning algorithm, automatically learns complex dependencies and shows strong generalization; SHAP (SHapley Additive exPlanations) quantifies factor contributions, enhancing model interpretability to reveal subsidence mechanisms [46,47,48,49]. Compared to traditional methods, XGBoost optimizes decision tree combinations via gradient boosting to reduce overfitting, while SHAP uses Shapley values from game theory to explain predictions globally and locally, identifying key drivers (e.g., groundwater changes and compressible layer thickness).

This study uses 2013–2023 InSAR data and PS-InSAR to obtain ground deformation information along the Beijing section. An explainable machine learning model quantifies the impacts of groundwater levels in each aquifer and compressible layer thickness on subsidence across periods, identifies dominant factors, and reveals the spatiotemporal evolution of land subsidence and the dynamic transformation mechanism of main controlling factors. This provides a scientific basis and new ideas for fine-scale geological environment assessment and effective prevention of differential subsidence disasters along high-speed railways, holding important practical significance for ensuring long-term safe operation of linear engineering.

2. Study Area and Dataset

2.1. Study Area

The Beijing–Tianjin Intercity Railway, China’s first high-speed railway designed for 350 km/h, serves as a rapid passenger corridor connecting Beijing and Tianjin. Running roughly northwest–southeast, it has five stations: Beijing South, Yizhuang, Yongle, Wuqing, and Tianjin. Starting from the east end of Beijing South Station, it follows the Jingshan Railway eastward, passes under Yuting Bridge along the South Moat to Zuoanmen, then turns southeast, exits Beijing via the Beijing–Tianjin Second Expressway east of Yizhuang Development Zone and Yongle New Town, and reaches Tianjin Station. The total length is about 117 km, with approximately 85% as viaducts. The Beijing section of the Beijing–Tianjin Intercity Railway was selected as the research area in this study, which is about 50 km long, including 42 km of viaducts (as shown in Figure 1).

The Beijing Plain, in the warm temperate zone, has a temperate semi-humid continental monsoon climate with distinct seasons. Based on long-term observation data from the Beijing Meteorological Observatory, the average annual temperature is 11.7 °C, with the highest daily temperature reaching 42.6 °C (15 June 1942) and the lowest extreme temperature −27.4 °C (22 February 1966). The peak annual precipitation occurred in 1959, reaching as high as 1406 mm, while the lowest value was merely 266.9 mm recorded in 1999. The annual average precipitation in the Beijing Plain is about 580 mm, showing significant temporal and spatial unevenness, concentrated in the flood season from June to September (60–80% of annual precipitation). The surface strata along the railway are Quaternary pluvial–alluvial (Qpl + al) loose sediments, underlain by bedrock mainly from the Jixian (Jx), Qingbaikou (Qn), and Cambrian (ϵ) systems. It crosses the Nanyuan–Tongzhou Fault and Xiadian–Mafang Fault from northwest to southeast. The Beijing section passes through the alluvial–proluvial fan subarea of the Yongding River groundwater system and the Yongding River alluvial–proluvial and lacustrine plain (as shown in Figure 1a). The Quaternary sediment thickness increases from northwest to southeast, with aquifer structures transitioning from single (piedmont) aquifers to multi-layer systems and sediment particle sizes fine from coarse with changing depositional environments. In the front zone of the Yongding River alluvial–proluvial fan (DK0–DK7 section), Quaternary sediments are thin, compressible clay layers are less developed, sediments are coarser than in the alluvial plain, and it benefits from both piedmont lateral runoff and atmospheric precipitation recharge. In contrast, the alluvial plain (DK7–DK25 section) has significantly thicker Quaternary sediments, finer lithology, and poorer groundwater recharge (as shown in Figure 1b). Under the same extraction intensity, different geomorphic units along the railway exhibit diverse land subsidence characteristics, making it the main geo-environmental issue in the region [50,51].

2.2. Dataset

The data used in this paper mainly include Sentinel-1A SAR images, RadarSAT-2 SAR images, dynamic monitoring data of underground water wells, hierarchical monitoring data, and hydrogeological background data. The specific datasets are as follows.

2.2.1. SAR Imagery

The InSAR data selected in this study are the data of 112 RADARSAT-2 from 2013.01 to ~2018.12 and the data of 68 Sentinel-1A from 2019.01 to ~2023.12. Launched by Canada in December 2007, the RADARSAT-2 satellite is a medium-resolution radar satellite with a large image range, a C-band sensor, and a 24-day revisit period. The SAR data for Sentinel1A are provided free of charge by the European Space Agency (ESA). At least one image datum is involved in interference processing each month to ensure sufficient time-domain resolution. The secondary DEM data are derived from external Digital Elevation Model (DEM) data from NASA’s Space Shuttle Radar Topographic Mission (SRTM) with a spatial resolution of 30 m. The coverage of the selected image data is shown in Figure 1, and the details are shown in

Table 1. InSAR dataset details.

Data Type	Radarsat-2	Sentinel-1A
Orbit Direction	Descending	Ascending
Spatial Resolution/m	100	5 × 20
Band (Wavelength)	C-band (5.63 cm)	C-band (5.5 cm)
Revisit Period/day	24	12
Number of Images	112	68
Time Range	January 2013–December 2018	January 2019–December 2023

.

2.2.2. Other Data

Leveling measurements for land subsidence were conducted by the Beijing Institute of Hydrogeology and Engineering Geology. First-order leveling surveys have been performed annually using Trimble DINI levels since 2005. The leveling monitoring network consists of approximately 500 benchmarks arranged in a closed-loop reticular structure, with the accidental mean square error per kilometer <0.45 mm and the total mean square error per kilometer <1.00 mm [5]. In this study, leveling data from 2013 to 2023 at several benchmarks (as shown in Figure 2a) were selected to validate the accuracy of InSAR results. Data from nine groundwater level observation wells located in the southeastern Beijing Plain, adjacent to the Beijing–Tianjin Intercity Railway (specific positions shown in Figure 2a), were also used. This area lies within the Yongding River alluvial–proluvial fan and shares the same groundwater system as the railway, thus representing groundwater level variation characteristics along the Beijing–Tianjin Intercity Railway. The Quaternary sedimentary environment in the Beijing Plain is complex, with sand layers and cohesive soil layers interlacing each other, featuring numerous layers and a complex structure. The strata dominated by silty clay, clay, or silt, interspersed with thin layers of silty sand or silty fine sand, are generalized as compressible layers. Based on borehole data from 110 drilling sites within the study area and integrated with geophysical exploration data, we obtained compressible thickness contour maps with a spatial resolution of 5 × 5 km along the high-speed railway through interpolation methods.

3. Research Methods

The overall methodology of this study is illustrated in Figure 3. First, GAMMA (v201710) software was employed to process 112 scenes of RadarSAT-2 (2013–2018) and 68 scenes of Sentinel-1A (2019–2023) covering the Beijing–Tianjin Intercity Railway using permanent scatterer interferometric synthetic aperture radar (PS-InSAR) technology, acquiring time-series vertical surface deformation information along and around the railway. To evaluate the accuracy of the InSAR results, the outcomes of 30 leveling points during 2013–2023 were selected for comparison with the InSAR monitoring results. Due to spatial discrepancies between InSAR and leveling measurements, a 100 m buffer zone around each leveling point was established. The mean value of InSAR measurements within the buffer was compared with the leveling results using linear analysis.

Based on the Specifications for Geological Hazard Risk Assessment, this study evaluated the development degree of land subsidence along the railway using two indicators: subsidence rate and cumulative subsidence, as shown in

Table 2. Evaluation standard of the development of land subsidence.

Standard	Severe	Moderate	Weak
Deformation rate (mm/yr)	>50	30–50	0–30
Cumulative deformation (mm)	>1500	500–1500	<500

Note: Meeting either of the two indicators mentioned above is sufficient.

. Three subsidence intervals were defined: severe subsidence areas with annual subsidence >50 mm, moderate areas (30–50 mm), and weak areas (<30 mm).

Using the time-series InSAR monitoring results, we first focused on analyzing the evolution of land deformation in the area along the railway over the long term from 2013 to 2023. Next, to analyze the impact of land subsidence on the Beijing–Tianjin high-speed railway, a 500 m buffer zone was constructed along the railway line based on InSAR deformation results from 2013 to 2023, extracting ground deformation distribution information for the Beijing section within the buffer and identifying sections with severe differential subsidence. Combined with dynamic groundwater level monitoring data, the response of land subsidence along the high-speed railway to groundwater level changes was analyzed. An explainable machine learning model (XGBoost + SHAP) was further applied to explore the response of land subsidence along the high-speed railway to groundwater level changes in each aquifer group across different years, identify the main controlling factors, and dissect the complex mechanisms of land subsidence mitigation, providing a scientific basis for land subsidence prevention and control along the high-speed railway and safe track operation.

3.1. Permanent Scatterer Interferometry Techniques

Permanent scatterer interferometry (PS-InSAR) is a well-established technique for monitoring surface deformation using SAR data, as proposed by Ferretti et al. (2001) [52]. By targeting stable scatterers (e.g., buildings and exposed rocks) with high temporal coherence, PS-InSAR effectively mitigates temporal decorrelation and atmospheric interference, enabling long-term deformation monitoring [52]. The interference phase of PS points comprises contributions from flat-earth effects, topography, deformation, atmospheric delays, and noise. In this study, we adopted the standard PS-InSAR workflow to process Radarsat-2 and Sentinel-1A datasets. Key steps included the following:

➀

PS Point Selection: Stable targets were identified based on amplitude dispersion and coherence thresholds.

➁

Phase Modeling: Differential interferometric phases were decomposed into deformation, topographic residuals, and atmospheric components.

➂

Atmospheric Correction: Iterative spatial filtering was applied to reduce atmospheric delays.

The deformation rates derived from PS-InSAR were validated using leveling data, ensuring measurement accuracy (RMSE < 2.0 mm/year). This approach enabled high-resolution (sub-centimeter) monitoring of land subsidence along the Beijing–Tianjin Intercity Railway.

3.2. Explainability Machine Learning Models

In this study, the open-source XGBoost framework (version 1.7.6) was used to build and train the model in the Python 3.9.21 environment. The random search function of hyperparameters provided by Scikit-learn is integrated into the model training process to achieve automatic tuning of key parameters. In order to improve the interpretability of the model, the SHAP method is introduced, and the TreeExplainer tool is used to analyze the importance of features and their influence on the prediction results [53,54,55]. The proportion of the test set is set to 20%, that is, the training set and the test set account for 80% and 20% of the total sample, respectively.

XGBoost is an efficient machine learning algorithm developed on the basis of the Gradient Boosting Decision Tree (GBDT) proposed by Chen et al. [56]. Compared with the traditional GBDT, XGBoost introduces a number of strategies such as second-derivative optimization, regularization control, column sampling, cache acceleration, and parallel computing, which not only significantly improves the computational efficiency and generalization ability of the model but also shows excellent performance in various tasks such as classification, return, and sorting. In each iteration, XGBoost builds a new regression tree (i.e., a weak learner) to minimize the residuals, uses additive modeling strategies to gradually approximate the true values, and finally integrates to form a strong predictive model. The objective function consists of two parts: one is the loss function, which measures the difference between the predicted value of the model and the true value; the second is regularization, which effectively suppresses overfitting by penalizing the complexity of the tree (such as the number of leaf nodes and the sum of squares of node weights), thereby enhancing the generalization ability of the model.

In land subsidence modeling, multi-source, multi-scale, and highly nonlinear environmental variables are involved, such as groundwater level, aquifer structure, soil compressibility, etc. [5,57].

Traditional linear or parametric models often struggle to accurately capture these complex relationships. With its strong fitting ability to nonlinear feature interaction and robustness to high-dimensional features, XGBoost can better explore the potential coupling mechanism between deformation and various environmental factors. In addition, its built-in feature importance evaluation function also provides strong support for the subsequent integration of SHAP.

It is an ensemble model composed of $k$ CART regression trees, where $x$ is the i-th feature and $y_i$ is the actual value of the i-th sample; then, the value of the i-th sample predicted by the t-based learner is given in Equation (1).

$$\begin{array}{c}{\widehat{y}}_i^{\left(t\right)}={\sum }_{k=1}^t{f}_k\left(x_i\right)={\widehat{y}}_i^{\left(t-1\right)}+f_t\left(x_i\right)\end{array}$$

(1)

In Equation (1), ${\widehat{y}}_i^{\left(t\right)}$ is the predicted value after the $t$ iteration, ${\widehat{y}}_i^{(t-1)}$ is the predicted value of $t-1$ tree, and $f_t\left(x_i\right)$ is the $t$ tree model.

Based on ${\widehat{y}}_i^{\left(t\right)}$, the objective function of the tth base learner of the model is obtained; see Equations (2) and (3).

$$\begin{array}{c}{X}^t={\sum }_{i=1}^{n}l\left(y_i,{\widehat{y}}_i\right)+{\sum }_{i=1}^t\Omega \left(f_i\right)\end{array}$$

(2)

$$\begin{array}{c}\Omega \left(f_i\right)=\gamma T+\lambda {\displaystyle \frac{1}{2}}{\displaystyle \sum _{j=1}^T}{\omega }_j^2\end{array}$$

(3)

In Equations (2) and (3), $l(y_i,{\widehat{y}}_i)$ is the loss function, ${\sum }_{i=1}^{n}l(y_i,{\widehat{y}}_i)$ is the training error, ${\sum }_{i=1}^t\Omega \left(f_i\right)$ is the regular term to prevent the model from overfitting, T is the number of leaf nodes of the tth base learner, $\gamma$ and $\lambda$ are the hyperparameters that can be artificially adjusted to control the penalty intensity, $\lambda$ is the score of the control leaf node, and $\omega$ is the score of the leaf node.

The value of the objective function can be obtained by solving the objective function; see Equation (4)

$$\begin{array}{c}{X}_{obj}={\displaystyle \sum _{j=1}^T}\left[\left({\displaystyle \sum _{iϵI_j}}{g}_i\right){\omega }_j+{\displaystyle \frac{1}{2}}\left({\displaystyle \sum _{iϵI_j}}{h}_i+\lambda \right){\omega }_j^2\right]+\lambda T\end{array}$$

(4)

In Equation (4), $g_i$ and $h_i$ are the first-order and second-order derivatives of the loss function, respectively, and $I_j$ is the set of samples at the $j$-th node.

The SHAP (SHapley Additive ExPlanations) model [58], proposed by Lundberg and Lee, aims to quantify the marginal contribution of each input feature to the prediction results of the machine learning model and provide interpretability from the local to the global level for the “black box model”. The SHAP method not only assesses the importance of features in a single sample but also reveals the specific direction and strength of the influence of each variable on the prediction results, showing significant advantages when dealing with complex nonlinear models (e.g., XGBoost, neural networks, etc.).

In the study of land subsidence, there are many influencing factors, and they are coupled with each other, such as groundwater level changes, aquifer characteristics, formation compressibility, and other variables; additionally, the relationship between variables is complex and nonlinear, and it is difficult for traditional statistical methods to accurately describe the causal structure between characteristics and subsidence response. The introduction of the SHAP method can effectively break through this bottleneck: it provides a global perspective of feature importance assessment and identifies the dominant influencing factors by calculating the mean of SHAP values for all samples.

The explanatory model g is a linear function of the feature attributes, which can be used to explain the individual predictions and the whole model prediction based on the average feature attributes of all sample points [59], as detailed in Equation (5).

$$\begin{array}{c}g\left(z^i\right)={\varphi }_0+{\sum }_{i=1}^M{\varphi }_i{z}_i^{’}\end{array}$$

(5)

In Equation (5), $z_i^{\prime }ϵ\left\{0,1\right\}$ is the number of input features, and ${\varphi }_i\in R$ is the feature attribute of feature i, the SHAP value.

The final factor contribution ${\varphi }_i\in R$ is the weighted average of all marginal contributions, and the relative importance of each variable is represented by its average absolute SHAP value. This article describes the relative importance of each factor by calculating the average absolute SHAP value.

This study selected shallow groundwater level change (f0), first confined aquifer level change (f1), second confined aquifer level change (f2), third confined aquifer level change (f3), and compressible layer thickness (CDT) as influencing factors to quantify the contributions of different factors to land subsidence.

4. Results

4.1. Accuracy Verification

The InSAR monitoring results exhibit good consistency with leveling measurements, as shown in Figure 4. The differences between PS-InSAR-derived land subsidence values and leveling results during 2017–2018 and 2020–2021 range from 2 mm to 10 mm and 2 mm to 5 mm, respectively, with correlation coefficients of 0.96 and 0.98. These results indicate a high degree of correlation between InSAR and leveling measurements, verifying the reliability of InSAR monitoring results.

4.2. Evolution of Land Deformation Derived from InSAR Data

Using RadarSAT-2 and Sentinel-1A data, PS-InSAR technology was employed to acquire land subsidence information in the Chaoyang and Tongzhou districts, which are key areas traversed by the high-speed railway from 2013 to 2023, yielding a total of 618,232 PS points, where positive values indicate uplift and negative values denote subsidence.

4.2.1. Regional Subsidence

As shown in Figure 5, land subsidence presented a patchy distribution from 2013 to 2023, with severe subsidence mainly concentrated in eastern Chaoyang District and western/northern Tongzhou District. In 2013, the severe subsidence area covered 615.74 km², with the maximum annual subsidence of 150 mm occurring near Louzizhuang and Magezhuang at the border of Chaoyang and Tongzhou. In the first three years after the South-to-North Water Diversion Project (2014–2017), the severe subsidence area significantly shrank, 494.64 km² in 2017, a 19.66% reduction from 2013. From 2018 to 2023, the severe subsidence area decreased from 369.27 km² to 0.4 km², and the maximum annual subsidence dropped from 98 mm to 62 mm.

4.2.2. Subsidence Characteristic Along the High-Speed Railway

As shown in Figure 6, influenced by the regional slowdown of land subsidence, the track subsidence also continuously decreased. From 2013 to 2023, the maximum track subsidence of the Beijing–Tianjin Intercity Railway decreased from 110 mm to 49.7 mm. The scope of severe track subsidence gradually narrowed until disappearance, and the track subsidence rate was significantly lower than the regional ground subsidence rate. As shown in Figure 7a, characteristic point P on the railway and point M within 500 m off the track were selected to extract their annual deformation rates and cumulative subsidence from 2013 to 2023, as shown in Figure 7b,c. Both the annual deformation rate and cumulative subsidence of point P on the track were smaller than those of point M off the track. Additionally, the deformation rates at both points P and M showed a trend of deceleration.

To further analyze the deformation along the high-speed railway, the track deformation from 2013 to 2023 was divided into three subsidence intervals according to Table 2, with the changes and proportions of each interval shown in Figure 8. From 2013 to 2014, the length of the track with subsidence rates of 0–30 mm/a ranged from 35.4 to 35.9 km. Since 2015, this length has gradually increased, with its proportion in the total route length continuously rising to 46.3 km (92.6% of the Beijing section) by 2023. This indicates that the weak subsidence zone along the high-speed railway expanded significantly and the subsidence rate gradually decreased during 2013–2023. The length of the track with subsidence rates of 30–50 mm/a decreased from 6.1 km (2013) to 3.7 km (2023), showing a continuous decline in its proportion. The length of the track with subsidence rates >50 mm/a was 9.0 km in 2013; it began to sharply decrease from 2018 and dropped to 0 km by 2023, a reduction of nearly 8 km.

Uneven ground deformation along high-speed railways can alter track gradients, affecting ride smoothness and operational safety. The land subsidence gradient is a critical indicator for measuring railway ride quality. The Beijing–Tianjin Intercity Railway imposes strict requirements on foundation stability, with the maximum allowable land subsidence gradient limited to 20‰ [7]. The subsidence rate curve and deformation gradient curve along the line can reflect the deformation curvature radius to a certain extent [3]. The gradient change between two points can be calculated using Equation (6):

$$\begin{array}{c}\mathrm{i}={\displaystyle \frac{∆\mathrm{h}}{\mathrm{L}}}={\displaystyle \frac{\left({\mathrm{a}}_2-{\mathrm{a}}_1\right)}{\mathrm{L}}}\end{array}$$

(6)

In Equation (6), ∆h represents the deformation difference between two points on the ground; a₂ − a₁ represent the deformation difference between the two points; L represents the straight-line distance between two points on the ground.

This study generated points at 200 m intervals along the Beijing–Tianjin Intercity Railway, extracted annual deformation values at these points, and plotted the mean annual deformation rate, cumulative deformation, and deformation gradient curves for the Beijing section of the railway from 2013 to 2023. As shown in Figure 9a, the deformation rates in the DK0–DK5 and DK25–DK50 sections of the Beijing–Tianjin Intercity Railway fluctuated between ±10 mm/a, while significant subsidence occurred in the DK17–DK23 section, with a maximum deformation rate reaching −64.64 mm/a and an absolute gradient value of 0.45‰, indicating substantial deformation variability. As illustrated in Figure 9b, the maximum cumulative subsidence in this section reached 711 mm, resulting in 0.65 m of differential subsidence, with an absolute cumulative deformation gradient value of 0.58‰ studied.

4.3. Relationship Between Groundwater and Land Deformation

The above research results show that InSAR technology can effectively monitor the subsidence along the Beijing section of the Beijing–Tianjin Intercity Railway. The monitoring data clearly present the regional subsidence situation and successfully identify a large number of permanent scatterers (PSs). The monitoring shows that the subsidence in this section has significantly slowed down, the subsidence rate along the line has continued to decline, and the maximum subsidence rate has decreased from −150 mm/a to −62 mm/a. A large number of studies have shown that groundwater extraction is the main driving factor of regional subsidence, and the subsidence trend is highly consistent with the groundwater extraction data [11,13].

To further analyze the relationship between land subsidence evolution and groundwater levels, nine wells near the high-speed railway were selected. The time series of groundwater levels in each well’s aquifer group was compared with the average deformation time series of InSAR points within the 100 m buffer zone of the wells, and the results are shown in Figure 10. Since 2017, the groundwater levels in the areas of Wells 1–3 and Well 6 have shown a significant upward trend, especially in the second confined aquifer, with the water level rising by about 10 m. The groundwater levels in Wells 4–5 and 7–9 have increased slightly. The ground deformation time series around each well also shows differences. Since 2021, the groundwater levels in each aquifer group of Wells 1–3 have rebounded in a fluctuating manner, and the surface has shown a trend of decreasing subsidence rate and slowing subsidence. At Well 6, the groundwater levels in each aquifer group have continued to rebound since 2017, and the surface deformation trend at this well is highly consistent with the change in groundwater levels, showing a situation of surface rebound with water level rise. In addition, at Wells 4–5 and 7–9, the groundwater levels in each aquifer remain relatively stable, but the correlation with ground deformation is not obvious, and the ground as a whole shows a continuous downward state without obvious seasonal characteristics and slowing trend. Therefore, from the comparison of time series, it can be seen that the ground deformation in the area along the high-speed railway shows different responses to the changes in groundwater levels.

The deformation of the land surface has a strong correlation with the changes in the groundwater level of each underground layer. To further explore the response relationship between the subsidence along the high-speed rail line at different periods and the changes in the groundwater level of each aquifer group along the line, and to identify the main controlling factors, an interpretable machine learning model (XGBoost + SHAP) was used for analysis. The simulation results are shown in Figure 11. In 2015, the SHAP relative feature importance scores for features f3 and f2 were the highest, respectively, at 11.073 and 7.849. In 2018, f3 and f2 still held the dominant position, with scores of 7.846 and 5.847, respectively. By 2022, the main controlling factors changed, with f0 and f2 having the highest SHAP relative feature importance scores at 3.108 and 1.998, respectively.

In 2015, the SHAP analysis identified groundwater level declines in the third (f3, 11.073) and second (f2, 7.849) confined aquifers as the primary drivers. The interactive effect between f3 and f2 contributed 18% of the total variance (Figure 11b). Due to excessive exploitation of groundwater in the middle-deep confined aquifers, the pore water pressure decreased with the decline of groundwater level, causing the effective stress to exceed and continuously increase beyond the pre-consolidation pressure of the stratum, leading to continuous stratum compression [60,61]. In 2018, while f3 (7.846) and f2 (5.847) remained dominant, their interactive contribution decreased to 12% (Figure 11d). The monitoring data showed that the groundwater level showed an upward trend during this stage. The rising water level increased the pore water pressure and reduced the effective stress, which fell below the pre-consolidation pressure, causing the soil layer to transition from plastic to elastic deformation. The second and third aquifers contain thick cohesive soil layers with low permeability and slow water release rates, leading to residual deformation in the stratum. The aquitards were further compacted [62]. Therefore, although the groundwater level had stabilized (or slightly risen), land subsidence continued.

In 2022, the influence shifted to the phreatic aquifer (f0, 3.108) and second confined aquifer (f2, 1.998), with a negative interaction (−8%) between f0 and f1 (Figure 11f). The phreatic aquifer was recharged by rainfall, causing the water level to rise rapidly (1–2 m), leading to rebound of shallow soil. Due to reduced exploitation of the middle-deep confined aquifers, their water levels gradually recovered, and the confined aquifers still played a major role in mitigating regional land subsidence [11].

4.4. Relationship Between Thickness of Compressible Layer and Surface Deformation

The ground subsidence along the Beijing section of the Beijing–Tianjin Intercity Railway exhibits significant spatial variability. The Quaternary sedimentary zoning along the railway is as follows: the DK0–DK7 section traverses the area northwest of the Nanyuan–Tongxian Fault, where Quaternary sediments accumulated to less than 100 m during the Quaternary period; the DK7–DK25 section passes through the region from the Nanyuan–Tongxian Fault to the Daxing Uplift Belt, with an average Quaternary sediment thickness of approximately 200 m; the DK35–DK50 section is located within the Dachang Depression and Gu’an–Wuqing Depression, where the Quaternary period was characterized by subsidence and received thick sedimentary deposits, reaching a maximum Quaternary thickness of about 350 m along the railway (as shown in Figure 1b). The distribution of Quaternary sedimentary environments and thicknesses shows good consistency with the spatial pattern of ground subsidence, indicating that differences in Quaternary sedimentary conditions are a key factor influencing the spatial development of ground subsidence.

Overlay analysis was conducted to create a 1 km buffer zone along the Beijing section of the Beijing–Tianjin Intercity Railway, and the mean annual subsidence rates and compressible layer thicknesses within this buffer zone from 2017 to 2023 were extracted (as shown in Figure 12a). Along the DK0–DK7 section, the compressible layer thickness ranges between 50 and 70 m. The relatively thin compressible clay layer, combined with favorable conditions for receiving lateral groundwater flow from piedmont areas in the alluvial–proluvial fan region and adequate atmospheric precipitation recharge, results in insignificant ground subsidence. In contrast, the DK11–DK23 section crosses the alluvial plain area with thick Quaternary deposits, where the compressible layer thickness increases gradually from 70 m to 120 m. This segment features extensive distribution of clay layers, finer sediment grain sizes, and poorer groundwater recharge conditions compared to the alluvial–proluvial fan area. The regional geological structural characteristics in this section lead to significant ground subsidence. Within the DK23–DK29 section, the compressible layer thickness decreases from 130 m to 90 m, accompanied by a reduction in subsidence rate. Although the compressible layer thickness increases again to 140 m after DK29, the section beyond DK29 is located far from the Dongbali–Zhaojiating subsidence center, and the subsidence rate shows no significant change, stabilizing at a relatively small value.

To more intuitively represent the relationship between compressible layer thickness and subsidence rate distribution, the compressible layer thickness was divided into 10 m intervals, and PS points within each thickness interval were extracted. The maximum, minimum, and mean subsidence rates for each thickness interval were statistically analyzed and compared. As shown in Figure 12b, the mean subsidence rate generally increases with compressible layer thickness in the 70–120 m range. The 110–120 m interval exhibits the highest mean and minimum subsidence rates among all intervals. Combining with Figure 12a, it is evident that the 110–120 m compressible layer thickness interval coincides with the maximum differential deformation section (DK11–DK23) along the railway, demonstrating that compressible layer thickness significantly influences the distribution and development of regional differential subsidence.

5. Discussion

The analysis results demonstrate a significant deceleration in land subsidence within the study area. The maximum annual subsidence rate at the Chaoyang–Tongzhou subsidence center decreased from 150 mm to 87.6 mm, representing a substantial reduction of 48%. Interpretable machine learning analysis reveals that rising groundwater levels constitute the primary driver of subsidence mitigation.

The South-to-North Water Diversion Project has crucially supported water management strategies. By 2020, Beijing had received a cumulative total of 601.08 million m³ of surface water from the Danjiangkou Reservoir, with 68% allocated to urban water treatment plants, providing alternative sources for public water supply. This has effectively facilitated the implementation of self-supply well closure policies and significantly reduced emergency water extraction [63]. The monitoring data indicate groundwater levels began recovering in 2015, with a total rise of 10 m. By 2018, the average groundwater depth in Beijing’s plain areas reached 23.03 m, reflecting a 1.94 m increase from late 2017 and corresponding to 990 million m³ of replenished groundwater storage [12].

According to effective stress principles, groundwater fluctuations directly influence effective stress variation. Rising water levels reduce effective stress. Based on the soil mechanics theory, water level elevation simultaneously decreases σ₁ and σ₃, causing Mohr’s circle to shift leftward [14]. When intersecting with the Mohr–Coulomb failure envelope, shear failure occurs. Under shear stress, soil experiences increased volumetric strain and dilatancy. This dilatancy process accompanies reduced yield strength and strain weakening, theoretically inducing particle rearrangement and soil layer rebound.

However, field monitoring detected no significant land rebound. Previous studies shown that there is competition between viscoplastic compression and elastic/viscoelastic rebound in the aquifer system [13]. The clay layers ongoing viscoplastic compression during water table recovery [14]. This phenomenon primarily is observed in the inelastic storage coefficient exceeding the elastic coefficient by 1–2 orders of magnitude [11]. Soil deformation calculations show that when water level decline surpasses historical minima, deformation derives from the inelastic storage coefficient and drawdown magnitude; during water level recovery, the elastic storage coefficient and rise magnitude govern calculations. The substantial disparity between storage coefficients results in significantly smaller rebound than compression under equivalent water level changes, generating residual deformation [14]. Consequently, aquifer systems exhibit delayed elastic recovery during water table recovery, manifesting solely as subsidence rate deceleration.

While changes in aquifer groundwater levels and the thickness of compressible layers are identified as the primary drivers, external factors such as tectonic activity and urban loading may also contribute to differential subsidence patterns. The study area spans the Nanyuan–Tongzhou Fault and the Xiadian–Mafang Fault (Section 2.1), and these fault zones can locally alter aquifer connectivity and stress distribution, thereby influencing subsidence gradients [64]. Furthermore, the rapid urbanization process in areas along the high-speed rail has led to a significant increase in surface loading, which exerts additional stress on the compressible Quaternary strata. Finite element simulation results show that the additional loads from high-rise buildings can cause considerable land subsidence within 3–4 years after their completion [65,66]. These factors are likely to act as secondary modifiers rather than dominant mechanisms. Future research should integrate InSAR with coupled hydromechanical modeling to quantify their relative contributions.

6. Conclusions

Based on medium-high resolution orbital satellite data from 2013 to 2023, this study accurately inverted decadal track deformation information of the Beijing section of the Beijing–Tianjin Intercity Railway using time-series InSAR technology, focusing on high-speed rail track subsidence and further identifying sections with significant track subsidence differences. By constructing an explainable machine learning model and fusing dynamic groundwater level monitoring data with compressible layer thickness data, the main controlling factors of land subsidence along the high-speed rail and their dynamic evolution laws in different periods were quantified, revealing the spatial variability and mitigation mechanisms of ground deformation along the railway. The main conclusions are as follows:

• After the South-to-North Water Diversion Project supplied water to Beijing, the ground subsidence rate along the high-speed railway gradually decreased. However, subsidence in the DK11–DK23 section remains significant, with a cumulative differential settlement of 0.65 m from 2013 to 2023 and a subsidence gradient of 0.6 per mil. The settlement rate of the high-speed railway track is significantly lower than the ground subsidence rate. In 2013, the maximum ground subsidence rate was 150 mm per year, while the maximum track settlement rate was 99.1 mm per year. By 2023, the maximum ground subsidence rate had dropped to 62 mm per year, and the maximum track settlement rate had further decreased to 49.7 mm per year, indicating that the high-speed railway bridges and subgrade structures have exerted effective control over settlement.
• The results from the explainable machine learning model show that the main controlling factors of settlement exhibit obvious temporal and spatial evolution characteristics: in 2015 and 2018, surface deformation was mainly controlled by water level changes in the 2nd and 3rd confined aquifers, whereas after 2022, the rise in the water level of the phreatic aquifer became the primary factor contributing to settlement mitigation. The spatial differences in the thickness of compressible layers and groundwater extraction intensity are the main causes of differential settlements along the line.
• Land mitigation is primarily attributed to rising groundwater levels driven by increased precipitation and improved water resource management, particularly the South-to-North Water Diversion Project, which reduced groundwater extraction and supported well closure policies. However, observed subsidence deceleration without significant land rebound suggests a competition between viscoplastic compression and elastic/viscoelastic rebound in the aquifer system. The dominance of inelastic storage results in residual deformation, delaying full elastic recovery despite water table rise.