Advances and Future Directions in Monitoring and Predicting Secondary Surface Subsidence in Abandoned Mines

Abstract

In recent years, the prolonged exploitation of coal resources has led to the depletion of coal reserves in some mining areas, resulting in the closure of certain mines worldwide. After mine closures, the fractured rock masses in abandoned mine cavities undergo weathering and degradation due to factors such as stress and groundwater, leading to reduced strength. This change alters the stress distribution and load-bearing capacity of the fractured rock within the abandoned voids, resulting in secondary or multiple deformations on the surface, which pose significant potential threats to surface infrastructure and public safety. Research into the mechanisms, patterns, and predictive methods of secondary surface subsidence in closed mines is thus of great theoretical and practical significance. Based on a literature review and practical monitoring experience in closed mine sites, this study systematically examines and analyzes the current state of secondary surface subsidence monitoring methods, formation mechanisms, spatiotemporal distribution patterns, and prediction methods in closed mines, as well as existing challenges. Initially, we compare the advantages and limitations of conventional surface deformation monitoring techniques with remote sensing techniques, emphasizing the benefits and issues of using InSAR technology for monitoring surface subsidence in closed mines. Next, by reviewing extensive data, we analyze the formation mechanisms and spatiotemporal evolution of secondary surface subsidence in closed mines. Building on this analysis, we discuss numerical and analytical methods for predicting secondary surface subsidence mechanisms in closed mines, evaluating the strengths and weaknesses of each approach. Predictive models for surface subsidence and uplift phases in the longwall collapse method are presented based on the constitutive relationships of fractured rock masses. Finally, the study highlights that the mechanisms and patterns of surface subsidence in closed mines represent a highly complex physical–mechanical process involving geological mining environments, fractured rock structures, constitutive relations, deformation characteristics, hydro-mechanical interactions, and groundwater dynamics, underscoring the need for further in-depth research.

1. Introduction

In the energy system, coal has always played the role of a stabilizer and a bottom-line safeguard. However, with the depletion of coal resources, structural reforms on the energy supply side, and the phase-out of outdated production capacities in the energy sector, the number of abandoned mines has significantly increased worldwide [1,2]. According to incomplete statistics, there are approximately 500,000 abandoned mines across the United States, with 60% of them located in West Virginia, Pennsylvania, and Kentucky [3]. According to a report by the Canadian Mining Watch organization [4], Canada has over 10,000 abandoned mines, with the majority located in Quebec and Ontario. In Australia, approximately 52,534 abandoned mines [5] are primarily concentrated in Western Australia, South Australia, Queensland, New South Wales, Victoria, and Tasmania. The United Kingdom is estimated to have around 100,000 abandoned mines [6], most of which were deserted in the early 20th century. In Northern Ireland alone, approximately 2400 abandoned mines are known, posing significant safety risks and being strictly off-limits to the public [7]. Between 2015 and 2020, China closed 5630 coal mines [8]. By 2030, it is projected that the number of closed mines in China will reach 15,000 [9,10].

After mine closures, the cessation of drainage systems leads to rising groundwater levels, resulting in frequent secondary surface subsidence events [11,12]. These phenomena manifest in various ways:

• Alteration of stress and load-bearing capacity of overlying rock structures: The changes in stress and structural integrity of the fractured rock masses and overburden result in surface movement and deformation. For example, in northern France, surface subsidence has continued in mining areas over 20 years after mining ceased [13]. In China, surface deformation occurred in the Xuzhou mining area of Jiangsu Province, where the Hanqiao and Jiahe mines experienced initial subsidence followed by uplift after closure, causing damage to residential buildings [14].
• Softening and failure of coal pillars: The weakening and collapse of coal and rock pillars contribute to geological events in mining areas. In the United Kingdom, shallow abandoned mines experienced surface subsidence nearly a century after closure due to seasonal groundwater fluctuations. Similarly, in Japan’s Miyagi and Iwate Prefectures, coal mine closures, combined with the effects of earthquakes and groundwater movement, led to the collapse of surrounding rock and coal pillars, causing surface subsidence [15].
• Reduction in shear strength and slope stability: The loss of shear strength in slope materials decreases the stability of slopes, increasing the risk of landslides [16].
• Water–rock interactions leading to fault reactivation: The interaction between groundwater and surrounding rock, particularly along faults, can trigger fault reactivation. For instance, in Wassenberg, Germany, the rise of groundwater levels following coal mine closures reactivated faults, causing damage to nine surface buildings [17].

Secondary surface subsidence from closed mines, as a continuation of mining-induced subsidence, poses a significant potential threat to the safety of surface structures in mining areas.

With the development of socio-economic activities, various infrastructure projects and residential or industrial buildings have inevitably been constructed above the goaf areas of abandoned mines. Examples include the Collingwood Park suburb in Ipswich, Queensland, Australia, which is situated above abandoned mine workings [18]; the Dorris School campus in Collinsville, Illinois, USA, and a four-lane highway in Ohio, both of which traverse areas above closed mines [19,20]; as well as residential neighborhoods and industrial parks in mining cities such as Tangshan, Xuzhou, and Huaibei in China. After mine closures, secondary surface deformation poses a significant threat to the safety of infrastructure such as transportation, electricity, and communications, as well as to residential and industrial buildings located above subsidence areas. The extent of such deformation is a critical factor in evaluating the safety risks to these structures and in devising appropriate technical mitigation measures. Unlike subsidence caused directly by underground coal mining, secondary surface subsidence over closed mines is not triggered by active mining activities but rather by the rise in groundwater levels after mine closure. Groundwater-induced instability or renewed deformation occurs in previously stable fractured rock masses, overlying strata, and coal (or rock) pillars. This can result in both subsidence and uplift of the surface [16]. Therefore, studying the mechanisms and predictive models of secondary surface subsidence in closed mines holds significant theoretical and practical value for assessing and mitigating the risks associated with secondary subsidence disasters. The prediction methods for mining subsidence have become relatively mature after years of development. Commonly used methods include the typical curve method, profile function method, influence function method, and subsidence grid method [21]. These methods have been widely applied in evaluating the degree of mining damage, selecting control measures for mining damage, optimizing mine design, and assessing foundation stability. Secondary surface subsidence after mine closure, as a continuation of mining subsidence, is characterized by long-term and complex deformation, typically involving both subsidence and uplift processes [13,17,22,23,24]. Due to the lack of measured surface data and geological–hydrological information for closed mines, there has been limited research on prediction methods for surface subsidence after mine closure. Currently, most research focuses on predicting surface subsidence using numerical simulation and analytical methods.

Some monitoring and analytical studies on secondary subsidence in closed mines have been conducted, but comprehensive and systematic research remains limited. The monitoring methods, including surface deformation and underground situation monitoring, are one of the main reasons. To advance the study of secondary subsidence in closed mines, this work reviews the existing research on monitoring, mechanisms, patterns, and prediction methods of secondary surface subsidence in closed mines globally. The achievements of current studies are summarized, and the findings from field monitoring of secondary subsidence in closed mines are integrated. The current state of research is analyzed from the perspectives of monitoring, mechanisms, subsidence patterns, and prediction methods. Additionally, key issues requiring further investigation are identified, with the aim of promoting the development of research on secondary subsidence in closed mines.

2. Current State of Research on Monitoring Secondary Subsidence in Closed Mines

Accurate field data on secondary surface subsidence in closed mines serve as the foundation for studying its spatiotemporal evolution patterns and developing predictive models. Such data are also critical for evaluating whether research outcomes align with real-world conditions. However, the lack of field measurements has hindered progress in understanding the mechanisms of secondary surface subsidence and refining predictive models. Therefore, the precise acquisition of secondary surface subsidence information for closed mines is of paramount importance.

Currently, surface subsidence monitoring methods primarily include conventional ground deformation monitoring techniques and aerial and satellite-based measurements. Conventional ground deformation monitoring techniques, such as leveling surveys and Global Navigation Satellite System (GNSS) measurements, are highly accurate and remain the preferred methods for monitoring local-level surface deformation. However, these methods are costly, labor-intensive, and unsuitable for large-scale surface deformation monitoring [25,26,27]. Aerial and satellite-based methods include photogrammetry and interferometric synthetic aperture radar (InSAR). Aerial photogrammetry is often conducted using unmanned aerial systems (UASs). Its advantages include a wide monitoring range and the ability to reconstruct pre-deformation states of the monitored area through images. However, its accuracy is relatively low, typically limited to decimeter-level precision [28,29,30,31,32,33,34]. InSAR technology, on the other hand, offers all-weather, all-day monitoring capabilities with wide spatial coverage and high precision. Using phase information from SAR (synthetic aperture radar) complex data, InSAR can extract deformation information from target areas with millimeter- or sub-centimeter-level accuracy [35,36,37]. Given the extensive and concealed nature of secondary subsidence in closed mines, InSAR technology is highly feasible for monitoring these phenomena. Additionally, archived SAR data can be utilized to trace historical deformation information.

Table 1. Methods for monitoring surface deformation.

Method	Advantages	Limitations	Applicable Scenarios	Ability to Trace Historical Deformation
Total Station/Leveling	High precision (up to mm level), mature technology, and simple instrument operation.	Discrete monitoring, labor-intensive, high cost, unable to monitor real-time surface displacement changes, weather-dependent.	Small areas, typically for a single mining zone or working face.	No
GNSS (Static/Dynamic)	High precision (up to mm level); automated GNSS monitoring systems enable real-time dynamic monitoring.	Discrete monitoring, high cost, susceptible to atmospheric and multipath effects.	Small areas (single mine or working face) or large areas (adjacent mines).	No
Ground/Airborne LiDAR	High density of measurement points; capable of acquiring 3D deformation information of monitoring points.	Severely affected by surface vegetation, moderate precision (cm or dm level), limited range, unable to perform real-time monitoring.	Small areas (single mine or working face) or large areas (adjacent mines).	No
UAV Photogrammetry	Convenient and fast; capable of acquiring 3D deformation information of monitoring points.	Severely affected by external conditions (e.g., cloud cover), moderate precision (cm or dm level), limited range, unable to perform real-time monitoring.	Small areas (single mine or working face).	No
InSAR	High precision, large coverage, all-weather capability; can trace historical deformation using archived data.	Affected by spatial–temporal decorrelation, unable to monitor large gradient deformations (typically limited to meters for single interferogram), not suitable for real-time monitoring.	Large surface areas, covering multiple adjacent mining zones.	Yes

summarizes the advantages and disadvantages of various methods for monitoring surface deformation.

Due to the low spatial density and limited coverage of conventional ground deformation monitoring methods, only a few researchers have utilized leveling surveys to obtain secondary subsidence data for closed mines. From 1974 to 1984, leveling surveys were conducted at the closed Limburg coal mines near the border of Germany and the Netherlands, capturing surface deformation data within the first decade after mine closure. Based on this dataset, Bekendam [38] analyzed the relationship between surface subsidence and uplift following mine closure and proposed a predictive model for surface uplift using poroelastic theory. Zheng [39] established 32 leveling observation points at the Jiahe and Pangzhuang mines in the Xuzhou mining area, collecting secondary subsidence data from September 2018 to June 2022 after mine closure. This dataset provides a critical basis for validating InSAR monitoring results, analyzing the patterns of secondary subsidence in closed mines, and assessing the reliability of predictive models.

Traditional InSAR techniques are susceptible to decorrelation caused by spatial and temporal baselines, as well as atmospheric effects, which can reduce accuracy in long-term deformation monitoring. To address these limitations, time-series InSAR techniques based on highly coherent targets have been developed. These include methods such as Permanent Scatterer InSAR (PS-InSAR) [40,41,42], Small Baseline Subset InSAR (SBAS-InSAR) [43], Temporarily Coherent Point InSAR (TCP-InSAR) [44,45,46], the Stanford Method for Persistent Scatterer (StaMPS) [47], and the Interferometric Point Target Analysis (IPTA) method proposed by Werner and Wegmüller [48]. These methods not only effectively mitigate the impacts of spatial–temporal decorrelation and atmospheric noise in interferograms but also enable deformation monitoring with millimeter- or even sub-millimeter-level precision [49]. Additionally, they provide valuable time-series deformation information. However, time-series InSAR technology faces challenges in vegetated areas and non-urban regions with few buildings, where the selected coherent points are sparse, making it difficult to obtain complete surface subsidence information. To increase the number of highly coherent points in time-series analysis, Ferretti et al. [50] combined PS and DS, proposing the SqueeSAR technique. This approach significantly increases the number and density of coherent targets through the identification of homogeneous pixels and phase optimization techniques, improving the completeness of surface subsidence monitoring with time-series InSAR technology and expanding its range of applications.

Early time-series InSAR techniques were primarily applied to monitor deformation during active mining operations [51,52,53,54]. With the increasing number of closed mines and the growing demand for resource utilization in these areas, acquiring data on secondary surface subsidence in closed mines has become increasingly critical. However, conventional ground deformation monitoring methods, which typically rely on discrete point or linear arrangements, offer limited coverage and insufficient density of observation points, making it challenging to comprehensively reveal the spatiotemporal evolution of secondary subsidence in closed mines. As a result, many researchers have employed InSAR technology to monitor and analyze secondary subsidence in closed mines, providing essential data for further exploration of subsidence mechanisms and the development of predictive models.

Table 2. Case studies on InSAR monitoring of secondary surface subsidence in closed mines.

Reference	Region	Deformation Velocity	Monitoring Time and Methods	Key Findings
G. Herrera et al. [55,56]	La Unión, Spain	∼−2.3 cm/year	1998–2004, DInSAR	Demonstrated spatial correlation between surface subsidence and mine tunnel locations; estimated collapse angle.
Jung et al. [57]	Gaeun, South Korea	∼−1.9 cm/year	1992–1998, PSInSAR	Validated monitoring reliability through comparison with field data; proved PSInSAR’s capability for subsidence monitoring.
Y. Guéguen et al. [13]	Nord/Pas-de-Calais, France	Subsidence > −1 cm/year; uplift ∼+2 cm/year	1992–2007, DInSAR, PSInSAR	The analysis of surface subsidence evolution from 1992 to 2007 for closed mines revealed an initial phase of subsidence, followed by a reduction in subsidence, and then an uplift phase. The uplift rate was found to be 20 mm/year.
Samsonov et al. [58]	Luxembourg, French–German border	Subsidence > −1 cm/year; uplift ∼+1 cm/year	1995–2011, MSBAS	Observed transition from subsidence to uplift due to groundwater level changes.
Cuenca et al. [17]	Border of Netherlands, Belgium, and Germany	Maximum uplift ∼+220 mm	1992–2009, PSI	Found uplift variation across fault zones; linked surface uplift to differential groundwater rebound.
QIN et al. [59]	Abandoned Mines, Indiana, USA	-	1992–2011, PSInSAR	Detected stable surface in most areas; minor deformations in abandoned mine goafs.
A. Vervoort et al. [22,60,61]	Houthalen, Winterslag, Zwartberg, Belgium	Subsidence ∼−6 to −16 mm/year; uplift ∼+10 mm/year	1992–2000, 2003–2010, InSAR	Observed residual subsidence 7–12 years post-closure followed by noticeable uplift.
David et al. [62]	Northumberland and Durham Coalfields, United Kingdom (UK)	Subsidence ∼−7.5 mm/year; uplift ∼+7.5 mm/year	1995–2000, 2002–2008, 2015–2016, ISBAS	The monitoring results indicate that surface uplift often occurs above the mined-out areas. The cause of this uplift is the increase in pore pressure within the overburden due to the rise in groundwater levels.
Milczarek et al. [63]	Walbrzych, Poland	Uplift ∼+6 mm/year	2002–2009, PSInSAR	Linked surface uplift to Carboniferous groundwater rebound.
Graniczny et al. [64,65]	Upper Silesia, Poland	≤+9.8 mm/year	2003–2010, PSInSAR	Highest uplift is located in the proximity of fault zone.
Graniczny et al. [64,65]	Upper Silesia, Poland	≤+9.8 mm/year	2003–2010, PSInSAR	Uplift is related to groundwater recharge, increase in hydrostatic pressure in the mine aquifer and stress in the overburden.
Blachowski et al. [66]	Ostrava, Czech Republic	≤+5 mm/year	2003–2010, PS-InSAR	Uplift is related to rising groundwater level.
Bateson et al. [67]	South Wales, UK	+10 mm/year	1992–1999, SBAS-InSAR	Uplift distribution is related to the attitude of coal seams and rock layers.
Yu and Huang [68,69]	Shandong, China	≤+19 mm/year	2015–2019, SBAS-InSAR	Some areas show first subsidence and later uplift. Uplift is directly caused by the rise of groundwater level.
Sowter et al. [70]	Leicestershire and south Derbyshire, UK	≤+11 mm/year	2003–2009, ISBAS-InSAR	Uplift is caused by groundwater inflow into previously drained area and water pressure increase.
Zhao and Konietzky [71]	Lugau-Oelsnitz, Germany	+0.5–2.0 mm/year	1972–2014, geodetic survey and InSAR	Uplift obtained by numerical simulation is consistent with geodetic survey and InSAR data.
Chen et al. [72]	Xuzhou, China	Subsidence ∼−43 mm/year; uplift ∼+29 mm/year	2015–2021, SBAS	Based on the evolution pattern of surface deformation, the surface deformation prediction model was proposed by integrating SBAS InSAR and an LSTM neural network.
Yin xiwen and Chai et al. [73,74].	Beipiao, China	Maximum uplift ∼+40 mm/year	2017–2021, SBAS	Combined InSAR uplift with Weibull distribution function to model the temporal evolution of surface uplifts on a point-by-point basis.
Zhang et al. [75]	Xuzhou, China	Subsidence ∼−33 mm/year; uplift ∼+36 mm/year	2015–2021, SBAS	Based on the InSAR results, surface tilt and curvature were inverted to assess the stability of buildings. The results indicated that the deformation has exceeded the allowable deformation threshold for the buildings, requiring reinforcement and continuous monitoring.
Zheng et al. [76]	Xuzhou, China	−40–35 mm/year	2006–2008, 2009–2010, 2016–2018, TCPInSAR	Comparison with the groundwater storage changes obtained from GRACE indicates that variations in groundwater have an impact on the surface deformation of closed mines.
Zheng et al. [23]	Huainan, China	Subsidence ∼−95 mm/year; uplift ∼+ 51 mm/year	2016–2022, PSInSAR, SBAS	The secondary surface subsidence patterns of closed mines in the Huainan mining area are summarized as comprising three distinct stages: a subsidence stage, a stabilization stage, and an uplift stage.

provides an overview of case studies utilizing InSAR for monitoring secondary surface subsidence in abandoned coal mines. From Table 2, it is evident that InSAR has been widely applied and studied in this field. In Table 2, a positive sign indicates uplift, while a negative sign indicates subsidence. Key findings from these studies focus on using InSAR to capture secondary surface subsidence, analyzing surface deformation mechanisms by integrating geological, mining, groundwater, and fault data, summarizing the spatiotemporal evolution patterns of subsidence, and predicting surface deformation. Based on a review of the literature on InSAR monitoring of secondary surface subsidence in closed mines, the following general conclusions can be drawn:

• Secondary surface subsidence in closed mines has become a major issue faced by most mines worldwide. It generally progresses through two stages: subsidence and uplift. The magnitude of secondary surface subsidence varies significantly under different hydrogeological and mining conditions.
• The primary cause of surface subsidence is the compaction of fractured rock masses in the goaf and the weakening of coal pillars under the influence of groundwater.
• The main cause of surface uplift is the rise in groundwater levels after mine closure, which increases pore pressure in the soil and rock masses.
• Hydrogeological and mining conditions, such as faults and goafs, significantly influence secondary surface subsidence in closed mines.

Although InSAR technology has made significant progress in recent years, there are still several limitations in its application for monitoring secondary subsidence in closed mines due to factors such as SAR system orbital errors, atmospheric delay errors in signal propagation, and side-looking imaging conditions. These limitations result in some shortcomings in the use of InSAR for this specific purpose:

• Due to the long duration, small magnitude, and high concealment of secondary subsidence in closed mines, such as in the case of Belgian coal mines and mining areas in northern France, where surface subsidence and uplift continued even 20 years after mine closure [13,17], InSAR technology is significantly affected by atmospheric noise and DEM errors. As a result, the subsidence information is of the same magnitude as the noise, making it difficult to separate the two. The use of external atmosphere models such as ERA5 is a solution, but the resolution (30 km) is too low for local deformation monitoring.
• Most mining areas are typically located in farmland or vegetated regions, and due to the prolonged duration of secondary subsidence after mine closure, the number of high-coherence points in the selected areas for time-series InSAR is limited. This sometimes makes it difficult for InSAR technology to obtain comprehensive secondary surface subsidence information. Therefore, under long time-series conditions, the key research question is how to obtain more distributed permanent scatterer points using InSAR technology.
• Due to the limited lifespan of SAR satellite platforms and the long duration of secondary subsidence following mine closure, a single SAR satellite platform is insufficient to effectively monitor the entire cycle of surface subsidence. Therefore, it is crucial to investigate the fusion processing of SAR images from different platforms to capture the full cycle of secondary surface subsidence in closed mining areas.
• Due to the side-looking imaging and polar orbit flight mode of SAR systems, existing research has primarily focused on vertical or line-of-sight one-dimensional deformations of the surface. Movements in other directions are often neglected, and the accuracy of north–south horizontal displacement derived from InSAR is relatively low. This makes it challenging for InSAR technology to effectively capture three-dimensional surface deformation in closed mining areas. Given the complexity of secondary surface subsidence in closed mines, including both subsidence and uplift, ignoring horizontal movements may lead to misjudgments in surface sinking or rising, preventing accurate interpretation of the secondary surface movement and deformation patterns of closed mines.
• InSAR is an excellent method for monitoring surface deformation. Its results, characterized by high spatial resolution and extensive coverage, with tens of thousands of high-precision deformation data points, can provide a strong foundation for inferring the underground situation. This is achieved by solving the inverse problem to determine the characteristics of the causative sources and their temporal evolution. Developing appropriate inversion methodologies is a fundamental step, as classical approaches are not efficient in handling the large amount of information provided by these new datasets [77,78]. An example of such an advanced interpretation methodology is Defsour [77,78], which has been well-validated in volcanic and earthquake test cases [77,78,79] and is now being tested for mining activities and other scenarios [80]. Therefore, these tools can be highly effective in studying underground deformation sources associated with surface deformation in closed mining areas.

To obtain a complete picture of secondary surface subsidence in closed mines, our research team addressed the limitation of the long subsidence period, which results in a low density of high-coherence points for PSI (Permanent Scatterer InSAR) and hampers the accurate representation of the spatial–temporal evolution of surface subsidence. We proposed a DSInSAR (Distributed Scatterer Synthetic Aperture Radar Interferometry) processing method that integrates homogeneous pixel identification and phase optimization into the StaMPS (Stanford Method for Persistent Scatterers) technique. Using 88 Sentinel-1A images from October 2016 to October 2019, we monitored surface subsidence in the western part of Xuzhou’s closed mining areas. To compare the DSInSAR results, we also used StaMPS to monitor the same region’s surface subsidence. The results are shown in Figure 1. As seen in Figure 1, DSInSAR significantly improved the point density, by 13.3 times compared to StaMPS. Furthermore, due to the increase in coherent points, DSInSAR detected three additional deformation regions compared to PSI, which identified five deformation areas. These included two subsidence regions located in the eastern part of the Jiahe Mine (A) and the northwest of the Shitun Mine (B), as well as three uplift regions located in the central part of the Jiahe Mine (C), northeast of the Pangzhuang Mine (D), and Yian Mine (E). DSInSAR detected eight clearly distinguishable deformation areas, five of which overlapped with those identified by PSI. The remaining three deformation regions, not detected by PSI, were located in the northwest of the Zhangxiaolou Mine (F), the southern part of the Pangzhuang Mine (G), and the southern part of the Jiahe Mine (H). Additionally, DSInSAR provided a more complete and clearer boundary for the deformations, reflecting the spatial–temporal evolution of surface subsidence with greater accuracy. When compared to measured leveling data (Figure 2), the root mean square error (RMSE) for DSInSAR was 3.81 mm, slightly higher than that for PSI (RMSE: 3.84 mm). Therefore, the DSInSAR technique not only enhanced the spatial integrity and continuity of surface subsidence detection in closed mining areas but also ensured the accuracy of the subsidence data, meeting the monitoring requirements for surface subsidence in closed mines.

3. Current Status of Research on the Secondary Subsidence Patterns and Mechanisms of Closed Mine

3.1. Research on the Patterns of Secondary Subsidence in Closed Mines

Understanding the patterns of secondary subsidence in closed mines and effectively controlling surface subsidence are essential for ensuring the safety and utility of surface structures and for providing a scientific basis for the development of surface subsidence prediction models. However, research on the patterns of secondary subsidence in closed mines is limited at present. Therefore, studying the spatiotemporal evolution of secondary subsidence in closed mines is crucial.

Some scholars have used numerical simulations to study the secondary surface subsidence patterns caused by mining in single coal seams of closed mines. Byungkyu [81] employed numerical simulations to investigate the secondary surface subsidence behavior after mine closure, identifying relationships between the geometric characteristics of goafs (such as depth, width, height, and dip angle), overburden properties, and secondary surface subsidence. Aydan [15] examined the stability of overburden and coal pillars in Japanese room-and-pillar coal mines after closure under seismic influences. The results showed that when the mining depth is less than 10–15 times the mining thickness, collapse pits are likely to form on the surface. Furthermore, when the goaf is filled with groundwater, vertical stress on the coal pillars is significantly reduced; however, prolonged water–rock interactions can decrease the strength of the coal pillars. Salmi [82] used numerical simulations to study the causes of surface subsidence in shallow closed mines in the United Kingdom nearly a century after their closure. The findings revealed that seasonal fluctuations in groundwater levels significantly impact surface subsidence.

Due to the complexity of secondary subsidence in closed mines, it is challenging to address this issue purely through theoretical methods. Field-measured data are essential. Herrera [56], using InSAR data, investigated secondary subsidence in closed mines in La Unión, Spain, demonstrating the spatial correlation between surface subsidence and underground mining roadways. The study also analyzed the evolution of the surface subsidence angle. Cuenca [17] analyzed secondary surface subsidence and fault data for closed coal mines in the southern Netherlands based on InSAR technology. The study highlighted how faults control the spatial development of surface uplift in closed mines. The groundwater retention effect of faults caused differences in groundwater rebound height and speed on either side of the faults, resulting in significant variations in surface uplift.

To summarize the patterns of secondary surface subsidence in closed mines, our research team used InSAR technology to obtain secondary surface subsidence data for the Xuzhou and Huainan mining areas. Based on these data, we further synthesized the patterns of secondary surface subsidence in closed mines [14,23,83]. Figure 3 illustrates the secondary surface subsidence and underground goaf conditions for the Jiahe Mine in western Xuzhou, as derived from Sentinel-1A data between October 2016 and October 2019. The end of the mining period and the depth of the selected workfaces are shown in

Table 3. End of mining period and depths of the selected work faces.

Workface	End of Mining Period	Depth (m)	Workface	End of Mining Period	Depth (m)
2442	August 2007	960	7445	March 2007	970
2447	November 2011	1018	7625	October 2002	625
2445	September 2009	947	7422	March 1999	610
2443	June 2006	857	7435	April 2004	832
2422	March 2002	517	7415	February 1988	430
2411	May 1984	308	7411	May 1982	378
2407	February 1978	280	7407	October 1978	312
204	September 1971	158	7218	April 2015	427
7448	March 2014	1150	9444	October 2013	1154
7444	June 2010	1050	9625	October 2003	653
7449	December 2014	1140	9422	March 2000	634
7447	August 2013	1075	9435	February 2006	878

. After the closure of the Jiahe Mine, two distinct deformation zones were identified on the surface, located in the northwest and southeast of the mine. The surface subsidence patterns were complex. To analyze the surface subsidence patterns following the closure of the Jiahe Mine, 12 points were selected based on surface subsidence and geological mining data to show the time-series deformation, as shown in Figure 4. The locations of these points are shown in Figure 3.

From Figure 4, it can be observed that after the closure of the Jiahe Mine, points JU1–JU5 experienced significant surface subsidence, but the duration was relatively short, ending by 13 June 2017 (Figure 4a,b). Points JU6–JU8 showed smaller surface subsidence, but the duration was comparatively longer, lasting until 13 January 2018 (Figure 4c). This pattern can be attributed to differences in the mining and geological conditions. The workfaces in the northwest of the Jiahe Mine ceased operations later than those in the southeast, resulting in lower compaction of the fractured rock mass in the northwest compared to the goaf areas in the southeast. Additionally, the mining depth in the northwest was greater. After the mine’s closure, groundwater rebounded earlier in the northwest. Under the influence of groundwater, the deformation modulus of the fractured rock mass decreased, leading to further compression of the rock mass and thus more significant surface subsidence. At the same time, the larger mining depth in the northwest, combined with rapid groundwater rebound and increased pore water pressure in the fractured rock mass, resulted in a reduction in effective stress. This slowed the surface subsidence, leading to a shorter duration of residual surface deformation in the northwest region of the Jiahe Mine.

From Figure 4a,b, it can be seen that between the subsidence and uplift phases, there was a relatively stable period in some areas of the Jiahe Mine from 13 June 2017 to 17 September 2017, lasting three months. This stability may have occurred because the compaction of fractured rock caused by groundwater was nearly complete, while the groundwater level had not yet risen sufficiently to induce upward movement of the strata, resulting in a period of relative stability for the overburden and surface.

Subsequently, with the continued groundwater rebound, points JU1–JU8 all exhibited surface uplift. However, the onset of surface uplift varied. For points JU1–JU5, surface uplift began on 17 September 2017, whereas for points JU6–JU8, it started on 3 January 2018 (Figure 4a–c). Analysis of the mining depth in the Jiahe Mine indicates that the depth of the goaf gradually decreases from northwest to southeast. After the mine’s closure, groundwater rebounded earlier in the deeper goaf areas in the northwest. The increasing pore water pressure in the fractured rock mass due to groundwater caused surface uplift in the northwest. In contrast, groundwater rebound in the shallower goaf areas in the southeast occurred later, delaying the onset of surface uplift in those areas.

In the early stages following the closure of the Jiahe Mine, subsidence was predominant in the southeastern part of the mining area (points JU9–JU12 in Figure 4d,e). Some areas exhibited a pattern of uniform subsidence initially, followed by accelerated subsidence. Point JU10, located above a strip-mining area, experienced accelerated subsidence as the coal pillars softened due to groundwater effects, leading to increased surface deformation under the stress of the overburden. Similarly, point JU9, near the strip-mining workface, may have been influenced by this effect, causing accelerated subsidence. Point JU11 is situated at the boundary of the goaf from the No. 2 coal seam, where the accelerated surface subsidence may be related to structural instability at the edges of the goaf. Point JU12 is located above the longwall caving goaf of the No. 7 coal seam, where mining had ceased for a considerable period. The fractured rock mass had already undergone natural compaction under the stress of the overburden, leaving minimal residual voids. Consequently, after the mine closure, the remaining compression of the fractured rock mass under the influence of groundwater was limited, resulting in slow surface subsidence at this location.

From the temporal deformation data for points JU9–JU12 in Figure 4d,e, it can be observed that during the InSAR monitoring period, no surface uplift occurred in the southeastern part of the Jiahe Mine. The likely reason is that groundwater had just begun to rebound in this area, resulting in only minor changes in pore water pressure, which were insufficient to cause surface uplift.

Based on the analysis of the temporal surface deformation after the closure of the Jiahe Mine, the surface subsidence patterns over time can be summarized as follows: (1) Under the influence of the goaf and groundwater, the surface initially subsides, followed by a relatively stable phase (or none at all), and eventually rises due to the effects of groundwater. (2) The surface undergoes slow subsidence under the combined effects of the goaf and groundwater. However, if coal pillars or voids are present beneath the surface, their softening or instability may cause accelerated surface subsidence.

Figure 5 and Figure 6 present the secondary surface subsidence and temporal deformation of selected points after the closures of the Lizuizi Mine and Xinzhuangzi Mine in the Huainan mining area, based on Sentinel-1A data from January 2016 to May 2022. From Figure 5, it is evident that after the closure of the Lizuizi Mine (closure date: December 2016), the surface continued to subside. However, the subsidence lasted for a relatively short period (about six months) and had a small magnitude, with the maximum subsidence at point P3 being −17.5 mm. By June 2017, the surface subsidence at five points slowed or stopped, entering a relatively stable phase. Except for point P5, which had a shorter stable phase (about two years), the other four points experienced a longer stable phase, with point P3’s stable phase lasting approximately three years. By June 2019, surface uplift began at point P5, followed by the remaining four points. Additionally, Figure 5 shows that during the uplift phase, surface elevation increased very linearly over time. The magnitude of surface uplift was greater at the ends of the mining area and smaller in the central region, with the maximum uplift observed at point P5, reaching approximately +77 mm.

Figure 6 shows the temporal deformation of five selected points in the Xinzhuangzi Mine. After the closure of the Xinzhuangzi Mine (closure date: December 2017), the secondary surface subsidence patterns were similar to those of the Lizuizi Mine. However, the Xinzhuangzi Mine did not exhibit any surface subsidence after closure. Subsidence had already slowed significantly prior to the closure. Additionally, points P9 and P10 did not experience a stable phase. Compared to the Lizuizi Mine, the stable period in the Xinzhuangzi Mine was shorter, lasting approximately 1.5 years. At the time of closure (December 2017), points P9 and P10 began to rise slowly, followed by surface uplift across the Xinzhuangzi Mine. As shown in Figure 6, during the uplift phase, the surface elevation increased either linearly or in an exponential function-like pattern over time. The magnitude of uplift was greater in the southeastern part of the mining area compared to the northwest, with point P9 experiencing the maximum uplift of approximately +168 mm.

Using data from ENVISAT, Sentinel-1A, and TerraSAR-X, along with existing studies by other researchers, our team analyzed the secondary surface subsidence of closed mines in the Xuzhou and Huainan mining areas. We summarized the patterns of secondary surface subsidence for single-coal-seam mining in closed mines into a “” shape, divided into five stages: (1) Initial stable stage; (2) subsidence stage; (3) intermediate stable stage; (4) uplift stage; and (5) final stable stage. We also examined the secondary subsidence patterns of closed mines in relation to factors such as mining thickness, mining methods, and groundwater level changes. The results indicate the following:

• Greater mining thickness results in taller fractured rock masses. When influenced by groundwater, the overburden and surface experience larger secondary subsidence. The relationship between subsidence and mining thickness can be either linear or nonlinear.
• In longwall caving goaf areas, central subsidence is primarily caused by the re-compaction of fractured rock masses weakened by groundwater, which reduces their strength and deformation modulus. When the groundwater level rises uniformly, secondary surface subsidence tends to increase linearly over time.
• At the edges of goaf areas, structural instability of overburden caused by groundwater can lead to sudden acceleration of secondary surface subsidence, displaying nonlinear changes over time. Pillar mining: Similarly, secondary surface subsidence in goaf areas from pillar mining may also exhibit accelerated subsidence phenomena.

3.2. Research on the Mechanism of Secondary Surface Subsidence After Mine Closure

From the analysis of the secondary surface subsidence patterns after mine closure, it is clear that both subsidence and uplift can occur. Therefore, by combining the overview of the mining-induced overburden and groundwater changes after mine closure, we can analyze the mechanisms of surface subsidence and uplift separately.

After the mine is closed, underground drainage systems cease operation, and groundwater levels rise. Under the influence of groundwater, the mining-induced overburden will be affected by the following factors during the first two stages of “”: (1) The friction between the fractured rock masses decreases, and their strength is reduced. The fractured rock masses undergo re-compaction under the overburden stress, leading to secondary movement and deformation of the overburden and surface. (2) Groundwater weakens the mining-induced overburden structure, potentially causing instability of the overburden, leading to the closure of voids at the goaf edges, and consequently causing secondary movement and deformation of the overburden and surface. (3) Groundwater weakens the strength of coal pillars, leading to their instability. The instability of the coal pillars further causes the closure of voids and re-compaction of the fractured rock masses, resulting in secondary movement and deformation of the overburden and surface. (4) Groundwater reduces the deformation modulus of the coal pillars, causing compressive deformation of the coal pillars, which leads to secondary movement and deformation of the overburden and surface. (5) In the case of strip mining and room-and-pillar mining, groundwater weakens the strength of both coal pillars and the roof, leading to instability of the coal pillars and roof collapse, which in turn causes secondary movement and deformation of the overburden and surface.

As the groundwater level continues to rise, the pore pressure inside the mining-induced fractured rock masses increases. The effective stress on the previously compressed fractured rock masses decreases, causing them to rebound, which in turn results in surface uplift; this occurs in the fourth and fifth stages of “”. At the same time, as the water level rises, when it reaches the loose layer, it increases the pore pressure in the soil, reduces the effective stress, and causes elastic deformation recovery of the soil, leading to surface uplift. Moreover, if the coal-bearing strata contain expansive rocks such as kaolin, montmorillonite, and mudstone, the groundwater’s rise to these expansive rocks may cause them to absorb water and expand, which would cause the overburden and surface to rise.

In summary, combining the spatiotemporal evolution patterns of surface subsidence after mine closure, the analysis of the mechanisms of overburden and surface subsidence can be divided into two parts: subsidence and uplift. During the early stages of mine closure, the rising groundwater level leads to re-compaction of fractured rock masses, instability of mining-induced overburden structures, coal pillar instability, re-compression of coal pillars, roof collapse in pillar mining, and other factors, resulting in secondary movement and deformation of the overburden and surface. When the water level reaches a certain height, the pore pressure in the fractured rock masses and loose layers increases, and effective stress decreases, causing rebound of the fractured rock masses and loose layers, leading to uplift of the overburden and surface. Additionally, if expansive rocks are present in the coal-bearing strata, they may expand upon absorbing water from rising groundwater, potentially causing uplift of the overburden and surface. From the above analysis, it can be seen that both domestic and international experimental studies have preliminarily established the patterns and mechanisms of secondary surface subsidence after mine closure. However, there are still several issues that require further investigation:

• Mining-induced fractured rock masses are the primary factor in the secondary surface subsidence of closed mines. Currently, there is a lack of systematic and in-depth research on the constitutive relationships, mechanical characteristics, water-rock coupling mechanisms, and the relationship with groundwater dynamics of these fractured rock masses. Additionally, the distribution patterns of mining-induced fractured rock masses under different geological and mining conditions have not been sufficiently studied.
• Mining-induced overburden structure is another major source of deformation in secondary subsidence after mine closure. There is insufficient in-depth research on the characteristics, stability, influencing factors, and the synergistic mechanisms with mining-induced fractured rock masses under various geological and mining conditions.
• The deformation mechanisms, patterns, and stability of the roof and coal (rock) pillars in the goaf area under the influence of water in pillar mining require further study.
• While much research has been conducted on the mechanisms and patterns of overburden and surface subsidence and uplift after mine closure, there is a lack of research on the horizontal movement and deformation mechanisms and patterns.

4. Research on the Prediction Model of Secondary Surface Subsidence After Mine Closure

Prediction methods for mining subsidence have matured over time, with commonly used techniques like the typical curve, profile function, influence function, and subsidence grid methods widely applied for assessing mining damage, control measures, design optimization, and foundation stability.

Secondary surface subsidence after mine closure involves long-term, complex deformation, including both subsidence and uplift. Limited data and geological–hydrological information for closed mines have constrained research in this area, with current studies mainly relying on numerical simulation and analytical methods for prediction.

4.1. The Numerical Simulation Method

The numerical simulation method is widely used for predicting surface uplift in closed mines. Its primary principle involves changes in the effective density of the goaf (mined-out area) and variations in pore pressure of the rock strata caused by the rise of groundwater after mine closure. This method primarily utilizes numerical simulation software, such as finite element analysis, to conduct mechanical modeling and predict surface subsidence over closed mines [84,85,86,87,88,89].

4.1.1. Effective Density Variation Method

Based on the assumption of changes in the effective density of the goaf, the prediction of surface subsidence for closed mines using numerical simulation can be divided into two cases: when the rock and soil body is located above the groundwater level and when it is below the groundwater level [84].

When the rock and soil body is above the groundwater level and its voids are fully filled with groundwater, the volumetric weight of the rock and soil body can be calculated using the following formula:

$${\gamma }_{\mathrm{sr}}=\left(1-n\right){\rho }_{s}g+n{\rho }_{w}g$$

(1)

where ${\gamma }_{\mathrm{sr}}$ is the volumetric weight of the rock and soil body above the groundwater level, in kN/m³; n is the porosity of the rock and soil body; ${\rho }_s$ is the density of the rock and soil, in kg/m³; ${\rho }_w$ is the density of water in kg/m³; and g is gravity in m/s².

When the rock and soil body is below the groundwater level and its voids are also fully filled with groundwater, according to Archimedes’ principle, the rock and soil body below the groundwater level does not bear a load but is subject to buoyancy. In this case, the volumetric weight of the rock and soil body can be calculated using Formula (2):

$${\gamma }^{\prime }=\left(1-n\right)\left({\rho }_s-{\rho }_w\right)g$$

(2)

where ${\gamma }^{\prime }$ is the volumetric weight of the rock and soil body below the groundwater level, in kN/m³.

Dudek et al. [84] based on the assumption of changes in effective density within the goaf (reducing from 2000 kg/m³ to 500 kg/m³), predicted the surface subsidence of a closed mine in Germany. This prediction is illustrated in Figure 7a, where the blue dots indicate the positions of leveling monitoring points. The numerical model’s predictions were compared with field-measured surface data, as shown in Figure 7b, where the blue dots represent leveling monitoring results, and the yellow curve represents the prediction results. The reliability of the numerical simulation in predicting surface uplift was thus verified.

4.1.2. Effective Stress Variation Method

To simplify the numerical simulation process for predicting surface subsidence in closed mines based on the assumption of effective stress variation, Todd et al. [89] applied hydraulic coupling using Darcy’s law for saturated media:

$${\mathrm{q}}_i=-k_{il}\widehat{k}\left(s\right){\left[p-{\rho }_f{x}_j{g}_j\right]}_l$$

(3)

where ${\mathrm{q}}_i$ is the flow vector; p the pore water pressure; $k_{il}$ the permeability tensor of the medium; $\widehat{k}\left(s\right)$ is the relative mobility coefficient, a function of fluid saturation $\left(s\right)$; ${\rho }_f$ is fluid density; $g_j$ the gravity vector; $x_j$ the medium volume; and ${[·]}_l$ the gradient in direction l.

For the numerical model, steady-state conditions are used. Deformations are calculated via the momentum balance equation:

$${\sigma }_{ij}+\rho g_j=0$$

(4)

where ${\sigma }_{ij}$ is the stress tensor and $\rho$ the bulk density, $\rho ={\rho }_d+ns{\rho }_w$, where ${\rho }_d$ is the dry matrix density and ${\rho }_w$ the fluid density, n is porosity, and s is saturation.

The stress–strain relationship is derived from the constitutive relationship

$${\sigma }_{ij}=E_{ij}{\epsilon }_{ij}$$

(5)

where $E_{ij}$ is the elastic modulus and ${\epsilon }_{ij}$ the strain tensor.

Terzaghi’s effective stress theory is as follows:

$${\sigma }_{ij}^{\prime }={\sigma }_{ij}-{\delta }_{ij}\alpha p$$

(6)

where ${\sigma }_{ij}^{\prime }$ is the effective stress tensor; ${\delta }_{ij}$ the unit tensor; $\alpha$ the Biot coefficient; and p the ore water pressure. By combining Equations (4)–(6), strain can be solved, leading to the calculation of deformation.

Todd et al. [89], based on the assumption of effective stress variation in the goaf, used the FEM OpenGeoSys numerical simulation software to predict surface uplift in the closed Lothian coalfield in the UK by increasing mine water pressure. The simulation results indicated that for every 1 m rise in groundwater, the surface uplifted by 1.4 mm, which closely matches InSAR monitoring results (1 mm/m).

However, predicting surface subsidence in closed mines using numerical simulation requires numerous parameters for the rock and soil body (e.g., deformation modulus of mining-induced fractured rock, permeability, fluid saturation, fluid density). These parameters are difficult to obtain through field measurements or laboratory tests, making the method’s efficiency and accuracy a topic for further study. In contrast, the prediction method based on the assumption of effective density variation in the goaf only requires the density of the mining-induced fractured rock. This method is rooted in classical geotechnical mechanics, making it more practical and widely applicable.

4.2. The Analytical Method

While numerical simulation methods provide high reliability for predicting surface subsidence in closed mines under complex geological and mining conditions, they are overly complex and demand highly detailed geological and mining data. In contrast, the analytical method, based on mathematical mechanics, can efficiently and straightforwardly determine the deformation and displacement fields of the prediction area. However, due to its consideration of fewer influencing factors, the results may differ from actual observations.

4.2.1. Subsidence Prediction Model

Based on the overburden structure and mechanisms of subsidence in closed mines discussed earlier, subsidence primarily arises from the compaction of voids and cavities within the mine. These voids are categorized into three parts: gaps between fractured rock masses, boundary voids near the coal seam, and separations between hard and soft layers in the overburden. By analyzing the spatial distribution and characteristics of these subsidence “sources”, a residual subsidence prediction model was established using the probability integration method.

• Subsidence Due to Compaction of Fractured Rock Voids
  Fractured rock masses, due to their dilative nature, occupy a larger volume than the original rock. The voids within fractured rock compress under stress, releasing space and causing residual subsidence. The released void height is calculated using Equation (7), and the residual subsidence caused by compaction of fractured rock is expressed using Equation (8):

  $$m_1=h_k(K-K^{\prime })$$

  (7)

  $$W_1\left(x\right)=\underset{s_0}{\overset{s_0+l}{\int }}{m}_1{\displaystyle \frac{1}{r_1}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{{r_1}^2}}}ds=\underset{s_0}{\overset{s_0+l}{\int }}{h}_k(K-K^{\prime }){\displaystyle \frac{1}{r_1}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{{r_1}^2}}}ds$$

  (8)

  where $W_1\left(x\right)$ is the residual subsidence caused by fractured rock compaction, l is the length of the fractured rock mass distribution, $s_0$ is the cantilever beam length, and $r_1$ is the primary influence radius of the first void.
• Subsidence Due to Compaction of Boundary Voids
  The boundary voids are located near the coal wall. Research indicates that the height of these voids gradually decreases as the distance from the coal wall increases, reducing from the mining thickness to zero. It is assumed that this subsidence pattern follows a linear function. Using the probability integration model, the residual surface subsidence caused by the compaction of boundary voids is expressed in Equation (9):

  $$\begin{array}{cc}\hfill W_2\left(x\right)& =\underset{0}{\overset{s_0}{\int }}{m}_2{\displaystyle \frac{1}{r}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{r^2}}}ds+\underset{s_0+l}{\overset{2s_0+l}{\int }}{m}_2{\displaystyle \frac{1}{r}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{r^2}}}ds\hfill \\ \hfill & =\underset{0}{\overset{s_0}{\int }}({\displaystyle \frac{-m_0}{s_0}}s+m_0){\displaystyle \frac{1}{r}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{r^2}}}ds+\underset{s_0+l}{\overset{2s_0+l}{\int }}({\displaystyle \frac{m_0}{s_0}}s-{\displaystyle \frac{m_0(s_0+l)}{s_0}}){\displaystyle \frac{1}{r}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{r^2}}}ds\hfill \end{array}$$

  (9)

  where $W_2\left(x\right)$ is the residual subsidence caused by boundary void compaction.
• Subsidence of Abandoned Land Caused by the Compaction of Overburden Separations
  Due to differences in the bending degrees of soft and hard layers, overburden separations may form between the upper hard layer and the lower soft layer after coal mining, typically exhibiting an arched distribution. Assuming the height of the overburden from the coal seam is $H_l$, the length from the development starting position of the overburden to the coal wall can be calculated using Equation (10). For simplicity in research, the shape of the overburden separations can be approximated as a triangle. The subsidence of abandoned land caused by the compaction of overburden separations is expressed using the probability integration model in Equation (11):

$$l_s=H_l·cot\phi$$

(10)

$$\begin{array}{cc}\hfill W_3\left(x\right)& =\underset{l_s}{\overset{2s_0+l-l_s}{\int }}\mathrm{\Delta }W{\displaystyle \frac{1}{r_3}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{{r_3}^2}}}ds=\underset{l_s}{\overset{s_0+{\displaystyle \frac{l}{2}}}{\int }}\mathrm{\Delta }W{\displaystyle \frac{1}{r_3}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{{r_3}^2}}}ds+\underset{s_0+{\displaystyle \frac{l}{2}}}{\overset{2s_0+l-l_s}{\int }}\mathrm{\Delta }W{\displaystyle \frac{1}{r_3}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{{r_3}^2}}}ds\hfill \\ \hfill & =\underset{l_s}{\overset{s_0+{\displaystyle \frac{l}{2}}}{\int }}\left({\displaystyle \frac{2(s-l_s)\mathrm{\Delta }{W}_{max}}{l+2s_0-2l_s}}\right){\displaystyle \frac{1}{r_3}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{{r_3}^2}}}ds\hfill \\ \hfill & +\underset{s_0+{\displaystyle \frac{l}{2}}}{\overset{2s_0+l-l_s}{\int }}\left({\displaystyle \frac{2\mathrm{\Delta }{W}_{max}(l+2s_0-l_s-s)}{l+2s_0-2l_s}}\right){\displaystyle \frac{1}{r_3}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{{r_3}^2}}}ds\hfill \end{array}$$

(11)

where $W_3\left(x\right)$ is the residual subsidence caused by the compaction of overburden separations; and $\mathrm{\Delta }{W}_{max}$ represents the maximum development width of the overburden separation.

By combining Equations (8), (9) and (11), the general expression for residual subsidence prediction in closed mines is derived as Equation (12).

$$\begin{array}{cc}\hfill W\left(x\right)& =W_1\left(x\right)+W_2\left(x\right)+W_3\left(x\right)\hfill \\ \hfill & =\underset{s_0}{\overset{s_0+l}{\int }}{h}_k(K-K^{\prime }){\displaystyle \frac{1}{r_1}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{{r_1}^2}}}ds+\underset{0}{\overset{s_0}{\int }}({\displaystyle \frac{-m_0}{s_0}}s+m_0){\displaystyle \frac{1}{r}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{r^2}}}ds\hfill \\ \hfill & +\underset{s_0+l}{\overset{2s_0+l}{\int }}({\displaystyle \frac{m_0}{s_0}}s-{\displaystyle \frac{m_0(s_0+l)}{s_0}}){\displaystyle \frac{1}{r}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{r^2}}}ds+\underset{l_s}{\overset{s_0+{\displaystyle \frac{l}{2}}}{\int }}\left({\displaystyle \frac{2(s-l_s)\mathrm{\Delta }{W}_{max}}{l+2s_0-2l_s}}\right){\displaystyle \frac{1}{r_3}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{{r_3}^2}}}ds\hfill \\ \hfill & +\underset{s_0+{\displaystyle \frac{l}{2}}}{\overset{2s_0+l-l_s}{\int }}\left({\displaystyle \frac{2\mathrm{\Delta }{W}_{max}(l+2s_0-l_s-s)}{l+2s_0-2l_s}}\right){\displaystyle \frac{1}{r_3}}{e}^{-{\displaystyle \frac{\pi {(x-s)}^2}{{r_3}^2}}}ds\hfill \end{array}$$

(12)

4.2.2. Uplift Prediction

Bekendam et al. [38] established a relationship between surface uplift and changes in pore water pressure based on poroelastic theory, assuming a linear relationship between surface uplift of closed mines and pore water pressure:

$$\mathrm{\Delta }h=h\ast D_m\ast \mathrm{\Delta }p$$

(13)

where h is the height of the fractured rock mass in the goaf, m; $D_m$ is the uniaxial expansion coefficient of the fractured rock mass, 1/Pa; $\mathrm{\Delta }p$ is the pore water pressure change in the fractured rock mass caused by mining, $Pa$; and $\mathrm{\Delta }h$ is the vertical expansion of an infinite horizontal rock mass, m. From Equation (13), it can be concluded that surface uplift is related to the height of the fractured rock mass in the goaf and the groundwater pressure.

The author’s team [83] attributed the causes of surface uplift in closed mines to increased pore pressure in the fractured rock mass caused by mining and in Quaternary loose layers under the influence of groundwater, leading to reduced effective stress and resulting in rebound uplift of the surface.

Additionally, based on the stress–strain relationship of fractured rock mass in goafs provided by SALAMON [90] and the initial deformation modulus $E_0$, swelling coefficient $k_0$, and compressive strength relationships of fractured rock mass provided by YAVUZ [91], the author’s team [83] developed a maximum subsidence prediction model for longwall caving mining in closed mines, incorporating the constitutive relationships of fractured rock mass, the height of the caving zone, and overburden stress:

$$W_s=h_m·\mathrm{\Delta }\epsilon ={\displaystyle \frac{100·{\gamma }_{\mathrm{r}}·H·h_m·{\epsilon }_m^2·\left(E_0-E_w\right)}{\left(100·E_w·{\epsilon }_m+{\gamma }_{\mathrm{r}}·H\right)\left(100·E_0·{\epsilon }_m+{\gamma }_{\mathrm{r}}·H\right)}}$$

(14)

where $W_s$ is the secondary subsidence of the closed mine, in mm; $h_m$ is the height of the caving zone, in m; ${\gamma }_{\mathrm{r}}$ is the average bulk density of the overburden, in t/m³; H is the mining depth, in m; $E_0$ is the initial deformation modulus of the rock mass, in MPa; $\epsilon$ is the axial strain; ${\epsilon }_m$ is the maximum strain the fractured rock mass may undergo to return to its original volume; and $E_w$ is the deformation modulus of the fractured rock mass under the influence of water, in MPa.

Simultaneously, based on the constitutive relationships of fractured rock mass, Terzaghi’s pore pressure theory, and overburden fracture height, the team provided a calculation formula for overburden and surface uplift caused by longwall caving mining under the influence of groundwater [83]:

$$W_u={\displaystyle \frac{100{\gamma }_{\mathrm{w}}\left(H-H_{\mathrm{w}}\right)E_w{\epsilon }_m^2{h}_m}{\left(100E_w{\epsilon }_m+{\gamma }_{\mathrm{r}}H\right)\left(100E_w{\epsilon }_m+{\gamma }_{\mathrm{r}}H-{\gamma }_{\mathrm{w}}\left(H-H_{\mathrm{w}}\right)\right)}}$$

(15)

where $W_u$ is the surface uplift caused by groundwater effects, in m; ${\gamma }_{\mathrm{w}}$ is the bulk density of water, in t/m³; and $H_{\mathrm{w}}$ is the recovery elevation of the mine water level, in m.

Using the above prediction models, the surface subsidence of closed mines in the eastern and western Xuzhou mining areas was predicted (Figure 8). The prediction results were compared with InSAR monitoring results to verify the applicability and reliability of the surface subsidence prediction models for closed mines. In Figure 8, (a) shows the mining conditions of the Jiahe Mine working face; (b) compares the predicted results of the model and InSAR monitoring for surface subsidence after the Jiahe Mine’s closure; (c) shows the mining conditions of the Hanqiao Mine’s working face; (d) compares the predicted results of the model and InSAR monitoring for surface uplift after the Hanqiao Mine’s closure.

As shown in Figure 8, there is a significant difference between the prediction deformations from the InSAR monitoring results. The main reasons are as follows:

• Parameter error: The parameters of the prediction model, such as the height of the caved zone, initial deformation, and deformation affected by underground water, are estimated based on empirical formulas with more or less noise, resulting in errors in the prediction results.
• Representativeness error: The uplift at the selected points represents the average deformation over a specific area, whereas the prediction model estimates the maximum uplift after mine closure. Thus, the representativeness error occurs when the two are compared.
• Model error: The model considers only the deformation of fractured rock masses influenced by underground water after mine closure and does not account for the water absorption expansion effect of Quaternary soil layers and expansive rocks in the strata. This omission may lead to discrepancies between the predicted results and actual monitoring results.
• Influence of neighboring goafs: The predicted model is constructed based on a single goaf and does not account for the impact of neighboring goafs.
• Groundwater level error: After the mine closure, the overall trend in groundwater level recovery is consistent. However, differences in groundwater levels at various locations are characterized by low spatial correlation in groundwater level changes across different sites. These inconsistencies lead to significant deviations in prediction results.
• InSAR monitoring error: InSAR technology is heavily influenced by atmospheric noise, spatiotemporal decorrelation noise, and DEM residuals. Although TS-InSAR technology can effectively suppress these noises through spatiotemporal filtering techniques, it cannot eliminate them. Therefore, errors in InSAR monitoring results are unavoidable.

Surface subsidence in closed mines is influenced by multiple factors, making it challenging for conventional prediction methods to comprehensively account for the relationships between various influencing factors and surface subsidence. With the rapid development of artificial intelligence, deep learning methods have been widely applied in the field of mining subsidence prediction [92,93,94]. Some researchers [72] integrated time-series InSAR deformation results with long short-term memory (LSTM) neural network algorithms and Weibull functions to establish surface deformation prediction models for closed mining areas. Based on these models, full-coverage surface deformation predictions within closed mines were conducted.

From the above analysis, it can be seen that the research on secondary subsidence prediction in closed mines is still in its infancy and faces the following problems:

• The factors considered are relatively singular. Most current methods only account for the impact of mining-induced fractured rock mass on overlying strata and secondary surface subsidence, without considering the effects of mining-induced overburden structures and geological structures. Furthermore, differences in the height of mining-induced fractured rock mass in the uphill and downhill directions of inclined and steeply inclined coal seams are not considered. Generally, the height of the fractured rock mass in the uphill direction is always higher than in the downhill direction. This indicates that existing methods are unsuitable for predicting secondary subsidence in closed mines with inclined or steeply inclined coal seams, necessitating further research and improvement.
• Research on secondary subsidence prediction in closed mines involving multi-seam mining is inadequate. Although some methods for predicting secondary subsidence in multi-seam mining have been proposed (e.g., in [83]), these do not fully consider the delayed deformation of mining-induced fractured rock mass under the influence of groundwater (in the initial stabilization stage). Multi-seam mining involves the superposition of upward movement of lower coal seams and downward movement of upper coal seams. In dynamic prediction, determining the timing and magnitude of downward movement in upper coal seams requires further investigation.
• Existing analytical methods only predict the maximum secondary subsidence and cannot forecast its spatial distribution. Whether the maximum secondary subsidence can be treated as an equivalent mining thickness for prediction using current mining subsidence prediction methods is a topic that needs further research.

5. Conclusions

• InSAR technology, as an economical and effective method for monitoring secondary surface subsidence in closed mines, should be further enhanced. Future research should focus on noise reduction methods for long-term SAR image sequences, methods for selecting DS points in vegetated areas, phase optimization techniques, and long-term 3D deformation inversion methods through multi-source SAR data fusion. Different wavelengths should also be considered and applied to different deformation gradient scales. L band is more suitable for large scales and X band is better for more refined detection. This will improve the capability and accuracy of InSAR technology in obtaining secondary subsidence data.
• The patterns of secondary surface subsidence in closed mines can be preliminarily summarized as a “” shape, consisting of five stages: initial phase, subsidence phase, relatively stable phase, uplift phase, and stabilization phase. Preliminary analyses have clarified the impact of groundwater on mining-induced fractured rock mass, residual voids in goafs, coal pillars, and mining-induced overburden structures. The mechanisms of overburden and surface subsidence and uplift, as well as the relative importance of different deformation sources, have been analyzed. However, current understanding of the mechanisms and patterns of secondary surface subsidence in closed mines remains incomplete. It is necessary to integrate secondary surface subsidence monitoring data, geological and mining observations, and groundwater studies to further analyze the spatial and temporal distribution patterns of overburden and secondary surface subsidence. Additionally, relationships with roof management methods, overburden lithology, mining depth, mining thickness, coal seam dip angle, relationships between upper and lower coal seams, goaf spatial distribution, and groundwater dynamics need to be clarified to fully understand the spatiotemporal distribution patterns and mechanisms of secondary subsidence in closed mines.
• Secondary subsidence prediction methods for closed mines mainly include numerical simulation and analytical methods. For complex geological and mining conditions, numerical simulation methods provide higher reliability but involve complex modeling and require detailed geological and mining data. For simpler mining conditions, analytical methods offer higher precision and efficiency. At this stage, research should focus on the constitutive relationships of mining-induced fractured rock masses in closed mines, mechanisms of mining-induced overburden structures and water–rock interactions, and groundwater dynamics. Combined with nonlinear dynamics theories, predictive models for overburden and surface subsidence and uplift under longwall full-extraction and multi-seam mining conditions should be developed separately for the subsidence and uplift phases.
• Groundwater seepage in closed mines involves complex media such as mining-induced fractured rock masses, mining-induced cracks, and separation zones, as well as roadways, edge voids in goafs, and other structures. The seepage media and pathways are highly complex, and research in this area is insufficient. It is essential to conduct in-depth studies on groundwater seepage patterns and dynamics in closed mines to clarify the mechanisms and patterns of water–rock interactions and their effects on mining-induced fractured rock masses and coal (rock) mechanics. This will provide theoretical support for understanding the mechanisms, patterns, and prediction methods of secondary subsidence.
• New next-generation interpretation methodologies applied to InSAR deformation data are very promising tools for studying the causes of secondary subsidence and their evolution.