Evaluating Surface Stability for Sustainable Development Following Cessation of Mining Exploitation

Abstract

While the cessation of underground mining operations reduces immediate risks to surface structures, it does not fully eliminate long-term surface hazards, which can hinder the sustainable development of post-mining communities. This study presents a combination of analytical and practical methods to quantitatively assess these persistent hazards, focusing on three critical areas: the risk of surface instability from discontinuous phenomena at shallow road headings, the progression of subsidence after mining has ceased, and surface uplift due to rising mine water levels. By providing practical examples, this research highlights the importance of ongoing monitoring and hazard assessment to support sustainable land use in former mining regions. These findings contribute to a broader understanding of post-mining environmental impacts, offering valuable insights into mitigating surface risks that can influence local sustainability efforts. This study supports the global drive toward sustainable development by addressing the long-term effects of resource extraction on land stability and community resilience.

1. Introduction

In recent years, heightened environmental consciousness, alongside the escalating costs associated with coal mining and mine closure, has prompted numerous countries, particularly across Europe, to initiate the phased closure of underground mining operations. These regions, with centuries of intensive mining activity, e.g., Ruhr and Saar Coal Basin (Germany), Lower and Upper Silesian Coal Basin (Poland), Ostrava-Karviná Coal Basin (Czechia), Campine Coal Basin (Belgium), are now confronted with the complex legacy of surface instability. These regions have been subject to intense underground mining activity for decades, posing a threat to surface facilities and buildings [1,2]. While the cessation of extraction mitigates immediate environmental and structural impacts, it does not fully resolve the persistent long-term hazards that can undermine the sustainable redevelopment of post-mining communities [3,4].

Mine closure strategies, often protracted due to intricate legal, technical, and environmental considerations, involve methods such as controlled flooding, which are tailored to specific geological, mining, and economic conditions. However, even after the conclusion of active mining, dynamic movements within the subsurface, including subsidence and rock mass reconsolidation, continue to affect surface stability [5]. These processes—driven by factors such as mining depth, rock composition, tectonic activity, and water infiltration—can persist for extended periods, manifesting as residual subsidence [6,7]. Moreover, the gradual rise in groundwater levels post-closure introduces the additional complexity of surface uplift [8,9], further challenging sustainable land use and development in former mining areas [10]. With the rising groundwater levels, mining tremors may also pose potential hazards [11].

The cessation of mining operations may reduce immediate risks; however, it does not eliminate long-term hazards such as subsidence and surface uplift, which can have severe consequences for both the environment and local communities [12]. Surface instability can lead to land degradation, affecting local ecosystems and biodiversity. The alteration of landforms can disrupt natural water drainage patterns, leading to increased erosion and sedimentation in nearby waterways. Additionally, the rise in groundwater levels post-mining can result in water quality deterioration, impacting both human populations and wildlife. Communities dependent on mining often face economic challenges post-closure due to land instability affecting property values and usability of land for agriculture or development. Surface instability poses risks to public safety, as it can lead to accidents or property damage. This can create a sense of insecurity among residents, impacting their quality of life [13]. Many studies focus primarily on immediate post-mining effects without adequately addressing the long-term stability of surfaces over decades. Understanding these long-term dynamics is essential for effective land use planning and risk management.

This study provides an integrated approach to quantitatively assessing these post-mining surface hazards through both analytical modelling and empirical evaluation [14]. It specifically addresses three critical aspects of surface instability: discontinuous phenomena at shallow road headings, the progression of subsidence after mining cessation, and surface uplift driven by rising mine water levels. Through practical case studies, this research emphasizes the necessity for sustained monitoring [15] and adaptive management to mitigate risks and ensure the long-term stability and resilience of post-mining landscapes. By enhancing our understanding of these hazards, this study contributes to broader efforts in promoting sustainable land use [16], environmental stewardship, and community resilience in line with global sustainability goals.

The purpose of the article is to highlight the hazards posed to surface terrain and their impact on the environment and infrastructure during and after the closure of underground mining facilities. This addresses the needs of local government authorities, mining supervision bodies, spatial planning institutions, and the real estate market concerning the reuse, safe redevelopment, and revitalization of post-mining areas. The lifecycle of an underground mine encompasses five stages: deposit exploration, facility design, mine development, exploitation, and closure.

The primary mining-induced impacts on surface terrain, specifically in terms of ground displacement, occur during the exploitation phase. These impacts pose the greatest threats to the environment and surface infrastructure. Over the years, these issues have been the focus of research in the protection of mining areas [17,18,19]. However, due to resource depletion and the energy transition in many European countries, decisions have been made to close underground coal mines. The resulting post-mining areas require assessment to determine their potential for reuse. One of the key criteria for revitalized post-mining areas is ground stability.

This article presents comprehensive solutions for evaluating surface terrain stability in post-mining areas in the context of underground mine closures. The study outlines methods for determining ground movements in three possible scenarios.

Scenario 1: Assessment of surface impacts caused by a mine gallery in a closed clay mine, including the potential occurrence of discontinuous deformations above the gallery.

Scenario 2: Analysis of completed mining operations in the Ruhr Basin, Germany. This includes a methodology for calculating post-mining surface subsidence, referred to as residual subsidence. Based on geodetic measurements conducted in the analysed area, the timeframe for the cessation of significant subsidence, meeting the ground stability criteria, is determined.

Scenario 3: Evaluation of the effects of flooding a coal mine on the surface terrain, also located in the Ruhr Basin. Predicted uplift values, which had not previously been considered as a mining-induced impact, enable appropriate planning of repairs to utility networks and infrastructure elements. The proposed solutions allow for scenario-based analyses depending on the established groundwater table level in the rock mass, primarily associated with the protection of groundwater resources for municipal and potable purposes.

2. Materials and Methods

2.1. Mining Galleries

Mining galleries located at shallow depths can threaten buildings situated on the surface. These galleries can lead to both surface subsidence and discontinuous phenomena in the form of local sinkholes. The subsidence recorded on the surface is generally caused by the progressive convergence of the mining gallery over time or the nearly simultaneous collapse of a longer section of the gallery due to the failure of the gallery support or the destruction of the overlying rock structure in the case of unsupported galleries. On the other hand, surface sinkholes occur when there is a localized point collapse of the overlying layers into the mining gallery.

2.1.1. Surface Subsidence Above a Mining Gallery

The assessment of the magnitude of surface subsidence above a mining gallery can be carried out using analytical methods provided by various authors, including Knothe [20], Peck [21], Sroka [22], Mair et al. [23], and Löbel and Sroka [24]. The common denominator of these methods is the influence function in the form of a Gaussian function [20]. According to the solution provided by [22,24], the distribution of subsidence on the surface, along a profile perpendicular to the axis of the tunnel, can be calculated using the following Formula (1):

$$s\left(x\right)=s_{max}\mathsf{\bullet }exp\left(-\pi {\displaystyle \frac{x^2}{R^2}}\right)$$

(1)

where

$R=H\mathsf{\bullet }cot\beta$ and $s_{max}=k\mathsf{\bullet }{\displaystyle \frac{F}{R}}$

The symbols used in Formula (1) have the following meanings:

$s\left(x\right)$—subsidence,

$x$—distance of the calculation point from the tunnel (gallery) axis,

$F$—cross-sectional area of the gallery,

$k$—convergence coefficient (0 ≤ k ≤ 1),

$H$—depth of the tunnel,

$\beta$—the angle of the main influence range (as defined by [25]),

$R$—radius of the main influence range.

The radius of the main influence range confines the extent of the influence to the zone where potential damage to buildings may occur. Beyond this boundary, the effects of surface deformation on structures are practically negligible and can be disregarded.

From the aforementioned works, those by Peck [21] and Mair [23] focus on calculating subsidence above tunnel structures. According to Peck, the equation for the subsidence trough profile running perpendicular to the tunnel axis is described by Equation (2):

$$s\left(x\right)=s_{max}\cdot exp\left(-{\displaystyle \frac{x^2}{2i^2}}\right)$$

(2)

where

$s_{max}={\displaystyle \frac{V_k}{i\sqrt{2\pi }}}$ and $i=K\mathsf{\bullet }H.$

The symbols used in Formula (2) have the following meanings:

$V_k$—volumetric convergence of 1 m of the tunnel [m³/m],

$i$—measure of the horizontal influence range [m] (identical to the standard deviation),

$K$—scale coefficient of the horizontal influence range dependent on the type of rock above the tunnel [-].

Comparing Formulas (1) and (2), we find that they yield identical subsidence calculation results for the relationship given by Equation (3):

$$R=\sqrt{2\pi }\mathsf{\bullet }i=2.507\mathsf{\bullet }i \mathrm{and} \beta =arctan{\displaystyle \frac{1}{\sqrt{2\pi }\mathsf{\bullet }K}}$$

(3)

Peck [21] states that for practical purposes, the range of subsidence above tunnels can be limited to a distance equal to 2.5 times the measure of the horizontal influence range $i$ from the tunnel axis, which fully corresponds to the radius of the main influence range $R$.

The distribution of horizontal displacement along a profile perpendicular to the axis of the gallery or tunnel is calculated based on Awierszyn’s hypothesis [26,27]. This hypothesis assumes proportionality between the horizontal displacement $U\left(x\right)$ and the horizontal gradient of the subsidence distribution, i.e., the slope $T\left(x\right)$:

$$U\left(x\right)=B\mathsf{\bullet }T\left(x\right),$$

where $B={\displaystyle \frac{R}{\sqrt{2\pi }}}=0.40\mathsf{\bullet }R$.

The assessment of the threat to buildings in terms of their resistance (sensitivity) to impacts caused by mining or tunnel construction is not based on the predicted values of subsidence and horizontal displacement, but rather on their horizontal gradients, i.e., tilt, curvature, and horizontal strain.

Based on the solution provided, among others, by [24], the maximum values of tilt, curvature, and horizontal strain can be calculated using the formulas provided below.

• − tilt (slope):

$$T_{max}=\sqrt{{\displaystyle \frac{2\pi }{e}}}\mathsf{\bullet }{\displaystyle \frac{s_{max}}{R}}=1.52\mathsf{\bullet }{\displaystyle \frac{s_{max}}{R}}$$

(4)

for $x={\displaystyle \frac{R}{\sqrt{2\pi }}}=0.40\mathsf{\bullet }R$,

• − curvature (concave):

$$K_{max}^{+}=2\pi \mathsf{\bullet }{\displaystyle \frac{s_{max}}{R^2}}=6.28\mathsf{\bullet }{\displaystyle \frac{s_{max}}{R^2}}$$

(5)

for $x=0$,

• − curvature (convex):

$$K_{max}^{-}=4\pi \mathsf{\bullet }exp\left({\displaystyle \raisebox{1ex}{$-3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)\mathsf{\bullet }{\displaystyle \frac{s_{max}}{R^2}}=2.80\mathsf{\bullet }{\displaystyle \frac{s_{max}}{R^2}}$$

(6)

for $x={\displaystyle \frac{\sqrt{3}}{2\pi }}\mathsf{\bullet }R=0.69\mathsf{\bullet }R$,

• − compressive strain:

$${\epsilon }_{max}^{-}=-\sqrt{2\pi }\mathsf{\bullet }{\displaystyle \frac{s_{max}}{R}}=-2.51\mathsf{\bullet }{\displaystyle \frac{s_{max}}{R}}$$

(7)

for $x=0$,

• − tensile strain:

$${\epsilon }_{max}^{+}=\sqrt{8\pi }\mathsf{\bullet }exp\left({\displaystyle \raisebox{1ex}{$-3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)\mathsf{\bullet }{\displaystyle \frac{s_{max}}{R^2}}=1.12\mathsf{\bullet }{\displaystyle \frac{s_{max}}{R^2}}$$

(8)

for $x={\displaystyle \frac{\sqrt{3}}{2\pi }}\mathsf{\bullet }R=0.69\mathsf{\bullet }R$.

To exemplify the surface deformation dynamics, a computational analysis was conducted for the shaft gallery of the former clay mine “Abendtal” for the given data:

–

average depth of the shaft gallery: $H$ = 67 m,

–

diameter of the circular gallery cross-section: $D$ = 2.2 m,

–

angle of the main influence range: $\beta$ = 39°,

–

convergence coefficients: $k$ = 0.10; 0.25; 0.50; 0.75 and 1.00.

The angle of the main influence range was determined using Formula (3), with the coefficient $K$ for clayey rocks assumed to be 0.5 [23]. The results are presented in Section 3.1.2.

2.1.2. Sinkholes Above Mining Galleries

The initiation of a sinkhole on the surface is triggered by a localized point collapse of the overlying rock layers into the gallery. This collapse extends vertically in the form of a cylindrical chimney towards the surface. The assessment of the potential threat to the surface due to the formation of a local sinkhole above a gallery can be effectively carried out, as demonstrated by numerous practical applications in mining, using the method of balancing the volume of loosened rock involved in the collapse within the cylindrical chimney and the active volume of the gallery collapse (e.g., [28,29,30,31,32]). The concept of this method is schematically illustrated in Figure 1.

The starting point is the balance equation (Formula (9)):

$$\eta \mathsf{\bullet }{V}_k=V_k+V_s \mathrm{so} V_s=V_k\mathsf{\bullet }\left(\eta -1\right)$$

(9)

where

$\eta$—loosening coefficient (collapse factor) for the rock in the chimney [-],

$V_k$—the volume of the collapsed chimney [m³], and

$V_s$—active collapse volume of the gallery [m³].

The criterion for the potential occurrence of a sinkhole on the surface can be expressed by Formula (10):

$$h_k>{\displaystyle \frac{H}{SF}}=h_{gr}$$

(10)

where

$h_k$—the height of the collapsed chimney needed to fill the chimney and the active collapse volume of the gallery with loosened rock [m],

$H$—depth of the gallery roof [m], and

$SF$—safety factor [-],

$h_{gr}$—the height limit [m].

In many cases, the collapsed chimney undergoes self-subsidence and does not reach the surface. Assuming that the collapsed chimney has the shape of a cylinder with a diameter $D_k$, we receive:

$$V_k={\displaystyle \frac{\pi }{4}}\mathsf{\bullet }{D}_k^2\mathsf{\bullet }{h}_k$$

(11)

using Formula (9), we have:

$$h_k={\displaystyle \frac{1}{\eta -1}}\mathsf{\bullet }{\displaystyle \frac{4}{\pi }}\mathsf{\bullet }{\displaystyle \frac{V_s}{D_k^2}}$$

(12)

For a gallery with height $h$ and width $b$, the active collapse volume is dependent on the specific case being analysed (Figure 1) and is described by the general Formula (13):

$$V_s={\displaystyle \frac{n}{2}}\mathsf{\bullet }{h}^2\mathsf{\bullet }b\mathsf{\bullet }cot\alpha +{\displaystyle \frac{\pi }{4}}\mathsf{\bullet }{D}_k^2\mathsf{\bullet }h$$

(13)

where

$n$—the number of possible departures from the collapse point in the gallery (Figure 1), and

$\alpha$—the angle of natural repose of the loosened rock in the collapsed chimney [°].

From the above, it follows that to determine the potential for a sinkhole caused by a localized collapse within the gallery, it is necessary to know the diameter of the collapsed chimney, the loosening coefficient for the rock, and the angle of natural repose of these rocks.

Previous experience, based not only on the literature but also on practical observations (e.g., [30,31,33,34]), indicates that the diameter of the collapsed chimney primarily depends on the width of the gallery.

For the scenarios depicted in Figure 1 regarding the location of the collapse point in the gallery, the following assumptions are recommended:

start/end of the gallery (case a, $n$ = 1): $D_k=b$,

single gallery (case b, $n$ = 2): $D_k=b$,

single departure (case c, $n$ = 3): ${b\le D}_k<b\sqrt{2}$,

intersection of two galleries (case d, $n$ = 4) $D_k=b\sqrt{2}$.

Assuming that the diameter of the cylindrical collapse chimney is equal to the width of the gallery b, for cases a, b, and c, the height of the collapsed chimney required to fill the cylinder and the active collapse volume in the gallery is given by:

$$h_k={\displaystyle \frac{h}{\eta -1}}\mathsf{\bullet }\left({\displaystyle \frac{2n}{\pi }}\mathsf{\bullet }{\displaystyle \frac{h}{b}}\mathsf{\bullet }cot\alpha +1\right)$$

(14)

For the intersection of two equivalent galleries (case d):

$$h_k={\displaystyle \frac{h}{\eta -1}}\mathsf{\bullet }\left({\displaystyle \frac{4}{\pi }}\mathsf{\bullet }{\displaystyle \frac{h}{b}}\mathsf{\bullet }cot\alpha +1\right)$$

(15)

For a gallery with a circular cross-section and diameter $D$, the height of the cylindrical collapse chimney can be approximated using Formula (16):

$$h_k={\displaystyle \frac{1}{\eta -1}}\mathsf{\bullet }{\displaystyle \frac{D^2}{D_k^2}}\left(D_k+{\displaystyle \frac{n}{2}}\mathsf{\bullet }D\mathsf{\bullet }cot\alpha \right).$$

(16)

For cases a, b, and c, we obtain:

$$h_k={\displaystyle \frac{D}{\eta -1}}\left({\displaystyle \frac{n}{2}}\mathsf{\bullet }cot\alpha +1\right)$$

(17)

For case d:

$$h_k={\displaystyle \frac{1}{\eta -1}}\mathsf{\bullet }{\displaystyle \frac{D^2}{D_k^2}}\left(D_k+{\displaystyle \frac{n}{2}}\mathsf{\bullet }D\mathsf{\bullet }cot\alpha \right).$$

(18)

The central geotechnical parameter in the presented method for assessing the potential for sinkhole formation above a mining gallery is the loosening coefficient for the overlying rocks. The loosening coefficient values for mining galleries at shallow (small) depths, as drawn from the literature, are summarized in

Table 1. Values of the loosening coefficient for overlying rocks.

Author	$\mathbf{Loosening} \mathbf{Coefficient}\mathit{\eta }$ [-]
Whittaker, Reddish (1989) [30]	$1.33 \le \eta \le$ 1.50
Meier (1991) [29]	$1.20 \le \eta \le$ 1.50
Zimmermann (2011) [35]	$1.30 \le \eta \le$ 1.40
Sroka et al. (2018) [31]	$\eta$ = 1.30
Clostermann et al. (2020) [32]	$1.26 \le \eta \le$ 1.46
Hager (2023) [33]	$\eta$ = 1.25

.

As a computational example, the assessment of the potential for sinkhole formation on the surface above the shaft gallery of the former “Abendtal” clay mine will be presented in Section 3.1.2.

The angle of natural repose for loosened rock material from a collapse typically ranges from 30° to 40°. For clayey rocks, this angle is approximately 30° according to Meier [29].

Calculations were performed for the following data:

–

average depth of the shaft gallery: $H$ = 67 m

–

diameter of the gallery cross-section:$D$ = 2.2 m

–

loosening coefficient: $\eta$ = 1.2

–

angle of natural repose: $\alpha$ = 30°, and

–

safety factor: $SF$ = 1.3.

2.2. Surface Subsidence After the Cessation of Mining Activities

The issue of surface subsidence over time after the cessation of mining operations is a significant and current problem. The usability of post-mining lands for full and safe utilization is mainly considered in terms of the “stability” of the surface. A key element is determining the expected final values of subsidence and the period after which further expected subsidence poses no threat to the safety of structures, i.e., from the perspective of their protection, it becomes negligible.

The manifestation of mining impacts on the surface occurs in three main phases:

• Preliminary Subsidence: During this phase, 5 to 15% of the final subsidence occurs.
• Main Phase: This phase involves the consolidation of the broken rock mass almost exclusively within the active mining period. This phase typically lasts from 6 to 12 months, during which approximately 75% of the final subsidence is revealed.
• Long-Term Consolidation: The final stage, where about 10% of the final subsidence occurs, is associated with the long-term consolidation of the goaf. This stage can last from a few months to several years after the cessation of mining operations. The duration of this phase is influenced by factors such as the depth and mining system, the total thickness of the exploited deposit, the number of mined seams, and the geological structure of the rock mass.

The basis for the solution regarding subsidence behaviour after the cessation of mining is the so-called wall model. Using Equation (19), the subsidence of a point on the surface over time $s\left(t\right)$ at any moment $t$ after the cessation of mining, where $t>t_i$ and $t_i$ is the moment of the first subsidence measurement after the cessation of mining at time $T$ (Figure 2), can be described as follows:

$$s\left(t>t_i\right)=s\left(t_i\right)+\left[s_e-s\left(t_i\right)\right]\mathsf{\bullet }\left[1-exp\left(-c\mathsf{\bullet }\left[t-t_i\right]\right)\right]$$

(19)

where

$s_e$—final subsidence value of the analysed point [m],

$c$—so-called time coefficient [Year⁻¹].

The method for determining the expected final subsidence $s_e$ and the time coefficient $c$ based on periodic (cyclic) subsidence measurements was published by Bartosik-Sroka, Pielok, and Sroka [36]. Depending on the available observational data, solutions are presented for two variants—the 3-point method and the 4-point method. For the simultaneous use of all available subsidence measurements after the cessation of mining operations (>3), the determination of the final subsidence value $s_e$and the time coefficient $c$ can be performed using the Gauss–Markov algorithm [37].

For example, using levelling measurements taken after the cessation of mining operations, where pairs of observations are made at the same time intervals such that$\Delta t=t_3-t_2=t_2-t_1$, the final subsidence value $s_e$and the time coefficient $c$ can be determined, for instance, using the 3-point method [36] with the following Formulas (20) and (21):

$$s_e={\displaystyle \frac{s_2^2-s_3\mathsf{\bullet }{s}_1}{{2\mathsf{\bullet }s}_2-\left(s_3+s_1\right)}}$$

(20)

$$c=-{\displaystyle \frac{1}{\mathsf{\Delta }t}}\mathsf{\bullet }\ln {\displaystyle \frac{s_3-s_2}{s_2-s_1}}$$

(21)

where

$s_1,s_2,s_3$—subsidence value observed in i-th measurement cycle.

Assuming that the measured subsidence values are subject to measurement errors $m_s$ (standard deviation), the errors in the computed values of final subsidence and the time coefficient can be estimated based on the law of error propagation using Formulas (22) and (23):

$$m_{s_e}={\displaystyle \frac{m_s}{{2\mathsf{\bullet }s}_2-\left(s_3+s_1\right)}}\sqrt{{\left(s_e-s_1\right)}^2+{4\mathsf{\bullet }\left(s_e-s_2\right)}^2+{\left(s_e-s_3\right)}^2}$$

(22)

$$m_c={\displaystyle \frac{m_s}{\mathsf{\Delta }t}}\sqrt{{\displaystyle \frac{1}{{\left(s_2-s_1\right)}^2}}+{\displaystyle \frac{1}{{\left(s_3-s_2\right)}^2}}+{\displaystyle \frac{{\left(s_3-s_1\right)}^2}{{{\left(s_2-s_1\right)}^2\mathsf{\bullet }\left(s_3-s_2\right)}^2}}}$$

(23)

According to Equation (19), subsidence after the cessation of mining proceeds asymptotically towards the expected final subsidence value $s_e$. Therefore, the moment of completion of the subsidence process $t_e\left({\Delta s}_{Gr}\right)$ is determined such that the increment in subsidence ${\Delta s}_{Gr}$ occurring after this moment is negligible for the environment and infrastructure. The period when residual subsidence, significant from the perspective of mining damage, diminishes is determined based on Equation (19), utilizing Formulas (24) and (25):

$$\mathsf{\Delta }{t}_i\left({\mathsf{\Delta }s}_{Gr}\right)=-{\displaystyle \frac{1}{c}}\mathrm{l}\mathrm{n}{\displaystyle \frac{{\mathsf{\Delta }s}_{Gr}}{s_e-s\left(t_i\right)}}$$

(24)

$$t_e\left({\mathsf{\Delta }s}_{Gr}\right)=t_i+\mathsf{\Delta }{t}_i\left({\mathsf{\Delta }s}_{Gr}\right)$$

(25)

The accuracy estimation of the time for the cessation of significant residual subsidence increments can be performed using Formula (26):

$$m_{t_e}={\displaystyle \frac{1}{c}}\sqrt{{\left(\mathsf{\Delta }t\left({\mathsf{\Delta }s}_{Gr}\right)\right)}^2\mathsf{\bullet }{m}_c^2+{\displaystyle \frac{m_{s_e}^2+m_s^2}{{\left(s_e-s\left(t_i\right)\right)}^2}}}$$

(26)

The explanation of the symbols used in Equations (24) and (25) is presented in Figure 2.

An example of the evaluation of residual subsidence was performed for observation point number 4312900232 from the area of the closed coal mine Ost, which was part of the RAG Aktiengesellschaft conglomerate and closed in 2010 (Section 3.2).

2.3. Flooding of Mines

To assess the potential negative effects of the rise in mine water levels, it is necessary to estimate the ground movements induced by the mine water rise using mathematical models. For this purpose, the analytical models of [37,38,39] are available.

The basis for Sroka’s method to predict uplift caused by the rise in mine water levels is a cause-effect model. By dividing the fractured body caused by mining, which in plain view is equal to the mined area, into small square fracture cells, it is possible to calculate the uplift for any point on the ground surface, with any mining geometry in space, using linear superposition. Uplift solutions for a single fracture cell, with the influence functions of Knothe [14,40] the Ruhrkohle method, and Geerstma [41], have already been presented in several publications (including [42,43]).

For a single fracture cell, the elementary uplift distribution on the ground surface is described by Equation (27) and shown in Figure 3:

$$h\left(r,t\right)={\displaystyle \frac{k}{\pi }}\mathsf{\bullet }{\displaystyle \frac{K\left(t\right)}{R_w^2}}\mathsf{\bullet }ex\mathrm{p}\left(-k{\displaystyle \frac{r^2}{R_w^2}}\right)$$

(27)

with:

$$R_w=H\mathsf{\bullet }cot{\gamma }_w$$

(28)

$$K\left(t\right)=d_m\mathsf{\bullet }∆p\left(t\right)\mathsf{\bullet }\lambda \mathsf{\bullet }M\mathsf{\bullet }{∆x}^2$$

(29)

$$∆p\left(t\right)=\left(z_w\left(t\right)-z_{Fl}\right)\mathsf{\bullet }{\sigma }_w$$

(30)

where the abbreviations stand for:

where

$h(r, t)$—distribution of uplift on the surface at time $t$ caused by the flooding of the consolidated caved (fractured) zone element [m],

$k$—constant of the Ruhrkohle method ($k=-ln0.01$) [-],

$K\left(t\right)$—increase in the volume of the fracture cell over time $t$ [m³],

$R_w$—radius of influence for the mine water rise [m],

$r—$horizontal distance between the calculation point and the fractured zone element [m],

${\gamma }_w$—boundary angle for the mine water rise [gon],

$∆x$—side length of the square base of the fractured zone element [m],

$d_m$—expansion coefficient [m²/MN],

$∆p\left(t\right)$—increase in pore pressure in the fractured zone, dependent on the height of the water column above this zone [kPa],

${\sigma }_w$—specific weight of water [kN/m³],

$\lambda$—relative height of the fractured rock element (e.g., $\lambda$ = 3 corresponds to an absolute height equal to three times the thickness of the mined seam) [-],

$M$—thickness of the mined seam [m],

$w$—absolute height of the caved (fractured) zone ($w=\lambda ·M$) [m],

$V$—volume of the caved zone element [m³],

$z_w\left(t\right)$—water level at time $t$ [m],

$z_{Fl}$—height of the flooded caved zone element [m],

$z_H$—surface level [m],

$H$—depth of the infarct zone element [m].

The values of the coefficients $d_m$, $\lambda$ and ${\gamma }_w$ necessary for determining the uplift coefficient, have been established and published by several authors based on in situ measurements using parameter identification. Notable works include those by Pöttgens [38,39], Goerke-Mallet [45] and Sroka and Preuße [43,46]. The results of these studies are compiled in

Table 2. Compilation of characteristic values of $d_m$, $\lambda$ and ${\gamma }_w$ for selected coal mining districts.

Coalfield	${\mathit{d}}_{\mathit{m}}$ [m2/MN]	$\mathit{\lambda }$ [-]	${\mathit{d}}_{\mathit{m}}\mathsf{\bullet }\mathit{\lambda }$ [m2/MN]	${\mathit{\gamma }}_{\mathit{w}}$ [gon]
Südlimburger Revier (Pöttgens [38])	0.350·10−2	4	1.40·10−2	-
Ibbenbüren/Westfeld (Goerke-Mallet [45])	0.460·10−2	3	1.38·10−2	-
Erkelenzer Revier/Sophia Jacoba (Sroka and Preuße [43])	0.265·10−2	4	1.06·10−2	7–15 $\overline{{\mathsf{\gamma }}_{\mathrm{w}}}$ = 12
Ruhrrevier/Königsborn (Sroka and Preuße [46])	0.364·10−2	3	1.092·10−2	12

.

The considerations will be illustrated by the example of the Haus Aden water province.

3. Discussion of Results

3.1. Examples of Land Deformations Above Old Mining Gallery

3.1.1. Continuous Land Surface Deformations

Calculations of subsidence distribution, tilt, curvature, horizontal displacement, and horizontal strain were carried out. The results of the deformation indicators along the profile perpendicular to the axis of the shaft gallery are presented in Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8, while the computed maximum values of the indicators for $k=1.00$ are shown in

Table 3. Calculated maximum values of the ground movement elements relevant to mining damage for the worst case ($k=1.00$).

	Ground Movement Elements	Max. Values	Position * [m]
vertical	Subsidence [mm]	45.9	0
	Tilt [mm/m]	0.84	33.0
	Curvature—concave [km−1]	0.0422	0
	Min. radius of curvature—concave [km]	23.7	0
	Curvature—convex [km−1]	0.0188	57.2
	Min. radius of curvature—convex [km]	53.1	57.2
horizontal	Horizontal displacement [mm]	27.8	33.0
	Horizontal deformation—compression [mm/m]	1.39	0
	Horizontal deformation—tension [mm/m]	0.62	57.2

* away from the tunnel axis.

.

The summarized results of the computed maximum values of tilt, curvature, and horizontal strain, in order to assess their impact on construction structures compared to the Polish resistance category of buildings in mining areas [47,48], are presented in Figure 9 and Figure 10.

They do not exceed the threshold values for Category 1 resistance of structures to mining impacts. Considering the extensive experience from the Ruhr and Upper Silesian coal basins, these values practically do not pose a threat to buildings located on the surface.

3.1.2. Example of Sinkholes Above Mining Galleries

The results of the calculations are summarized in

Table 4. Calculation results of the height of the collapse chimney for possible route configurations.

Case	Assumptions	${\mathit{h}}_{\mathit{k}}$ [m]	${\mathit{h}}_{\mathit{g}\mathit{r}}=\frac{\mathit{H}}{\mathit{S}\mathit{F}}$ [m]
a.* start/end of the route	$D_k=b$$(n=1)$	20.5	51.5
b.* individual route	$D_k=b$$(n=2)$	30.1
c.* route branch	$D_k=b$$(n=3)$	39.6
	$D_k=b\mathsf{\bullet }\sqrt{2}$$(n=3)$	22.1
d * route intersection	$D_k=b\mathsf{\bullet }\sqrt{2}$$(n=4)$	26.8

* See Figure 1 for graphical explanation of cases.

.

Comparison of the obtained calculation results with the critical threshold value of 51.5 m indicates that, in the analysed case, there is no risk of surface hazards in the form of localized sinkholes.

Simulative calculations conducted by the authors for various typical mining gallery cases lead to the conclusion that for gallery depths greater than 50 m, the occurrence of sinkholes can be excluded with high probability. This fact is confirmed by long-term experience in coal mining in the Saar Basin, the Ruhr Basin, and the Upper Silesian Basin.

3.2. Example of Surface Subsidence After the Cessation of Mining Activities

Mining activities in the analysed area ceased in 2004. Available elevation measurement results cover the years 2004 to 2018 and were taken every 2 years (

Table 5. Summary of observations of subsidence at the point 4312900232 carried out in 2004–2018.

Id	Date (Year)	Subsidence [mm]
1 *	2004	740
2	2006	782
3	2008	813
4 *	2010	831
5	2012	840
6	2014	850
7 *	2016	862
8	2018	865

* Measurements with Ids 1, 4, and 7 have been highlighted using color as they were used in the three-point method.

). For the calculations, it was assumed that the standard deviation of the measured subsidence values for all measurements is equal and amounts to $m_s=\pm 2 \mathrm{m}\mathrm{m}$.

For the three-point method calculations, measurements 1, 4, and 7 were used, yielding the following values for final subsidence $s_e$ and the time coefficient $c$, along with their associated errors:

$$s_e=878.0 \mathrm{m}\mathrm{m} c=0.1795 \mathrm{Y}\mathrm{e}\mathrm{a}{\mathrm{r}}^{-1}$$

$$m_{s_e}=\pm 5.6 \mathrm{m}\mathrm{m} m_c=\pm 0.0184 \mathrm{Y}\mathrm{e}\mathrm{a}{\mathrm{r}}^{-1}$$

The calculated values of subsidence, using the Formula (19), from 2004 to 2024 at 2-year intervals, are presented in

Table 6. Prediction and calculated subsidence in the period of 2004–2024.

Date [Year]	Subsidence [mm]
	Measured	Calculated	Difference
2004 *	740	740.0	0.0
2006	782	781.6	−0.4
2008	813	810.7	−2.3
2010 *	831	831.0	0.0
2012	840	845.2	5.2
2014	850	855.1	5.1
2016 *	862	862.0	0.0
2018	865	866.8	1.8
2020	-	870.2	-
2022	-	872.6	-
2024	-	874.2	-

* Measurements with dates 2004, 2010, and 2016 have been highlighted using color as they were used in the three-point method.

. Additionally, a comparison of calculated subsidence and measured subsidence from 2004 to 2018 was performed.

3.3. Flooding of Abandoned Mines: A Practical Example

The coal company RAG Aktiengesellschaft plans to raise the water level to −380 m a.s.l. as part of the mine water concept in the Haus Aden water province.

The Haus Aden water province is shown in Figure 11. It is approximately 33 km long and 15 km wide, with an area of about 323 km². This region includes partially heavily urbanized areas of strategic industrial and transportation significance.

The data on the conducted mining activities included 10,075 individual mining fields in over 100 seams, with 6615 fields located below the −380 m a.s.l. (Figure 12).

The predictive calculations were performed using the following parameter values:

• $d_m$ = 0.364∙10⁻² m²/MN,
• $\lambda$ = 3,
• ${\gamma }_w$ = 12 gon (ca. 10.8°).

The results of the calculations for surface uplift in the Haus Aden water province are shown in Figure 13, and the calculated maximum values of the deformation indicators are presented in

Table 7. Predicted maximum values of the ground movement relevant to mining damage during the mine water uplift to the final level of −380 m above sea level.

Water Province	${\mathit{h}}_{\mathit{m}\mathit{a}\mathit{x}}$ [mm]	${\mathit{T}}_{\mathit{m}\mathit{a}\mathit{x}}$ [mm/m]	${\mathit{\epsilon }}_{\mathit{m}\mathit{a}\mathit{x}}^{-}$ [mm/m]	${\mathit{\epsilon }}_{\mathit{m}\mathit{a}\mathit{x}}^{+}$ [mm/m]
Haus Aden	303.1	0.091	−0.058	0.101

.

The calculated maximum values of tilt and horizontal strain do not pose any practical threat to the buildings located on the surface.

This study closely examines the stability issues of land surfaces in areas affected by post-mining activities, with a focus on supporting sustainable redevelopment. The findings show that while stopping mining operations reduces some immediate surface hazards, certain risks remain due to ongoing residual subsidence and surface uplift caused by rising groundwater levels. The primary method for minimizing surface subsidence after the cessation of mining operations involves backfilling mine workings with filling materials such as sand, dust, or fly ash. However, due to the very high implementation costs, this method is rarely applied in modern mining practices. This research builds on earlier studies about the lasting effects of mining on surface stability, particularly the work of Knothe and Sroka, who modelled how subsidence spreads above mine tunnels using Gaussian-based functions. By applying these models to current cases, our study shows that these methods are still relevant and useful for today’s mining industry challenges.

The analysis points out that surface subsidence and potential sinkhole formations are still serious issues, especially in areas with shallow mining galleries where localized collapses can still happen. A key finding of our study is that post-mining water level rise can cause surface uplift, which affects long-term land use and infrastructure stability. The model by Sroka for estimating ground changes due to rising water levels provides a useful framework, which our study further supports with real-world data. This predictive approach is critical for ongoing land management and risk mitigation in former mining regions.

Overall, this study highlights the importance of constant monitoring of both subsidence and uplift for safe redevelopment. The trends identified suggest that future research should aim to improve predictive algorithms, while the development of real-time monitoring technologies could enhance our ability to adapt to surface changes as they occur, helping create more resilient infrastructure in former mining areas.

4. Conclusions

This study emphasizes the ongoing and complex surface stability issues that arise after the end of mining activities, underscoring the critical need for continuous monitoring and adaptable management practices in areas affected by historic mining. The findings highlight that while traditional methods offer valuable foundational insights into land deformation processes, there is a growing need to incorporate modern predictive models to more accurately account for not only subsidence but also for discontinuous phenomena at shallow road headings and uplift effects that continue long after mining operations cease.

Our research confirms that these surface stability challenges are not just short-term risks but are persistent issues that can impact land usability, infrastructure integrity, and community safety over extended periods. By integrating newer predictive models alongside established methods, this study provides a more comprehensive approach to understanding and mitigating these risks. The combination of both traditional and advanced predictive tools enables more precise forecasting and risk assessment, making it possible to develop more effective long-term strategies for surface stability in former mining regions.

Furthermore, this study contributes to the global sustainability agenda by offering practical, data-backed methodologies for assessing surface risks in post-mining landscapes. These methods support the development of safer, more resilient communities by providing tools for land managers and policymakers to proactively address the challenges mainly of discontinuous phenomena, subsidence and uplift. Ultimately, by focusing on sustainable redevelopment practices and long-term land stability, this research aligns with broader environmental and social goals, aiming to facilitate safer living conditions and more sustainable land use in areas impacted by past mining activities.

A comprehensive approach to assessing the occurrence of post-mining surface deformations following the cessation of mining operations has been presented. The study considers the primary identified hazards in post-mining areas, including discontinuous deformations (sinkholes), residual subsidence, and surface uplift. This approach enables the determination of hazard types, as well as their quantitative and qualitative characteristics, based on the date of mining cessation and mining-geological factors (e.g., depth, mining methods). In essence, it facilitates the prediction of surface displacements for defined types of post-mining deformations. This information can be integrated into risk management and spatial planning processes.