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Modern mining within ecologically fragile areas is under enormous pressure from the ecological and geological environment. Using abandoned coal mines as underground water reservoirs is an effective idea for reducing eco-geological risks in mining districts. Accurate estimation of reservoir capacity is conducive to guiding the construction of an underground water reservoir. In this paper, estimation models of underground water storage capacity were established, which were divided into two kinds: horizontal mining district and inclined mining district. Furthermore, the minimum porosity of broken rock mass was analyzed based on laboratory experiments, and the fitted equation of minimum porosity was developed. A modern coal mine in northwest China was taken as an example, and the feasibility of the proposed model was verified by in-situ measurement. Finally, the effects of porosity of broken rock mass, water storage height and coal seam dip angle on water storage capacity were presented. The coal seam dip angle should be the principal consideration in choosing the site of an underground water reservoir.

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  • Underground water reservoir can realize sustainable development in mining areas.

  • Prediction model of underground water storage capacity was established.

  • The minimum void ratio of broken rock mass with different gradations was studied.

  • The coal seam dip angle significantly affects underground water storage capacity.

Graphical Abstract

Graphical Abstract
Graphical Abstract
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Graphical Abstract
Graphical Abstract
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broken rock mass, minimum porosity, modern coal mining, storage capacity, storage of mine water
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Coal resources make a great contribution to China's national economic development, and accounted for 56.0% of China's primary energy consumption in 2021 (Liu et al. 2022). It is considered that coal resources will continue to account for more than 50% of energy production and consumption before 2030 (Gu 2015; Xue et al. 2018; Fan et al. 2022). With the gradual exhaustion of coal resources, many collieries have or are facing closure in eastern and central China. The focus of coal mining has rapidly transferred to western mining districts of China, where the ecological environment is fragile, but the proven reserves and buried depth of the coal resource are massive and shallow, respectively (S. L. Liu et al. 2019). High-intensity and large-scale modern coal mining in thick coal seams must result in varying degrees of disturbance to the geological conditions, hydrogeological structure, ecological and natural environment within a mining district (Gunson et al. 2012; Fan et al. 2022). The delicate ecological balance will be destroyed when mining-induced disturbance exceeds the carrying capacity of the eco-geological system within the mining district. In recent years, mining-induced eco-geological environment and public health problems, such as water shortages, water pollution, vegetation death, desertification, and high human health risk, have received more and more attention (Wessman et al. 2014; Xue et al. 2018; Sun et al. 2020). In addition, statistics indicate that about 8 billion tons of mine water resource have been discharged by China's coal mining annually, and the utilization percentage of mine water is only about 25% (Gu 2015; Zhang et al. 2021). It is a huge waste of water resources, especially for a country where the per capita fresh water resource is far below that of the global average. Therefore, two key issues that must be solved for the establishment of ecological civilization and the sustainable development of a modern coal mining industry are water-resource-preserving mining and reasonable mine water treatment, especially within ecologically fragile mining districts (Mhlongo et al. 2018; Fan 2019).

To settle the two problems above, there have been several important studies from many disciplines using comprehensive research methods. Through site observation, Liu et al. (2022), Wei et al. (2017) and Fan et al. (2022) studied the forming process and distribution characteristics of mining-induced horizontal fracture and vertical fracture over the longwall panel in western mining districts of China. According to the affect degree of underground coal mining on the phreatic aquifer water table, four types of environmental engineering geological patterns, i.e., basically unaffected model, gradually restored model after destruction, gradually deteriorated model, and disaster model, were proposed and defined by Liu & Li (2019). Furthermore, according to field investigation of mining-induced hydrogeological conditions and normalized difference vegetation index, Chen et al. (2021) found that the emergence of phreatic water at the land surface in low-lying areas of the working faces may induce the formation of an oasis and wetland system in arid and semi-arid areas. In view of the lack of water resources in arid and semi-arid areas, Chi et al. (2021) presented the scale of coal mining in arid and semi-arid areas under the constraint of the water resources carrying capacity with the aim of realizing mining that conserves the ecological environment. Moreover, many researchers reported some interesting applications of water preservation mining techniques in ecologically fragile mining districts, for example underground water storage (Cairney 1973; Q. Liu et al. 2019; Song et al. 2020), limited-height mining (Miao et al. 2009), backfill mining (Liu et al. 2021), and room-and-pillar mining (Shi & Hou 2006). Among them, the most influential and promising method is underground water storage (Kallioras & Rusinski 2011; Li et al. 2014; Wang et al. 2018).

The concept of mine water storage in underground abandoned mine areas was first proposed by Cairney (1973). From then on, the research work on the basic condition and mechanism of underground water storage was deeper and wider. According to the designed parameters of one coal mining district in China, Fan et al. (2020) believed that only one typical abandoned coal mine with 6 m mining thickness and a 3 × 5 km2 area could have a usable storage capacity of 1.58 × 106 m3. Furthermore, in the Shendong mining district, western China, this method has been successfully applied over 20 years, using the fissure spaces between the broken rock mass in the overburden to store mine water (Gu et al. 2016). Song et al. (2020) believed that the total water storage for 18 typical underground reservoirs in Shendong mining district was 1.857 × 106 m3. The water storage area of an underground reservoir has the function of filtration and precipitation, and the purification of mine water could also be realized to a certain degree (Wang et al. 2018). Some water can be directly used in underground mining (Figure 1), and most mine water can be used as the source of industrial, agricultural and domestic water after further treatment (Zhang et al. 2021; Chi et al. 2022). Currently, 35 coal mine underground water reservoirs have been established in the Shendong mining district and 95% of the water used for industrial, domestic, and ecological uses in the mining area is provided in this way, which greatly reduces the cost of purchasing and transporting water (Gu 2015; Song et al. 2020).
Figure 1
Sketch map of underground water reservoirs and mine water utilization (Zhang et al. 2021).
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Sketch map of underground water reservoirs and mine water utilization (Zhang et al. 2021).

Figure 1
Sketch map of underground water reservoirs and mine water utilization (Zhang et al. 2021).
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Sketch map of underground water reservoirs and mine water utilization (Zhang et al. 2021).

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The present situation of underground water reservoirs is still in the early stages. Based on the investigation of the hydrogeological conditions and operation management of the Dagu River underground reservoir, a new assessment system for the operation effects of the underground reservoir was established by Li et al. (2019). Taking Bulianta coal mine as the research background, a discrete element fluid–solid coupling numerical simulation model was constructed to analyze the development characteristics of mining-induced fractures after coal seam mining, and the water replenishment channel of the coal mine underground reservoirs was determined by Chi et al. (2022). How to accurately assess the storage capacity of an abandoned coal mine is considered an urgent problem to settle for extending the technology (Li et al. 2019; Zhang et al. 2021). Mining scope and overburden destruction are important considerations in the storage capacity forecast (Wang et al. 2018; Song et al. 2020), but the effect of the compaction characteristics of broken rock mass and coal seam dip angle are ignored in most predictive models. The result is, in current practice, that most predictive models do not perform well. In this study, prediction models of underground water storage capacity in a flat seam mining district and inclined mining district are established, respectively, and the compaction characteristics of broken rock mass are introduced based on laboratory experiments. Furthermore, the accuracy of the prediction model is verified by engineering practice. Finally, the effects of different factors, i.e., porosity of broken rock mass, water storage height and coal seam dip angle, are discussed. This study can provide helpful guidance for site selection and construction of underground water reservoirs.

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The water storage capacity of an underground abandoned coal mine depends critically on the damage characteristics of the roof strata after coal mining (Wang et al. 2018; Chi et al. 2022). Along the horizontal direction, on the basis of the displacement angle and the boundary angle, as shown in Figure 2, the roof strata movement and fracture can be described using three zones, i.e., in-situ stress zone, coal pillar supporting zone and re-compaction zone (Palchik 2003). Meanwhile, along the vertical direction (Figure 2), the roof strata movement caused by the underground mining can be divided into three distinct zones (caved zone, fractured zone and bending zone, ordered from bottom to top) according to their fracture development characteristics (Fan et al. 2022). In the caved zone, rock strata fall to the mine floor not only completely broken into irregular shapes of various sizes, but also with extremely strong permeability due to the disorganized distribution of fractures (Palchik 2003). Above the caved zone is the fractured zone, in which strata are mainly destroyed by horizontal fractures and through-going vertical fractures (Wei et al. 2017). The bending zone above the fractured zone moves downward without apparent breaking. However, the cracks in the surface layer may also result in flow loss (Figure 2).
Figure 2
Overburden destruction and water migration triggered by underground coal mining.
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Overburden destruction and water migration triggered by underground coal mining.

Figure 2
Overburden destruction and water migration triggered by underground coal mining.
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Overburden destruction and water migration triggered by underground coal mining.

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The combined height of the caved zone and the fractured zone is the water flowing fractured zone (WFFZ) in which water can flow through. The water flowing fractured zone contains the majority of the void volume and has most of the water-conducting channels (Palchik 2003). If the height of the WFFZ penetrates the aquifer, i.e., the aquifuge is destroyed, water from the phreatic aquifer and surface flow into the working panel (Kim et al. 1997; Karaman et al. 2001; Liu et al. 2022), causing enormous pressure for the mine water drainage system and the eco-geological environment degradation problem on the surface (Figure 2). The change of abandoned underground void space into underground mine water storage area can effectively ameliorate and even eliminate local eco-geological environment risks, and also saves the costs of mine water drainage (Zhang et al. 2021).

The underground water storage area is realized through connecting the independent coal pillar dam in the goaf by the construction of an artificial dam. According to production practices and the research results of engineering geology and hydrogeology at China's coalfields, there are some factors that directly affect the water storage capacity of an underground reservoir under normal conditions. (1) Mining thickness: this index reflects the effect of the underground excavation height on the stress redistribution and fracture of the roof rock mass (Li et al. 2014; Fan et al. 2022). (2) Mining area: this index reflects the basal area of the underground reservoir. Meanwhile, larger-scale coal mining will have a greater degree of roof rock fracturing according to some research (Wang et al. 2018). (3) The strength of the dam: this index reflects the highest water storage height of the underground reservoir (Yao et al. 2019). (4) Porosity of the broken rock mass: within the water storage area, as shown in Figure 3(b), the broken rock mass is compacted under its own weight and overburden load from the upper strata group (Palchik 2003; Fan et al. 2022), and the porosity or storage volume decreases with the increase of compressive time and stress (Figure 3(c)), which leads to water storage capacity loss (Figure 3(d)). The minimum porosity of the broken rock mass determines the smallest capacity of water storage, and its value must be determined at the design stage. However, the compaction characteristics of the broken rock mass are not sufficiently considered in current practice. (5) Coal seam dip angle: this index is mainly a determining factor of the shape of the underground reservoir, and its effect is also rarely considered in current practice.
Figure 3
Sketch map of the storage capacity loss of underground water reservoirs in a mining district (modified after Zhang et al. 2021).
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Sketch map of the storage capacity loss of underground water reservoirs in a mining district (modified after Zhang et al. 2021).

Figure 3
Sketch map of the storage capacity loss of underground water reservoirs in a mining district (modified after Zhang et al. 2021).
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Sketch map of the storage capacity loss of underground water reservoirs in a mining district (modified after Zhang et al. 2021).

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Storage capacity of reservoir in horizontal mining district

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They are two important parameters required for the calculation of underground water storage capacity, i.e., the boundary of the fracture-rich zone and porosity of the broken rock mass, as Figure 4 shows. In three-dimensional space, the mining-induced fracture-rich zone, i.e., the main water storage area of the underground reservoir, presents a ‘trapezoidal’ type after flat coal seam mining (Wei et al. 2017). In the vertical direction, the water storage area includes three zones, i.e., goaf, caving zone and the fractured zone (Figure 5(a)). For a specific overburden of a coal mine panel, the boundary and sectional area of the water storage area can be determined according to the geometrical relationship as Figure 5 shows.
Figure 4
Flowchart of the methodology.
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Flowchart of the methodology.

Figure 4
Flowchart of the methodology.
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Flowchart of the methodology.

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Figure 5
Sketch map for calculation of water storage capacity in horizontal mining area.
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Sketch map for calculation of water storage capacity in horizontal mining area.

Figure 5
Sketch map for calculation of water storage capacity in horizontal mining area.
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Sketch map for calculation of water storage capacity in horizontal mining area.

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As for the porosity of the broken rock mass, this parameter is affected by many things such as fall height, size and shape of rock mass, rock lithology and strength, and even loading stress and the elapsing of time (Guo et al. 2002; Palchik 2003; Liang et al. 2016). It is an expensive, time-consuming and challenging task to measure on-site the porosity of all broken rock within the mining-induced fracture-rich zone. Estimating the porosity of the broken rock mass according to the fracture and distribution characteristics in the post-mining overburden is a more practical way. In a specific coal mine panel, practice has proven that the value of porosity decreases along the vertical direction from bottom to top, and the value of porosity decreases to 0 at the top interface of the WFFZ (Guo et al. 2002). The values of porosity are basically the same at the same height level. In other words, the broken rock mass at different distances from the mining seam has different porosity characteristics. Guo et al. (2002) and Liang et al. (2016) proposed that the variation of porosity of the broken strata can be well described by a logarithmic function in flat coal seam mining, as follows:
(1)
where h is the burial depth of the overlying stratum; γ is the gravity density of the rock layer; c′, d′ are coefficients.

Storage capacity of goaf in horizontal mining district

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The coal goaf area has the maximum value of porosity of the broken strata according to the foregoing analysis. In addition, the coal goaf area is rectangular. So, the coordinate origin is chosen at the center of the goaf. The x-direction is the advancing direction of the working panel; the y-direction is the inclined direction of the underground reservoir; and the positive z-direction is straight up. In this coordinate system, the values of porosity at the same level are assumed to be the same. According to Equation (1), the equation of porosity of the broken strata e(z) is as follows:
(2)
where H is the burial depth of the coal floor; c′, d′ are coefficients.

The coefficients of Equation (2), i.e., c′ and d, can be obtained through the two data of porosity and thus the porosity of broken strata at other locations in the WFFZ can be predicted according to e(z). In addition, the porosity of the broken strata at the top interface of the WFFZ is 0, and the height of the WFFZ is readily accessible. So, it only takes one other datum of porosity to solve the coefficients of Equation (2).

When 0 < hw ≤ M (hw is the height of the mine water and M is the mining thickness), the goaf area begins to store water. Considering the shape of the goaf, the actual water storage volume Vg of an underground reservoir in a coal mine can then be calculated as follows:
(3)
where Swg is the horizontal cross-sectional area of the goaf zone, and can be calculated as follows:
(4)
where Lgx is the length of the goaf zone; Lgy is the width of the goaf zone.

Storage capacity of WFFZ in horizontal mining district

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When M < hw ≤ (M + hc + hf), the goaf zone is fully filled with water, and the caving zone and even the fractured zone begin to store water. The water storage volume Vc of an underground reservoir in a coal mine can then be calculated as follows:
(5)
where Swc is the horizontal cross-sectional area of the caving zone or fractured zone, and can be calculated as follows:
(6)
where Lwx is the length of the caving zone or fractured zone; Lwy is the width of the caving zone or fractured zone; α and β are the caving angle of the rock strata.

In addition, the parameters is of hc, hf, α and β are generally determined by field measurements or regional experience.

Storage capacity of reservoir in inclined mining district

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The foregoing analysis reveals the prediction method of water storage capacity in a horizontal mining district. However, the majority of coal resources are inclined seams, and the inclined angle has a great impact on the distribution of water, which may decrease the accuracy of the above model. Hence, it is necessary to find a method in which the inclined angle has been taken into account.

The failure zone of overburden caused by nearly flat coal mining is similar to an inverted funnel (Sun et al. 2021). In an inclined mining district, as shown in Figure 6, the water storage area can be divided into three parts along the mining direction, one rectangle and two triangles. Along the mining direction, the length of rectangular part lwx1 can be calculated as follows:
(7)
where θ is inclined angle of the coal seam; and the lgx can be calculated as follows:
(8)
Figure 6
Sketch map for calculation of water storage capacity in an inclined mining district.
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Sketch map for calculation of water storage capacity in an inclined mining district.

Figure 6
Sketch map for calculation of water storage capacity in an inclined mining district.
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Sketch map for calculation of water storage capacity in an inclined mining district.

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So, the water storage volume V1 of the rectangular part can be calculated as follows:
(9)
For the second part of the water storage area, the length along the mining direction lwx2 can be calculated as follows:
(10)
The water storage volume V2 of the second part can be calculated as follows:
(11)
The third part of the water storage area is above the caving zone, and the height of this part h3 satisfies the following equation:
(12)
Further, substituting Equation (7) into Equation (12) and simplifying it:
(13)
The length of the third part of the water storage area along the mining direction lwx3 can be calculated as follows:
(14)
The water storage volume V3 of the third part can be calculated as follows:
(15)
So, the actual water storage volume Vc of an underground reservoir in a coal mine can then be calculated as follows:
(16)
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Background

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The Lijiahao coal mine is located in the southeast part of Ordos city, Inner Mongolia Autonomous Region. The production capacity and service life of this coal mine are 6.0 Mt/a and 80 years, respectively. The eco-geological environment in this area is all too fragile and prone to be destroyed by high-intensity underground mining. To reduce the conflict between efficient coal mining and underground water loss, taking the mining-induced broken zone of No. 31108 and No. 31109 working face as water storage space, an underground water storage reservoir has been constructed. In this area, the coal mining seam has an elevation of about −256.19 m and the original structure is simple. The average mining thickness is 3.3 m, with average dip angle of 1.7°. The width and length of the water storage area are 581.3 m and 3,338.3 m, respectively. The roof of the coal mining seam is mainly sandstone and sandy mudstone The thickness of the caving zone and fractured zone is 19.8 m and 75.9 m (i.e., hc = 19.8 m, hf = 75.9 m) according to field measurements, respectively. In addition, the limit water head value of the artificial dam and coal pillar dam is 13.5 m according to the field test (Ju et al. 2017).

Minimum porosity of broken rock mass

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Gradation of the broken rock mass

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The gradation has a significant effect on the compaction behavior of the broken rock mass (Makedon et al. 2009). Accurate description of the gradation curve is one of the most important premises for researching the quantitative relationship between the porosity and the gradation of the broken rock mass. Quite a few models have been proposed to quantitatively describe the gradation curve (Wu et al. 2020). In this study, the samples are designed by the gradation equation model of Zhu et al. (2018), as shown in Equation (17):
(17)
where P is the percentage passing; b and m are parameters; dmax is the maximum grain size; and d is the grain size.
As mentioned above, the porosity of broken rock is an important parameter for predicting the volume of an underground reservoir. Equation (2) shows that the broken rock at the goaf center has the minimum porosity. However, it is a challenging task to measure on-site the porosity of the broken rock at the goaf center. So, in this study, 32 groups of gradation curves were designed according to Equation (17) (Figure 7), and the optimum grade curve, i.e., the minimum porosity of the broken rock, was determined by a compression test. In the test, the fresh broken rock mass used was the sandstone collected from the immediate roof of Lijiahao coal mine in China. Using a roller crusher, the rock mass was broken into particles with a diameter of 60 mm, and the particles were further crushed by a hammer. Then, the rock particles were screened by grading sieves. Finally, corresponding original gradation curves were designed, as shown in Figure 7.
Figure 7
Gradation curves of broken rock mass in this test.
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Gradation curves of broken rock mass in this test.

Figure 7
Gradation curves of broken rock mass in this test.
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Gradation curves of broken rock mass in this test.

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Testing apparatus

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A self-built instrument, as shown in Figure 8, was used in this experimental study. This large-scale compression apparatus mainly includes a steel column, cylinder, chassis, steel plates and steel balls between the steel plates. The cylinder has dimensions of 395 mm (in height) × 185 mm (in diameter). The compressive stress is provided by a servo-testing machine with a maximum capacity of 19 MPa, and the velocity of the loading force is 1 kN/s. The axial loading force is determined by load transducer, and the maximum axial force reached is 12 MPa.
Figure 8
Experimental equipment: (a) the physical diagram; (b) schematic of the internal structure.
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Experimental equipment: (a) the physical diagram; (b) schematic of the internal structure.

Figure 8
Experimental equipment: (a) the physical diagram; (b) schematic of the internal structure.
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Experimental equipment: (a) the physical diagram; (b) schematic of the internal structure.

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The test sample was a dry broken rock sample, and the test was carried out at room temperature. To remove moisture from the broken rock sample, the broken rock sample was dried in a drying oven before the test (the internal temperature of the drying oven was 50 °C, and the drying time was 2 h).

Test results and analysis

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A given gradation of broken rock mass only corresponds to one minimum porosity, so there is a mathematical relationship between gradation and minimum porosity (Wu et al. 2020). In other words, the porosity of the broken rock mass can be predicted by the characteristics of the gradation curve. In previous studies, the area surrounded by d = dmax, d = dk = 0.075 mm and the gradation curve is often used as a parameter, S, to represent the characteristics of the gradation curve (Figure 9).
Figure 9
Gradation curve area of the sample.
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Gradation curve area of the sample.

Figure 9
Gradation curve area of the sample.
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Gradation curve area of the sample.

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According to Equation (17), S can be deduced as follows:
(18)
where k is the percentage when d = dk, and in this study, dk = 0.075 mm.
As Figure 7(c) shows, broken rock mass with different maximum grain size, dmax, is considered in this test. So, a new parameter, p, is introduced to describe the characteristics of the gradation curve in this test as follows:
(19)

The p of the broken rock mass was calculated according to Equation (19), and the minimum porosity, emin, of the sample was summarized according to the test results.

Based on the mathematical statistics, as shown in Figure 10, the relationship between emin and p is a quadratic function. The emin of broken rock mass rapidly decreases at higher p value if the p less than 0.314. The emin of the sample in this test reaches 0.276 when the p is 0.071, while emin decreases to a minimum of 0.117 when p is 0.314. However, when p ranges from 0.314 to 0.608, emin increases at higher p value. The emin is 0.324 when p further increases to 0.608. This indicates that there is a best compaction property of broken rock mass, i.e., a minimum value of emin at a certain value of p. As shown in Figure 10, the fitting formula between emin and p can be expressed as:
(20)
Figure 10
Variations of minimum porosity with variable p.
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Variations of minimum porosity with variable p.

Figure 10
Variations of minimum porosity with variable p.
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Variations of minimum porosity with variable p.

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The determination R2 coefficient of the fitting formula is 0.939, indicating that the minimum porosity of broken rock mass can be well predicted by Equation (20). The minimum value of emin is 0.121 according to Equation (20), which can be considered the porosity of the broken rock mass at the center of the goaf.

Calculation and validation

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Firstly, according to laboratory experiments and Equation (20), the minimum porosity of broken rock mass at the center of the goaf is 0.121, i.e., e(z = 0 m) = 0.121. Furthermore, at the top of the fractured zone, the porosity narrows almost to 0, i.e., e(z = 99 m) = 0. Then the coefficients of Equation (2) are solved out.

Secondly, the height of the mine water is 13.5 m, while the mining thickness is 3.3 m, and the water storage area includes the goaf area and caving zone. In addition, the dip angle is 1.7°. So, the water storage volume Vc of this underground reservoir should be calculated by Equation (16). The water storage volume is 195,922.5 m3.

Mining engineers of the Lijiahao mining district had conducted a drainage experiment after injecting mine water into the goaf. When the height of the reservoir water storage is 13.5 m, the volume of water discharged is 185,759 m3. The relative error of the theoretical calculation and the measured values is only 5.5%, indicating the suitability of the proposed model.

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In fact, water resources protection in arid and semi-arid regions has always been an important issue that needs to be solved. As a new type of hydraulic structure, underground reservoirs use abandoned goaf to store mine water, which has the characteristics of no land occupation, large storage capacity and small evaporation loss. Underground reservoirs allow for the rational allocation of water resources to meet the needs of coal enterprises in water-scarce areas. At the beginning of the construction of underground reservoirs in abandoned goaf, it is necessary to design the storage capacity to ensure that the water level and storage capacity of the underground reservoir remain within the safe range, so that the underground reservoirs are safe and reliable. The existing research results have been mainly based on empirical formulae, numerical analysis or actual monitoring of mine water inflow (Zhang et al. 2021). These studies often simplify the actual complex and changeable field conditions into a single assessment parameter, and lack of knowledge regarding the choice of important assessment parameter results in difficulties in assessing and designing the storage capacity of underground reservoirs. For example, the parameter of storage coefficient is widely used in the evaluation of reservoir volume in practical engineering applications (Wang et al. 2018; Song et al. 2020; Zhang et al. 2021), which is the comprehensive reflection of reservoir morphology, porosity and water storage height. However, there is no accurate and concrete formula for calculating a storage coefficient, which makes it impossible to determine the storage capacity reasonably (Wang et al. 2018; Song et al. 2020).

A theoretical framework of a storage capacity analytical method for an underground reservoir, which takes a full account of geological and mining conditions, is the focus of the current research. Based on this research gap, this study simplifies the WFFZ into a trapezoidal body, and solves the underground reservoir capacity of horizontal and inclined coal seams with porosity as the intermediate quantity. On this basis, the model in this study organically combines the geological conditions and mining conditions, i.e., mining thickness, mining area, porosity of broken rock mass, coal seam dip angle and the development of the WFFZ. The model is more accurate and credible in the process of practical application due to calculation parameters that are much easier to access and choose. In addition, the model in this study can be used to analyze the impact of different physical parameters on water storage capacity of underground reservoirs from the perspective of quantification.

Effect of porosity on water storage capacity

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To eliminate the influence of the porosity of broken rock mass on the underground water storage capacity, taking the underground water storage reservoir of Lijiahao mining district as the research background, only the porosity value of broken rock mass at the center of the goaf is changed and other parameters are kept constant, and the relationship between porosity value and water storage capacity are obtained according to the proposed model (Figure 11). With the increase of porosity value of broken rock mass, the water storage capacity increases gradually. So, an abandoned mine with a large porosity of broken rock mass is a wise site choice for an underground reservoir.
Figure 11
Water storage capacity of the underground reservoir versus porosity.
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Water storage capacity of the underground reservoir versus porosity.

Figure 11
Water storage capacity of the underground reservoir versus porosity.
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Water storage capacity of the underground reservoir versus porosity.

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Effect of storage height on water storage capacity

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Similarly, the relationship between water storage height and water storage capacity has been obtained according to the proposed model. Significantly, the dip angle is 1.7° for all the cases.

As depicted in Figure 12, the storage capacity of the underground reservoir increases with water storage height. When water storage height ≤10 m, the increase amplitude of storage capacity of the underground reservoir is not obvious with the change of water storage height. When water storage height >10 m, the change of water storage height has a great influence on water storage capacity. However, the water storage height of an underground reservoir depends on the strength and thickness of the artificial dam, and greater strength and thickness of the artificial dam mean higher average investment. In practice, the highest head value of an artificial dam and coal pillar dam is less than 20 m in general (Yao et al. 2019). It is a challenging and expensive option to increase the storage capacity of the underground reservoir by enhancing the water storage height.
Figure 12
Water storage capacity of the underground reservoir versus water storage height.
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Water storage capacity of the underground reservoir versus water storage height.

Figure 12
Water storage capacity of the underground reservoir versus water storage height.
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Water storage capacity of the underground reservoir versus water storage height.

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Effect of dip angle on water storage capacity

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Wide variations in dip angle also exist in different areas. However, the effect of dip angle on water storage capacity is seldom considered in previous studies. According to the proposed model in this study, the underground water storage capacity with different dip angles is presented in Figure 13. Significantly, the maximum height of the water allowed to be stored is 13.5 m for all the cases.
Figure 13
Water storage capacity of the underground reservoir versus dip angle.
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Water storage capacity of the underground reservoir versus dip angle.

Figure 13
Water storage capacity of the underground reservoir versus dip angle.
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Water storage capacity of the underground reservoir versus dip angle.

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At the same water storage height, the results in Figure 13 indicate that the angle of the underground reservoir has a marked impact on the water storage capacity. The value of water storage capacity decreases with the increase of dip angle value. The water storage capacity attenuates largely before the dip angle reaches 1°, and then tends toward stability with increasing dip angle. The water storage capacity of the underground reservoir reaches a maximum of 2,990,954.4 m3 when the dip angle is 0°, while the value of water storage decreases to 353,260.3 m3 when the dip angle increases to 1°. The change of the water storage capacity of the underground reservoir is 88.19% when the range of the dip angle is from 0° to 1°. That can explain the shape and sectional area of underground reservoir decreasing considerably as dip angle increases. Although the maximum height of the water allowed to be stored in an underground reservoir, which depends on the strength of the dam, can be different at different dipping angles in actual engineering, the results in Figure 13 suggest that the dip angle should be the principal consideration in choosing the site of an underground reservoir.

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Underground water reservoirs provide a new and efficient method of achieving green mining and sustainable development in ecologically fragile mining districts. In this paper, the prediction model of water storage capacity was researched in detail based on laboratory experiments, theoretical calculation and field verification. The main conclusions are summarized as follows.

  • (1)

    For a specified water storage height, the storage capacity of underground reservoirs depends on the shape of the underground reservoirs and the distribution of porosity. Through simplifying the shape of the WFFZ into a trapezoid, the prediction model of underground water storage capacity in a flat seam mining district and inclined mining district are established through an empirical equation of porosity of the broken strata.

  • (2)

    Taking Lijiahao underground reservoir as an example, the compaction characteristics of broken rock mass are introduced based on laboratory experiments. The porosity of the broken rock mass (emin) shows a parabolic curve relationship with the characteristic parameter of the gradation curve (p). The emin of the broken rock mass can be well predicted by the fitting curve. The minimum value of emin is 0.121 in Lijiahao coal mine, which is considered to be the porosity of the broken rock at the goaf center. The predicted and experimental results of water storage capacity are 195,922.5 m3 and 185,759 m3 respectively. Measured results indicate that the error between predicted and measured values is only 5.5%. The validation and correctness of the prediction model is demonstrated.

  • (3)

    The effect of different physical parameters on the water storage capacity of underground reservoirs is researched based on the background of Lijiahao underground reservoir. The storage capacity of underground water storage is positively regression correlated with the porosity of broken rock mass and water storage height, and negatively regression correlated with the coal seam dip angle. The coal seam dip angle should be the principal consideration in choosing the site of an underground reservoir, because a small increase of the dip angle could lead to a significant decrease in the water storage capacity of the underground reservoir.

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Financial support for this work is provided by the Central Public-Interest Scientific Institution Basal Research Fund (No. Y320010) and Natural Science Foundation of Jiangsu Province (BK20190646).

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All relevant data are included in the paper or its Supplementary Information.

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The authors declare there is no conflict.

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