Introduction

China is one of several countries faced with mitigating the threat of water-related coal mining disasters. As the average depth of coal mining in China has increased, safe production is increasingly threatened (Dong 2010; Hu ; Jin et al. 2013; Wu 2014; Wu et al. 2013; Xu et al. 2012). With greater water pressure on coal seam floors, water flowing in mining-induced fractures and mine tunnels can easily become connected to high-pressure karst water in these floors (Dong and Hu 2007). This can lead to major water inrush accidents, resulting in multiple casualties and significant economic losses. At present, efforts to prevent and mitigate major coal mine-related water inrush disasters rely on the detection, prediction, and monitoring of w2013ater inrush threats (known as the “three-detection technology”) and geophysical prospecting, drilling, and chemical prospecting (Lian et al. 2014). According to Liu et al. (2014), the parameters of multi-technology should be analyzed together to predict and prevent mine water disasters.

The prediction of mine water inflow rates and the estimation of water volumes of abnormal bodies (mainly karst water and goaf water) in the vicinity of mining are important steps in determining the likely risk of mine-related water disasters. Much research has been done worldwide on the prediction of mine water inflow. The main approaches that have been adopted include numerical methods, analytical methods, and neural network methods (Lian et al. 2014; Yang and Chen 2009). The results yielded by these have an average margin of error of more than 200 % when compared with the actual measured data. Meanwhile, direct current (DC) resistivity and transient electromagnetic method (TEM) have proven successful in estimating water volumes in abnormal bodies (Benkabbour et al. 2004; Danielsen et al. 2003; Jiang et al. 2010; Yu et al. 2007a, b; Yue and Li 1997). However, given the multiplicity of solutions obtained with different geophysical methods, it is likely that errors will be incurred where a single method is used to estimate the amount of karst mine floor water. This could, in turn, lead to the incorrect use of these data. Geophysical mine interpretation is still in the qualitative research phase and quantitative mine interpretation studies are rare. To reduce the uncertainty associated with the application of a single predictive technology or geophysical method, this study used an integrated set of geophysical methods (the DC resistivity method, TEM, and the seismic scattered wave imaging method) to investigate the relationships between geophysical parameters and the groundwater flowing along the coal seam floor (or the water in an abnormal body). The estimates of water quantity along the coal seam were tested using the measured data. This approach should contribute considerably to the prediction of mine water inrush and the prevention and mitigation of mine water disasters.

The quantitative relationships between water volume and electrical parameters (apparent resistivity and primary field current) have been established by experimentation (Liu et al. 2010, 2013), and form the foundation for this research. Based on an integrated set of geophysical methods and a knowledge of the characteristics of groundwater in karst settings, a physical model of seam floor water in limestone was constructed. Based on this model, seam floor water volumes were quantitatively modeled in terms of geophysical parameters. This quantitative model, populated with experimental data collected in the field, was then used to predict seam floor water volumes.

Design of Physical Simulation

A physical simulation model of a coal seam was built in accordance with the theory of similarity and simulation (see Supplemental Fig. 1). Details regarding materials used in the model’s construction are presented in Supplemental Table 1. A square water tank (30 cm long, 15 cm wide, and 40 cm high), representing an abnormal body, was built into the middle of the physical model. The profile lines necessary for the DC resistivity method and the receiver coils required by the TEM were embedded into the model during construction.

DC Resistivity Method

The observation system arrangement for the DC resistivity survey is shown in Supplemental Fig. 2. Lines 1 and 2 were on the edge of the model. The horizontal distance between line 1 and the water tank boundary was 18 cm, and the horizontal distance between line 2 and the water tank boundary was 28 cm. There was a height difference of 14 cm between lines 1 and 2, and 64 electrodes were mounted along each line. Each line was 126 cm long, and the distance between adjacent electrodes was 2 cm. The electrodes were made of copper wire (0.5 mm diameter). A parallel network instrument (hereafter referred to by its Chinese abbreviation, WBD (Liu et al. 2007) was used for data acquisition. WBD has two acquisition modes—AM and ABM. AM allows for the collection of all pole–pole and pole–dipole array data, whilst ABM allows for the collection of all of the four electrodes array data, such as Wenner array, dipole–dipole array and Schlumberger array. The acquisition mode selected was ABM (Liu and Zhang 2006); the duration of charge was 0.2 s, the sampling interval was 100 ms, and the service voltage was 96 V. The DC electrical survey data were collected four times: when the water tank was injected with 0, 6, 10, and 16 L of water, respectively.

Transient Electromagnetic Method

On the physical model, coils 1# and 2# were arranged symmetrically facing the water tank. Their spatial position is described in Fig. 1 (the green coil represents the receiving coil and the red coil represents the transmitting coil). A YCS 360 multichannel TEM instrument, which is manufactured in China, was used for data acquisition. The acquisition and coil parameters are presented in Tables 1 and 2. The TEM data were collected when the water tank was injected with 0, 5.71, 9.08, and 14.23 L of water, respectively.

Fig. 1
figure 1

Observation system arrangement with respect to transient electromagnetic method. a Vertical view, b side view, c first injection, d second injection, e third injection

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Table 1 Acquisition parameters with respect to transient electromagnetic method
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Table 2 Coil parameters with respect to transient electromagnetic method
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Seismic Scattered Wave Imaging Method

The seismic survey line was 90 cm long. It was mounted on the long side of the model, 10 cm from the top. The horizontal distance from the line to the water tank was 30 cm. Head and tail sensors were placed 15 cm from either end of the line, respectively. Six adjacent sensors were glued to the side of the model at 12 cm intervals along the line. Thirty-one shot points were stimulated at 3 cm intervals from the left of the line. The observation system arrangement with respect to the seismic scattered wave imaging method is depicted in Fig. 2.

Fig. 2
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The observation system arrangement with respect to seismic scattered wave imaging

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A DH5920N dynamic signal system was used for seismic data acquisition by a DH187 acceleration sensor. The source of the shots was a low capacity air gun. Each shot emitted the same amount of energy. The sampling frequency was 1 MHz, the sampling duration was 8 K, and the delay duration was 1 K.

Physical Model Data Analysis

Analysis of DC Resistivity Survey Data

Apparent DC resistivity was assessed at a range of tank water volumes along two lines. Mean apparent resistivity was calculated for each line spanning the cross-sectional area of the water tank. This was achieved by processing data from three different Wenner arrays (i.e. alpha, beta, and gamma). Next, it was assessed whether there was a correlation between the water volume and the apparent resistivity mean measured at the cross section of the tank (see Fig. 3). Analysis of the data for both lines 1 and 2 revealed that as the water volume increased, the apparent resistivity mean gradually decreased. Through mathematical fitting, the relationship between water volume and the apparent resistivity mean can be expressed as follows:

$$\rho_{s1} = - a_{1} \cdot \ln Q + b_{1}$$
(1)

where ρ s1 (Ω·m) is the apparent resistivity mean obtained through the DC resistivity survey, Q (ml) is the volume of water in the tank, and a 1 and b 1 are constants. For the physical simulation, a 1 = 1.256–3.837, and b 1 = 46.185–99.216, with R 2 = 0.3868–0.8429.

Fig. 3
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Water volume versus apparent resistivity mean according to DC resistivity survey

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Analysis of Data Obtained Through the Transient Electromagnetic Method

Figure 4 depicts the induced voltage decay curves for the secondary fields of coils 1# and 2#. We found that the induced voltages were at a minimum when the water tank contained no water, and after t = 342.4 μs. As the volume of water in the tank increased, the induced voltage decay curves for the secondary fields of both coils 1# and 2# gradually escalated. The increased amplitude of the curve with respect to coil 2# was slightly more marked than that for coil 1#, which implies that the induced voltage of the secondary field of coil 2# was more sensitive to a change in water volume.

Fig. 4
figure 4

The induced voltage decay curves for the secondary fields of coil 1# and coil 2#. a Coil 1#. b Coil 2#

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The variation characteristics of the induced voltage decay curves at points A (coil 1#) and B (coil 2#) were essentially consistent. The induced voltages for observation point B were obtained when the water tank contained no water, and then when it contained 5.7135, 9.0835, and 14.2315 L of water, respectively.

Late-time apparent resistivity values at t1, t2, and t3 were calculated and compared (see Fig. 5). By mathematical fitting of the curve in Fig. 5, the relationship between water volume and the apparent resistivity mean can be expressed as follows:

$$\rho_{s2} = - a_{2} \cdot \ln Q + b_{2}$$
(2)

where ρ s1 (Ω m) is the apparent resistivity mean obtained through the TEM, Q (mL) is the volume of water in the tank, and a 2 and b 2 are constants. For the physical simulation, a 2 = 2.72–4.39, and b 2 = 26.50–39.87, with R 2 = 0.737–0.851.

Fig. 5
figure 5

Water volume versus apparent resistivity for coil 2# (at t1, t2, and t3)

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Analysis of Data Obtained Using the Seismic Scattered Wave Imaging Method

Analyzing wave migration for a common scattering point is mainly applied in the seismic scattered wave imaging. In theory, as long as the seismic record is long enough, the energy of any scattering point in the detection region can be found in any of the channels according to the travel time of its propagation. In exploring scattered wave migration for common scattering points, the detection region is discretized into a grid with cells representing scattering points. The energy of different seismic track records is classified into the grid according to corresponding scattering imaging points, forming the scattered migrated-superimposed signal (Fig. 6).

Fig. 6
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Superimposed signals of scatter migration

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Fractured zones and water-rich areas are often accompanied by changes in lithology. Thus, the scattered migrated-superimposed signals were reprocessed by adopting the relative extremum method, which is used to delineate anomaly boundaries. The scattered migrated-superimposed signals were considered according to their amplitudes in the horizontal direction (prospecting length) and the vertical direction (depth), respectively. The amplitude of every signal (where energy exceeded a fixed threshold) was obtained. The relative extremum relationships between gathers were compared in the horizontal direction, simultaneously, to demarcate the anomaly boundary.

For Fig. 6, the energy threshold was set at 20 % of the maximum energy of each gather signal. In the range of 0–1 ms, the amplitude was registered for each signal when it exceeded this threshold. Each 1 ms signal was divided into ten units of 0.1 ms each. Amplitudes were recorded for each of these 0.1 ms time windows. To eliminate the effects of direct waves, extreme values were normalized. The abnormal body’s boundary delineated by the relative extremum method (where the relative extreme value was >4) is displayed as Fig. 7.

Fig. 7
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Abnormal body’s boundary delineated according to the relative extremum method

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Integrated Geophysical Modeling

From data obtained through the physical simulation exercise, a composite and integrated water volume prediction formula was derived by integrating the relationships and patterns revealed by each of the geophysical methods employed in the simulation (i.e., DC resistivity survey, the transient method, and the seismic scattered wave imaging method).

  1. 1.

    DC resistivity method:

    $$Q = e^{{_{{a_{1} }}^{{b_{1} }} -_{{a_{1} }}^{1} \cdot \rho_{s1} }}$$
    (3)

    where Q is the water volume and ρ s1 is the apparent resistivity (where a 1 = 1.256–3.837, b 1 = 46.185–99.216), with R 2 = 0.3868–0.8429.

  2. 2.

    Transient electromagnetic method:

    $$Q = e^{{_{{a_{2} }}^{{b_{2} }} -_{{a_{2} }}^{1} \cdot \rho_{s2} }}$$
    (4)

    where Q is the water volume and ρ s2 is the apparent resistivity (where a 2 = 2.72–4.39, b 2 = 26.50–39.87), with R 2 = 0.737–0.851.

  3. 3.

    Seismic scattered wave imaging method: the abnormal energy of scattered seismic waves can provide the basis for the delineation of water-bearing spaces. Where lithology is constant, the energy of scattered seismic waves can be used to reveal the existence and extent of abnormal bodies. Using the relative extremum method, the two-dimensional space of abnormity was obtained.

  4. 4.

    The rule of multi-parameter integration: First, there is an exponential relationship between water volume and the apparent resistivity measurements obtained through the DC resistivity method and TEM. Also, rock resistivity is closely related to moisture content and the number/extent of fissures in it. Thus, \(e^{{a + b \cdot \rho_{s} }}\) expresses rock moisture content, where \(\rho_{s}\) is the composite apparent resistivity based on the resistivity measurements obtained through the DC resistivity method and the TEM. The contribution of each of these methods is weighted according to the actual characteristics of a particular mine. This is because that the electrical parameters of the DC resistivity method and the TEM are more sensitive to mine water.

Second, water-containing spaces between crack boundaries in rock strata can be delineated as “abnormal spaces” based on the boundary features of the abnormal energy of seismic scattered waves. Not all cracks are water-containing areas. Low resistivity areas identified by the DC resistivity survey and the transient electromagnetic method could also be explained by changes in mineral composition or particular lithology (such as mudstone) of rock strata. Therefore, the effective water-containing spaces are defined as those where seismically detected “abnormal space” and electrically delineated low resistivity areas overlap.

According to the abovementioned rules of multi-parameter integration, an integrated water volume prediction formula can be expressed as follows:

$$Q = k \cdot e^{{a + b \cdot \rho_{s} }} \cdot V$$
(5)

where Q (m 3) is water volume and k is the correction coefficient determined by water inflow data in mine experimental section (the default is 1); \(e^{{a + b \cdot \rho_{s} }}\) is the rock moisture factor (a and b are constants determined by experimental conditions); V represents water-containing space determined by V SS  ∩ (V DC  ∪ V TEM ),which is the intersection of crack areas identified through seismic detection and low resistivity areas delineated by the DC resistivity and transient EM methods. Where seismic data is lacking, V mainly relies on V DC  ∪ V TEM .

Project Application

Derivation of Formula Constants from Field Data

Because of inevitable differences between the laboratory-based physical model and actual geological settings, the unknown parameters of the water volume prediction formula described above were determined using data collected in the field, with the hope of improving the overall accuracy of the quantitative model. Thus, parameters a and b were derived using data collected in a mine in the Huainan mining area between 2011 and 2012.

A DC resistivity survey of a limestone water discharge channel at a depth of 490 m was completed in March 2011. Very little groundwater drainage had been done at that stage, which meant that the low resistivity areas identified by this survey constituted a reliable reflection of true water-bearing zones in the limestone matrix. Seismic data were collected in 2012, but the time difference is considered negligible as seismic survey results of abnormal body’s boundary are not significantly influenced by changes in water discharge. A TEM survey was also completed in 2012, but its results were seriously affected by water discharge, and were thus not considered suitable for use in deriving a composite water volume prediction formula. Thus, the water-containing space V was determined using the results of only the DC electrical resistivity survey and the seismic scattered wave method.

The relationship between the three-dimensional water-containing space and the two-dimensional cross-sectional area S is calculated as follows (assuming that the water-containing space is a sphere):

$$V \approx S^{2/3}$$
(6)

where V is the water-containing area and S is the cross-sectional area.

Nine water-containing areas were delineated in the field study. After calculating the mean apparent resistivity (according to the DC resistivity survey method) of the water-containing areas, the following integrated water volume prediction formula was derived:

$$Q = k \cdot e^{{0.69704 - 0.363\rho_{s} }} \cdot V$$
(7)

where Q (m 3) is water volume, ρ s (Ω m) is apparent resistivity, and k is a correction constant. Figure 8 shows the graph of Q/QV.Vand the apparent resistivities of the nine water-containing spaces identified along the 490-m-deep groundwater discharge channel. The marks Ve-1, Ve-2, Ve-3, Ve-4, Vw-1, Vw-2, Vw-3, Vw-4, and Vw-5 stand for the names of different water-containing space in Fig. 8.

Fig. 8
figure 8

Q/V and apparent resistivity of groundwater discharge channel measured in the field

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Testing of the Quantitative Model

Using Eq. 7, the water volumes of six abnormal water-containing areas along the east limestone water discharge tunnel (at a depth of 580 m) were predicted. Because of the influences of water discharge, the resistivity of the discharge tunnel at a depth of 490 m was less than that of the tunnel at a depth of 580 m east of the limestone water discharge roadway. Thus, the water volumes predicted for the −580 m section were generally inflated, leading to an adjustment of the correction coefficient to k = 0.25. Table 3 shows the parameters used to predict the water volumes of water-bearing areas along the −580 m eastern limestone water discharge roadway. The predicted water volumes were consistent with actual groundwater inflows, and agree with actual measured water volumes. The average accuracy of the predicted water volumes was 75.8 %. A comparison of the predicted and actual water volumes (Q P and Q 0) is presented in Fig. 9.

Table 3 Parameters used to predict water volumes of abnormal bodies along the −580-m eastern limestone water discharge roadway
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Fig. 9
figure 9

Comparison between predicted and actual water volumes (Q P and Q 0)

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Conclusion

In summary, this paper presents a method to quantitatively predict mine water inflow and water volumes in abnormal bodies. This new integrated approach takes the form of a quantitative model derived through multi-parameter integration following the simultaneous application of several relevant geophysical methods. It is important to adjust the predictive formula based on field data for a specific site, because the valid application region of the equation is limited by mine geology characteristics. The experimental apparatus should be improved and modified in the future by accounting for the complex geological conditions of the mine. It is necessary to consider the influences of lithological variations, such as fractures, porosity, and mineral composition. The comprehensive geophysical characteristics of coal, sandstone, mudstone, and limestone, which are affected by mine water, should also be analyzed and compared. Comprehensive geophysical modeling is mainly depended on the detection of floor limestone water in the Huainan mining area. The quantitative formula should be further corrected when used in other mining areas based on the specific geological conditions. It would also be good to improve the design of the physical model to maximize the applicability of the theoretical prediction formula derived from it.