1 Introduction

China is the biggest coal producer in the world where some of the most serious coal mine groundwater disasters have been recorded (Jin et al. 2011; Wu et al. 2013; Huang et al. 2014). An increasing number of coal mines in North China focus their operations on the coal seams present in the Lower Carboniferous formations. In many of these mines, it is expected that the risk of water flowing from the Ordovician confined limestone aquifer through the floor of overlying excavation to be significant during mining (Zhang 2005; Wu et al. 2011, 2013). The flood hazard is even greater if the aquiclude occurring between the coal seam and the Ordovician confined limestone aquifer is damaged during mining because it may not be able to withstand the water pressure from the aquifer. Therefore, providing a better estimate of the failure depth of a coal seam floor (FDCSF) due to mining is of great significance for avoiding the flooding of the mine and, therefore, assuring a safe and efficient coal production (Zhu et al. 2014).

There are many possible mechanisms responsible for the failure of the coal seam floor during mining and they can be explained by employing (1) the improved Hoek–Brown rock mass strength criterion, (2) the “down three zones theory” (Li 1999), (3) the “down four zones theory” (Shi and Han 2004), (4) the “key strata theory” (Li 1995; Qian et al. 1995), (5) the “thin plate model theory” (Zhang et al. 1997; Zhang 2005), (6) and the “situ tensile fracture and zero failure theory” (Wang and Liu 1993). In addition, recent studies have also made us of some classic methods such as field tests (Li et al. 2013; Zhu et al. 2013; Sun et al. 2013; Liang et al. 2014), numerical and analog simulations (Li et al. 2013), and analytic calculations (Zhang et al. 1997; Zhang 2005; Kumar and Das 2005; Wang et al. 2013). To understand and model the failure process under coal seam floor in different mining areas, researchers have commonly used the basic method of in situ measurements (Tan et al. 2010), laboratory experiment, numerical method, and empirical formulas.

Even though these methods are all important and useful for researching the failure depth of floor strata, there are disadvantages if applied individually (Tan et al. 2010). Furthermore, FDCSF varies from not only one coal field to another but also within different areas of the same coal field due to the complexity of the geological and hydrogeological conditions as well as different mining methods used. The FDCSF values can be affected by many factors (Zhang 2005; Wang and Liu 1993) including mining depth, longwall panels width, mining method, dip angle of the coal seam, mined thickness, lithology, and composite structure at the top and floor (Zhu et al. 2013). Therefore, the most dependent and effective method to determine the FDCSF in such complicated conditions is to combine multiple methods. This approach results in a more reliable FDCSF determination since multiple methods compensate and validate each other and thus can overcome the limitations of any single method. Simultaneously, an appropriate approach to predict FDCSF can also be obtained by comparing results of various methods as well as using FDCSF estimates of different working faces under similar conditions.

Based on the above considerations, we measured the FDCSF in situ with water injection tests at the longwall-mined working face no. 1601 in Nantun Coal Mine, Yanzhou Mining Area, Shandong Province, China. In addition to field testing we used theoretical calculations, empirical formulas, and numerical simulations to model the FDCSF on the first working face of coal seam no. 16 in the same coal mine.

The main objective of this research is to provide a more accurate value for the FDCSF for a flat area at a working face excavated by longwall mining not affected by folds and faults. The main goals of this study are to:

  • apply the four classic methods currently used by many researchers to predict the FDCSF value for the specific conditions in the Nantun coal mine,

  • contrast/compare the results of the four methods and analyze the pros and cons of each method, and

  • obtain the most appropriate FDCSF value at a working face and use this value to propose anew empirical formula that can be used to calculate the FDCSF value for different mining areas.

This study contributes to a better understanding of the failure depth on floor strata during longwall mining by investigating the key parameters to prevent water inrush and thus has implications for implementing preventive measures to address the problem of flooding thus improving both worker safety and mine productivity.

2 Study Area

The Nantun coal mine is located in the southern Yanzhou coal field, which is the main coal production area in the Shandong province, eastern China (Fig. 1). The mine is located in the central south portion of the Yanzhou coal field, covers an area of 51.69 km2, and has an annual coal production of 4.0 million tons. From top to bottom, the stratigraphic succession is comprised of strata of Quaternary, Jurassic, Permian, Carboniferous, and Ordovician age. The main minable coal seams belong to formations of Carboniferous-Permian age. The two coal seams that have been extensively mined are the no. 16 coal seam from the Taiyuan formation (Pennsylvanian) and no. 3 coal seam from the Shanxi formation. The no. 16 coal seam will likely remain one of the most exploited coal seams for the foreseeable future. The mining method employed is longwall with backward extraction. The coal seam has a monoclinal structure with a strike of NEE and NS and a dip of about 2°–12°N. The main faults are divided into three groups with directions of NW, NNW and NE, respectively. The main aquifers consist of gravel in Quaternary, red and medium to coarse-grained sandstone in Jurassic, sandstone in Permian, and limestone in Carboniferous and Ordovician. The Ordovician limestone confined aquifer is responsible for the groundwater-related disasters during the excavation of no. 16 coal seam (Zhang 2005).

Fig. 1
figure 1

Location of nantun coal mine

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The 1601 working face of the no. 16 coal seam was the first to be mined in the southern part of Nantun coal mine. The depth of overburden from surface ranges from 418 to 433 m. The longwall panels are ~200 m wide and up to 830 m long, and the mining area is ~166,000 m2, as shown in Fig. 2. The thickness of the no. 16 coal seam ranges from 0.76 to 1.05 m, with an average of 0.85 m, and its dip angle is 2°–5°. The main roof of the longwall panels consists of a ~10 m-thick, fine-grained sandstone while the immediate roof is the no.10 limestone with a thickness of ~4 m. The immediate floor of the longwall panels consists of mudstone or siltstone and the main floor consists of fine–grained sandstone, shale, limestone and a thin coal seam, and there are mudstones and limestone under the main floor, which lies between the no. 16 coal seam and Ordovician limestone confined aquifer.

Fig. 2
figure 2

Position of test boreholes in no. 1601 working face of Nantun coal mine

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The main confined aquifers under the no. 16 coal seam are the Carboniferous no. 13, the no. 14 limestone, and the Ordovician limestone, the representative strata are shown on Table 5. They are separated by 36, 47 and 68 m-thick aquicludes composed of mudstone, siltstone and fine-grained sandstone. The no. 13 and no. 14 limestone strata are 9 and 8 m thick, respectively. The in situ measured hydraulic conductivity of no. 13 limestone was 2.25–3.82 × 10−5 m/day with a water pressure of 0.5–3.20 MPa and the specific capacity of the no. 14 limestone was 0.000392–0.0138 (l/s)/m and hydraulic conductivity was 0.0000238–0.08817 m/d with a water pressure of 0.6–3.60 MPa. The massive Ordovician confined limestone aquifer was ~800 m thick and had a measured specific capacity of 0.0006–0.506 (l/s)/m and hydraulic conductivity of 0.000343–2.093 m/day and had a water pressure of 5.6 MPa. The Ordovician aquifer is a confined karst aquifer containing an abundant supply of water under high pressure (Zhang 2005), therefore, it is considered the most serious hazard aquifer affect to safe during the no. 1601 working face mining.

3 Methods

3.1 Theoretical Calculations

The theoretical calculations used in this study to estimate the FDCSF employed the (1) stress analysis using the Mohr–Coulomb criteria (Wang et al. 2013), (2) boundary integral formula of semi-plane elastic (Zhu et al. 2007), (3) elastic–plastic theory (Zhang 2005), and (4) ultimate bearing capacity formula with plastic slide (A. S. Vesic). Zhang’s elasto-plastic calculation formula is one of the most popular methods and it was used in this research to calculate the FDCSF value at no. 1601 working face.

3.2 Empirical Formulas

The most common empirical formula for calculating the FDCSF is published in the “Regulations of buildings, water, rail way and main well lane leaving coal pillar and press coal mining” (RoBWRM; National Coal Industrial Bureau 2000) and is calculating the FDCSF value as a function of the depth of mining, dip angle of coal seam, thickness of coal seam, and longwall panels width. However, this formula was derived statistically using limited field data and a variable value for the coal seam depth (ranges from 100 to 1000 m; Wei et al. 2010). In this paper we have employed the principal component analysis to identify the possible factors affecting FDCSF and to establish an updated empirical formula. In addition, a multivariate linear statistical analysis was employed using the FDCSF values obtained at different sites to determine a relationship between the measured FDCSF value and various local factors including depth of mining, dip angle, thickness of coal seam, and longwall panels width like in the RoBWRM. This relationship is expressed in the in Eq. (1).

$$h_{1} = w_{1} H + w_{2} A + w_{3} M + w_{4} L + w_{0}$$
(1)

where, h 1 is the FDCSF, w i is a weight coefficient attributed to each factor, H is the depth of mining, A is the dip angle of coal seam, M is the thickness of coal seam, L is the longwall panels width, and w 0 is the intercept.

3.3 Water Injection Test (WIT)

Several field tests have been performed to determine FDCSF by employing direct and indirect methods. Indirect methods include the stress and strain induction method (Zhu et al. 2013) and geophysical techniques such as acoustic detection method (Cheng et al. 2001), electric resistivity method (Sun et al. 2013), ground penetration radar (Zhang et al. 1997), ultrasonic imaging in the borehole (Zhu et al. 2013), micro-seismic, and seismic wave CT method (Zhang et al. 2006). Direct test approaches include the borehole camera technology (Zhang et al. 2014), and water injection test method (Li et al. 2013). Water injection test in a borehole is the most common and perfected techniques which has widely been used in many coal mines (Tan et al. 2010; Shi et al. 2005). Double end seal leak detection drilling (Patent No. 90225165.1) was applied for the no. 1601 working face as the main method for water injection. This method employs the inflow leak detection at different depths in the borehole using drilling equipment capable of double end seal leak detection, because the injected water would leak through fractures induced by mining pressure in the coal seam floor, as shown in Fig. 3. Water at a pressure of 0.1 MPa was injected through hollow-drill steel into the middle of the detection between the two gasbags, and gas at a pressure of 0.5 MPa was inputted through gas pipes into the two gasbags. Firstly, gasbags were expanded to fix the position, and then the water was injected between the two gasbags. If there were fractures surrounding the borehole, the quantity of water injection decreased by a certain amount which was measured by a water-consumption gauge. Therefore, different leakages were measured with this equipment turn by turn from bottom to top in a borehole. Additional details regarding this method were described previously by Shi et al. (2005).

Fig. 3
figure 3

Schematic of double end seal leak detection in a borehole under coal seam

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3.4 Numerical Simulation

Numerical simulation is a common and useful tool to express the laws of stresses and deformations during mining (Yang et al. 2011; Liu et al. 2015). The available numerous and widely adopted numerical software packages capable of taking into account sophisticated material behaviors (Yang et al. 2011) include FLAC, UDEC/3DEC, ANSYS, COMSOL, and RFPA. RFPA is one of the most widely used numerical software tools employed for rock mechanics calculations (Yang et al. 2007) being particularly suitable for solving nonlinear large deformation problems in geotechnical mechanical engineering and it is widely used in the field of mining engineering, among other fields (Yang et al. 2007). RFPA provides a variety of options for performing the excavation process of mining, stress analysis and failure analysis based on the principle of continuum and damage mechanics. Stress analysis uses the finite element method while damage analysis uses the rule of revised Mohr–Coulomb criterion to calibrate the damaged cell parameters using the method of stiffness degradation and reconstruction (Li et al. 2009; Tang et al. 2002). The mechanical properties of rocks are heterogeneous and vary according to the Weibull distribution (Wang et al. 2012; Yang et al. 2007):

$$w = \frac{m}{{s_{0} }}\left( {\frac{s}{{s_{0} }}} \right)^{m - 1} \exp \left[ { - \left( {\frac{s}{{s_{0} }}} \right)^{m} } \right]$$
(2)

where s is the mechanical parameter (Young’s modulus or strength) of the elements; s 0 is the mean of parameters; m is a homogeneity index, which can be obtained from the statistical distribution of rock mass parameters with value of 1.1, 3, 5 and 7 (Wang et al. 2012; Yang et al. 2007).

4 Results and Discussion

4.1 Theoretical Calculations

Following the plastic sliding theory, Zhang considered a coal seam to be an elastic material and derived a formula shown in Eq. 3 (Zhang et al. 1997; Zhang 2005), which has been widely used in coal mining applications. In the present research, to calculate the FDCSF value for the no. 1601 working face we also employed Eq. 3, as following:

$$h_{1} = \frac{{x_{a} \cos \varphi_{0} }}{{2\cos \left( {\frac{\pi }{4} + \frac{{\varphi_{0} }}{2}} \right)}}e^{{\left( {\frac{\pi }{4} + \frac{{\varphi_{0} }}{2}} \right)\tan \varphi_{0} }}$$
(3)

where x a is the length of failure zone of the coal seam around the mining face (Zhang et al. 1997; Zhang 2005), which can be calculated from Eq. 4, φ 0 is the angle of internal friction of rock mass.

$$x_{a} = \frac{M}{F}\ln \left( {10\gamma H} \right)$$
(4)

where γ is the density of rock mass, M and H are as same as Eq. 1, and F can be calculated from Eq. 5.

$$F = \frac{K - 1}{\sqrt K } + \left( {\frac{K - 1}{\sqrt K }} \right)^{2} \tan^{ - 1} \sqrt K$$
(5)

where \(K = \frac{1 + \sin \varphi }{1 - \sin \varphi }\), and φ is the angle of internal friction of coal seam.

According to the conditions determined at the no. 1601 working face and the test reports, the values of M, H, γ, φ, φ 0 were 1.0, 425 m, 2450 kg/m3, 30°, and 41.1°, respectively. Therefore, K, F and x a are equal to 3, 2.55 and 3.58 m, respectively. With these parameters, the FDCSF value calculated using Eq. 2 was 8.8 m.

This approach was used simple to calculate the FDCSF value with the basic parameters include M, H, γ, φ, φ 0, which were easy to obtain and only the φ, φ 0 needed to be tested. However, in this case we considered a simplified situation and considered that the coal seam and rock mass as elastic materials, which may not fully incorporate all the field variables. Also, in the Eqs. 3 and 4, there is a 1:1 linear relationship between the FDCSF value and the thickness of coal seam (M), which it implies that for instance, the FDCSF value would double when the thickness of coal seam increased from 1.0 to 2.0 m, which is unreasonable. Therefore, by Eq. 2, we calculated a FDCSF value of 8.8 m using a value of 1.0 m for the mean thickness of no. 16 coal seam at the no. 1601 working face.

4.2 Empirical Formulas

Failure of coal seam floor during mining was caused by the development of underground pressure focused on the base of the coal seam. Because the underground pressure increases with depth, in this research we established two empirical formulas to calculate FDCSF value with a depth threshold of 650 m (Wei et al. 2010), thus allowing us to use this approach for all mining areas in Nantun coal mine.

We took into account the depth of mining, coal seam thickness, coal seam dip angle, and longwall panels width, which had a direct relationship with FDCSF value. We used a multivariate linear statistical approach to find the relationship between FDCSF value and the main factors determined at different sites (Tables 1, 2). These relationships can be expressed as shown in Eqs. 6 and 7, according to the data from Tables 1 and 2, respectively.

Table 1 Statistical field tested data of FDCSF and factors in different sites (H < 650 m)
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Table 2 Statistical field tested data of FDCSF and factors in different sites (H ≥ 650 m)
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$$H < 650\,m:h_{1} = 0.0123\;H + 0.1061\;A + 0.3430\;M + 0.03205\;L + 3.8602$$
(6)
$$H \ge 650\,m:h_{1} = 0.0227\;H + 0.0325\;A + 0.3795\;M + 0.0125\;L + 7.4605$$
(7)

where all the symbols are as same as Eq. 1.

According to the conditions at the no. 1601 working face, the values of H, A, M, and L were 425 m, 3°, 1.0 and 200 m, respectively. Therefore, with these parameters and using Eq. 6, we calculated a FDCSF value of 16.5 m for no. 1601 working face.

This approach has been one of the most popular and economic tools used not only by engineers but also by many researchers and designers, especially before planning for longwall panel or other mining activities. This method was very convenient since to calculate FDCSF value one didn’t need any field tests but only the value of H, A, M, and L, which were the basic parameters for a longwall panel. One more appropriate empirical formula needs large measured databases. Here, we included measured coal seam parameters from 29 working faces and using a depth threshold of 650 m, we divided them into two groups, group 1 containing 16 datasets (Table 1) and group 2 containing 13 datasets (Table 2) and use these data to produce two empirical formulas, one for mining depth less than 650 m and the second for mining depth more than 650 m. Equation 6 was employed to calculate the FDCSF value since the average depth of the no. 1601 working face was 425 m. Although, we had collected 29 working faces data and some were similar to the condition of no. 1604 working face, unfortunately, all of the collected data were not exactly same to our case, the depth and longwall panels width as the example, which maybe induced error using the Eq. 6.

4.3 Water Injection Tests

The analysis of the geological parameters and mining conditions present at the no. 1601 working face predicted a FDCSF value of ~16 m, which proved useful in designing the position and depth of the boreholes in headgate (Fig. 2). Water injection test boreholes were drilled on November 15, 2007 at a distance of 10 m from the terminal mining line and their depths and main parameters are listed in Table 3. During the drilling, no water leaks from the boreholes were detected, which suggest that the coal seam floor was not fractured within the depth explored by these boreholes.

Table 3 Basic parameters of two boreholes
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Data from the water injection test data are listed in Table 4 and were used to determine the FDCSF value by taking into account the leakage of the two boreholes at different depths (Fig. 4). Figure 4 shows that the water leakage extended from 12.8 to 20.8 and 11.2–24.0 m at the direction of length in K1 and K2 test boreholes, respectively. Water leakage ranged from zero to 2 l/min and zero to 3.8 l/min in K1 and K2 test boreholes, respectively, which zero indicated there were no fracture occurrences on both natural and induced by underground pressure with mining. The maximum values of FDCSF were 14.6 and 13.8 m at the vertical direction in K1 and K2 test boreholes, respectively. Thus, at the no. 1601 working face we obtained a maximum FDCSF value of 14.6 m using the water injection tests.

Table 4 Date of water injection test of K1 and K2 boreholes
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Fig. 4
figure 4

Profile figure of FDCSF with data from water injection test at 1601 working face

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The field water injection test had the advantage that it was accomplished in situ using the field data of the working face. Therefore, in case of a specific working face, this approach was the most precise with respect to estimating the FDCSF. However, the field test are expensive and work intensive, and take time to perform. In addition, the quality of boreholes carried a significant influence on the test results because parameters such as smoothness of the borehole wall and the presence of undetected natural fractures or faults can affect the results. In our case, the test position was located on a flat area without being influenced by folds and faults and no quality problems were reported during the boreholes construction or during the water injection test. Hence, the FDCSF value reported here is representative for the conditions found at the no. 1601 working face.

4.4 Numerical Simulation

RFPA is a numerical software used frequently in the mining industry to display the deformation and damage of rock masses present on the floor and roof of coal seams (Yang et al. 2007). The strength and other parameters of coal and surrounding rocks, listed in Table 5, are in agreement with the test reports from the Nantun coal mine and other coal mines in Yanzhou coal field (Li 2008). A numerical model was built with the RFPA software taking into account the general geological, hydrogeological, geometric and mining condition of the no. 1601 working face. As shown in Fig. 5, the model simulated a domain 200 m long and 100 m high, gridded into 200 × 100 elements for a total of 20,000 elements each with a uniform dimension of 1 m × 1 m, and containing a total of 30 layers of coal seams and rocks. The bottom and both the left and right boundaries were constrained in the vertical and horizon direction, respectively. A pressure of 10 MPa was applied on the top boundary of the model as the in situ stress.

Table 5 Rock mass and coal mechanics parameters
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Fig. 5
figure 5

Conditions used for the numerical modeling

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During the modeling, the no. 16 coal seam was set to be mined from left to right. Each 15-m mining length involved seven steps. As the mining advanced, roof and floor failures along the coal seam were recorded; Young’s modulus was used at different mining steps as shown in Fig. 6a–d. The black points near the no. 16 coal seam represent the failure points. The more the mining activities progress (more mining steps) and, consequently, the mining face advances the more failures occur in both the floor and bottom of the coal seam and they progressively acquire a fissure-like character. The maximum value of FDCSF was about 14 m and remained relatively constant for the rest of the simulation.

Fig. 6
figure 6

Numerical evolutions of Young’s modulus with different mining steps. a The no. 1 mining steps (15 m); b the no. 3 mining steps (45 m); c the no. 5 mining steps (75 m); d the no. 7 mining steps (105 m)

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Numerical simulations are an important and widely used tool to calculate the FDCSF. In addition, they offer helpful information for understanding and predicting the deformation and damage evolution during coal mining. However, in many cases the reality in the mine is more complicated than the numerical models suggest. For an accurate prediction, all the properties of rocks and coal seams need to be tested, which is generally costly. Our numerical simulation shows that the overall shape of the maximum failures depth zone under the coal seam is similar to a waves (Fig. 6c, d), which indicates that the FDCSF were induced by periodic increase in underground pressure with increasing mining activities, and the periodic weighting distance was ~19 m.

4.5 Contrasting/Comparing the Results of the Four Methods

The specific FDCSF values obtained by employing the four different methods are listed in Table 6. The calculated FDCSF values at the no. 1601 working face ranged from 8.8 to 16.5 m, and the average value was 13.5 m. The FDCSF values obtained by using the four theoretical and numerical methods, if compared to the average, vary from −34.8 to +3.7 %, with the minimum and maximum values resulting from using theoretical and empirical methods, respectively.

Table 6 Contrast with four methods results
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The FDCSF minimum value was determined by theoretical calculations, probably because the thickness of the no. 16 coal seam was relatively small therefore the contribution of the thickness was 1.0, which in turn as mentioned above in Eqs. 3 and 4, affected the length of failure zone of the coal seam around the mining face, x a .

While the empirical formula gave a maximum FDCSF value because, as shown by Eq. 6, there is a linear relationship between the longwall panels width and depth of the coal seam, and the relative contribution of each factor was 0.03205 and 0.0123, respectively, and the longwall panels width and depth values were 200 and 425 m, respectively. Therefore, in this case these two factors had the most important influence on the calculated FDCSF value.

Numerical simulation provided a reference point for the other methods, and in our case the FDCSF value was about 14 m, which was the closest value to the average FDCSF value. The numerical simulation method not only allowed us to calculate a value for the maximum failure depth but also displayed the dynamic and complete development of fracture generation, extension, broadening, and coalescence under coal seam during mining. Therefore, the numerical simulation method is an important and useful tool to obtain the FDCSF value of one working face, with the caves at all the geological parameters and mining conditions are available.

By contrast, the field water injection test at the no. 1601 working face provided a FDCSF value at the end of the field test in situ, values which was 1.1 m (+8.1 %) higher than the calculated FDCSF average value.

In summary, analyzing the results obtained from each method, using field data of the actual condition at no. 1601 working face, and comparing the FDCSF values obtained from these four approaches, we considered that a value of 14.6 m, which was obtained by water injection test was the most appropriate FDCSF value for no. 1601 working face, because the in situ test had the advantage of using current field data and thus was more suitable for obtaining a more precise value at an actual working face (Tan et al. 2010).

When comparing the results of the water injection test with the results of the other methods, as shown in Table 6, we found that errors were −5.8 m (−39.7 %), +1.9 m (+13 %) and −0.6 m (−4.1 %), compared to the theoretical, empirical and numerical methods, respectively. The different errors shown that the result from numerical simulation method was the closest to the results from water injection test, and the FDCSF value from empirical formula method took the second place and the result from theoretical formula was the maximum differentiation to the appropriate FDCSF value. Based on our analysis at no. 1601 working face in Nantun coal mine, we suggest that besides of water injection tests, which should be the first choice to obtain a value for the FDCSF, the numerical simulation method can also be a reliable approach to obtain a FDCSF value of a working face, if all the parameter required for the simulation are available. Otherwise, the empirical formula method can be used to estimate the FDCSF value, as this method is the most cost-efficient method and can be applied at any time during mining and for coal mines with various designs, mining practices. In addition, based on the results obtained in this study, we recommend the empirical formulas (Eqs. 6, 7) to be used for calculating FDSCF values in other areas of the Nantun coal mine. Although the in situ water injection test was the most appropriate approach for estimating FDCSF value in a longwall panel, this approach has been used just few times and in one coal mine only, owing to its man power, material, and financial requirements. However, regardless of the requirements, the water injection test was necessary in order to validate the other methods.

5 Conclusions

  1. 1.

    In this study we estimated the FDCSF value of the no. 1601 working face by using four distinct methods, namely: (1) the theoretical formula associated with the plastic sliding theory, (2) the empirical formula, (3) the water injection test, and (4) the numerical simulation. Multiple methods can compensate for and validate each other and can overcome the limitations of any single method. We analyzed the advantages and disadvantages of using each method, and comparing the FDCSF values obtained in each case, we concluded that water injection test was the most appropriate approach for estimating FDCSF value. The other methods can also be used to estimate the FDCSF value and, when possible, their use should be prioritized in the following order: numerical simulation, empirical formula and theoretical formula.

  2. 2.

    In order to account for all the areas in the Nantun coal mine, to estimate the FDCSF value we employed a multivariate linear statistical analysis of measured coal seam parameters from 29 working faces and two empirical formulas (Eqs. 6, 7) using a depth threshold of 650 m, any working faces in different depth or location in a coal mine could be estimated by the two empirical formulas.

  3. 3.

    In the particular case of the coal face mined, we recommend the value of 14.6 m obtained by the water injection test be used for FDCSF to be the most effective. The FDCSF value is critical for predicting the effective thickness of water-resistant layer under the coal seam. The results of this study may help mitigate the groundwater hazards from coal seam floor at the Nantun coal mine during the exploration and mining of the no. 16 coal seam. They may also be applied to other mines in the Yanzhou coal field or other areas with similar geological, hydrogeological and mining condition.