1 Introduction

Coal resource plays an important role in energy production and consumption system in China. Coal consumption ratio has remained at around 70% in recent years (Yang et al. 2011), which is fairly high as compared with other countries in the world. In 2015, the coal output had reached to 3.68 billion with the persistent increase over the past decade from 1.299 in the year 2000 to 3.5 billion tons in 2011, and it is predicted that the coal consumption ratio will still accounts for over 50% among the whole energy consumption. Thus, coal will continue to play the leading role in the energy structure of china with its dominant advantage for a long period of time. In recent years, China’s production safety situation in coal mine has been improved, but the death accidents caused by gas accident still continue. For example, 350 miners died from gas accident in whole year of 2012 (Li et al. 2014). Generally China’s coal seam is in the state of high stress, rich in methane with extremely low permeability, which is the biggest impediment to the effective flow of gas, and it leads to technical difficulties to exploitation of the coalbed methane and increases risk for gas gathering. So effective security measures should be taken to reduce and avoid the gas disasters.

Longwall mining method is widely used around the world because of its most important advantage of high efficiency in recent years. As longwall face always has large excavation, the immediate roof will fall to the floor and are broken into irregular shapes of various sizes after advancing powered roof supports. The downward moving of the roof strata will gradually extends to upwards then cause the main strata broken which we called main roof pressure. Thus, the overburden pressure will be redistributed. Many researchers and investigators have found that there are three distinct zones in the overburden rock mass above longwall coal mines. Singh and Kendorski (1981) found that there are three distinct zones of disturbance in the overburden strata induced by longwall mining, including caved zone, fractured zone and continuous deformation zone. As is shown in Fig. 1. Zones of overburden movement has been widely accepted and applied around the world. In the fractured zone, there are always two kinds of fractures, one is vertical or oblique fissures coming from the strata layers bend and tension; the other is horizontal fracture due to bed separation. According to the study of Palchik (2003), the fractured zone can be divided into three parts: rock blocks, through-going vertical fractures and separate horizontal fractures. In the lower part of the fractured zone, the rock layers are broken into rock blocks by vertical and horizontal fractures, so the different rock layers are connected by these fractures. In the middle part of the fracture, most of the fractures are horizontal due to bed separation and there are only little vertical fractures, the different rock layers are partly connected. There are only horizontal fracture in the upper part of the fracture zone. Then the caved zone, rock blocks and through-going vertical fractures constitute the main moving fissure of gas and ground water. So it is very meaningful to know the height and scope of these zones, then it can guide people to do gas drainage and protect working face from water in-rush. The extent of fractured zone are influenced by many factors, the seam thickness, width of panel, depth of extraction, type and intensity of overburden strata, geological conditions, etc. So the main objective of this paper is to estimate the height and scope of fractured zone based on different gob behavior and found its proper gob behavior for the case mine.

Fig. 1
figure 1

(adapted from Peng and Chiang 1984)

Disturbed zones duo to excavation of a panel in longwall mining

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2 Literature Review

2.1 Existing Views of Fracture Height

The immediate roof will collapse and fall into the extracted panel space with the longwall face advancing. The movement of the lower layers will gradually affect the rock layers above the immediate roof depend on the volume expansion of fractured rock mass in the gob. The original stress and the hydraulic conductivity will be changed due to the downward movement of the roof strata. Researchers have done lots of work about the height of disturbed zones in the roof after extraction of the longwall panel. As there are many factors that will influence the roof strata bahavior, including the coal seam thickness, thickness and number of roof rock layers, strength of the rock mass, panel width and length, so the results they get are somewhat different. National Coal Board (NCB) (1975), Chuen (1979) and Peng and Chiang (1984) proposed an empirical approaches to estimate the caving and fracture zones based on lots of experiences gained from the USA longwall mines as well as British coal mines. Fawcett et al. (1986) quoted an alternative formula which is based on the panel width rather than the extraction thickness to predict fracture heights at typical width between 100 and 200 m. Palchik (1989) thought the extent of the zones over longwall mining may vary significantly and the height of fracture zones varies from 20 to 100 times the coal seam thickness. The fractured area extends upward 30–60 times of the coal seam thickness depending on the properties of the overlying rock layers according to Richard et al. (1990). Zhou (1991) modified the empirical equation given by Peng and Chiang (1984) based on geometric function of the height of mining and further field measurements. Chekan and Listak (1993) mentioned three distinct zones in the roof in response to longwall mining, caving zone, fractured zone and the continuous deformation zone. According to their results, the combined height of caved and fracture zone is about 50 times of the coal seam thickness. Palchik (2003) used the vertical wells drilled from the ground surface to the overburden of working face to measure the height of fracture zone, the results showed that the height of the zone of interconnected fractures may reach 19–41 times of the height of extraction. According to Karacan and Goodman (2009), the fracture zone extends from the mining level to 30–58 times the thickness. Islam et al. (2009) shows that the fracture propagation would be about 80 times of the coal seam height by employing a two-dimensional boundary element modeling. Zhang et al. (2011) did field measurement by an aquifer protection mining technique in panel 51201 in Shangwan coal mine, China. The overburden failure, ground subsidence, surface cracks, water level of the unconsolidated aquifer was monitored by a series of boreholes and also by surface surveys and nearby water well. The results showed that the caved zone was 5 to 6 times of mining extraction, while the height of fracture zone was about 10 to 11 times the mining extraction.

In regard to these referred views about he height of fracture zone, Some existing empirical criteria concluded by those researchers that are used to estimate the height of caving and fracture zone are reviewed and present in Table 1.

Table 1 Fracture height prediction empirical formulas extracted from the existing literature
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In the remaining equations given in Table 1, W is the panel width, Hf is the fracture height, hs is the extracted thickness and quantities are in meters.

2.2 Existing Views of Stress Distribution in the Gob

The lower roof will move downward and collapse after the coal seam is extracted. The weight of the upper strata will be supported by both sides of the panel as the lower strata fall into the extracted space. The stress in the gob area will be redistributed due to coal seam extraction. The pressure arch will develop across the solid coal and the destressed zone will be formed above the gob. As the long wall face retreats and the caving process continues, the caved material comes into contact with the roof and takes load from the upper strata due to the combined influence of floor heave, roof sag, and waste rock bulking. And then the stress in the gob will make a further redistribution. Unfortunately, gob load characteristics were not available for the studied mine site in China. Little research has been conducted into the stress distribution in the gob because the stress measurements in the gob is difficult and potentially dangerous to obtain. The values used in the numerical model varies from 6 to over 1800 MPa (Khaled and Syd 2002), and this will greatly affect the accuracy of the results. So it is really important to have a better understanding of the gob behavior and the strata movement above the gob for validating empirical and numerical models.

Few studies on pressure re-establishment in gob of longwall mining are found in China and other countries. Most of the researchers regard the stress recovery in the goaf as a linear performance. Figure 2 shows the strata pressure redistribution in the plane of the seam around a longwall face after extraction. It shows that the abutment stress in the ribs gradually decrease to the original stress with the increasing distance from the rib-edge. And the loading in the waste area gradually recover its original stress after the gob material are compacted and can take some load from the overburden. Peng et al. (1980) developed a three-dimensional element analysis and studied the supporting role of material in the waste area. They found that the front and side abutment stress will decrease considerably because of the support offered by the compacted rock mass in the gob and the change of the abutment stress is not sensitive to the packing degree of the gob material, the height of caving as long as the gob takes the load from the overlying strata. They divided the gob into three different zones from gob side to face side, well packed zone, packed zone, loosely packed zone. Whittaker (1974) found that the cover pressure re-establishment distance is related to the mining depth. And the compacted gob began to support the roof at 0.3–0.4 times the coal seam depth from the solid abutment (coal face side) in his research, the gob continues to compact until the face has advanced a sufficient distance (0.6 times mining depth) that cover pressure is restored. Wilson and Carr (1982) also proposed that the vertical stress in the gob increases linearly from 0 at the rib and up to the in situ stress at a distance of 0.2–0.3 times the overburden depth. Whittaker and Singh (1979) claimed that whether the gob can recover its original stress or not only depended on the width of the panel, and the gob began to take the load at a distance of 45 m from the coal face. Campoli et al. (1993) found that the stress recover distance in the gob was approximately 0.2 times of coal seam depth (360 m) from investigating the longwall gob behavior by field measurements under varying sets of geological conditions in No. 3 coal seam of Pocahontas. Modeling of longwall mining with consideration of gob behaviors has also been documented in previous studies. The gob was regarded as a strain-hardening material he and “double yield” elements were incorporated in their simulation model. Li et al. (2015) and Zhang et al. (2017) investigated the loading process and stress distribution in longwall pillars with various pillar width in order to find the principle for yield pillar design by Flac3D numerical modeling. The gob was regarded as a strain-hardening material he and “double yield” elements were incorporated in their simulation model. Song et al. (2017) developed a Phase2D model to study the effect of gob characteristics on face stability by considering gob as a backfill material with varying stiffness. Zhang et al. (2018) and Song and Chugh (2018) constructed several estimated gob models to perform sensitivity analyses of the gob loading characteristics.

Fig. 2
figure 2

(adapted from Whittaker 1974)

Strata pressure redistribution in the plane of the seam around a longwall face

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2.3 Literature Review Summary

According to the above literature review, we can know that there are several research methods to determine the height of cave zone and fracture zone above the mined panel roof in longwall mining: theoretical calculation, mathematical modeling, in situ measurement, laboratory physical simulation, numerical modeling, etc. Theoretical calculation may be the easiest and fastest way to get the results, but there are always accompanied by random error, sometimes it is not very reliable with parameter changing. Although in situ measurement can provide reliable data and results, it is a little cumbersome and costly for determining the height of cave zone and fracture zone. Laboratory physical simulation has its limitations for model construction length of time and cost to carry the experiment, and it can be only applied stable properties of rock ass at one time. The last two remaining method are the least costly, simplest and may provide reliable results. Estimation of the stress recover distance mainly depend on the depth of the coal seam and the width of the panel. Few research has been done according to the properties of the gob material. In this paper, three models are developed to study the effect of gob bahavior to the scope of fractured zone by considering gob as a backfill material with varying stiffness.

3 Theoretical Analysis for Case Mine

3.1 Engineering Background

This analysis are based on the 4314 large mining height longwall face of changing mine in China. Inclined longwall coal-mining and large mining height method is used in 4314 working face in changping coal seam, The coal thickness of 4314 is about 6 m, and the panel length and width are 1703.80 m and 220.70 m respectively, the inclination of the coal seam is about 1°–10°, and it is almost flat, as shown in Fig. 3, The roadway of working face are 43,142, 43,141, 43,143, the length of coal pillar is 70 m, the layout of 4314 longwall face is retreat type.

Fig. 3
figure 3

Roadway layout of 4314 working face

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According to the gas geological map of 4314 and field gas measurement, the gas content increases from the east to the west, the average gas content from the cutting hole to the 600 m away is about 5.9–7.6 m3/t, and the maximum is up to 8.6 m3/t, while the value is about 6.3–9.4 m3/t in the left panel, and the maximum value is up to 10.99 m3/t. So the gas disaster is more easily happen in the west part of the panel.

3.2 Empirical Criterion in China

After many years of production practice, the empirical equation concluded by Chinese mining researchers for all kinds of Strata lithology is shown in Table 2. And this will be able to provide a rough result to guide the field measurement.

Table 2 Coefficients for average height of fractured zone (Du and Meng 2009)
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For the case mine, the overburden strata is mainly sandstone, so its strata lithology is medium strong, then (Eq. 1)

$$ H_{f} = \frac{100\sum M }{{c_{1} \sum {M + c_{2} } }} \pm c_{3} $$
(1)

where c1 = 1.6, c2 = 3.6, c3 = 5.6.

Then Hf = 39.85–51.05 m.

4 Numerical Simulation

4.1 Simulation Model

Numerical models are finding more and more popular as a tool for solving underground mine design with their versatility and ever increasing computational power available to mine researchers. Phase2D is a 2-dimensional elastic–plastic finite element program for calculating stresses and displacements around underground openings, and can be used to solve a wide range of mining, geotechnical and civil engineering problems. The model is built according to the geological conditions of the Chang-ping mine 4314 working face of Jincheng Anthracite Mining Group. Hoek–Brown failure criterion is used in this model. The height, length of the model is 100 m and 260 m respectively. Progressing mining is simulated by incrementally advancing the model in 1 m steps. And the case mine’s model is shown in Fig. 4. 8.6 MPa vertical stress is applied on the top of the model to represent the weight of the overburden strata. And the horizontal stress are 9.2 MPa (out of plane) and 8.2 MPa respectively according to the field measurement.

Fig. 4
figure 4

Phase 2D numerical model

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The basic parameters of 4314 longwall face is shown in Table 3.

Table 3 Rock mass properties with Hoek–Brown criteria
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Generally speaking, the modulus of deformation increases with increasing compaction, and the gob material is strain hardening, Terzagh and Salamon built their models to describe the hardening behavior of the gob material, Eqs. (2) and (3) are the stress–strain relationship for Terzagh’s and Salamon’s (1990) model respectively.

$$ \sigma = \frac{{R_{0} E_{i} }}{a}\left( {e^{\varepsilon a} - 1} \right) $$
(2)

where \( \sigma \) is normal stress, \( E_{i} \) is intact modulus, \( \varepsilon \) is normal strain, \( a \) and \( R_{0} \) are constant.

$$ \sigma = \frac{{E_{0} \varepsilon }}{{1 - ({\varepsilon \mathord{\left/ {\vphantom {\varepsilon {\varepsilon_{m} }}} \right. \kern-0pt} {\varepsilon_{m} }})}} $$
(3)

where \( \varepsilon \) is the strain occurring under the applied stress, \( \sigma \) is the uniaxial stress applied to the material, \( \varepsilon_{m} \) is the maximum possible strain of the bulked rock material and \( E_{0} \) is the initial tangent modulus.\( \varepsilon_{m} \) merely depends on the initial bulking factor b, and \( \varepsilon_{m} = {{(b - 1)} \mathord{\left/ {\vphantom {{(b - 1)} b}} \right. \kern-0pt} b} \).

Pappas and Mark (1993) described the strain hardening character of gob material with sandstone and shale fragments by using uniaxial compression tests and displacement measurements. The results are shown in Fig. 5.

Fig. 5
figure 5

(adapt from Marks et al. 2014)

Stress–strain curves for shale and weak sandstone

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In this paper, three models with different gob material are built according to the strain hardening by back-fill way. As the gob is inaccessible and direct measurements cannot be easily taken. So three kinds of gob modulus are used compared with coal seam modulus. Combing with the previous literature review, the modulus used in different location of the gob is shown in Table 4. The other parameters used in the gob are same with the coal. The Young’s modulus of the gob material will keep changing with the face moving forward till the gob reach its original stress. And this process will be calculated by computer. The author try to figure out the relationship between the gob stress stiffness, the stress recover distance and gob modulus, stress redistribution in the roof.

Table 4 Young’s modulus of gob material used in numerical models
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4.2 Simulation Results

Figure 6 shows the vertical stress concentration factor (VSCF) of different gob material for 160 m face advance. d/h is used to represent the face location, and h represents the mining depth, which is 400 m. d is the distance to the face. As can be seen from the Fig. 4, the compaction in the gob is lager in the initial loading, but the vertical stress will reach the original stress eventually, and then the gob material will not deform any more. In general, the stiffness of these three gobs are different, gob 2 and gob 1 exhibit a stiff response compared with gob 3. The VSCF in gob 1 increases very quickly, and gob 1 reaches its original stress at a distance of 0.05 times the mining depth. While the gob 2 and gob 3 have a stress recover distance of 0.15 and 0.17 times the extraction depth respectively. And it shows the gob 2 increases to the original cover pressure and resists further deformation at a distance of 67.5 m. This means the stress recover distance (76.5 m) in gob 3 is just 9 m larger than gob 2. The stress recover distance in gob 3 increases by 13% compared with gob 2. While the modulus factor 1 used in gob 3 is 45 m later than gob 2, and this value accounts for 45% of gob 2. Figure 4 also shows us that the abutment stress ahead of the face are different for different gob behaviors. The larger the stiffness of the gob is, the smaller the stress abutment will be. This is because the gob with larger stiffness can pick up the load more quickly and take more loading around the face area.

Fig. 6
figure 6

Vertical stress concentration factor in the gob

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When the longwall panel is extracted, the shield supports advance and the immediate roof will collapse and fall into the floor, then the gob will be formed through this process. And the in situ stress will redistribute among the mine-induced area at the same time. The pillar around the extraction, the gob and the solid coal face will take the load from the overburden strata together. The gradually upward movement of roof strata will disturb the upper strata, then the upper roof strata will become destressed, the basic roof will cave with the face keep on moving forward, there will be first pressure formed in the roof and the destressed zone becomes larger, the roof pressure relief area will reach its peak value after the working face advance to a certain distance. The distressed zone in the roof will be dynamic change along with the periodic pressure above the working face. The hydraulic conductivity will be changed due to the roof strata’s downward movements. At the same time, the caved and fractured rock mass will deform and expand, and then they will be gradually compressed by the downward movement of the roof. The stress recovered character and the scope of the destressed zone will be different for different geologic setting and mining method. Research shows that the extent of the destressed zone in the overburden will be stable for a certain face advance. In this case, the destressed zone will be stable for 60 m face advance.

Figure 7 shows the vertical stress contour in the overburden strata after 60 m face advance for different gob behavior. The boundary of the pressure relief area is calculated on the basis of 10% less than of the original stress (Zhang et al. 2018). As can be seen from Fig. 7, the height of destressed zone for gob 1, gob 2 and gob 3 are 23.8 m, 27.5 m, 41.5 m respectively. The stress in the boundary of destressed zone is 11% less than the in situ stress for gob 1, and the value is 16% and 10.2% for gob 2 and gob 3 respectively. It also shows that the extent of the destressed zone is also different, gob 3 has the largest range of destressed zone among these 3 gob behavior. So further field study is necessary for determining the height and extent of the destressed zone in the overlying strata after extraction.

Fig. 7
figure 7

Vertical stress contours in the overburden strata after 60 m face advance

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The destressed zone (fractured zone) will expand during the completion of the caving process. There will be vertical fracture formed during the rock layers break, and the horizontal fractures will form due to the bedding layer separation. And these fractures make up of the flow fissure for gas. Figure 8 shows the vertical strain changes of sandy mudstone (22.5–26.5 m high above the working face) during the development of the fractured zone in relationship to face advance. Positive values mean the rock mass layer expand while the negative values mean compression. In the 2D model, the thickness change of the rocks layers can represent the volumetric change of the overburden strata. Jozefowicz (1997) developed a third-degree polynomial curve representing permeability with volumetric strain, \( k = - 4 * 10^{ - 16} \varepsilon_{vol}^{3} - 6 * 10^{ - 15} \varepsilon_{vol}^{2} - 7 * 10^{ - 14} \varepsilon_{vol} + 1 * 10^{ - 11} \left[ {m^{2} } \right] \),where \( \varepsilon_{vol} \) is the volumetric and \( k \) is the coefficient of permeability (m2). According to the data plotted, the sub-surface strata exhibit somewhat similar deformation characteristics for different gob behavior and mining length, however, there are differences in magnitudes, depending on the cover pressure distance. When the coal seam is mined 60 m (Fig. 8a), the cure without gob behavior is symmetric, it gives an unrealistic representation of the mining process. If the model is implemented the gob behavior, the symmetry is no longer present, as shown in Fig. 8, comparing the red, blue and black curves. Overall, the overlying layer above the extraction will expand, and the maximum expansion occurs 0–40 m behind the face. This is because the gob behind the face is gradually compacted by the overburden movement and to varying degrees to pick the load. The expansion-compression gradually tend to 0 for a certain distance behind the face. As can be seen from Fig. 8, the stiffer the gob is, the quicker stress recovery will be. And the expansion-compression degree of gob 3 is much larger than gob 1 and gob 2 at same location. This tells us that the long distance of the stress recover will be help to the stress relief of the overburden strata, and this will largely improve the gas drainage. The Fig. 8 also shows that the overlying strata will be compressed around the cutting hole and the face location where the stress concentration occurs.

Fig. 8
figure 8

Change of vertical length of sandy mudstone layer in the fractured zone depending on face position

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5 Field Study

5.1 Borehole Design

Four long boreholes are designed in the roof of 4314 working face, as shown in Fig. 9, in order to evaluate the gas drainage result in different location of the roof and strata layers, the No. 1, No. 2, No. 3, No. 4 borehole are 55.5 m, 43.5 m, 31.5 m and 19.5 m far away from the south wall of 43,141 roadway respectively, the horizontal distance of these boreholes are 12 m. The valid section of No. 1 drainage borehole is located 54 m high in the roof, and the value are 44–49 m, 43 m, 39 m respectively for No. 2, No. 3 and No. 4 boreholes. All of these four boreholes are drilled by ø170 mm bit for the first 12 m, then ø96 mm bit and ø73 mm positive displacement motor is used for the other drill.

Fig. 9
figure 9

The plan graph for layout of directional high borehole in the roof of 4314 gob from 8# connection roadway

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All of these boreholes are drilled from the No. 8 connection roadway, the height of No. 1 borehole is 2.5 m, the dip angle is 25°, the azimuth is 174°, the target azimuth is 121°, the length of the borehole is 402 m, making sure the distance between the end of borehole to the cutting hole is larger than 80 m at same time, the track of No. 1 borehole is shown in Fig 9. For No. 2, No. 3 and No. 4 borehole, the height of borehole are all 2.5 m, the dip angle is 25°, 20°, 15° respectively, the azimuth is 163°, 154° and 146° respectively, the target azimuth is all 121°, the length of borehole will be adjusted according to the distance between the end of borehole to the cutting hole, making sure the distance is larger than 80 m. The sectional graph for layout of No. 1 directional high borehole in the roof of 4314 gob from 8# connection roadway is shown in Fig. 10.

Fig. 10
figure 10

The sectional graph for layout of No. 1 directional high borehole in the roof of 4314 gob from 8# connection roadway

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5.2 Results Analysis

The gas concentration extracted from No. 8 connection roadway in January (2015) is shown in Fig. 11, as the data of 11st is missing, so the gas concentration data of the other 29 days is plotted in Fig. 11, as can be seen from Fig. 11, the gas concentration is almost below 10% before 11st, and the value reach its peak on 12nd (18.6%), then the value decreases gradually and stabilize on around 14%.

Fig. 11
figure 11

The gas concentration extracted from No. 8 connection roadway in January

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In order to find the best location for gas drainage, the gas concentration data from every borehole is collected and analyzed, as the gas concentration will not stable until 23rd, so the data is plotted in Fig. 12 after 23rd, Fig. 12 shows the change trend of gas concentration from all the four boreholes is almost the same, the value is stable except the 24th, the No. 1 curve and No. 4 curve cross each other, and No. 2 and No. 3 curve cross each other, but taken as a whole, the value of No. 2 and No. 3 is a little higher than that No. 1 and No. 4.

Fig. 12
figure 12

The gas concentration of 1–4 boreholes

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In conclusion, the best location of gas extraction for 4314 working face of Changping mine are No. 2 and No. 3 boreholes, that means the best height for gas extraction in the roof is 43–54 m, the value is much closer to 43 m, the field measurement results are exactly consistent with numerical simulation result of Gob 3.

6 Conclusion

  1. 1.

    The roof will move downward when the coal seam is extracted, three zones will be formed above the extraction space, the fallen rock mass lying on the back of working face and form the gob material, the movement of the overburden strata and the deformation of gob material will affect each other, three models with different gob material shows that the stress recover in the gob is sensitive to the Young’s modulus of the gob material, and these three models have a stress recover distance of 45 m, 67.5 m, 76.5 m respectively.

  2. 2.

    The overlying strata will deform after the extraction of coal seam, the sub-surface strata exhibit somewhat similar deformation characteristics for different gob behavior and mining length, however, there are differences in magnitudes, depending on the cover pressure distance. And the expansion-compression degree of gob 3 is much larger than gob 1 and gob 2 at same location.

  3. 3.

    The field measurement shows that the No. 2 and No. 3 boreholes have larger gas concentration than No. 1 and No. 4 boreholes, concluding that the best height for gas extraction is much closer to 43 m, the field measurement results are exactly consistent with numerical simulation result of gob 3.