1 Introduction

The overlying strata of coal face are damaged to different degrees during longwall mining (Tan et al. 2012, 2013). The area where water can flow through is named water-conducting fractured zone (Du and Wang 2013; Tan et al. 2011). The development law of the water-conducting fractured zone, especially its height, is of significant importance for the safety of underground excavations. Quantitatively forecasting the height of the water-conducting fractured zone is not only helpful to prevent water inrush induced disasters but also instructive to the design of longwall mining (Liu et al. 2011; Zhang et al. 2011, 2014).

Researchers have made great contributions on forecasting and monitoring the height of the water-conducting fractured zone in various conditions (Xu et al. 2010; Khanal et al. 2012; Booth and Bertsch 1999; Cherubini 2008). For example, Miao et al. (2011) monitored the height of the water-conducting fractured zone in undermined rock strata of Bulianta Coal Mine and proposed that the thick and strong rock layer termed key stratum plays an important role in controlling the height. Guo et al. (2012) studied the height of the water-conducting fractured zone in longwall mining of deep coal mines by using piezometers and compared it with that obtained from empirical formulae used in China. However, because of the differences in buried depth and depositional age, the damage law of overlying strata in shallow coal seams differs a lot from that of others (Huang 2002; Liu et al. 2014; Lokhande et al. 2012). Compared with other conditions, less research is reported in the literature on the development of water-conducting fractured zones above shallow coal seams.

Furthermore, because the height of the water-conducting fractured zone is significantly influenced by mining method, geometric condition, roof type and many other factors, the analytic solution can hardly be obtained (Wu et al. 2000; Xu et al. 2012; Adhikary and Guo 2014). The numerical simulation software FLAC3D is increasingly used to estimate the development of water-conducting fractured zones (Zhang 2011).

This article aims to study the variations of the height of water-conducting fractured zones. It begins with the establishment of numerical models of no. 1101 coal face at Luxin Mine, China, using FLAC3D. We then calculate the damage zone using numerical models and obtain the heights of water-conducting fractured zones for different face lengths and mining thicknesses. At last, the mining method, face length and mining thickness of no. 11 coal seam are determined.

2 Numerical Modelling

2.1 Geological and Mining Conditions

Numerical models were built based on no. 11 coal seam at Luxin Mine, China. No. 1101 coal face is the first face of no. 11 coal seam in Luxin Mine. The depth of no. 1101 coal face ranges from 168 to 256 m, with an average of 218 m. The thickness of the coal seam ranges from 0.6 to 20.9 m, with an average of 10.76 m. The dip angle ranges from 3° to 5°, with an average of 4.1°. The coal seam is simple in geological formation and rich in joint development. The main roof is sandy mudstone with thickness ranging from 29.8 to 48.2 m, and the immediate roof is also sandy mudstone with thickness ranging from 18.9 to 31.7 m. Characteristics of roof and floor are shown in Table 1. There is a water-rich aquifer in the strata overlying the coal seam, and its distance from the coal seam ranges from 70 to 93.6 m.

Table 1 Characteristics of roof and floor of no. 1101 coal face
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2.2 Model Building

2.2.1 Model Size and Grid

Based on “Pillar design and mining regulations under buildings, water, rails and major roadways” in China, the height of the water-conducting fractured zone can be obtained from the following empirical formula (National Bureau of Coal Industry of China 2000).

$$H_{\text{li}} = \frac{100\sum M }{{1.6\sum {M + 3.6} }} \pm 5.6$$
(1)

where H li is the height of the water-conducting fractured zone, m; M is the mining thickness, m.

The calculated heights of the water-conducting fractured zone of no. 1101 coal face range from 46.1 to 57.3 m. According to the mining practices, the height of the water-conducting fractured zone does not increase with excavating any more when the working face advances more than 300 m. To ensure that there are no significant boundary effects, two groups of numerical models are built, group A and group B. The size of the numerical model in group A (length × width × height) is set to 2l (l = face length) × 300 × 200 m and the vertical distance below the seam is set to 30 m. The depths of no. 11 coal seam in both groups are set to 218 m. The size of the numerical model in group B is set to 3l × 300 × 220 m and the vertical distance below the seam is set to 50 m. Both the haulage way and tail roadway are excavated in the coal seam along the floor of the coal face, with 4 m in width and 3 m in height.

The brick shape is used to create the FLAC3D grid. To improve the accuracy, the elements of coal, immediate roof, main roof and floor should be small, the side length of which is less than 2.0 m. The side length of other elements ranges from 3.0 to 5.0 m. The model grid of group A is shown in Fig. 1.

Fig. 1
figure 1

Grid for no. 1101 coal face model in group A

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2.2.2 Boundary Conditions

Displacement boundary condition is applied on the boundaries of the model (Itasca Consulting Group, Inc., 1997). X-velocity is set to be zero at both left and right boundaries. Y-velocity is set to zero at both front and back boundaries. X-velocity, y-velocity and z-velocity are all set to be zero at bottom boundary. The top boundary is free.

2.2.3 Initial Conditions

To reach the equilibrium state rapidly, the vertical and horizontal stress are initialized to σ v and σ h, respectively, where σ v is obtained from Eq. (2) and σ h is obtained from Eq. (3) (Itasca Consulting Group, Inc., 1997).

$$\sigma_{v} = \gamma h$$
(2)
$$\sigma_{h} = \frac{\mu }{1 - \mu }\sigma_{v}$$
(3)

where σ v is the vertical stress based on gravity loading of overlying strata, Pa; σ h is the horizontal stress due to self-loading following Poisson’s effect, Pa; γ is bulk density of rock masses, N/m3; h is the depth of coal seam, m; μ is the Poisson’s ratio.

2.2.4 Constitutive Model

Coal and rock in model are represented using Mohr–Coulomb plasticity model. The roadway and goaf excavated are represented using null model. The shear yield of zones complies with the Mohr–Coulomb criterion, as shown in Eq. (4). The tensile yield is estimated by tensile strength, as shown in Eq. (5).

$$f_{s} = \sigma_{1} - \sigma_{3} \frac{1 + \sin \varphi }{1 - \sin \varphi } - 2c\sqrt {\frac{1 + \sin \varphi }{1 - \sin \varphi }} > 0$$
(4)
$$\sigma_{1} = \left[ \sigma \right]$$
(5)

where σ 1 is the maximum principal stress, MPa; σ 3 is the minimum principal stress, MPa; φ is the internal friction angle, °; c is the cohesion, MPa; [σ] is the tensile strength, MPa.

2.2.5 Material Properties

There are ten rock strata in the model. The physical and mechanical parameters of coal and rocks are listed in Table 2.

Table 2 Physical and mechanical parameters of coal and rocks in model
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2.2.6 Calculating Procedures

The calculating procedures are as follows:

  1. 1.

    Calculating the model to its initial stress equilibrium state without any excavation. Results show that the vertical stress, the maximum horizontal stress and the minimum horizontal stress are 4.58, 1.93 and 1.12 MPa, respectively, as shown in Fig. 2. Comparing with the measured results (4.6, 1.9 and 1.1 MPa) by the hydrofracturing method, we can reach the conclusion that the numerical model can describe the real stress state of no. 11 coal seam in Luxin Mine.

    Fig. 2
    figure 2

    The resulting horizontal stress distribution without excavation: a vertical stress, b the maximum horizontal stress

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  2. 2.

    For each group, excavating no. 1101 coal face with different face lengths and mining thicknesses as shown in Table 3 and iterating to the stress equilibrium state.

    Table 3 Face lengths and mining thicknesses of different models
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  3. 3.

    Comparing vertical stress, horizontal stress, vertical displacement and damage zone distribution of model in group A with those of corresponding model in group B to find out whether there are significant boundary effects, as shown in Fig. 3. It can be easily concluded from the comparisons that any boundary effects are indeed negligible.

    Fig. 3
    figure 3

    Some numerical results of models (face length 150 m, mining thickness 3.0 m) in group A and group B: a vertical stress, b damage zone distribution, c horizontal stress, d vertical displacement (paralleling the face, at y = 150 m)

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  4. 4.

    By analyzing the damage zone distribution in models of group A, the area consisting of damage zones that directly connect the goaf can be seen as water-conducting fractured zone, as shown in Fig. 4. Then the heights of water-conducting fractured zones of different models can be obtained.

    Fig. 4
    figure 4

    The water-conducting fractured zone obtained from the damage zone distribution in model (paralleling the face, at y = 150 m). Blue is no-failure zone; Red is failure in tension; Light magenta is failure in shear; Green is failure in the past

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3 Results and Discussions

3.1 Effects of Face Length on the Height of the Water-Conducting Fractured Zone

The results of Models 1–1 to 1–6 are shown in Fig. 5. Results of other models are similar to Fig. 5 and not listed. By analyzing the damage zone distribution in models, the heights of the water-conducting fractured zone were obtained. The variations of the height of the water-conducting fractured zone with different face lengths are shown in Fig. 6.

Fig. 5
figure 5

The damage zone distribution in models: a Model 1–1, b Model 1–2, c Model 1–3, d Model 1–4, e Model 1–5, f Model 1–6 (paralleling the face, at y = 150 m)

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Fig. 6
figure 6

Heights of water-conducting fractured zones for different face lengths. The different curves are for different mining thicknesses, 3.0, 4.5, 6.0, 7.5 and 9.0 m, respectively

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As shown in Fig. 6, for the same mining thickness, the heights of water-conducting fractured zones increase with the face length. Many curves of the heights hit inflection points at the face length of 250 m. The heights increase slowly before the inflection points and rapidly thereafter. Then the heights reach peak values at the face length of 300 m and remain nearly constant. The largest height of the water-conducting fractured zone ranges from 140 to 180 m, about 3 times larger than that at the face length of 100 m. It can be concluded that in shallow coal seams the height of the water-conducting fractured zone generally increases with the face length. And there is a critical value of face length where the height of the water-conducting fractured zone remains nearly constant after the face length increases to the critical value. The critical value of face length of no. 11 coal seam is about 300 m.

3.2 Effects of Mining Thickness on the Height of the Water-Conducting Fractured Zone

The variations of the height of the water-conducting fractured zone with mining thickness are shown in Fig. 7. The height of the water-conducting fractured zone generally increases steadily with the mining thickness.

Fig. 7
figure 7

Heights of water-conducting fractured zones with different mining thicknesses. The different curves are for different face lengths, 100, 150, 200, 250, 300 and 350 m, respectively

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3.3 Determination of the Face Length and Mining Thickness

To ensure the safety of the shallow coal mine, the mining induced water-conducting fractured zone cannot reach the water-rich aquifer in the overburden. And there must be a certain thickness of the protective layer between the water-rich aquifer and the water-conducting fractured zone. According to “Pillar design and mining regulations under buildings, water, rails and major roadways” in China, the minimum thickness of the protective layer needed can be obtained from Eq. (6). The thicknesses of the protective layer in Models 1–1 to 5–6 can be obtained from Eq. (7). The minimum thicknesses needed and the thicknesses of protective layers in Models 1–1 to 5–6 are shown in Table 4.

$$H_{\hbox{min} } = 3M$$
(6)

where H min is the minimum thickness of the protective layer needed, m; M is the mining thickness, m.

$$H_{N} = \left\{ {\begin{array}{*{20}l} {H - H_{li} } \hfill & {H > H_{li} } \hfill \\ 0 \hfill & {H \le H_{li} } \hfill \\ \end{array} } \right.$$
(7)

where H N is the thickness of the protective layer in the numerical model, m; H is the minimum distance between coal seam and the water-rich aquifer, m; H li is the height of the water-conducting fractured zone obtained from numerical calculations, m.

Table 4 The minimum thicknesses needed and the thicknesses of protective layers in numerical models
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As shown in Table 4, only Models 1–1, 1–2, 1–3, 2–1 and 2–2 can ensure enough thickness of the protective layer during mining. Therefore, no. 11 coal seam had to adopt slicing mining method. Comparing Models 1–1, 1–2, 1–3, 2–1 and 2–2, it was easy to exclude Models 1–1, 1–2 and 2–1 for their relatively inefficiency in mining. Considering that the abutment pressure of coal face with larger mining thickness is much higher, we selected Model 1–3 as the mining model in the first slice of no. 11 coal seam. Of course, to mine the remaining resources of no. 11 coal seam, some measures such as borehole dewatering and draining should be adopted to dewater the water-rich aquifers in the overburden. Or we can use some special mining methods such as backfill mining to greatly reduce the height of the water-conducting fractured zone.

4 Conclusions

  1. 1.

    Numerical simulations show that the height of the water-conducting fractured zone increases with both the face length and mining thickness of coal face in a shallow coal seam. And there is a critical value of face length, which is about 300 m in no. 11 coal seam at Luxin Mine, China.

  2. 2.

    The slicing mining method is suggested to be adopted in no. 11 coal seam, and the face length and mining thickness of the first slice are recommended as 200 and 3.0 m, respectively. The thickness of the protective layer is expected to be 11.3 m.

  3. 3.

    To mine of next slice of no. 11 coal seam, measures such as borehole pumping should be adopted to dewater the water-rich aquifer in overburden. Or some special mining methods such as backfill mining should be used.