Keywords

1 Introduction

China is a country with large resource demand, and coal resources occupy important strategic position in Chinese energy sector, which will not change in the next 50 years. In recent years, with the increase and expansion of mining depth, mining intensity and mining scale, the calamity of high-pressure confined karstic water of North China type coal field which is an important part of China’s coal is increasing day by day, especially the stability of mine roadway formed by water-bearing Ordovician limestone is substandard, and it has a phenomenon of a wide range of gushing water, which make support operation very difficult. The Ordovician limestone fault can easily lead to severe sudden water inflow, which severely threaten to coal mine safety production, so how to control Ordovician limestone water inrush has become one of the key factors to ensure the deep mining safety production.

In consideration of water inrush from coal floor, domestic and foreign scholars had made researches on the topic from the beginning of last century. In 1944 the Hungarian scholar M.S. Reibieic [1] first proposed the concept of relatively impermeable layers; In 1988 O. Sammarco [2] found that warning of mine water inrush can be achieved by precursor information of monitor in water bursts such as sudden changes in water levels; According to the layer structure characteristics of floor rock mass, Qian Minggao, Li Liangjie [3] built the key layer of floor water inrush mechanism; Gao Yanfa [4] discussed in detail the mechanism of grouting reinforcement.

At present, study on the mechanism, monitoring and forecasting and management of coal seam floor water inrush has made great progress, however, because of the special geological conditions of Baizhuang coal mine in Feicheng coal field, there are two problems in control of Ordovician limestone water inrush under coal seam floor: In the coal mine, karst fissures are developed, Ordovician limestone water level is high and the water quantity is large and the recharge is also abundant, so drainage for decreasing water pressure is failed; Then with the mining of coal is into the deep areas, floor grouting transformation technology [4] of long-term implementation which is to reinforce No. 5 limestone can’t fully meet the safety mining requirements of 9, 10 coal seam. In the light of this situation, this paper adopt a method of grouting transform of Ordovician top on basis of geological condition in Baizhuang coal mine by means of numerical simulation, and study quantitatively grouting effect.

2 Engineering Situation

Baizhuang coal mine is located in the west of Feicheng coal field. It was built in 1970, the mine field is about 4.0 km long, about 2.5 km in slope and an area of 15.8 km2. The topography of mine is that northeast is higher than southwest, elevation is +71~+125 m. The boundary of all around are faults, and more faults in the field make No. 4 limestone, No. 5 limestone, Ordovician limestone connect or water-bearing stratum and water-resisting layer connect. The Ordovician limestone aquifer which is widely exposed in the mountains around basin is located in the coal strata chassis, and about 800 m thick, and directly accepts the supply of atmospheric precipitation which is rich. In addition, it is the nourishment source of coal measure aquifer.

3 Establishment of Numerical Model

3.1 Generation of Discrete Fracture Network of Ordovician Limestone

The core of problem of gushing water from fractured rock mass is to determine actual crack distribution and effect tendency of grouting transform on crack density, crack aperture, so variation of water inflow can be analyzed before and after grouting reconstruction. First of all we need to use the mathematical statistics theory to establish statistical model of crack distribution. In the calculation of this paper, according to field investigation, assuming that crack size density obeys distribution law of power function:

$$ n(l) = - \alpha \cdot l^{ - r} $$
(1)

Assuming that whole area is a square with a side length of L, the total number of fissures contained in the rock mass can be obtained by integrating above equation to l.

$$ n(l_{\hbox{min} } \le l \le l_{\hbox{max} } ) = \alpha \left( {\frac{{l_{2}^{1 - r} - l_{1}^{1 - r} }}{1 - r} \cdot L^{3} } \right) $$
(2)

Where n(l) represents number of cracks per unit area, l represents size of the crack, namely length, α represents scaling index.

3.2 Model and Boundary Conditions

According to the layout of working face, the three-dimensional geometric model of fissure water gushing of Ordovician limestone floor is established, as shown in Fig. 1. Main geometric size of the model and boundary conditions are shown in Fig. 2, in which, the length of mine stope is 400 m, the width is 100 m, influencing depth of the floor transformation is 300 m, bilateralis are coal pillars. Assuming that stope floor is a free-out boundary condition and other boundaries are impervious boundary. In order to ensure the accuracy of calculation, save time and improve calculation efficiency, vicinity of the stope is encrypted and the distance should reduce grid and number of elements in the process of grid segmentation and element generation. The floor below 300 m and surrounding area are approximate replaced by infinite domain.

Fig. 1.
figure 1

Numerical model and fracture network generation

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Fig. 2.
figure 2

Three-dimensional model mesh generation of stope

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3.3 Control Equation

During grouting, the flow of slurry is fast in the fracture, but slow in the rock mass. Grout pressure is continuously distributed in the fissures and adjacent rock mass. Flow of the slurry in the rock mass obey to Darcy’s law.

$$ \rho S\frac{\partial p}{\partial t} - \nabla \cdot (\rho u) = Q_{m} $$
(3)
$$ u = \frac{k}{\mu }(\nabla p + \rho gN) $$
(4)

Where p is grout pressure in the pores, S is comprehensive compression coefficient, \( Q_{m} \) is source. is permeability of the rock mass, ρ is slurry density, \( \mu \) is dynamic viscosity of the slurry, u is Darcy speed of the slurry in the rock, g is gravity acceleration, N is unit vector along direction of gravity.

The flow of the slurry can be calculated in accordance with laminar flow formula in the perforated and highly permeable cracks. However the permeability coefficient of cracks is often affected by filling, roughness and connectivity, making the permeability of fracture low. Therefore flow of slurry should be described by Darcy’s law in less permeable and non-penetrating cracks.

In the interior of crack, flow direction of slurry is parallel to crack surface, so the formula (3) and (4) of the Darcy’s Law are modified to tangent formula (5), (6) and (7):

$$ \rho S_{c} d_{c} \frac{\partial p}{\partial t} + \nabla_{T} \cdot (\rho q_{c} ) = d_{c} Q_{m} $$
(5)
$$ q_{c} = \frac{{k_{c} }}{\mu }d_{c} (\nabla_{T} p + \rho gN) $$
(6)
$$ u_{c} = \frac{{q_{c} }}{{d_{c} }} $$
(7)

Where \( q_{c} \) is volume flow rate per unit length in the cracks, \( k_{c} \) is permeability of the cracks, \( d_{c} \) is fissure width, \( \nabla_{T} \) is gradient operator along fracture tangent plane, \( u_{c} \) is average velocity in the cracks, \( S_{c} \) is comprehensive compressibility coefficient of cracks.

4 Calculation and Analysis of Grouting Reinforcement

It can be seen from Figs. 3 and 4 that the distribution of groundwater pressure field is relatively regular. According to comparison of Figs. 3 and 4, it is found that distribution of groundwater pressure field exhibits anisotropic characteristics under disturbance of water-conducting fissure, and the closer the distance to surface is, the greater the pressure gradient is, the more serious the gushing water is. After grouting transform of Ordovician top, pressure gradient near the free face gradually became smooth, spatial distribution of pressure gradually became uniform, and degree of anisotropy decreased. The results show that after grouting transformation, cracks in the Ordovician limestone are basically blocked and greatly improve water-resisting properties. At the same time, with increase of depth of grouting, the affected area is widening, water-insulating capability of Ordovician top is improved

Fig. 3.
figure 3

Change of groundwater pressure field without consideration of fracture distribution

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Fig. 4.
figure 4

Distribution of pressure field at different depths of grouting

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Figures 5 and 6 show the changes of flow field and stress field of the Ordovician limestone before and after grouting transform. It can be seen from the figure that the streamline distribution of flow field is very dense, and connectivity of different fissure units is very strong before grouting transform. At the same time, because of mechanical function of groundwater on the Ordovician limestone, stress gradient inside rock mass is very large, which seriously affects the self-stabilizing ability of rock mass. The coupling between groundwater and rock mass is very significant, which leads to serious water inrush. But after the grouting transform, the boundary condition of the limestone layer is changed, so it limits its field strength and distribution range. It can be seen from Fig. 6b that streamline distribution becomes very sparse in the coal floor and its adjacent area. So grouting material plays a role in blocking the water pressure of Ordovician limestone, this limits the whole flow field and groundwater pressure in the deeper position, avoiding its influence on the coal floor. At the same time, stress gradient of the Ordovician limestone is obviously reduced, and self-stabilizing ability of the rock mass is higher through the grouting transformation.

Fig. 5.
figure 5

Flow field distribution of Ordovician limestone before and after grouting

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Fig. 6.
figure 6

Stress field distribution of Ordovician limestone before and after grouting

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The variation of water inflow of mining stope with depth of grouting can be obtained by parameterizing the different diffusion range of grouting and integrating water inflow in the whole field under different working conditions, as shown in Fig. 7. As can be seen from graph, variation of water inflow with the depth of grouting is nonlinear and the rate of change is gradually reduced and tend to be stabilized. When the depth of grouting is increased to 60 m, water inflow of the whole stope is reduced to about 50 m3/h, so the effect of grouting on water blocking capacity of Ordovician limestone is significant. With the sequential increase of the depth of grouting, water inflow is further reduced, but the degree of change is reduced. According to practical engineering needs and economic factors, the grouting depth is determined to 60 m, this can effectively control the water inrush and ensure the stability and safety of the of water project.

Fig. 7.
figure 7

Variation curve gushing quantity with grouting depth

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5 Conclusion

  1. 1.

    The result of numerical simulation shows that after the grouting reconstruction of Ordovician limestone roof, the anisotropy of the distribution of groundwater pressure field decreases, streamline distribution of flow field becomes very sparse, stress gradient is obviously reduced, the fissures in the Ordovician are basically blocked, and self-stabilizing ability of rock mass is higher. With the increase of the depth of grouting, spatial distribution of groundwater pressure field becomes more uniform, and water blocking capacity of roof is higher.

  2. 2.

    Based on the principle of safety, taking the economic benefit as the goal, the optimal depth of grouting transformation of Ordovician limestone roof is 60 m.