Introduction

Coal is the main energy resource in China and is expected to account for 50–70% of primary energy production for the foreseeable future (Gui and Lin 2016; Li and Wu 2019; Qian et al. 2018; Zhang 2005). Water inrush disasters are common in China’s underground coal mines because of complex geological and hydrogeological conditions, particularly in northern China where karst aquifers underlie coal seams (Gui and Lin 2016; Li and Wu 2019; Shi and Singh 2001; Yin et al. 2016; Zhang et al. 2014). Although statistical information regarding water inrush events remains incomplete, approximately 80% of water inrush events in coal mines are known to be closely related to fault zones (Huang et al. 2010; Liu et al. 2017; Li and Wu 2019; Qian et al. 2018; Zhang 2005; Zhang et al. 2014), which are considered to play an important role during water inrush processes (Yin et al. 2015; Wu et al. 2004; Wu and Wang 2006). Most of these fault zones are impervious natural media that transform into water-conducting media under mining conditions (Li et al. 2002; Shi et al. 2017; Wu et al. 2004, 2011; Xu et al. 2012; Zhu et al. 2014). This type of water inrush is characterized by hysteresis, strong concealment, and capacity to inflict substantial harm (Wu et al. 2004, 2011; Zhu et al. 2014). Water inrush from fault zones into mines not only threatens safe production, but also presents environmental problems (Shi et al. 2017; Wu et al. 2004; Yin et al. 2015; Zhang 2005; Zhu and Wei 2011). A better understanding of water inrush mechanisms is therefore required.

Fault zones often act as channels during mine water inrush events (Wu et al. 2019a, b; Yin et al. 2015; Zhang 2005; Zhou et al. 2018), yet the mechanism of this process remains poorly understood (Li and Wu 2019; Wu et al. 2019a, b; Zhang et al. 2017; Zhou et al. 2018; Zhu and Wei 2011). The occurrence and intensity of water inrush from a fault zone is controlled by its intrinsic properties, including stress state, fault displacement, rock mass structure, dip angle, cementation characteristics, and mineral composition (Li et al. 1999, 2011; Huang et al. 2010; Ma et al. 2016; Meng et al. 2012; Wu et al. 2004; Zhang 2005), and is also influenced by mining activities, aquiclude thickness, water yield property of aquifers, and hydraulic pressure of aquifers (Meng et al. 2012; Wu et al. 2004; Wu and Wang 2006; Zhang 2005; Zhang et al. 2014).

Three reasons are generally used to explain why fault zones often serve as a major passageway for water inrush. First, most fault zones are weak with high fissure ratios and low strength compared to surrounding rock, which significantly weakens their resistance to hydraulic pressure (Meng et al. 2001; Wu et al. 2004, 2019a, b). Second, interaction between groundwater and fault zones further weakens the fault zone strength while increasing permeability, leading to dissolution, softening, hydrostatic pressure, and subsurface erosion (Li et al. 1999, 2011; Qian et al. 2018; Zhang et al. 2014). A third cause is enhanced fault-zone permeability resulting from mining activity involving damage and fault activation (Zhang 2005; Zhang et al. 2014, 2015; Zhu et al. 2014; Zhu and Wei 2011), which has been verified by water pressure tests (Wang et al. 1997; Yin et al. 2015).

Nevertheless, qualitative analyses do not satisfactorily explain fault zone processes such as deformation, failure, and seepage flow, as well as their interrelationship. Quantitative methods used in previous studies include theoretical calculations, similar material simulations, and numerical simulations of fluid–solid coupling. Previous theoretical studies established based on mining rock mechanics and/or hydraulic fracturing theories (Shi and Singh 2001; Zhang 2005) analyzed stress variation, crack extension, and fault zone failure, and broadly discussed their effects on permeability (Bu and Mao 2009; Huang et al. 2010; Shi and Singh 2001; Yin et al. 2015; Zhang 2005). These theoretical calculations failed, however, to directly observe the phenomenon of fault zone deformation, failure, and seepage flow, and similar material simulations, though possible, remain inappropriate for practice (Li et al. 1997; Sun et al. 2015; Zhang et al. 2015, 2016, 2017; Zhu et al. 2017).

Numerical simulations of fluid–solid coupling using finite difference methods (FDM) or finite element methods (FEM) have been shown to overcome these shortcomings (Liu et al. 2017; Shi et al. 2017; Wu et al. 2004; Zhu et al. 2014; Zhou et al. 2018; Zhu and Wei 2011). This approach is therefore widely used to explore the mechanisms of mine water inrush from fault zones on the basis of elastic–plastic or rheological mechanics and Biot’s consolidation theories (Liu et al. 2017; Wu et al. 2011; Yin et al. 2016; Zhu et al. 2014). Many studies have been performed using FLAC3D, RFPA2D-FLOW, and Comsol Multiphysics (Shi et al. 2017; Wu et al. 2011; Yin et al. 2016; Zhu and Wei 2011). The results show that a fault zone undergoes significant deformation and failure because of its low strength and stress redistribution under mining conditions (Bu and Mao 2009; Li et al. 2011; Liu et al. 2017; Shi et al. 2017; Wu et al. 2004, 2011; Yin et al. 2015, 2016; Zhang et al. 2015; Zhu et al. 2014), and that pore water pressure in aquifers increases because of additional stress (Wu et al. 2011; Zhang et al. 2016; Zhu et al. 2014). These changes induce groundwater bursts along fault zones into mines (Liu et al. 2017; Wu et al. 2004; Yin et al. 2016; Zhang et al. 2017). Few previous studies have reported the mechanism of water inrush from confined aquifers through fault zones disturbed by mine dewatering nor the evolution of fault zone hydraulic properties of natural vs. disturbed-state faults.

In this study, we consider these aforementioned questions using a typical water inrush event in a coal mine. We identified the water inrush source and the role of fault zones during the inrush, and analyzed the rock’s mass mechanical characteristics. We present a mathematical model of fluid–solid coupling based on ideal elastic–plastic and Biot’s consolidation theories that dynamically consider the effect of mean principal stress and pore water pressure on fault zone permeability. We apply the fluid–solid coupling numerical model to identify the water inrush mechanism through fault zones disturbed by mine dewatering.

Study Area

Geological and Hydrogeological Setting

The Beiyangzhuang coal mine is located in Yuxian County, Hebei Province, in northern China (Fig. 1), in a transition zone between semi-humid and semi-arid environments. Rainfall is concentrated between June and September with a long-term mean rainfall of ≈ 400 mm/year. The long-term average evaporation is ≈ 1600 mm/year. The geomorphology is dominated by an alluvial plain (Fig. 1), and the topography is relatively flat, with an elevation difference of about 140 m.

Fig. 1
figure 1

Location and hydrogeological map of the study area

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The study area is a synclinal structure with a dip angle on both limbs of ≈ 10°, and the axial plane of the syncline extends approximately W–E (Fig. 2). Large faults with throw of a few tens of meters are relatively infrequent, but small faults with < 10 m throws are fairly common. The main strata include Cambrian–Ordovician carbonates, Jurassic clastic rocks, and Quaternary alluvial deposits. The coal seam occurs in the lower part of the Jurassic strata (Fig. 2).

Fig. 2
figure 2

A-A’ hydrogeological profile in Fig. 1

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The hydrogeological structure of the study area is vertically divided according to lithological associations into three aquifers (Cambrian–Ordovician karst aquifer, Jurassic fissure aquifer, Quaternary pore aquifer), and two aquifuges (Jurassic aquifuge, Quaternary aquifuge) (Fig. 2).

The karst aquifer is characterized by a dual structure, where the upper part is thick-layered limestone and the lower part is thin-layered limestone. The thickness of the karst aquifer is ≈ 100 m (Fig. 2). The hydraulic conductivity ranges from 0.01 to 13.1 m/d, with an average of 3.2 m/day, which suggests significantly heterogeneous permeability. The specific yield ranges from 0.0004 to 16.6 L/(m·s), with an average of 2.5 L/(m·s) (Fig. 1), which suggests very heterogeneous water yield properties (Wu et al. 2006).

The fissure aquifer located in the upper part of the Jurassic strata is composed of 100–200 m of conglomerate (Fig. 2). The hydraulic conductivity ranges from 0.001 to 0.73 m/day, with an average of 0.25 m/day, and the specific yield ranges from 0.0003 to 0.17 L/(m·s), with an average of 0.07 L/(m·s) (Fig. 1). This suggests that the water yield property ranges from weak to medium. In general, the heterogeneity of the permeability and water yield property of the fissure aquifer is weaker than that of the karst aquifer.

The pore aquifer consists of interbedded sand and silty clay with a thickness ranging from 150 to 200 m (Fig. 2). The hydraulic conductivity ranges from 0.1 to 3.6 m/day, with an average of 1.8 m/day, and the specific yield ranges from 0.2 to 1.4 L/(m·s), with an average of 0.7 L/(m·s) (Fig. 1). The specific yield indicates that the water yield property varies from medium to strong. On the whole, the permeability and water yield property of the pore aquifer are relatively homogeneous.

The Jurassic aquifuge is located in the lower part of the Jurassic strata and its lithology includes mudstone, siltstone, and fine sandstone (Fig. 2). It therefore hydraulically separates the karst and fissure aquifers. The Quaternary aquifuge consists of silty clay located in the bottom of the Quaternary strata (Fig. 2), hydraulically isolating the pore and fissure aquifers.

Conceptual Model

Water Inrush Process

The mine began dewatering using the no. 1 dewatering borehole near the F1 fault on June 4, 2014, because of high hydraulic pressure (4.4 MPa) and the strong water yield property of the karst aquifer (Figs. 3, 4). The mine then also began dewatering using the no. 2 dewatering borehole near the F1 fault on Aug. 31, 2014 (Figs. 3, 4) (Mu 2018). The average mine water yield was about 300 m3/h from June 4 to Sept. 26, 2014 (supplemental Fig. S-1). On Sept. 27, 2014, a large amount of water (about 550 m3/h) burst into the roadway from the coal wall around the no. 2 dewatering boreholes, and the mine’s water yield quickly increased to the maximum (about 2200 m3/h) on Nov. 2, 2014 (Fig. S-1) (Mu 2018). A water gate wall was used to control the water hazard on Nov. 3, 2014, which reduced the mine’s water yield to ≈ 1900 m3/h, and it roughly remained at this level until July 6, 2015 (Fig. S-1). The water inrush pathway was blocked by grouting between July 7 and Aug. 10, 2015, causing the mine’s water yield to quickly drop to ≈ 40 m3/h (Fig. S-1).

Fig. 3
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Conceptual model of water inrush through fault zones

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Fig. 4
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A-A’ Engineering geological profile in Fig. 3 in the a natural state and b disturbed state

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The drainage stage was divided into three stages to embody the difference ways groundwater entered the mine (Fig. S-1): the dewatering stage (June 4, 2014–Sept. 26, 2014), the water inrush (Sept. 27, 2014–July 6, 2015), and the water-level recovery stage (July 7, 2015–Aug. 10, 2015).

Water Source Identification

The planar distance of observation hole BG6 from the water inrush point was ≈ 1500 m, while the planar distance of observation hole BG7 from the inrush point was ≈ 600 m (Fig. 1). BG6 was intended to measure the karst water regime during the mine water inrush process, and was used to analyze the influence of mine water inrush on the karst water level. Similarly, BG7 was intended to measure the pore water regime during the inrush process, and was used to analyze the influence of the inrush on the karst water level.

A strong negative correlation was observed between the karst water regime at observation hole BG6 and the variation of water yield of mine during the water inrush process (Fig. S-1) (Wu et al. 2019a, b). The water level at the observation hole decreased by 22 m during the inrush and increased by 21 m after the grouting. This indicates that karst water was the main source of the water inrush (Fig. S-1). In addition, the response of the karst water level at BG6 was measured in three pressure tests for the water gate wall (Fig. S-1).

In contrast, no correlation was observed between the pore water regime at BG7 and the change in mine water yield during the inrush process (Fig. S-1). The pore water regime at the observation hole was influenced by atmospheric precipitation, groundwater exploitation for agriculture, and snowmelt (Wu et al. 2019a, b), which suggests that pore water does not contribute substantially to water inrush (Mu 2018).

A Piper diagram was used to classify the hydrochemical types of the water samples. The pore water is mainly HCO3–Na type, the fissure water is mainly HCO3–Na and HCO3·Cl–Na types, and the karst water is mainly HCO3·Cl and HCO3·SO4 types (Fig. S-2). The hydrochemical facies of water samples from the water inrush point is HCO3·SO4 type, clearly resembling the karst water in the Piper diagram (Wu et al. 2019a, b). In combination with groundwater level measurements, we can infer that the karst aquifer below the coal seam was the water inrush source. The hydrochemical characteristics also indirectly confirm that the hydraulic connections are not close among the three aquifers (supplemental Fig. S-2).

Role of the Fault

The exposure site of the F1 fault is ≈ 50 m from the no. 2 dewatering boreholes in the roadway, and its role in the water inrush process was roughly analyzed (Figs. 3, 4). The average throw of the F1 fault is 4.8 m and the fault zone width is 4.5 m. It is a normal fault and the lithology of each wall includes fine sandstone, siltstone, and mudstone (Figs. 3, 4). The fault zone is naturally impermeable, according to roadway exposure. No water was observed when the no. 1 dewatering borehole exposed the fault in late May 2014. But, a large amount of water was observed when the no. 2 dewatering borehole exposed the fault at the end of August 2014, indicating that the hydraulic property of the fault zone changed from impermeable to water-conducting. In other words, fault activation occurred near the end of August 2014.

The coal near the inrush points was unmined before the end of August 2014 or late May 2014, so the fault activation was not mining related. Mine dewatering was carried out near the fault from late May 2014 to the end of August 2014 (Figs. 3, 4). Therefore, the fault activation was possibly related to the mine dewatering, based on the following reasoning: the fault zone intersects the dewatering boreholes in the Jurassic aquifuge below the coal seam (Figs. 3, 4). The groundwater in the borehole permeates the fault zone under high hydraulic pressure. The fault zone is composed of clay minerals, including an illite-montmorillonite mixed-layer, illite, and kaolinite (Mu 2018). Due to the high hydrophilicity of clay minerals, the strength of the fault zone was therefore significantly reduced, which activated the fault and enhanced the fault zone’s permeability. The Jurassic aquifuge contains the same clay minerals and the softening induced the karst water to flow along the fault and failure zones in the rock surrounding the dewatering boreholes, and eventually burst into the roadway. When the grouting cut off the connection between the fault zone and karst aquifer, the water yield of the mine sharply decreased (Fig. S-1), verifying the role that fault zones play in water inrush passage.

Materials and Methods

Sample Collection and Testing

Twenty-five samples were collected from the lower part of the Jurassic strata because the mechanical properties of this layer are closely related to water inrush from the coal floor. Among these samples, eight were fine sandstone, eight were siltstone, and nine were mudstone (Fig. S-3). The samples were tested for physical and mechanical parameters including bulk density, porosity, water absorption, cohesion, internal friction angle, and uniaxial compressive strength (UCS). These test results are listed in Table 1.

Table 1 Test results of physical and mechanic of rock mass
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Methods Overview

Fault zones are generally classified as fracture zones and influenced zones from inside to outside. Fracture zones are composed of fine particles, while influenced zones are composed of rock blocks and fissure networks (Meng et al. 2001; Zhang et al. 2014; Zhou et al. 2018). Rock mass structures of fault zones are therefore successively structurally classified as granular and cataclastic from inside to outside, respectively (Zhou et al. 2018). Although a fault zone is relatively heterogeneous compared with soil mass, it can still be approximatively regarded as an equivalent porous media at the macroscopic scale (Wu et al. 2011). On this basis, we used a mathematical model of fluid–solid coupling to describe the deformation, failure, and seepage of fault zones.

The coupled model consists of the ideal elastic–plastic and Biot’s consolidation models. Volumetric strain plays a bridge role in the coupled model. The effects of average principal stress and pore water pressure on the fracture zone permeability are considered by coupling the models. The FLAC3D (Fast Lagrangian analysis of continua in three dimensions) software was then employed using finite difference methods to perform numerical simulations of fluid–solid coupling based on the conceptual model of water inrush, rock physics and mechanics test results, and mathematical model of the fluid–solid coupling.

Mathematical Model of Fluid–Solid Coupling

Ideal Elastic–Plastic Model

According to Hooke’s law, the relationship between principal stress increment and principal strain increment in the elastic stage is expressed by (Mu 2018):

$$\left\{ \begin{aligned} \Delta \sigma_{1} = \alpha_{1} \Delta e_{1}^{e} + \alpha_{2} (\Delta e_{2}^{e} + \Delta e_{2}^{e} ) \hfill \\ \Delta \sigma_{2} = \alpha_{1} \Delta e_{2}^{e} + \alpha_{2} (\Delta e_{1}^{e} + \Delta e_{2}^{e} ) \hfill \\ \Delta \sigma_{3} = \alpha_{1} \Delta e_{3}^{e} + \alpha_{2} (\Delta e_{1}^{e} + \Delta e_{3}^{e} ) \hfill \\ \end{aligned} \right.$$
(1)

where \(\Delta \sigma_{i} (i = 1, 3)\) is the principal stress increment, \(\Delta e_{i}^{e} (i = 1,3)\) is the principal strain increment in the elastic stage, and \(\alpha_{1}\) and \(\alpha_{2}\) are related to bulk modulus and shear modulus, and are defined by:

$$\alpha_{1} = B + (4/3)S,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \alpha_{2} = B + (2/3)S$$
(2)

where \(B\) and \(S\) are the bulk modulus and shear modulus, respectively. The Mohr–Coulomb yield function (\(f_{s}\)) is defined as:

$$f_{s} = \sigma_{1} - \sigma_{3} N_{\phi } + 2cN_{\phi }$$
(3)

where \(\sigma_{1}\) and \(\sigma_{3}\) are the maximum principal stress and minimum principal stress, respectively, \(c\) is cohesion, and \(N_{\phi }\) is the parameter related to internal friction angle defined as:

$$N_{\phi } = \frac{{1{ + }\sin \phi }}{1 - \sin \phi }$$
(4)

where \(\phi\) is the internal friction angle. The shear potential function (\(g^{s}\)) is defined as (Mu 2018):

$$g^{s} = \sigma^{t} - \sigma_{3} N_{\varphi }$$
(5)

where \(\sigma^{t}\) is the tensile strength, and \(N_{\varphi }\) is a parameter which is related to internal friction angle, which is defined as follows:

$$N_{\varphi } = \frac{{1{ + }\sin \varphi }}{1 - \sin \varphi }$$
(6)

where \(\varphi\) is a parameter related to dilation angle. When the material is in shear yield, the strain increment in the plastic stage is determined according to the shear potential function and plastic flow rule (Mu 2018):

$$\Delta e_{i}^{p} = \lambda^{s} \frac{{\partial g^{s} }}{{\partial \sigma_{i} }}{\kern 1pt} \;\;{\kern 1pt} {\kern 1pt} i = 1,3$$
(7)

where \(\Delta e_{i}^{p}\) is the strain increment in the plastic stage and \(\lambda^{s}\) is the shear plasticity factor. The total principal strain increment includes the strain increment in the elastic stage and the plastic strain increment in the plastic stage:

$$\Delta e_{i} = \Delta e_{i}^{e} + \Delta e_{i}^{p} \;{\kern 1pt} {\kern 1pt} i = 1,3$$
(8)

where \(\Delta e_{i}\) is the total principal strain increment. The relationship between the principal stress increment and total principal strain increment is obtained from Eqs. (7) and (8) applied to Eq. (1):

$$\left\{ \begin{aligned} \Delta \sigma_{1} = \alpha_{1} \Delta e_{1} + \alpha_{2} (\Delta e_{2} + \Delta e_{2} ) - \lambda^{s} (\alpha_{1} - \alpha_{2} N_{\varphi } ) \hfill \\ \Delta \sigma_{2} = \alpha_{1} \Delta e_{2} + \alpha_{2} (\Delta e_{1} + \Delta e_{2} ) - \lambda^{s} \alpha_{2} (1 - N_{\varphi } ) \hfill \\ \Delta \sigma_{3} = \alpha_{1} \Delta e_{3}^{e} + \alpha_{2} (\Delta e_{1}^{e} + \Delta e_{3}^{e} ) - \lambda^{s} ( - \alpha_{1} N_{\varphi } + \alpha_{1} ) \hfill \\ \end{aligned} \right.$$
(9)

Biot’s Consolidation Model

According to Darcy’s law, the seepage velocity of groundwater is described by:

$$v_{i} = \frac{K}{{\rho_{w} g}}\frac{{\partial (p + \rho_{w} gz)}}{{\partial x_{i} }}$$
(10)

where \(v_{i}\) is the seepage velocity, \(p\) is the pore water pressure, \(K\) is the hydraulic conductivity, \(\rho_{w}\) is the groundwater density, \(z\) is the elevation head, and g is the gravitational acceleration. The continuity equation of groundwater is (Wang et al. 2018):

$$\frac{{\partial V_{i} }}{{\partial x_{i} }} = \frac{\partial \varsigma }{\partial t}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (i = 1,3)$$
(11)

where \(\varsigma\) is the volume variation of groundwater in unit volume of the aquifer. The constitutive equations of groundwater are defined by (Wang et al. 2018):

$$\frac{\partial \varsigma }{\partial t} = \frac{1}{M}\frac{\partial p}{\partial t} + \alpha \frac{{\partial \varepsilon_{V} }}{\partial t}$$
(12)

where \(\alpha\) is the Biot consolidation coefficient, \(M\) is the Biot modulus, and \(\varepsilon_{V}\) is the volumetric strain. The volumetric strain is a link for the coupling of the seepage field and stress field:

$$\varepsilon_{V} = \sum\limits_{i = 1}^{3} {\varepsilon_{i} }$$
(13)

where \(\varepsilon_{i}\) is the total principal strain.

Relationship Among Permeability, Stress, and Pore Pressure

Many studies have shown that fault zone permeability is influenced by principal stress and pore water pressure (Wu et al. 2011). In general, there is a negative correlation between hydraulic conductivity and principal stress of fault zones because of compaction, and their relationship is frequently described by a negative exponential function (Li and Wu 2019; Li et al. 2011; Wu et al. 2011; Zhu and Wei 2011; Zhu et al. 2014). However, there is a positive correlation between hydraulic conductivity and pore water pressure of fault zones because of wedging action (Li et al. 2002, 2011). A natural exponential function model was used to describe the relationship among hydraulic conductivity, mean principal stress, and pore water pressure for fault zones on the basis of the above analysis (Wu et al. 2011; Zhu et al. 2014):

$$K = K_{0} e^{{ - \alpha (\sigma_{m} - p)}}$$
(14)

where \(\sigma_{m}\) is the mean principal stress, α is a fitting parameter, \(p\) is the pore water pressure, and \(K\) is the hydraulic conductivity when the mean principal stress is equal to pore water pressure. The mean principal stress is defined as:

$$\sigma_{m} = \frac{1}{3}\sum\limits_{i = 1}^{3} {\sigma_{i} }$$
(15)

where \(\sigma_{i} (i = 1,3)\) is principal stress. According to the time of fault activation (about 90-100 days), the parameters in Eq. (14) are identified by application of parameter inversion. In Eq. (14), \(a\) is equal to 1.5, and \(K_{0}\) is equal to 1.45 × 10−2 cm/s.

Numerical Model

Geological Structure

The geologic structure model is naturally divided into four groups based on their lithologic features: the Cambrian–Ordovician limestone, the Jurassic sandstone and mudstone, the Jurassic conglomerate, and the fault zone (Fig. 4a). To embody the softening effect of the groundwater on the rock mass, the Jurassic sandstone and mudstone as well as the fault zone, were further divided into disturbed and undisturbed zones (Fig. 4b), while the other groups remained the same. The model was therefore divided into six groups in the disturbed state.

Parameters and Boundary Conditions

The physical and mechanical parameters of the model in the natural state were determined using laboratory tests and field investigations (Table 2). Similarly, the physical and mechanical parameters of the model were determined in the disturbed state. The mechanical parameters of the disturbed rock mass were clearly weaker than those of the same rock mass in the natural state (Table 3).

Table 2 Physical and mechanical parameters of rock mass in the natural state
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Table 3 Physical and mechanical parameters of rock mass in the disturbed state
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According to our water inrush source analysis, the inrush was only related to the karst aquifer, so to simplify calculations, the seepage model considers only the karst aquifer; the other materials were regarded as impermeable media, except for the fault zone and the disturbed Jurassic rock mass.

The hydraulic conductivity of the karst aquifer was measured from the pumping test to be 5.78 × 10−3 cm/s. The natural hydraulic conductivity of the fault zone was 1.89 × 10−8 cm/s, according to the hydrogeological tests and field investigation. The hydraulic conductivity of the disturbed rock mass in the fault zone was dynamically calculated using Eq. (14). The lateral and bottom boundaries in the mechanical model were defined as the boundary with a normal displacement of 0 m (Fig. 4). The top boundary was defined as a stress boundary to simulate gravitational stress of the overlying strata (Fig. 4), and a vertical stress of 8.8 MPa was calculated, based on the unit weight and thickness of the overlying strata including the Jurassic conglomerate and Quaternary alluvial deposits (Fig. 2).

The right and south boundaries in the seepage model were defined as the fixed pore pressure, while the other boundaries were regarded as confining boundaries. The pore water pressure in the left and right boundaries was identified according to the pore water pressure of the observation well before mine dewatering and ranged from 4.4 to 5.4 MPa.

Simulation Scheme

Understanding the evolution of hydraulic properties from the natural to the disturbed state is the key to identifying the mechanism of water inrush through fault zones. We designed two simulation schemes based on the conceptual model, one for the natural state and the other for the disturbed state. Comparing the deformation, failure, and seepage of fault zones in both states should reveal the inrush mechanism of the fault zone

The initial seepage is believed to have begun in late May, 2014. The seepage time in the natural state simulation was set at 120 days, slightly exceeding the time of fault activation (about 90–100 days). The seepage time in the disturbed state was set at 160 days, to exceed the actual delay of mine water inrush (about 120–130 days). The model parameters were calibrated by model inversion, based on the time of fault activation.

Results and Discussion

Mechanical Characteristics of the Rock Mass

The porosity of the fine sandstone ranges from 5.8 to 19.3%, averaging 12.7%; that of the siltstone ranges from 2.0 to 13.9%, averaging 9.3%; and that of the mudstone ranges from 1.6 to 27.8%, averaging 14.0%. The porosity was therefore relatively developed, which indicates relatively poor cementation.

The water absorption of the fine sandstone ranges from 4.4 to 36%, with an average of 13.1%; that of siltstone ranges from 1.2 to 32%, averaging 11.5%; and that of the mudstone ranges from 4.5 to 29.3%, averaging 14.0%. These percentages are relatively large, due to the strong hydrophilicity of the clay minerals.

The UCS of the rocks is influenced by the poor cementation and strong hydrophilicity. The UCS of the fine sandstone ranges from 10.5 to 23.4 MPa, with an average of 16.9 MPa; that of the siltstone ranges from 10.3 to 60.9 MPa, averaging 23 MPa; and that of the mudstone ranges from 13 to 26 MPa, with an average of 17.5 MPa. The UCS is less than 30 MPa, which is characteristic of soft rock. The softening coefficient of rocks ranges from 0.25 to 0.42, which suggests that water plays a critical role in strength deterioration.

Deformation, Failure, and Seepage Characteristics

Natural state

The shear strain increment at the bottom of the fault zone was considerably larger than in other areas of the natural state simulation (Fig. 5). The volume strain increment and horizontal displacement showed the same trend (Fig. 6). The deformation slowly increases with seepage time, and the deformation concentration of fault zones presents a punctiform distribution (Fig. 7). Only the fault zone bottom undergoes failure, whereas other areas of the fault zone do not (Fig. 8).

Fig. 5
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Shear strain increment for different seepage times in the natural state: a 30 days; b 60 days; c 90 days; d 120 days

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Fig. 6
figure 6

Volume strain increment for different seepage times in the natural state: a 30 days; b 60 days; c 90 days; d 120 days

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Fig. 7
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Horizontal displacement for different seepage times in the natural state: a 30 days; b 60 days; c 90 days; d 120 days

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Fig. 8
figure 8

Plastic zones for different seepage times in the natural state: a 30 days; b 120 days

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The deformation and failure are concentrated at the bottom of the fault zone because of its low strength in the natural state, which provides favorable conditions for water inrush along fault zones. Groundwater from the karst aquifer moves slowly along the fault zone under high pore water pressure, with a seepage velocity of 1.5 cm/day (Fig. 9). The fault zone can therefore be regarded as a naturally fairly impermeable medium.

Fig. 9
figure 9

Pore water pressure for different seepage times in the natural state: a 30 days; b 60 days; c 90 days; d 120 days

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Disturbed State

The shear strain increment of the disturbed zone of the fault zone was substantially larger than in the other areas in the disturbed state, and about 40 times greater than the natural state (Fig. 10). The volume strain increment and horizontal displacement also show the same relationship, and were enhanced by about an order of magnitude (Fig. 11). The deformation concentration of fault zones presents a zonal distribution (Fig. 12). Note that the fault zone was in a state of volume expansion, based on the volume strain increment in the disturbed state, which shows that the porosity of fault zones increased (Liu et al. 2009; Wang et al. 2001).

Fig. 10
figure 10

Shear strain increment for different seepage times in the disturbed state: a 30 days; b 60 days; c 90 days; d 120 days

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Fig. 11
figure 11

Volume strain increment for different seepage times in the disturbed state: a 30 days; b 60 days; c 90 days; d 120 days

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Fig. 12
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Horizontal displacement for different seepage times in the disturbed state: a 30 days; b 60 days; c 90 days; d 120 days

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The failure of the fault zone initiated in the bottom of the disturbed area, and gradually developed upward (Fig. 13). The entire disturbed zone underwent failure due to the pore water pressure (Liu et al. 2017). The natural deformation and failure characteristics of the fault zone were enhanced in the disturbed state (Figs. 7, 8, 12, 13).

Fig. 13
figure 13

Plastic zones for different seepage times in the disturbed state: a 30 days; b 60 days; c 90 days; d 120 days; e 130 days; f 160 days

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Groundwater moved upward 3 m along the fault zone after 30 days (Figs. 14a, S-4), 6.5 m after 60 days (Figs. 14b, S-4), 11 m after 90 days (Figs. 14c, S-4), and 16.2 m after 120 days (Figs. 14d, S-4). This indicates that the seepage velocity gradually increased with time, which fully embodied the groundwater’s wedge action. The hydraulic gradient of groundwater was ≈ 20 and fine particles in the fault zone were removed under the high seepage pressure after the fault zone fails (Jiang et al. 2013; Ma et al. 2016; Zhang et al. 2014). The seepage deformation accelerated groundwater movement along the fault zone (Figs. 14e, f, S-4).

Fig. 14
figure 14

Pore water pressure for the different seepage time under the disturbed state: a 30 days; b 60 days; c 90 days; d 120 days; e 130 days; f 160 days

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The rock surrounding dewatering boreholes can fail due to softening and hydraulic fracturing (Fig. 13e, f), which leads to a significant increase in the media permeability (Li and Wu 2019; Wang et al. 2001; Yin et al. 2015). Groundwater from the karst aquifer bursts into the mine along the fault zone and weak areas in the surrounding rock (supplemental Fig. S-4).

The time of water inrush could have been predicted by monitoring the hydraulic pressure at points in the fault zone and the rock surrounding the dewatering boreholes. The simulation results indicate an inrush delay of about 150 days (Fig. S-4), slightly longer than the actual delay time (about 120–130 days). This confirms that the numerical model of fluid–solid coupling is reasonable for this study.

Water Inrush Mechanism

The deformation and failure were concentrated at the bottom of the fault zone because of its natural weakness there (Figs. 7, 8). The mechanical properties of the fault zone are very sensitive to water because of the strong hydrophilicity of the clay minerals, such as the illite-montmorillonite mixed-layer and illite, which created favorable conditions for water inrush (Mu 2018).

The maximum principal stress of the fault zone decreased substantially in the disturbed state due to softening (Figs. S-5, S-6), which loosened the material (Wu et al. 2011), which was already in a state of volume expansion (Wu et al. 2004). This enhanced the fault zone’s permeability, causing groundwater to enter it. The pore water pressure then further enhanced the fault zone’s permeability (Fig. 15) and initiated failure because of the reduced effective stress (Liu et al. 2017). This also promoted upward groundwater movement. Fine particles were removed under the high seepage pressure after the fault zone failed, which further increased permeability (Jiang et al. 2014; Ma et al. 2016; Zhang et al. 2014) and groundwater movement along the fault zone (Fig. 14e, f).

Fig. 15
figure 15

Permeability variation of fault zones as a function of seepage time in the disturbed state

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The hydraulic properties of the fault zone transformed from an impermeable medium in the natural state to a water-conducting medium, causing rapid movement of groundwater along the fault zone (Figs. 13, S-4) (Qian et al. 2018). The rock surrounding the dewatering boreholes also underwent failure because of the low strength and softening (Fig. 13) (Yin et al. 2016). Groundwater eventually burst into the mine along the fault zone and where the surrounding rock failed (Fig. S-4).

An essential component of the water inrush was the feedback effect. First, hydration between media and water led to strength deterioration when groundwater in the dewatering boreholes encountered the fault zone. Strength deterioration then reduced the maximum principal stress and volume expansion, which enhanced fault zone permeability, which in turn further increased the pore water pressure, which promoted failure and further permeability increase. The failure of the fault zone conversely enhanced its permeability and contributed to seepage deformation.

Although both mine dewatering or coal mining near fault zones can transform the hydraulic properties of fault zones transform from impermeable to water-conducting, the mechanisms are different (Wu et al. 2011). The mechanism of water inrush from fault zones disturbed by mining is mainly due to fault zone failure and the increase of pore water pressure because of stress redistribution (Wu et al. 2011; Zhu et al. 2014), while disturbance by mine dewatering is mainly due to feedback effects between the groundwater and fault zone.

To the best of our knowledge, the mechanism of water inrush from fault zones disturbed by mine dewatering is rarely reported (Mu 2018). The results of this study therefore not only provides important information for understanding water inrush from fault zones, but also has practical significance in preventing groundwater inrush events in coal mines.

To prevent water inrush through fault zones disturbed by mine dewatering, dewatering boreholes should, whenever possible, be drilled away from the fault zone. Next, attention should be paid to the mine’s water yield and whether the groundwater contains fine particles in the process of mine inflow. Finally, geophysical prospecting technology should be used to investigate the evolution of fault zones’ hydraulic properties.

Conclusion

The low strength and water sensitivity of media containing clay minerals is the fundamental reason of water inrush along a fault zone disturbed by mine dewatering. The mechanical action and erosive effect of water–rock interactions then promotes water inrush along the fault zone.

The fault zone can be regarded as an almost impermeable medium in its natural state, but transforms into a water-conducting medium due to the feedback effect between the fault zone and groundwater. The numerical model of fluid–solid coupling presented here considers the effect of mean principal stress and pore water pressure on the permeability of fault zones. Consequently, the model can reveal well the mechanism of water inrush through fault zones disturbed by mine dewatering, and can be used to guide to design a dewatering scheme near fault zones in similar mining areas.