Effect of Crack Propagation on Mining-Induced Delayer Water Inrush Hazard of Hidden Fault

Hidden faults in deep coal seam ﬂ oor threaten the exploitation of coal resources. Under the in ﬂ uence of mining and water con ﬁ ned in the ﬂ oor, the cemented ﬁ ller in the hidden fault will be eroded by water ﬂ ow, in order to investigate the fracture characteristics and water inrush risk of hidden faults in ﬂ oors above con ﬁ ned aquifer. Using the 27305 working face as geological background, the in ﬂ uence of the seepage scouring ﬁ ller on the mechanism of water inrush from hidden faults was assessed by developing a stress-seepage coupling model and employing the ﬁ nite di ﬀ erence method to simulate the seepage process of hidden faults under the combined action of high ground stress and high con ﬁ ned water. The evolution of seepage, shear stress, and plastic zone was also assessed. The in ﬂ uence of the hydraulic pressure of the aquifer and the thickness of a waterproof rock ﬂ oor on the formation of the water inrush pathway was analyzed. Results indicate that (1) under the in ﬂ uence of mining, the hidden fault experienced the change process of stress stability, stress concentration, and stress release. The shear stress increases ﬁ rst and then decreases. The compressive stress decreases gradually due to stress release. (2) Water inrush disaster will not occur immediately when the working face is above the hidden fault. The delayed water inrush occurs in the mined-out area when the working face advances to 160m, the ﬂ oor failure zone is connected with the hidden fault failure zone, and the delayed water inrush channel is formed. (3) With the mining advances, the water pressure of aquifer is the same. The larger-angle fault leads to the thinner thickness of ﬂ oor aquifer. The greater the in ﬂ uence of hidden fault on coal seam mining, the higher the danger of water inrush.


Introduction
Water inrush in coal mine is one of the major disasters in mine safety production [1]. With the increasing year by year of mining depth and coal output in China, more and more coal reserves are threatened by water inrush, and many mines have entered the stage of deep mining [2]. During the mining process will inevitable be affected by the complex mechanical environment of high crustal stress, high geotemperature, high confined water, and strong mining disturbance, resulting in a series of disasters accidents [3][4][5]. According to the statistics of relevant departments in China, water disasters are second only to gas explosions in grave accidents in coal mines [6]. About 3% of coal mine safety accidents from 2005 to 2019 were caused by water inrush [7] (see Figure 1). Com-pared with other types of accidents, water disasters have caused in a number of deaths and huge economic losses [8,9]. It is more and more important to effectively prevent and control these disasters [10].
Water inrush from mine floor is a phenomenon of local instability in the mining process, especially the water inrush from fault structure is the most serious [11,12]. Under the influence of mining activities, the hydrogeology condition of coal floor changes and the impermeable layer is destroyed, which causes the confined water under the floor to flow into the working face through faults and tectonic fissure, causing water inrush from the coal floor to cause safety problems [13][14][15]. In addition, water inrush disasters also lead to environmental damage, such as surface collapse and groundwater contamination [16,17]. For a long time, the water inrush from hidden fault has been one of the important topics in rock and hydraulic mechanics studies [18][19][20].
In recent years, many researchers have conducted a large number studies on the water inrush mechanism of the hidden fault in the floor from different research directions. At present, a number of mechanism for the formation of water inrush, including floor relative water resisting layer thickness, Hoek-Brown improvement [21], lower three zone theory [22], in situ tensile fracture and failure at zero position [23], key stratum theory [24], nonlinear catastrophic model [25], critical water outburst coefficient [26], and other water inrush criteria and theory, have been studied. These achievements have played a positive guiding role in preventing water inrush from the coal floor. However, there are still obviously insufficient in the study mechanism of fault-induced water inrush. For some water inrush accidents induced by hidden fault, it is obviously no longer applicable to use the previous theory for prediction and analysis. In the study of delayed water inrush from hidden fault in floor, the occurrence of floor water invasion can be days, weeks, or longer [27]. This is closely related to the fault structure, the fracture development, and the confined water. Therefore, it is very important to study the water inrush law of hidden fault from the interaction of stress field and seepage field, and it will be more consistent with reality [28,29].
Numerical simulation and laboratory test are important means to predict the risk of fault water inrush and formulate corresponding prevention measures. Shi and Yang [30] analyzed the evolution of particle migration and seepage properties of the water inrush through broken rock mass by a numerical case. Guo et al. [31] used the Comsol Multiphysics software to study the fault water inrush and current flow mechanism under the effect of stress and water pressure. Based on the theory of fluid-structure coupling mechanics and multitechnical means, the formation characteristics of water inrush channel damaged by mining rock strata, the precursor information of microseismic activity of water inrush rock strata, and the numerical simulation results of parallel seepage coupling are comprehensively inversed [32,33]. Zhang et al. [34] used the FLAC 3D fluid-solid coupling model and variable parameter rheological model, the influencing factors and mechanism of delayed groundwater inrush induced by hidden fault coal seam are studied, and the influencing factors of permeability of hidden fault are analyzed.
Many researchers at home and abroad have made a body of researches and have gained great achievements on mechanism of the water inrush from coal floor comprehension studies [35][36][37]. There are few studies on mechanics model of water inrush from mining fault and risk criterion of water inrush from fault activation in coal floor. In this paper, a damage evolution mechanics model of coal seam floor with hidden fault in confined water is established. This paper conducts FLAC 3D to simulate the temporal and spatial distribution characteristics of the hidden fault activation, and the change of confined water is obtained. Analyze the process of the delayed evolution of the hidden fault floor in the confined water from new perspective.   The hidden fault can be regarded as kind of "porous media," and is finely meshed by the finite element method. The basic equilibrium equations for rock strata and hidden faults are the same, but their constitutive equations are different. The macroscopic analysis assumes that the porous medium can be regarded as the continuous medium, and the volume change of porous media in time t is equivalent to the volume change of the fluid [38,39].

Stress-Seepage
where ξ is the volume change of fluid in pores of a unit volume, α is Biot's coefficient, ε is the volume strain of porous media, N is the Biot modulus, and p is the pore pressure.

Strength Criteria of Hidden Fault.
To investigate the evolution law of stress field, seepage field and failure range of roof and floor during the mining process, the local grid of deformation and failure of roof and floor refined. For hidden fault and surrounding rock materials in this paper, Mohr-Coulomb criterion [40,41] is used and the shear strength criterion f c ′ and the tensile strength criterion f t ′ are expressed as: where σ 1 and σ 3 are the maximum and minimum principal stress, c is the cohesive force, θ is the internal friction angle, and σ t is the tensile strength. When f t = 0, the rock mass will undergo tension failure, and when f c = 0, the rock mass will undergo shear failure.

Flow and Fine Particle Migration
Equations. The constitutive relation for groundwater fluid flow can be expressed by Darcy's law [42] as follows: where q w is the velocity of fluid flow, k is the permeability coefficient, ρ w is the density of water, g is gravitational acceleration, and μ w is the viscosity of the water. Substitution of Equation (3) into the conservation equation of fluid results in [43,44], where where φ is porosity, β l denotes the bulk modulus of fluid, v u is undrained Poisson's ratio of porous medium, and K s is the effective bulk modulus of the solid constituent.
To investigate the mechanism of particle migration, by referring to the theoretical work of solid particle erosion in hidden faults. According to a generalized Exner equation, sediment mass balance can be described [45] as follows: where ε 0 can also be expressed as ð1 − λ p Þ, λ p equals the bed porosity, q s is the negative divergence solid particle, and σ is positive with an increase in elevation over time and is negative with a decrease in elevation over time.

Permeability Evolution Equation.
According to the permeability test of rock in the deformation and failure process, the expression formula between permeability and volumetric strain for relatively complete rock can be written as follows: where β 1 and β 2 are two coefficients reflecting the permeability before and after peak value under compaction and damage, respectively, and ε r is the volumetric strain in the rock expansion stage. For the granular rock mass inside the hidden fault, the relation between permeability and volume strain is as follows: Since the Carman-Kozeny equation can investigate granular rocks accurately [46], it is used to model the relationship between permeability and porosity of hidden fault as follows: where k f is a parameter related to rock properties of hidden fault, which can be determined experimentally.

Numerical Simulations on Hidden Fault
Delayer Water Inrush mining of the working face. The geological conditions related to the 27305 working face of the coal seam are shown in Figure 2.
When the hidden fault existing in the coal seam floor connects the Ordovician limestone aquifer, under the infiltration of confined water, the upward developed water flowing fracture occurs at the top interface of the aquifer, and the uplift height of confined water caused by structure is usually small. In the process of working face mining, the front coal seam floor strata produce compression deformation under the condition of advanced support pressure and floor stress redistribution, which causes the development and expansion of floor cracks. When the working face continues to advance, the floor rock expands and deforms under the stress release state, and the floor damage cracks further develop to form the floor failure zone with water conductivity. As shown in Figure 3, the rock around the hidden fault in the floor is easily activated by mining, and the fissures expand and develop along the fault to form fault failure zones. Under the syner-gistic effect of vertical stress of floor and Ordovician limestone water pressure, the confined water body rises further along the original confined water conduction zone and hidden fault failure zone and then forms confined water heads with different conduction heights. During the advancing process of the working face, the floor rock of the floor failure zone of the working face is compressed and destroyed by the advance support pressure. After unloading, it will expand and deform and eventually form a floor rock failure zone. The hidden fault and its surrounding rock are activated and destructed by shear force and then the confined waterconducting zone. When the coal seam floor failure zone is connected with the water diversion zone of the hidden fault, the water inrush channel is formed, which causes the water inrush of the hidden fault. 4 Geofluids (FLAC 3D ), which can simulate the mechanical behavior of failure plastic flow of geological materials when they reach the strength limit. It is especially suitable for analyzing progressive failure and instability and simulating large deformation, and is very accurate in simulating plastic failure and flow of materials. The explicit Lagrangian method is a new numerical analytical method different from the implicit difference method. It divides the computational domain into several quadrilateral elements, each of which is endowed with physicalmechanical properties, and simulates the three-dimensional mechanical behavior of rock or other materials. In the simulation, the grid cell can be deformed with the deformation of the material [47]. This algorithm is very suitable for simulating large deformation for rock. Figure 4 shows such a specific loop calculation relationship. This relation first calls the equation of motion to derive new velocities and displacements from stresses and external forces. The strain rate is derived from the velocity, and new stresses are derived from the strain rate. For each cycle of the cycle, we use a time step.

Simplified Geological Model of Mining-Activated Water
Inrush from Hidden Fault in Coal Floor. As shown in Figure 5 Figure 6).
The boundary of the model is constrained in X and Y directions; the full constraint is applied to the bottom of the model; the vertical equivalent uniform load of 10 MPa is applied to the top boundary of the model. At the same time, in order to better simulate the fluid-solid coupling between seepage of high confined water along hidden fault and floor failure, the pore water pressure in the aquifer under the initial condition is 4 MPa and that of the remaining strata is 0 MPa.
Two monitoring lines along and perpendicular to the hidden fault direction are arranged on the coal seam floor of the model (Y = 100 m), with a total of 5 monitoring points (see Figure 6). The thickness of waterproof layer of coal seam floor is 50 m. In the process of numerical simulated calculating, elastic-plastic constitutive model and Mohr-Coulomb failure criterion are used to calculate the mining failure characteristics of coal seam floor.
According to the actual process of the numerical model, the excavation should be used to realize, waiting for the model to reach the preequilibrium. Through the excavation calculation of the model stopping space, the mining thickness of the coal seam is 4.5 m, and the excavation step is 10 m in the quality calculation; the stress field, displacement field, and seepage field are calculated once every 10 m excavation. After finishing the face mining, the seepage field is calculated by 2000 steps. At this time, the maximum unbalanced force of the model tends to 0, and then, the failure range of the impermeable layer in the coal floor tends to be stable.
In the calculation process, the structural stress of the rock formation is ignored, and parameters are set as follows: the model is divided into eleven layers in line with the actual situation, the coal seam is in the fifth layer, and the floor is in the sixth to eighth layers. Table 1 shows mechanical parameters of each rock layer.

Results and Discussion
This study addressed the main concerns described in Introduction, which are the evolution of large deformation, stress field, and seepage field   When mining had advanced 120 m, the failure of the original stress field is intensified due to the large mining stress, and the surrounding of the pinch-out of the fault is subjected to tensile and shear forces, which is in the extended state, and the active fissures of the hidden fault gradually develop to working face. When mining had advanced 140 m, the hidden fault is directly below the working face, the mining stress and the confined water pressure of the floor are more intense, the damage is more obvious, and the hidden fault is in a stable state of damage accumulation.  the failure and destruction of the impermeable layer between the plastic zone of the floor and the active expansion of hidden fault are continuously reduced, and the water-conducting fissure zone is continuously expanded and developed. When mining had advanced 160 m, the water flow channel is formally formed and the failure mode is shear failure. At this time, the coal seam floor has completely lost its water-blocking capacity. With the advancement of working face, the initial stress redistributes due to the stress unloading effect, and the influence range of the vertical stress of the floor is gradually increasing. The stress concentration appears on both sides of working face, and the initial stress field around the hidden fault is gradually increasing due to the influence of the vertical stress of the floor. The vertical stress plays an important role in the initiation, expansion, and development of fissures in hidden faults.

Analysis of the Vertical Stress
When mining had advanced 80 m, it can be seen that the vertical stress in the hidden fault and surrounding rock is accumulated. The stress concentration area first occurs at the bottom of the hidden fault, which is mainly affected by the vertical stress of the floor and the pore pressure of the aquifer. At the same time, the roof and floor fissure zone increases with the roof caving and ground heave, and the influence range of the stress relaxation area expands accordingly. The hidden fault fracture zone and surrounding rock mass will produce initial activated fissures under the action of vertical stress. When mining had advanced 120 m or 140 m (when the working face is above the hidden fault), the vertical stress around the hidden fault gradually tends to be unified from the bottom stress concentration to the overall stress. The hidden fault and the floor impermeable layer are in the stage of fissure expansion and development and accumulate stress energy. At the same time, the floor and the hidden collapse column are also easily affected by the failure of the goaf ground heave. When mining had advanced 150 m or 160 m, combined with the failure characteristics of the plastic zone, it is found that the vertical stress distribution near the hidden fault tends to be stable due to the influence of the mining work, which indicates that the hidden fault and surrounding rock are damaged, and the surrounding rock and its internal stress energy release. The water inrush   Figure 9. Usually, after the coal is extracted, the floor stress released and forms a relief area under the goaf, and the roof above the goaf is affected by stress concentration and forms a pressurized area. Affected by the concentration and release of shear stress, the pressure relief area and pressurized area are formed in front of working face and the roof and floor of coal seam. The change of shear stress affects the fracture propagation and activation failure of rock mass in hidden faults.
With the advancement of working face, the influence area range of the shear stress gradually increases, and the stress concentration in front of working face has stronger influence on the hidden fault. The shear stress field around the hidden fault gradually increases, and the maximum shear stress reaches -6 MPa. The shear stress plays a leading role in the activation, development, and destruction of hidden fault during mining.
When mining had advanced 80 m, the shear stress field inside the hidden fault and the surrounding rock began to increase, indicating that the hidden fault and the surrounding rock mass began to be activated and deformed, and partial failure occurs to release the shear stress. Meanwhile, the stress accumulation began in the middle and upper of the hidden fault and the surrounding rock. The influence range of the roof and floor fissured zone and the stress relaxation zone reached the maximum with the advancement of working face. When mining had advanced 120 m or 140 m (when the working face is above the hidden fault), the stress on the floor impermeable layer between the working face and the hidden fault is relatively concentrated, and the hidden fault and the floor impermeable layer are rapid deformation stage. Meanwhile, the hidden fault is easily damaged by shear stress. When mining had advanced 150 m or 160 m, the mined-out area floor continues to develop and destroy, and the influence range of shear stress field of the hidden fault little changes, indicating that the hidden fault interior and the surrounding rock have been completely destroyed, the shear stress is released, and the water inrush channel is formed.  Figure 10 shows the relationship between vertical stress and shear stress at each measuring point as the advancing distance changes. The following results can be obtained: When excavation is 0 m to 60 m, the compressive stress and shear stress of the monitoring point are fixed load, and the stress of the monitoring point does not change. When excavation is 60 m to 140 m, the shear stress of the monitoring points in the hidden fault gradually increases, while the vertical stress gradually decreases. The compressive stress of monitoring points 4 and 5 increases at first then decreases. The stress redistribution will reverse increased in the initial stage of shear stress, and the stress redistribution will increase the circumferential stress and decrease the radial stress, and then, the stress recovered and reached the maximum shear stress at 130 m and 140 m, respectively. When excavation is 140 m to 160 m, due to the failure deformation of the surrounding rock and the hidden fault, the release stress leads to the compressive stress and shear stress corresponding to the monitoring point that gradually decreases.  Figure 11 shows the failure area diagram and the seepage vector diagram of the hidden fault.
In the process of mining, hidden fault will be activated and destroyed under the action of shear stress, when the fissure will occur. Meanwhile, the confined water in the aquifer softens and erodes the fault, which leads to the failure of the faults cut into the aquifer. Under the same other geological conditions, hidden faults with large angle are easy to destroy the failure zone of connected floor. When the dip angle of the hidden fault is 60°or 75°and mining had advanced 160 m, the hidden fault and the surrounding rock failure zone are connected with the floor failure zone. Combined with the expansion of seepage vector and path distribution of hidden fault, it can be seen that floor delayer water inrush has occurred at this time. When the dip angle of the hidden fault is 45, the failure area of the hidden fault cannot be connected with the failure zone of the mining floor, and the seepage vector around the hidden fault is small, so the hysteresis water inrush disaster will not occur.

Conclusions
A numerical model of underground mining with a hidden fault was developed to analyze the mechanism of water inrush due to hidden fault activation in the mining process. The evolution of stress field, seepage field, and plastic zone around the hidden fault during the advancing process was simulated. The influence of the thickness of the aquifer and its water pressure on the water inrush was analyzed, reaching the following conclusions: (1) The working face has a great influence on the distribution of the shear stress in the hidden fault. The shear stress increases first and then decreases, while the compressive stress decreases gradually due to the release of stress energy in the mined-out area. When the working face is excavated above the hidden fault, the shear stress inside the fault and surrounding rock reaches its peak value and the critical state of failure 10 Geofluids failure zone and the hidden fault. The delayed water inrush in the mined-out area occurs when mining had advanced 160 m, the floor failure zone is connected with the hidden fault failure zone, and the delayed water inrush channel is formed (3) When the working face advances above the hidden fault, the stability of the floor of the impermeable layer decreases, and the large-angle hidden fault easily produces fissures that penetrate the coal seam floor and aquifer. The dominant seepage channel is formed by the fractures, and seepage is mainly concentrated under the working face. When the water pressure of aquifer is the same, the larger-angle fault leads to the thinner thickness of the floor of the aquifer. In addition, the greater the influence of the hidden fault on coal seam mining, the higher the danger of water inrush

Data Availability
The data used to support the findings of this study are included in the article.

Conflicts of Interest
The authors declare that they have no conflicts of interest to this work.