Abstract
Under the environment that the safety problem of coal mining is becoming more and more serious, research on coal seam has become one of the hot topics. Among them, the water inrush from coal seam floor is one of the main threats to coal mine safety. Based on this, the mechanism of water inrush from coal seam floor was revealed by the coupling of seepage and stress and the variation regularity of permeability of rock during the whole stress-strain process was analyzed, and the effects of confining pressure and osmotic pressure on permeability were studied and the dynamic evolution models of rock permeability and the equation of permeability and volume strain were established. The permeability and failure process of rock were analyzed and rock engineering system (ORES) method was proposed. The seepage stress coupling mechanism of coal seam floor was analyzed and the governing equations of seepage stress coupling of coal seam floor were constructed. Hebei Xingtai North wells in Dongpang Coal Mine 9208 working face water inrush examples were analyzed. This study can provide technical support for the analysis of coal seam floor water disaster and the treatment of water inrush.
Introduction
Coal mine water disaster is a kind of phenomenon that surface water and groundwater as well as other water bodies suddenly into the mine, and when the drainage capacity is insufficient, it submerges mining space in the process of coal mine construction and production [1]. Coal mine water disaster will affect mine production, resulting in property damage, and even cause serious personal injury [2, 3]. The problem of water inrush from coal seam floor is a hot and difficult problem in all kinds of water disasters. The breakthrough of the confined water breakthrough into the mining space is the water inrush from coal seam floor [4]. The change of mining conditions leads to an increase in the risk of water inrush from coal seam floor, and the research on the mechanism of water inrush from coal seam floor and the improvement of the prevention and control technology of coal seam floor water disaster is of great significance to the safety production of coal mine [5]. The essence of water inrush from coal seam floor is the problem of deformation and failure of rock mass under the disturbance of mining and the seepage of underground water into the mining space [6, 7]. The problem of water inrush is a typical seepage stress coupling problem. On the one hand, the mining disturbance changes the distribution of the stress field in the rock mass, which affects the structure of the rock mass, which results in the change of the internal pressure [8]. On the other hand, seepage affects the deformation and failure process of rock mass. With the development of deep mining and lower coal mining, the coupling of seepage and stress plays a more and more important role in the mechanism of water inrush from floor [9]. Beginning with the simplest theory of water inrush coefficient, people realize that the water inrush from coal seam floor is the result of the influence of confined water and diaphragm [10]. With the development of experiment and simulation, the concept and technology of seepage stress coupling have been applied to various fields of solid deformation and seepage. It also provides an effective and powerful research ideas and means for the study of water inrush from coal seam floor [11, 12]. This study is concerned with the deformation and failure of rock mass and groundwater seepage. The effect of seepage stress coupling on the water inrush from coal seam floor can reveal the mechanism of water inrush from coal seam floor [13]. The prevention and control of water disaster in coal seam floor are related to mine safety. The coal mine hydrogeological personnel are the main body of water disaster prevention and control work in the actual work. Only the production line of technical staff on the occurrence of water inrush has a certain pre judgment in order to achieve better water hazard control effect [14]. Water disaster prevention and control work are a very strong experience. Based on the analysis of the mechanism of water inrush from coal seam floor, this paper finds out the cause and effect relationship between the hidden water inrush and the formation of simple and easy analytical model [15, 16]. Therefore, the seepage stress coupling is taken as the main line and the mechanism of water inrush is studied, and the technical basis for flood control is provided in this paper [17].
More and more scholars paid attention to the role of seepage stress coupling in the process of water inrush in the study of water inrush from coal seam floor [18]. The coupling of seepage and stress has become an important part of the research on the water inrush from coal seam floor. At present, the study on the mechanism of water inrush from coal seam floor has been taken into account in the process of water inrush, the failure form of the bottom plate, coupling and other factors. The research on water inrush mechanism is based on two basic problems: how to destroy the bottom plate and how the groundwater flows into the mine [19]. These two problems are also the focus of the study of seepage stress coupling. More and more researches have been done to analyze the water inrush from the perspective of seepage stress coupling [20–22].
Rock characteristics analysis
Rock strength
The rocks of coal measures strata are sedimentary rocks. On the one hand, the strength and deformation characteristics of rock are affected by the composition and structure of the rock particles. On the other hand, it is related to the stress environment and groundwater environment. Due to the mining disturbance, the stress environment of rock changes and the local stress concentration occurs, resulting in cracks and damage in the process of mining. The physical and chemical properties of the rock mass influence the mechanical properties of rock material in the process of water inrush. The mechanical properties of rock materials reflect the ability of deformation and failure of materials. The rock mechanics parameters include the strength parameters and deformation parameters of rock. It is the coupling effect of stress and seepage in rock material (Fig. 1).

Different types of Coal rocks.
The mechanical properties of rocks include the strength properties of rock and the deformation properties of rock. The strength of rock is the maximum stress that the rock can bear under different loads. The strength index is not an inherent property of rock, but it is a kind of index to resist the destruction of rock under certain internal and external conditions. The mining rock mass is still a certain strength after failure in the actual mining work. The rock is destroyed after the peak strength in the process of rock specimen test, but there is still some residual strength. Under the action of the stress, the deformation of the rock and the localization of the deformation lead to the crack. With the increase of deformation, the rock is damaged. The most important rock deformation parameters are elastic modulus (E) and Poisson’s ratio (μ). Under different pore water pressure, the variation of rock strength (σ1) with confining pressure (σ3) in fine sandstone, medium sandstone, coarse sandstone and limestone is shown in Table 1:
Strength parameter infiltration data
When confining pressure increases from 4 MPa to 16 MPa, the peak strength of fine sandstone saturated rock mass increases from 60.33 MPa to 144.33 MPa. With the increase of 84 MPa, the rock strength increases by 139%, and the variation rate of strength with confining pressure is about 7. When the water pressure is 0 MPa, the residual strength of fine sand rock post peak increased from 49.66 MPa to 114.56 MPa. With the increase of 64.9 MPa, the strength increases by 131%, and the change rate of strength with confining pressure is about 5.41. When the water pressure is 3 MPa, the residual strength of fine sandstone failure rock specimen increased from 22.99 MPa to 82.56 MPa. With the increase of 59.57 MPa, the strength increases by 259%, and the change rate of strength with confining pressure is about 4.96. The confining pressure effect of fine sandstone decreases with the increase of water pressure. When confining pressure increases from 4MPa to 16 MPa, the peak strength of the sandstone saturated rock mass increases from 76.05 MPa to 194.65 MPa with an increase of 118.6 MPa and the strength increased by 156%. The change rate of strength with confining pressure is 9.88. When the water pressure is 0 MPa, the residual strength of rock sand in the post peak increased from 39.56 MPa to 104.47 MPa. With the increase of 64.91 MPa, the strength increases by 164%, and the change rate of strength with confining pressure is about 5.41. When the water pressure is 3 MPa, the residual strength of rock sand in the post peak increased from 22.47 MPa to 77.95 MPa. With the increase of 55.48 MPa, the strength increases by 247%, and the change rate of strength with confining pressure is about 4.62. When confining pressure increases from 4 MPa to 16 MPa, the peak strength of coarse grained saturated rock mass increases from 59.3 MPa to 130.85 MPa. With the increase of 71.55 MPa, the strength increases by 121%, and the change rate of strength with confining pressure is about 5.96. The strength of the saturated rock block with different lithology is related to the confining pressure. With the increase of confining pressure, the confining pressure effect of rock strength increases. The rock strength is linear with the confining pressure when the pressure is 0 MPa. The confining pressure effect of rock strength remained unchanged with the increase of confining pressure. When the hydraulic pressure is 3 MPa, the rock strength and the confining pressure are logarithmic. The confining pressure effect of rock strength decreases with the increase of confining pressure.
SSE (and variance), (coefficient of determination), Adj. (adjusted coefficient of determination) and RMSE (root mean square) are goodness of fit inspection indexes. SSE is the sum of the square of the error between the fitting data and the original data, and RMSE is the square root of the sum of the square error of the fitting data and the original data. The smaller the SSE and RMSE, the better the fit is. R2 (coefficient of determination) is the ratio of the sum of squares of the difference between the fitted data and the original data (SSR) and the sum of squares of the difference between the original data and its mean (SST). R2 and Adj.R2 are closer to 1, which shows that the explanatory power of independent variable to dependent variable is stronger (Table 2).
Water pressure fitting equation
The permeability of rock is not only related to the structure of rock medium itself, but also to the deformation and failure process of rock and the stress environment of rock. Rock mass permeability is low. But, with the initiation and propagation of cracks, the permeability changes in the process of rock deformation and failure. The destruction process is shown in Fig. 2.

Coal seam osmosis failure diagram.
Seepage is the flow of fluid through porous media, and the porous Darcy law:
In the formula, V is the seepage velocity and K is the permeability coefficient, and J is the hydraulic gradient.
Permeability is used to represent the seepage capacity of porous media. The instantaneous flow Q
w
through the cross section of the fluid is proportional to the permeability of the interface normal direction k
x
and the hydrodynamic viscosity μ
f
and the hydraulic gradient
In the formula, Q w represents the flow rate and p2 - p1 = ∂p indicates the pressure difference. x2 - x1 = ∂x is the distance and μ f represents the fluid dynamic viscosity, and k x is permeability of x direction.
The expression of Darcy flux v
f
is obtained by means of formula (2):
Because gravity affects the vertical pressure change of water flow in three-dimensional space, Darcy’s law considers the role of gravity. By means of the permeability tensor, the Darcy law is as follows:
In the formula, K is an arbitrary point in the porous medium and (x, y, z) represents the absolute permeability tensor, and g is the acceleration of gravity.
There is a difference between the permeability coefficient K and permeability k. The permeability coefficient K is also called the hydraulic conductivity, and the dimension and velocity are the same as [L/T]. Permeability is only related to the nature of the skeleton with dimension [L2]. It is a macroscopic description of porous media seepage capacity. The relationship between permeability coefficient and permeability is as follows:
In the formula, ρ is the fluid density and γ is fluid gravity.
Darcy seepage is linear seepage. Without considering the structure and interface effect of rock mass, there are some non-Darcy flows or nonlinear seepage in rock mass. One is the non-Darcy flow with the starting pressure gradient, and the percolation occurs in the porous media with low permeability and low flow velocity. A kind is high speed nonlinear seepage flow with high hydraulic gradient and high Reynolds number, which is shown in Fig. 3.

Permeability-stress coupling diagram. (a) Complete rock: σ1 = σ3 = 4/8/12/46 Mpa. (b) The peakrock: σ1 = σ3 = 4/8/12/46 Mpa, p1 = p2 = 0/3/6/9 Mpa. (c) Complete rock: σ1 = σ3 = 4/8/12/46 Mpa, p1 = 0/3/6/9 Mpa, p2 = 0 Mpa. (d) The peakrock: σ1 = σ3 = 4/8/12/46 Mpa, p1 = 0/3/6/9 Mpa, p2 = 0 Mpa.
The influence of confining pressure and pore water pressure on the strength and deformation characteristics of rock and the influence of confining pressure and seepage pressure on rock permeability are obtained through the seepage stress coupling test of different rock specimens to further reveal the coupling mechanism of seepage and stress, which provides the basis for further analysis and application.
Rock failure process can be divided into 5 stages, as shown in Fig. 4: compression stage, linear elastic stage, nonlinear stage, strain softening stage and residual strength stage. The first stage: OA-compression stage: in the beginning of the experiment, the slope increases gradually, and the cracks and pores are compressed and the volume is reduced. The second stage: AB-linear elastic stage: the rock specimen enters the elastic stage, the slope of the curve is close to the constant, the volume is the compression state, the strain can be restored after unloading, and the strength of the B point is the yield strength. The third stage: BC-nonlinear phase: the slope of the curve gradually becomes slow after the B point, and the rock enters the plasticity and damage stage. The stress-strain relation is nonlinear. The plastic stage occurs before the rock failure, which produces the non-recoverable plastic deformation. It begins to appear dilatancy phenomenon from the point of B. The fourth stage: CD-strain softening stage: the strength of the C point corresponds to the peak strength, the rock is destroyed, and the rock corresponding to the C point is the post peak rock. When the C point is reached, the volume of rock is compressed into volume. The CD segment curve began to decline, and the rock strength decreases from peak strength to residual strength. The fifth stage: DE-residual strength stage: After the D point, the rock is in the residual strength stage, and the permeability of rock can be used to analyze the permeability characteristics of rock mass in this stage.

Stress – strain curve of rock.
Seepage stress coupling effect
In order to study the water inrush from coal seam floor through the coupling of seepage and stress, in addition to the experimental study, it is necessary to further study the mechanism of the coal seam mining and the prevention and control of the coupling effect of the water project. Coal seam mining, mine drainage, grouting and other engineering measures affect the rock and groundwater system directly, which belongs to the coal seam floor water inrush problems in the role of the project. Water inrush is the result of rock mass destruction and groundwater entering into mining space, and excavation of coal and rock mass is the inducement of water inrush. The excavation of coal and rock mass includes the mining process of rock roadway and coal seam roadway and working face mining. Mining effect is reflected in three aspects mainly. First, the two stress field is formed, and the rock mass structural plane changes. The second is that the rock mass is affected by the mining stress, which causes the structural damage and the regional damage. The third is to change the boundary condition of rock mass, and the rock mass stress field and seepage field will change. In order to reveal the effect of mining and the seepage stress coupling mechanism of coal seam floor, rock engineering system is introduced (Rock Engineering Systems, RES. This method studies the problem of water inrush from coal floor, and the matrix loop is shown in Fig. 5.

Stress – strain interaction matrix.
The two element interaction matrix can be extended to form a multivariate interaction matrix, namely RES system. RES matrix form can be expressed as:
Formula (6) is n orders matrix. The elements on the main diagonal x ij , i = j, is the interaction of the object and is the interaction of the actors. Non-diagonal elements x ij , i ≠ j describe the interaction of element x ii , x jj . Among them, x ii is the independent variable and x jj is the dependent variable. The non-diagonal element contains the result of interaction, and it can also include the interaction mechanism in the RES matrix.
Because of the coupling of seepage stress coupling, the coupling effect changes the original single field control equation. In order to accurately describe the coupling of seepage and stress, it is necessary to establish a set of governing equations which can reflect the action mechanism. The basic assumptions are as follows. The influence of temperature on seepage stress coupling is not considered, and the compression of the solid skeleton of the rock mass is mainly pore compression without considering the compressibility of solid particles. The porous medium is filled with groundwater and is a single-phase fluid. Groundwater seepage obeys Darcy’s law.
The geometry equation of rock mass is Cauchy equation:
In the formula: μ represents displacement.
The elastic stage is represented by the generalized Hooke’s law:
In the formula, λ is lame coefficient and G indicates stiffness modulus.
Fluid pressure variable P
f
can be expressed by pressure head, and Hydrostatic pressure distribution equation is as follows:
In the formula, z is the elevation head, and represents the potential energy of unit weight fluid. p/γ is the pressure head, which represents the pressure energy of the unit weight fluid. Compressible fluid pressure head is as follows:
The pressure head is the sum of the elevation head and the pressure head:
The water pressure is expressed as the pressure head and the elevation head:
By using the above formula, we can obtain the governing equations with the displacement variable and the variable of the head:
It can be concluded that the control equation of groundwater seepage field is expressed by the displacement variable and the head variable:
So the seepage stress coupling control equations are:
The mechanism of interaction between seepage field and stress field is described by the coupled seepage stress coupling equations. In practical engineering applications, the coupling effect of seepage and stress is calculated by setting the conditions of accurate solution. The seepage stress coupling control equations are the mathematical expression of the seepage stress coupling mechanism of coal seam floor.
Coal seam floor
The effect of seepage stress coupling on the water inrush from coal seam floor is controlled by the rock mass structure of coal seam floor. In the problem of water inrush from coal seam floor, the research object is not only confined to the surrounding rock mass, but also to the confined aquifer. The scope of the research system is larger than the actual mining engineering scale. In addition, the rock mass structure of coal seam floor is affected by the structure of fractures and faults. This makes the complex structure of the floor rock mass. The occurrence of water inrush means that there is a water inrush channel between the mining space and confined aquifer. Because of the sudden and catastrophic water inrush, the water inrush is greater than the normal water inflow, and the equivalent cross-sectional area of the water inrush channel is larger than the pore area of the rock mass. The water inrush channel is formed under the coupling action of mining activity, stress field and seepage field, and it is the superimposed effect of the rock mass structure and mining failure, hydraulic fracturing and so on.
The whole floor is one of the most common models of coal seam floor, and this paper focuses on the seepage stress coupling model of the whole floor. The integrity of the floor is that there is no obvious fracture, fault and other structures that can be explored by drilling and geophysical prospecting. It is shown in Fig. 6.

Complete floor diagram.
Hebei Xingtai North 9208 dongpangkuang wells of water inrush in working face was made as an example to illustrate the complete floor water inrush characteristics. Specific analysis is as follows:
Mining engineering: 9208 working face is third working face in Dongpang Coal Mine No. 9 coal mining of North wells. Mine has been mined 9202, 9201 working face. 9208 working face elevation is –120∼–210 m. The distance from coal seam to Ordovician ash is 32–44 m, average 34.4 m. Aquifer elevation is +72 m. Mining activities are threatened by Ordovician limestone water inrush from coal seam floor.
Stress characteristics: Based on FLAC3D numerical simulation software, the numerical model of working face mining is established to obtain the stress field characteristics of surrounding rock. Based on Fiber Bragg grating sensor technology, the stress characteristics of the working face floor are monitored. Through simulation, the initial stress field is changed by working face mining. With the advance of the working face, the roof rock mass of the mined out area causes the stress release and the vertical stress decreases. Stress concentration concentrates at mining location and the maximum vertical stress appears in front of the working face. The coal floor has the front compression in the process of working face advancing. The expansion and recovery of the three stages promote repeated with the work face.
Rock mass structure: no fault structure was found in the course of track Lane, belt lane of 9208 working face. The comprehensive geophysical prospecting and drilling exploration work was carried out before the working face mining. There are no faults and other structures in the floor rock mass by transient electromagnetic method, audio frequency electric perspective and electric sounding. According to the local fracture zone, the drilling and grouting were carried out. The constructions include the 57 floor grouting drilling footage of 3626.7 m with injection of cement 644.83t. Through the inspection of the borehole, the bottom of the 9208 working face is a complete floor. There are no faults, fractures, karst collapse pillars and other water diversion channels before the working face is removed.
Seepage characteristics: The porosity of the floor rock mass is small, and the pore water pressure is not revealed. The hydraulic pressure is 2.36∼3.16 MPa at the bottom of the rock bearing. After the occurrence of water inrush, the water level is reduced in different degrees, and the water depth of Ida 1 hole is 17.57 m. When the working face is pushed to 680 m, water inrush occurs, and the initial water content is 50 m3/h. Since then gradually increased, the surge of water to 1550 m3/h after 7 hours. 9 hours later, the water is reduced to 1250 m3/h and gradually stabilized. The water discharge duration curve is shown in Fig. 7.

Sudden drop of 69208 working space in water profile.
Water inrush characteristics: Water inrush increases gradually and a small amount of attenuation maintains at a certain level. The gradual change of water inrush reflects the increase of water inrush channel. After the water inrush, the karst collapse column is not found through exploration. The water inrush channel is the source of water inrush from the bottom of the rock mass and the fissure in the mining space. Under the coupling of seepage and stress, the rock mass is destroyed and the water inrush channel is formed. The water inrush point is located at the rear of the hydraulic support 5 m, and the water inrush is not lag. This position is consistent with the location of the stress change near the mining distance sensor. It shows that the depth of the bottom of the stress concentration is larger.
Coupling characteristics of seepage and stress: The thickness of the whole floor water inrush floor is usually thin. In the initial stage of water inrush channel, due to the low effective porosity of rock and the poor permeability of rock mass, the pore water pressure is applied to the bottom rock mass, and the boundary water head is changed. The hydraulic pressure is 0. Under the influence of mining stress, the deformation of rock mass, the internal crack initiation and the rock permeability increase gradually. The pore water pressure increases, and the effective stress of rock mass decreases. In the position of stress change, the floor rock mass is the most destructive. When the cracks are communicated with each other, the passage of the groundwater to the mine is formed. Under the coupling of seepage and stress, the water inrush channel develops to a certain level. Therefore, the water inrush shows a linear gradual process. In the mining process, the crack has a certain bridge in the stress recovery zone, and the water inrush occurs in the stress change.
The coupling of seepage and stress are the essence of water inrush from coal seam floor. The occurrence of water inrush is caused by the seepage of groundwater through the coupling of seepage and stress, which leads to safety accidents. Based on different confining pressure and different water pressure conditions, the strength parameters of rock, such as fine sandstone, medium sandstone, coarse sand, limestone, the conclusion that peak strength of saturated rock mass increased with the increase of confining pressure was obtained in this paper. The residual strength of the rock was positively correlated with the confining pressure, and the residual strength decreased with the increase of water pressure. Based on Darcy’s law, the permeability law of different rock layers was analyzed, and the rock permeability decreased with the increase of confining pressure. With the increase of the osmotic pressure, the change of the confining pressure caused the rock deformation and the permeability change, and the increase of osmotic pressure caused the destruction of the rock layer at the inlet. In addition, the coupling mechanism of seepage and stress was analyzed by using the method of rock engineering system (RES), and the active control equations were established, which provided a theoretical basis for the theoretical study of coal seam floor. Finally, based on the model of intact bottom plate, Hebei Xingtai North dongpangkuang wells 9208 working face water inrush examples were analyzed. It has been found that the phenomenon of water inrush generally occurred in the location of stress change and the water inrush was instantaneous, which provided a theoretical basis for preventing water inrush. In summary, this study can provide technical support for the water inrush mechanism and performance characteristics of coal seam floor, which can directly promote the development of coal seam mining and its prevention and control technology.
