A Water-Rock Coupled Model for Fault Water Inrush : A Case Study in Xiaochang Coal Mine , China

Water inrush disasters in mining frequently occur under the influence of confined water-bearing fault zones. +erefore, investigating the fault water inrush mechanism is necessary to reduce the number of occurrences of this type of disaster. In fault zones, the rock is highly fractured, and the mechanism of water conduction is complex. In this research, the seepage mechanism of fractured sandstone in fault zones is studied through experiments, and the results indicate that the permeability coefficient of fractured sandstone depends on the axial stress and particle size. +e relationship between the permeability coefficient and axial stress was an exponential relationship. +en, a water-rock coupled model is proposed based on the experimental results, which considers the different water flow patterns during water inrush disasters. Finally, a numerical simulation combined with the waterrock coupled model is conducted to investigate the fault water inrush mechanism of a case study, and the results reveal that when water inrush disasters occur during mining, two types of conditions are required. One is that the connection among the fractured zone of the coal seam roof, fault fracture zone, and aquifer fails, and the other is that the connection among the fractured zone of the water inrush prevention pillar, fault fracture zone, and aquifer fails. +is study contributes to an increased understanding of the mechanism of water inrush disasters and the design of water inrush prevention pillars.


Introduction
Fault zones are the outcome of active tectonic movement that occurs for a long period of time; fault zones have the following characteristics: (1) there are a large number of fracture surfaces in the fault fracture zone; (2) there is a lack of integrity and association between the structural fracture surfaces and rock mass that can easily result in flow deformation; (3) highly developed fractures are present, and the rock is highly fragmented in the fracture zone.Because of these characteristics, sufficient space is created for the confined water to flow along fault zone fractures.Moreover, fault zones often isolate confined water-bearing rock strata from coal seams.As a result, the aforementioned fault zones can act as water inrush channels between the confined water-bearing strata and adjacent working faces in the mine [1,2]; the latter can easily result in water inrush accidents if no preventative measures are implemented.Figure 1 clarifies the above statements.erefore, it is necessary to study the water inrush mechanism between a confined water-bearing seam and coal seam working face in the presence of adjacent faults that contain water to reduce the number of water inrush accidents.Several researchers have considered water inrush disasters to be the result of water and rock interactions during mining.Li et al. [3] proposed that an excessive amount of fracture displacement and fault seepage erosion, which is caused by confined water in key layers of fault zones, constitute the floor water inrush mechanism of fault zones based on a structural layer model.Li et al. [4] proposed an activation mechanics model for the water-separated layer with faults based on the principle of a water-bearing layer.However, the aforementioned researchers did not consider the water-weakening effect, in that the compressive strength of rock containing water becomes lower than that of rock without water; in addition, the influence degree was related to the moisture content of the rock [5].e water-weakening effect on different types of rocks has also been studied by numerous researchers [6][7][8][9][10], and certain experiments have also been conducted to investigate the water-rock interaction effects on the mechanical and seepage properties of rocks [11][12][13].Terzaghi pioneered the theory of the effective stress of saturated soils with regards to the mechanical effect of water acting on rocks, where the effective stress was defined as the difference between the total stress and the pore water pressure as follows: where σ ij is the total stress, p is the pore water pressure, σ ij ′ is the effective stress, δ ij is the Kronecker symbol, and α is the effective stress coefficient.Since then, effective stress principles have been widely applied by several scholars as part of the fluid-solid coupled theory [14][15][16][17][18]. e Darcy law explains the flow of water in rocks with regards to the effect of rocks on water, and since then, other scholars have conducted numerous studies on the relationships among the pore pressure (pp), permeability coefficient, and strain and stress [13,17,19,20].In addition, numerous simulation studies have been performed to address water inrush issues [4,15,[21][22][23][24].However, these studies regarded the fault only as a discrete face, thereby neglecting the fault fracture zone and the water-rock coupling effect.Certain experiments and studies have also been conducted to investigate the seepage properties of fractured rocks [25][26][27][28][29][30]; however, the seepage properties were not associated with the fault water inrush mechanism.In addition, these investigations were mainly focused on continuous and quasi-continuous media and neglected the presence of a water-bearing fault in the mining zone; the physical and mechanical properties of rocks and rock masses are greatly affected and different from those of rocks and rock masses without faults.Furthermore, these investigations focused on an analysis of the mechanics, and only a few focused on the fault water inrush mechanism considering the water-rock coupled theory.e limitations are as follows: fault water inrush investigations focused on the stress analysis of the surrounding rock without considering the influence of the seepage field; the evolution of fault water inrush channels was not clearly represented in the mining process adjacent to a fault zone; and at the same time, the percolation evolution of fractured rock in the fault fracture zone has rarely been studied.In contrast to other studies, this paper investigates the percolation evolution of fractured rock in the fault fracture zone through experiments.en, a water-rock coupled model is established and the evolution of fault water inrush channels is investigated through numerical simulation.

Research Methodology
e research methodology is shown in Figure 2. First, the seepage mechanism of fractured rock in the fault fracture zone is studied through experiments.e experimental steps are shown in Figure 2(a).Second, the water-rock coupled model is extended based on the experimental results, and the water-rock coupled process is proposed, as shown in Figure 2(b).
ird, numerical simulation is conducted to analyze the fault water inrush process, and the calculation process is shown in Figure 2(c).e research methods are introduced in the following sections.

Seepage Experiments of Fractured Rock
2.1.1.Sample Preparation.Samples were taken from the Mount Er Gang fault in the Xiao Chang coal mine in Changzhi city, Shanxi Province, China.e drilling locations of the samples are adjacent to the fault (Figure 3).e drilled samples were sandstone, which were relatively fractured (Figure 4).e samples were ground to obtain a smaller particle size and then graded using grading sieves. 2 Advances in Civil Engineering e particle size ranges of each grade were size 1 (5-10 mm), size 2 (10-15 mm), size 3 (15-20 mm), and size 4 (20-26.5 mm), which are shown in Figure 4. ree groups of specimens were prepared for each particle size range to ensure that the experimental results were representative.

Experimental
Programme.An MTS815.02electrohydraulic servo controller rock mechanics testing system and a self-regulating seepage apparatus were used in the test, and the experimental apparatus components are shown in Figure 5.
e apparatus could not only conduct steady penetration experiments but could also conduct transient penetration experiments.However, the pore pressure difference between the circular sections of the specimen rapidly disappeared during the transient penetration experiment because of the high permeability of the fractured medium.Hence, a steady-state experiment was conducted.e load was controlled below 20 kN after preparing and installing the samples, and the pore pressure did not exceed 0.5 MPa under the in uence of open water circulation control; as a result of the latter, the medium was fully saturated.en, the test equipment was loaded automatically according to the design procedure.Detailed experimental steps are shown in Fig- ure 2. e seepage calculation of the fractured sandstone experiment is shown below; with regards to the steady-state experiment, the permeability coe cient was calculated with the Darcy law as follows (equation (2)): where k is the permeability of samples, v is the seepage velocity, q is the quantity, A s is the cross-sectional area of the samples, l is the length of the samples, h 1 and h 2 represent the waterhead, and J is the hydraulic gradient.Moreover, to evaluate whether the seepage was in agreement with Darcy seepage, the Reynolds number was calculated with the following equation: where R e is the Reynolds number, d is the particle diameter, and c w is the water kinematic viscosity.Hence, R e max was 0.44 as calculated by using equations ( 2) and (3), which con rmed that the seepage observed during the experiment was the Darcy seepage.
(1) Analysis experimental results: the experimental results with regards to the relationship between k and axial stress σ of sandstone consisting of di erent particle sizes are shown in Figures 6(a)-6(d).
From the abovementioned diagrams, the following conclusions could be drawn: (1) given the same axial stress, the smaller the particle was, the smaller the permeability coe cient was; (2) the ow rate of water had little e ect on the permeability coe cient, which increased slightly with increasing ow rate; (3) the permeability coe cient of fractured sandstone was much higher than that of intact sandstone under the action of axial stress; and (4) the fractured rock became compacted, and the permeability coe cient decreased as the axial stress increased.Moreover, the relationship between the permeability coe cient and axial stress was nonlinear, so an exponential function (equation ( 4)) was used to describe the nonlinear relationship.e relationship between the experimental permeability coe cient k and axial stress σ is shown in Figures 6(a where a 1 and b 1 are coe cients related to the particle size, whose values are shown in Table 1, and k 0 is the initial permeability coe cient.Water-rock coupled model Advances in Civil Engineering equation (5) in which the Mohr-Coulomb strength criterion is treated as the yield criterion.e element shear and element stretch fracturing conditions are given in equations ( 6) and (7), which consider the water-weakening e ect on the rock compressive strength, as follows:

Water-Rock
where σ ij,j is the total stress tensor, αp is the osmotic hydraulic gradient expressed as the force of an equivalent volume applied to the rock mass skeleton, F i is the applied load, and η s is the rock shear strength weakening coe cient and η s 0.759 [28].

Seepage Analysis.
e seepage di erential control equation can be provided as follows: where p is the pore water pressure, e is the volume deformation, W is the water source, t is the time, and k is the permeability coe cient, which can be calculated with the following equation [17]:  Advances in Civil Engineering where ξ 1 1.0 and β 0.5 for nonfractured surrounding rock, ξ 1 1000 and β 1.0 for fractured surrounding rock, Θ is the volume stress, Θ σ 1 + σ 2 + σ 3 , and e is the volume strain, which is subject to e ε 1 + ε 2 + ε 3 .
e permeability coe cient of the fractured rock mass of the fault zone is calculated with equation ( 4). e evaluation of the stress and seepage could be investigated with water-rock coupled model I, which is shown in Figure 3(a); the gure shows that the fractured zone of the coal seam roof, coal seam oor, and fault were interconnected, and water inrush occurred during mining of the coal seam.
e nonlinear water ow in the water inrush channel could be represented by using the Darcy-Weisbach equation (10) if the fractured zone of the coal seam roof, water-bearing fault fracture zone, and con ned aquifer were interconnected or if the fractured zone of the coal seam oor and water-bearing fault where ΔH is the waterhead loss, l is the length of the water inrush channel, d is the inner diameter of the water inrush channel, u is the average velocity in the channel, g is the gravity acceleration, and f is the friction coefficient (dimensionless), whose value can be calculated based on the Nikuradse experiment curve as shown below: If the voidage of the water inrush channel is 1, then v � u and J � ΔH/l, and the following relationship can be acquired based on equation (10) [31]: en, an equivalent permeability coefficient K d can be calculated with equation (12), where v is the water velocity: erefore, the water inrush process could be approximated by a nonlinear seepage equation after water inrush was generated and occurred.e evolution of stress and seepage could be investigated by water-rock coupled model II, which is shown in Figure 3

Engineering Background.
e Xiao Chang coal mine is located in the Xiao Chang field, Changzhi city, Shanxi Province, China.e southern normal fault of the Mount Er Gang is the western boundary of the Xiao Chang mine and the boundary fault of the mine; the other geological conditions are shown in Figure 7. e fault contains water and cuts off the #3 coal seam.As a result of the stratigraphic throw reaching 300 m, the #3 coal seam in the upper part of the southern normal fault of the Mount Er Gang is directly connected with the Ordovician water-bearing rock stratum in the lower part of the fault, as shown in Figure 1.
Working face 30225 with adjacent faults will be mined and the water-bearing fault zone.If the fractured zone of the floor, roof, reserved coal pillar, fault zone, and surrounding rock are interconnected during mining of the coal seam, water inrush accidents will occur; the mining situation is shown in Figure 1.erefore, when coal seams with adjacent faults that contain water are mined, it is necessary to study the water inrush mechanism between the confined water-bearing rock stratum and mining work face for the prevention and control of water inrush.

Numerical Simulation of the Water Inrush Process.
Numerical simulation was performed to investigate the water inrush mechanism of coal seam mining with adjacent faults that contain water at the Xiao Chang coal mine, and the simulated location is shown in Figure 7. e constitutive calculation model described in Section 2 was used for the numerical simulations based on the geological conditions shown in Figure 2(c).e numerical simulation results are shown in Figures 8-10.
Figure 8(a) shows that the mining process disturbed the stress field of the surrounding rock during mining of the coal seam, and when the mining width reached 40 m, the rocks within the fault zone and surrounding rock above the fault had fractured.Furthermore, the fractured zone of the roof and floor of the coal seam expanded gradually with increasing mining width.As shown in Figure 8(b), when the mining width reached 140 m, the water inrush prevention pillar was destroyed as a result of damage and stress concentration effects in the rock surrounding the fault zone caused by mining.e latter contributed to the flow of water from the confined aquifer to the fault zone, then to the reserved water inrush prevention pillar, and finally to the gob, which created the conditions to form a water inrush channel.In addition, although there was no connection between the destroyed roof zone and the fault activation zone, the aforementioned zones had a tendency to become interconnected.Since water always flows from high to low potential energy, the change in pore water pressure could reflect the flow of water.Based on the pore water pressure isoline distribution (Figure 9), fault water inrush to the gob occurred under the action of a high hydraulic gradient as the mining width reached 140 m, and the first water inrush channel (aquifer-fault zone-reserved water inrush prevention pillar-gob zone) was generated; the latter is shown and labelled in Figure 9. Furthermore, the flow variation in the monitoring element #1 also indicated that the process of water inrush had occurred, which is shown in Figure 11.When the mining width reached 100 m, the water flow was 7.056 m 3 /h and increased gradually; when the fault width reached 140 m, the water flow increased abruptly to 331.632 m 3 /h, and when the mining width reached 180 m, the water flow reached a maximum value of 749.916 m 3 /h; thereafter, the water flow decreased gradually, which was caused by the sudden release of water potential energy after formation of the first water inrush channel.
When the mining width reached 170 m, the fractured zone of the coal seam roof connected with the fault fracture zone, as shown in Figure 8(c), and created conditions suitable for the flow of water to occur from the water-bearing strata to the gob through the fault and fractured zone of the roof and contributed to the formation of a second water inrush channel (confined aquifer-fault zone-faults surrounding the fractured rock zone-fractured roof zone-gob zone).Advances in Civil Engineering e second water inrush channel is re ected by the pore water pressure isoline distribution (Figure 10).e ow of water in the gob would increase greatly with the increase in the number of water inrush channels, which would result in great hazards to working face 30225.Hence, it was important to calculate and monitor the evolution of the fractured zone of the coal seam roof, oor, and water inrush prevention pillar to determine the water inrush mechanism.Furthermore, the ow variation in the monitoring element #2 also indicated that the process of water inrush had occurred at roof, which is shown in Figure 11.When the mining width reached 140 m, the water ow was 0.014 m 3 /h and increased gradually; when the fault width reached 180 m, the water ow increased abruptly to 216.138 m 3 /h, and when the mining width reached 220 m, the water ow reached a maximum value of 574.005 m 3 /h; thereafter, the water ow decreased gradually, which was caused by the sudden release of water potential energy after formation of the second water inrush channel.

Discussion
is paper presented the water inrush mechanism in the mining process under engineering conditions where there was a water-bearing fault zone near the coal seam and a water-bearing fault zone connected with a con ned aquifer.Advances in Civil Engineering fault zone was investigated through experiments.We found that the ow rate of water had little e ect on the permeability coe cient, which increased slightly with increasing ow rate; the permeability coe cient of fractured sandstone was much higher than that of intact sandstone under the action of axial stress; the fractured rock became compacted, and the permeability coe cient decreased as the axial stress increased.Moreover, the relationship between the permeability coe cient and axial stress was nonlinear, so an exponential function (equation ( 4)) was used to describe the nonlinear relationship.
e other study results show that permeability parameter k of crushed rock has a polynomial relationship with e ective stress σ ′ in inverse proportion [23,25,26,28,31,32].

Water-Rock Coupled Model.
Compared with previous studies [18,[33][34][35], the water-rock coupled model presented in this paper was di erent in that (1) the model considered the water-weakening e ect on the rock strength; (2) the model relied on di erent seepage coe cients based on the di erent water ow patterns before and after water inrush occurred; and (3) di erent calculation models were adopted for di erent engineering conditions that better conformed to the actual situation.In other studies, the seepage character of fault broken zone is always ignored [17].e disadvantage of the model is that we do not consider the in uence of temperature and cannot calculate the analytical solution of the model.Furthermore, the experiment did not consider triaxial stress conditions, which means that the e ect of the con ning pressure on the permeability coe cient of the fractured rock mass was ignored in this study, which could be considered in the future by designing corresponding equipment.We hypothesized that fractured rock was a continuous medium.erefore, evaluating the applicability of the water-rock coupled model is necessary in future research.

Numerical Simulation.
e numerical simulation results of the fault water inrush process indicated that the connection among fractured zones is a prerequisite for the occurrence of a water inrush disaster during mining.In addition, there are two water inrush tunnels: the rst water inrush channel (aquifer-fault zone-reserved water inrush prevention pillargob zone) and the second water inrush channel (con ned aquifer-fault zone-faults surrounding the fractured rock zonefractured roof zone-gob zone).However, scholars also need to pay attention to additional water inrush channels [9,25,36] for di erent geological conditions, including the condition where the aquifer-fault-oor fractured zone may also function as the water inrush channel.

Conclusions
is paper addressed the fault water inrush mechanism through seepage experiments with fractured rock samples from a fault zone, water-rock coupled models, and numerical simulations.e following conclusions were drawn: (1) e ow rate of water had little e ect on the permeability coe cient, which increased slightly with increasing ow rate; the permeability coe cient of fractured sandstone was much higher than that of intact sandstone under the action of axial stress; the 10 Advances in Civil Engineering fractured rock became compacted, and the permeability coefficient decreased as the axial stress increased.Moreover, the relationship between the permeability coefficient and axial stress was nonlinear.(2) Using different seepage coefficients based on the different water flow patterns before and after water inrush occurred resulted in the determination of the fault water inrush mechanism.Two water-rock coupled models are processed in the manuscript, and both models consider the seepage law of broken rock and whole rock.One is used in the situation where the broken areas do not interconnect, and the other is used in the situation where the broken area interconnects.
(3) e fault zone affected the fracture evolution of the coal seam roof, and the fractured zone of the adjacent fault became larger and wider than the other zone.e connection among the fractured zone of the coal seam roof, fault fracture zone, and aquifer, or among the fractured zone of the water inrush prevention pillar, fault fracture zone, and aquifer was a requirement for the occurrence of water inrush disasters during mining.
is study contributes an increased understanding of the mechanism of water inrush disasters and provides helpful suggestions for the design of water inrush prevention pillars.

Figure 1 :
Figure 1: Description about fault water inrush in mining.

Figure 2 :
Figure 2: e research process of the paper

Figure 5 :
Figure 5: Testing system of the seepage evolution law.
shear-p tension-p Shear-n shear-p Tension-n shear-p tension-p Tension-n tension-p Tension-p Shear-p tension-p Shear-n tension-n shear-p tension-

Figure 8 :
Figure 8: e evolution laws of broken zone caused by mining.

Figure 7 :
Figure 7: Engineering environment in Xiao Chang coal mine.

Figure 10 :
Figure 10: Pore pressure distribution when mining width reaches 170 m.

Figure 11 :
Figure 11: Flow variation of monitor element.

Table 1 :
Values of a 1 and b 1 in equation (4).