The Assessment and Evolution of Water-Conducting Rules under the Influence of Mining-Induced Stress

It is important to study the mechanism of water inrush on a seam floor by exploring the rules of permeability variations during rock deformation on the seam floor and in the course of fracturing as well as their responses to characteristics of the macromechanical environment such as mine ground pressure, engineering geology, and fluid mechanics. First, through the analysis of bearing pressure changes in the process of exploiting the working face, a mechanical model for the seam floor above the confined water is established. Based on the graphic data-processing software Mathcad, the computational process and methods for assessing the vertical, horizontal, and shear stresses are provided together with the corresponding variation curve of the rock stratum 5m below the floor, covering the entire process from a position 120m away from the working face to a position 280m behind it. Second, the permeability coefficients of different lithologies are measured in the laboratory. For rock stratum 5m below the floor, the corresponding external loading path is set up according to its actual stress. *e actual dynamic stress environment of the rocks is simulated, and their permeability characteristics are studied. In addition, based on data fitting, the permeability coefficient variations in the mining process are determined for a rock stratum 5m below the floor. Finally, in accordance with the permeability variation law of the floor of the working face, the seam floor is divided into six areas, namely, the compression and expansion zone, the bed separation and expansion zone, the pressure relief zone, the compression zone, the stable recovery zone, and the stability zone. *us, the water-resisting performance of the floor can be expressed more objectively.


Introduction
According to incomplete statistics, there were 181 water inrush accidents that occurred from 2001 to 2017 in China with 1,801 deaths and 73 people missing.During the four years from April 2013 to April 2017, there were 33 water inrush accidents that occurred on the floor, resulting in the deaths of 155 people.During the two time periods, the mortality rates were 42.8% and 45%, respectively, and indicated that the quantity of water inrushing on the floor has an impact on the degree of hazard of water inrush accidents.Massive studies on water inrush on the seam floor have been carried out by foreign and domestic scholars.In the 1940s, Smfsarfc [1] from the former Soviet Union believed that the seam floor was a clamped-clamped beam structure with a uniformly distributed load and derived a formula for designing a safe water pressure, as shown in the following equation: where P 0 , h, and c are the safe water pressure, thickness, and bulk density of the water-resisting layer of the floor, respectively; K p is the tensile strength in MPa; and L is the roadway width in m.According to B. Slisalif, water inrush on the floor will occur when the actual water pressure P > P 0 .
According to mechanical equilibrium, the actual water inrush issue on the seam floor has been converted into a theoretical model, which lays a foundation for subsequent theoretical development regarding the mechanism of water inrush on the seam oor.By the 1980s, Santos and Bieniawski [2] had introduced dimensionless parameters m and s, which are relevant to the lithologic parameter and rock mass rating (RMR) on the basis of H-B criterion modi cation, thus further improving the expression of the oor loading capacity.It has also been noted that the ratio between the horizontal stress and the vertical stress of the oor could have an in uence on oor security.In countries with a developed mining industry such as the United States and European countries, although there are many theoretical studies on rock mechanics and elasticplastic mechanics, few have covered water inrush on the oor despite the simple seam structure and advanced mining facilities.From the 1960s to the 1970s, the water inrush coe cient T (shown in Equation ( 2)) as well as its modi ed formula T c (shown in Equation ( 3)) was brought forward by Chinese scholars and institutions [3,4]: where H is the total thickness of the water-resisting layer of the oor; h i is the strati cation thickness of the ith waterresisting layer; h p is the depth of the oor destroyed by ground pressure; and a i is a thickness coe cient representing the transition of the ith water-resisting layer to mudstone, the value of which ranges from 0 to 1. e water inrush coe cient is gradually becoming an important reference for water-proo ng work in coal mines in China.
In 1980, Baiying [5][6][7] explored coal mining below con ned water with Ordovician limestone, proposing the " ree Underlying Belts eory," a schematic diagram of which is shown in Figure 1. e formula for computing the water inrush coe cient based on this theory is shown in Equation (4).
Because of the division of three underlying belts, the formula for computing the water bursting coe cient can be modi ed into the equation as follows: where T stands for the water inrush coe cient.H, H 1 , H 2 , and H 3 represent the total thickness and the thicknesses of belts 1, 2, and 3, respectively.e ree Underlying Belts eory emphasizes that the oor has a structure similar to the three belts of an overburdened roof.It also notes that the oor failure mechanism can be described as the process of water inrush on the aquifer oor caused by the communication between the mining ssure zone and the aquifer under the combined action of water pressure and mine ground pressure.
At the beginning of the 20th century, a modi ed formula for water pressure reduction was proposed by Hu and Yan [8] and Weiyue et al. [9,10] based on the ree Underlying Belts eory.Speci cally, head pressure subjected to an e ective water-resisting seam oor will show pressure loss due to water head intrusion.A schematic diagram of the pressure loss in the aquifer is given in Figure 2. e formula for computing the water inrush coe cient based on water pressure loss in the aquifer is shown in Equation (6).P c represents the water pressure after the reduction.More factors in uencing the hydraulic mining of the coal seam have been taken into account after the improvement, including not only the zonation of the water-resisting layer on the seam oor but also the residual water pressure, which is likely to be neglected.As a result, the modi ed formula for the water inrush coe cient can help us to more faithfully and e ectively evaluate the security of hydraulic mining, bene tting the practice of mining.Additionally, according to the in situ ssure and original destruction theory raised by Zuoyu et al. [11][12][13], the horizontal in uence of the waterresisting layer on the actual working face of the mine is mainly divided into the advanced pressure compression section, the pressure relief-based expansion section, and the postmining stable compression section because of the joint e ect of the mine pressure and the hydraulic pressure.According to the key stratum theory raised by Minggao et al. [14,15], there is a key stratum similar to the overlying stratum on the roof on the seam oor, and this stratum is the main inducer of water inrush on the seam oor during hydraulic mining in the control belt.Using an analytic hierarchy process (AHP) and geographic information system (GIS), Wu et al. [16,17] proposed the brittleness index method and established an AHP evaluation model to de ne the threshold of each risk level to guide the operation of mining areas.Peng et al. [18] have combined double-unit face mining technology and strip mining and performed studies on coal mining above the con ned water, guaranteeing the safety of mining upon con ned water from the perspective of mining technology.e in situ measurement conducted by Huang et al. [19] targeted the permeability of the fractured zone on the oor in Yangcun Coal Mine and Xinglong Zhuang Coal Mine in Shandong Province of Eastern China.e rock permeability and the permeability variation under conditions of varied water pressure were measured; Meng et al. [20] established a coal oor water inrush risk assessment method based on a conventional   [24] studied the permeability change of mining ssured rock mass and its e ect on groundwater inrush.Liu et al. [25,26] studied the mechanical characteristics of the rocks from multiple scales, and particularly they made analysis and prediction of rock hydraulic properties under water-rock coupling from a microperspective, providing new ideas and methods for researches on water inrush from seam oor.Practical studies suggest that oor seepage is an extremely complex water-rock coupling issue triggered by characteristics of the macromechanical environment such as mine ground pressure, engineering geology, and uid mechanics.In this paper, a mechanical model of oor stress has been established to describe dynamic variations in the oor stress during the dynamic stress variation of the working face.Permeability characteristics have also been measured in the laboratory under conditions of diverse stress states.Speci c to rules of rock permeability change in the entire stress-strain process on the working face, the seam oor is divided into six zones, that is, the compression and expansion zone, the bed separation and expansion zone, the pressure relief zone, the compression zone, the stable recovery zone, and the stability zone.In this way, the waterresisting performance of the oor is represented more objectively.

Analysis of the Stress State Distribution on the Floor of the
Slope.In regard to mining upon con ned water, the stress state distribution on the roof is given in Figure 3. e reason that curves in areas with low stress from primary rock are longer than those in traditional mining-induced stress zones is that a masonry structure is formed by overlying strata, creating a stress vacuum area with a length approximately equal to a periodic weighting step [27,28].
e area exists between the goaf caving end and the elastic zone of the working face.For the convenience of calculation, the curve was simpli ed into a triangle.en, stress variation could be expressed as Δσ y σ upper − σ lower .Selecting A as the coordinate center, the coordinate of any point denoted by M(m, −n) was taken within the carmine box.Furthermore, the oor was assumed to be homogeneously elastic, and a numerical calculation model for the oor stress distribution was established, as presented in Figure 4.
As assumed, mining was not completed until periodic weighting; in which case, the stress of the mine supporting pressure in an area to the right of point M can be expressed in the following equation: e normal stress presented in Figure 4 is divided into 4 sections, AB, BC, CD, and DE.Taking Haizi Coal Mine in Anhui Province as an example, both the geological conditions of the working face and the behavior of the mine ground pressure measured during working face advance are obtained, where the length of S1 and S2 is 10 m and 30 m, respectively; the stress concentration factor K is equal to 2.5; the length L2 is 10 m; and the distance from the working face to the origin of the coordinates is 40 m.By using Mathcad as the mathematical analysis software, section AB was solved rst: Subsequently, solutions to sections BC, CD, and DE were acquired.In this context, the stress distribution law of the stress increment bearing pressure on the oor along the working face could be further obtained.V 1 and V 2 can be obtained as follows: An RTR high-temperature high-pressure rock triaxial apparatus manufactured by GCTS and adopted for the experiment could complete rock permeability coe cient measurements at di erent con ning pressures.Based on computer process control, the preset con ning pressure loading scheme was implemented in an unceasing manner targeted at the same specimen.
e main research elements are as follows: (1) Rock permeability variation law in a complete stressstrain path (2) Rock permeability variation law subjected to different con ning pressures (3) Rock permeability variation law subjected to a particular loading path

Results and Discussion
(1) e permeability variation rules in a complete stressstrain path were investigated since excessively low con ning pressure may a ect the related experimental e ects.Meanwhile, the specimen depth, position, stress conditions, and so on were all taken into account.e corresponding con ning pressure was set as P c 4 MPa.e laboratory apparatus and specimens utilized are presented in Figures 5. Fig With regard to rocks of di erent types of lithology, their permeability coe cient (K) variation curves with stress ε are given in Figure 7.  Advances in Civil Engineering e permeability of four kinds of rocks slightly decreases with the increase in stress at the very beginning (at the stage of initial crack closure) or has no obvious change (initial cracks not developed) [29,30].It increases slightly as the load increases before reaching the peak intensity.At the elastic-plastic stage, rocks go through dilated deformation and crack holing starts.
e rock permeability coe cient arrives at its peak value at the postpeak phase and is reduced in the remaining stages.What is noteworthy is that the peak of the permeability coe cient falls behind that of rock strength.erefore, strain softening supervision and control after rock failure have critical signi cance for preventing water bursting on the seam oor.In the condition of identical con ning and seepage pressure, rocks can be ranked as coal, sandy shale, sandstone, and mudstone in the descending order according to their permeability.Respectively, they take values of 128, 52.38, 27.90, and 0.048 unit(s) de ned as × 10 −10 m•s −1 .
At the very beginning, permeability slightly increases and decreases with the increase of stress for the mudstone, which is di erent from other rock samples.e reason is the relatively large ssures within the other rock samples narrow with the increase of axial pressure, leading to a slightly decreased permeability, while there is not a similar process for mudstone within which the ssures are small.e increase of axial pressure will create small ssures within mudstone, and more increment will lead to interior fracture; detritus thereby produced will block the permeation channels resulting in a temporary reduction of the permeability.
With further increase of axial pressure, the degree of fracture aggravates, and the permeability increases rapidly.
(2) Speci c to rock permeability variation rules subjected to di erent con ning pressures, the peak strain ε max of the rock specimens was rst achieved by loading.en, in the conditions of diverse conning pressures, namely, P c 1.5 MPa, 2 MPa, 3 MPa, 4 MPa, 6 MPa, 8 MPa, 10 MPa, 12 MPa, and 14 MPa, the corresponding permeability coe cients denoted as K were determined.At the beginning of the experiment, the con ning pressure increases from 1 MPa.When the experiment is complete, the rubber membrane around the rock specimen should be checked.A damaged rubber membrane indicates that the con ning pressure adopted during the experiment was excessively low and the test should be valid since the con ning pressure P c is equal to 1.5 MPa.
Subjected to diverse con ning pressures, the permeability variation rules of di erent rocks are presented in Figure 8.
As demonstrated by the experiment, the permeability coe cient is closely related to the con ning pressure.e greater the con ning pressure is, the lower the permeability will be.Meanwhile, all four kinds of rocks with relevant values of 0.9 and above show a rule of multinomial distribution.It has been found by Peng et al. [31] according to their investigations on rocks from diverse geologic ages that a logarithmic relation exists between them; in fact, their variation rules are consistent.Furthermore, the relation between permeability and con ning pressures can be expressed in the equation below: where K refers to the permeability coe cient, P c refers to the con ning pressure, and parameters a, b, and c are all constants.
Comparatively speaking, coal permeability is the most sensitive to the in uence of con ning pressure, while the sensitivity of rock permeability at the postpeak phase to the in uence of con ning pressure ranks last.At the time of coal mining, the permeability coe cients of coal and rocks beneath it increase.However, the great water-resisting property of mudstone guarantees oor safety.Despite the fact that an increase in mudstone permeability is accompanied by a substantial increase in the probability of the seam oor water bursting, the water-resisting performance in the upper part of the mudstone plays a critical role in improving the con ning pressure on the water-resisting layer at the bottom, which has been proven by the theoretical model in Part One. e Advances in Civil Engineering e ective con ning pressure of deep rocks is greater than that of rocks in the upper part.e speci c mechanism should be further explored according to concrete rock stresses.For this reason, rock permeability variation rules were explored based on the premises of particular loading paths.
(3) Speci c to rock permeability variation rules subjected to particular loading paths, 5 points, below the oor, were selected.For other points of di erent depths, the relevant research method is the same.During coal mining, the con ning pressures in the goaf and the certain space deep in the surrounding oor are di erent, that is, δ2 ≠ δ3.Due to limitations of the experimental instrument, theoretical formula (9) was employed to determine the values of δ1 and δ2.Regardless of the squeezing action on the rock from one side, the weak con ning pressure should be deemed e ective.Such an assumption has no inuence on the experimental objectives of the paper.Figure 9   e computational formulae of maximum principal stress σ 1 , minimum principal stress σ 2 , and σ x σ x τ xy are given as follows: where the values of σ 1 , σ 2 , σ x , σ y , and τ xy are obtained by Mathcad, the mining depth is de ned to be 500 m, and the speci c gravity c is 2.4•10 4 kN/m .It can be observed from Figure 9(a) that the stress of point M shows a general decreasing tendency followed by an increase before nally recovering to a normal form.When it is approximately 15 m away from the working face, the vertical stress began to decrease sharply and reached zero when the distance was no greater than 15 m.In addition, transient negative pressure would appear below the working face.After the advancement of the working face, the vertical stress would quickly concentrate at 20 m, and the maximum stress increment coe cient would be as high as 2.2.Subsequently, when the advancement of the working face was beyond 160 m, point M would gradually return to the stress of primary rock.e variation laws of the horizontal stress and shear stress are similar to those of the vertical stress, as indicated in Figures 9(b) and 9(c).Due to stress concentration, the rock mass on the seam oor was compressed, while that below the goaf was expanded due to the existence of release space.For this, there is a shear stress increment area between the two zones, which were also the sections with the most substantial rock destruction.e maximum shear stress reached approximately 6.2 MPa, which was 0.47 times the vertical stress of primary rock.It also tilted toward the lower part of goaf, so the stratum thickness would be dramatically reduced by the shear stress, which was one of the most important reasons for water inrush on the oor.
In Figure 10, the position at y 120 of the x-axis stands for the working face.As indicated, the con ning pressure within a range of 10 m beneath the working face is negative.
e reason is that failure in the rock caving beneath the working face gives rise to a temporary empty-support area in the oor.In addition, the chart of maximum principal stress shows that the maximum principal stress abruptly and continuously climbs to a position 40 m beneath the working face, that is, between 120 and 160 in this chart.us, this is an area where the rock compresses under the load, forming the dilation space in it.
Although the maximum principal stress fails to reach the intensity of the rock failure peak, positions 40 m, 20 m, and 5 m in front of the working face and 10 m, 20 m, 40 m, and 100 m behind it were selected as points in the loading path considering that the con ning pressure abruptly changes and that the minimum principal stress is negative.e load time for each point was de ned to be 1 h.As the con ning pressure should be above 1.5 MPa during the laboratory experiment for the purpose of acquiring accurate results, a tting method was utilized for positions 4 m in front of or 9 m behind the working face.e corresponding outcome is shown in Figure 11.
According to Figure 11, the permeability for areas outside the working face is below 10 × 10 −10 m•s −1 .Compared with those described in Figure 7, the permeability values in positions within a range of 10 m in front of and 15 m behind the working face exceed 27.9 × 10 −10 m•s −1 , which is the peak of sandstone in the case of P c 4 MPa; in addition, the measured maximum value is 92.510 × 10 −10 m•s −1 .Pursuant to the section of seepage classi cation for rock-soil bodies speci ed in the Code for Engineering Geological Investigation of Water Resources and Hydropower of the National Standard of People's Republic of China GB 50487-2008 [32], as shown in Table 1, the lithology of the ground in this area already starts to transform from being impermeable to weakly permeable, which veri es that areas in the range of approximately 5 m in front of and 5 m behind the working face are the most likely to su er water inrush.
During coal mining, working face advance preferably makes the complete stress-strain process of rocks reappear.
e failure zone in the working face gradually changes to  Advances in Civil Engineering plastic and elastic zones deep in the oor.e strike of the goaf oor also exhibits a tendency toward a compression zoneseparation zone and stability restoration zone.According to the opinions of Shi et al. [33][34][35], oor strata that have been subjected to compression failure in the mine can be divided into four zones from top to bottom.Nevertheless, water inrush only begins rst in a certain area during practical production activities.Instead of the entire rock formation, there are usually several water gushing points.Considering this, the goaf oor was classi ed into 6 zones depending on the likelihood of water inrush occurrence, namely, a compression-expansion zone, a bed separation expansion zone, a pressure relief zone, a compression zone, a stability recovery zone, and a stable zone, as shown in Figure 12.
In ideal conditions, 6 zones of water inrush from seam oor risk were de ned in line with rock permeability and rock failure.
Zone I: a compression-expansion zone.Due to the in uence of advanced support pressure, rock compression here leads to plastic deformation; meanwhile, mining of the goaf results in stress and volume release space.As the most dangerous area, it is the most likely area for water inrush from the seam oor to occur.e lower parts of positions approximately 5 m in front of and 15 m behind the working face all tilt toward the direction along which the working face advances.

Advances in Civil Engineering
Zone II: a bed separation expansion zone.Under the horizontal squeezing action of advanced support pressure and lateral support pressure, the stress of Zone II is less than that of Zone I.However, an empty-support area is formed temporarily in the roof, or roof falling is extremely insufficient here.As a consequence, rock formation has enough release space so that it is likely that the floor will heave and that separation layers will develop in the formation, which dramatically lowers both the integrity and the water-resisting performance of the rock.Once separation layers and dilation have been formed in the floor, the surrounding rock no longer supports or protects the lower formation, which leads to water inrush risks [36,37].In positions with an entire length of approximately 40-80 m at least 15 m beneath the working face in this zone, they exhibit an inverted trapezoidal shape on the whole.Zone III: a pressure relief zone.Free of highly compressive stress or excessively great tensile stress caused by sideways extrusion, Zone III is under enormous influence from Zones I and II.Zone IV: a compression zone.Within the range of 25-35 m in front of the working face, the face is influenced by advanced pressure, and the floor is deformed because of compression without dilation.erefore, the axial pressure and confining pressure here are high.e relevant permeability coefficient is also lower than the normal value of rocks.Zone V: a stability recovery zone.In the process of gradual compression caused by the goaf collapsing to the rear, floor displacement no longer changes and results in a safe stage at positions approximately 60-100 m beneath the working face.Zone VI: a stable zone.Independent of any mininginduced influence, it is also an area with the stress of the primary rock.

Conclusion
A permeability testing process for rocks subjected to external pressure was presented in this paper together with the application of this process in floor stability estimation.As floor seepage was under the influence of characteristics of the macromechanical environments such as the mine ground pressure, engineering geology, and fluid mechanics, a floor stress model was established to theoretically calculate dynamic variations in the stress during working face advance and to predict the permeability in such stress states.Additionally, rock permeability coefficients in a complete stress-strain process of the rock in the working face floor were sorted in a descending order to categorize the seam floor into 6 zones.In this way, the water-resisting performance of the floor can be represented more objectively.

- ure 6
is the schematic diagram of the concrete measurement principle.

Figure 4 :
Figure 4: Bearing pressure distribution of the oor upon con ned water.

Figure 10 FIGURE 9 :Figure 8 :
Figure 10 signi es maximum principal stress and minimum principal stress variations concerned with point M 5 m beneath the oor during working face advance, that FIGURE 10: e change of the maximum principal stress and the minimum principal stress along the strike direction at point M. (a) Maximum principal stress.(b) Minimum principal stress.

Table 1 :
Permeability classi cation of rock-soil bodies.