Deformation and Stress Distribution of the Effective Water-Resisting Rock Beam under Water-Rock Coupling Action inside the Panel Floor

School of Mining and Safety Engineering, Anhui University of Science and Technology, Road Taifeng No. 168, Huainan, Anhui 232001, China State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China Key Laboratory of Coal Mine Safety and Efficiently Caving of Ministry of Education, Anhui University of Science and Technology, Huainan, Anhui 232001, China


Introduction
China is one of the countries that have been affected seriously by damage caused by water in coal mines.e increase in mining depth and widespread application of comprehensive mechanized coal mining and top coal caving have resulted in an increase in floor breaking and water disaster due to mining over pressurized water [1].
ree zones similar to the overlying rock by mining can be found inside the coal floor [2][3][4].
ese are the water-guiding zones broken by mining on the top and the central complete rock, the water-flowing zone on the bottom artesian water, and the water-resisting zone on the central complete rock, which plays an important part in resisting water inrush from the seam floor.During coal seam mining, the thicknesses of the water-guiding and water-flowing zones differ for different mining conditions.Hence, water burst will occur when the thickness of the effective water-resisting zone is not sufficient to bear the water pressure from the bottom artesian water.
Panel floor rock instability is the direct cause of artesian water inrush.erefore, the jointed rock mass damagecoupling mechanical model [5][6][7], jointed rock mass transfusion-damage-breakage-coupling mathematical model [8,9], elastic-plastic damage microcosmic model [10], and two-body system mechanical model [11] have been established to analyze the conditions and processes of stress deformation and system destabilization.e aim is to identify the critical condition of rock mass dynamic instability.Floor water inrush is the process that results in crack initiation, extension, connection, and eventual failure.e combined action between mining dynamic pressure and hydraulic pressure should be considered in the systematic investigation of the stress and deformation of an e ective water-resisting rock beam.
Based on the three zones of the panel oor, this paper takes the water-guiding zone broken by mining as a viscoelastic body and the e ective water-resisting rock beam as an elastomer.Under the combined action of mining dynamic and hydraulic pressures, the resistance to bending decreased with the time accumulated for the amount of growth.e de ection and stress of the complete rock beam in the oor change, and a comparison of the maximum bearing capacity of rock mass can determine its stability.

Floor Load-Bearing Partition and Failure Mechanism.
Coal seam and surrounding rock are in the stress state of equilibrium with the in situ stress state.However, when the coal seam or rock layer is excavated, the stress state of equilibrium is destroyed, causing the surrounding rock stress to be redistributed and the deformation and failure to occur [12].Figure 1 shows that the coal wall, coal seam, and oor are located in the supercharged region because of the abutment pressure.is region is called the compression zone in which the coal seam oor is compressed.With the advancement of the working face, the oor of this region will transform from the compressed state into the expanded state, resulting in the generation of the oor heave and the appearance of bedding rock cracks.is region is called the in ation-pressure relief zone.As the working face advances once more, the caving rock blocks in the gob become overburdened and compacted.e oor of this region is located in a new pressure zone because of the overburden pressure and the movement from the expansion to the compaction state.erefore, any section of the coal seam oor always experiences some form of abutment pressure from the compression fracture zone to the postharvest overhang unloading expansion damage zone and from the shear failure zone around the gob and roof caving recompacting zone.
As the working face advances, all points in the oor undergo the process of compression, stress relief, and recompression [13].A similar simulation experiment result can be observed in Figure 2. e degree of damage of the roof strata is small in an area that ranges from 20 m to 40 m behind the working face.e weight of the overburden undertaken by its structure plays an important role in the oor heave.Waterowing fractures appear in the oor rock strata, and the waterproof ability of the strata disappears [14], causing it to transform into a water inrush area.e stress slowly recovers the in situ stress in the oor rock strata of the recompacting zone.e fractures are closed, and the upper boundary stress in the oor increases, which could reduce the possibility of water inrush in the oor.Hence, the in ation-pressure relief zone is the key area for resisting oor water inrush.In this paper, the stress and deformation are analyzed to estimate the water-resisting rock beam stability.

Mechanical
Test.An MTS-815 hydraulic servo-loading test system (Figure 3) is used in the test with a standard sample size of 100 mm × 50 mm.Following the conventional compression tests for postpeak fracture sample and instantaneous fracture strength by single step loading, the maximum load is applied into several levels on the same specimen from step loading, with a load duration of 24 hours.According to the test method for rock, the loading rate is 0.5 MPa/s.e creep value generated at t time after n + 1 level load is the pre-N load and the n + 1-level load increment, which produces the superposition value of creep at the corresponding time.e con ning pressure (4 MPa) was also set.Under a loading of 20 MPa, the loading levels are set as 25 MPa, 30 MPa, 35 MPa, 40 MPa, 45 MPa, and 50 MPa as shown Figure 4. e loading time of all levels is set to 24 hours (1440 min).
According to the experimental data, the creep characteristics of the di erent loads are analyzed (Figure 5).
e following tting formula shows the creep of the specimen is in accordance with the deformation characteristics of the Maxwell model as shown in Table 1: 2 Advances in Civil Engineering where E 0 is the initial elastic module, t is the time course, and σ 0 is the initial stress.e relaxation properties of the rock can be obtained based on the relationship between creep exibility and the relaxation modulus of elasticity: where E(t) represents the elastic modulus of relaxation and J(t) refers to the creep exibility.
Figure 6 shows the relaxation characteristics of the specimens under di erent loads.

Permeability Test.
e permeability test of the standard rock sample is carried out on the rock mechanics experiment system of MTS-815; three samples of sandy mudstone are taken from the oor of coal group A. e seepage uid is water, and the surrounding rock is set at 4 MPa; according to the experimental collection of pore pressure di erence, the  Advances in Civil Engineering 3 permeability coe cient K of the Darcy ow is calculated.e method of rock sample encapsulation is shown in Figure 7.
Figure 8 shows the variation rule of the permeability coe cient K with strain ε of sandy mudstone: (1) at the elastic deformation stage, a small number of microcracks in the sandstone sample began to show tensile deformation, the porosity of the sample increased, and the permeability coe cient K increased gradually; (2) when the strain value is greater than 0.0109, the permeability coe cient increases sharply and reaches the maximum value 280.01 × 10 −11 m•s −1 ; at this point, the crack in the sample expands and penetrates, forming an obvious macroscopic failure of the structural surface; (3) when the strain is greater than 0.0118, the permeability coe cient decreases rapidly to about 50% of the maximum value; (4) when the strain exceeds 0.0134, the permeability coe cient K decreases slowly and stabilizes around 123.62 × 10 −11 m•s −1 .At this stage, the crack structure space of the sample is lled with small broken particles, which reduced the porosity of the sample and decreased the permeability coe cient K.  show that the rock failure will increase the permeability, reduce the risk of water inrush from the oor, reduce the in uence of the mining stress on the oor, and make the oor aquifers to not form the channel of water guide, so as to ensure the ability of the water barrier in the oor rock.

Mechanical Model.
It can be seen from Figure 5 that the deformation characteristics of the rock after the peak conform to the Maxwell model.With the increase of the action time, the rock shows signi cant relaxation characteristics.After coal seam mining, the water-resisting rock strata in the oor could be taken as the clamped beam of both ends to analyze the dip direction of the working face as shown in Figure 9. Within the scope of in ation, pressure relief, and failure zones, the oor is forced by pressure stress q 1 (x) from the caving gangue of the direct roof.e oor water-resisting rock beam close to the coal seam oor is taken as the mining failure rock beam with a thickness of h 1 , and its mechanical property is considered as viscoelasticity [15][16][17][18].e e ective water-resisting rock beam with thickness h 2 between the con ned aquifer and mining failure rock beam represents an elastic deformation sustained by the bottom boundary water pressure p. Suppose a common displacement boundary between mining failure rock beam and e ective water-resisting rock beam exists and it is taken as the medium with certain thickness under the e ective water-resisting rock beam as the elastic medium.e medium approximately satis es the assumption of the Winkler elastic foundation.Hence, the acting force q 2 (x) in the oor rock beam during the process of pressure relief is represented as follows: where λ is the comprehensive volume-weight of overburden (N/m 3 ), h is the burial depth of the coal seam (m), k is the coe cient of the Winkler soil reaction, and v is the exural de ection of the rock beam.

Mechanical Solution of Flexural De ection in the Floor
Rock Beam.e total energy of the rock beam is composed of three parts of elastic beam (e ective water-resisting rock beam) U e , viscoelastic beam (mining failure rock beam) U p , and external work (U q 1 + U q 2 + U s ). at is, Following the virtual work principle and energy functional variational conditions [19], the equation of the rock beam de ection curve v(x, t) should make δΠ 0 and δ 2 Π > 0. e strain energy and external work in the rock beam are analyzed as follows.

Advances in Civil Engineering
(1) Strain energy of the effective water-resisting rock beam where E is the elasticity (GPa) and I is the cross-sectional moment of inertia.
(2) Strain energy of the mining failure rock beam where Y(t) is the loosen modulus, Y(t) � Ee −Et/η , η is the coefficient of viscosity (GPa•h), and t is the time (h).
(3) External work e expression of total system potential energy is Equation (7).
e type is simplified to Making a second-order variational for potential function Π, that is, Obviously, formula (10) is greater than 0.
From δΠ � 0, formula ( 9) is changed as follows: From boundary conditions, Finally, the deflection curve v(x) of the floor rock beam is obtained.

Case Analysis
e coal seams of A1 and A3 (Figure 10) are mined in the A team of Panxie mining area, Huainan Mining Group, with an average dip angle of 16 °.e thickness of A1 coal seam ranges from 1.56 m to 7.77 m with an average thickness of 2.8 m. e thickness of A3 coal seam ranges from 2.09 m to 9.17 m with an average thickness of 5.8 m.
e distance ranges from 1 m to 5 m between A1 and A3, and in some areas, the two coal seams are combined into one coal seam.
e floor of the coal seam has strong aquifers of Taiyuan group limestone and Ordovician limestone.A strong aquifer C 3  3 (lower) which poses a potential risk of water damage for the coal seam mining of A team under the A3 with the distance of 29.1 m can be found.e aquifer thickness of C 3 3 (lower) is 7.8 m with an original water pressure of 4.5 MPa.
e damage degree of the floor is taken into consideration in the process of thick coal seam mining; thus, the coal seam A3 is excavated by slicing, and the thickness of the upper slice is 3.0 m. e inclined length of the panel is 120 m, and the average buried depth of the coal seam is 450 m.

Relevant Parameter Confirmation
(1) Mining failure zone depth With the increase of mining depth, the weight of overburden, in situ stress, and rock pressure of the working face will also increase, causing the coal seam floor failure to become increasingly serious.A direct proportion 6 Advances in Civil Engineering relationship between the oor failure depth and the mining depth exists [20].According to the speci c mining conditions of the panel, the mining failure depth h 1 obtained is 12.47 m in the oor: where α is the dip angle of the coal seam, 0.279 rad, and l is the inclined length of the panel, 120 m.For the distance of 29.1 m between the oor of A3 and the strong aquifer C 3 3 (lower), and after the mining of the upper slice, the thickness of the e ective water-resisting rock beam h 2 is as follows: (2) Depth of the caving zone and other parameter con rmation e oor pressure stress q 1 (x) is formed by the weight of the caving gangue from the direct roof.Considering the strata columnar section of the panel in Figure 3, the lithology is worse in the range 11 m of A3 coal seam roof, and the roof will cave after the panel is excavated.
en, q 1 (x) 2.5 × 10 4 × 11 0.275 MPa.In formula (11), λ is the average unit weight of overburden with the data of 2.5 × 10 4 N/m 3 , and the Winkler coe cient of soil reaction k is 100 MPa.

Result Analysis.
e oor rock beam deformation in di erent mechanical properties and oor water pressures is studied by analyzing the de ection curve with the time development by changing the elasticity modulus E, the coe cient of viscosity η, and the water pressure p.
(1) In uence of elastic modulus on the oor Before making the drainage measurements in the panel, the oor water pressure p is 4.5 MPa.
e coe cient of viscosity is 45 GPa•h.When the elasticity moduli E are 15 GPa, 25 GPa, and 35 GPa, the de ection curves of oor deformation are shown in Figure 11.
e convex was observed in the de ection curve and the de ection peak was located in the middle right part of the panel.e maximum de ections are 980 mm, 592 mm, and 441 mm, respectively, which correspond to the elastic moduli of 15 GPa, 25 GPa, and 35 GPa.Hence, improving the elastic mechanical property of oor rock has contributed to the enhancement of the ability to resist deformation.
(2) In uence of coe cient of viscosity on the oor e oor water pressure is 4.5 MPa.And the elastic modulus has the same data of 35 GPa.When the coe cients of viscosity η are 40 GPa•h (amount to 1.67 GPa•d), 50 GPa•h (amount to 2.08 GPa•d), and 60 GPa•h (amount to 2.5 GPa•d), respectively, the de ection curves of oor deformation are shown in Figure 12.
Figure 12 shows that under the water-rock coupling action, the maximum de ection of the oor provides the same data with 440 mm in di erent coe cients of viscosity.However, the deformation resistance was reinforced when the coe cient of viscosity increased.
(3) In uence of water pressure on the oor e coe cient of viscosity η is 35 GPa•h, and the elastic modulus had the same data as 35 GPa. e de ection curves of deformation when the water pressures are at 1.5 MPa, 2.5 MPa, and 4.5 MPa are shown in Figure 13.e de ection of the oor rock beam is increased as the water pressure increased.Figure 13 shows that the maximum de ection is 276 mm with a water pressure of 1.5 MPa.
e maximum de ection is 441 mm with a water pressure of 4.5 MPa. e process is an increasing one as time increases.Advances in Civil Engineering (4) Stress analysis of the rock beam Suppose (x i , t i ) is the stationary value point, the discriminant of the extreme value point is at is, Using the tensile stress formula (17) of the oor rock beam, the stress values can be obtained in di erent depths to judge the stability of the full rock beam.We take E 35 GPa, η 45 GPa•h, and p 4.5 MPa as examples to analyze the stress distribution of the full rock beam as shown in Figure 14.
e z-axis is the stress, the y-axis is the distance between the neutral axis of e ective water-resisting rock beam and the upper and lower boundary stresses and the x-axis is the length of the panel (m).
Figure 14 shows that after the elastic rock beam was forced, it became compressive at the two ends and tense in the middle.e maximum tension stress was found to be greater than the maximum crushing stress, which is in contrast with the neutral axis.e increase in action time caused the appearance of an increased tendency in the maximum tension stress and the maximum crushing stress of the rock beam.

Figure 3 :
Figure 3: Standard rock samples in the test.

Table 1 :
Specimen lateral creep parameters at every level of stress.