Influence,of,backfilling,rate,on,the,stability,of,the,“backfilling,bodyimmediate,roof”,cooperative,bearing,structure

Xianjie Du ,Guorui Feng ,Min Zhang ,Zehua Wang ,Wenhao Liu

a College of Mining Engineering,Taiyuan University of Technology,Taiyuan 030024,China

b Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering,Taiyuan 030024,China

c Key Laboratory of Shanxi Province for Mine Rock Strata Control and Disaster Prevention,Taiyuan 030024,China

d State Key Laboratory for GeoMechanics and Deep Underground Engineering,China University of Mining and Technology,Xuzhou 221116,China

e Zhengzhou Coal Industry (Group) Co,Ltd,Zhengzhou 450007,China

f College of Civil Engineering,Taiyuan University of Technology,Taiyuan 030024,China

ABSTRACT To reduce the cost of backfilling coal mining and utilize the underground space of coal mines,a new backfilling mining method with low backfilling rate called constructional backfilling coal mining (CBCM) is proposed.The “backfilling body-immediate roof” cooperative bearing structure of CBCM is analyzed by establishing the model of the medium thick plate on an elastic foundation.The influence of the backfilling rate on the stability of overlying strata is analyzed by the numerical simulation experiment.The control effect of CBCM is verified by a physic similar simulation test.The economic benefit of CBCM is analyzed.The conclusions are:the deformation characteristics of the immediate roof and critical backfilling spacing in CBCM can be analyzed based on the Hu Haichang’s theory.Exerting the bearing capacity of the immediate roof is beneficial to the stability of the overlying strata.The CBCM has a good control effect on the overburden in Xinyang Mine when the backfilling rate is lower than 25%.The backfilling cost of per ton coal is 37.39 yuan/t when the backfilling rate is 13.7%,with a decrease rate of 56.63% than the full-filling.The research results can provide theoretical support for the application of CBCM in coal mining.

Keywords:Constructional backfilling coal mining Immediate roof Cooperative bearing structure Medium thick plate on elastic foundation Backfilling rate Overlying strata

Coal resources,which as the main energy in the world,have made a great contribution to economic construction and social development for a long time [1].However,the environmental problems caused by coal mining are increasingly prominent [2].At the same time,coal resources in many areas are exhausted increasingly,while there are many residual coal resources such as the coal under buildings,railways,water bodies,etc.[3].The traditional methods of mining residual coal resources and controlling surface subsidence include partial mining and backfilling mining,or the combination of the two ways [4,5].Many coal pillars need to be reserved for traditional partial mining methods such as room-and-pillar mining and strip mining,which results in a low coal recovery rate of the coal resources [6,7].And backfilling mining has the advantages of a high recovery rate and protection of the ecological environment,which can avoid the problems caused by traditional partial mining [8,9].So,backfilling mining has been an important development direction of green mining [10].In the long run,backfilling mining has obvious advantages in the safe and efficient coal mining such as residual coal resources and deep coal resources [11-13].

Since the 21st century,under the guidance of the idea of“Green Mining”,some scholars and enterprise technical backbones have implemented backfilling mining in many coal seams by researching various new backfilling materials [14],such as gangue solid materials,paste materials,high water materials,and developing various new backfilling technology and equipment such as strip backfilling,roadway backfilling,pier-column backfilling and grouting backfilling in overburden separation zone etc.[15-18].But at present,the backfilling mining is not widely used by coal enterprises yet because of the high backfilling cost [19].At the same time,the large volume of backfilling material occupies the underground space formed by tunneling and mining engineering,which makes the underground space difficult to be utilized,resulting in the waste of underground space in coal mines.But reducing the backfilling rate of backfilling mining is an effective measure to reduce the cost of backfilling mining and utilize the underground space of coal mines.Therefore,a new backfilling mining method with a low backfilling rate called constructional backfilling coal mining (CBCM) is proposed [20].

As shown in Fig.1,the CBCM is a new backfilling mining technology with a low backfilling rate,which is constructed by unconfined backfilling bodies arranged at intervals in the mining stope.The key to the success of CBCM lies in the formation of a stable“backfilling body-immediate roof” cooperative bearing structure[20].The bearing capacity of the immediate roof can be brought into full play by arranging the backfilling bodies at the key position of the goaf.Given this,the stability of CBCM with low backfilling rate is studied in this paper.The deformation characteristics of the immediate roof in CBCM are analyzed by establishing the mechanical model of the “backfilling body-immediate roof” cooperative bearing structure.The influence of the backfilling rate on the stability of overlying strata is analyzed by a numerical simulation experiment.The control effect on the strata movement of CBCM is studied by a physic similar simulation test.Our results can provide a theoretical basis for the application of the CBCM in coal mining.

2.1.Concept of constructional backfilling coal mining

As shown in Fig.2,to control the surface subsidence and reduce the backfilling cost,unconfined backfilling bodies such as column(pier),strip (wall),cross shape,box shape and other structures are arranged at the key positions of the mining stope through pre-planning according to the surrounding rock conditions.The“backfilling body-immediate roof” cooperative bearing structure is formed along with the backfilling process.The movement and deformation of overlying strata can be effectively controlled by the cooperative bearing structure.At the same time,a large amount of long-term stable underground space that can be used according to the demand is constructed in the goaf of the coal mine,such as underground storage of water and other supplies[20,21].

Fig.1.Constructional backfilling coal mining with low backfilling rate [20].

Fig.2.Schematic diagram of constructional backfilling coal mining [20].

The key technologies of CBCM include [20]: (1) the development of new solid-waste backfilling materials to reduce the cost of backfilling materials by optimizing the shape and particle size distribution of gangue aggregate,the development of low-cost new cementitious materials,new additives and various alternative raw materials,etc.;(2) the construction of the composite bearing structure of “backfilling body-immediate roof” through the construction of high strength backfilling structure and selfsupporting structure of immediate roof;and (3) the development of the underground integrated backfilling system including intelligent preparation system,visual delivery system,independent construction system,mobile pouring system,and three-dimensional monitoring system to improve the efficiency of backfilling mining.

2.2.Establishment of medium thick plate model on elastic foundation

As shown in Fig.3,the movement and deformation characteristics of overlying strata with CBCM are analyzed.It is assumed thatais the width of the backfilling body;bthe backfilling spacing;hthe height of the backfilling body;h1the thickness of the immediate roof;and φ the diffusion angle of the influence of the backfilling body,which is the complement angle of the collapse angle of immediate roof[22].The backfilling bodies support the immediate roof,and the two parts together support the overlying strata [23].When the backfilling spacingbis small enough,there will be no separation between the immediate roof and the overlying strata,which can form the“backfilling body-immediate roof”cooperative bearing structure [24].

In the CBCM,the space between backfilling bodies is usually small,which generally meets the condition ofh1/b>1/5-1/8 whenh1>1.0 m [25,26].Therefore,to obtain the reasonable backfilling spacingb,the immediate roof can be simplified as a medium thick plate structure,and the backfilling bodies can be analyzed as Winkler elastic foundation [27,28].The structure is simplified according to symmetry,and the rectangular medium thick plate model on the elastic foundation of the“backfilling body-immediate roof”cooperative bearing structure is established as shown in Fig.4.The backfilling body provides vertical elastic support for the immediate roof.The model boundary provides horizontal and bending moment constraints for the inner immediate roof.The immediate roof above the backfilling body bears the overlying strata pressure and the gravity of the immediate roof itself.With the increase of the distance from the backfilling body,the overburden pressure on the immediate roof decreases gradually.The immediate roof is separate from the overlying strata above the center of the goaf,and only bears its gravity.

Fig.3.“Backfilling body-immediate roof” cooperative bearing structure.

Fig.4.Mechanical model of the “backfilling column-immediate roof” structure.

In Fig.4,the model is divided into 3 sections,namelyL1,L2,andL3,according to the force bearing characteristics,and2(L1+L2+L3)=a+b,2(L2+L3)=b,L1=a/2,L2=h1tanφ.q1is the gravitational stress of the immediate roof γ1h1,where γ1is the volume density of the immediate roof;q2the vertical stress on the immediate roof above the backfilling body;andkthe elastic foundation coefficient of the backfilling body.According to the static equilibrium in the vertical direction,Eq.(1) can be obtained.

whereqcrepresents the average vertical stress of the immediate roof and overlying strata to the backfilling columns;qthe average vertical stress of the immediate roof and overlying strata to the backfilling body when full-filling,andq=∑γihi,γiis the unit weight of theithlayer above the backfilling body andhiis the thickness of theithlayer above the backfilling body;ω the displacement of the immediate roof along thezdirection.qc≤[σ] is required to ensure the stability of the backfilling column,and [σ] is the design value of backfilling body strength.

2.3.Deformation equation analysis of the immediate roof

According to Hu Haichang’s theory [29],two undirected functionsF(x,y)andf(x,y)are introduced to solve the bending of a rectangular medium thick plate on Winkler’s elastic foundation,which attribute to solving the following two partial differentials as shown in Eqs.(2) and (3) [30,31]:

By solving Eq.(3),Eq.(4) can be concluded as:

As shown in Fig.3,the internal force and deformation of any point in the plate can be expressed by the following Eqs.(5)-(12):

where φxand φyare the rotation angles of the immediate roof in the plane ofx-zandy-zrespectively;Mx,MyandMxythe bending moments of the immediate roof along the direction ofx,yandz,respectively;andQxandQythe shear forces on the vertical plane of surfacexandy,respectively.

It can be seen from Fig.4 that the bearing structure is symmetric about thex=yplane,wheny≤x≤L1,kx,y=k,qx,y=q2.Substituting them into Eq.(2),we can get Eq.(13).

whereYm（y）=Amφ1m（y）+Bmφ2m（y）+Cmφ3m（y）+Dmφ4m（y）;Am,Bm,CmandDmare integral constants.

Whenl4=k/D-k2/(4C2)>0,φ1m(y),φ2m(y),φ3m(y),φ4m(y)can be obtained according to Eqs.(15)-(18):

WhenL1≤x≤L1+L2,andy≤x,we can getkx,y=0 andSubstituting them into Eq.(2),we can get Eq.(19).

By solving Eq.(19),we can get Eq.(20).

WhenL1+L2≤x≤L1+L2+L3andy≤x,we can getkx,y=0 andqx,y=q1.Substituting them into Eq.(2),we can get Eq.(21).

By solving Eq.(21),we can get Eq.(22).

According to the boundary conditions of sliding support,Eqs.(23)-(28) can be obtained:

According to the boundary conditions Eqs.(23)-(28)and continuity conditions atx=L1andx=L1+L2,the expressions of integral constantsam,bm,Am,Bm,Cm,Dm,and undetermined coefficientsC21,C22,C23,C24,C31,C32,C33,C34about the parametersk,C,D,μ,q1,q2,L1,L2,L3can be got with the help of MATLAB software[32,33].

The control principle of the CBCM is that the immediate roof will not break and the deformation is within the allowable range as Eqs.(29)-(32) [20].

whereRtis the tensile strength of the immediate roof;Rsthe shear strength of the immediate roof;Rcthe compressive strength of the immediate roof;[ω]the allowable deflection of the immediate roof;and σtmax,τmax,σcmax,and ωmaxthe maximum tensile stress,maximum shear stress,maximum compressive stress and maximum deflection of the immediate roof,respectively.In general,tensile failure or shear failure will occur in the immediate roof [27].Combined with the engineering conditions,the critical backfilling spacing 2(L2+L3)can be calculated.Since this method is an approximate solution after simplifying the structure model,the safety factor of 1.2 times is taken to ensure the engineering safety.that is,the maximum backfilling spacingbmax=0.6(L2+L3).

3.1.Simulation scheme

According to the stratigraphic column of the Xinyang mine in Fig.5,the 200 m×60 m×50 m (length×thickness×height)model is established by FLAC3Dnumerical simulation software in Fig.6 [34].The model adopts the Mohr-Coulomb constitutive model,and the vertical displacement of the bottom and the horizontal displacement of the side are fixed.Calculation according to the engineering geological conditions and buried depth,the vertical stress on the backfilling body is 5.09 MPa when full-filling.To simulate the actual mining depth of 215 m,a uniform load of 4.75 MPa was applied on the top of the model.Excavate and backfilling about 100 m of the length direction in the middle of coal seam 2 from front to back.The excavation step is determined according to the size of the backfilling column,which is the sum of backfilling column sizeaand backfilling spacingb,as shown in Fig.7.According to the geological conditions and strata parameters of the Xinyang mine,the immediate roof is the sandy mudstone (1.5 m),the basic roof is the fine-grained sandstone (3 m),and the main roof is the medium grained sandstone (15 m) [21].The backfilling spacingbis fixed at 2.5 m in CBCM when the critical backfilling spacing of immediate roof breaking is about 3.2 m.

Fig.5.Stratigraphic column of the Xinyang mine.

Fig.6.Model of numerical simulation.

Fig.7.Sequence and width of mining and backfilling.

The backfilling rate and the backfilling column width are designed in Table 1.The backfilling rate refers to the proportion of the total cross-sectional area of the backfilling bodies to the area of the whole mining stope in this paper.The backfilling column width is determined as 5.0,2.5 and 1.5 m based on the mining height(2.5 m),taking into account the backfilling rate and backfilling spacing,and making it evenly distributed in the mining stope,which is 2.0,1.0 and 0.6 times of the backfilling column height(2.5 m).Taking the subsidence of the immediate roof,the plastic zone and vertical stress of backfilling body,the vertical stress at the top of immediate roof and basic roof,the vertical stress at the bottom of the main roof as monitoring objects,the influence of different backfilling rate on the stability of the overlying strata is analyzed.

Table 1 Backfilling column width and backfilling rate.

Table 2 Cost of forming 1 m3 backfilling body with different strength in the goaf.

Table 3 Backfilling cost under different backfilling rates.

3.2.Sinking distance of the immediate roof

It can be seen from Fig.8 that the sinking distance of the immediate roof in the mining stope increases gently when full-filling,and the maximum value of the sinking distance is 9.38 mm in the middle of the mining stope.However,when CBCM is adopted,the sinking distance of the immediate roof above the backfilling body is less than that above the goaf,and the wave type subsidence of the immediate roof is formed in the mining stope.When the backfilling rate is 43.3%,the maximum sinking distance of the immediate roof is 13.21 mm,which is 40.8% larger than fullfilling.When the backfilling rate is 24.4%,the maximum sinking distance of the immediate roof is 15.80 mm,which is 68.4% larger than full-filling.When the backfilling rate is 13.7%,the maximum sinking distance of the immediate roof is 16.48 mm,which is 75.7% larger than full-filling.It can be seen that with the decrease in backfilling rate,the control effect of backfilling bodies on the deformation of immediate roof is gradually weakened.However,the change in the sinking distance of the immediate roof is small,especially when the backfilling rate decreased from 24.4% to 13.7%.

3.3.Plastic zone and vertical stress of the backfilling body

Fig.9 shows the plastic zone and vertical stress of the backfilling body in the middle of the mining stope.When the backfilling rate is 43.3% and backfilling width is 5 m,the vertical stress of the backfilling body is different obviously,which is 18.00 MPa at the top and bottom corners of backfilling body and 9.63 MPa at the center of backfilling body.It means when the backfilling width is large,the bearing capacity of the backfilling body is uneven.The maximum stress of the backfilling body is 27.7% higher than the design strength of 14.1 MPa.The stress concentration is formed at the top and bottom corners of the backfilling body,and the plastic shear failure of the four edges is occurred,which is not conducive to the stability of the backfilling body [35].However,the elastic core is formed in the middle of the backfilling body,and the backfilling body will not lose its stability completely [36].When the backfilling rate is 24.4% and the backfilling width is 2.5 m,the vertical stress of backfilling body is still difference obviously,which is 31.64 MPa at the top and bottom corners of backfilling body and 14.51 MPa at the center of the backfilling body.The maximum stress of backfilling body is 26.6% higher than the design strength of 25.0 MPa.The stress concentration is formed at the top and bottom corners of the backfilling body,and the plastic shear failure of the top and bottom corners is caused.However,the height of plastic zone decreases.The elastic core is formed in the middle of the backfilling body,and the backfilling body will not lose its stability completely.When the backfilling rate is 13.7% and the backfilling width is 1.5 m,the vertical stress of the backfilling body is still difference obviously,which is 56.73 MPa at the top and bottom corners of backfilling body and 15.57 MPa at the center of backfilling body.The maximum stress of backfilling body is 29.5% higher than the design strength 43.8 MPa.The stress concentration is formed at the top and bottom corners of the backfilling body,and the plastic shear failure of the bottom corners is caused.However,the height of the plastic zone decreases further.The elastic core is formed in the middle of the backfilling body,and the backfilling body will not lose its stability completely.But appropriate reinforcement measures should be taken for the corners of the backfilling body to prevent further extension of the damage,such as using split anchor bolt (cable) or hoop stirrups[37].

Fig.8.Immediate roof subsidence with different backfilling rate.

Fig.9.Plastic zone and vertical stress of backfilling body with different backfilling rate.

3.4.Vertical stress at the top of the immediate roof

It can be seen from Fig.10 that the vertical stress at the top of the immediate roof in the middle of the mining stope is about 5.04 MPa when full-filling.The maximum stress of the immediate roof above the coal pillars is 6.18 MPa on both sides of the mining stope.The minimum stress of the immediate roof is 4.00 MPa at the edges of the mining stope.When the backfilling rate is 43.3%,the vertical stress at the top of the immediate roof is different obviously in the mining stope.It is 8.48 MPa above the center of the backfilling body in the middle of the mining stope,and 1.55 MPa above the center of the goaf at the edges of the mining stope.It shows that the immediate roof plays a role in bearing capacity to the overlying strata.When the backfilling rate is 24.4%,the vertical stress at the top of the immediate roof is slightly increased in the mining stope.It is 8.78 MPa above the center of the backfilling body in the middle of the mining stope,and 1.89 MPa above the center of the goaf at the edges of the mining stope.It shows that the bearing effect of the immediate roof is increased.When the backfilling rate is 13.7%,the difference in the vertical stress at the top of the immediate roof is slightly reduced in the mining stope.It is 8.28 MPa above the center of the backfilling body in the middle of the mining stope,and 2.32 MPa above the center of the goaf at the edges of the mining stope.It shows that the bearing effect of the immediate roof is increased above the center of the goaf.It means that the bearing effect of the immediate roof has little change with the decrease of backfilling rate in CBCM,but the bearing capacity of the immediate roof above the goaf to the overlying strata is slightly improved.

Fig.10.Vertical stress at the top of the immediate roof with different backfilling rate.

3.5.Vertical stress at the top of the basic roof

It can be seen from Fig.11 that the vertical stress at the top of the basic roof(first sub key stratum)is about 4.95 MPa in the middle of the mining stope when full-filling.The maximum stress of the basic roof above the coal pillars is 5.52 MPa on both sides of the mining stope.The minimum stress of the basic roof is 4.40 MPa at the edges of the mining stope.When the backfilling rate is 43.3%,the vertical stress at the top of the basic roof is different obviously in the mining stope.It is 5.41 MPa above the center of the backfilling body in the middle of the mining stope.The maximum stress of the basic roof above the coal pillars is 5.65 MPa on both sides of the goaf.The minimum stress of the basic roof is 4.04 MPa at the edges of the mining stope.When the backfilling rate is 24.4%,the difference in vertical stress at the top of the basic roof is decreasing in the mining stope.It is 5.08 MPa above the center of the backfilling body in the middle of the mining stope.The maximum stress of the basic roof above the coal pillars is 5.79 MPa on both sides of the mining stope.The minimum stress of the basic roof is 4.12 MPa at the edges of the mining stope.It shows that the bearing effect of the basic roof is increasing.When the backfilling rate is 13.7%,the vertical stress at the top of the basic roof is no obvious difference in the mining stope.It is 5.00 MPa above the center of the backfilling body in the middle of the mining stope,which is close to the bearing effect of fullfilling.The maximum stress of the basic roof above the coal pillars is 5.84 MPa on both sides of the mining stope.The minimum stress of the basic roof is 4.17 MPa at the edges of the mining stope.It shows that the bearing effect of the basic roof is further enhanced.It means that when the immediate roof plays a bearing role,it is conducive to the bearing effect of the basic roof.

Fig.11.Vertical stress at the top of the basic roof with different backfilling rate.

3.6.Vertical stress at the bottom of the main roof

It can be seen from Fig.12 that the vertical stress at the bottom of the main roof is about 4.84 MPa in the middle of the mining stope when full-filling.The maximum stress of the main roof above the coal pillars is 5.06 MPa on both sides of the mining stope.The minimum stress of the main roof is 4.58 MPa at the edges of the mining stope.When the backfilling rate is 43.3%,the vertical stress at the bottom of the main roof is about 4.84 MPa in the middle of the mining stope.The maximum stress of the main roof above the coal pillars is 5.11 MPa on both sides of the goaf.The minimum stress of the main roof is 4.55 MPa at the edges of the mining stope.When the backfilling rate is 24.4%,the vertical stress at the bottom of the main roof is about 4.85 MPa in the middle of the mining stope.The maximum stress of the main roof above the coal pillars is 5.18 MPa on both sides of the mining stope.The minimum stress of the main roof is 4.49 MPa at the edges of the mining stope.When the backfilling rate is 13.7%,the vertical stress of the main roof is 4.85 MPa in the middle of the mining stope.The maximum stress of the main roof above the coal pillars is 5.19 MPa on both sides of the mining stope.The minimum stress of the main roof is 4.48 MPa at the edges of the mining stope.It shows that the bearing effect of the main roof has little change with the decrease in backfilling rate.It means that the control effect of full-filling on the overlying key strata can be achieved through CBCM with a low backfilling rate.

4.1.Evolution characteristics of overlying strata

A large-scale physical similar simulation experiment was used to verify the control effect of the CBCM [38],which is 2.0 m×0.4 m×1.5 m (length× thickness×height) according to the size of the testing machine as shown in Fig.13a.The geometric similarity ratio is 1:25,the bulk density similarity ratio is 1:1.5,the stress similarity ratio is 1:37.5,and the time similarity ratio is 1:5[39].According to the calculation,the actual strata scope of the test simulation is 50 m×10 m×30 m(length×thickness×height)of the Xinyang mine.In order to simulate the actual buried depth,a uniform load of 0.12 MPa was applied on the top of the model.River sand,gypsum and lime are mixed with water to make rock and coal seams.Cement,fly ash and fine coal gangue (＜5 mm) are mixed with water to prefabricate the backfilling body.As shown in Fig.13b,excavate and backfill the middle 1.3 m length of the coal seam 2 from left to right.The size and spacing of the backfilling bodies are both 100 mm in the similar model.According to the daily footage of 6 m,the excavation of the model is 50 mm per hour.When each 200 mm coal seam is excavated,a row of two backfilling bodies will be backfilled.In order to monitor the bearing capacity of backfilling and roofs,pressure sensors are installed at the top of the immediate roof and the basic roof,and the bottom of the main roof.

Fig.12.Vertical stress at the bottom of the main roof with different backfilling rate.

Fig.13.Schematic and backfilling scheme of physical similar simulation model.

As shown in Fig.13c,when the coal seam is not filled,the immediate roof of sandy mudstone and basic roof of fine sandstone in the middle of the mining stope will bend and form two cracks with the advance of the mining process.With the passage of time,the cracks gradually expand and cause the immediate roof and the basic roof to collapse eventually.The upper mudstone and coal seam 1 are obviously bent.But when the coal seam is mined with CBCM in Fig.13d,the immediate roof is supported by the backfilling bodies,and the immediate roof and upper stratus have no obvious bending subsidence.There is no crack development and a roof collapse in overlying strata after standing for a long time.The similar simulation results show that the CBCM can keep the stability of overlying strata,and ensure the stability of underground space.

Fig.14.Bearing capacity variation of overlying strata in physical similar simulation experiment.

As shown in Fig.14a,the vertical stress at the top of the immediate roof above the mining stope with CBCM is obviously larger than that without backfilling,while the vertical stress at the top of the immediate roof above the coal pillar with CBCM is obviously smaller than that without backfilling.Especially at 0.55 and 0.95 m in the mining stope,the vertical stress of the immediate roof with CBCM is obviously greater than the original rock stress.It shows that the immediate roof above the backfilling bodies shares the load of the immediate roof above the coal pillar.The bearing capacity of the immediate roof above the goaf is exerted.As shown in Fig.14b,the vertical stress at the top of the basic roof with CBCM is obviously larger than that without backfilling above the mining stope,while the vertical stress at the top of the basic roof with CBCM is obviously smaller than that without backfilling above the coal pillar.It shows that the bearing effect of the immediate roof is transferred to the basic roof.As shown in Fig.14c,the vertical stress at the bottom of the main roof with CBCM is obviously larger than that without backfilling above the middle part of the mining stope,while the vertical stress at the top of the main roof with CBCM is obviously smaller than that without backfilling above the edge part of mining stope.The stress state of the main roof is close to that before excavation.It shows that exerting the bearing capacity of the immediate roof is beneficial to the stability of the key strata above.The results of the physical similar simulation are consistent with those of numerical simulation.

4.2.Economic benefit analysis

The backfilling face under buildings of the Xinyang coal mine plans to produce 0.364 million tons of coal per year when fullfilling,which with a unit weight of 1.35 t/m3.Table 2 shows the cost of forming 1 m3backfilling body with different strengths in the goaf.Table 3 shows the backfilling cost of per ton coal under different backfilling rates.The economic benefit is calculated only from the perspective of backfilling material.The cost of the backfilling material with a strength of 6.1 MPa is determined according to the preparation price of cemented coal gangue material that has been applied in the full-filling mining project of the Xinyang mine.The cost of the backfilling material with strengths 14.1,25.0 and 43.8 MPa are determined by reference to the price of commercial concrete (C15/C25/C45) on the market.It can be seen from the tables and Fig.15,that the cost of forming 1 m3backfilling body increases with the strength of the backfilling body,but the backfilling cost of per ton coal decreases with the decrease in backfilling rate.The backfilling cost is 86.22 yuan/t when full-filling.The backfilling cost of per ton coal is 76.53 yuan/t when backfilling rate is 43.3%,it is 9.69 yuan/t less than the full-filling with a decrease rate of 11.24%.The backfilling cost of per ton coal is 50.77 yuan/t when the backfilling rate is 24.4%,it is 35.54 yuan/t less than the fullfilling with a decrease rate of 41.12%.The backfilling cost of per ton coal is 37.39 yuan/t when the backfilling rate is 13.7%,it is 48.83 yuan/t less than the full-filling with a decrease rate of 56.63%.It can save up to 17.77 million yuan per year in the backfilling face under buildings of the Xinyang coal mine by adopting CBCM with a backfilling rate of 13.7%.At the same time,it can also reduce the initial investment of backfilling equipment and improve coal production through CBCM,which is worthy of application.

Fig.15.Curve of cost changing with backfilling rate.

(1) The medium thick plate model of Winkler elastic foundation of “backfilling body-immediate roof” cooperative bearing structure is established.The deformation characteristics of the immediate roof and the critical backfilling spacing can be analyzed based on Hu Haichang’s theory.

(2) The effects of backfilling rate on the stability of the cooperative bearing structure in Xinyang mine are studied by FLAC3Dnumerical simulation.The results show that the control effect of full-filling on the overlying key strata can be achieved through CBCM with a low backfilling rate.But the corners of the unconfined backfilling body are easy to be damaged,and appropriate reinforcement measures should be taken for the backfilling body in CBCM to prevent further extension of the damage.

(3) The physical similar simulation test shows that the CBCM has good structural stability in Xinyang Mine when the backfilling rate is lower than 25% and the backfilling spacing is 2.5 m.It shows that exerting the bearing capacity of the immediate roof is beneficial to the stability of the key strata above.

(4) The backfilling cost of per ton coal is 37.39 yuan/t when the backfilling rate is 13.7%,and it is 48.83 yuan/t less than the full-filling with a decrease rate of 56.63%.It can save up to 17.77 million yuan per year by adopting CBCM in the backfilling face under buildings of the Xinyang coal mine,which plans to produce 0.364 million tons of coal per year.At the same time,it can also reduce the initial investment of backfilling equipment and improve coal production through CBCM,which is worthy of application.

Acknowledgements

This research was supported by the Youth Funds of National Natural Science Foundation of China (No.52004173),the Distinguished Youth Funds of National Natural Science Foundation of China(No.51925402),the Science and Technology Innovation Project of Colleges and Universities in Shanxi Province (No.2020L0066),the China Postdoctoral Science Foundation (No.2022M712922),and the Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering (Nos.2021SX-TD001 and 2022SXTD008).