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Mechanical mechanism of overlying strata breaking and development of fractured zone during close-distance coal seam group mining

2020-04-21JianguoNingJunWangYunliangTanQiangXu

矿业科学技术学报 2020年2期

Jianguo Ning,Jun Wang,Yunliang Tan,Qiang Xu

College of Mining and Safety Engineering,State Key Laboratory Breeding Base for Mining Disaster Prevention and Control,Shandong University of Science and Technology,Qingdao 266590,China

Keywords:Coal seam group Activation mechanism Separation Water-flowing fractured zone Modified formula

ABSTRACT This study mainly investigates the mechanical mechanism of overlying strata breaking and the development of fractured zones during close-distance coal seam group mining in the Gaojialiang coal mine.First,a mechanical model for the second‘‘activation”of broken overlying strata is established,and the related mechanical ‘‘activation”conditions are obtained.A recursive formula for calculating the separation distance of overlying strata is deduced.Second,a height determining method for predicting the height of fractured zones during close-distance coal seam group mining is proposed based on two values,namely,the separation distance and ultimate subsidence value of overlying strata.This method is applied to calculate the fractured zone heights in nos.20107 and 20307 mining faces.The calculated results are almost equal to the field observation results.Third,a modified formula for calculating the height of a waterflowing fractured zone is proposed.A comparison of the calculated and observed results shows that the errors are small.The height determining method and modified formula not only build a theoretical foundation for water conservation mining at the Gaojialiang coal mine,but also provide a reference for estimating the height of water-flowing fractured zones in other coal mines with similar conditions.

1.Introduction

Deformation,failure,and movement may occur in overlying strata after the exploitation of coal seams.Three zones,namely,caved,fractured,and sagging zones,generally form above the goaf[1].A water-flowing channel could appear when a strong aquifer exists in overlying strata and the fractured zone reaches this area,which might lead to roof seepage accidents[2,3].A fractured zone that reaches the surface water in mining areas with shallow-buried coal seam groups could easily cause loss of surface water and damage to the ecological environment[4-6].The main factors influencing the height at which these three zones develop include the mining height,mining length,and roof lithology [7-9].The development height of the three zones for close-distance coal seam group mining is larger than for mining of a single coal seam because of the multiple mining activities.This could lead to safety accidents such as water flowing off mining faces.Therefore,research on the movement of overlying strata and the development of fractured zones is highly significant to safety and water conservation during close-distance coal seam group mining.

Scholars are currently conducting extensive research on these topics.Yao et al.used RFPA2D to study the influence of multiple mining activities on the height extension and vertical stress change in fractured zones.They obtained the rules for fracture development and re-development of overlying strata [10].Jiang et al.determined the mechanism of mining seism by analyzing the rules of fall and movement of overlying strata and structural shapes,force conditions,as well as fracture instability characteristics of key blocks in heavy and thick rocks caused by repeated mining[11].Liu et al.used Weibull’s multi-parameter distribution function and physical simulation experiments to analyze the stability of broken roof group structures in the multi-gob area as well as the characteristics of the underground pressure in lower working faces[12].Wang et al.studied the relationship between the surface subsidence coefficient and interlayer spacing of coal seams,mining thickness,and the initial subsidence coefficient of the first mining phase[13].Zhai et al.used in situ observations,empirical formulas,and numerical simulation methods to investigate the height of water-flowing zones in close-distance coal seams[14].Jin analyzed the relationship between the limit breaking step and the effective height of the subsidence space under the fracture or tensile failure of the rock formation in combination with physical simulations,numerical calculations,and theoretical analysis to establish the relationship between the crack width of the water barrier and its maximum subsidence value [15].Huang studied the development of fractured zones of overlying strata in double coal seams at the Chengjiazhuang coal mine through physical tests and numerical simulations,and found that the height of water-flowing fractured zones calculated by the empirical formula was relatively small compared with those of the physical tests and numerical simulations [16].Hu used the UEDC numerical simulation software and found that the key strata had a critical influence on the height expansion of water-flowing fractured zones under repeated mining.He also analyzed the mining factors that could affect the development of water-flowing fractured zones [17].Some progress in research on the development laws of fractured zones in closedistance coal seams has been recorded.However,the second‘‘activation”process of overlying strata is not fully understood,and the relationship between the ‘‘activation”process and the development of water-flowing fractured zones during close-distance coal seam group mining need to be further studied.

Therefore,this study investigates the mechanical mechanism of overlying strata breaking and the development of fractured zones during close-distance coal seam group mining based on conditions in the Gaojialiang coal mine.First,an effective method for determining the development height of fractured zones is proposed.This method is then applied to calculate the height of fractured zones in two mining faces.Third,a modified formula for calculating the height of water-flowing fractured zones is proposed based on theoretical results.The height determining method and modified formula not only build a general theoretical foundation for water conservation mining at the Gaojialiang coal mine,but also provide a reference for estimating the height of water-flowing fractured zones in other coal mines with similar conditions.

2.Engineering overview

The Gaojialiang coal mine is located in Ordos City,Inner Mongolia.The surface of the mining area is a region of low hills and sparse vegetation,which belongs to a semi-desert region.The surface level is +1337-+1520 m.The ecological environment is fragile,and the loose layer is rich in water resources.The mining area consists of six mining coal seams,namely 2-2up,2-2mid,3-1,4-2mid,5-1,and 6-2mid.Nos.20107,20108,and 20109 mining faces are located in the no.201 panel of the 2-2upcoal seam.Stoping of nos.20108 and 20109 mining faces had finished in 2011 and 2012,respectively.The longwall face length of the no.20107 mining face is 196 m,and the average mining depth is 156.06 m.The average thickness of the coal seam is 2.97 m,and the average dip angle is 2°-5°.The immediate roof is coarse sandstone with 7-13 m thickness and uniaxial compressive strength of 18.3 MPa.The main roof is medium sandstone with 20-22.78 m thickness and uniaxial compressive strength of 17.8 MPa.

Nos.20306 and 20307 mining faces are located in the no.203 panel of the 2-2midcoal seam.Stoping of no.20306 mining face had finished in 2011.The longwall face length of no.20307 mining face is 272 m with average mining depth of 167.49 m.The average thickness of the coal seam is 3.5 m,and the average dip angle is 2°-4°.The immediate roof is the interval layer of the 2-2upand 2-2midcoal seams.The lithology is mainly coarse-grained sandstone and mudstone with 6.65-11.9 m thickness and uniaxial compressive strength of 17.27 MPa.Figs.1 and 2 show the layout of nos.20107 and 20307 mining faces and the rock strata histogram,respectively.The downside and fully mechanized mining methods are applied to these mining faces,and stoping of the nos.20107 and 20307 mining faces had finished in 2010 and 2012,respectively.

Fig.1.Layout of mining faces and detection boreholes.

Fig.2.Strata histogram of mining faces.

3.Mechanical mechanism of overlying strata breaking during close-distance coal seam group mining

3.1.Second ‘‘activation”process of fractured overlying strata during close-distance coal seam group mining

The overburden strata begin to hang,bend,and sink under gravity when the upper coal seam is mined and as the mining face advances.The strata gradually separate from bottom to top because of differences in the thickness and lithology of various strata.It will break or collapse when the separation distance Snreaches the ultimate subsidence value Scn.Before initial breaking of the overburden in the mining face,the rock strata can be modeled as double-clamped rock beams loaded by uniform loads.The ends of the rock beams crack as the mining face advances.The bending moment of the rock beams at the ends becomes smaller,and the bending moment in the middle becomes larger.Consequently,the supporting conditions are changed to simply supported beams.Fig.3a and b show that the maximum deflection of a simple beam is the ultimate subsidence value.When the rock beam is periodically breaking,the rock strata can be modeled as a cantilever beam if the extrusion pressure between the rock blocks is neglected (Fig.3c and d).The overlying strata will continue to break and sink when the separation distance Snis larger than the ultimate subsidence value Scn;otherwise,the rock formation will not break.The vertical distance between the broken rock and the roof of the coal seam at this time is the height of the fractured zone shown in Fig.4a.

Fig.3.Simplified mechanical model of strata deformation.

The key indicator for mining safety and water conservation in the evaluation of mining faces is the development height of the fractured zone [5-8,14].Therefore,this study will not discuss the other characteristics of the fractured zone,such as the space morphology.As the mining face advances,the interval rock stratum gradually breaks down,and a caved zone forms.The gangue in the goaf of the upper coal seam will subside under the dead weight.Moreover,the separation distance between the gangue and the overlying strata in the upper coal seam fractured zone increases.The overlying strata will move,that is,the ‘‘activation”phenomenon occurs when the separation distance reaches a certain value.Fig.4 shows that the‘‘activation”phase of the overlying strata can be divided into six stages as follows:

(a)The interval layer does not collapse,and the overlying strata in the goaf of the upper coal seam and the fractured zone are not affected by the second mining phase.

(b)The interval layer will collapse when the mining face in the lower coal seam advances to a certain distance.The goaf of the upper and lower coal seams will then penetrate the interval layer.The gangue in the goaf of the upper coal seam gradually moves downward as the mining space increases,and it is then separated from the overlying strata.The overhanging area of overlying strata increases as the mining face advances.Rock blocks 1 and 2 will form a three-hinged arch structure [18]shown in Fig.3b.The broken overlying rocks also begin to separate at this time.

(c)When certain conditions are met,the three-hinged arch structure will be unstable,and rock blocks 1 and 2 will rotate and subside.They will come into contact with the gangue in the goaf,and the separation distance of the upper strata will increase.

(d)The gangue in the goaf of the upper coal seam gradually moves downward as the mining face continues to move forward.Rock block 3 forms a cantilever beam structure with one end suspended and the other end constrained by overlying strata,lateral rock blocks,and gangue.The instability of rock block 3 occurs with the gradual increase of the suspended area.The remaining rock blocks are in the same situation as rock block 3 (i.e.,periodic caving occurs).

(e)The upper rock structure in the fractured zone gradually destabilizes and degrades with the increase of the separation distance.Stages (b),(c),and (d)will not be described here because the same rules apply.

(f)The ‘‘activation”process of the fractured overlying strata ends.As a result,the mining space is increased,and the residual bulging coefficient of overburden strata will decrease and be affected by repeated mining [13],which increases the separation distance of the fractured zone in the upper coal seam and the intact rock strata in the original sagging zone.The rock strata will first break,followed by a periodic breaking when the separation distance reaches the ultimate subsidence value.Some rock strata in the original sagging zone will then evolve into a new fractured zone.As a result,the fractured zone height increases and the fractured zone range expands with the increased advancing distance of the mining face.

Fig.4.Schematic diagram of the ‘‘activation”mechanism of overlying strata during close-distance coal seam group mining.

3.2.Structural mechanical model for the second ‘‘activation”of fractured overlying strata

A mechanical model for the ‘‘activation”structure of broken overlying strata in the close-distance coal seam group mining was established based on earlier analysis to study the structural instability mechanism of overlying strata during the ‘‘activation”process.Figs.5 and 6 depict that during Stage (b),rock blocks 1 and 2 formed a three-hinged arch structure [18].

For Fig.6a,let x be the horizontal direction and y be the vertical direction.Mechanical equilibrium equation is established when

Resulting in TA=TCand RA=qncn.The horizontal thrust TCis presented as follows:

Buy using the geometric relations

Eq.(3)is substituted into Eq.(2),and the horizontal thrust TCrepresented by the separation distance can be obtained after simplification.

where TCis the horizontal thrust in point C,N;cnthe periodic breaking step of the nth layer rock strata,m;mnthe thickness of the nth layer rock strata,m;qnthe average load of the rock block in the nth layer rock strata,N/m;qn=γmncn;γ the average unit weight of the rock,N/m3;and Snthe separation distance of the nth layer rock strata,m.

According to ‘‘masonry beam”theory,the horizontal thrust becomes larger with an increase of the exposed area,causing the corner of the rock block to be crushed and deformed[19].The condition is as follows:

Fig.5.Mechanical model of three-hinged arch structure.

where α is the area of the extrusion contact surface of rocks,and α=(mn-cnsinθn)/2,m2;ησcthe crushing strength of the nth layer rock strata,MPa;and η=0.3.

Substituting Eq.(4)into Eq.(5)yields:

According to Eq.(6),when the geometry and the lithology of the rock blocks are fixed,the instability of the three-hinged arch structure is mainly determined by the separation distance Sn.

Fig.7 shows that when the overlying strata periodically collapse during Stage(d),the left end of rock block 3 is suspended,and the right end face is constrained by the overburden rock,lateral rock block,and gangue,which can be assumed a cantilever beam structure[15].Its instability conditions are the same as those of the first mining phase.

3.3.Discussions

Based on the earlier analysis,when the upper coal seam is exploited,the separation distance and the ultimate subsidence value of the overlying strata can be used to judge whether the rock strata will break or fall.The overlying strata formed some structures in the fractured zone during the mining stage of the lower coal seam.Moreover,the separation distance of the overlying strata can be used as a condition to determine the structural instability.The intact rock strata in the original sagging zone of the upper coal seam can also be determined according to the relationship between the separation distance and the ultimate subsidence value.Therefore,determining the separation distance and ultimate subsidence value is key to predicting the development height of the fractured zone in the close-distance coal seam group mining.

Fig.6.Force analysis of rock blocks.

Fig.7.Force analysis of rock block 3.

4.Method for determining the development height of fractured zones during close-distance coal seam group mining

4.1.Analysis of the composite structure of overlying strata

Many rock strata at the top of the immediate roof in stopes have different thicknesses and strengths.Mining practices have shown that each strata movement is often not a separate process,but a synchronous and coordinated movement of several rock strata consisting of a rock beam composite structure supported by a key stratum,which is usually thick and hard.Whether or not adjacent rock strata can form rock beam composite structures can be judged based on the principle of composite beam and key strata theory [19].

According to key strata theory,the key strata need to meet the load and strength conditions at the same time:

where qnis the load of the nth layer rock strata on the first strata,N;ljthe breaking distance of the jth hard strata,m;and k the number of hard strata determined by Eq.(7).The formulas for calculating qnand ljcan be found in the literature [19].

The position of the key strata can be determined according to the key strata discriminant formulas (Eqs.(7)and (8))and the strata histogram (Fig.2).The rock strata can then be divided into different rock beam composite structures.Fig.2 illustrates the composite structures of overlying strata of the nos.20107 and 20307 mining faces.

4.2.Determination of the separation distance of overlying strata

4.2.1.Determination of the separation distance Snof overlying strata during single coal seam mining phase

The separation distance Snof overlying strata was determined by the mining height,thickness of the rock beam composite structure,and their residual bulging coefficients.Fig.8 shows that after the coal seam has been mined,the immediate roof falls to form gangue.Each composite structure above the immediate roof then gradually suspends,breaks,turns and sinks from bottom to top until the gangue and the underlying rock beam composite structures are compacted.The distance between the initial position of the composite structure and the final position is the separation distance Sn.

The following relationships can be observed for the first,second,and third rock beam composite structures:

Fig.8.Calculation model of separation distances of rock beam composite structures.

where M is the coal thickness,m;mnthe original thickness of the nth layer rock beam composite structure,m;Kpnthe residual bulging coefficient of the nth layer composite structure;and Snthe separation distance of the (n+1)th layer rock beam composite structure,m.

Then,

where Wn-1and Wnare the absolute subsidence value of the(n-1)th layer rock beam composite structure and the nth layer rock beam composite structure respectively,m.

Each Sncan be derived from the above relationship as follows

4.2.2.Determination of the separation distance sn’ of overlying strata during the second coal seam mining phase

When the second coal seam was mined,the fractured overlying strata were affected by the initial mining,and the residual bulging coefficients were reduced [13].Sn’ is presented as:

where Sn’is the separation distance of the(n+1)th layer rock beam composite structure,m;M’ the thickness of the second coal seam,m;andthe residual bulging coefficient of the nth layer rock beam composite structure after the second coal seam has been mined.Note that n should be calculated from the immediate roof of the second coal seam.

4.3.Determination of the ultimate subsidence value Scnof overlying strata

The advancing distance of the mining face is normally very large.Hence,only the ultimate subsidence value of the periodic breaking of the rock beam composite structure was considered here.It can be calculated by the mechanical model of the cantilever beam [15].

where Scnis the ultimate subsidence value of the nth layer rock beam composite structure,m;γ the average bulk unit weight of the rock,22.64 kN/m3;cnthe periodic breaking step of the nth layer rock beam composite structurem,and here σtnis the tensile strength of the nth layer rock beam,MPa);and Enthe elastic modulus of the nth layer rock beam,GPa.

4.4.Calculation of the height of fractured zones

When a single coal seam is mined,the rock beam composite structure can be judged from bottom to top according to the separation distance Snand the ultimate subsidence value Scn.The rock beam composite structure will not break when Snis less than Scn.The vertical distance from the fractured rock strata to the roof of the coal seam at this moment is the development height of the fractured zone.When the second coal seam is mined,Eq.(6)can be used to first determine whether the three-hinged arch structure will be unstable.Subsequently,whether the cantilever beam structure and the intact strata in the original sagging zone will be destabilized or not can be determined based on the relationship between the separation distance Sn’ and the ultimate subsidence value Scn’.When the separation distance Sn’ of strata is less than the ultimate subsidence value Scn,the vertical distance between the rock strata and the roof of the second coal seam is the development height of the fractured zone when the coal seam group is mined.

Fig.2 shows the histogram of the rock strata in mining faces of the Gaojialiang coal mine as well as the rock beam composite structures.Table 1 shows the selected calculation parameters,of which the residual bulging coefficient was obtained through a strata displacement observation (Section 5).The compressive strength,tensile strength,and elastic modulus of each rock beam composite structure were obtained from indoor rock mechanics tests.

The separation distance and ultimate subsidence value of each rock beam composite structure were calculated using Eqs.(17),(18),and (19).The results were plotted as curves,as shown in Fig.9.The separation distances gradually decrease with an increase in the height of the rock beam composite structure.After mining the no.20107 mining face,Sn≤ Scnwhen composite structure 3 was reached.The vertical distance between the overlying strata and the roof of the 2-2upcoal seam was 27.54 m(intersection point 1,Fig.9),that is,the development height of the fractured zone was 27.54 m.After mining the no.20307 mining face,the three-hinged arch structure will be unstable,according to Eq.(6).The development height of the fractured zone was judged according to the separation distance and ultimate subsidence value.The vertical distance between the overlying strata and the roof of the 2-2midcoal seam was 129.67 m when composite structure 6 was reached,(Fig.9,intersection 2 abscissa 118.46 m plus coal seam thickness and spacer thickness 11.21 m).The development height of the fractured zone at this time was 129.67 m,with an increase of 105.1 m over the first mining phase.

5.In situ observations

5.1.Observation instruments and schemes

5.1.1.Drilling arrangement and construction elements

Fig.9.Calculated results.

Fig.10.Profile of borehole layout.

Three monitoring stations (#I,#II,and #III)were set up at the no.6 crossheading in the no.20307 mining face to study the development law of fractured zones in the close-distance coal seam group.Inclined boreholes were drilled toward the mining face.The drilling position and inclination met the following conditions:a certain distance between the boreholes and the goaf had to be maintained to prevent the roof collapse from damaging the boreholes.The boreholes required a sufficient angle to ensure that the movement of the rock strata over a large area above the stope could be detected.Figs.1 and 10 show the layout of the boreholes.Table 2 presents the drilling construction factors.

5.1.2.Observation instruments and methods

A detection device was used to determine the development height of fractured zones in #I and #II monitoring stations.Fig.11 shows its structure.The device was composed of a flow meter,pressure gauge,pressure-regulating valve,double-ended water plugging device,and a pressure hose.The pressureregulating valve and flow meter,supplied by constant pressure water,were connected via the drill pipe or manpower hollow putter (water injection pipeline)to the sealing-hole section.It measured the amount of water injected into the hole section and that leaked through the hole wall cracks per unit time to determine the development of a fracture in the rock strata.As a result,the upper boundary height of the fractured zone could be determined.

The movement of rock strata was detected by self-made deep multi-point displacement detectors in the #III monitoring station.Fig.12 shows its structure.The detector was composed of a num-ber of points,a plugging tube,reading plate,and steel wires.It could monitor 11 points,and the point diameter was 56 mm.The points were secured in different rock beam composite structures according to the strata histogram of the mining faces.The displacement detectors were installed,and the initial readings were recorded.Uninterrupted readings were obtained as the mining faces advanced.

Table 1 Calculation parameters.

Table 2 Construction factors of boreholes.

Fig.11.Detection device for determining the height of water-flowing fractured zone.

Fig.12.Deep multi-point displacement detector.

5.2.Observation results

Data measured by the deep multi-point displacement detector was processed to obtain the subsidence value of each rock beam composite structure.The residual bulging coefficient of each composite structure was then calculated using Eq.(13).Table 1 presents the results while Fig.13 depicts the curves of leakage rates at different borehole depths.The observation results indicate that the development height of the water-flowing fractured zone can be determined.After mining the no.20107 mining face,the development height of the water-flowing fractured zone was 32.50 m,which was 4.96 m larger than the theoretical value.After mining the no.20307 mining face,the development height of the waterflowing fractured zone was 120.40 m,which was 9.27 m less than the theoretical value.

6.Empirical formula modification and comparison

According to the empirical formula of the State Coal Industry Bureau of China,the height of the water-flowing fractured zone(for the lithology of the overburden)is calculated as follows [20].where M is the sum of two coal thicknesses as the thickness of the interval stratum is small.

Fig.13.Leakage rate curves of nos.20107 and 20307 coal faces.

Table 3 Comparison of calculation results.

The empirical formula Eq.(20)was based on a large quantity of field observation data and obtained by regression analysis,but factors affecting strata movement were not considered.Founded on the analysis of overlying strata ‘‘activation”during close-distance coal seam group mining,and the theoretical calculations of fractured zone height(Section 4.4),this study introduced a linear correction to Eq.(20)to obtain a modified formula for calculating the height of a water-flowing fractured zone.

The height of the water-flowing fractured zone was then calculated using the empirical and modified formulas,as shown in Table 3.The result of the empirical formula for the first mining phase was 24.90 m,which was close to 27.54 m,the result of the modified formula.The relative errors were -23.4% and -15.3%,indicating that,for the first mining phase,the result of the modified formula was closer to the in situ observation than the result of the empirical formula.The result calculated by the empirical formula for the second mining phase was 33.07 m,which was much smaller than the in situ observation of 120.40 m,resulting in a relative error of -72.5%.The result calculated by the modified formula was 129.64 m,with a relative error of +7.8%.The results showed that the modified formula calculated the height much more accurate than the empirical formula.Moreover,the height of the water-flowing fractured zone can be more accurately estimated than calculated by the empirical formula.

It is notable that:according to the lithology of the overburden,the empirical formula in literature is Hli=[100∑M/(3.1∑M+5.0)]±4.0[20].The thickness of the interval stratum is small;hence,the sum of two coal thicknesses is M.

7.Conclusions

The following conclusions are drawn from this study:

(1)During close-distance coal seam mining,the fractured overlying strata of the upper coal seam experienced a second‘‘activation”process caused by exploitation of the underlying coal seams.This process included six stages,i.e.(a)non-caving of the interval layer,(b)caving of the interval layer,(c)instability of the three-hinged arch structure,(d)periodic caving of the lower rock blocks,(e)instability and periodic caving of the upper rock blocks and (f)end of the‘‘activation”process of fractured overlying strata.

(2)A structural mechanical model for the second‘‘activation”of fractured overlying strata was established and its mechanical conditions were obtained.When stoping the upper coal seam,the breaking and falling of rock strata could be judged by the separation distance and ultimate subsidence values.When stoping the underlying coal seam,the overlying strata formed some structures in the fractured zone.The separation distance can be used to judge the condition of the structural instability,but the fracture of intact strata in the sagging zone of the upper coal seam must be determined according to the relationship between the separation distance and the ultimate subsidence value.

(3)The recursive formula for calculating the separation distance of overlying strata was deduced.In addition,a method for determining the development height of a fractured zone during close-distance coal seam mining was proposed.This method was applied in nos.20107 and 20307 mining faces.The heights of the water-flowing fractured zones were calculated as 27.54 m and 129.67 m,which were close to those obtained from the in situ observations (i.e.,32.50 m and 120.40 m,respectively).

(4)Strata movement was not considered in the empirical formula for calculating the development height of waterflowing fractured zones.Therefore,this study provided a modified formula based on the analysis of overlying strata‘‘activation”during close-distance coal seam mining,which could be used to calculate the height of fractured zones in close-distance coal seam mining areas.The results showed that the errors were small for the two coal seam mining stages.The height determining method and modified formula proposed in this study not only provide theoretical support for the water conservation mining at the Gaojialiang coal mine and adjacent mines,but also provide a reference for the prediction of the development height of waterflowing fractured zones in other coal mines with similar mining conditions.

Acknowledgments

This study was supported by the National Natural Science Foundation of China (Nos.51474137,and 51574154),Shandong Province Natural Science Fund (No.ZR201709180101),Tai’shan Scholar Engineering Construction Fund of Shandong Province of China,and Postgraduate Technology Innovation Project of Shandong University of Science and Technology (No.SDKDYC 180103).


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