research article analytical analysis and field observation...

Research ArticleAnalytical Analysis and Field Observation of Break Line in theMain Roof over the Goaf Edge of Longwall Coal Mines

Zhang Guangchao1 He Fulian1 and Jiang Lishuai2

1College of Resources amp Safety Engineering China University of Mining amp Technology (Beijing) Beijing 100083 China2Shandong University of Science amp Technology Qingdao 266510 China

Correspondence should be addressed to Zhang Guangchao 874557858qqcom

Received 9 May 2016 Revised 12 June 2016 Accepted 15 September 2016

Academic Editor Marek Lefik

Copyright copy 2016 Zhang Guangchao et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper presents an integrated approach for analytical analysis and field tests to estimate the break line in a main roof overthe goaf edge An analytical model which treated the main roof as a beam seating on the Winkler foundation and subjected tononuniformity roof loading was established Further analysis of the bending moment distribution of such a main roof beam wasundertaken Based on the geological conditions pertaining to a case study at Wangjialing coal mine Shanxi Province China thebreak line in the main roof in a typical longwall panel was calculated in the rib-sides at a distance of 56 to 74m from the goaf edgeThe influence of main roof flexural rigidity and foundation rigidity and so forth on the bending moment distribution was revealedby a parametric study Borehole camera detection was employed to further validate the analytical model and its results The resultsof the field test demonstrated that the break line detected in the main roof was about 55 to 68m away from the goaf edge whichwas in good agreement with the analytical model

1 Introduction

Entry driven along goaf edge (EDG) is a kind of gateroadwhich is excavated as the tailgate or headgate for future panelby retaining a narrow coal pillar along the goaf edge of theprevious panel [1] The application of the EDG techniquenot only can increase coal recovery rate and achieve hugeeconomic benefits but also can improve the drivage efficiencyto shorten the time needed to prepare future panel [2]Both generalised models and investigations show that afterexcavation of the adjacent panel a destressed zone and anoverstressed zone are created in the rib-sides due to stressredistribution induced by the rotation and subsidence of thelateral main roof and the two zones are demarcated by thebreak line where the main roof is broken above the rib-sides [1 3] The low stress environment in the destressedzone benefits the excavation and maintenance of EDG andcan prevent dynamic disasters due to high stress [2] such asfloor heave and coal bumps Therefore it is of significance intheoretical research and engineering application to acquirethe stress distribution in the rib-sides especially the break

line of the lateral main roof for designing pillar width forEDG ground stability

To date considerable investigations have provided acomprehensive understanding with respect to the spatialstructural characteristics of overlying strata near a goaf Forinstance Peng treated the main roof above the caved zoneas a cantilever beam structure for determination of shieldroof loading [4] Smart and Davies presented a roof beam tilttheory in which the inclination angle of the main roof strataand the rotation fulcrum position were considered as theimportant parameters for pillar width design [5] Howeverboth of the aforementioned analytical methods focus on thestructural characteristics of broken roof strata while how toobtain the break line in the main roof is often overlooked Shiet al proposed an analytical model for analysing the bendingmoment distribution along the main roof and found that thebreak line in the lateralmain roof was just sited above the goafedge [6] In their model the lateral main roof was simplifiedto be a cantilever beam fixed at a rigid abutment with zerovertical deflection However in reality some investigationsdemonstrated that the break line in the lateral main roof was

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 4720867 11 pageshttpdxdoiorg10115520164720867

2 Mathematical Problems in Engineering

Strata CStrata A

II

Strata B

Panel 1Panel 2

EDG

Set-up room

Advancing direction

(a) Arc-triangle section of the lateral main roof after breakage

Strata A

Strata CStrata B

EDG Pillar Coal

Goaf

(b) The lateral hinged structure over the EDG (section I-I in Figure 1(a))

Figure 1 Schematic arc-top structure above GDE

usually several metres away from the goaf edge For exampleZhang et al performed physical experiments in which thelateral main roof broke at a distance of 3 to 8m from thegoaf edge and the break line moved closer to the goaf edgewith immediate roof thickness decreasing [7] Zhao andQianestablished an elastic foundation beam model which treatedthe lateral main roof as an elastic beam resting on a Winklermedium [8] Some results from their study demonstrated thatthe break line in the main roof lies in the rib-sides and varieswith respect to the foundation rigidity Unfortunately thecover stress and side abutment pressure induced by adjacentpanel mining were neglected in their model

In addition some scholars attempt to detect the breakline in the lateral main roof by field studies For instanceWang et al applied borehole stress meters to monitor thestress distribution in the rib-sides and got distributions ofside abutment pressure [9] Liu et al presented experimentalstudies of strata movement above the goaf edge by seismicmeasurement techniques [10] During the breakage processof the main roof numerous vertical and subvertical fracturesand horizontal cracks are sharply developed in the rock massneighbouring the break line [4] According to these char-acteristics Zhang et al presented an experimental researchinto the break line in the main roof by observing fracturesevolution in a 10m long borehole drilled on the GDE roof[11] The results suggested that compared to other moni-toring methods borehole camera detection was an effectivestraightforwardmethod to estimate the break line in themainroof

In this paper considering the deformation characteristicsof coal seam a simple analytical model was established todeduce the break line in the lateral main roof Taking the caseof panel 20105 Wangjialing coal mine China as an examplethe influencing factors were investigated by a parametricstudy such as Youngrsquos modulus coal seam thickness andfoundation rigidity The analytical solution was obtained andcompared to a field study using borehole camera detectiontechniques for validation

2 Mechanical Analysis

In longwall mining when the work face advances a certaindistance the immediate roof collapses at first then themain roof begins to bend and sag causing crack generationand propagation in roof strata once cracks coalesce intolarge fractures the main roofs are broken into blocks Thebroken strata hinge with adjacent strata and thus form anarticulated structure above the coal face [12] Meanwhileperpendicular to the retreat direction of the work facethe lateral main roof shaped like arc-triangle section willbe formed at the end of the mining panel as shown inFigure 1(a) According to Bai [13] the lateral main roofwill break in the rib-sides and then a lateral articulatedstructure is formed by broken strata A B and C as illus-trated in Figure 1(b) Investigations show that the structuralcharacteristics of the lateral main roof especially the breakline thereof will greatly affect the stress distribution in therib-sides

The section of lateral main roof before breakage is illus-trated in Figure 2(a) where 119871 is the length of the cantileverroof strata above the goaf and 119887 is the extent of affectedzone by side abutment pressure which is about 40 to 60mConsidering the fact that coal seams and their surroundingrock strata are relatively soft and weak compared to roofstrata they are considered to meet Winkler foundationassumptions [8 14ndash16] According to the available literature[15] the characteristic length of main roof is about 32 to63m while the distribution area of side abutment pressureis about 40 to 60m wide which is about 5 to 20 times thecharacteristic length Hence the main roof above the rib-sides can be assumed to be a semi-infinite long beam onthe Winkler foundation and the main roof above the goafis simplified to a cantilever supported by broken strata Cas shown in Figure 2(b) In Figure 2(b) 1198720 1198760 and 119873are the bending moment and shear and horizontal forceacting at point 119909 = 0 1198731015840 and 1198761015840 are the horizontal andshear force exerted by strata C which act on the rear end of

Mathematical Problems in Engineering 3

Strata A Strata BStrata C

Goaf

Lb

(a) Spatial structure

L

y

x b

Winkler foundation

N

q0

q1

M0M0

Q0Q0

qc

N998400

Q998400

(b) Analytical model layout

Figure 2 The main roof beam on a Winkler foundation

the cantilever district The roof beam atop the abutment isloaded by pressure 119902(119909) which consists of the overburdenpressure 1199020 and side abutment pressure In this paper thecoal seam and its surrounding rock strata are assumed tobe in perfectly elastic state thus the location of the sideabutment peak pressure is considered to be right abovethe work face wall In practice the location of the sideabutment peak pressure varies with respect to the failure ofcoal which is beyond the scope of the current study andwill be further investigated in the future Therefore the sideabutment pressure in this study is simplified to follow a linearrelationship which ranges from 1199021 at 119909 = 0 to 0 at 119909 = 119887 Thepressure 119902(119909) can be expressed by

119902 (119909) = 1199020 + 119887 minus 119909119887 1199021 (1)

where 1199020 = 120574119867 1199021 = 119896120574119867 120574 is unit weight of overlyingstrata 119867 is the depth of panel below the ground face andk is a stress increment coefficient which is usually close to 1[12]The uniformly distributed load 119902119888 shown in Figure 2(b)represents the overlying pressure on the cantilever districtgiven by [12]

119902119888 = 1198641ℎ31 (1205741ℎ1 + 1205742ℎ2 + sdot sdot sdot + 120574119899ℎ119899)1198641ℎ31 + 1198642ℎ32 + sdot sdot sdot + 119864119899ℎ3119899 (2)

where 119864119899 is Youngrsquos modulus of 119899th layer above the panel 120574119899is unit weight of 119899th layer and ℎ119899 is the thickness of 119899th layer

According to Winklerrsquos assumption [17] the relationshipbetween pressure 119875 and vertical deflection 119910 of a foundationis given by

119875 = minus119870119910 (3)

where 119875 is the vertical stress acting on the beam due tothe deflection of the foundation y is the deflection of thefoundation and K is the stiffness modulus of the foundationwhich is determined by the properties of rock strata belowthe main roof Generally the foundation can be considered

as the combination of the immediate roof coal seam andimmediate floor Their interrelationship can be expressed as

1119870 = 119898sum

1

1119870119898

119870119898 = 119864119898(1 minus 1199062119898) ℎ119898 (4)

where119870119898 is the stiffnessmodulus of119898th layer below themainroof 119864119898 119906119898 and ℎ119898 are Youngrsquos modulus Poissonrsquos ratioand thickness of 119898th layer According to the theory of beambending on elastic foundation [18] the governing differentialequation is

11986411986811988941199101198891199094 + 11987311988921199101198891199092 = 119902 (119909) + 119901 (5)

where 119864 is Youngrsquos modulus of the main roof which underplane strain conditions is given by 119864(1 minus 1199062) 119868 = 119889ℎ312119889 and ℎ are the width and thickness of the main roofrespectively Substituting (3) into (5) and assuming that 119904 =119873119864119868 and 1199032 = 119870119864119868 the following equation can be givenfrom (5)

11988941199101198891199094 + 119904

11988921199101198891199092 + 1199032119910 =

119902 (119909)119864119868 (6)

According to the literature [12 19] the general solution tohomogeneous equation with respect to (6) is

119884 (119909) = 119890minus120572119909 (119860 cos120573119909 + 119861 sin120573119909) (7)

where 120572 = (1199032 minus 1199044)12 and 120573 = (1199032 + 1199044)12 The parti-cular solution to (6) is

119884lowast (119909) = 119902 (119909)1198641198681205742 (8)

Thus the general solution to (5) is

119910 (119909) = 119890minus120572119909 (119860 cos120573119909 + 119861 sin120573119909) + 119902 (119909)1198641198681205742 (9)


From Figure 2(b) the following relationships can be obtainedat 119909 = 0

1198720 = 119864119868119910101584010158400

1198760 = 1198641198681199101015840101584010158400 + 11987311991010158400(10)

Substituting (9) into (10) the roof beam deflection 119910 is givenby

119910 = 119890minus120572119909 [(1205741198720 + 21205721198760119864119868120574 (120574 minus 119904) + 412057211990211199042119896119887119903 (119903 minus 119904)) cos120573119909

minus ( 21205721205741198720 + 11990411987602119864119868120574 (120574 minus 119904) 120573 + 119902111990422119896119887119903 (119903 minus 119904) 120573) sin120573119909] (11)

According to the bending moment expression 11986411986811991010158401015840 = 119872(119909)the bending moment119872 is given by

119872 = 11986411986811991010158401015840 = 119890minus120572119909 1198720 cos120573119909

+ [120572 (120574 + 119904)1198720 + 1205741198760(120574 minus 119904) 120573 + 1199021119904119887119903 (119903 minus 119904) 120573] sin120573119909 (12)

The tensile stress in the main roof gradually increaseswith internal bending moment increasing the main roofstrata break off when the maximum tensile stress reaches itslimited strengthHence the break line in themain roof can beobtained by calculating the location of themaximumbendingmoment Take derivative to (12) and set1198721015840 = 0 the locationof maximum bending moment 1199090 can be obtained as follows

tan1205731199090 = [(3119886119904 minus 119886119903)1198720 + 1205741198760 + 1199021119904119887119903] 2120573(21205742 minus 1199042 + 21205741205732 minus 21199041205732)1198720 + 21205721205741198760 + 21198861199041199021119887119903

1199090 = tanminus1 ([(3119886119904 minus 119886119903)1198720 + 1205741198760 + 1199021119904119887119903] 120573 ((1205742 + 1205741205732 minus 1199041205732)1198720 + 1205721205741198760 + 1198861199041199021119887119903))120573

(13)

According to the equilibrium conditions and a voussoirbeam theory [13] 11987601198720 1198761015840 and119873 are given as follows

1198760 = 119902119888119871 + 11987610158401198720 = 1

21199021198881198712 + 1198761015840119871 + 1198731015840 (ℎ2 + Δ1199041)

119873 = 11987111987610158402 (ℎ minus Δ119904)

1198761015840 = 119871120574ℎ

(14)

where Δ119904 = ℎ6 Δ119904 is the deflection of broken strata Δ1199041 isthe deflection of the rear end of cantilever roof strata relativeto the position where 119909 = 0 which can be neglected due toits small value

3 Case Study

31 Background of Wangjialing Coal Mine To demonstratethe theoretical results a case study was conducted inWangjialing coal mine Shanxi Province China The miningarea of the Wangjialing coal mine is 70 km long and 258 kmwide and covers a total of mining area of 1806 km2 Longwallpanels 20103 and 20105 were selected for this case study Thetwopanelswere 260mwide in the strike direction and 1400mlong in the dip direction serving for number 2 coal seamNumber 2 coal seam was buried at a depth of 300m withan average thickness of 62m The immediate roof is sandymudstone with an average thickness of 20m The main roofis siltstone with an average thickness of 92mThe immediate

floor ismudstonewith an average thickness of 16mTheden-sity Youngrsquos modulus Poissonrsquos ratio uniaxial compressivestrength (UCS) cohesion and friction angle were measuredby laboratory testing of samples cored fromWangjialing coalmine as presented in Table 1 All of rockcoal properties werebased on laboratory tests on coal and rock samples reportedby North China Institute of Science and Technology [20]Mechanical property laboratory tests of rock core samples ofthe coal seam have been conducted on a servo-controlledspecial testing system (TAW-2000) having a maximum axialload of 2000 kN maximum shear load of 500 kN and maxi-mum lateral pressure of 500 kN It is noticed that the frictionangle of coal is approximately the same as sandstone whilethe cohesion and UCS of the coal are far smaller comparedto sandstone Without any evidence to suggest that the testresults were erroneous this value was used in the study

After panel 20105 had been mined out number 20103headgate was developed along the goaf edge for panel 20103as shown in Figure 3 The pillar between adjacent panels was8m wide

32 Determination ofModel Parameters Based on the data inTable 1 RocLab softwarewas used to determine the rockmassstrength parameters Related parameters are listed in Table 2where GSI 119872119894 and 119863 are the geological strength index theintact parameters and disturbance factor respectively UCSand 119864119894 are the uniaxial compression strength and Youngrsquosmodulus of intact rock respectively and 119864rm is Youngrsquosmodulus of the rock mass

33 Bending Moment Distribution According to (4) and themechanical properties of the immediate roof coal seam


Table1Generalise

dstratig

raph

yandkeygeotechn

icalparameters

Stratum

number

Geological

legend

Rock

type

Rock

thickn

ess(m)

Density(kgm3)Yo

ungrsquos

mod

ulus

(GPa)Po

issonrsquosratio

UCS

(MPa)Coh

esion(M

Pa)Frictio

nangle(∘)

Maxim

umMinim

umAv

erage

1Fine

sand

stone

49

622

56

2700

2773

022

1653

116

4164

2Mud

stone

149

212

182140

685

024

446

26

32

3Fine

sand

stone

02

152

09

2700

2773

022

1653

116

4164

4Mud

stone

09

158

132140

685

024

446

26

32

5Medium

sand

stone

189

256

23

2675

2814

021

1462

109

4764

6Gritsto

ne14

22

172730

3266

024

1624

124

4823

7Coalseam

09

1210

1412

206

036

1389

23

4434

8Mud

stone

21

32

23

2140

685

024

446

26

32

9Siltstone

89

126

922680

3073

022

1423

943942

10Sand

ymud

stone

166

23

20

2659

1158

027

6328

89

4739

11Coalseam

2596

66

62

1412

206

036

1389

23

4434

12Mud

stone

1418

162140

685

024

446

26

32

13Siltstone

59

7768

2680

3073

022

1423

943942


Number 20103 mining panel

Advancing direction

Goaf of number 20105 panel

Number 20103 headgate

Number 20103 tailgate

Mai

ns

Test area

Stop

line

Stop

line

500

550

NSe

t-up

room

f11 ang50∘ H = 15ndash17 m82 ang50 ∘H = 15 m

61 ang60 ∘H

= 15m

32 ang60∘ H = 25 m27 ang50∘

H = 15 m

Yield pillar (8 m wide)

570

Figure 3 Layout of panels 20105 and 20103 and location of test area in number 20103 headgate

Table 2 Properties of coal and roof formation

Lithology UCS(MPa) GSI 119872119894 119863 119864119894(GPa) 119864rm(GPa)Fine sandstone 1653 64 14 07 2773 1455Medium sandstone 1462 66 16 07 2814 16327Gritstone 1624 72 17 07 3266 2306Siltstone 1423 70 16 07 3073 2055Sandy mudstone 6328 43 11 07 1158 346Coal seam 1389 14 4 07 206 030Mudstone 446 47 9 07 685 365

and floor in Table 2 the stiffness modulus of foundation 119870is calculated to be 006GPa

Based on the key stratum theory strata number 2 tonumber 9 will deflect with the main roof strata Using (2)and the data from Table 2 cantilever district roof beam loadintensity 119902119888 = 050MPa

Youngrsquos modulus of main roof is calculated to be2159GPa the moment of inertia 119868 is 6489m4 and thus theflexural rigidity is 140098GNsdotm2

The length of cantilever is consistent with the periodicweighting length which is 14m We have the following

1198761015840 = 14m times (25KNm2 times 92m) = 322MN119873 = 14m times 322MN(5 times 92m3) = 294MN1198760 = 050MNm times 14m + 322MN = 1022MN119872 = 050MNmtimes14mtimes14m2+322MNtimes14m+294MN times 46m = 10760MN sdotm

Then 120574 = 0007mminus2 and s = 2099 times 10minus6mminus2Substituting parameters into (11) and (12) the deflection

and bending moment in the main roof can be obtained asshown in Figure 4 and Table 3

The distribution of bending moment in the main roof isshown in Figure 4 The bending moment increases from thegoaf edge and hit the peak at a distance of 6 to 7m awayfrom the goaf edge and then it decreases to zero in distance

Breakage

0

20

40

60

80

100

120

140Be

ndin

g m

omen

t (M

Nmiddotm

)

0 10 20x (m)

30 40 50 60

Figure 4 Distribution of bending moment along beam

from goaf edge within 60m This differs from traditionalmodels employing the assumption of rigid abutment in thatthemaximumbendingmoment occurs in the rib-sides ratherthan just above the goaf edge It highlights the benefit of thepresent model treating the coal seam abutment as an elasticfoundation The bending moment is greater than 139MNsdotmat a distance of 56 to 74m from the goaf edge yet it is lowerthan 139MN elsewhere as shown in Table 3 It can thereforebe concluded that the break line in the main roof is located ata distance of 56 to 74m from the goaf edge

4 Model Parametric Study

41 Effect of Foundation Rigidity The effect of foundationrigidity on the bending moment distribution along mainroof is shown in Figure 5 Figure 6 shows the magnitudeand location of the maximum bending moment for differentfoundation rigidities As the foundation rigidity increasesfrom 0025GPa to 1 GPa the maximum bending momentdecreases linearly from 1536MNsdotm to 1186MNsdotm the loca-tion of the maximum bending moment moves from 103m


Table 3 Variation of bending moment and deflection along the beam

119909119898 0 1 2 3 4 5 6 7 8 10 12 15 20 25 30 40 50Bending moment (MNsdotm) 107 117 124 130 134 137 139 139 138 135 128 115 89 63 40 98 33

0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)

K = 0025 GPaK = 005 GPaK = 01 GPa

K = 02GPaK = 05 GPaK = 1 GPa

Figure 5 Bending moment distribution along the main roof fordifferent foundation rigidities

103

82

66

53

37

24

1536

1437

1357

1294

12271186

LocationBending moment

1

2

3

4

5

6

7

8

9

10

11

x (m

)

005 01 02 05 10025Foundation rigidity

110

120

130

140

150

160

Bend

ing

mom

ent (

MNmiddotm

)

Figure 6 Relationship between bending moment and foundationrigidity

from the goaf edge to 24m from itThese results suggest thatthe foundation rigidity has a pronounced effect on the beambending moment distribution

According to (4) the modulus of foundation rigidity isseriously affected by the mechanical properties and thicknessof the coal seam Hence the break line in the main roof canbe greatly influenced by the foundation rigidity that is therigidity of the coal seam which is of great significance indetermination of the location of EDG

0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)10 20 30 40 50 600

x (m)

ℎ = 4 mℎ = 6 mℎ = 8 m

ℎ = 10 mℎ = 12 m

Figure 7 Bending moment distribution along the main roof fordifferent coal seam thicknesses

67

75

83

92

101

1387

1425

1458

14881516

6 8 10 124Coal seam thickness

6

7

8

9

10

11

x (m

)

130

135

140

145

150

155

160

Bend

ing

mom

ent (

MNmiddotm

)


Figure 8 Relationship between bending moment and coal seamthickness

42 Effect of Coal Seam Thickness Figure 7 shows the effectof coal seam thickness on the bending moment distributionalong the main roof Figure 8 shows the magnitude andlocation of the maximum bending moment for different coalseam thickness As the coal seam thickness increases themaximum bending moment increases from 1387MNsdotm to1516MNsdotm the location of the maximum bending momentmoves from 67m to 101m These changes can be attributed


0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)

E = 5 GPaE = 10 GPaE = 15 GPa

E = 20 GPaE = 25 GPaE = 35GPa

Figure 9 Bending moment distribution along the main roof fordifferent Youngrsquos modulus of main roof

49

58

66

72

7984

1274

1331

1372

1404

14321454


4

5

6

7

8

9

x (m

)

10 15 20 25 305Youngrsquos modulus of main roof (GPa)

120

125

130

135

140

145

150

Bend

ing

mom

ent (

MNmiddotm

)

Figure 10 Relationship between bending moment and Youngrsquosmodulus of main roof

to the reduced foundation rigidity as coal seam thicknessincreases (see (4)) Similarly according to (4) the thicknessof the immediate roof or floor strata has the same effect onthe bending moment distribution along the main roof

43 Effect of Main Roof Flexural Rigidity The bendingmoment distribution along main roof for different roof rsquosYoungrsquos modulus is shown in Figure 9 The magnitudeand location of the maximum bending moment also varywith Youngrsquos modulus as illustrated in Figure 10 As theroof rsquos Youngrsquos modulus increases from 5GPa to 30GPa themaximum bending moment increases from 1274MNsdotm to1454MNsdotm and the location of maximum bending moment

10 20 30 40 50 600x (m)

L= 4 mL= 8 mL= 10m

L= 12 mL= 16 mL= 20 m

0

50

100

150

200

250

300

350

400

Bend

ing

mom

ent (

MNmiddotm

)Figure 11 Bending moment distribution along the main roof withdifferent cantilever roof lengths

123

9684

7

63

55226

587

1099

1768

2607

3605

5

6

7

8

9

10

11

12

13


x (m

)

0

100

200

300

400

Bend

ing

mom

ent (

MNmiddotm

)

8 12 16 20 244L (m)


moves from49m to 84mThe results suggest that a variationin main roof rigidity has a significant effect on the break linein the main roof and thereby explains the high side abutmentpressure concentration region over 60m deep into the goafedge on the conditions that the main roof is with thick andhard strata [21]

44 Effect of Cantilever Roof Length The bending momentalong the main roof is directly influenced by the length ofthe cantilever roof Figure 11 shows the bending momentdistribution along the main roof for different cantileverroof lengths As can be seen significant bending momentprofile difference along roof beam can be noticed with asmall increase of cantilever roof length Figure 12 shows


Camera

Borehole case

Sleeve

Camera position recorder Host

Display screenDateline

(a) (b)

Figure 13 Schematic of theYSZ(B) panoramic borehole camera system (a)Digital panoramic borehole camera system composed of a camerasleeve a camera position recorder dateline and a host (b) Test equipment

Borehole 7Borehole 6


Pillar

Immediate roof

Main roof

Goaf

Borehole 3

Borehole 2

Borehole 1

Borehole 8

Borehole 9

Number 20103 coal face

Fracture line

Annular fracturesVertical fractures

Developed annular fracturesDeveloped vertical fractures

(a)



5800

9100

68495454

8000

Borehole 7

65 ∘

(b)

Figure 14 Detected roof fracture zones (a) detected roof fracture zones and (b) determination of fracture line location

the relationship between maximum bending moment andcantilever roof length As cantilever length increases from4 to 24m the maximum bending moment increases from226MNsdotm to 3605MNsdotm while the location of maximumbending moment moves from 123m to 55m As expectedthe length of cantilever roof plays an important role in thebroken behaviour of the main roof

5 Field Tests and Discussion

51 Borehole Camera Detection To validate the analyticalmodel borehole camera detectionwas employed to detect thebreak line in the main roof As shown in Figure 13 YSZ(B)panoramic borehole camera system consists of a camerasleeves data lines a camera position recorder and a host

The corresponding borehole with which it works is 28mm indiameter During observation the video or image down theborehole can be recorded and transmitted to the host in realtime And then we can acquire the break line in themain roofby observing the crack propagation in rock masses

52 Analysis of Borehole Camera Detection Data A sectionalong number 20103 headgate and 500m from the set-uproom was selected as a test area to assess the break line inthe main roof as shown in Figure 3 The arrangement ofboreholes and the distribution of fractures along borehole areillustrated in Figure 14

As shown from the images of borehole 2 annularfractures were well developed at a depth of 0 to 15mdown the borehole rock was almost intact at a depth of


15 to 20m with some tiny annular or vertical fractures Inthe depth of 25m and beyond the rock mass was intact Forborehole 4 annular fractures were developed at a depth of0 to 12m Only some tiny vertical fractures were observedat a depth of 12 to 20m At 20m and beyond the rock wasintact For borehole 7 the fracture densities in the boreholeincreased compared with boreholes 2 and 4 Both annularand vertical fractures were observed in the region of 0 to30m down the borehole At a depth of 30 to 49m thefractures densities decreased slightly At 49m and beyondvertical fractures becamewell developed even throughout theborehole resulting in serious damage and collapse at a depthof 72 to 89mThe rock remained intact beyond 10m As seenin borehole 8 annular fractures and tiny vertical fractureswere observed at a depth of 0 to 38m along the boreholeVertical fractures were well developed at a depth of 44 to76m No fractures were observed beyond a depth of 76m

Based on the above analysis fractures in rock massescan be classified into four types namely annular verticaldeveloped annular and developed vertical fractures Thefollowing therefore can be concluded

(1) The damaged zone in boreholes 1 to 6 was about12 to 25m while the damaged zone in boreholes 7 to8 developed to the main roof strata In addition theasymmetric deformation was also observed in situ severesqueezing failure and step convergence occurred at the roofof pillar side while the roof of solid coal side remained intactmainly This asymmetric failure was due to the asymmetricdistributed side abutment pressure along the roof beaminduced by main roof breakage

(2) The top-slice coal was severely damaged with devel-oped annular fractures and rock separation The reason wasthat the top-slice coal was with lower strength than siltstoneand sandy mudstone which was easily failed affected by thedynamic pressure exerted by the adjacent panel mining andheadgate development

(3) Compared with roof of solid coal side vertical frac-tures were well developed in the deep of main roof above thecoal pillarThese highly developed vertical fractures indicatedthat the break line inmain roof was more likely located abovethe coal pillarThat is because rock mass is a weaker materialwith low tensile strength numerous vertical and subverticalfractures developed in rock masses during the process ofmain roof breakage

(4) The images of borehole 7 revealed that the verticalfractures developed throughout the borehole and formed acrushed zone at a depth of 58 to 91m down the boreholeas shown in Figure 14(a) According to the length andinclination angle of borehole 7 it can then be deduced thatthe crushed zone was at a distance of 5454 to 6847m fromthe goaf edge in other words the break line in the mainroof is 55 to 68m away from the goaf edge as presented inFigure 14(b)

Based on the analysis above the break line in the mainroof detected in situ is in good agreement with the analyt-ical model which implies that the model is capable of anassessment of the break line in the lateral main roof Theresearch provides a simple and reliable analytical method toestimate the break line in the lateral main roof which will be

significant when designing the pillar width for a safe stableEDG condition

6 Conclusion

Accurately acquiring the break line in main roof is of greatimportance in pillar width design and EDG maintenanceIn this research the break line was acquired through anintegrated method combining theoretical analysis and fieldtests By comparison with previous studies this work con-tained the following original aspects (1) The spatial modelwhich treated the lateral main roof as a beam supported bya Winkler foundation and subjected to nonuniform loadingwas proposedThebreak line in themain roof can be obtainedby calculating the maximum bending moment along the roofbeam (2) The break line in the main roof was influenced bythe foundation rigidity Youngrsquosmodulus of themain roof andcoal seams and the length of the cantilever roof (3) Manyvertical and subvertical fractures sharply developed in rockmasses during the process of main roof breakage Thus thebreak line in the main roof can be detected by observing thefractures distribution in the roof strata

Field tests conducted in number 20103 headgateWangjialing coalmine Shanxi Province demonstrated thatthe break line in the main roof detected in situ was in goodagreement with the analytical analysis which verified thevalidity of the analytical model

It should be noted that the side abutment pressure wassimplified to a triangular distribution and the peak sideabutment pressure was located at the goaf edge Furtherresearch was deemed necessary to perfect the distribution ofside abutment stress to improve the model In addition morefield tests should be conducted to validate the model

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by National Natural Science Foun-dation of China under Grant 51574243 and the FundamentalResearch Funds for the Central Universities under Grant2010YZ02

References

[1] S Yan J Bai X Wang and L Huo ldquoAn innovative approachfor gateroad layout in highly gassy longwall top coal cavingrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 59 pp 33ndash41 2013

[2] W Li J Bai S Peng X Wang and Y Xu ldquoNumerical modelingfor yield pillar design a case studyrdquo Rock Mechanics and RockEngineering vol 48 no 1 pp 305ndash318 2015

[3] H Yavuz ldquoAn estimation method for cover pressure re-estab-lishment distance and pressure distribution in the goaf oflongwall coal minesrdquo International Journal of Rock Mechanicsand Mining Sciences vol 41 no 2 pp 193ndash205 2004


[4] S Peng Coal Mine Ground Control Department of MiningEngineeringCollege of Engineering and Mineral ResourcesMorgantown WVa USA 2008

[5] B Smart and D Davies ldquoApplication of the rock-strata-titleapproach to the pack design in an arch-sharped roadwayrdquoMinerals Engineering vol 144 no 9 pp 91ndash178 1982

[6] J J Shi N J Ma and Z S Bai ldquoAnalysis on roof broken locationof gateway retained along goaf and technology of roof supportrdquoCoal Science and Technology vol 41 no 7 pp 35ndash42 2013

[7] N Zhang L Yuan C Han J Xue and J Kan ldquoStability anddeformation of surrounding rock in pillarless gob-side entryretainingrdquo Safety Science vol 50 no 4 pp 593ndash599 2012

[8] G J Zhao and M G Qian ldquoThe behaviour of the main rooffracture in longwall mining and its effect on roof pressurerdquo inProceedings of the 28th US Symposium on Rock Mechanics pp1ndash8 Tucson Ariz USA June-July 1987

[9] D Wang S Li Q Wang et al ldquoExperimental study of reason-able coal pillar width in fully mechanized top coal caving faceof deep thick coal seamrdquo Chinese Journal of RockMechanics andEngineering vol 33 no 3 pp 539ndash548 2014

[10] J H Liu F X Jiang N G Wang Z S Li and Z G ZhangldquoResearch on reasonable width of segment pillar of fullymechanized caving face in extra-thick coal seam of deep shaftrdquoChinese Journal of Rock Mechanics and Engineering vol 31 no5 pp 921ndash927 2012

[11] Y Zhang Z-J Wan F-C Li et al ldquoLarge deformation mech-anism of roadway driving along goaf under unstable overlyingrock stratardquo Journal of Mining and Safety Engineering vol 29no 4 pp 451ndash458 2012

[12] M G Qian and P W Shi Mining Pressure and Strata ControlChina University of Mining and Technology Press XuzhouChina 2003

[13] J Bai Surrounding Rock Control of Gob-Side Entry DrivingChina University of Mining and Technology Press XuzhouChina 2006

[14] J Q Jiang Surrounding Rock Stress and Movement in StopeChina Coal Industry Publishing House Beijing China 1993

[15] X Li N Ma Y Zhong and Q Gao ldquoStorage and release regularof elastic energy distribution in tight roof fracturingrdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 1 pp2786ndash2793 2007

[16] L Jiang H S Mitri N Ma and X Zhao ldquoEffect of foundationrigidity on stratified roadway roof stability in underground coalminesrdquo Arabian Journal of Geosciences vol 9 no 1 pp 1ndash122016

[17] E Winkler Die Lehre yon der Elastizitat und Festigkeit HDominicus Prague Czech Republic 1867

[18] M Hetenyi Beams on Elastic Foundation Theory with Appli-cations in the Fields of Civil and Mechanical Engineering TheUniversity of Michigan Press Ann Arbor Mich USA 1971

[19] S Timoshenko Mechanics of Materials Science Press BeijingChina 1979

[20] G C Zhang and F L He ldquoAsymmetric failure mechanism andcontrol countermeasures of large cross-section gob-side entryroof with fully-mechanized caving miningrdquo Chinese Journal ofRock Mechanics and Engineering vol 35 pp 806ndash817 2016

[21] B Yu C Y Liu and L J Rong ldquoMechanism and control tech-nology of pressure occurrence in roadway with extra thicknessand mechanized caving coal seam in Datong mining areardquoChinese Journal of Rock Mechanics and Engineering vol 33 pp1863ndash1872 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Strata CStrata A

II

Strata B

Panel 1Panel 2

EDG

Set-up room

Advancing direction

(a) Arc-triangle section of the lateral main roof after breakage

Strata A

Strata CStrata B

EDG Pillar Coal

Goaf

(b) The lateral hinged structure over the EDG (section I-I in Figure 1(a))

Figure 1 Schematic arc-top structure above GDE

usually several metres away from the goaf edge For exampleZhang et al performed physical experiments in which thelateral main roof broke at a distance of 3 to 8m from thegoaf edge and the break line moved closer to the goaf edgewith immediate roof thickness decreasing [7] Zhao andQianestablished an elastic foundation beam model which treatedthe lateral main roof as an elastic beam resting on a Winklermedium [8] Some results from their study demonstrated thatthe break line in the main roof lies in the rib-sides and varieswith respect to the foundation rigidity Unfortunately thecover stress and side abutment pressure induced by adjacentpanel mining were neglected in their model

In addition some scholars attempt to detect the breakline in the lateral main roof by field studies For instanceWang et al applied borehole stress meters to monitor thestress distribution in the rib-sides and got distributions ofside abutment pressure [9] Liu et al presented experimentalstudies of strata movement above the goaf edge by seismicmeasurement techniques [10] During the breakage processof the main roof numerous vertical and subvertical fracturesand horizontal cracks are sharply developed in the rock massneighbouring the break line [4] According to these char-acteristics Zhang et al presented an experimental researchinto the break line in the main roof by observing fracturesevolution in a 10m long borehole drilled on the GDE roof[11] The results suggested that compared to other moni-toring methods borehole camera detection was an effectivestraightforwardmethod to estimate the break line in themainroof

In this paper considering the deformation characteristicsof coal seam a simple analytical model was established todeduce the break line in the lateral main roof Taking the caseof panel 20105 Wangjialing coal mine China as an examplethe influencing factors were investigated by a parametricstudy such as Youngrsquos modulus coal seam thickness andfoundation rigidity The analytical solution was obtained andcompared to a field study using borehole camera detectiontechniques for validation

2 Mechanical Analysis

In longwall mining when the work face advances a certaindistance the immediate roof collapses at first then themain roof begins to bend and sag causing crack generationand propagation in roof strata once cracks coalesce intolarge fractures the main roofs are broken into blocks Thebroken strata hinge with adjacent strata and thus form anarticulated structure above the coal face [12] Meanwhileperpendicular to the retreat direction of the work facethe lateral main roof shaped like arc-triangle section willbe formed at the end of the mining panel as shown inFigure 1(a) According to Bai [13] the lateral main roofwill break in the rib-sides and then a lateral articulatedstructure is formed by broken strata A B and C as illus-trated in Figure 1(b) Investigations show that the structuralcharacteristics of the lateral main roof especially the breakline thereof will greatly affect the stress distribution in therib-sides

The section of lateral main roof before breakage is illus-trated in Figure 2(a) where 119871 is the length of the cantileverroof strata above the goaf and 119887 is the extent of affectedzone by side abutment pressure which is about 40 to 60mConsidering the fact that coal seams and their surroundingrock strata are relatively soft and weak compared to roofstrata they are considered to meet Winkler foundationassumptions [8 14ndash16] According to the available literature[15] the characteristic length of main roof is about 32 to63m while the distribution area of side abutment pressureis about 40 to 60m wide which is about 5 to 20 times thecharacteristic length Hence the main roof above the rib-sides can be assumed to be a semi-infinite long beam onthe Winkler foundation and the main roof above the goafis simplified to a cantilever supported by broken strata Cas shown in Figure 2(b) In Figure 2(b) 1198720 1198760 and 119873are the bending moment and shear and horizontal forceacting at point 119909 = 0 1198731015840 and 1198761015840 are the horizontal andshear force exerted by strata C which act on the rear end of



Goaf

Lb


L

y

x b

Winkler foundation

N

q0

q1

M0M0

Q0Q0

qc

N998400

Q998400




119902 (119909) = 1199020 + 119887 minus 119909119887 1199021 (1)





119875 = minus119870119910 (3)



1119870 = 119898sum

1

1119870119898

119870119898 = 119864119898(1 minus 1199062119898) ℎ119898 (4)


11986411986811988941199101198891199094 + 11987311988921199101198891199092 = 119902 (119909) + 119901 (5)


11988941199101198891199094 + 119904

11988921199101198891199092 + 1199032119910 =

119902 (119909)119864119868 (6)


119884 (119909) = 119890minus120572119909 (119860 cos120573119909 + 119861 sin120573119909) (7)


119884lowast (119909) = 119902 (119909)1198641198681205742 (8)


119910 (119909) = 119890minus120572119909 (119860 cos120573119909 + 119861 sin120573119909) + 119902 (119909)1198641198681205742 (9)



1198720 = 119864119868119910101584010158400

1198760 = 1198641198681199101015840101584010158400 + 11987311991010158400(10)





119872 = 11986411986811991010158401015840 = 119890minus120572119909 1198720 cos120573119909

+ [120572 (120574 + 119904)1198720 + 1205741198760(120574 minus 119904) 120573 + 1199021119904119887119903 (119903 minus 119904) 120573] sin120573119909 (12)




(13)


1198760 = 119902119888119871 + 11987610158401198720 = 1

21199021198881198712 + 1198761015840119871 + 1198731015840 (ℎ2 + Δ1199041)

119873 = 11987111987610158402 (ℎ minus Δ119904)

1198761015840 = 119871120574ℎ

(14)


3 Case Study







Table1Generalise

dstratig

raph

yandkeygeotechn

icalparameters

Stratum

number

Geological

legend

Rock

type

Rock

thickn

ess(m)

Density(kgm3)Yo

ungrsquos

mod

ulus

(GPa)Po

issonrsquosratio

UCS

(MPa)Coh

esion(M

Pa)Frictio

nangle(∘)

Maxim

umMinim

umAv

erage

1Fine

sand

stone

49

622

56

2700

2773

022

1653

116

4164

2Mud

stone

149

212

182140

685

024

446

26

32

3Fine

sand

stone

02

152

09

2700

2773

022

1653

116

4164

4Mud

stone

09

158

132140

685

024

446

26

32

5Medium

sand

stone

189

256

23

2675

2814

021

1462

109

4764

6Gritsto

ne14

22

172730

3266

024

1624

124

4823

7Coalseam

09

1210

1412

206

036

1389

23

4434

8Mud

stone

21

32

23

2140

685

024

446

26

32

9Siltstone

89

126

922680

3073

022

1423

943942

10Sand

ymud

stone

166

23

20

2659

1158

027

6328

89

4739

11Coalseam

2596

66

62

1412

206

036

1389

23

4434

12Mud

stone

1418

162140

685

024

446

26

32

13Siltstone

59

7768

2680

3073

022

1423

943942



Advancing direction




Mai

ns

Test area

Stop

line

Stop

line

500

550

NSe

t-up

room


61 ang60 ∘H

= 15m

32 ang60∘ H = 25 m27 ang50∘

H = 15 m


570












Breakage

0

20

40

60

80

100

120

140Be

ndin

g m

omen

t (M

Nmiddotm

)

0 10 20x (m)

30 40 50 60








0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)

K = 0025 GPaK = 005 GPaK = 01 GPa



103

82

66

53

37

24

1536

1437

1357

1294

12271186


1

2

3

4

5

6

7

8

9

10

11

x (m

)


110

120

130

140

150

160

Bend

ing

mom

ent (

MNmiddotm

)




0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)10 20 30 40 50 600

x (m)

ℎ = 4 mℎ = 6 mℎ = 8 m

ℎ = 10 mℎ = 12 m


67

75

83

92

101

1387

1425

1458

14881516


6

7

8

9

10

11

x (m

)

130

135

140

145

150

155

160

Bend

ing

mom

ent (

MNmiddotm

)





0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)




49

58

66

72

7984

1274

1331

1372

1404

14321454


4

5

6

7

8

9

x (m

)


120

125

130

135

140

145

150

Bend

ing

mom

ent (

MNmiddotm

)




10 20 30 40 50 600x (m)

L= 4 mL= 8 mL= 10m

L= 12 mL= 16 mL= 20 m

0

50

100

150

200

250

300

350

400

Bend

ing

mom

ent (

MNmiddotm


123

9684

7

63

55226

587

1099

1768

2607

3605

5

6

7

8

9

10

11

12

13


x (m

)

0

100

200

300

400

Bend

ing

mom

ent (

MNmiddotm

)

8 12 16 20 244L (m)





Camera

Borehole case

Sleeve



(a) (b)




Pillar

Immediate roof

Main roof

Goaf

Borehole 3

Borehole 2

Borehole 1

Borehole 8

Borehole 9


Fracture line



(a)



5800

9100

68495454

8000

Borehole 7

65 ∘

(b)

















6 Conclusion




Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Goaf

Lb


L

y

x b

Winkler foundation

N

q0

q1

M0M0

Q0Q0

qc

N998400

Q998400




119902 (119909) = 1199020 + 119887 minus 119909119887 1199021 (1)





119875 = minus119870119910 (3)



1119870 = 119898sum

1

1119870119898

119870119898 = 119864119898(1 minus 1199062119898) ℎ119898 (4)


11986411986811988941199101198891199094 + 11987311988921199101198891199092 = 119902 (119909) + 119901 (5)


11988941199101198891199094 + 119904

11988921199101198891199092 + 1199032119910 =

119902 (119909)119864119868 (6)


119884 (119909) = 119890minus120572119909 (119860 cos120573119909 + 119861 sin120573119909) (7)


119884lowast (119909) = 119902 (119909)1198641198681205742 (8)


119910 (119909) = 119890minus120572119909 (119860 cos120573119909 + 119861 sin120573119909) + 119902 (119909)1198641198681205742 (9)



1198720 = 119864119868119910101584010158400

1198760 = 1198641198681199101015840101584010158400 + 11987311991010158400(10)





119872 = 11986411986811991010158401015840 = 119890minus120572119909 1198720 cos120573119909

+ [120572 (120574 + 119904)1198720 + 1205741198760(120574 minus 119904) 120573 + 1199021119904119887119903 (119903 minus 119904) 120573] sin120573119909 (12)




(13)


1198760 = 119902119888119871 + 11987610158401198720 = 1

21199021198881198712 + 1198761015840119871 + 1198731015840 (ℎ2 + Δ1199041)

119873 = 11987111987610158402 (ℎ minus Δ119904)

1198761015840 = 119871120574ℎ

(14)


3 Case Study







Table1Generalise

dstratig

raph

yandkeygeotechn

icalparameters

Stratum

number

Geological

legend

Rock

type

Rock

thickn

ess(m)

Density(kgm3)Yo

ungrsquos

mod

ulus

(GPa)Po

issonrsquosratio

UCS

(MPa)Coh

esion(M

Pa)Frictio

nangle(∘)

Maxim

umMinim

umAv

erage

1Fine

sand

stone

49

622

56

2700

2773

022

1653

116

4164

2Mud

stone

149

212

182140

685

024

446

26

32

3Fine

sand

stone

02

152

09

2700

2773

022

1653

116

4164

4Mud

stone

09

158

132140

685

024

446

26

32

5Medium

sand

stone

189

256

23

2675

2814

021

1462

109

4764

6Gritsto

ne14

22

172730

3266

024

1624

124

4823

7Coalseam

09

1210

1412

206

036

1389

23

4434

8Mud

stone

21

32

23

2140

685

024

446

26

32

9Siltstone

89

126

922680

3073

022

1423

943942

10Sand

ymud

stone

166

23

20

2659

1158

027

6328

89

4739

11Coalseam

2596

66

62

1412

206

036

1389

23

4434

12Mud

stone

1418

162140

685

024

446

26

32

13Siltstone

59

7768

2680

3073

022

1423

943942



Advancing direction




Mai

ns

Test area

Stop

line

Stop

line

500

550

NSe

t-up

room


61 ang60 ∘H

= 15m

32 ang60∘ H = 25 m27 ang50∘

H = 15 m


570












Breakage

0

20

40

60

80

100

120

140Be

ndin

g m

omen

t (M

Nmiddotm

)

0 10 20x (m)

30 40 50 60








0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)

K = 0025 GPaK = 005 GPaK = 01 GPa



103

82

66

53

37

24

1536

1437

1357

1294

12271186


1

2

3

4

5

6

7

8

9

10

11

x (m

)


110

120

130

140

150

160

Bend

ing

mom

ent (

MNmiddotm

)




0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)10 20 30 40 50 600

x (m)

ℎ = 4 mℎ = 6 mℎ = 8 m

ℎ = 10 mℎ = 12 m


67

75

83

92

101

1387

1425

1458

14881516


6

7

8

9

10

11

x (m

)

130

135

140

145

150

155

160

Bend

ing

mom

ent (

MNmiddotm

)





0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)




49

58

66

72

7984

1274

1331

1372

1404

14321454


4

5

6

7

8

9

x (m

)


120

125

130

135

140

145

150

Bend

ing

mom

ent (

MNmiddotm

)




10 20 30 40 50 600x (m)

L= 4 mL= 8 mL= 10m

L= 12 mL= 16 mL= 20 m

0

50

100

150

200

250

300

350

400

Bend

ing

mom

ent (

MNmiddotm


123

9684

7

63

55226

587

1099

1768

2607

3605

5

6

7

8

9

10

11

12

13


x (m

)

0

100

200

300

400

Bend

ing

mom

ent (

MNmiddotm

)

8 12 16 20 244L (m)





Camera

Borehole case

Sleeve



(a) (b)




Pillar

Immediate roof

Main roof

Goaf

Borehole 3

Borehole 2

Borehole 1

Borehole 8

Borehole 9


Fracture line



(a)



5800

9100

68495454

8000

Borehole 7

65 ∘

(b)

















6 Conclusion




Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1198720 = 119864119868119910101584010158400

1198760 = 1198641198681199101015840101584010158400 + 11987311991010158400(10)





119872 = 11986411986811991010158401015840 = 119890minus120572119909 1198720 cos120573119909

+ [120572 (120574 + 119904)1198720 + 1205741198760(120574 minus 119904) 120573 + 1199021119904119887119903 (119903 minus 119904) 120573] sin120573119909 (12)




(13)


1198760 = 119902119888119871 + 11987610158401198720 = 1

21199021198881198712 + 1198761015840119871 + 1198731015840 (ℎ2 + Δ1199041)

119873 = 11987111987610158402 (ℎ minus Δ119904)

1198761015840 = 119871120574ℎ

(14)


3 Case Study







Table1Generalise

dstratig

raph

yandkeygeotechn

icalparameters

Stratum

number

Geological

legend

Rock

type

Rock

thickn

ess(m)

Density(kgm3)Yo

ungrsquos

mod

ulus

(GPa)Po

issonrsquosratio

UCS

(MPa)Coh

esion(M

Pa)Frictio

nangle(∘)

Maxim

umMinim

umAv

erage

1Fine

sand

stone

49

622

56

2700

2773

022

1653

116

4164

2Mud

stone

149

212

182140

685

024

446

26

32

3Fine

sand

stone

02

152

09

2700

2773

022

1653

116

4164

4Mud

stone

09

158

132140

685

024

446

26

32

5Medium

sand

stone

189

256

23

2675

2814

021

1462

109

4764

6Gritsto

ne14

22

172730

3266

024

1624

124

4823

7Coalseam

09

1210

1412

206

036

1389

23

4434

8Mud

stone

21

32

23

2140

685

024

446

26

32

9Siltstone

89

126

922680

3073

022

1423

943942

10Sand

ymud

stone

166

23

20

2659

1158

027

6328

89

4739

11Coalseam

2596

66

62

1412

206

036

1389

23

4434

12Mud

stone

1418

162140

685

024

446

26

32

13Siltstone

59

7768

2680

3073

022

1423

943942



Advancing direction




Mai

ns

Test area

Stop

line

Stop

line

500

550

NSe

t-up

room


61 ang60 ∘H

= 15m

32 ang60∘ H = 25 m27 ang50∘

H = 15 m


570












Breakage

0

20

40

60

80

100

120

140Be

ndin

g m

omen

t (M

Nmiddotm

)

0 10 20x (m)

30 40 50 60








0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)

K = 0025 GPaK = 005 GPaK = 01 GPa



103

82

66

53

37

24

1536

1437

1357

1294

12271186


1

2

3

4

5

6

7

8

9

10

11

x (m

)


110

120

130

140

150

160

Bend

ing

mom

ent (

MNmiddotm

)




0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)10 20 30 40 50 600

x (m)

ℎ = 4 mℎ = 6 mℎ = 8 m

ℎ = 10 mℎ = 12 m


67

75

83

92

101

1387

1425

1458

14881516


6

7

8

9

10

11

x (m

)

130

135

140

145

150

155

160

Bend

ing

mom

ent (

MNmiddotm

)





0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)




49

58

66

72

7984

1274

1331

1372

1404

14321454


4

5

6

7

8

9

x (m

)


120

125

130

135

140

145

150

Bend

ing

mom

ent (

MNmiddotm

)




10 20 30 40 50 600x (m)

L= 4 mL= 8 mL= 10m

L= 12 mL= 16 mL= 20 m

0

50

100

150

200

250

300

350

400

Bend

ing

mom

ent (

MNmiddotm


123

9684

7

63

55226

587

1099

1768

2607

3605

5

6

7

8

9

10

11

12

13


x (m

)

0

100

200

300

400

Bend

ing

mom

ent (

MNmiddotm

)

8 12 16 20 244L (m)





Camera

Borehole case

Sleeve



(a) (b)




Pillar

Immediate roof

Main roof

Goaf

Borehole 3

Borehole 2

Borehole 1

Borehole 8

Borehole 9


Fracture line



(a)



5800

9100

68495454

8000

Borehole 7

65 ∘

(b)

















6 Conclusion




Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table1Generalise

dstratig

raph

yandkeygeotechn

icalparameters

Stratum

number

Geological

legend

Rock

type

Rock

thickn

ess(m)

Density(kgm3)Yo

ungrsquos

mod

ulus

(GPa)Po

issonrsquosratio

UCS

(MPa)Coh

esion(M

Pa)Frictio

nangle(∘)

Maxim

umMinim

umAv

erage

1Fine

sand

stone

49

622

56

2700

2773

022

1653

116

4164

2Mud

stone

149

212

182140

685

024

446

26

32

3Fine

sand

stone

02

152

09

2700

2773

022

1653

116

4164

4Mud

stone

09

158

132140

685

024

446

26

32

5Medium

sand

stone

189

256

23

2675

2814

021

1462

109

4764

6Gritsto

ne14

22

172730

3266

024

1624

124

4823

7Coalseam

09

1210

1412

206

036

1389

23

4434

8Mud

stone

21

32

23

2140

685

024

446

26

32

9Siltstone

89

126

922680

3073

022

1423

943942

10Sand

ymud

stone

166

23

20

2659

1158

027

6328

89

4739

11Coalseam

2596

66

62

1412

206

036

1389

23

4434

12Mud

stone

1418

162140

685

024

446

26

32

13Siltstone

59

7768

2680

3073

022

1423

943942



Advancing direction




Mai

ns

Test area

Stop

line

Stop

line

500

550

NSe

t-up

room


61 ang60 ∘H

= 15m

32 ang60∘ H = 25 m27 ang50∘

H = 15 m


570












Breakage

0

20

40

60

80

100

120

140Be

ndin

g m

omen

t (M

Nmiddotm

)

0 10 20x (m)

30 40 50 60








0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)

K = 0025 GPaK = 005 GPaK = 01 GPa



103

82

66

53

37

24

1536

1437

1357

1294

12271186


1

2

3

4

5

6

7

8

9

10

11

x (m

)


110

120

130

140

150

160

Bend

ing

mom

ent (

MNmiddotm

)




0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)10 20 30 40 50 600

x (m)

ℎ = 4 mℎ = 6 mℎ = 8 m

ℎ = 10 mℎ = 12 m


67

75

83

92

101

1387

1425

1458

14881516


6

7

8

9

10

11

x (m

)

130

135

140

145

150

155

160

Bend

ing

mom

ent (

MNmiddotm

)





0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)




49

58

66

72

7984

1274

1331

1372

1404

14321454


4

5

6

7

8

9

x (m

)


120

125

130

135

140

145

150

Bend

ing

mom

ent (

MNmiddotm

)




10 20 30 40 50 600x (m)

L= 4 mL= 8 mL= 10m

L= 12 mL= 16 mL= 20 m

0

50

100

150

200

250

300

350

400

Bend

ing

mom

ent (

MNmiddotm


123

9684

7

63

55226

587

1099

1768

2607

3605

5

6

7

8

9

10

11

12

13


x (m

)

0

100

200

300

400

Bend

ing

mom

ent (

MNmiddotm

)

8 12 16 20 244L (m)





Camera

Borehole case

Sleeve



(a) (b)




Pillar

Immediate roof

Main roof

Goaf

Borehole 3

Borehole 2

Borehole 1

Borehole 8

Borehole 9


Fracture line



(a)



5800

9100

68495454

8000

Borehole 7

65 ∘

(b)

















6 Conclusion




Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Advancing direction




Mai

ns

Test area

Stop

line

Stop

line

500

550

NSe

t-up

room


61 ang60 ∘H

= 15m

32 ang60∘ H = 25 m27 ang50∘

H = 15 m


570












Breakage

0

20

40

60

80

100

120

140Be

ndin

g m

omen

t (M

Nmiddotm

)

0 10 20x (m)

30 40 50 60








0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)

K = 0025 GPaK = 005 GPaK = 01 GPa



103

82

66

53

37

24

1536

1437

1357

1294

12271186


1

2

3

4

5

6

7

8

9

10

11

x (m

)


110

120

130

140

150

160

Bend

ing

mom

ent (

MNmiddotm

)




0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)10 20 30 40 50 600

x (m)

ℎ = 4 mℎ = 6 mℎ = 8 m

ℎ = 10 mℎ = 12 m


67

75

83

92

101

1387

1425

1458

14881516


6

7

8

9

10

11

x (m

)

130

135

140

145

150

155

160

Bend

ing

mom

ent (

MNmiddotm

)





0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)




49

58

66

72

7984

1274

1331

1372

1404

14321454


4

5

6

7

8

9

x (m

)


120

125

130

135

140

145

150

Bend

ing

mom

ent (

MNmiddotm

)




10 20 30 40 50 600x (m)

L= 4 mL= 8 mL= 10m

L= 12 mL= 16 mL= 20 m

0

50

100

150

200

250

300

350

400

Bend

ing

mom

ent (

MNmiddotm


123

9684

7

63

55226

587

1099

1768

2607

3605

5

6

7

8

9

10

11

12

13


x (m

)

0

100

200

300

400

Bend

ing

mom

ent (

MNmiddotm

)

8 12 16 20 244L (m)





Camera

Borehole case

Sleeve



(a) (b)




Pillar

Immediate roof

Main roof

Goaf

Borehole 3

Borehole 2

Borehole 1

Borehole 8

Borehole 9


Fracture line



(a)



5800

9100

68495454

8000

Borehole 7

65 ∘

(b)

















6 Conclusion




Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)

K = 0025 GPaK = 005 GPaK = 01 GPa



103

82

66

53

37

24

1536

1437

1357

1294

12271186


1

2

3

4

5

6

7

8

9

10

11

x (m

)


110

120

130

140

150

160

Bend

ing

mom

ent (

MNmiddotm

)




0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)10 20 30 40 50 600

x (m)

ℎ = 4 mℎ = 6 mℎ = 8 m

ℎ = 10 mℎ = 12 m


67

75

83

92

101

1387

1425

1458

14881516


6

7

8

9

10

11

x (m

)

130

135

140

145

150

155

160

Bend

ing

mom

ent (

MNmiddotm

)





0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)




49

58

66

72

7984

1274

1331

1372

1404

14321454


4

5

6

7

8

9

x (m

)


120

125

130

135

140

145

150

Bend

ing

mom

ent (

MNmiddotm

)




10 20 30 40 50 600x (m)

L= 4 mL= 8 mL= 10m

L= 12 mL= 16 mL= 20 m

0

50

100

150

200

250

300

350

400

Bend

ing

mom

ent (

MNmiddotm


123

9684

7

63

55226

587

1099

1768

2607

3605

5

6

7

8

9

10

11

12

13


x (m

)

0

100

200

300

400

Bend

ing

mom

ent (

MNmiddotm

)

8 12 16 20 244L (m)





Camera

Borehole case

Sleeve



(a) (b)




Pillar

Immediate roof

Main roof

Goaf

Borehole 3

Borehole 2

Borehole 1

Borehole 8

Borehole 9


Fracture line



(a)



5800

9100

68495454

8000

Borehole 7

65 ∘

(b)

















6 Conclusion




Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

20

40

60

80

100

120

140

160

Bend

ing

mom

ent (

MNmiddotm

)

10 20 30 40 50 600x (m)




49

58

66

72

7984

1274

1331

1372

1404

14321454


4

5

6

7

8

9

x (m

)


120

125

130

135

140

145

150

Bend

ing

mom

ent (

MNmiddotm

)




10 20 30 40 50 600x (m)

L= 4 mL= 8 mL= 10m

L= 12 mL= 16 mL= 20 m

0

50

100

150

200

250

300

350

400

Bend

ing

mom

ent (

MNmiddotm


123

9684

7

63

55226

587

1099

1768

2607

3605

5

6

7

8

9

10

11

12

13


x (m

)

0

100

200

300

400

Bend

ing

mom

ent (

MNmiddotm

)

8 12 16 20 244L (m)





Camera

Borehole case

Sleeve



(a) (b)




Pillar

Immediate roof

Main roof

Goaf

Borehole 3

Borehole 2

Borehole 1

Borehole 8

Borehole 9


Fracture line



(a)



5800

9100

68495454

8000

Borehole 7

65 ∘

(b)

















6 Conclusion




Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Camera

Borehole case

Sleeve



(a) (b)




Pillar

Immediate roof

Main roof

Goaf

Borehole 3

Borehole 2

Borehole 1

Borehole 8

Borehole 9


Fracture line



(a)



5800

9100

68495454

8000

Borehole 7

65 ∘

(b)

















6 Conclusion




Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















6 Conclusion




Competing Interests


Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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