Research on Failure Mechanism and Strengthening of Broken

Research ArticleResearch on Failure Mechanism and Strengthening of BrokenRoadway Affected by Upper Coal Pillar

Fulian He12 Zheng Zheng 1 Hengzhong Zhu1 and Bo Yang1

1College of Resources amp Safety Engineering China University of Mining amp Technology (Beijing) Beijing 100083 China2Beijing Key Laboratory for Precise Mining of Intergrown Energy and ResourcesChina University of Mining amp Technology (Beijing) Beijing 100083 China

Correspondence should be addressed to Zheng Zheng 1422308269qqcom

Received 4 September 2018 Revised 3 January 2019 Accepted 24 January 2019 Published 1 April 2019

Academic Editor Hugo Rodrigues

Copyright copy 2019 Fulian He et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+e principal stress difference is introduced as a new evaluation index in order to better understand the failure mechanism ofroadways affected by upper coal pillars and characterize failure of rock mass Compared with traditional methods it facilitatesquantitative analysis Moreover we combine the semiplane theory and we obtain the stress distribution on the coal pillarrsquosbedrock and the strengthening control area from the ldquochange pointrdquo position along a 21m horizontal line +e influence ofmultiple stresses induced frommining on a roadway is analyzed It is found that rock failure is most likely while mining the 051606working face followed by mining the 051604 working face and the stress influence on the upper pillar has the lowest failureprobability In addition based on the asymmetry of the surrounding rock stress distribution this study proposes strengtheningcontrol technology of surrounding rock on the basis of a highly stressed bolting support and anchor cable adding to the steelladder beam steel mesh and shed supportrsquos protective function to the roadwayrsquos roof and ribs Finally through field observationsit is concluded that the roadway deformation is within the controllable range

1 Introduction

In recent years with the increasing use of energy Chinarsquosannual coal production has accounted for nearly half of theworldrsquos production [1ndash3] Moreover it brings a solid energyfoundation for national economic construction [4ndash6] InChina with the increase of mining intensity more and moreclose coal seams are being mined [7] In the close-up coalseam the upper coal seam will leave the coal pillar aftermining and the overlying stratum load will produce stressconcentration on these pillars which will directly affect theintegrity and strength of the lower coal roof [8] Especiallywhen the roadway in lower coal crosses the pillar of theupper coal seam in space it greatly increases the difficulty ofsupporting in the lower coal seam roadway If the supple-ment support parameters cannot be reasonably selected it islikely to lead to large-scale roof caving in this roadway

Experts and scholars have done a lot of research on thecharacteristics of strata behavior in the close distance seammining Lu et al [9 10] explained the quantitative relationship

between Z and X +e vertical distance between the roadwayand the upper coal seam is Z And the horizontal distancebetween the roadway and the edge of the upper coal pillar isXwhich provided the main basis for correctly selecting the Xvalue and the relative position relationship between theroadway and the upper coal seam mining space Guan and Li[11] calculated the distribution of stress displacement andfailure area of surrounding rock after coal mining obtainingthe limit load of floor rock mass and the empirical formula forcalculating the maximum failure depth of coal seam floorZhang and Zhang [12] in multi coal seam joint mining re-search determined the distance of outward alternate entriesas 12ndash14m by using FLAC3D numerical simulation softwareto simulate the change of stress and displacement in roof floorand two sides of roadway Wilson [13] analyzed the stabilityfactors of soft rock roadway and comprehensively discussedthe failure mechanism of soft rock under the influence of coalpillar width and working face mining Xu and Zhang [14]considered that themain cause of roadway failure in the lowercoal seam was the principal stress difference Li et al [15] set

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 8132817 13 pageshttpsdoiorg10115520198132817

the gob as strain hardeningmodel and the coal pillar as strain-softening model according to the actual mechanical charac-teristics of coal and rock mass +e accuracy of the numericalmodel is greatly improved Sui et al [16] proposed a newindex ldquoDividing Line Drdquo to define the overburden failure stateand using it to discuss the interactions of overburden damagezones in close-up coalbed mining Zhu [17] established themechanics model of breaking block structure of key seam andanalyzed the influence of breaking line position in upper coalseam roof on the structural stability in lower coal seam Anunderground engineering is generally a complex dynamicalsystem +e important work during mining is to control thedeformation of coal mine roadway and coal-face In essencethe mine deformations are the final result of the interaction ofsome disaster factors In 2000 Qiao [18 19] dealt with theconverse theorem of the Leau-Fatou petal theorem oncomplex dynamical systems and revealed an impressive rulewhich said that the geometrical properties of the unstable setcould impact the structural stability of dynamical systemsdirectly

Scholars have been exploring failure of surrounding rockand strata after close-up coal seam mining for a long timeGenerally the reasonable location of the working face androadway in lower coal is the primary focus of this researchHowever under the influence of boundary pillars in uppercoal seam areas there is relatively little research on theroadway crossing through this boundary pillar section in thelower coal seam Under these conditions the strengtheningcontrol area cannot be determined directly In additionusing vertical stress to characterize failure of surroundingrock in traditional research is inappropriate +ereforeaccording to the relative position of the Mohr circle andenvelope curve it is more scientific to use ldquoprincipal stressdifferencerdquo to quantify the integrity of the surrounding rock

2 Engineering Background

+e 051606 working face 265m average depth is located inthe 16 coal seam of the fifth mining area in the Ling Xin CoalMine Ningxia Province China +e eastern part is 560mapart from the fault the southern side is about 204m awayfrom the exploration line the western side and the 051604working face have 20m protective coal pillars and thedistance from the northern side to rail rise of the fifth miningarea is about 46m 15 coal seam exploited is about 21mabove the 051606 working face +erefore in the process ofdriving 051606 ventilation roadway it crosses throughsuccessively the 051504 goaf the 35m boundary pillar andW1415 goaf in space +e 20m protective coal pillar is leftbetween 051504 goaf and 051506 goaf as well as 051604 goafand 051606 working face Its space position is shown inFigure 1 16 coal seam is medium thick coal seam itsaverage thickness in the working face area is 502m and theroof is a harder silt and fine sandstone +e section of theroadway under the influence of the upper boundary pillarhas a stronger strata behavior +at is ldquospecial failure sec-tionrdquo in Figure 1 +rough field observation the roadwayrsquosroof of the most serious section had obvious step subsidencethe two shoulder angles were damaged seriously some bolt

pallets failed and part of anchor cable had the phenomenonof breaking +e othersrsquo roadway is placed on the undersideof the upper coal seam goaf which is basically in a low stressstate Its surrounding rock is relatively complete and cansatisfy pedestrians and transportation functions

3 Principal Stress Difference

31 StressTransferModel In order to analyze the influence ofstress on the upper coal pillar and goaf we use the semiplanetheory from elastic mechanics [20] to calculate the stress inthe coal and rockmass below At this time the boundary pillarforms the border between two adjacent mining areas As thetwo sides of the working face are pushed forward the roofbreaks in the form of ldquoO-Xrdquo [21] According to reliable dataobtained from numerous field experiments the goaf expe-riences the same stress as virgin rocks when it is about 012 to03 times of the buried depth from the edge of coal pillar [21]In other words the original rock stress begins to appear about35ndash90m into the goaf +e effect of stress is only analyzed60m into the goaf in this study +e mechanical model inFigure 2 can be used to describe this situation where X pointsvertically and Y points horizontally

In order to simplify the calculation without sacrificingaccuracy [22] rock in the upper seam floor is assumed to beaffected by the superposition of L1 L3 gobs and L2 boundarypillar where the total pressure from these three loads can becalculated at point M Under the influence of concentratedstress q1 by L1 gob stress at point M (r θ) in the bedrock isshown as follows [20]

σ1x 2q1cos3θ

rπ

σ1y 2q1 cos θ sin2θ

rπ

τ1xy 2q1cos2θ sin θ

rπ

(1)

In this formula σ1x σ1x and τ1xy are the vertical hori-zontal and shear stress components at M under the influ-ence of L1 gob respectively and q1 is the uniform load valuein L1 gob A small length dη is selected at the coordinate η onthe x-axis (0le xle L1) and its uniform load is q(η) λ0cH+erefore the vertical and horizontal distances between M(x y) and η are x and (yminus η) respectively +e differentialstress dη at M is defined as follows

dσ1x minus2λ0cH dη

πx3

x2 +(yminus η)21113960 11139612

dσ1y minus2λ0cH dη

πx(yminus η)2

x2 +(yminus η)21113960 11139612

dτ1xy minus2λ0cH dη

πx2(yminus η)

x2 +(yminus η)21113960 11139612

(2)

where λ0 is the L1 gob stress concentration factor cH is theinitial crustal stress of 15 coal seam and x and y are the

2 Advances in Civil Engineering

coordinates of M +e stress produced by L1 gob at M isdefined as follows

σ1x minus2λ0cH

π1113946

L1

0

x3

x2 +(yminus η)21113960 11139612 dη

σ1y minus2λ0cH

π1113946

L1

0

x(yminus η)2

x2 +(yminus η)21113960 11139612 dη

τ1xy minus2λ0cH

π1113946

L1

0

x2(yminus η)

x2 +(yminus η)21113960 11139612 dη

(3)

where L1 is the gob length in the mechanics model As wecan see the stress from L1 gob at M can be obtainedSimilarly the stress of the L2 boundary pillar and L3 goaf atM can be calculated

32 Principal Stress Difference Analysis +e traditionalsemiplane theory is usually used to calculate the verticalhorizontal and shear stresses but it is obviously difficult to

analyze the stress on coal and rock mass using three in-dependent stress components due to the complicated con-ditions and stress transfer characteristics Based on Mohrrsquoscircle [23] it is proposed that the dilatancy deformation ofcoal and rock mass be analyzed using the principal stressdifference (σ1 minus σ3) In Figure 3 it is assumed that the stresscomponents of the block element are (σx minus τxy) and(σy minus τxy) which satisfy

p σx + σy1113872 11138732

r

σx minus σy1113872 111387321113960 11139612

+ τ2xy

1113970

σ1 p + r

σ3 pminus r

σ1 minus σ3( 1113857k 2r 2

σkx minus σk

y1113872 111387321113960 11139612

+ τkxy1113872 1113873

21113970

(4)

where p is the average stress r is the radius of this circle σ1and σ3 are the maximum and minimum principal stressesrespectively σ1 minus σ3 is the principal stress difference andindex k refers to segments 1 2 and 3

+e shear strength of rock mass (τ) does not depend onσ2 when the cohesion (c) and internal friction angle (φ) aregiven Moreover the principal stress difference (σ1 minus σ3)determines whether equilibrium is reached In other wordsσ3 is smaller when σ1 is constant thus the probability offailure is larger When σ3 is constant the rock mass is morelikely to fail if σ1 is larger +erefore the principal stressdifference can be used to directly determine rock massfailure +is is directly incorporated into the stress transfermodel which overcomes the deficiency that the traditionalmodel cannot be used to quantitatively analyze pressureMoreover it is more intuitive in judging the stability of arock mass structure

According to the special conditions and stress charac-teristics in this coal seam the boundary pillar is set to 35mand the average buried depth of 15 coal seam is 244m thusthe crustal stress is about 6MPa Considering the stressdistribution after coal seam mining the stress concentration

Special failure section(passing through the upper

coal pillar)

051606working face

20mprotective pillar


35mboundary pillar

051606ventilation roadway

051604 goaf

051504 goafW1415 goaf

21m

laye

r spa

cing

051506 goaf

35mboundary pillar

Figure 1 +e relationship of space arrangement between the 051606 working face and the upper coal

L1

Pillar

λ1γH

λ0γH λ0γH

θ1θ2

δyτyx

δxτxy

M

L3 L2

0

x

y

Figure 2 Load transfer model of the boundary coal pillar

Advances in Civil Engineering 3

coefficient in the two-sided gobs and boundary pillar is 05and 14 respectively [22] MATLAB was used to solveequation (3) using superposition yielding the principalstress difference distribution shown in Figure 4 A moni-toring line is placed every 3m along the direction of 15 coalseam floor +e principal stress difference at different depthsin the bedrock is shown in Figure 5

Figures 4 and 5 show the following

(1) +e principal stress difference distribution in thefloor of 15 coal seam exhibits a fan-shaped diffu-sion+e principal stress difference is high at the twoends of the boundary pillar and stress graduallytransfers downward along these two points +estress gradually decreases and the diffusion rangeincreases as the buried depth increases Due topressure relief in the shallow rock mass of the gobfloor the principal stress difference increases grad-ually from 0MPa to its maximum value and themaximum value occurs at a depth of 20m +eprincipal stress difference subsequently decreases toa minimum value due to the influence of burieddepth

(2) +e depth curve at 0ndash18m exhibits two peaks wherethe peak positions are at each end of the boundarypillar As the buried depth increases the two peaksconverge into a single peak which begins to appearat the position of 16 coal roof (buried depth of21m) At this time the peak principal stress dif-ference value is 56MPa +e peak position appearsin the middle of the upper coal pillar +e maximumfailure plane will be at the peak position if the 051606roadway is excavated at this depth When the depthis greater than 21m the peak value decreases and thestability of the coal and rock mass is obviouslyimproved

(3) +ere are unique envelope curves at different depthswhich directly reflect the principal stress differencedistribution at the rock mass boundary in this areaIn other words the numerical value on this envelopecurve represents the maximum failure probability atthis location Obviously when the stress exceeds thisrange the rock mass will inevitably experience ex-tremely strong plastic deformation Due to stressdiffusion the high stress range at the position of 16

coal roof (buried depth of 21m) increases evidently+e curve corresponding to a burial depth of 21msuddenly deviates from the envelope curve and formsa change point +is point is a critical point thatindicates when the dilatancy failure degree begins tochange from gob-dominant to boundary pillar-dominant When the upper boundary pillar isdominant it is also more reasonable to regard therange between the two change points as astrengthening control area Later it is called thespecial failure section in the 051606 ventilationroadway According to Figure 5 the change point

σ3

C

σ

τ

p

φ

σ1

(σy τyx)

(σx τxy)

r

O

Figure 3 Mohrrsquos circle describing the stress state

σ1 ndash σ3

0

15

3

45

6

75

Horizontal distribution range (m)

Floo

r dep

th (m

)

140

140

120

120

100

100

80

80

60

60

40

40

20

20

0

0

Figure 4 Distribution of principal stress difference in bedrock

0 20 40 60 80 100 120 140 160

1

2

3

4

5

6

7

Prin

cipa

l str

ess d

iffer

ence

(MPa

)


3m6m9m12m15m

18m21m24m27m

30m33m36m39m

Position of the boundary pillar

Change pointEnvelope curve

Figure 5 Principal stress difference curves at different depths


pressure on 16 coal roof position (buried depth of21m) is about 45MPa Furthermore from a safetystandpoint the scope of the reinforced support inthis roadway under the influence of boundary coalpillar should be increased to 45m with the co-ordinate axis 55ndash100m

4 Numerical Simulation in FLAC3D

41 Numerical Model +e 051606 ventilation roadway isprimarily affected by the mining area boundary pillar in 15coal seam 051604 goaf and 051606 working face in 16 coalseam In order to simplify the calculation process and obtainan objective research rule the influence area of W1415 and051504 goaf is set to 60m +e size of the model is140times156times 65m3 and constrained displacement boundaryconditions are defined at the bottom and all around Over-burden stress is applied to the upper part of this numericalmodel as the stress boundary of the external load Figure 6shows the numerical model of the coal seam +e roof col-lapsed and formed the coal gangue in the goaf which plays animportant role in supporting roof As the porosity decreasesafter compaction and the carrying capacity of gangue is alsogreatly increased exhibiting obvious strain-hardening char-acteristics +erefore it is more appropriate to describe thegoaf as double-yield model [24] In addition the remainingcoal and rock masses are all set as Mohr-Columnmodels andtheir mechanical parameters are shown in Table 1

42 Failure Mechanism of Surrounding Rock During theprocess of close-up coal seammining mining of the workingface in the upper coal seam influences the stress on the rocksurrounding the lower coal seam +e drastic stress fieldgradually tends to stabilize over time While tunneling the051606 ventilation roadway deformation of the rock sur-rounding the roadway is more complicated under thesupport pressure influence by upper boundary pillar and the051604 adjacent gob +erefore we can analyze the de-formation in the surrounding rock and roadway failurebased on the coal seam mining sequence +e surroundingrock fracture mechanism and stress evolution characteristicsunder this influence of multiple mining-induced stresses canbe obtained which helps determining the optimal roadwaysupport parameters

421 Effect of 15 Coal Seam Mining on 16 Coal Seam15 and 16 coal seams are 21m apart and belong to theclose-up coal seam Before mining the lower coal seam thestress environment of the surrounding rock was damageddue to mining-induced stress in the upper coal seam andpressure becomes concentrated in the bedrock of upperboundary pillar [25] In order to study deformation andfailure of the surrounding rock under the influence once15 coal seam is mined-out we can use the principal stressdifference to characterize the integrity of the coal androck mass [14] We monitored σ1 and σ3 of the rock massin 16 coal seam floor roof and 7 and 14m above 16 coalseam roof A 3D principal stress difference map was built

using the postprocessing software-SURFER as shown inFigure 7

Figures 7(a)ndash7(d) show the following

(1) +e principal stress difference peak value in 16 coalseam floor reaches 35MPa (see Figure 7(a)) and thatat the roof reaches 44MPa (see Figure 7(b)) due tothe residual support pressure of the upper coal seamand the peak position is basically distributed in themiddle of the boundary coal pillar floor +is sec-tionrsquos surrounding rock has already undergone acertain degree of dilatancy failure Later excavationof the 051606 ventilation roadway and working facemining near this section may result in more seriousstrata behavior like roof leakage and an increasedanchor cable failure rate

(2) Figure 7(c) shows that the high stress area exhibitstwo peaks+e higher peak position is basically at theedge of the boundary pillar In addition the upperboundary pillar is a large pillar with a width of 35mand there is an elastic core area with a certain widthin the middle of the pillar +erefore rock pressureunder the floor of the elastic core area is relativelysmall However both sides of the boundary coalpillar such as the arch foot position of the fracturearch bear the greatest weight from the overburdenstrata in the goaf +e rock surrounding both sides ofthe pillar experiences larger crushing deformation

(3) +e principal stress difference in the strata is greaterand is much more strongly influenced by upper coalmining when the distance to the upper coal seam iscloser +e principal stress difference curve graduallytransforms from one peak to two peaks which isbasically consistent with the transmission state de-rived from the semiplane theory However there is acertain difference in the peak principal stress dif-ference value which is due to the rock mass char-acteristics According to the layered theory [24]compared with a single rock in semiplane theory theadditional stress near the middle axial line undergoes

051504 goaf

W1415 goaf

Mining area boundary coal pillar

Sectioncoalpillar

051506

goaf

051604goaf

20m coal pillar


051606working face

Figure 6 Initial numerical model


stress diffusion when the hard layer covers the softlayer in the actual numerical model In other wordsthe stress distribution is slightly higher at the twosides than in the middle as shown in Figure 8 At thistime the floating range is basically controlled within20sim25 thus the theoretical results are consistentwith simulation results

In summary because the distance between the two coalseams is 21m the stress decreases as stress transfersdownward layer-by-layer +ough the rock surroundingthe special failure roadway is destroyed under due to upperseam mining to a certain extent it can still satisfy the basic

functions of a roadway if roadway deformation is main-tained by reasonable supports +erefore reasonable sup-ports and scientific mining methods are particularlyimportant

422 Influence of 051604 Goaf on Special Failure RoadwayWhen the upper coal seam is mined the dynamic pressure isfully released in the coal and rockmass after a period of timeWhile mining the lower coal seam the 051604 workingface is mined first and miners subsequently apply a widelyused layout where 20m coal pillars are used to protect theroadway At this time under the superposition of the 051604

Table 1 Mechanical parameters of coal and rock mass

Rock stratum Density(gcm3) Bulk modulus (GPa) Shear modulus (GPa) Cohesion (MPa) Internal friction angle (deg) +ickness (m)

Silt 265 91 78 72 34 35Fine sand 27 133 10 102 37 45Medium sand 234 123 91 52 37 1115 coal seam 13 5 208 168 28 3Silt 265 91 78 72 34 2Fine sand 27 133 10 102 37 2Sandy mudstone 263 125 10 10 35 15Medium sand 234 123 91 52 37 25Coarse sand 305 99 106 108 34 10Silt 265 91 78 72 34 2Mudstone 224 32 669 81 36 116 coal seam 13 5 208 168 28 5Fine sand 27 133 10 102 37 8Silt 265 91 78 72 34 9

35MPa

3MPa

25MPa

2MPa

15MPa

1MPa

Single peak

(a)

Single peak

41MPa

36MPa

31MPa

21MPa

16MPa

26MPa

11MPa

06MPa

(b)

Double peaks

7MPa

6MPa

5MPa

4MPa

3MPa

2MPa

1MPa

(c)

Double peaks

9MPa8MPa7MPa6MPa5MPa4MPa3MPa2MPa1MPa

(d)

Figure 7 Distribution of principal stress difference under the upper coal floor (a) 16 coal seam floor (b) 16 coal seam roof (c) 7m above16 coal seam (d) 14m above 16 coal seam


adjacent goaf and the upper boundary pillar the roof and ribof the coal pillar side in the special failure section are se-riously damaged In order to explore the effect of the 051604adjacent goaf mining of 15 and 16 coal seams and miningof only 16 coal seam are simulated (Figure 9) Furthermoreaccording to the analysis of the upper section the peakposition is in the middle section due to the boundary pillarinfluence+erefore deformation of the surrounding rock inthis section with the most serious damage (the middleposition of the boundary coal pillar) is studied further +iswill be named the maximum failure plane later

An analysis of themaximum failure plane (upper boundarycoal pillar middle line position) shows the following

(1) +ree monitoring lines on the roadway roof showthat the principle stress different on the roof ofthe coal pillar side is the largest followed by themidline and the roof of the virgin coal side is thesmallest after mining 15 and 16 coal seams (seeFigure 9(a))+e load is significantly asymmetric andresults in failure of the roof surrounding rock whilethe principal stress difference on the virgin coal sidedecreases gradually One can see that the shallow coalis fragmented and the deep coal tends to be stable+e principal stress difference distribution in the coalpillar is bimodal and the peak value on the goaf sideis much higher than that on the roadway side

(2) +e principal stress difference on the rock sur-rounding the roof and virgin coal exhibits negativeindex after mining the 051604 working face (seeFigure 9(b)) +eir maximum principal stress dif-ference is 8MPa Figure 9(a) shows that the principalstress difference increases by 2ndash4MPa at the sameposition Meanwhile the damage in the coal pillarmass is the most remarkable+e peak value near theroadway side is increased by 42MPa (sim40 in-crease) +e peak value on the gob-side increasesfrom 159MPa to 228MPa Deformation of thesurrounding rock in this special failure section in-creased compared with only the 051604 goaf influ-ence +e anchor cable approaches failure underthese stress conditions

+erefore we can see that the natural pressure reliefprocess requires significant time after upper coal seam

mining when the coal seams are separated by 21m thus theprincipal stress difference is not large on the roof and virgincoal However destruction of the coal pillar should not bedisregarded In order to prevent stress on the roof and tworibs of the roadway from increasing while mining theworking face reinforcements should be installed in thespecial section during mining

423 Influence of 051606 Working Face Mining After ex-cavation of the 051606 ventilation roadway the surroundingrock in the special failure section is relatively broken underthe influence of the upper pillar Some anchor cables arebroken and some anchor plates slip and fail +erefore weshould improve the mechanical properties of the supportingstructure and stress state of the surrounding rock which canenhance the carrying capacity and meet the stability re-quirements during mining Determining the supplementsupporting parameters should also fully consider the latermining-induced stress influence Under the mining influ-ence the special failure section will inevitably experiencelarger deformation due to the superposition of multiplestress fields +is will greatly affect the ventilation and pe-destrian function of this roadway and even lead to miningaccidents such as the large-scale roof collapse +erefore itis very important to fully understand the deformationmechanism of the roadway due to mining-induced stress inthe 051606 working face

To research the superposition effect of mining on thespecial failure section as the 051606 working face ad-vances we should fully consider the influence of the upperpillar using the semiplane theory +e distances betweenthe working face end and the edge of upper boundarypillar were set to 24 16 8 0 minus8 and minus175m (middleposition of the pillar) +e profile along the roof of the051606 roadway is shown in Figure 10 We consideradvance of the face end to the middle of the upper pillar asthe length is changed +e stress on the rock surroundingthe ventilation roadway is activated again by the sideabutment pressure and shear dilatancy failure of rockmass is the most serious when the face end is pushed to themiddle position of the pillar (see Figure 10(f ))

+e dynamic progress of the working face shows thefollowing

(1) In the 20m section of the coal pillar stress near the051604 goaf side is more concentrated and themaximum principal stress difference reaches25MPa +e cracks in this part are more developedand fragmented Meanwhile the principal stressdifference near the ventilation roadway side is re-duced to 8MPa and the stress reduction is as highas 68 One can see that the integrity of this coalpillar section increases gradually from the 051604gob-side to the ventilation roadway side At thistime the middle of the coal pillar cannot form aneffective elastic core area to maintain the stabilityof the coal pillar Furthermore based on the in-teraction between coal pillar failure and the sur-rounding rock stability of the gob-side roadway

q

Layered theoryE2

Homogeneous semi-infinite

Hard layer E1

b

Figure 8 Stress diffusion when E1gtE2


the stress environment of the surrounding rock inthis special failure section is not ideal

(2) When the face end is 24 and 16m away from theedge stress fluctuations on the roadway roof in thespecial failure section are not great as mining ad-vances from the face end to the edge of the upperboundary pillar However the roof stress increasesobviously when the face end is 8m from the edge ofthe upper pillar It is concluded that the advanceabutment pressure begins to affect this roadwaysection when the face end is about 16m from theupper pillar +is stage is called the nonstress in-fluence section Subsequently during advance from

16 to 0m the low stress range in the 20m coal pillaron the ventilation roadway side decreases greatlywhich directly affects the integrity of the coal pillarand seriously deteriorates roof stress in the specialfailure section +e maximum principal stress dif-ference on the roof reaches 13MPa +is stage iscalled the advance stress influence section As theface end advances from the edge to the midline of theboundary pillar the value and range of the principalstress difference in this roadway roof section in-creases further and its influence is obviouslystronger than that in the previous stage due to stresssuperposition frommining and the upper pillar +is

0 5 10 15 20

5

10

15

20

25Pr

inci

pal s

tress

diff

eren

ce (M

Pa)

Depth of surrounding rock (m)

Coal pillar

Roof of pillar sideVirgin coal

Midline roofRoof of virgin coal side

24222018161412108642

σ1 ndash σ3(MPa)

4

6

68

8

8

10

10

10

10

10

12

12

12

14

14

14

1416

16

10

18

2022051604 goaf

(a)

3

3

4 4

4

5

6

66

7

77

8

8

8

9

9

9

10

14

10

11

1112

134

051604 goaf

σ1 ndash σ3(MPa)

151413121110987654321

5 10 15 200

4

8

12

16

Prin

cipa

l stre

ss d

iffer

ence

(MPa

)


Coal pillar



(b)

Figure 9 Principal stress difference distribution between single and double layer mining (a) 15 coal seam in exploited conditions (b) 15coal seam in unexploited conditions


stage is called the superimposed stress influencesection Furthermore the stability of the sur-rounding rock in the special failure section decreasesgreatly as the stress increases from 11MPa to18MPa At this time when the working face ad-vances to the midline position of the upper boundarypillar the principal stress difference of the rocksurrounding the roof reaches its peak value

In summary according to the influence of the miningprocess on the special failure section the advancing processcan be divided into three stages the nonstress influencesection (24m to 16m from the coal pillar) the advance stressinfluence section (16m to 0m from the coal pillar) and thesuperimposed stress influence section (from 0m to minus175m

from the coal pillar) +ese three stages are summarized inTable 2

43 Analysis of Pressure in the Special Failure SectionDestruction of the surrounding rock in the ventilationroadway can be divided into three parts based on an analysisand comparison of the roadway damage during differentimpact stages +e first is the stress impact stage from theupper boundary pillar the second is the influence of miningthe 051604 adjacent working face and the third is a secondarymining effect on the 051606 working face +e stress changesduring these different stages are summarized in Table 3

+e rock surrounding the 051606 roadway roof suffersstrong support pressure that is transmitted along the floor of

24m

Advancingworking face

051606ventilationroadway

Maximumfailure plane Boundary pillar

location

20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(a)

16m

051606ventilationroadway Advancing

working face

20mcoal pillar

Maximum failure plane

Boundary pillarlocation

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(b)

8m


working face

20mcoal pillar


location

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(c)


Advancing working face


Maximumfailure plane

20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(d)

8m



Boundary pillarlocation20m

coal pillar


4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(e)

175m





coal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(f )

Figure 10 Stress state on rock surrounding vents while advancing the working face (a) 24m from face end to pillar (b) 16m from face endto pillar (c) 8m from face end to pillar (d) 0m from face end to pillar (e) minus8m from face end to pillar (f ) minus175m from face end to pillar


the upper pillar +e peak principal stress difference in thespecial failure section is basically located at the midlineposition of the upper pillar During adjacent working facemining the peak principal stress difference in the roof of thespecial failure section reaches 10MPa and the stress envi-ronment of the surrounding rock deteriorated furtherSubsequently the integrity of the surrounding rock is sig-nificantly reduced while mining the 051606 working faceWhen the face end is located at the middle of the upper pillar(see Figure 10(f )) shear failure is most likely to occur in theroof on the coal pillar side and the principal stress differencereaches 18MPa +e simulation results show that this maycause serious roof collapse if the serious stress environmentis not improved as the working face advances

5 Surrounding Rock Control Technology

51 Difficulties in Surrounding Rock Control According todamage from superimposed stress on the rock surroundingthe ventilation roadway the pedestrian and ventilationfunction can be maintained if the following three points areconsidered

511 Asymmetric Zone Caused by Roadway Section Features+e051606 ventilation roadway has a sloping roof with 332mhigher rib and 23m lower rib Under the influence of thesefeatures the actual suspension length of the layered roofincreases greatly when the roadway ribs are unstable +esuspension length of the higher rib support is significantlygreater than that of the lower rib resulting in a remarkableasymmetric stability distribution on the rock surroundingboth sides of the roof Furthermore based on the interactionbetween the roof and the rock surrounding the two ribsasymmetric damage on the roof rock mass will be super-imposed on the high and low ribs +e higher rib will deformvertically the lower rib will be removed and the roof shoulderwill bend asymmetrically

512 Strengthening the Control Area During excavation ofthe working face in the upper coal seam the strata weight ofthe gob roof is transferred to the upper boundary pillar

through the arch structure According to the semiplanetheory stress diffuses along the floor of the coal pillar to thelower coal seam Determining reasonable roadway pro-tection is a major difficulty

513 Second Mining-Induced Stress Activates the OriginalStress Environment +e bedrock of the upper coal pillar isaffected by the high support pressure which is transmittedby the overlying coal pillar and roadway excavation in thishigh stress region will cause a rapid release of vertical stresson the roadway roof Meanwhile stress concentration in theshoulders and ribs of the roadway will increase [26] +esurrounding rock stress environment is activated again aftersecondary mining of the working face forming more intensestrata behavior

52 Support Parameters of Surrounding Rock Strata be-haviors are objective natural phenomena It is impossible tocompletely eliminate strata behaviors during mining [15]+erefore under the premise of mine production safetytheoretical analysis and numerical simulation in FLAC3Dwere used to comprehensively determine the dynamicdamage process and stress distribution on the upperboundary pillar and the lower ventilation roadway At lastcombined with the particularity of roadway section shapethe most scientific roadway support scheme is selected

15 coal seam is a monoclinic structure with an averageinclination of 116deg while the 051606 roadway is designed as aspecial-shaped rectangular roadway with a higher rib heightof 332m lower rib height of 23m and intermediate heightof 281m with net cross sectional area is 1349m2 +isroadway uses a new form of support based on the highlystressed bolting support and anchor cable +is assists thesteel ladder beam steel mesh and shed support in protectingthe roof and ribs of the roadway +e specific supportscheme is shown in Figure 11

+e roof bolting support includes a φ20times 2500mm left-handed and nonlongitudinal rebar threaded steel bolt +erow and line spacing is 770times 900mm and each row isarranged with 7 anchor bolts +e bolts connecting the tworibs and roof form a 60deg angle and the other bolts are

Table 2 +ree stages of stress change during advance

Unstressedinfluence section

Advance stressinfluence section

Superimposed stressinfluence section

Roof stress in maximum failure plane (MPa) 10 11 18Peak stress of roadway roof (MPa) 10 13 18Peak position (m) minus175 0 minus175

Table 3 Analysis of principal stress difference on the rock surrounding the roof during failure

Influence ofboundary pillar

Influence of the 051604working face


Influence value of each stage (MPa) 44 56 8Total impact value (MPa) 44 10 18Influence degree Strong Stronger Extremely strong


arranged vertically e steel ladder beam is made ofφ16mm round welded steel beams 4800times 80mm in sizeEach anchor cable measures φ178times 7000mm and twoanchor cables are used in each rowe row and line space is1800times 2700mm and the two anchor cables are arrangedvertically on the roof ere are three bolts in the high riband two bolts in the low rib ese are φ18times 2000mm steelbolts and are perpendicular to the ribs with row and linespacing of 1000times 900mm According to the shape of thesection the heights of the shed legs are 24m and 34m etwo shed legs are embedded 100mm in oor and the shedbeam is 49m

is scheme uses high stressed bolts (cable) a steelladder beam steel mesh and shed for support iscomposite beam structure is formed by the interactionbetween the bolt and shallow surrounding rock with theanchor cable and overlying hard main roof as the sus-pending structure e roadway support asymmetry ef-fectively reduces the bearing area In addition the strongprotective ability of the steel mesh and shed support canbetter control the dilatancy deformation in the shallowsurrounding rock With this support method the residualstrength of the surrounding rock has increased e sur-rounding rock and the supports form an eective bearing

1000

770

143

144

900

770

10002810

Cable φ178 times 7000mm

400

φ20 times 2500mm threaded steel bolt

1500

Row and line 1000 times 900mm

φ18 times 2000mm steel bolt

60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840

φ16 steel ladder beamL = 4800

900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)

Figure 11 051606 ventilation way supplement support scheme (a) Elevation view of support scheme (b) Horizontal projection of supportscheme


structure which greatly reduces or even prevents largedeformation in the surrounding rock

6 Control Effect of Strengthening Support

During actual mine construction the 051606 roadwaycrosses through the upper boundary of the coal pillar inspace +is roadway should be strong enough to supportdriving +e surrounding rock in the special failure sectionprovides this functionality +e coal mass on the roof ex-hibits layered slippage the coal mass in the rib shoulder fallsand bulges to form a string bag and more damage accu-mulates in the higher rib than in the lower rib+erefore it ispossible to adopt emergency measures for supporting re-inforcement after excavation proceeds for 10 days Rooffloor and rib displacement can be subsequently measuredusing the crossing method in this special failure section +erock deformation curve is shown in Figure 12

One can see that stabilization of the surrounding rockafter excavation is a dynamic process until equilibrium isreached [27] Roof deformation tends to become stableabout 20 days after implementing supports and the two ribsand floor rock become stable after about 15 days Stress inthe surrounding rock can stabilize after a short time +emaximum convergence of roof rock is approximately200mm and the minimum floor convergence is only about100mm+emaximum convergence between the roof floorand ribs due to mining-induced stress is about 300mmAccording to the relationship between the support structureand the surrounding rock design of the roadway supportbased on a controlled load is not suitable thus controlleddeformation should be used +erefore although the rocksurrounding the roadway experiences some deformation to acertain extent under the influence of strong stress the basicventilation and pedestrian functions will not be directly lostif the roadway is maintained by reasonable supportingforms It can be also seen that this reinforcing support canprotect the roof and ribs while the surrounding rock has alsoreached an internal balance after a relatively short period oftime We find that the reinforcing support method has amore remarkable effect on roadway maintenance

7 Conclusions

+is study uses the methods of theoretical analysis FLACnumerical simulation and engineering practice to obtain thefollowing conclusions

(1) Semiplane theory can be used to deduce andmathematically calculate the stress distributionon the floor Furthermore the principal stress dif-ference is introduced into this solution model It isconcluded that the stress distribution under thiscondition exhibits fan-shaped diffusion +e stressdistribution on 16 coal seam roof has a single peak+e maximum failure plane is located in the middleof the upper coal pillar Finally we found that thestrengthening control area in the 051606 ventilationroadway is 45m from the change point position on16 coal seam roof

(2) FLAC3D was used to successively simulate the in-fluence of the upper boundary pillar the 051604 goband the 051606 working face It is concluded thatmining the 051606 working face is the greatest de-terminant of stability of the rock surrounding theroadway followed by mining the 051604 workingface

(3) +e principal stress difference distribution in therock surrounding the special failure section exhibitsobvious asymmetric characteristics +erefore anasymmetric support form is proposed that useshighly stressed bolts an anchor cable steel ladderbeam steel mesh and a shed to add support to theroof and ribs of the roadway +is support structurewas successfully applied in a real project

Data Availability

All data supporting the conclusions drawn by this study canbe obtained from the corresponding author upon request

Disclosure

+e funders had no role in the design of the study in thecollection analyses or interpretation of data in the writingof the manuscript and in the decision to publish the results

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Authorsrsquo Contributions

Zheng Zheng conceived and designed the paper Fulian HeHengzhong Zhu and Bo Yang analyzed the data All au-thors have written reviewed and approved the finalmanuscript

0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor

Figure 12 Strata behavior curve


Acknowledgments

+is project was supported by the National Natural ScienceFoundation of China (no 51574243) by the Yue Qi Dis-tinguished Scholar Project (800015Z1138) China Universityof Mining amp Technology Beijing and also by the Funda-mental Research Funds for the Central Universities(800015J6)

References

[1] L Yuan ldquoKey technique of safe mining in low permeabilityand methane-rich seam grouprdquo Chinese Journal of RockMechanics and Engineering vol 27 pp 1371ndash1378 2008

[2] C F Yuan ldquoDevelopment and application of gas-geology inChinardquo Journal of China Coal Society vol 22 pp 566ndash5701997

[3] Y P Cheng and Q X YU ldquoDevelopment of regional gascontrol technology for Chinese coalminesrdquo Journal of Miningand Safety Engineering vol 24 no 10 pp 383ndash390 2007

[4] F P Gong and X B Li ldquoCatastrophe progression method forstability classification of underground engineering sur-rounding rockrdquo Journal of Central South University ofTechnology vol 39 pp 1081ndash1086 2008

[5] W-Y Guo T-B Zhao Y-L Tan F-H Yu S-C Hu andF-Q Yang ldquoProgressive mitigation method of rock burstsunder complicated geological conditionsrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 96pp 11ndash22 2017

[6] W Y Guo Y L Tan and F H Yu ldquoMechanical behavior ofrock-coal-rock specimens with different coal thicknessesrdquoGeomechanics and Engineering vol 15 no 4 pp 1017ndash10272018

[7] J W Cassie and P B Cartwright ldquoCoal pillar behavior fromunderground stress measurementsrdquo in Proceedings of 9thInternational Congress on Rock Mechanics pp 1347ndash1354Paris France August 1999

[8] J K Jiao andW J JU ldquoMulti-factors analysis of the stability ofroadway under coal pillar based on response surface methodrdquoJournal ofMining and Safety Engineering vol 34 pp 933ndash9392017

[9] S L Lu and L Y Sun ldquoSelection of horizontal distance Xbetween roadway and the edge of its upper pillarrdquo Journal ofChina University of Mining amp Technology vol 22 pp 1ndash71993

[10] S L Lu and Y D Jiang ldquo+e selection of vertical distance Zbetween roadway and its upper coal seamrdquo Journal of ChinaUniversity of Mining amp Technology vol 22 pp 1ndash7 1993

[11] Y B Guan and H M Li ldquoResearch of No19coal seam floorrsquosfracture regularity in Xiandewang Coal Minerdquo Journal ofChina Coal Society vol 28 pp 121ndash125 2003

[12] Y Zhang and C L Zhang ldquo+e study on roadway layout incoordination of mining coal seams base on failure of floorstratardquo in Engineering Solutions for Manufacturing ProcessesIV pts 1 and 2 Z Jiang X Liu and J Han Eds vol 889-890pp 1362ndash1374 Trans Tech Publications Ltd Stafa-ZurichSwitzerland 2014

[13] A H Wilson ldquo+e stability of underground workings in thesoft rocks of the Coal Measuresrdquo International Journal ofMining Engineering vol 1 pp 91ndash187 1983

[14] L Xu and H L Zhang ldquoPrincipal stress difference evolutionin floor under pillar and roadway layoutrdquo Journal of Miningand Safety Engineering vol 32 pp 478ndash484 2015

[15] W Li J Bai S Peng X Wang and Y Xu ldquoNumericalmodeling for yield pillar design a case studyrdquo RockMechanicsand Rock Engineering vol 48 no 1 pp 305ndash318 2014

[16] W Sui Y Hang L Ma et al ldquoInteractions of overburdenfailure zones due to multiple-seam mining using longwallcavingrdquo Bulletin of Engineering Geology and the Environmentvol 74 no 3 pp 1019ndash1035 2014

[17] W B Zhu Study on the Instability Mechanism of Key StrataStructure in Repeat Mining of Shallow Close Distance SeamsChina University of Mining and Technology Xuzhou China2010

[18] J Qiao ldquoOn the preimages of parabolic periodic pointsrdquoNonlinearity vol 13 no 3 pp 813ndash818 2000

[19] J Y Qiao Complex Dynamics of Renormalization Trans-formations Science Press Beijing China 2010 in Chinese

[20] Z G Xu Elasticity Higher Education Press Beijing China2006

[21] M G Qian and P W Shi Kuangshan Yali Yu YancengKongzhi China University of Mining and Technology PressXuzhou China 2010

[22] B Yu and Y C Liu ldquoMechanism of strong pressure revealunder the influence of mining dual system of coal pillar inDatong mining areardquo Journal of China Coal Society vol 39pp 40ndash46 2014

[23] G X Li and B Y Zhang Soil Mechanics Tsinghua UniversityPress Beijing China 2013

[24] G Zhang S Liang Y Tan F Xie S Chen and H JialdquoNumerical modeling for longwall pillar design a case studyfrom a typical longwall panel in Chinardquo Journal of Geophysicsand Engineering vol 15 no 1 pp 121ndash134 2018

[25] B S Zhang S S Yang and L X Kang ldquoDiscussion onmethod for determining reasonable position of roadway forultra-close multi-seamrdquo Chinese Journal of Rock Mechanicsand Engineering vol 27 pp 97ndash101 2008

[26] X G Su X M Song and H H Yuan ldquoStability control of theroadway group under the influence of overlying goafrdquo Journalof Mining and Safety Engineering vol 33 pp 415ndash422 2016

[27] K X Zhang Y J Zhang and Z Q Ma ldquoDetermination of thenarrow pillar width of gob-side entry drivingrdquo Journal ofMining and Safety Engineering vol 32 pp 446ndash452 2015


International Journal of

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Submit your manuscripts atwwwhindawicom

the gob as strain hardeningmodel and the coal pillar as strain-softening model according to the actual mechanical charac-teristics of coal and rock mass +e accuracy of the numericalmodel is greatly improved Sui et al [16] proposed a newindex ldquoDividing Line Drdquo to define the overburden failure stateand using it to discuss the interactions of overburden damagezones in close-up coalbed mining Zhu [17] established themechanics model of breaking block structure of key seam andanalyzed the influence of breaking line position in upper coalseam roof on the structural stability in lower coal seam Anunderground engineering is generally a complex dynamicalsystem +e important work during mining is to control thedeformation of coal mine roadway and coal-face In essencethe mine deformations are the final result of the interaction ofsome disaster factors In 2000 Qiao [18 19] dealt with theconverse theorem of the Leau-Fatou petal theorem oncomplex dynamical systems and revealed an impressive rulewhich said that the geometrical properties of the unstable setcould impact the structural stability of dynamical systemsdirectly

Scholars have been exploring failure of surrounding rockand strata after close-up coal seam mining for a long timeGenerally the reasonable location of the working face androadway in lower coal is the primary focus of this researchHowever under the influence of boundary pillars in uppercoal seam areas there is relatively little research on theroadway crossing through this boundary pillar section in thelower coal seam Under these conditions the strengtheningcontrol area cannot be determined directly In additionusing vertical stress to characterize failure of surroundingrock in traditional research is inappropriate +ereforeaccording to the relative position of the Mohr circle andenvelope curve it is more scientific to use ldquoprincipal stressdifferencerdquo to quantify the integrity of the surrounding rock

2 Engineering Background

+e 051606 working face 265m average depth is located inthe 16 coal seam of the fifth mining area in the Ling Xin CoalMine Ningxia Province China +e eastern part is 560mapart from the fault the southern side is about 204m awayfrom the exploration line the western side and the 051604working face have 20m protective coal pillars and thedistance from the northern side to rail rise of the fifth miningarea is about 46m 15 coal seam exploited is about 21mabove the 051606 working face +erefore in the process ofdriving 051606 ventilation roadway it crosses throughsuccessively the 051504 goaf the 35m boundary pillar andW1415 goaf in space +e 20m protective coal pillar is leftbetween 051504 goaf and 051506 goaf as well as 051604 goafand 051606 working face Its space position is shown inFigure 1 16 coal seam is medium thick coal seam itsaverage thickness in the working face area is 502m and theroof is a harder silt and fine sandstone +e section of theroadway under the influence of the upper boundary pillarhas a stronger strata behavior +at is ldquospecial failure sec-tionrdquo in Figure 1 +rough field observation the roadwayrsquosroof of the most serious section had obvious step subsidencethe two shoulder angles were damaged seriously some bolt

pallets failed and part of anchor cable had the phenomenonof breaking +e othersrsquo roadway is placed on the undersideof the upper coal seam goaf which is basically in a low stressstate Its surrounding rock is relatively complete and cansatisfy pedestrians and transportation functions

3 Principal Stress Difference

31 StressTransferModel In order to analyze the influence ofstress on the upper coal pillar and goaf we use the semiplanetheory from elastic mechanics [20] to calculate the stress inthe coal and rockmass below At this time the boundary pillarforms the border between two adjacent mining areas As thetwo sides of the working face are pushed forward the roofbreaks in the form of ldquoO-Xrdquo [21] According to reliable dataobtained from numerous field experiments the goaf expe-riences the same stress as virgin rocks when it is about 012 to03 times of the buried depth from the edge of coal pillar [21]In other words the original rock stress begins to appear about35ndash90m into the goaf +e effect of stress is only analyzed60m into the goaf in this study +e mechanical model inFigure 2 can be used to describe this situation where X pointsvertically and Y points horizontally

In order to simplify the calculation without sacrificingaccuracy [22] rock in the upper seam floor is assumed to beaffected by the superposition of L1 L3 gobs and L2 boundarypillar where the total pressure from these three loads can becalculated at point M Under the influence of concentratedstress q1 by L1 gob stress at point M (r θ) in the bedrock isshown as follows [20]

σ1x 2q1cos3θ

rπ

σ1y 2q1 cos θ sin2θ

rπ

τ1xy 2q1cos2θ sin θ

rπ

(1)

In this formula σ1x σ1x and τ1xy are the vertical hori-zontal and shear stress components at M under the influ-ence of L1 gob respectively and q1 is the uniform load valuein L1 gob A small length dη is selected at the coordinate η onthe x-axis (0le xle L1) and its uniform load is q(η) λ0cH+erefore the vertical and horizontal distances between M(x y) and η are x and (yminus η) respectively +e differentialstress dη at M is defined as follows

dσ1x minus2λ0cH dη

πx3

x2 +(yminus η)21113960 11139612

dσ1y minus2λ0cH dη

πx(yminus η)2

x2 +(yminus η)21113960 11139612

dτ1xy minus2λ0cH dη

πx2(yminus η)

x2 +(yminus η)21113960 11139612

(2)

where λ0 is the L1 gob stress concentration factor cH is theinitial crustal stress of 15 coal seam and x and y are the



σ1x minus2λ0cH

π1113946

L1

0

x3

x2 +(yminus η)21113960 11139612 dη

σ1y minus2λ0cH

π1113946

L1

0

x(yminus η)2

x2 +(yminus η)21113960 11139612 dη

τ1xy minus2λ0cH

π1113946

L1

0

x2(yminus η)

x2 +(yminus η)21113960 11139612 dη

(3)




p σx + σy1113872 11138732

r

σx minus σy1113872 111387321113960 11139612

+ τ2xy

1113970

σ1 p + r

σ3 pminus r

σ1 minus σ3( 1113857k 2r 2

σkx minus σk

y1113872 111387321113960 11139612

+ τkxy1113872 1113873

21113970

(4)





coal pillar)

051606working face



35mboundary pillar


051604 goaf


21m

laye

r spa

cing

051506 goaf

35mboundary pillar


L1

Pillar

λ1γH

λ0γH λ0γH

θ1θ2

δyτyx

δxτxy

M

L3 L2

0

x

y









σ3

C

σ

τ

p

φ

σ1

(σy τyx)

(σx τxy)

r

O


σ1 ndash σ3

0

15

3

45

6

75


Floo

r dep

th (m

)

140

140

120

120

100

100

80

80

60

60

40

40

20

20

0

0


0 20 40 60 80 100 120 140 160

1

2

3

4

5

6

7

Prin

cipa

l str

ess d

iffer

ence

(MPa

)


3m6m9m12m15m

18m21m24m27m

30m33m36m39m















051504 goaf

W1415 goaf


Sectioncoalpillar

051506

goaf

051604goaf

20m coal pillar


051606working face










35MPa

3MPa

25MPa

2MPa

15MPa

1MPa

Single peak

(a)

Single peak

41MPa

36MPa

31MPa

21MPa

16MPa

26MPa

11MPa

06MPa

(b)

Double peaks

7MPa

6MPa

5MPa

4MPa

3MPa

2MPa

1MPa

(c)

Double peaks


(d)













q

Layered theoryE2


Hard layer E1

b






0 5 10 15 20

5

10

15

20

25Pr

inci

pal s

tress

diff

eren

ce (M

Pa)


Coal pillar



24222018161412108642

σ1 ndash σ3(MPa)

4

6

68

8

8

10

10

10

10

10

12

12

12

14

14

14

1416

16

10

18

2022051604 goaf

(a)

3

3

4 4

4

5

6

66

7

77

8

8

8

9

9

9

10

14

10

11

1112

134

051604 goaf

σ1 ndash σ3(MPa)

151413121110987654321

5 10 15 200

4

8

12

16

Prin

cipa

l stre

ss d

iffer

ence

(MPa

)


Coal pillar



(b)








24m




location

20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(a)

16m


working face

20mcoal pillar



4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(b)

8m


working face

20mcoal pillar


location

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(c)





20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(d)

8m




coal pillar


4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(e)

175m





coal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(f )


























1000

770

143

144

900

770

10002810


400


1500



60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840


900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)







7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



σ1x minus2λ0cH

π1113946

L1

0

x3

x2 +(yminus η)21113960 11139612 dη

σ1y minus2λ0cH

π1113946

L1

0

x(yminus η)2

x2 +(yminus η)21113960 11139612 dη

τ1xy minus2λ0cH

π1113946

L1

0

x2(yminus η)

x2 +(yminus η)21113960 11139612 dη

(3)




p σx + σy1113872 11138732

r

σx minus σy1113872 111387321113960 11139612

+ τ2xy

1113970

σ1 p + r

σ3 pminus r

σ1 minus σ3( 1113857k 2r 2

σkx minus σk

y1113872 111387321113960 11139612

+ τkxy1113872 1113873

21113970

(4)





coal pillar)

051606working face



35mboundary pillar


051604 goaf


21m

laye

r spa

cing

051506 goaf

35mboundary pillar


L1

Pillar

λ1γH

λ0γH λ0γH

θ1θ2

δyτyx

δxτxy

M

L3 L2

0

x

y









σ3

C

σ

τ

p

φ

σ1

(σy τyx)

(σx τxy)

r

O


σ1 ndash σ3

0

15

3

45

6

75


Floo

r dep

th (m

)

140

140

120

120

100

100

80

80

60

60

40

40

20

20

0

0


0 20 40 60 80 100 120 140 160

1

2

3

4

5

6

7

Prin

cipa

l str

ess d

iffer

ence

(MPa

)


3m6m9m12m15m

18m21m24m27m

30m33m36m39m















051504 goaf

W1415 goaf


Sectioncoalpillar

051506

goaf

051604goaf

20m coal pillar


051606working face










35MPa

3MPa

25MPa

2MPa

15MPa

1MPa

Single peak

(a)

Single peak

41MPa

36MPa

31MPa

21MPa

16MPa

26MPa

11MPa

06MPa

(b)

Double peaks

7MPa

6MPa

5MPa

4MPa

3MPa

2MPa

1MPa

(c)

Double peaks


(d)













q

Layered theoryE2


Hard layer E1

b






0 5 10 15 20

5

10

15

20

25Pr

inci

pal s

tress

diff

eren

ce (M

Pa)


Coal pillar



24222018161412108642

σ1 ndash σ3(MPa)

4

6

68

8

8

10

10

10

10

10

12

12

12

14

14

14

1416

16

10

18

2022051604 goaf

(a)

3

3

4 4

4

5

6

66

7

77

8

8

8

9

9

9

10

14

10

11

1112

134

051604 goaf

σ1 ndash σ3(MPa)

151413121110987654321

5 10 15 200

4

8

12

16

Prin

cipa

l stre

ss d

iffer

ence

(MPa

)


Coal pillar



(b)








24m




location

20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(a)

16m


working face

20mcoal pillar



4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(b)

8m


working face

20mcoal pillar


location

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(c)





20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(d)

8m




coal pillar


4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(e)

175m





coal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(f )


























1000

770

143

144

900

770

10002810


400


1500



60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840


900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)







7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








σ3

C

σ

τ

p

φ

σ1

(σy τyx)

(σx τxy)

r

O


σ1 ndash σ3

0

15

3

45

6

75


Floo

r dep

th (m

)

140

140

120

120

100

100

80

80

60

60

40

40

20

20

0

0


0 20 40 60 80 100 120 140 160

1

2

3

4

5

6

7

Prin

cipa

l str

ess d

iffer

ence

(MPa

)


3m6m9m12m15m

18m21m24m27m

30m33m36m39m















051504 goaf

W1415 goaf


Sectioncoalpillar

051506

goaf

051604goaf

20m coal pillar


051606working face










35MPa

3MPa

25MPa

2MPa

15MPa

1MPa

Single peak

(a)

Single peak

41MPa

36MPa

31MPa

21MPa

16MPa

26MPa

11MPa

06MPa

(b)

Double peaks

7MPa

6MPa

5MPa

4MPa

3MPa

2MPa

1MPa

(c)

Double peaks


(d)













q

Layered theoryE2


Hard layer E1

b






0 5 10 15 20

5

10

15

20

25Pr

inci

pal s

tress

diff

eren

ce (M

Pa)


Coal pillar



24222018161412108642

σ1 ndash σ3(MPa)

4

6

68

8

8

10

10

10

10

10

12

12

12

14

14

14

1416

16

10

18

2022051604 goaf

(a)

3

3

4 4

4

5

6

66

7

77

8

8

8

9

9

9

10

14

10

11

1112

134

051604 goaf

σ1 ndash σ3(MPa)

151413121110987654321

5 10 15 200

4

8

12

16

Prin

cipa

l stre

ss d

iffer

ence

(MPa

)


Coal pillar



(b)








24m




location

20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(a)

16m


working face

20mcoal pillar



4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(b)

8m


working face

20mcoal pillar


location

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(c)





20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(d)

8m




coal pillar


4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(e)

175m





coal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(f )


























1000

770

143

144

900

770

10002810


400


1500



60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840


900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)







7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












051504 goaf

W1415 goaf


Sectioncoalpillar

051506

goaf

051604goaf

20m coal pillar


051606working face










35MPa

3MPa

25MPa

2MPa

15MPa

1MPa

Single peak

(a)

Single peak

41MPa

36MPa

31MPa

21MPa

16MPa

26MPa

11MPa

06MPa

(b)

Double peaks

7MPa

6MPa

5MPa

4MPa

3MPa

2MPa

1MPa

(c)

Double peaks


(d)













q

Layered theoryE2


Hard layer E1

b






0 5 10 15 20

5

10

15

20

25Pr

inci

pal s

tress

diff

eren

ce (M

Pa)


Coal pillar



24222018161412108642

σ1 ndash σ3(MPa)

4

6

68

8

8

10

10

10

10

10

12

12

12

14

14

14

1416

16

10

18

2022051604 goaf

(a)

3

3

4 4

4

5

6

66

7

77

8

8

8

9

9

9

10

14

10

11

1112

134

051604 goaf

σ1 ndash σ3(MPa)

151413121110987654321

5 10 15 200

4

8

12

16

Prin

cipa

l stre

ss d

iffer

ence

(MPa

)


Coal pillar



(b)








24m




location

20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(a)

16m


working face

20mcoal pillar



4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(b)

8m


working face

20mcoal pillar


location

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(c)





20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(d)

8m




coal pillar


4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(e)

175m





coal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(f )


























1000

770

143

144

900

770

10002810


400


1500



60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840


900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)







7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









35MPa

3MPa

25MPa

2MPa

15MPa

1MPa

Single peak

(a)

Single peak

41MPa

36MPa

31MPa

21MPa

16MPa

26MPa

11MPa

06MPa

(b)

Double peaks

7MPa

6MPa

5MPa

4MPa

3MPa

2MPa

1MPa

(c)

Double peaks


(d)













q

Layered theoryE2


Hard layer E1

b






0 5 10 15 20

5

10

15

20

25Pr

inci

pal s

tress

diff

eren

ce (M

Pa)


Coal pillar



24222018161412108642

σ1 ndash σ3(MPa)

4

6

68

8

8

10

10

10

10

10

12

12

12

14

14

14

1416

16

10

18

2022051604 goaf

(a)

3

3

4 4

4

5

6

66

7

77

8

8

8

9

9

9

10

14

10

11

1112

134

051604 goaf

σ1 ndash σ3(MPa)

151413121110987654321

5 10 15 200

4

8

12

16

Prin

cipa

l stre

ss d

iffer

ence

(MPa

)


Coal pillar



(b)








24m




location

20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(a)

16m


working face

20mcoal pillar



4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(b)

8m


working face

20mcoal pillar


location

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(c)





20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(d)

8m




coal pillar


4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(e)

175m





coal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(f )


























1000

770

143

144

900

770

10002810


400


1500



60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840


900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)







7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












q

Layered theoryE2


Hard layer E1

b






0 5 10 15 20

5

10

15

20

25Pr

inci

pal s

tress

diff

eren

ce (M

Pa)


Coal pillar



24222018161412108642

σ1 ndash σ3(MPa)

4

6

68

8

8

10

10

10

10

10

12

12

12

14

14

14

1416

16

10

18

2022051604 goaf

(a)

3

3

4 4

4

5

6

66

7

77

8

8

8

9

9

9

10

14

10

11

1112

134

051604 goaf

σ1 ndash σ3(MPa)

151413121110987654321

5 10 15 200

4

8

12

16

Prin

cipa

l stre

ss d

iffer

ence

(MPa

)


Coal pillar



(b)








24m




location

20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(a)

16m


working face

20mcoal pillar



4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(b)

8m


working face

20mcoal pillar


location

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(c)





20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(d)

8m




coal pillar


4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(e)

175m





coal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(f )


























1000

770

143

144

900

770

10002810


400


1500



60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840


900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)







7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





0 5 10 15 20

5

10

15

20

25Pr

inci

pal s

tress

diff

eren

ce (M

Pa)


Coal pillar



24222018161412108642

σ1 ndash σ3(MPa)

4

6

68

8

8

10

10

10

10

10

12

12

12

14

14

14

1416

16

10

18

2022051604 goaf

(a)

3

3

4 4

4

5

6

66

7

77

8

8

8

9

9

9

10

14

10

11

1112

134

051604 goaf

σ1 ndash σ3(MPa)

151413121110987654321

5 10 15 200

4

8

12

16

Prin

cipa

l stre

ss d

iffer

ence

(MPa

)


Coal pillar



(b)








24m




location

20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(a)

16m


working face

20mcoal pillar



4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(b)

8m


working face

20mcoal pillar


location

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(c)





20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(d)

8m




coal pillar


4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(e)

175m





coal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(f )


























1000

770

143

144

900

770

10002810


400


1500



60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840


900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)







7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







24m




location

20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(a)

16m


working face

20mcoal pillar



4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(b)

8m


working face

20mcoal pillar


location

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(c)





20mcoal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(d)

8m




coal pillar


4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(e)

175m





coal pillar

4 6 8 10 12 14 16 18 20 22 24σ1 ndash σ3 (MPa)

(f )


























1000

770

143

144

900

770

10002810


400


1500



60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840


900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)







7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

























1000

770

143

144

900

770

10002810


400


1500



60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840


900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)







7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




1000

770

143

144

900

770

10002810


400


1500



60deg

4800

60deg



Roadwaycenterline


1000

770 770


770

1500

400

1800

770

920

(a)

2700

900

770143

1840


900

770

1534 1534

2700

770 770

φ65 steel mesh

900

770 770

(b)







7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






7 Conclusions





Data Availability


Disclosure






0 10 20 30 40 50

90

120

150

180

210

Conv

erge

nt d

efor

mat

ion

(mm

)

Observation days

RoofHigher rib

Lower ribFloor



Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Research on Failure Mechanism and Strengthening of Broken