sensitivityanalysisandexperimentalverificationofboltsuppor...

Research ArticleSensitivityAnalysis andExperimentalVerificationofBolt SupportParameters Based on Orthogonal Experiment

Kun Zhang 1 Jinpeng Su 12 Zengkai Liu1 Hongyue Chen3 Qiang Zhang1

and Shaoan Sun1

1College ofMechanical and Electronic Engineering Shandong University of Science and Technology No 579 Qianwangang RoadQingdao 266590 Shandong China2State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University Dongchuan Road 800Shanghai 200240 China3School of Mechanical Engineering Liaoning Technical University No 88 Yulong Road Fuxin 123000 Liaoning China

Correspondence should be addressed to Jinpeng Su suchenalumnisjtueducn

Received 26 March 2020 Revised 9 July 2020 Accepted 3 September 2020 Published 18 September 2020

Academic Editor Fabio Rizzo

Copyright copy 2020 Kun Zhang 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

is paper presents a unified supporting parameter optimization procedure for the coupled bolt-rock systems by using theorthogonal experimental methods Convergence of surrounding rock surface and deformations in the rock are taken as theobjective functions for the stability of the surrounding rock of the roadwaye key support parameters of the bolt are consideredas input variables e simulation software FLAC3D is employed to develop the mechanical model for the coupled bolt-rocksystem and the objective functions of the coupled system are therefore obtained in the software Combining the variance andmultivariate linear regression analysis an approach is derived to investigate the sensitivity of the support parameters to theobjective functions e corresponding support parameters are then optimized e 15106 working of a practical mine inYangquan is taken as an example According to the similar simulation theory corresponding simulation experiments areperformed us the proposed method is validated and its robust performance for optimization of supporting parameters of thebolt is also demonstrated e method provides a theoretical basis for the determination of bolt support parameters for miningroadway in a fully mechanized mining face

1 Introduction

e bolt support technology has been developed for morethan a century since it was first used in the North Walesopen-air shale mine in 1872 in the UK [1] Due to its ad-vantages such as low cost simple operation and less con-struction space it has been widely used in surfaceengineering and underground chamber construction inmining tunnels slopes deep soil rock foundation pits andso forth [2ndash4] In recent years with the development ofcorresponding science and technology the demand for coalresources in industry and human life is still urgent eshallow coal resources have gradually dried up Deep miningwill therefore play more and more important roles in thecoal mining engineering [5] However deep wells lead to

more complex geological conditions in the working face andhigh ground stress Hence mining in the coal layer canseverely affect the stability of the surrounding rock of theroadway and cause serious damage [6ndash9] As shown inFigure 1 the bolt will fail to support the roadway ereforethe requirements for the surrounding rock support tech-nology of the roadway are getting higher and higher and it isnecessary to optimize the design of the parameters of thesupporting bolt the main support equipment

Many experts and scholars at home and abroad haveconducted systematic researches on the bolt support tech-nology Li [10] developed a new type of bolt support deviceand experimentally verified the performance and reliabilityof the new bolt support device in three mines Charette andPlouffe [11] proposed a bolt with constant resistance which

HindawiShock and VibrationVolume 2020 Article ID 8844282 13 pageshttpsdoiorg10115520208844282

is suitable for soft rock roadway support Jager [12] designedan energy-absorbing bolt device Varden et al [13] putforward a new type of bolt support equipment for thegeological conditions of the Kanowna Belle mine and testedits mechanical properties using the Kalgoorlie dynamic testequipment at University of Minnesota in Australia

Based on the elastic theory Gu et al [14] established acoordinated deformation model of surrounding rock andsolids (rock and bolt complex) and proposed a method forevaluating the stability of the surrounding rock Based on theasymmetrical assumption of lane strain Wu et al [15]established the equilibrium equation and compatibilityequation of a bolt-rock system and obtained the analyticalsolution of the coupled model e influences of bolt androck properties on the transmission of the reinforcementeffect in the rock were revealed Wang et al [16] developed astatic-dynamic loading test system e system wasemployed to implement the static tensile tests of equal-strength and non-equal-strength rebar bolts and the dy-namic impact tests with or without prestress Zou et al [17]presented a strategy for excavating circular roadways inbrittle and soft rocks with bolt support and established anevolution equation of the surrounding rocks with boltsupportWang et al [18] adopted the discrete mechanics andfriction coupling (DMFC) to study the spatiotemporalevolution of the mechanical properties of the bolts andsurrounding rocks In their theoretical model the Maxwellmodel was used to describe the surrounding rock and theKelvin model was used to describe the characteristics of thebolt Hu and Chen [19] deduced the vibration properties ofbolts subject to blasting seismic waves

It can be found from the above literature review thatcoupled bolt-rock system is a sophisticated coupled me-chanical system Key parameters of the anchor bolts havesignificant and complex influences on the mechanical be-haviors of the coupled system Numerous example analyseswill be needed if the sensitivities of all the key parameters ofthe bolts are equally studied Moreover the most useful toolto calculate the static responses of these coupled systems isnumerical software such as FLAC3D which can be time-consuming Fortunately various orthogonal experimental

methods were developed to perform the multiparameteranalysis and widely used in parameter optimization formaterial processing hydraulic machines mechanical designand so on To date few literatures have been published onthe parameter optimization of the bolts with orthogonalexperimental methods

Motivated by this the authors tried to develop a unifiedparameter optimization procedure for the coupled bolt-rocksystems by using the orthogonal experimental methodsConvergence of surrounding rock surface and deformationsin the rock are taken as the objective functions e keysupport parameters of the bolt are considered as inputvariables e simulation software FLAC3D is employed todevelop the mechanical model for the coupled bolt-rocksystem and the objective functions of the coupled system aretherefore obtained in the software Combining the varianceand multivariate linear regression analysis an approach isderived to investigate the sensitivity of the support pa-rameters e corresponding support parameters are thenoptimized In order to validate the proposed method and todemonstrate its robust performance a working face of apractical mine in Yangquan is taken as a numerical exampleand a corresponding experiment is carried out

2 Numerical Simulation

21 Numerical Modeling FLAC3D is a powerful tool tocalculate the stress and plastic flow of the soil and rockmaterials erefore FLAC3D is also adopted to establish thesimulation model in this paper as shown in Figure 2

e empty part is utilized to simulate the roadwayDuring the excavation process the Mohr-Coulomb con-stitutive model [20] is employed for the coal and rock asshown in equation (1) e section of the roadway is formedat the same time and the joints and faults in the rockformation are not considered e explicit Lagrangian al-gorithm and hybrid-discrete partitioning technique are usedfor plastic failure and flow of the coal and rock in the model

σ1 qp + Mlowastp

σ3qp

1113888 1113889

a

(1)

(a) (b)

Figure 1 Failure site of bolt and cable support

2 Shock and Vibration

where M is the maximum principal stress N is the minimumprincipal stress M is the unconfined compressive strength ofthe rock measured by triaxial compression experiments

e physical andmechanical parameters of coal and rockmass were obtained by laboratory tests According to [21]the elastic modulus cohesion and tensile strength param-eters of coal and rock mass during the simulation experi-ment were taken as 16 of the laboratory test resultsPoissonrsquos ratio is 125 times of the laboratory test results

As for the supporting parts the cable element is used tosimulate the bolt and cables and the beam element isemployed for the steel belt e connection between thenode and zone at the head of the cable is automaticallyestablished e bolt trays are simulated with rigid chainse free section and the bolting section of the bolts aredistinguished by setting different parameterse pretensionforce is applied to the free section of the bolt (cable) [20]

With regard to the boundary conditions of the modelthe normal displacements of the front back left and rightrock surfaces in the model are restrained e bottom of themodel is fixed for displacements in all three directions

22 Determination of the Compensation Load Since thepractical coal and rocks considered in this paper have infinitelength it is impossible to model the whole part of the coal androcks in FLAC3D and the larger the mechanical model is themore time will be consumed for the calculation Fortunatelywith proper self-weight stress added relatively accurate resultscan be obtained when only a part of the rock mass is con-sidered and this paper is focused on the coupling between thebolt (cable) and rocks (coal) us a finite length model isdeveloped and compensation load for self-weight of the rocksunconsidered in the mechanical model is also introduced[22ndash24] as shown in Figure 3 H is the distance from theground surface to the model surface in the vertical direction

e added self-weight stress σzminusCompensation in the verticaldirection may be expressed in the following equation

σzminusCompensation 1113944n

i1ci times Hi (2)

where ci is the bulk density of each coal rock i 1 2 3 Hi is the thickness of each coal rock layer with total lengthH

In the calculation it is necessary not only to apply the self-weight stress in the vertical direction but also to compensate forthe horizontal and lateral stresses σx and σy According to thegeneralized Hookersquos law [25 26] the corresponding rela-tionship between the self-weight stress in the other two di-rections and the vertical stress can be defined as

εx 1E

σx minus μ σy + σz1113872 11138731113960 1113961 0

εy 1E

σy minus μ σx + σz( 11138571113960 1113961 0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(3)

namely

σx σy μ

1 minus μσzminusCompensation χσzminusCompensation (4)

where χ is the side pressure coefficient of the coal rock layer

3 Orthogonal Experiment Design andParameter Sensitivity Analysis Method

31 Orthogonal Experimental Design According to theexisting research [27] 5 parameters of the bolt haveconsiderable influences on the stability of the surroundingrock of the roadway If the effects of the 5 parameters aretested one by one more than 7000 experimental schemesare required which can be expressive Moreover thesensitivity of the parameters to the objective functionscannot be comprehensively studied e orthogonal ex-periment provides a robust way to select some repre-sentative factors and levels from the comprehensiveexperiments for profound investigations [28ndash30] eserepresentative experiments have the characteristics ofldquouniform dispersion and neat comparisonrdquo [31] whichcan significantly reduce the experiment quantity and thesensitivity of the parameters to the objective functions canalso be obtained

erefore the L16 (45) orthogonal table is employed todesign the orthogonal experiment scheme 4 levels are

σZndashcompensation

Z

Ground surface

Y

X

Hi

σxndashcompensation

σyndashcompensation

Figure 3 Schematic diagram of the experimental modelrsquos self-weight stress and compensation stress

Anchor cable

Coal

Top bolt

Gang anchorRoadway

Rock

ZoneColorby group any

Laodi

CableColorby uniform

Uniform

LaodingMeiWeidingZhijidiZhijieding

Figure 2 Experimental simulation model

Shock and Vibration 3

selected for each parameter of the 5 support parameters ofbolts as shown in Table 1 e surrounding rock form of theroadway supported by bolts is shown in Figure 4

According to the supporting mechanism of bolts andcables to the surrounding rock of the roadway the con-vergence of the roof surface of the mining roadway anddeformations in the rock (2m away from the roadway roof)are taken as the objective functions to be optimized in thedesigned orthogonal experiments

32 Parameter Sensitivity Analysis Method

321 Variance Analysis Method e variance method is amathematical method to distinguish the difference amongthe experimental results caused by the changes of the pa-rameter levels and fluctuation of errors [32]

e sensitivity of the parameter to the evaluation index isjudged by the sum of the squares of the total deviations S2Te sum of squares of deviations caused by each parameter isexpressed as S2j e total sum of squared deviations and thesum of squared deviations of various factors may be ex-panded as

S2T 1113944

n

i1yi minus y( 1113857 1113944

n

iminus1y2i minus

1n

1113944

n

i1yi

⎛⎝ ⎞⎠

2

S2j

r

n1113944

r

i1y2i

⎛⎝ ⎞⎠ minus

1113944

n

i1yi

⎛⎝ ⎞⎠

2

n

y 1n

1113944

n

i1yi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

where n is the number of the experiments r represents thenumber of factors y is the assessment index value y is theaverage evaluation index

en the required degrees of freedom can be obtained asfollows

fT n minus 1

fj r minus 1

fe 1113944 fEmpty column

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(6)

where fT is the degree of freedom of the sum of squares ofthe total deviation fj is the degree of freedom of the sum ofsquared deviations of various factors fe is the degree offreedom of errors

e analysis of variance determines the significant fac-tors through the F test of each factor [20] e criteria forsignificance of each factor are given in Table 2 e F test iscalculated by

Fj S2jfj1113872 1113873

S2efe1113872 1113873

F1minusα fj fΔ1113872 1113873 (7)

where S2e is the sum of squares of errors α is a significantlevel

322 Multiple Linear Regression Analysis Supposing thatthe objective function and the selected parameters for eachexperiment are yi and xij respectively wherei 1 2 3 n j 1 2 3 m and m is the number ofthe selected parameters the relationship between yi and xi

can be defined as [29]

yi δ0 + δ1xi1 + δ2xi2 + middot middot middot + δmxim + κi 1113954yi + κi (8)

where δj is the sensitivity factor of the corresponding factore errors κi are independent from each other and follow theN(0 σ2) distribution

For the case with multiple objective functions yqi con-sidered in this paper and m 5 equation (8) can be ex-panded as

yqi δ0 + δ1xi1 + δ2xi2 + δ3xi3 + δ4xi4 + δ5xi5 + κqi 1113954yqi + κqi

(9)

In order to make sure the error is the smallest accordingto the principle for the extreme value [33] the sensitivityfactors can be obtained by

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi1 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi1 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi1 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi1 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi1 1113944

n

i1yqi minus 1113954yq1113872 1113873xi1

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi2 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi2 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi2 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi2 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi2 1113944

n

i1yqi minus 1113954yq1113872 1113873xi2

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi3 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi3 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi3 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi3 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi3 1113944

n

i1yqi minus 1113954yq1113872 1113873xi3

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi4 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi4 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi4 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi4 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi4 1113944

n

i1yqi minus 1113954yq1113872 1113873xi4

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi5 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi5 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi5 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi5 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi5 1113944

n

i1yqi minus 1113954yq1113872 1113873xi5

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)


Assume that

gjs 1113944n

i1xij minus xj1113872 1113873

xij 1113944n

i1xij minus xj1113872 1113873 xis minus xs( 1113857

gjy 1113944n

i1yqi minus 1113954yq1113872 1113873

xij 1113944

n

i1yqi minus 1113954yq1113872 1113873 xij minus xj1113872 1113873

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)

where j s 1 2 3 4 5Equation (10) can be simplified as

g111113954δ1 + g12

1113954δ2 + g131113954δ3 + g14

1113954δ4 + g151113954δ5 g1yp

g211113954δ1 + g22

1113954δ2 + g231113954δ3 + g24

1113954δ4 + g251113954δ5 g2yp

g311113954δ1 + g32

1113954δ2 + g331113954δ3 + g34

1113954δ4 + g351113954δ5 g3yp

g411113954δ1 + g42

1113954δ2 + g431113954δ3 + g44

1113954δ4 + g451113954δ5 g4yp

g511113954δ1 + g52

1113954δ2 + g531113954δ3 + g54

1113954δ4 + g551113954δ5 g5yp

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)

Combining equations (9) and (12) the multiple re-gression model can be obtained as

1113954yp 1113954δ0 + 1113954δ1x1 + 1113954δ2x2 + 1113954δ3x3 + 1113954δ4x4 + 1113954δ5x5 (13)

4 Analysis of Orthogonal Experiment Results

41 Geological Conditions e orthogonal experimentalmodel is based on the geological parameters of the 15106working face of Wenjiazhuang Coal Mine in YangquanShanxi Province e experimental model shown in Figure 2is established and the experimental analysis is performed inconjunction with the orthogonal experimental schemedesigned

Table 2 Significance of each factor

F value range Category Sensitivity statementFge F 099 I Highly significantF 095le F＜ F 099 II Generally highly significantF 090le F＜ F 095 III Relatively remarkableF＜ F 090 IV Generally significant

Table 1 Orthogonal experiment level design

Influencing factors Number of levels1 2 3 4

A Bolt spacing (mm) 700 800 900 1000B Bolt distance between two rows (mm) 700 800 900 1000C Bolt length (mm) 1800 2000 2200 2400D Horizontal contained angle (deg) 0deg 20deg 40deg 60degE Pretightening force (kN) 60 80 100 120

250 800 800 800 800 800 250 200

1000

1000

800

Reinforced steel belt

Metal net

Coal pillar side

W-steel strip

3000

4500Direction of roadway end face

800Bolt

Metal net

CableCableCable

Bolt Bolt

Bolt

Horizontalcontained angle


Roadway

Roof

Figure 4 Working state and parameter representation of bolt


e overall shape of the 15106 working face of Wen-jiazhuang Coal Mine is a monoclinic structuree elevationof the working face is +6953m～+7632m the coal seamdepth is 4883m～4981m and the strike length is 19483me air inlet roadway air return airway high extractionroadway and roof low extraction roadway are dug on bothsides of the working face

e coal seam of the working face belongs to thelimestone mining area under pressure in the Taiyuan For-mation Mine coal is soft high in gas content and poor ingas permeability Hydrological types are classified as me-dium Coal seam inclination angle is on average 6deg and coal islumpy and powdery Mirror coal is the main followed bybright coal which is a bright briquette e recoverableindex of the coal seam is 1 the coefficient of variation is 9and the coal seam is generally stable

e immediate roof of the No 15 coal seam is thelimestone of K2 and the thickness is 232memain roof issandy mudstone with a thickness of 905m including whitemica flakes e bottom is sandy mudstone with a thicknessof 33m with many sandstone bandse old bottom is fine-grained sandstone with a thickness of 434m includingmany blackminerals and a small number of carbon shavingse width of the roadway of the working face is 45m andthe height is 3m e specific geological parameters for eachlayer are shown in Figure 5

42 Analysis of Variance of Experimental ResultsAccording to the modeling method in Section 21 a me-chanical model for the 15106 working face is developed inFLAC3D as shown in Figure 6 e entire model size isdesigned to be 100m 100m and 37m in the x y and zdirections respectively e mechanical parameters of eachlayer of coal and rock are set according to the geologicalparameters in Figure 5e average coal-rockmass Poissonrsquosratio is 03 and the average bulk density of the rock layer is18 tm3 According to equations (2)sim(4) the verticalcompensation load is 7174 tm3 and the compensationloads in other directions applied in the calculations are 307 tm3

e convergence of surrounding rock surface anddeformation in the rock of the roadway roof aremonitored at 24 different positions in which 12monitoring points are uniformly distributed on thesurrounding rock surface and 12 other monitoringpoints are evenly located in the rock surface 2 mapart from the surrounding rock surface All moni-toring points are at the center-line position of theroadway roof and the distance between two adjacentmonitoring points is 05 m as shown in Figure 7

Table 3 shows the variance analysis of the experimentalresults of the convergence of surrounding rock surface of theroadway roof with different bolt support parameters Basedon the definition of significance of a factor in Table 2 thesignificance of the bolt distance between two rows for theobjective functions is highe bolt preload and bolt spacingare generally highly significant while the bolt length andhorizontal angle are generally significant

Table 4 shows the variance analysis of the experimentalresults for the deformations in the rock of the roadway roofwith various bolt support parameters Based on the defi-nition of significance of a factor in Table 2 the influences ofthe bolt distance between two rows and the bolt preload onthe deformations in the deep rock are generally highlysignificant e effect of bolt length is relatively remarkablewhile the effects of the horizontal angle of the bolts and boltspacing are generally significant

Significant impacts of the support parameters of the boltson the convergence of surrounding rock surface and de-formations in the rock of the roadway roof can be observedIn the process of supporting the surrounding rock of theroadway with bolts bolt distance between two rows the boltspacing and preload force need to be considered

43 Multiple Linear Regression Analysis of ExperimentalResults Using the econometric software EconometricsViews to perform multivariate linear fitting on convergenceof surrounding rock surface and depth of the experimentalroadway to test the established regression model to obtainthe regression coefficient and reliability of the model andthen compare the regression coefficients of the model todetermine the influencing factors and Correlation betweenevaluation indicators Calculate the goodness of fit to de-termine the reliability of the regression model the closer thegoodness of fit is to 1 the higher the reliability of the re-gression model is e regression coefficients and modelreliability indicators of the regression model are shown inTable 5

It can be seen from Table 5 that factor A (bolt spacing)and factor B (bolt distance between two rows) have a positivecorrelation with the convergence of surrounding rocksurface and depth of the roadway roof at is the larger thebolt support row and line space the greater the convergenceof surrounding rock surface and depth of the roadway roofand the smaller the bolt support row and line space thesmaller the convergence of surrounding rock surface anddepth of the roadway roof

Factor C (anchor length) has a negative correlation withthe convergence of surrounding rock surface and depth ofthe roadway roof at is the longer the bolt rod length isthe smaller the convergence of surrounding rock surface anddepth of the roadway roof e shorter the bolt rod lengththe greater the convergence of surrounding rock surface anddepth of the roadway roof

Factor D (horizontal angle of the bolt rod) has a negativecorrelation with the convergence of surrounding rocksurface and depth of the roadway roof e larger thehorizontal angle of the bolt rod the smaller the convergenceof surrounding rock surface and depth of the roadway roofand the smaller the horizontal angle of the bolt rod thegreater the convergence of surrounding rock surface anddepth of the roadway roof

Factor E (bolt preload) is negatively related to theconvergence of surrounding rock surface and depth of theroadway roof that is the greater the bolt preload the smallerthe convergence of surrounding rock surface and depth of


the roadway roof and the smaller the preload the greater theconvergence of surrounding rock surface and depth of theroadway roof

rough the analysis of multiple linear regressionmodels the influence law of various influencing factors on

the evaluation index is obtained e ranking results of theconvergence of surrounding rock surface and depth of theroadway roof are consistent with the analysis results ofvariance which verify the accuracy of the results of thisorthogonal experiment

Stratigraphicunit

Pale

ozoi

c

Carb

onife

rous

Shan

gton

g

Taiy

uan

form

atio

n

Slicethickness

(m)

416 416Fine-

sandstoneIt is mainly composed of quartz and feldspar

and is jointed

628 1044Sandy

mudstoneBrittle flat fracture large sand content sandstone

bands and plant fragments fossils

322 1366 LimestoneK4It is hard the fissures are filled with cakcite veins and the lower

part is muddy

035 1401 Coal seam11

12

K3

13

e coal is fast mainly bright coal and belongs to bright briquette

802 2203Sandy

mudstoneBrittle flat fracture containing pyrite crystals sandstone bands and

plant rhizome fossils

177 2308 Coal seamCoal is lumpy mirror coal is the most important and

light coal is the second 073 (030) and 074

109 2489 Mudstone It is brittle and the fracture is uneven rich in pyrite crystals andfossils of plant rhizomes

246 2735 Limestone Hard pure with fine veins of calcite marine animal fossils

K2

K2under

570 3939 Limestone Hard and pure with fissures and fine veins of calcite

144 2879 Mudstone Brittle flat fracture containing pyrite crystals calcite veins

452 3369 Sandymudstone

It is brittle with uneven fractures containing fossils of plantrhizomes and uneven sand content


Brittle fracture-like containing plant fossils

300 4395Fine-

sandstonee main ingredients are quartz and feldspar containing a small

amount of mica flakes and black minerals

905 5300Sandy

mudstone

Brittle flat fracture sandstone bands a largenumber of plant fragments fossils and white mica

flakes

232 5532 Limestone Sex hard Pure with fine veins of calcie cracks are not developed

15316 5848 Coal seame coal is lumpy with bright coal as the main component and mirror coal

followed by dark coat which is a bright briquette Coal seam structure is 116(03) 170

330 6178Sandy

mudstoneHard flat fracture large sand content a large number of sandstone

bands containing plant rhizome fossils and pyrite crystals

434 6612Fine-

sandstone

It is mainly composed of quartz and feldspar containing white micaflakes dark minerals pyrite crystals and is well rounded calcareous

and parallel layering

202 6814Sandy

mudstoneBrittle flat fracture partly mudstone middle and lower partcontaining aluminum plant fragments fossiles and joints

038 2917 Coal seam Help the handle

Totalthickness

(m)Columnar

1200 Rock name Lithology

Levelmeasure

mentnumber

(m)

Figure 5 Synthesis column map of 15106 working face


Figure 6 Frame system of the test bench and building completion model


LaodiLaodingMeiWeidingZhijidiZhijieding

CableColor by uniform

UniformRoadway roof

Monitoring points

Layout ofroadway roofmonitoring

points05m

Experimentalroadway

Figure 7 Orthogonal experimental model

Table 3 Variance analysis of convergences of surrounding rock surface of the roadway roof

Factor Sum of squared deviations Degrees of freedom F value SaliencyA 169 3 1622 IIB 527 3 5070 IC 015 3 145 IVD 010 3 100 IVE 161 3 1552 II

Table 4 Variance analysis of deformations in the deep rock (with depth of 2m) of the roadway roof

Factor Sum of squared deviations Degrees of freedom F value SaliencyA 010 3 289 IVB 099 3 2764 IIC 022 3 617 IIID 004 3 100 IVE 035 3 969 II


In the process of supporting the surrounding rock of theroadway with bolts the smaller convergence of surroundingrock surface and depth of the roadway roof is the morebeneficial it is erefore by the significance of the influenceof the bolt support parameters on the convergence of sur-rounding rock surface and depth of the roadway roof it canbe determined that the best solution for supporting thesurrounding rock of the roadway by bolts is A1B1C4D4E4(bolt spacing 700mm bolt row spacing 700mm bolt length2400mm bolt horizontal included angle 60deg and boltpreload force 60 kN)

5 Example Analysis and Similar SimulationExperiment Verification

51 Design of Similar Simulation Experiments e three-dimensional similarity simulation experimental platformdesigned by the ldquoKey Laboratory of Mine Subsidence Di-saster Prevention of Liaoning Education Departmentrdquo isemployed to implement the corresponding similar simula-tion experiments e test rig is shown in Figure 6

e test system provides the equipment for the com-pensation loading in all the three directions Based on thegeometric size of the experimental rig the geometric sim-ilarity constant of the similar simulation experiment is takenas 40 1 the bulk density similarity constant is 16 1 thetime similarity constant is

40

radic 1 and the strength similarity

constant is 64 1 [34 35]According to the synthesis column map of the coal seam

15106 in Wenjiazhuang Coal Mine Yangquan Shanxi limeand gypsum as cementing materials and sand as aggregateare used for similar experimental model casting e usageamount of the material for each layer is obtained as

G lm times dm times hm times cm (14)

where G is the total weight of the model layered material lmis the length of the model dm is the model width hm is thethickness of the simulated layer cm is the bulk density of thesimulated rock formation

Moreover an appropriate amount of 45 mesh micapowder is added as natural bedding and 10 mesh micapowder is used as interlayer fractures and joints After themodel is naturally dried the surrounding baffle is removedfor further drying treatment During the drying process anappropriate amount of watering treatment is performedevery 12 hours to prevent the model from cracking due toexternal factors such as temperature changes After 10 daysof maintenance the experimental test work can be carriedout Figure 6 shows the experimental model

In order to simultaneously validate the accuracy of themechanical model and the robust performance of theproposed method to optimize the support parameters twocases with support parameters A1B1C4D4E4 andA2B1C2D3E4 are analyzed with both similar simulationexperiments and numerical simulations e experimentalmodel has two experimental roadways e No 1 experi-mental roadway is used to simulate the A1B1C4D4E4scheme support and the No 2 experimental roadway is usedto simulate the A2B1C2D3E4 scheme support e roadwaylayout is shown in Figure 8

In the similar simulation experiment φ19 fuse is used tosimulate the bolt and φ22 fuse is used for the anchor cablePolyvinyl acetate emulsion is taken as the anchoring agent A10mm times 10mm times 05mm iron sheet metal is employed forthe bolt tray At the same time special pliers are used toapply the preload bolting force of the blots To ensure theaccuracy of the experiment there is a 100m (actual 4m) coalpillar for the practical boundary condition at the front of theworking face As shown in Figure 9(a) there are 32 cables in4 rows and 16 bolts in 2 rows in the roof of the roadway Atotal of 6 rows of 36 simulated bolts are arranged on the leftand right sides as shown in Figure 9(c) As shown inFigure 9(a) 28 displacement sensors are employed in theexperiment to measure the deformation of the roadway roofe miniature round tube self-resetting KSP-25mm dis-placement sensor produced by Shenzhen Milang Tech-nology Co Ltd is taken as the displacement sensor asshown in Figure 9(b) e main technical parameters of thedisplacement sensor are shown in Table 6

e ADAM-4117-AE (a rugged 8-way differential ADinput module) in cooperation with the acquisition programsis employed for acquisition of the displacement signals asshown in Figure 10 e acquisition system can meet therequirements of the real-time online test and the accuracy ofthe test data transmission

In the similar simulation experiment the verticalcompensation load (1791 tm3) and the compensation loadin the other two directions (77 tm3) are applied by using thehydraulic devices as shown in Figure 8

52 Comparison of Experimental Results e experimentalroadway after excavation is shown in Figure 11 Rock col-lapses and bolt fall are observed in the roof of the roadwayhowever the roadway morphology remains stable

e convergence of surrounding rock surface along thetrend of the roadway at the center line of the roof in No 1and No 2 experimental roadways is compared with thesimulation results Since the measured convergences of

Table 5 Regression equation coefficients and reliability tests

Assessment index Constant A B C D E Goodness offit

Residual sum ofsquares

Convergence of surrounding rock surface of theroadway roof 6423 0004 0005 minus103eminus4 minus0003 minus0015 0966 030

Convergence of surrounding rock depth of theroadway roof 3518 0001 0002 minus824eminus5 minus0022 minus0007 0851 026


surrounding rock surface are for the roof of roadway within150mm (corresponding to 6m in practice) both numericalresults and measured results for the roadway within 6malong the roadway direction are taken for comparison andanalysis Using the geometric similarity constant and

strength similarity constant the experimental results areconverted to those for the real-size model e experimentalresults and numerical results are compared in Figure 12

It can be seen from Figure 12 that the numerical resultsfor the A2B1C2D3E4 support scheme have a maximum

Vertical compensationloading system

Loading board

Horizontal compensationloading system

2Experimentalroadway (A2B1C2D3E4)


955mm200mm

540mm

300mm10

00m

m

872

mm

150mm15106 coal seam

Figure 8 Similar experimental model design and experimental roadway layout

150mm

125m

m

100mm 175mm250mm

BoundaryconditionsBack-end

Lane bolt

Top

bolt

Displacementsensor

Top

bolt

cabl

e

(a) (b)

Experimental laneway

Displacement sensor

(c)

Figure 9 Simulated bolts (cables) arrangement and sensor arrangement in the experiments (a) Simulation experiment sensor arrangement(b) e displacement sensor (c) Bolts (cables) layout of simulated experimental roadway


error of 1206 compared with the experimental results andthe numerical results for the A1B1C4D4E4 support schemehave a maximum error of 1233 compared with the ex-perimental results e distributions of the numerical resultsin the roadway trend directions agree well with those of theexperimental results Overall the accuracy and reliability ofthe mechanical simulations in this paper are validated

Moreover it can be seen that the maximum convergenceof surrounding rock surface at the center-line position of theroof for the A1B1C4D4E4 support scheme is reduced by1156mm compared with that for the A2B1C2D3E4 supportscheme e bolt support following the A1B1C4D4E4support scheme can significantly decrease the convergenceof surrounding rock surface and help maintain the stability

of the surrounding rock of the roadway Hence it isdemonstrated that the proposed method can be successfullyemployed to optimize the bolt support parameters

6 Conclusion

is paper focuses on the sensitivity of the convergence ofsurrounding rock surface and deformations in the deep rockof the roadways to the bolt support parameters Mechanicalmodels for the rock-bolt coupled systems are developed andnumerical simulations are performed in FLAC3D e or-thogonal experimental method is used to design the ex-perimental scheme and the numerical results are analyzedby the analysis of variance A multivariate linear regressionanalysis model of the bolt support parameters is establishedand the influences of the key parameters of the bolts arequantified e support parameters of the bolt are thereforeoptimized Finally corresponding simulation experimentsare designed and implemented to validate the proposedmechanical model and optimal method

It is found that the bolt spacing and the bolt distancebetween two rows are positively related to the stability of thesurrounding rock of the roadway roof while the anchorlength the horizontal angle of the bolt and the bolt preloadare in a negative correlation with the stability of the sur-rounding rock of the roadway roof e best solution forsupporting the surrounding rock of the roadway by boltsamong the more than 7000 cases listed in Table 1 is theA1B1C4D4E4 support scheme e maximum error

Table 6 Main technical parameters of KSP-25 displacement sensor

Linear accuracy Sensitivity Workload characteristic Temperature coefficient Repeatability errors (mm)plusmn01 1 ge10mA le15 ppmdegC 001

Figure 10 Experimental data test acquisition system

Some residual anchors

Partial collapse

Figure 11 Roadway morphology after excavation in theexperiments

50

55

60

65

70

75

80

Roof

surfa

ce si

nkag

e (m

m)

1 2 3 4 5 60Roadway trend direction (m)

A2B1C2D3E4 supportscheme simulationresults A2B1C2D3E4 supportscheme experimental results

A1B1C4D4E4 supportscheme simulation results A1B1C4D4E4 supportscheme experimental results

Figure 12 Comparison of experimental results and simulationresults


between the simulated results and experimental results is1233 and the distributions of the deformations obtainedby numerical simulations and experiments agree well witheach other so that the accuracy of the mechanical model isvalidated In addition the convergence of surrounding rocksurface for the optimal support scheme determined by thepresented method decreases by 1156mm compared to thatfor the A2B1C2D3E4 support scheme It is demonstratedthat the proposed optimal framework provides a powerfulway to optimize the support parameters of the bolt

Data Availability

e experimental test data used to support the findings ofthis study are included within the article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the China Postdoctoral ScienceFoundation (no 2020M672089) National Key Research andDevelopment Plan of Ministry of Science and Technology ofthe Peoplersquos Republic of China (2017YFC0804305) and theMajor Science and Technology Innovation Projects inShandong Province (2019SDZY04)

References

[1] S Li and Z Wu Concise Course of Rock Mechanics CoalIndustry Press Beijing China 1997

[2] L Wang M Li and X Wang ldquoStudy on mechanisms andtechnology for bolting and grouting in special soft rockroadways under high stressrdquo Chinese Journal of Rock Me-chanics and Engineering vol 24 no 16 pp 2890ndash2893 2005

[3] J Bai X Wang and M Jia ldquoeory and application ofsupporting in deep soft roadwayrdquo Chinese Journal of Geo-technical Engineering vol 30 no 5 pp 632ndash635 2008

[4] C Tang F Chen X Sun T Ma and Y Du ldquoNumericalanalysis for support mechanism of constant-resistance boltsrdquoChinese Journal of Geotechnical Engineering vol 40 no 12pp 2281ndash2288 2018

[5] C O Hargrave C A James and J C Ralston ldquoInfrastruc-ture-based localisation of automated coal mining equipmentrdquoInternational Journal of Coal Science amp Technology vol 4no 3 pp 252ndash261 2017

[6] H Kang J Wang and J Lin ldquoHigh pretensioned stress andintensive bolting system and its application in deep road-waysrdquo Journal of China Coal Society vol 32 no 12pp 1233ndash1238 2007

[7] P Wang H Jia and P Zheng ldquoSensitivity analysis of burstingliability for different coal-rock combinations based on theirinhomogeneous characteristicsrdquo Geomatics Natural Hazardsand Risk vol 11 no 1 pp 149ndash159 2020

[8] H Xie F Gao and Y Ju ldquoResearch and development of rockmechanics in deep ground engineeringrdquo Chinese Journal ofRock Mechanics and Engineering vol 34 no 11 pp 2161ndash2178 2015

[9] W Yu B Pan F Zhang S Yao and F Liu ldquoDeformationcharacteristics and determination of optimum supporting

time of alteration rock mass in deep minerdquo KSCE Journal ofCivil Engineering vol 23 no 11 pp 4921ndash4932 2019

[10] C Li ldquoA new energy-absorbing bolt for rock support in highstress rock massesrdquo International Journal of Rock Mechanicsand Mining Sciences vol 47 pp 396ndash404 2010

[11] F Charette and M Plouffe ldquoRoofex-results of laboratorytesting of a new concept of yieldable tendonrdquo Deep Miningvol 7 pp 395ndash404 2007

[12] A J Jager ldquoTwo new support units for the control of rockburst damagerdquo in Proceedings of the International Symposiumon Rock Support pp 621ndash631 Sudbury Canada June 1992

[13] R Varden R Lachenicht J Player et al ldquoDevelopment andimplementation of the garford dynamic bolt at the KanownaBelle minerdquo in Proceedings of the 10th Underground Opera-torsrsquo Conference vol 395ndash404 Australian Centre for Geo-mechanics Launceston Australia April 2008

[14] S Gu P Zhou and R Huang ldquoStability analysis of tunnelsupported by bolt-surrounding rock bearing structurerdquo Rockand Soil Mechanics vol 39 no 1 pp 122ndash130 2018

[15] X Wu Y Jiang Z Guan and G Wang ldquoEstimating thesupport effect of energy-absorbing rock bolts based on themechanical work transfer abilityrdquo International Journal ofRock Mechanics and Mining Sciences vol 103 pp 168ndash1782018

[16] A Wang Q Gao L Dai Y Pan J Zhang and J Chen ldquoStaticand dynamic performance of rebar bolts and its adaptabilityunder impact loadingrdquo Journal of China Coal Society vol 43no 11 pp 2999ndash3006 2018

[17] J Zou K Chen and Q Pan ldquoAn improved numerical ap-proach in surrounding rock incorporating rockbolt effec-tiveness and seepage forcerdquo Acta Geotechnica vol 13 no 3pp 707ndash727 2018

[18] G Wang C Liu Y Jiang X Wu and S Wang ldquoRheologicalmodel of DMFC rockbolt and rockmass in a circular tunnelrdquoRock Mechanics and Rock Engineering vol 48 no 6pp 2319ndash2357 2015

[19] S Hu and S Chen ldquoAnalytical solution of dynamic responseof rock bolt under blasting vibrationrdquo Rock and Soil Me-chanics vol 40 no 1 pp 281ndash287 2019

[20] Z Zhong X Li Q Yao M Ju and D Li ldquoOrthogonal ex-perimental research on instability factor of roadway with coal-rock interbred roofrdquo Journal of China University of Mining ampTechnology vol 44 no 2 pp 220ndash226 2015

[21] M Cai M He and D Liu Rock Mechanics and Engineeringpp 69ndash75 Science Press Beijing China 2nd edition 2013

[22] Q BaiMechanism and Control on Mining Induced InfluencesAround Longwall Top Coal Caving Face in Extra Seam withComplex Structures China University of Mining XuzhouChina 2015

[23] S Yang and J Yang Rock Mechanics Machinery IndustryPress Taichung Taiwan 2008

[24] J Li and C Zhou Mine Rock Mechanics Metallurgical In-dustry Press Beijing China 2016

[25] H Liu Mechanics of Materials Higher Education PressBeijing China 2006

[26] W Shen Study on Stress Path Variation of Surrounding Rockand Mechanism of Rock burst in Coal Roadway ExcavationChina University of Mining Xuzhou China 2018

[27] L Cai Study on the Stability of Wall Rock and ControlTechnology on Underground Mining Lanzhou UniversityLanzhou China 2009

[28] T Yu C Liu K Yu and W Wang ldquoExperimental study onlaser heat-assisted grinding quartz glassrdquo Journal of


Northeastern University(Natural Science) vol 40 no 10pp 1467ndash1473 2019

[29] C Zhou T Liu H Zhu G Deng and J Li ldquoTemperatureprediction approach of piezo stacks used in jet valverdquo Optikvol 198 Article ID 163234 2019

[30] R Lin X Diao T Ma S Tang L Chen and D Liu ldquoOp-timized microporous layer for improving polymer exchangemembrane fuel cell performance using orthogonal test de-signrdquo Applied Energy vol 254 Article ID 113714 2019

[31] Y Ge Q Liang G Wang and H Ding Experimental DesignMethod and Design-Expert Software Application Harbin In-stitute of Technology Press 2014

[32] W He W Xue and B Tang Optimization Experiment DesignMethod and Data Analysis Chemical Industry Press HarbinChina 2012

[33] G Pastorelli S Cao I Cigic C Cucci A Elnaggar andM Strlic ldquoDevelopment of dose-response functions for his-toric paper degradation using exposure to natural conditionsand multivariate regressionrdquo Polymer Degradation and Sta-bility vol 168 Article ID 108944 2019

[34] C Liu Study on Fracture Field Evolution of Surrounding Rockand Gas Migration Law in Steeply Inclined Coal Seam withSublevel Mining Xirsquoan University of Science and TechnologyXirsquoan China 2018

[35] Z Lv Research on Mechanism and Instability Control of Coal-Rock Mass Due to Mining Disturbance Near Fault Zone XirsquoanUniversity of Science and Technology Xirsquoan China 2017


is suitable for soft rock roadway support Jager [12] designedan energy-absorbing bolt device Varden et al [13] putforward a new type of bolt support equipment for thegeological conditions of the Kanowna Belle mine and testedits mechanical properties using the Kalgoorlie dynamic testequipment at University of Minnesota in Australia

Based on the elastic theory Gu et al [14] established acoordinated deformation model of surrounding rock andsolids (rock and bolt complex) and proposed a method forevaluating the stability of the surrounding rock Based on theasymmetrical assumption of lane strain Wu et al [15]established the equilibrium equation and compatibilityequation of a bolt-rock system and obtained the analyticalsolution of the coupled model e influences of bolt androck properties on the transmission of the reinforcementeffect in the rock were revealed Wang et al [16] developed astatic-dynamic loading test system e system wasemployed to implement the static tensile tests of equal-strength and non-equal-strength rebar bolts and the dy-namic impact tests with or without prestress Zou et al [17]presented a strategy for excavating circular roadways inbrittle and soft rocks with bolt support and established anevolution equation of the surrounding rocks with boltsupportWang et al [18] adopted the discrete mechanics andfriction coupling (DMFC) to study the spatiotemporalevolution of the mechanical properties of the bolts andsurrounding rocks In their theoretical model the Maxwellmodel was used to describe the surrounding rock and theKelvin model was used to describe the characteristics of thebolt Hu and Chen [19] deduced the vibration properties ofbolts subject to blasting seismic waves

It can be found from the above literature review thatcoupled bolt-rock system is a sophisticated coupled me-chanical system Key parameters of the anchor bolts havesignificant and complex influences on the mechanical be-haviors of the coupled system Numerous example analyseswill be needed if the sensitivities of all the key parameters ofthe bolts are equally studied Moreover the most useful toolto calculate the static responses of these coupled systems isnumerical software such as FLAC3D which can be time-consuming Fortunately various orthogonal experimental

methods were developed to perform the multiparameteranalysis and widely used in parameter optimization formaterial processing hydraulic machines mechanical designand so on To date few literatures have been published onthe parameter optimization of the bolts with orthogonalexperimental methods

Motivated by this the authors tried to develop a unifiedparameter optimization procedure for the coupled bolt-rocksystems by using the orthogonal experimental methodsConvergence of surrounding rock surface and deformationsin the rock are taken as the objective functions e keysupport parameters of the bolt are considered as inputvariables e simulation software FLAC3D is employed todevelop the mechanical model for the coupled bolt-rocksystem and the objective functions of the coupled system aretherefore obtained in the software Combining the varianceand multivariate linear regression analysis an approach isderived to investigate the sensitivity of the support pa-rameters e corresponding support parameters are thenoptimized In order to validate the proposed method and todemonstrate its robust performance a working face of apractical mine in Yangquan is taken as a numerical exampleand a corresponding experiment is carried out

2 Numerical Simulation

21 Numerical Modeling FLAC3D is a powerful tool tocalculate the stress and plastic flow of the soil and rockmaterials erefore FLAC3D is also adopted to establish thesimulation model in this paper as shown in Figure 2

e empty part is utilized to simulate the roadwayDuring the excavation process the Mohr-Coulomb con-stitutive model [20] is employed for the coal and rock asshown in equation (1) e section of the roadway is formedat the same time and the joints and faults in the rockformation are not considered e explicit Lagrangian al-gorithm and hybrid-discrete partitioning technique are usedfor plastic failure and flow of the coal and rock in the model

σ1 qp + Mlowastp

σ3qp

1113888 1113889

a

(1)

(a) (b)

Figure 1 Failure site of bolt and cable support









i1ci times Hi (2)



εx 1E

σx minus μ σy + σz1113872 11138731113960 1113961 0

εy 1E

σy minus μ σx + σz( 11138571113960 1113961 0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(3)

namely

σx σy μ







Z

Ground surface

Y

X

Hi




Anchor cable

Coal

Top bolt

Gang anchorRoadway

Rock


Laodi


Uniform









S2T 1113944

n

i1yi minus y( 1113857 1113944

n

iminus1y2i minus

1n

1113944

n

i1yi

⎛⎝ ⎞⎠

2

S2j

r

n1113944

r

i1y2i

⎛⎝ ⎞⎠ minus

1113944

n

i1yi

⎛⎝ ⎞⎠

2

n

y 1n

1113944

n

i1yi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)



fT n minus 1

fj r minus 1


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(6)



Fj S2jfj1113872 1113873

S2efe1113872 1113873

F1minusα fj fΔ1113872 1113873 (7)








(9)


1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi1 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi1 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi1 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi1 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi1 1113944

n

i1yqi minus 1113954yq1113872 1113873xi1

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi2 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi2 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi2 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi2 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi2 1113944

n

i1yqi minus 1113954yq1113872 1113873xi2

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi3 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi3 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi3 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi3 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi3 1113944

n

i1yqi minus 1113954yq1113872 1113873xi3

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi4 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi4 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi4 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi4 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi4 1113944

n

i1yqi minus 1113954yq1113872 1113873xi4

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi5 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi5 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi5 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi5 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi5 1113944

n

i1yqi minus 1113954yq1113872 1113873xi5

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)


Assume that

gjs 1113944n

i1xij minus xj1113872 1113873

xij 1113944n


gjy 1113944n

i1yqi minus 1113954yq1113872 1113873

xij 1113944

n


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


g111113954δ1 + g12

1113954δ2 + g131113954δ3 + g14

1113954δ4 + g151113954δ5 g1yp

g211113954δ1 + g22

1113954δ2 + g231113954δ3 + g24

1113954δ4 + g251113954δ5 g2yp

g311113954δ1 + g32

1113954δ2 + g331113954δ3 + g34

1113954δ4 + g351113954δ5 g3yp

g411113954δ1 + g42

1113954δ2 + g431113954δ3 + g44

1113954δ4 + g451113954δ5 g4yp

g511113954δ1 + g52

1113954δ2 + g531113954δ3 + g54

1113954δ4 + g551113954δ5 g5yp

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)


1113954yp 1113954δ0 + 1113954δ1x1 + 1113954δ2x2 + 1113954δ3x3 + 1113954δ4x4 + 1113954δ5x5 (13)








250 800 800 800 800 800 250 200

1000

1000

800


Metal net

Coal pillar side

W-steel strip

3000


800Bolt

Metal net

CableCableCable

Bolt Bolt

Bolt



Roadway

Roof




















Stratigraphicunit

Pale

ozoi

c

Carb

onife

rous

Shan

gton

g

Taiy

uan

form

atio

n

Slicethickness

(m)

416 416Fine-


and is jointed

628 1044Sandy




part is muddy


12

K3

13


802 2203Sandy







K2

K2under







300 4395Fine-



905 5300Sandy

mudstone


flakes




330 6178Sandy



434 6612Fine-

sandstone



202 6814Sandy



Totalthickness

(m)Columnar


Levelmeasure

mentnumber

(m)







UniformRoadway roof

Monitoring points


points05m

Experimentalroadway











40























Loading board




955mm200mm

540mm

300mm10

00m

m

872

mm



150mm

125m

m

100mm 175mm250mm


Lane bolt

Top

bolt

Displacementsensor

Top

bolt

cabl

e

(a) (b)


Displacement sensor

(c)






6 Conclusion







Partial collapse


50

55

60

65

70

75

80

Roof

surfa

ce si

nkag

e (m

m)







Data Availability




Acknowledgments


References















































i1ci times Hi (2)



εx 1E

σx minus μ σy + σz1113872 11138731113960 1113961 0

εy 1E

σy minus μ σx + σz( 11138571113960 1113961 0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(3)

namely

σx σy μ







Z

Ground surface

Y

X

Hi




Anchor cable

Coal

Top bolt

Gang anchorRoadway

Rock


Laodi


Uniform









S2T 1113944

n

i1yi minus y( 1113857 1113944

n

iminus1y2i minus

1n

1113944

n

i1yi

⎛⎝ ⎞⎠

2

S2j

r

n1113944

r

i1y2i

⎛⎝ ⎞⎠ minus

1113944

n

i1yi

⎛⎝ ⎞⎠

2

n

y 1n

1113944

n

i1yi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)



fT n minus 1

fj r minus 1


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(6)



Fj S2jfj1113872 1113873

S2efe1113872 1113873

F1minusα fj fΔ1113872 1113873 (7)








(9)


1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi1 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi1 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi1 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi1 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi1 1113944

n

i1yqi minus 1113954yq1113872 1113873xi1

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi2 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi2 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi2 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi2 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi2 1113944

n

i1yqi minus 1113954yq1113872 1113873xi2

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi3 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi3 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi3 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi3 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi3 1113944

n

i1yqi minus 1113954yq1113872 1113873xi3

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi4 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi4 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi4 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi4 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi4 1113944

n

i1yqi minus 1113954yq1113872 1113873xi4

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi5 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi5 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi5 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi5 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi5 1113944

n

i1yqi minus 1113954yq1113872 1113873xi5

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)


Assume that

gjs 1113944n

i1xij minus xj1113872 1113873

xij 1113944n


gjy 1113944n

i1yqi minus 1113954yq1113872 1113873

xij 1113944

n


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


g111113954δ1 + g12

1113954δ2 + g131113954δ3 + g14

1113954δ4 + g151113954δ5 g1yp

g211113954δ1 + g22

1113954δ2 + g231113954δ3 + g24

1113954δ4 + g251113954δ5 g2yp

g311113954δ1 + g32

1113954δ2 + g331113954δ3 + g34

1113954δ4 + g351113954δ5 g3yp

g411113954δ1 + g42

1113954δ2 + g431113954δ3 + g44

1113954δ4 + g451113954δ5 g4yp

g511113954δ1 + g52

1113954δ2 + g531113954δ3 + g54

1113954δ4 + g551113954δ5 g5yp

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)


1113954yp 1113954δ0 + 1113954δ1x1 + 1113954δ2x2 + 1113954δ3x3 + 1113954δ4x4 + 1113954δ5x5 (13)








250 800 800 800 800 800 250 200

1000

1000

800


Metal net

Coal pillar side

W-steel strip

3000


800Bolt

Metal net

CableCableCable

Bolt Bolt

Bolt



Roadway

Roof




















Stratigraphicunit

Pale

ozoi

c

Carb

onife

rous

Shan

gton

g

Taiy

uan

form

atio

n

Slicethickness

(m)

416 416Fine-


and is jointed

628 1044Sandy




part is muddy


12

K3

13


802 2203Sandy







K2

K2under







300 4395Fine-



905 5300Sandy

mudstone


flakes




330 6178Sandy



434 6612Fine-

sandstone



202 6814Sandy



Totalthickness

(m)Columnar


Levelmeasure

mentnumber

(m)







UniformRoadway roof

Monitoring points


points05m

Experimentalroadway











40























Loading board




955mm200mm

540mm

300mm10

00m

m

872

mm



150mm

125m

m

100mm 175mm250mm


Lane bolt

Top

bolt

Displacementsensor

Top

bolt

cabl

e

(a) (b)


Displacement sensor

(c)






6 Conclusion







Partial collapse


50

55

60

65

70

75

80

Roof

surfa

ce si

nkag

e (m

m)







Data Availability




Acknowledgments


References













































S2T 1113944

n

i1yi minus y( 1113857 1113944

n

iminus1y2i minus

1n

1113944

n

i1yi

⎛⎝ ⎞⎠

2

S2j

r

n1113944

r

i1y2i

⎛⎝ ⎞⎠ minus

1113944

n

i1yi

⎛⎝ ⎞⎠

2

n

y 1n

1113944

n

i1yi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)



fT n minus 1

fj r minus 1


⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(6)



Fj S2jfj1113872 1113873

S2efe1113872 1113873

F1minusα fj fΔ1113872 1113873 (7)








(9)


1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi1 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi1 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi1 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi1 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi1 1113944

n

i1yqi minus 1113954yq1113872 1113873xi1

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi2 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi2 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi2 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi2 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi2 1113944

n

i1yqi minus 1113954yq1113872 1113873xi2

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi3 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi3 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi3 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi3 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi3 1113944

n

i1yqi minus 1113954yq1113872 1113873xi3

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi4 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi4 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi4 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi4 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi4 1113944

n

i1yqi minus 1113954yq1113872 1113873xi4

1113954δ1 1113944

n

i1xi1 minus x1( 1113857xi5 + 1113954δ2 1113944

n

i1xi2 minus x2( 1113857xi5 + 1113954δ3 1113944

n

i1xi3 minus x3( 1113857xi5 + 1113954δ4 1113944

n

i1xi4 minus x4( 1113857xi5 + 1113954δ5 1113944

n

i1xi5 minus x5( 1113857xi5 1113944

n

i1yqi minus 1113954yq1113872 1113873xi5

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)


Assume that

gjs 1113944n

i1xij minus xj1113872 1113873

xij 1113944n


gjy 1113944n

i1yqi minus 1113954yq1113872 1113873

xij 1113944

n


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


g111113954δ1 + g12

1113954δ2 + g131113954δ3 + g14

1113954δ4 + g151113954δ5 g1yp

g211113954δ1 + g22

1113954δ2 + g231113954δ3 + g24

1113954δ4 + g251113954δ5 g2yp

g311113954δ1 + g32

1113954δ2 + g331113954δ3 + g34

1113954δ4 + g351113954δ5 g3yp

g411113954δ1 + g42

1113954δ2 + g431113954δ3 + g44

1113954δ4 + g451113954δ5 g4yp

g511113954δ1 + g52

1113954δ2 + g531113954δ3 + g54

1113954δ4 + g551113954δ5 g5yp

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)


1113954yp 1113954δ0 + 1113954δ1x1 + 1113954δ2x2 + 1113954δ3x3 + 1113954δ4x4 + 1113954δ5x5 (13)








250 800 800 800 800 800 250 200

1000

1000

800


Metal net

Coal pillar side

W-steel strip

3000


800Bolt

Metal net

CableCableCable

Bolt Bolt

Bolt



Roadway

Roof




















Stratigraphicunit

Pale

ozoi

c

Carb

onife

rous

Shan

gton

g

Taiy

uan

form

atio

n

Slicethickness

(m)

416 416Fine-


and is jointed

628 1044Sandy




part is muddy


12

K3

13


802 2203Sandy







K2

K2under







300 4395Fine-



905 5300Sandy

mudstone


flakes




330 6178Sandy



434 6612Fine-

sandstone



202 6814Sandy



Totalthickness

(m)Columnar


Levelmeasure

mentnumber

(m)







UniformRoadway roof

Monitoring points


points05m

Experimentalroadway











40























Loading board




955mm200mm

540mm

300mm10

00m

m

872

mm



150mm

125m

m

100mm 175mm250mm


Lane bolt

Top

bolt

Displacementsensor

Top

bolt

cabl

e

(a) (b)


Displacement sensor

(c)






6 Conclusion







Partial collapse


50

55

60

65

70

75

80

Roof

surfa

ce si

nkag

e (m

m)







Data Availability




Acknowledgments


References








































Assume that

gjs 1113944n

i1xij minus xj1113872 1113873

xij 1113944n


gjy 1113944n

i1yqi minus 1113954yq1113872 1113873

xij 1113944

n


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(11)


g111113954δ1 + g12

1113954δ2 + g131113954δ3 + g14

1113954δ4 + g151113954δ5 g1yp

g211113954δ1 + g22

1113954δ2 + g231113954δ3 + g24

1113954δ4 + g251113954δ5 g2yp

g311113954δ1 + g32

1113954δ2 + g331113954δ3 + g34

1113954δ4 + g351113954δ5 g3yp

g411113954δ1 + g42

1113954δ2 + g431113954δ3 + g44

1113954δ4 + g451113954δ5 g4yp

g511113954δ1 + g52

1113954δ2 + g531113954δ3 + g54

1113954δ4 + g551113954δ5 g5yp

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(12)


1113954yp 1113954δ0 + 1113954δ1x1 + 1113954δ2x2 + 1113954δ3x3 + 1113954δ4x4 + 1113954δ5x5 (13)








250 800 800 800 800 800 250 200

1000

1000

800


Metal net

Coal pillar side

W-steel strip

3000


800Bolt

Metal net

CableCableCable

Bolt Bolt

Bolt



Roadway

Roof




















Stratigraphicunit

Pale

ozoi

c

Carb

onife

rous

Shan

gton

g

Taiy

uan

form

atio

n

Slicethickness

(m)

416 416Fine-


and is jointed

628 1044Sandy




part is muddy


12

K3

13


802 2203Sandy







K2

K2under







300 4395Fine-



905 5300Sandy

mudstone


flakes




330 6178Sandy



434 6612Fine-

sandstone



202 6814Sandy



Totalthickness

(m)Columnar


Levelmeasure

mentnumber

(m)







UniformRoadway roof

Monitoring points


points05m

Experimentalroadway











40























Loading board




955mm200mm

540mm

300mm10

00m

m

872

mm



150mm

125m

m

100mm 175mm250mm


Lane bolt

Top

bolt

Displacementsensor

Top

bolt

cabl

e

(a) (b)


Displacement sensor

(c)






6 Conclusion







Partial collapse


50

55

60

65

70

75

80

Roof

surfa

ce si

nkag

e (m

m)







Data Availability




Acknowledgments


References

























































Stratigraphicunit

Pale

ozoi

c

Carb

onife

rous

Shan

gton

g

Taiy

uan

form

atio

n

Slicethickness

(m)

416 416Fine-


and is jointed

628 1044Sandy




part is muddy


12

K3

13


802 2203Sandy







K2

K2under







300 4395Fine-



905 5300Sandy

mudstone


flakes




330 6178Sandy



434 6612Fine-

sandstone



202 6814Sandy



Totalthickness

(m)Columnar


Levelmeasure

mentnumber

(m)







UniformRoadway roof

Monitoring points


points05m

Experimentalroadway











40























Loading board




955mm200mm

540mm

300mm10

00m

m

872

mm



150mm

125m

m

100mm 175mm250mm


Lane bolt

Top

bolt

Displacementsensor

Top

bolt

cabl

e

(a) (b)


Displacement sensor

(c)






6 Conclusion







Partial collapse


50

55

60

65

70

75

80

Roof

surfa

ce si

nkag

e (m

m)







Data Availability




Acknowledgments


References












































UniformRoadway roof

Monitoring points


points05m

Experimentalroadway











40























Loading board




955mm200mm

540mm

300mm10

00m

m

872

mm



150mm

125m

m

100mm 175mm250mm


Lane bolt

Top

bolt

Displacementsensor

Top

bolt

cabl

e

(a) (b)


Displacement sensor

(c)






6 Conclusion







Partial collapse


50

55

60

65

70

75

80

Roof

surfa

ce si

nkag

e (m

m)







Data Availability




Acknowledgments


References












































40























Loading board




955mm200mm

540mm

300mm10

00m

m

872

mm



150mm

125m

m

100mm 175mm250mm


Lane bolt

Top

bolt

Displacementsensor

Top

bolt

cabl

e

(a) (b)


Displacement sensor

(c)






6 Conclusion







Partial collapse


50

55

60

65

70

75

80

Roof

surfa

ce si

nkag

e (m

m)







Data Availability




Acknowledgments


References












































Loading board




955mm200mm

540mm

300mm10

00m

m

872

mm



150mm

125m

m

100mm 175mm250mm


Lane bolt

Top

bolt

Displacementsensor

Top

bolt

cabl

e

(a) (b)


Displacement sensor

(c)






6 Conclusion







Partial collapse


50

55

60

65

70

75

80

Roof

surfa

ce si

nkag

e (m

m)







Data Availability




Acknowledgments


References











































6 Conclusion







Partial collapse


50

55

60

65

70

75

80

Roof

surfa

ce si

nkag

e (m

m)







Data Availability




Acknowledgments


References









































Data Availability




Acknowledgments


References








































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