Research ArticleFinite Element Analysis of Surrounding Rock with a ThermalInsulation Layer in a Deep Mine

Hao Wang and Qianyu Zhou

School of Architecture and Environmental Engineering Shenzhen Polytechnic Shenzhen 518055 China

Correspondence should be addressed to Hao Wang wanghao6755126com

Received 15 June 2020 Accepted 12 August 2020 Published 30 September 2020

Academic Editor Akhil Garg

Copyright copy 2020 Hao Wang and Qianyu Zhou +is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

As the main heat source surrounding rock heat dissipation is a very important factor in the prediction of mine climate conditionsespecially in deep high-temperature mines To reveal the heat control mechanism of surrounding rocks due to the thermalinsulation of deep roadways a mathematical model of the surrounding rocks around deep roadways with heat insulation wasestablished with the finite element method and a corresponding calculation program was developed A series of results weredetermined to show how setting an insulation layer could affect the distribution law of the temperature field within and aroundtunnels+erefore rules of the variation in wall temperature and temperature gradient with thermal conductivity coefficients wereobtained within and around tunnels +e heat release capacity of the surrounding rocks of the roadways is significantly reducedafter introducing a thermal insulation layer into the roadway design under different schemes these design schemes were de-termined by further engineering example analysis It was found that the heat insulation layer design can cool the surroundingrocks of deep mine roadways

1 Introduction

Over the years the number of deep mines has been in-creasing rapidly worldwide According to the relevant datastatistics a large number of mining companies are facingissues related to thermal disasters due to the increase inmining depth [1ndash4] Compared to low-temperature envi-ronments in high-temperature environments the laborproduction rate is greatly reduced and the health of coalminers is greatly endangered [5ndash8] +erefore reasonablecoolingmeasures in coal mines are necessary to prevent deepmine roadways from being destroyed by thermal disasteraccidents

+e thermal convection between the wall rock and theairflow for a high-temperature roadway in a deep mine is avery complicated unsteady-state process and many scholarshave done much research work on it He considered theproblems existing in coal mines and proposed HEMScooling technology for the status characteristics and

countermeasures of cooling in deep mines [9] Krasnoshteinet al presented mathematical relations of heat exchangebetween mine air and rock mass during fire [10] +e rockpressure and virgin rock temperature increase significantlywith increasing mining depth Sasmito et al assessed thethermal management of underground mines by computa-tional fluid dynamics (CFD) and the effects of cooling loadventilation flow rate and original rock temperature onthermal comfort [11] Anderson and Souza proposed amethod that may be considered by ventilation specialists toeffectively implement a thermal management control sys-tem and a case based on a detailed heat management as-sessment conducted for a potash mine in SaskatchewanCanada was introduced [12] Zhang et al used ANSYSsoftware to simulate the velocity and temperature distri-bution of air in a pipe and discussed the insulation effectaccording to the ventilation of the heading face in a deep

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 5021853 11 pageshttpsdoiorg10115520205021853

mine [13] Habibi et al carried out a stratigraphic thermalstudy on an active panel to determine rock properties whenstudying the influence of underground thermal change [14]

+e heat dissipation capacity of the rock surrounding theroadway is very large due to the influence of the mining scaleand the increase in the geothermal gradient [15] Relevantresearch has shown that reducing the heat dissipation rateand the range of temperature disturbance of surroundingrocks can prevent the generation of thermal hazards Un-fortunately neither the mechanism of heat dissipation ofhigh-temperature roadways by insulation layers nor theapplication of cooling technology has been studied in detailRelevant work urgently needs to be performed It was proventhat the finite element method was suitable for solving manythermal problems [16 17] In this paper an experimentalplatform for the heat control mechanism of surroundingrocks is established and the corresponding mathematicalmodel is constructed according to the finite element methodSimultaneously the thermal insulation control mechanismfor the surrounding rocks is also discussed and analyzed indetail from both experimental and simulation aspects Fi-nally the effects of various insulation control measures willbe discussed in conjunction with engineering examples

2 Experimental Section

21 ExperimentRig +e schematic of the experimental rig isshown in Figure 1 which is mainly composed of three partsair temperature control systems similar simulation exper-iment systems and temperature monitoring systems +eairflow temperature control system includes high- and low-temperature airflow test box 1 frequency conversion blower2 air inlet pipe 3 and air return pipe 4 A similar simulationexperiment system includes the main body of roadwaymodel 5 temperature sensor 6 and similar simulationroadway 7 +e temperature monitoring system includessignal transmission line 8 computer 9 and data collector 10

+e aim of the experiment is to analyze the law oftemperature variation inside the similar material of roadwaysurrounding rock +erefore the experimental part ofmeasuring the change in temperature of similar materialsshould be the main part of the surrounding rock experi-mental system of the tunnel Considering all kinds ofinfluencing factors the size of the main body of the roadwaymodel is determined to be 900times 900times 400mm3 and theradius of the tunnel is 50mm +e distance between thetemperature sensors is 25mm as shown in Figure 2 +efresh airflow in the surrounding rock of the tunnel isprovided by the high- and low-temperature airflow test boxas shown in Figure 3

22 Experimental Materials Generally similar simulationmaterials have the characteristics of rapid molding gooduniformity easy access low cost and convenient produc-tion +e similar simulation experiment in this paper in-volves the simulation of the temperature field of thesurrounding rock of a roadway +erefore it is necessary toconsider the thermal conductivity of common rocks in coal

measure strata and the thermal physical properties of ma-terials when selecting similar materials

Table 1 shows that the thermal conductivity of commonrocks in coal-bearing strata is generally approximately 2W(mmiddotdegC) +erefore sandstone powder is selected as a similarmaterial to simulate the rock surrounding the roadway Inthis paper sandstone powder is selected to make similarsurrounding rock materials A thermal conductivity mea-suring instrument and specific heat capacity measuringinstrument are used to measure the thermodynamic pa-rameters of similar materials in the laboratory as shown inFigures 4 and 5

123

5

7

68

4

9

10

Figure 1 Sketch of the experiment rig

R = 50mm

L = 900mm

L =

900m

m

Insulation layer

Surrounding rock

Measuring point

Figure 2 Measuring point arrangement

2 Mathematical Problems in Engineering

In addition the main purpose of this experiment is totest the effect of the thermal insulation layer +erefore thethermal insulation layer is composed of similar materialswith a small thermal conductivity A similar insulation layermaterial is made by mixing gypsum with water in a certainproportion or by foam cement alone Similar materialscommonly used in experiments are shown in Figure 6 Fe2O3powder as a conductive material can adjust the thermalconductivity of similar materials To prepare experimentalmaterials with a thermal conductivity that meets the ex-perimental requirements Fe2O3 powder with differentcontents is used to improve the thermal conductivity ofgypsum +e specimens were prepared by the direct in-corporation method and the water consumption of thegypsum preparation standard consistency was 05 Aftermolding the specimens were cured at room temperature of20degC for 24 hours and then dried in an incubator +en thespecimens were tested after curing for 5 days under theconditions of an environmental humidity of 65 and 85+e proportioning scheme of the gypsum-containing similarmaterials was designed by orthogonal testing +e orthog-onal experiment table L4 (23) was used in the experiment+e factor level and experimental results are shown inTable 2

In this paper a foam cement block with small thermalconductivity is selected as another thermal insulation ma-terial After groups of tests the thermal conductivity of thesimilar surrounding rock made of sandstone powder and thethermal insulation layer made of foam cement block are2233W(mmiddotdegC) and 019W(mmiddotdegC) respectively In addi-tion this paper uses the medium proportion scheme of Test2 to make gypsum similar materials Based on the abovework the experimental scheme for testing the thermalinsulation effect is finally determined +e parameter valuesunder the corresponding experimental scheme are shown inTable 3

23 Experimental Procedure

(1) Using the direct pouring method to layer similaranalog materials the temperature sensors arearranged in the corresponding position and thetemperature sensors and data collector areconnected

(2) One side of the high- and low-temperature testchamber is equipped with two vents and the ven-tilation pipe is connected to the air vent At the sametime the variable frequency blower is installed on thetop of the test chamber

(3) +e temperature probe and the computer are con-nected and the test system software is installed onthe computer to complete the temperature moni-toring system setup

(4) +e test system including the mechanical connec-tions power systems and test systems is checked toensure that it is in good condition after completingthe above system installation

Table 1 Common thermophysical parameters of coal measurestrata

Parameters Shale Mudstone Limestone Unit

Conductivity coefficient 177 226 228 W(mmiddotdegC)

Density 2570 2723 2679 kgm3

Specific heat 0905 0934 0909 kJ(kgmiddotdegC)

Figure 3 High- and low-temperature airflow test box

Figure 4 +ermal conductivity measuring instrument

Figure 5 Specific heat capacity measuring instrument

Mathematical Problems in Engineering 3

(5) +e set parameters are input into the instrumentaccording to the test contents after the high- andlow-temperature test chamber and frequency con-version fan are opened +e experimental data aresaved after the experiment is completed

(6) A new experiment is started after adjusting the ex-perimental scheme

3 Construction of the Finite Element Model

In recent decades numerical simulation methods havebecome an effective way to solve heat transfer problems[18 19] In this paper the finite element method is used toestablish the thermal insulation mathematical model forthe temperature field of roadway surrounding rock +eheat exchange between the wall rock and the airflow isextremely complicated so it is necessary to make someassumptions as follows It is first assumed that the tem-perature field of the surrounding rocks of the roadwaywithout an internal heat source is homogeneous andisotropic +e temperature gradient does not changesignificantly along the axis of the tunnel and the heattransfer conditions are the same +e roadway crosssection is round and the internal temperature of thesurrounding rocks far from the wall face is the virgin rocktemperature +erefore the problem can be simplifiedwithout causing a significant difference in the calculationof the temperature field Based on the above analysis the

heat conduction differential equation and its boundarycondition are established for the surrounding rock tem-perature field according to the conservation of energy andFourierrsquos law

zT

zτ

λρc

z2T

zx2 +

z2T

zy21113888 1113889

Tτ0 Tgu

minusλzT

zr

1113868111386811138681113868111386811138681113868 Γ1 h Tw minus Tf1113872 1113873

TΓ2 Tgu

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

where λ is the heat conductivity coefficient of the sur-rounding rocks W(mmiddotdegC) ρ is the surrounding rock den-sity kgm3 c is the specific heat at constant pressure J(kgmiddotK) Tτ0 is the initial rock temperature degC Tgu is thevirgin rock temperature degC Γ1 is the third boundary con-dition of the wall face Γ2 is the Dirichlet boundary conditionof the surrounding rocks far from the wall face Tw is the wallrock temperature degC and Tf is the airflow temperature degC

+e mathematical description of the above temperaturefield is a partial differential equation and it cannot be solvedby an analytic method +erefore the finite element methodis adopted to solve the above problem If the calculated areaD is divided into E units and n nodes then the distribution of

(a) (b) (c)

Figure 6 Simulation materials (a) Gypsum (b) Sandstone powder (c) Iron oxide

Table 2 Factor level table and test results

Parameters Test 1 Test 2 Test 3 Test 4 UnitHumidity of curing environment 65 65 85 85 Mass fraction of iron powder 06 08 06 08 Test ambient temperature 175 20 20 175 degCConductivity coefficient 0619 0673 0625 0658 W(mmiddotdegC)

Table 3 Experimental scheme

Parameters Symbol Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of surrounding rocks λ1 2233 2233 2233 W(mmiddotdegC)+ermal diffusivity of surrounding rocks a1 1109 1109 1109 10minus6 (m2s)Conductivity coefficient of the insulation layer λ2 2233 0673 019 W(mmiddotdegC)+ermal diffusivity of the insulation layer a2 1109 06669 03619 10minus6 (m2s)

4 Mathematical Problems in Engineering

the surrounding rock temperature can be discretized into theundetermined temperature values of n nodes as shown inFigure 7 +e variational computation can be carried out inthe element so the basic finite element formula can beobtained according to the variational principle

zJe

zTl

Be

λzWl

zx

zT

zx+

zWl

zy

zT

zy1113888 11138891113890

+ ρcWl

zT

zτ1113891dxdy (l i j m)

(2)

where the superscript or subscript e represents the units i jand m are the three vertices of the triangular element andsubscript l denotes the node number

Wl is a weighted function according to the Galerkinmethod

Wl zT

zTl

(l i j m) (3)

According to the calculation formula of the temperatureinterpolation function for the finite element method [20]the following formulas are deduced

zWi

zx

bi

2S

zWi

zy

ci

2S

zT

zx

biTi + bjTj + bmTm1113872 1113873

2S

zT

zy

ciTi + cjTj + cmTm1113872 1113873

2S

zT

zτ Ni

zTi

zτ+ Nj

zTj

zτ+ Nm

zTm

zτ

(4)

Equation (4) is substituted into equation (2) so equation(2) can be written as follows

zJe

zTi

λ4S

b2i + c

2i1113872 1113873Ti + bibj + cicj1113872 1113873Tj + bibm + cicm( 1113857Tm1113960 1113961 + ρc

zTi

zτB

eN

2i dxdy +

zTj

zτB

eNiNjdxdy +

zTm

zτB

eNiNmdxdy1113877

λ4S

b2i + c

2i1113872 1113873Ti + bibj + cicj1113872 1113873Tj + bibm + cicm( 1113857Tm1113960 1113961 +

ρcS

122

zTi

zτ+

zTj

zτ+

zTm

zτ1113888 11138891113890

(5)

In the same way the contribution of each unit to nodes jand m can be deduced

zJe

zTj

λ4S

bibj + cicj1113872 1113873Ti + b2j + c

2j1113872 1113873Tj + bjbm + cjcm1113872 1113873Tm1113960 1113961 +

ρcS

12zTi

zτ+ 2

zTj

zτ+

zTm

zτ1113888 1113889 (6)

zJe

zTm

λ4S

bibm + cicm( 1113857Ti + bjbm + cjcm1113872 1113873Tj + b2m + c

2m1113872 1113873Tm1113960 1113961 +

ρcS

12zTi

zτ+

zTj

zτ+ 2

zTm

zτ1113888 1113889 (7)

1

2 3

4 5 6

7 8

1

2

3

4

5

6

i

jm

ij

m

i j

m i

j

mij

mi

j

mD

Figure 7 Unit partitioning of the computational region

Mathematical Problems in Engineering 5

To program the calculation program equations (5) (6)and (7) are converted into matrix forms to be expressed as

zJe

zTi

zJe

zTj

zJe

zTm

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

kii kij kim

kji kjj kjm

kmi kmj kmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ti

Tj

Tm

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭

+

nii nij nim

nji njj njm

nmi nmj nmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

zTi

zτ

zTj

zτ

zTm

zτ

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where

kll λ4S

b2l + c

2l1113872 1113873

kln knl λ4S

blbn + clcn( 1113857

nll Sρc

6

nln nnl Sρc

12

(l n i j m lne n)

(9)

When the symbol m is the internal node of the com-putational region the boundary nodes of the element arerepresented by the symbols i and j +erefore the contri-bution of the internal triangular element to any node iscalculated using the above method Similarly the contri-bution of each boundary element to the correspondingboundary node is calculated and represented as a matrix asfollows

θi

θj

⎡⎣ ⎤⎦ uii uij

uji ujj

⎡⎣ ⎤⎦Ti

Tj

⎡⎣ ⎤⎦ +vi

vj

⎡⎣ ⎤⎦ (10)

where

uii ujj hS

3

uij uji hS

6

vi vj hSTf

2

(11)

By solving the above equations the temperature valuesof all the nodes in the discrete region can be calculated andthe temperature field can be obtained Taking the ventilationtime of 3 hours of Scheme 1 in Table 1 as an example thetransient temperature contours obtained by the abovemethods are shown in Figure 7

As shown in Figure 8 the temperature of the wall facebegins to decrease after ventilation begins and the tem-perature contours extend outward in the form of concentric

circles+e temperature in the deep surrounding rocks is notaffected by the decrease in the temperature of the wall faceand maintain the virgin temperature

4 Results and Discussion

41 FiniteElementMethodCalculationResults To ensure theaccuracy of the experimental results the change in thetemperature field in three hours is taken as an example +efinite element method is used to calculate the results for thethree schemes in Table 1 and the obtained results are plottedwith Tecplot software for comparative analysis

As shown in Figure 9 the temperature at the wall surfacedecreases sequentially from (a) to (c) +e wall temperaturein Scheme 1 is approximately 135degC while the wall tem-perature in Scheme 3 is reduced to approximately 7degC Inaddition the temperature disturbance range decreases inturn from (a) to (c) +e temperature disturbance range inScheme 1 is approximately 026m while the disturbancerange of temperature in Scheme 3 is reduced to approxi-mately 021m

+ere is no insulation system in Scheme 1 unlike inScheme 2 and Scheme 3 +e results show that the tem-perature of the wall face and the temperature disturbancerange of the surrounding rocks are greatly reduced due tothe effect of the thermal insulation layer

42 Characteristics of the Temperature Distribution in theRoadway To verify the correctness of the finite elementsimulation results the experimental results of the tem-perature field of the surrounding rocks within 01 hours05 hours 1 hour and 3 hours are selected and comparedwith the simulation results as shown in Figures 9(a)ndash10(d)

Figure 10 shows that the general distribution charac-teristics of the temperature field with the heat insulationlayer (Scheme 2 and Scheme 3) are consistent with those ofthe temperature field without the insulation layer (Scheme

T (degC)20195191851817517165161551514514135

Figure 8 Transient temperature contours

6 Mathematical Problems in Engineering

1) +e temperature gradually increases with increasingdistance in the radial direction At the wall face the walltemperature gradually decreases as the conductivity of theinsulation layer decreases Due to the influence of thethermal insulation layer the temperature of the surroundingrocks with the insulation layer is higher than that of thesurrounding rocks without the insulation layer after anintersection of curves when the curve extends to the internaltemperature field of the surrounding rocks In addition theexperimental values are roughly distributed on the curvecalculated by the finite element method and their resultsvalidate each other

43 Variation Law of the Temperature Gradient in the Tem-perature Field As shown in Figure 11 near the wall face thesmaller the conductivity coefficient of the insulation layer isthe larger the temperature gradient is When the curveextends to a certain position inside the surrounding rocksthe smaller the conductivity coefficient of the insulationlayer is the smaller the temperature gradient is

44 Variation Law of the Temperature of the Wall Face withTime As shown in Figure 12 the wall temperature of theroad under the three schemes shows a decreasing trend tovarying degrees after the start of ventilation +e reductionrange of Scheme 1 is the smallest +e reduction range of thewall temperature increases with the decrease in the con-ductivity coefficient of the insulating layer and its reductionrange reaches a maximum under Scheme 3 Similarly therate of change in the curves of each scheme follows the abovelaw that is this rate is the lowest for Scheme 1 and thehighest for Scheme 3 In addition the experimental resultsare basically consistent with the finite element method re-sults and the trends of both curves are consistent

45 Analysis of the 5ermal Insulation Effect for EngineeringExample Applications +e main purpose of analyzing theheat control mechanism of the surrounding rocks with heatinsulation in the roadway is to reduce the heat dissipationcapacity and control the thermal hazard of the surroundingrocks of the deep roadway Here a circular tunnel with a

Distance to the center of the roadway on the X-axis (m)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

20195191851817517165161551514514135

(a)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

2019181716151413121110

(b)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

0452019181716151413121110

T (degC)

987

(c)

Figure 9 +ree-hour cloud chart (a) Scheme 1 (b) Scheme 2 (c) Scheme 3

Mathematical Problems in Engineering 7

radius of 2m is taken as an example to illustrate the heatdissipation law of surrounding rocks +e airflow velocity inthe roadway is 3ms +e excess temperature of the virginrock relative to the airflow temperature is 13degC +e order ofthe structure from the roadway wall is the insulation layerthe concrete layer and the rock stratum +e thermalphysical parameters and calculation scheme of the sur-rounding rocks are shown in Table 4

In this paper the wall temperature of the surroundingrocks of the roadway obtained by the finite elementmethod and the Newton cooling formula is used to cal-culate the thermal dissipation capacity of the surroundingrocks for the insulated roadway +e wall temperaturechanges sharply in the initial heat dissipation stage afterventilation +e heat-dissipating capacity of the

surrounding rocks varies greatly during this unsteadyprocess To improve the calculation accuracy we dividedthe time of the unsteady state process of the temperaturefield into a geometric progression +e whole time is di-vided into n segments and the heat dissipation capacity ofthe surrounding rocks at each time was thus represented asQ1 Q2 Qn +e total time was L and the time of eachperiod was L1 L2 L3

As shown in Figure 13 the thermal dissipation of thesurrounding rocks enters a relatively stable stage after 3 yearsof ventilation +e conductivity coefficient of the insulationlayer decreases successively from Scheme 1 to Scheme 3+eheat dissipation capacity of the surrounding rocks of theroadway is significantly reduced when the heat insulationlayer is as designed in Scheme 3

000 005 010 015 020 025 0306

9

12

15

18

21

Distance to wall surface (m)

Tem

pera

ture

(degC)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(a)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(b)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(c)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(d)

Figure 10 Internal temperature field of surrounding rocks (a) 01H (b) 05H (c) 1H (d) 3H

8 Mathematical Problems in Engineering

005 010 015 020 0250

20

40

60

80

100

120

140

160

Distance to wall surface (m)

Tem

pera

ture

gra

dien

t (degC

middotmndash1

)

Scheme 1

Scheme 2

Scheme 3

Figure 11 Variation law of the temperature gradient

00 05 10 15 20 256

9

12

15

18

21

Tem

pera

ture

(degC)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

Figure 12 Comparison of the variation laws for wall temperature

Table 4 Calculation scheme

Parameters Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of stratum (λ) 264 264 264 W(mmiddotdegC)+ermal diffusivity of stratum (a) 113 113 113 10minus6 (m2s)Conductivity coefficient of the concrete layer (λ) None 151 151 W(mmiddotdegC)+ermal diffusivity of the concrete layer (a) None 07136 07136 10minus6 (m2s)+ickness of concrete layer (L) None 01 01 mConductivity coefficient of insulation layer (λ) 264 076 023 W(mmiddotdegC)+ermal diffusivity of insulation layer (a) 113 04825 04319 10minus6 (m2s)Insulating material None Lime gypsum mortar Coalgangue block + Expanded perlite NoneInsulation layer thickness (L) None 018 018 m

Mathematical Problems in Engineering 9

To accurately calculate the average emission reductionratio under the three schemes we use the weighted averagemethod to calculate the heat dissipation capacity of thesurrounding rocks as shown in

Qm Q1 + Q2( 11138572( 1113857L1 + Q2 + Q3( 11138572( 1113857L2 + middot middot middot + Qn + Qn+1( 11138572( 1113857Ln

L

(12)

Table 5 shows the emission reduction ratios at different timepoints under the two schemes +e designs of Scheme 2 andScheme 3 showed good emission reduction effects+e emissionreduction ratio reaches 8499 in one month of ventilation8761 in one year and 8941 in thirty years when the heatinsulation layer is as designed in Scheme 3 +erefore theconstruction of a heat insulation layer is very effective in re-ducing the heat dissipation capacity of surrounding rocks

5 Conclusions

(1) A mathematical model of surrounding rocks withheat insulation around deep roadways was estab-lished with the finite element method Experimentalresults were used to verify the numerical results andthese results agreed well

(2) +e wall temperature and the disturbance range ofthe temperature of the surrounding rocks are

greatly reduced due to the effect of the thermalinsulation layer Near the wall face the smaller theconductivity coefficient of the insulation layer isthe lower the wall temperature is and the largerthe temperature gradient is Within the sur-rounding rocks far from the wall face the smallerthe conductivity coefficient of the insulation layeris the higher the temperature of the surroundingrocks is and the smaller the temperature gradientis In addition the numerical analysis of thevariation law of the temperature of the wall facewith time shows that the smaller the conductivitycoefficient of the insulation layer is the larger thereduction range of the wall temperature and therate of change in the curves is

(3) +e heat dissipation capacity of the surroundingrocks of the roadway is significantly reduced whenthe heat insulation layer is introduced into the designof the roadway It is explained in detail in this paperthat this heat insulation layer design can cool thesurrounding rock of deep mine roadways

Data Availability

+e data used to support the findings of this study are in-cluded within the article

50 times 104 10 times 105 15 times 105 20 times 105 25 times 105100

101

102

103

104

Diss

ipat

ion

capa

city

(W)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Figure 13 Variation curves of the dissipation capacity of the surrounding rocks with unit length

Table 5 Emission reduction ratio with an insulation layer relative to that with no insulation layer

Time Emission reduction ratio of scheme 2 () Emission reduction ratio of scheme 3 ()1 day 1162 65871 month 5414 84991 year 6095 876110 years 6448 889120 years 6533 892130 years 6589 8941

10 Mathematical Problems in Engineering

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+is work has been financially funded by the Natural ScienceFoundation of China (Grant number 51574249)

Supplementary Materials

+e supplementary material consists of three parts one forrelated data and the other two for related graphics (Sup-plementary Materials)

References

[1] H P Xie H W Zhou D J Xue H W Wang R Zhang andF Gao ldquoResearch and consideration on deep coal mining andcritical mining depthrdquo Journal of China Coal Society vol 37no 4 pp 535ndash542 2012

[2] H Yan F He T Yang L Li S Zhang and J Zhang ldquo+emechanism of bedding separation in roof strata overlying aroadway within a thick coal seam a case study from thePingshuo Coalfield Chinardquo Engineering Failure Analysisvol 62 pp 75ndash92 2016

[3] G E Plessis L Liebenberg and E H Mathews ldquoCase studythe effects of a variable flow energy saving strategy on a deep-mine cooling systemrdquo Applied Energy vol 36 no 1pp 101ndash104 2012

[4] S J Luo X F Wang F Liu L Yan and Y Xie ldquoSome keyproblems and technical countermeasures for deep miningrdquoCoal Technology vol 33 no 11 pp 309ndash311 2014

[5] M Sunkpal P Roghanchi and K C Kocsis ldquoA method toprotect mine workers in hot and humid environmentsrdquo Safetyand Health at Work vol 6 no 11 pp 1ndash10 2017

[6] D J Brake and G P Bates ldquoFluid losses and hydration statusof industrial workers under thermal stress working extendedshiftsrdquo Occupational and Environmental Medicine vol 60no 2 pp 90ndash96 2003

[7] R Pedram K C Kocsis and M Sunkpal ldquoSensitivity analysisof the effect of airflow velocity on the thermal comfort inunderground minesrdquo Journal of Sustainable Mining vol 15no 4 pp 175ndash180 2016

[8] B You C Wu J Li and H Liao ldquoPhysiological responses ofpeople in working faces of deep underground minesrdquo In-ternational Journal of Mining Science and Technology vol 24no 5 pp 683ndash688 2014

[9] M-c He ldquoApplication of HEMS cooling technology in deepmine heat hazard controlrdquo Mining Science and Technology(China) vol 19 no 3 pp 269ndash275 2009

[10] A E Krasnoshtein B P Kazakov and A V ShalimovldquoMathematical modeling of heat exchange between mine airand rock mass during firerdquo Journal of Mining Science vol 42no 3 pp 287ndash295 2006

[11] A P Sasmito J C Kurnia E Birgersson andA S Mujumdar ldquoComputational evaluation of thermalmanagement strategies in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1444ndash1150 2015

[12] R Anderson and E D Souza ldquoHeat stress management inunderground minesrdquo International Journal of Mining Scienceand Technology vol 27 no 4 pp 651ndash655 2017

[13] S P Zhang J Qin and G Chen ldquoHeat transfer analysis ondouble-skin air tube in ventilation of deepmine heading facerdquoProcedia Engineering vol 26 pp 1626ndash1632 2011

[14] A Habibi R B Kramer and A D S Gillies ldquoInvestigating theeffects of heat changes in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1164ndash1171 2015

[15] Y Zhang Z Wan B Gu H Zhang and P Zhou ldquoFinitedifference analysis of transient heat transfer in surroundingrock mass of high geothermal roadwayrdquo MathematicalProblems in Engineering vol 2016 Article ID 89515247 pages 2016

[16] P Duda ldquoFinite element method formulation in polar co-ordinates for transient heat conduction problemsrdquo Journal of5ermal Science vol 25 no 2 pp 188ndash194 2016

[17] J J del Coz Dıaz P J Garcıa Nieto C Betegon Biempica andM B Prendes Gero ldquoAnalysis and optimization of the heat-insulating light concrete hollow brick walls design by the finiteelement methodrdquo Applied5ermal Engineering vol 27 no 8-9 pp 1445ndash1456 2007

[18] C Guo X Nian Y Liu C Qi J Song andW Yu ldquoAnalysis of2D flow and heat transfer modeling in fracture of porousmediardquo Journal of 5ermal Science vol 26 no 4 pp 331ndash3382017

[19] J Kim and H Choi ldquoAn immersed-boundary finite-volumemethod for simulation of heat transfer in complex geome-triesrdquo Ksme International Journal vol 18 no 6pp 1026ndash1035 2004

[20] Q Wu Y P Qin L Guo and Q Y Wu ldquoCalculation of theheat emitting from the wall rock at drifting face with finiteelement methodrdquo China Safety Science Journal vol 12 no 6pp 33ndash36 2002

Mathematical Problems in Engineering 11

In addition the main purpose of this experiment is totest the effect of the thermal insulation layer +erefore thethermal insulation layer is composed of similar materialswith a small thermal conductivity A similar insulation layermaterial is made by mixing gypsum with water in a certainproportion or by foam cement alone Similar materialscommonly used in experiments are shown in Figure 6 Fe2O3powder as a conductive material can adjust the thermalconductivity of similar materials To prepare experimentalmaterials with a thermal conductivity that meets the ex-perimental requirements Fe2O3 powder with differentcontents is used to improve the thermal conductivity ofgypsum +e specimens were prepared by the direct in-corporation method and the water consumption of thegypsum preparation standard consistency was 05 Aftermolding the specimens were cured at room temperature of20degC for 24 hours and then dried in an incubator +en thespecimens were tested after curing for 5 days under theconditions of an environmental humidity of 65 and 85+e proportioning scheme of the gypsum-containing similarmaterials was designed by orthogonal testing +e orthog-onal experiment table L4 (23) was used in the experiment+e factor level and experimental results are shown inTable 2

In this paper a foam cement block with small thermalconductivity is selected as another thermal insulation ma-terial After groups of tests the thermal conductivity of thesimilar surrounding rock made of sandstone powder and thethermal insulation layer made of foam cement block are2233W(mmiddotdegC) and 019W(mmiddotdegC) respectively In addi-tion this paper uses the medium proportion scheme of Test2 to make gypsum similar materials Based on the abovework the experimental scheme for testing the thermalinsulation effect is finally determined +e parameter valuesunder the corresponding experimental scheme are shown inTable 3

23 Experimental Procedure

(1) Using the direct pouring method to layer similaranalog materials the temperature sensors arearranged in the corresponding position and thetemperature sensors and data collector areconnected

(2) One side of the high- and low-temperature testchamber is equipped with two vents and the ven-tilation pipe is connected to the air vent At the sametime the variable frequency blower is installed on thetop of the test chamber

(3) +e temperature probe and the computer are con-nected and the test system software is installed onthe computer to complete the temperature moni-toring system setup

(4) +e test system including the mechanical connec-tions power systems and test systems is checked toensure that it is in good condition after completingthe above system installation

Table 1 Common thermophysical parameters of coal measurestrata

Parameters Shale Mudstone Limestone Unit

Conductivity coefficient 177 226 228 W(mmiddotdegC)

Density 2570 2723 2679 kgm3

Specific heat 0905 0934 0909 kJ(kgmiddotdegC)

Figure 3 High- and low-temperature airflow test box

Figure 4 +ermal conductivity measuring instrument

Figure 5 Specific heat capacity measuring instrument

Mathematical Problems in Engineering 3

(5) +e set parameters are input into the instrumentaccording to the test contents after the high- andlow-temperature test chamber and frequency con-version fan are opened +e experimental data aresaved after the experiment is completed

(6) A new experiment is started after adjusting the ex-perimental scheme

3 Construction of the Finite Element Model

In recent decades numerical simulation methods havebecome an effective way to solve heat transfer problems[18 19] In this paper the finite element method is used toestablish the thermal insulation mathematical model forthe temperature field of roadway surrounding rock +eheat exchange between the wall rock and the airflow isextremely complicated so it is necessary to make someassumptions as follows It is first assumed that the tem-perature field of the surrounding rocks of the roadwaywithout an internal heat source is homogeneous andisotropic +e temperature gradient does not changesignificantly along the axis of the tunnel and the heattransfer conditions are the same +e roadway crosssection is round and the internal temperature of thesurrounding rocks far from the wall face is the virgin rocktemperature +erefore the problem can be simplifiedwithout causing a significant difference in the calculationof the temperature field Based on the above analysis the

heat conduction differential equation and its boundarycondition are established for the surrounding rock tem-perature field according to the conservation of energy andFourierrsquos law

zT

zτ

λρc

z2T

zx2 +

z2T

zy21113888 1113889

Tτ0 Tgu

minusλzT

zr

1113868111386811138681113868111386811138681113868 Γ1 h Tw minus Tf1113872 1113873

TΓ2 Tgu

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

where λ is the heat conductivity coefficient of the sur-rounding rocks W(mmiddotdegC) ρ is the surrounding rock den-sity kgm3 c is the specific heat at constant pressure J(kgmiddotK) Tτ0 is the initial rock temperature degC Tgu is thevirgin rock temperature degC Γ1 is the third boundary con-dition of the wall face Γ2 is the Dirichlet boundary conditionof the surrounding rocks far from the wall face Tw is the wallrock temperature degC and Tf is the airflow temperature degC

+e mathematical description of the above temperaturefield is a partial differential equation and it cannot be solvedby an analytic method +erefore the finite element methodis adopted to solve the above problem If the calculated areaD is divided into E units and n nodes then the distribution of

(a) (b) (c)

Figure 6 Simulation materials (a) Gypsum (b) Sandstone powder (c) Iron oxide

Table 2 Factor level table and test results

Parameters Test 1 Test 2 Test 3 Test 4 UnitHumidity of curing environment 65 65 85 85 Mass fraction of iron powder 06 08 06 08 Test ambient temperature 175 20 20 175 degCConductivity coefficient 0619 0673 0625 0658 W(mmiddotdegC)

Table 3 Experimental scheme

Parameters Symbol Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of surrounding rocks λ1 2233 2233 2233 W(mmiddotdegC)+ermal diffusivity of surrounding rocks a1 1109 1109 1109 10minus6 (m2s)Conductivity coefficient of the insulation layer λ2 2233 0673 019 W(mmiddotdegC)+ermal diffusivity of the insulation layer a2 1109 06669 03619 10minus6 (m2s)

4 Mathematical Problems in Engineering

the surrounding rock temperature can be discretized into theundetermined temperature values of n nodes as shown inFigure 7 +e variational computation can be carried out inthe element so the basic finite element formula can beobtained according to the variational principle

zJe

zTl

Be

λzWl

zx

zT

zx+

zWl

zy

zT

zy1113888 11138891113890

+ ρcWl

zT

zτ1113891dxdy (l i j m)

(2)

where the superscript or subscript e represents the units i jand m are the three vertices of the triangular element andsubscript l denotes the node number

Wl is a weighted function according to the Galerkinmethod

Wl zT

zTl

(l i j m) (3)

According to the calculation formula of the temperatureinterpolation function for the finite element method [20]the following formulas are deduced

zWi

zx

bi

2S

zWi

zy

ci

2S

zT

zx

biTi + bjTj + bmTm1113872 1113873

2S

zT

zy

ciTi + cjTj + cmTm1113872 1113873

2S

zT

zτ Ni

zTi

zτ+ Nj

zTj

zτ+ Nm

zTm

zτ

(4)

Equation (4) is substituted into equation (2) so equation(2) can be written as follows

zJe

zTi

λ4S

b2i + c

2i1113872 1113873Ti + bibj + cicj1113872 1113873Tj + bibm + cicm( 1113857Tm1113960 1113961 + ρc

zTi

zτB

eN

2i dxdy +

zTj

zτB

eNiNjdxdy +

zTm

zτB

eNiNmdxdy1113877

λ4S

b2i + c

2i1113872 1113873Ti + bibj + cicj1113872 1113873Tj + bibm + cicm( 1113857Tm1113960 1113961 +

ρcS

122

zTi

zτ+

zTj

zτ+

zTm

zτ1113888 11138891113890

(5)

In the same way the contribution of each unit to nodes jand m can be deduced

zJe

zTj

λ4S

bibj + cicj1113872 1113873Ti + b2j + c

2j1113872 1113873Tj + bjbm + cjcm1113872 1113873Tm1113960 1113961 +

ρcS

12zTi

zτ+ 2

zTj

zτ+

zTm

zτ1113888 1113889 (6)

zJe

zTm

λ4S

bibm + cicm( 1113857Ti + bjbm + cjcm1113872 1113873Tj + b2m + c

2m1113872 1113873Tm1113960 1113961 +

ρcS

12zTi

zτ+

zTj

zτ+ 2

zTm

zτ1113888 1113889 (7)

1

2 3

4 5 6

7 8

1

2

3

4

5

6

i

jm

ij

m

i j

m i

j

mij

mi

j

mD

Figure 7 Unit partitioning of the computational region

Mathematical Problems in Engineering 5

To program the calculation program equations (5) (6)and (7) are converted into matrix forms to be expressed as

zJe

zTi

zJe

zTj

zJe

zTm

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

kii kij kim

kji kjj kjm

kmi kmj kmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ti

Tj

Tm

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭

+

nii nij nim

nji njj njm

nmi nmj nmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

zTi

zτ

zTj

zτ

zTm

zτ

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where

kll λ4S

b2l + c

2l1113872 1113873

kln knl λ4S

blbn + clcn( 1113857

nll Sρc

6

nln nnl Sρc

12

(l n i j m lne n)

(9)

When the symbol m is the internal node of the com-putational region the boundary nodes of the element arerepresented by the symbols i and j +erefore the contri-bution of the internal triangular element to any node iscalculated using the above method Similarly the contri-bution of each boundary element to the correspondingboundary node is calculated and represented as a matrix asfollows

θi

θj

⎡⎣ ⎤⎦ uii uij

uji ujj

⎡⎣ ⎤⎦Ti

Tj

⎡⎣ ⎤⎦ +vi

vj

⎡⎣ ⎤⎦ (10)

where

uii ujj hS

3

uij uji hS

6

vi vj hSTf

2

(11)

By solving the above equations the temperature valuesof all the nodes in the discrete region can be calculated andthe temperature field can be obtained Taking the ventilationtime of 3 hours of Scheme 1 in Table 1 as an example thetransient temperature contours obtained by the abovemethods are shown in Figure 7

As shown in Figure 8 the temperature of the wall facebegins to decrease after ventilation begins and the tem-perature contours extend outward in the form of concentric

circles+e temperature in the deep surrounding rocks is notaffected by the decrease in the temperature of the wall faceand maintain the virgin temperature

4 Results and Discussion

41 FiniteElementMethodCalculationResults To ensure theaccuracy of the experimental results the change in thetemperature field in three hours is taken as an example +efinite element method is used to calculate the results for thethree schemes in Table 1 and the obtained results are plottedwith Tecplot software for comparative analysis

As shown in Figure 9 the temperature at the wall surfacedecreases sequentially from (a) to (c) +e wall temperaturein Scheme 1 is approximately 135degC while the wall tem-perature in Scheme 3 is reduced to approximately 7degC Inaddition the temperature disturbance range decreases inturn from (a) to (c) +e temperature disturbance range inScheme 1 is approximately 026m while the disturbancerange of temperature in Scheme 3 is reduced to approxi-mately 021m

+ere is no insulation system in Scheme 1 unlike inScheme 2 and Scheme 3 +e results show that the tem-perature of the wall face and the temperature disturbancerange of the surrounding rocks are greatly reduced due tothe effect of the thermal insulation layer

42 Characteristics of the Temperature Distribution in theRoadway To verify the correctness of the finite elementsimulation results the experimental results of the tem-perature field of the surrounding rocks within 01 hours05 hours 1 hour and 3 hours are selected and comparedwith the simulation results as shown in Figures 9(a)ndash10(d)

Figure 10 shows that the general distribution charac-teristics of the temperature field with the heat insulationlayer (Scheme 2 and Scheme 3) are consistent with those ofthe temperature field without the insulation layer (Scheme

T (degC)20195191851817517165161551514514135

Figure 8 Transient temperature contours

6 Mathematical Problems in Engineering

1) +e temperature gradually increases with increasingdistance in the radial direction At the wall face the walltemperature gradually decreases as the conductivity of theinsulation layer decreases Due to the influence of thethermal insulation layer the temperature of the surroundingrocks with the insulation layer is higher than that of thesurrounding rocks without the insulation layer after anintersection of curves when the curve extends to the internaltemperature field of the surrounding rocks In addition theexperimental values are roughly distributed on the curvecalculated by the finite element method and their resultsvalidate each other

43 Variation Law of the Temperature Gradient in the Tem-perature Field As shown in Figure 11 near the wall face thesmaller the conductivity coefficient of the insulation layer isthe larger the temperature gradient is When the curveextends to a certain position inside the surrounding rocksthe smaller the conductivity coefficient of the insulationlayer is the smaller the temperature gradient is

44 Variation Law of the Temperature of the Wall Face withTime As shown in Figure 12 the wall temperature of theroad under the three schemes shows a decreasing trend tovarying degrees after the start of ventilation +e reductionrange of Scheme 1 is the smallest +e reduction range of thewall temperature increases with the decrease in the con-ductivity coefficient of the insulating layer and its reductionrange reaches a maximum under Scheme 3 Similarly therate of change in the curves of each scheme follows the abovelaw that is this rate is the lowest for Scheme 1 and thehighest for Scheme 3 In addition the experimental resultsare basically consistent with the finite element method re-sults and the trends of both curves are consistent

45 Analysis of the 5ermal Insulation Effect for EngineeringExample Applications +e main purpose of analyzing theheat control mechanism of the surrounding rocks with heatinsulation in the roadway is to reduce the heat dissipationcapacity and control the thermal hazard of the surroundingrocks of the deep roadway Here a circular tunnel with a

Distance to the center of the roadway on the X-axis (m)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

20195191851817517165161551514514135

(a)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

2019181716151413121110

(b)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

0452019181716151413121110

T (degC)

987

(c)

Figure 9 +ree-hour cloud chart (a) Scheme 1 (b) Scheme 2 (c) Scheme 3

Mathematical Problems in Engineering 7

radius of 2m is taken as an example to illustrate the heatdissipation law of surrounding rocks +e airflow velocity inthe roadway is 3ms +e excess temperature of the virginrock relative to the airflow temperature is 13degC +e order ofthe structure from the roadway wall is the insulation layerthe concrete layer and the rock stratum +e thermalphysical parameters and calculation scheme of the sur-rounding rocks are shown in Table 4

In this paper the wall temperature of the surroundingrocks of the roadway obtained by the finite elementmethod and the Newton cooling formula is used to cal-culate the thermal dissipation capacity of the surroundingrocks for the insulated roadway +e wall temperaturechanges sharply in the initial heat dissipation stage afterventilation +e heat-dissipating capacity of the

surrounding rocks varies greatly during this unsteadyprocess To improve the calculation accuracy we dividedthe time of the unsteady state process of the temperaturefield into a geometric progression +e whole time is di-vided into n segments and the heat dissipation capacity ofthe surrounding rocks at each time was thus represented asQ1 Q2 Qn +e total time was L and the time of eachperiod was L1 L2 L3

As shown in Figure 13 the thermal dissipation of thesurrounding rocks enters a relatively stable stage after 3 yearsof ventilation +e conductivity coefficient of the insulationlayer decreases successively from Scheme 1 to Scheme 3+eheat dissipation capacity of the surrounding rocks of theroadway is significantly reduced when the heat insulationlayer is as designed in Scheme 3

000 005 010 015 020 025 0306

9

12

15

18

21

Distance to wall surface (m)

Tem

pera

ture

(degC)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(a)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(b)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(c)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(d)

Figure 10 Internal temperature field of surrounding rocks (a) 01H (b) 05H (c) 1H (d) 3H

8 Mathematical Problems in Engineering

005 010 015 020 0250

20

40

60

80

100

120

140

160

Distance to wall surface (m)

Tem

pera

ture

gra

dien

t (degC

middotmndash1

)

Scheme 1

Scheme 2

Scheme 3

Figure 11 Variation law of the temperature gradient

00 05 10 15 20 256

9

12

15

18

21

Tem

pera

ture

(degC)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

Figure 12 Comparison of the variation laws for wall temperature

Table 4 Calculation scheme

Parameters Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of stratum (λ) 264 264 264 W(mmiddotdegC)+ermal diffusivity of stratum (a) 113 113 113 10minus6 (m2s)Conductivity coefficient of the concrete layer (λ) None 151 151 W(mmiddotdegC)+ermal diffusivity of the concrete layer (a) None 07136 07136 10minus6 (m2s)+ickness of concrete layer (L) None 01 01 mConductivity coefficient of insulation layer (λ) 264 076 023 W(mmiddotdegC)+ermal diffusivity of insulation layer (a) 113 04825 04319 10minus6 (m2s)Insulating material None Lime gypsum mortar Coalgangue block + Expanded perlite NoneInsulation layer thickness (L) None 018 018 m

Mathematical Problems in Engineering 9

To accurately calculate the average emission reductionratio under the three schemes we use the weighted averagemethod to calculate the heat dissipation capacity of thesurrounding rocks as shown in

Qm Q1 + Q2( 11138572( 1113857L1 + Q2 + Q3( 11138572( 1113857L2 + middot middot middot + Qn + Qn+1( 11138572( 1113857Ln

L

(12)

Table 5 shows the emission reduction ratios at different timepoints under the two schemes +e designs of Scheme 2 andScheme 3 showed good emission reduction effects+e emissionreduction ratio reaches 8499 in one month of ventilation8761 in one year and 8941 in thirty years when the heatinsulation layer is as designed in Scheme 3 +erefore theconstruction of a heat insulation layer is very effective in re-ducing the heat dissipation capacity of surrounding rocks

5 Conclusions

(1) A mathematical model of surrounding rocks withheat insulation around deep roadways was estab-lished with the finite element method Experimentalresults were used to verify the numerical results andthese results agreed well

(2) +e wall temperature and the disturbance range ofthe temperature of the surrounding rocks are

greatly reduced due to the effect of the thermalinsulation layer Near the wall face the smaller theconductivity coefficient of the insulation layer isthe lower the wall temperature is and the largerthe temperature gradient is Within the sur-rounding rocks far from the wall face the smallerthe conductivity coefficient of the insulation layeris the higher the temperature of the surroundingrocks is and the smaller the temperature gradientis In addition the numerical analysis of thevariation law of the temperature of the wall facewith time shows that the smaller the conductivitycoefficient of the insulation layer is the larger thereduction range of the wall temperature and therate of change in the curves is

(3) +e heat dissipation capacity of the surroundingrocks of the roadway is significantly reduced whenthe heat insulation layer is introduced into the designof the roadway It is explained in detail in this paperthat this heat insulation layer design can cool thesurrounding rock of deep mine roadways

Data Availability

+e data used to support the findings of this study are in-cluded within the article

50 times 104 10 times 105 15 times 105 20 times 105 25 times 105100

101

102

103

104

Diss

ipat

ion

capa

city

(W)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Figure 13 Variation curves of the dissipation capacity of the surrounding rocks with unit length

Table 5 Emission reduction ratio with an insulation layer relative to that with no insulation layer

Time Emission reduction ratio of scheme 2 () Emission reduction ratio of scheme 3 ()1 day 1162 65871 month 5414 84991 year 6095 876110 years 6448 889120 years 6533 892130 years 6589 8941

10 Mathematical Problems in Engineering

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+is work has been financially funded by the Natural ScienceFoundation of China (Grant number 51574249)

Supplementary Materials

+e supplementary material consists of three parts one forrelated data and the other two for related graphics (Sup-plementary Materials)

References

[1] H P Xie H W Zhou D J Xue H W Wang R Zhang andF Gao ldquoResearch and consideration on deep coal mining andcritical mining depthrdquo Journal of China Coal Society vol 37no 4 pp 535ndash542 2012

[2] H Yan F He T Yang L Li S Zhang and J Zhang ldquo+emechanism of bedding separation in roof strata overlying aroadway within a thick coal seam a case study from thePingshuo Coalfield Chinardquo Engineering Failure Analysisvol 62 pp 75ndash92 2016

[3] G E Plessis L Liebenberg and E H Mathews ldquoCase studythe effects of a variable flow energy saving strategy on a deep-mine cooling systemrdquo Applied Energy vol 36 no 1pp 101ndash104 2012

[4] S J Luo X F Wang F Liu L Yan and Y Xie ldquoSome keyproblems and technical countermeasures for deep miningrdquoCoal Technology vol 33 no 11 pp 309ndash311 2014

[5] M Sunkpal P Roghanchi and K C Kocsis ldquoA method toprotect mine workers in hot and humid environmentsrdquo Safetyand Health at Work vol 6 no 11 pp 1ndash10 2017

[6] D J Brake and G P Bates ldquoFluid losses and hydration statusof industrial workers under thermal stress working extendedshiftsrdquo Occupational and Environmental Medicine vol 60no 2 pp 90ndash96 2003

[7] R Pedram K C Kocsis and M Sunkpal ldquoSensitivity analysisof the effect of airflow velocity on the thermal comfort inunderground minesrdquo Journal of Sustainable Mining vol 15no 4 pp 175ndash180 2016

[8] B You C Wu J Li and H Liao ldquoPhysiological responses ofpeople in working faces of deep underground minesrdquo In-ternational Journal of Mining Science and Technology vol 24no 5 pp 683ndash688 2014

[9] M-c He ldquoApplication of HEMS cooling technology in deepmine heat hazard controlrdquo Mining Science and Technology(China) vol 19 no 3 pp 269ndash275 2009

[10] A E Krasnoshtein B P Kazakov and A V ShalimovldquoMathematical modeling of heat exchange between mine airand rock mass during firerdquo Journal of Mining Science vol 42no 3 pp 287ndash295 2006

[11] A P Sasmito J C Kurnia E Birgersson andA S Mujumdar ldquoComputational evaluation of thermalmanagement strategies in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1444ndash1150 2015

[12] R Anderson and E D Souza ldquoHeat stress management inunderground minesrdquo International Journal of Mining Scienceand Technology vol 27 no 4 pp 651ndash655 2017

[13] S P Zhang J Qin and G Chen ldquoHeat transfer analysis ondouble-skin air tube in ventilation of deepmine heading facerdquoProcedia Engineering vol 26 pp 1626ndash1632 2011

[14] A Habibi R B Kramer and A D S Gillies ldquoInvestigating theeffects of heat changes in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1164ndash1171 2015

[15] Y Zhang Z Wan B Gu H Zhang and P Zhou ldquoFinitedifference analysis of transient heat transfer in surroundingrock mass of high geothermal roadwayrdquo MathematicalProblems in Engineering vol 2016 Article ID 89515247 pages 2016

[16] P Duda ldquoFinite element method formulation in polar co-ordinates for transient heat conduction problemsrdquo Journal of5ermal Science vol 25 no 2 pp 188ndash194 2016

[17] J J del Coz Dıaz P J Garcıa Nieto C Betegon Biempica andM B Prendes Gero ldquoAnalysis and optimization of the heat-insulating light concrete hollow brick walls design by the finiteelement methodrdquo Applied5ermal Engineering vol 27 no 8-9 pp 1445ndash1456 2007

[18] C Guo X Nian Y Liu C Qi J Song andW Yu ldquoAnalysis of2D flow and heat transfer modeling in fracture of porousmediardquo Journal of 5ermal Science vol 26 no 4 pp 331ndash3382017

[19] J Kim and H Choi ldquoAn immersed-boundary finite-volumemethod for simulation of heat transfer in complex geome-triesrdquo Ksme International Journal vol 18 no 6pp 1026ndash1035 2004

[20] Q Wu Y P Qin L Guo and Q Y Wu ldquoCalculation of theheat emitting from the wall rock at drifting face with finiteelement methodrdquo China Safety Science Journal vol 12 no 6pp 33ndash36 2002

Mathematical Problems in Engineering 11

(5) +e set parameters are input into the instrumentaccording to the test contents after the high- andlow-temperature test chamber and frequency con-version fan are opened +e experimental data aresaved after the experiment is completed

(6) A new experiment is started after adjusting the ex-perimental scheme

3 Construction of the Finite Element Model

In recent decades numerical simulation methods havebecome an effective way to solve heat transfer problems[18 19] In this paper the finite element method is used toestablish the thermal insulation mathematical model forthe temperature field of roadway surrounding rock +eheat exchange between the wall rock and the airflow isextremely complicated so it is necessary to make someassumptions as follows It is first assumed that the tem-perature field of the surrounding rocks of the roadwaywithout an internal heat source is homogeneous andisotropic +e temperature gradient does not changesignificantly along the axis of the tunnel and the heattransfer conditions are the same +e roadway crosssection is round and the internal temperature of thesurrounding rocks far from the wall face is the virgin rocktemperature +erefore the problem can be simplifiedwithout causing a significant difference in the calculationof the temperature field Based on the above analysis the

heat conduction differential equation and its boundarycondition are established for the surrounding rock tem-perature field according to the conservation of energy andFourierrsquos law

zT

zτ

λρc

z2T

zx2 +

z2T

zy21113888 1113889

Tτ0 Tgu

minusλzT

zr

1113868111386811138681113868111386811138681113868 Γ1 h Tw minus Tf1113872 1113873

TΓ2 Tgu

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

where λ is the heat conductivity coefficient of the sur-rounding rocks W(mmiddotdegC) ρ is the surrounding rock den-sity kgm3 c is the specific heat at constant pressure J(kgmiddotK) Tτ0 is the initial rock temperature degC Tgu is thevirgin rock temperature degC Γ1 is the third boundary con-dition of the wall face Γ2 is the Dirichlet boundary conditionof the surrounding rocks far from the wall face Tw is the wallrock temperature degC and Tf is the airflow temperature degC

+e mathematical description of the above temperaturefield is a partial differential equation and it cannot be solvedby an analytic method +erefore the finite element methodis adopted to solve the above problem If the calculated areaD is divided into E units and n nodes then the distribution of

(a) (b) (c)

Figure 6 Simulation materials (a) Gypsum (b) Sandstone powder (c) Iron oxide

Table 2 Factor level table and test results

Parameters Test 1 Test 2 Test 3 Test 4 UnitHumidity of curing environment 65 65 85 85 Mass fraction of iron powder 06 08 06 08 Test ambient temperature 175 20 20 175 degCConductivity coefficient 0619 0673 0625 0658 W(mmiddotdegC)

Table 3 Experimental scheme

Parameters Symbol Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of surrounding rocks λ1 2233 2233 2233 W(mmiddotdegC)+ermal diffusivity of surrounding rocks a1 1109 1109 1109 10minus6 (m2s)Conductivity coefficient of the insulation layer λ2 2233 0673 019 W(mmiddotdegC)+ermal diffusivity of the insulation layer a2 1109 06669 03619 10minus6 (m2s)

4 Mathematical Problems in Engineering

the surrounding rock temperature can be discretized into theundetermined temperature values of n nodes as shown inFigure 7 +e variational computation can be carried out inthe element so the basic finite element formula can beobtained according to the variational principle

zJe

zTl

Be

λzWl

zx

zT

zx+

zWl

zy

zT

zy1113888 11138891113890

+ ρcWl

zT

zτ1113891dxdy (l i j m)

(2)

where the superscript or subscript e represents the units i jand m are the three vertices of the triangular element andsubscript l denotes the node number

Wl is a weighted function according to the Galerkinmethod

Wl zT

zTl

(l i j m) (3)

According to the calculation formula of the temperatureinterpolation function for the finite element method [20]the following formulas are deduced

zWi

zx

bi

2S

zWi

zy

ci

2S

zT

zx

biTi + bjTj + bmTm1113872 1113873

2S

zT

zy

ciTi + cjTj + cmTm1113872 1113873

2S

zT

zτ Ni

zTi

zτ+ Nj

zTj

zτ+ Nm

zTm

zτ

(4)

Equation (4) is substituted into equation (2) so equation(2) can be written as follows

zJe

zTi

λ4S

b2i + c

2i1113872 1113873Ti + bibj + cicj1113872 1113873Tj + bibm + cicm( 1113857Tm1113960 1113961 + ρc

zTi

zτB

eN

2i dxdy +

zTj

zτB

eNiNjdxdy +

zTm

zτB

eNiNmdxdy1113877

λ4S

b2i + c

2i1113872 1113873Ti + bibj + cicj1113872 1113873Tj + bibm + cicm( 1113857Tm1113960 1113961 +

ρcS

122

zTi

zτ+

zTj

zτ+

zTm

zτ1113888 11138891113890

(5)

In the same way the contribution of each unit to nodes jand m can be deduced

zJe

zTj

λ4S

bibj + cicj1113872 1113873Ti + b2j + c

2j1113872 1113873Tj + bjbm + cjcm1113872 1113873Tm1113960 1113961 +

ρcS

12zTi

zτ+ 2

zTj

zτ+

zTm

zτ1113888 1113889 (6)

zJe

zTm

λ4S

bibm + cicm( 1113857Ti + bjbm + cjcm1113872 1113873Tj + b2m + c

2m1113872 1113873Tm1113960 1113961 +

ρcS

12zTi

zτ+

zTj

zτ+ 2

zTm

zτ1113888 1113889 (7)

1

2 3

4 5 6

7 8

1

2

3

4

5

6

i

jm

ij

m

i j

m i

j

mij

mi

j

mD

Figure 7 Unit partitioning of the computational region

Mathematical Problems in Engineering 5

To program the calculation program equations (5) (6)and (7) are converted into matrix forms to be expressed as

zJe

zTi

zJe

zTj

zJe

zTm

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

kii kij kim

kji kjj kjm

kmi kmj kmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ti

Tj

Tm

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭

+

nii nij nim

nji njj njm

nmi nmj nmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

zTi

zτ

zTj

zτ

zTm

zτ

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where

kll λ4S

b2l + c

2l1113872 1113873

kln knl λ4S

blbn + clcn( 1113857

nll Sρc

6

nln nnl Sρc

12

(l n i j m lne n)

(9)

When the symbol m is the internal node of the com-putational region the boundary nodes of the element arerepresented by the symbols i and j +erefore the contri-bution of the internal triangular element to any node iscalculated using the above method Similarly the contri-bution of each boundary element to the correspondingboundary node is calculated and represented as a matrix asfollows

θi

θj

⎡⎣ ⎤⎦ uii uij

uji ujj

⎡⎣ ⎤⎦Ti

Tj

⎡⎣ ⎤⎦ +vi

vj

⎡⎣ ⎤⎦ (10)

where

uii ujj hS

3

uij uji hS

6

vi vj hSTf

2

(11)

By solving the above equations the temperature valuesof all the nodes in the discrete region can be calculated andthe temperature field can be obtained Taking the ventilationtime of 3 hours of Scheme 1 in Table 1 as an example thetransient temperature contours obtained by the abovemethods are shown in Figure 7

As shown in Figure 8 the temperature of the wall facebegins to decrease after ventilation begins and the tem-perature contours extend outward in the form of concentric

circles+e temperature in the deep surrounding rocks is notaffected by the decrease in the temperature of the wall faceand maintain the virgin temperature

4 Results and Discussion

41 FiniteElementMethodCalculationResults To ensure theaccuracy of the experimental results the change in thetemperature field in three hours is taken as an example +efinite element method is used to calculate the results for thethree schemes in Table 1 and the obtained results are plottedwith Tecplot software for comparative analysis

As shown in Figure 9 the temperature at the wall surfacedecreases sequentially from (a) to (c) +e wall temperaturein Scheme 1 is approximately 135degC while the wall tem-perature in Scheme 3 is reduced to approximately 7degC Inaddition the temperature disturbance range decreases inturn from (a) to (c) +e temperature disturbance range inScheme 1 is approximately 026m while the disturbancerange of temperature in Scheme 3 is reduced to approxi-mately 021m

+ere is no insulation system in Scheme 1 unlike inScheme 2 and Scheme 3 +e results show that the tem-perature of the wall face and the temperature disturbancerange of the surrounding rocks are greatly reduced due tothe effect of the thermal insulation layer

42 Characteristics of the Temperature Distribution in theRoadway To verify the correctness of the finite elementsimulation results the experimental results of the tem-perature field of the surrounding rocks within 01 hours05 hours 1 hour and 3 hours are selected and comparedwith the simulation results as shown in Figures 9(a)ndash10(d)

Figure 10 shows that the general distribution charac-teristics of the temperature field with the heat insulationlayer (Scheme 2 and Scheme 3) are consistent with those ofthe temperature field without the insulation layer (Scheme

T (degC)20195191851817517165161551514514135

Figure 8 Transient temperature contours

6 Mathematical Problems in Engineering

1) +e temperature gradually increases with increasingdistance in the radial direction At the wall face the walltemperature gradually decreases as the conductivity of theinsulation layer decreases Due to the influence of thethermal insulation layer the temperature of the surroundingrocks with the insulation layer is higher than that of thesurrounding rocks without the insulation layer after anintersection of curves when the curve extends to the internaltemperature field of the surrounding rocks In addition theexperimental values are roughly distributed on the curvecalculated by the finite element method and their resultsvalidate each other

43 Variation Law of the Temperature Gradient in the Tem-perature Field As shown in Figure 11 near the wall face thesmaller the conductivity coefficient of the insulation layer isthe larger the temperature gradient is When the curveextends to a certain position inside the surrounding rocksthe smaller the conductivity coefficient of the insulationlayer is the smaller the temperature gradient is

44 Variation Law of the Temperature of the Wall Face withTime As shown in Figure 12 the wall temperature of theroad under the three schemes shows a decreasing trend tovarying degrees after the start of ventilation +e reductionrange of Scheme 1 is the smallest +e reduction range of thewall temperature increases with the decrease in the con-ductivity coefficient of the insulating layer and its reductionrange reaches a maximum under Scheme 3 Similarly therate of change in the curves of each scheme follows the abovelaw that is this rate is the lowest for Scheme 1 and thehighest for Scheme 3 In addition the experimental resultsare basically consistent with the finite element method re-sults and the trends of both curves are consistent

45 Analysis of the 5ermal Insulation Effect for EngineeringExample Applications +e main purpose of analyzing theheat control mechanism of the surrounding rocks with heatinsulation in the roadway is to reduce the heat dissipationcapacity and control the thermal hazard of the surroundingrocks of the deep roadway Here a circular tunnel with a

Distance to the center of the roadway on the X-axis (m)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

20195191851817517165161551514514135

(a)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

2019181716151413121110

(b)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

0452019181716151413121110

T (degC)

987

(c)

Figure 9 +ree-hour cloud chart (a) Scheme 1 (b) Scheme 2 (c) Scheme 3

Mathematical Problems in Engineering 7

radius of 2m is taken as an example to illustrate the heatdissipation law of surrounding rocks +e airflow velocity inthe roadway is 3ms +e excess temperature of the virginrock relative to the airflow temperature is 13degC +e order ofthe structure from the roadway wall is the insulation layerthe concrete layer and the rock stratum +e thermalphysical parameters and calculation scheme of the sur-rounding rocks are shown in Table 4

In this paper the wall temperature of the surroundingrocks of the roadway obtained by the finite elementmethod and the Newton cooling formula is used to cal-culate the thermal dissipation capacity of the surroundingrocks for the insulated roadway +e wall temperaturechanges sharply in the initial heat dissipation stage afterventilation +e heat-dissipating capacity of the

surrounding rocks varies greatly during this unsteadyprocess To improve the calculation accuracy we dividedthe time of the unsteady state process of the temperaturefield into a geometric progression +e whole time is di-vided into n segments and the heat dissipation capacity ofthe surrounding rocks at each time was thus represented asQ1 Q2 Qn +e total time was L and the time of eachperiod was L1 L2 L3

As shown in Figure 13 the thermal dissipation of thesurrounding rocks enters a relatively stable stage after 3 yearsof ventilation +e conductivity coefficient of the insulationlayer decreases successively from Scheme 1 to Scheme 3+eheat dissipation capacity of the surrounding rocks of theroadway is significantly reduced when the heat insulationlayer is as designed in Scheme 3

000 005 010 015 020 025 0306

9

12

15

18

21

Distance to wall surface (m)

Tem

pera

ture

(degC)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(a)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(b)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(c)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(d)

Figure 10 Internal temperature field of surrounding rocks (a) 01H (b) 05H (c) 1H (d) 3H

8 Mathematical Problems in Engineering

005 010 015 020 0250

20

40

60

80

100

120

140

160

Distance to wall surface (m)

Tem

pera

ture

gra

dien

t (degC

middotmndash1

)

Scheme 1

Scheme 2

Scheme 3

Figure 11 Variation law of the temperature gradient

00 05 10 15 20 256

9

12

15

18

21

Tem

pera

ture

(degC)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

Figure 12 Comparison of the variation laws for wall temperature

Table 4 Calculation scheme

Parameters Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of stratum (λ) 264 264 264 W(mmiddotdegC)+ermal diffusivity of stratum (a) 113 113 113 10minus6 (m2s)Conductivity coefficient of the concrete layer (λ) None 151 151 W(mmiddotdegC)+ermal diffusivity of the concrete layer (a) None 07136 07136 10minus6 (m2s)+ickness of concrete layer (L) None 01 01 mConductivity coefficient of insulation layer (λ) 264 076 023 W(mmiddotdegC)+ermal diffusivity of insulation layer (a) 113 04825 04319 10minus6 (m2s)Insulating material None Lime gypsum mortar Coalgangue block + Expanded perlite NoneInsulation layer thickness (L) None 018 018 m

Mathematical Problems in Engineering 9

To accurately calculate the average emission reductionratio under the three schemes we use the weighted averagemethod to calculate the heat dissipation capacity of thesurrounding rocks as shown in

Qm Q1 + Q2( 11138572( 1113857L1 + Q2 + Q3( 11138572( 1113857L2 + middot middot middot + Qn + Qn+1( 11138572( 1113857Ln

L

(12)

Table 5 shows the emission reduction ratios at different timepoints under the two schemes +e designs of Scheme 2 andScheme 3 showed good emission reduction effects+e emissionreduction ratio reaches 8499 in one month of ventilation8761 in one year and 8941 in thirty years when the heatinsulation layer is as designed in Scheme 3 +erefore theconstruction of a heat insulation layer is very effective in re-ducing the heat dissipation capacity of surrounding rocks

5 Conclusions

(1) A mathematical model of surrounding rocks withheat insulation around deep roadways was estab-lished with the finite element method Experimentalresults were used to verify the numerical results andthese results agreed well

(2) +e wall temperature and the disturbance range ofthe temperature of the surrounding rocks are

greatly reduced due to the effect of the thermalinsulation layer Near the wall face the smaller theconductivity coefficient of the insulation layer isthe lower the wall temperature is and the largerthe temperature gradient is Within the sur-rounding rocks far from the wall face the smallerthe conductivity coefficient of the insulation layeris the higher the temperature of the surroundingrocks is and the smaller the temperature gradientis In addition the numerical analysis of thevariation law of the temperature of the wall facewith time shows that the smaller the conductivitycoefficient of the insulation layer is the larger thereduction range of the wall temperature and therate of change in the curves is

(3) +e heat dissipation capacity of the surroundingrocks of the roadway is significantly reduced whenthe heat insulation layer is introduced into the designof the roadway It is explained in detail in this paperthat this heat insulation layer design can cool thesurrounding rock of deep mine roadways

Data Availability

+e data used to support the findings of this study are in-cluded within the article

50 times 104 10 times 105 15 times 105 20 times 105 25 times 105100

101

102

103

104

Diss

ipat

ion

capa

city

(W)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Figure 13 Variation curves of the dissipation capacity of the surrounding rocks with unit length

Table 5 Emission reduction ratio with an insulation layer relative to that with no insulation layer

Time Emission reduction ratio of scheme 2 () Emission reduction ratio of scheme 3 ()1 day 1162 65871 month 5414 84991 year 6095 876110 years 6448 889120 years 6533 892130 years 6589 8941

10 Mathematical Problems in Engineering

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+is work has been financially funded by the Natural ScienceFoundation of China (Grant number 51574249)

Supplementary Materials

+e supplementary material consists of three parts one forrelated data and the other two for related graphics (Sup-plementary Materials)

References

[1] H P Xie H W Zhou D J Xue H W Wang R Zhang andF Gao ldquoResearch and consideration on deep coal mining andcritical mining depthrdquo Journal of China Coal Society vol 37no 4 pp 535ndash542 2012

[2] H Yan F He T Yang L Li S Zhang and J Zhang ldquo+emechanism of bedding separation in roof strata overlying aroadway within a thick coal seam a case study from thePingshuo Coalfield Chinardquo Engineering Failure Analysisvol 62 pp 75ndash92 2016

[3] G E Plessis L Liebenberg and E H Mathews ldquoCase studythe effects of a variable flow energy saving strategy on a deep-mine cooling systemrdquo Applied Energy vol 36 no 1pp 101ndash104 2012

[4] S J Luo X F Wang F Liu L Yan and Y Xie ldquoSome keyproblems and technical countermeasures for deep miningrdquoCoal Technology vol 33 no 11 pp 309ndash311 2014

[5] M Sunkpal P Roghanchi and K C Kocsis ldquoA method toprotect mine workers in hot and humid environmentsrdquo Safetyand Health at Work vol 6 no 11 pp 1ndash10 2017

[6] D J Brake and G P Bates ldquoFluid losses and hydration statusof industrial workers under thermal stress working extendedshiftsrdquo Occupational and Environmental Medicine vol 60no 2 pp 90ndash96 2003

[7] R Pedram K C Kocsis and M Sunkpal ldquoSensitivity analysisof the effect of airflow velocity on the thermal comfort inunderground minesrdquo Journal of Sustainable Mining vol 15no 4 pp 175ndash180 2016

[8] B You C Wu J Li and H Liao ldquoPhysiological responses ofpeople in working faces of deep underground minesrdquo In-ternational Journal of Mining Science and Technology vol 24no 5 pp 683ndash688 2014

[9] M-c He ldquoApplication of HEMS cooling technology in deepmine heat hazard controlrdquo Mining Science and Technology(China) vol 19 no 3 pp 269ndash275 2009

[10] A E Krasnoshtein B P Kazakov and A V ShalimovldquoMathematical modeling of heat exchange between mine airand rock mass during firerdquo Journal of Mining Science vol 42no 3 pp 287ndash295 2006

[11] A P Sasmito J C Kurnia E Birgersson andA S Mujumdar ldquoComputational evaluation of thermalmanagement strategies in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1444ndash1150 2015

[12] R Anderson and E D Souza ldquoHeat stress management inunderground minesrdquo International Journal of Mining Scienceand Technology vol 27 no 4 pp 651ndash655 2017

[13] S P Zhang J Qin and G Chen ldquoHeat transfer analysis ondouble-skin air tube in ventilation of deepmine heading facerdquoProcedia Engineering vol 26 pp 1626ndash1632 2011

[14] A Habibi R B Kramer and A D S Gillies ldquoInvestigating theeffects of heat changes in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1164ndash1171 2015

[15] Y Zhang Z Wan B Gu H Zhang and P Zhou ldquoFinitedifference analysis of transient heat transfer in surroundingrock mass of high geothermal roadwayrdquo MathematicalProblems in Engineering vol 2016 Article ID 89515247 pages 2016

[16] P Duda ldquoFinite element method formulation in polar co-ordinates for transient heat conduction problemsrdquo Journal of5ermal Science vol 25 no 2 pp 188ndash194 2016

[17] J J del Coz Dıaz P J Garcıa Nieto C Betegon Biempica andM B Prendes Gero ldquoAnalysis and optimization of the heat-insulating light concrete hollow brick walls design by the finiteelement methodrdquo Applied5ermal Engineering vol 27 no 8-9 pp 1445ndash1456 2007

[18] C Guo X Nian Y Liu C Qi J Song andW Yu ldquoAnalysis of2D flow and heat transfer modeling in fracture of porousmediardquo Journal of 5ermal Science vol 26 no 4 pp 331ndash3382017

[19] J Kim and H Choi ldquoAn immersed-boundary finite-volumemethod for simulation of heat transfer in complex geome-triesrdquo Ksme International Journal vol 18 no 6pp 1026ndash1035 2004

[20] Q Wu Y P Qin L Guo and Q Y Wu ldquoCalculation of theheat emitting from the wall rock at drifting face with finiteelement methodrdquo China Safety Science Journal vol 12 no 6pp 33ndash36 2002

Mathematical Problems in Engineering 11

the surrounding rock temperature can be discretized into theundetermined temperature values of n nodes as shown inFigure 7 +e variational computation can be carried out inthe element so the basic finite element formula can beobtained according to the variational principle

zJe

zTl

Be

λzWl

zx

zT

zx+

zWl

zy

zT

zy1113888 11138891113890

+ ρcWl

zT

zτ1113891dxdy (l i j m)

(2)

where the superscript or subscript e represents the units i jand m are the three vertices of the triangular element andsubscript l denotes the node number

Wl is a weighted function according to the Galerkinmethod

Wl zT

zTl

(l i j m) (3)

According to the calculation formula of the temperatureinterpolation function for the finite element method [20]the following formulas are deduced

zWi

zx

bi

2S

zWi

zy

ci

2S

zT

zx

biTi + bjTj + bmTm1113872 1113873

2S

zT

zy

ciTi + cjTj + cmTm1113872 1113873

2S

zT

zτ Ni

zTi

zτ+ Nj

zTj

zτ+ Nm

zTm

zτ

(4)

Equation (4) is substituted into equation (2) so equation(2) can be written as follows

zJe

zTi

λ4S

b2i + c

2i1113872 1113873Ti + bibj + cicj1113872 1113873Tj + bibm + cicm( 1113857Tm1113960 1113961 + ρc

zTi

zτB

eN

2i dxdy +

zTj

zτB

eNiNjdxdy +

zTm

zτB

eNiNmdxdy1113877

λ4S

b2i + c

2i1113872 1113873Ti + bibj + cicj1113872 1113873Tj + bibm + cicm( 1113857Tm1113960 1113961 +

ρcS

122

zTi

zτ+

zTj

zτ+

zTm

zτ1113888 11138891113890

(5)

In the same way the contribution of each unit to nodes jand m can be deduced

zJe

zTj

λ4S

bibj + cicj1113872 1113873Ti + b2j + c

2j1113872 1113873Tj + bjbm + cjcm1113872 1113873Tm1113960 1113961 +

ρcS

12zTi

zτ+ 2

zTj

zτ+

zTm

zτ1113888 1113889 (6)

zJe

zTm

λ4S

bibm + cicm( 1113857Ti + bjbm + cjcm1113872 1113873Tj + b2m + c

2m1113872 1113873Tm1113960 1113961 +

ρcS

12zTi

zτ+

zTj

zτ+ 2

zTm

zτ1113888 1113889 (7)

1

2 3

4 5 6

7 8

1

2

3

4

5

6

i

jm

ij

m

i j

m i

j

mij

mi

j

mD

Figure 7 Unit partitioning of the computational region

Mathematical Problems in Engineering 5

To program the calculation program equations (5) (6)and (7) are converted into matrix forms to be expressed as

zJe

zTi

zJe

zTj

zJe

zTm

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

kii kij kim

kji kjj kjm

kmi kmj kmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ti

Tj

Tm

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭

+

nii nij nim

nji njj njm

nmi nmj nmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

zTi

zτ

zTj

zτ

zTm

zτ

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where

kll λ4S

b2l + c

2l1113872 1113873

kln knl λ4S

blbn + clcn( 1113857

nll Sρc

6

nln nnl Sρc

12

(l n i j m lne n)

(9)

When the symbol m is the internal node of the com-putational region the boundary nodes of the element arerepresented by the symbols i and j +erefore the contri-bution of the internal triangular element to any node iscalculated using the above method Similarly the contri-bution of each boundary element to the correspondingboundary node is calculated and represented as a matrix asfollows

θi

θj

⎡⎣ ⎤⎦ uii uij

uji ujj

⎡⎣ ⎤⎦Ti

Tj

⎡⎣ ⎤⎦ +vi

vj

⎡⎣ ⎤⎦ (10)

where

uii ujj hS

3

uij uji hS

6

vi vj hSTf

2

(11)

By solving the above equations the temperature valuesof all the nodes in the discrete region can be calculated andthe temperature field can be obtained Taking the ventilationtime of 3 hours of Scheme 1 in Table 1 as an example thetransient temperature contours obtained by the abovemethods are shown in Figure 7

As shown in Figure 8 the temperature of the wall facebegins to decrease after ventilation begins and the tem-perature contours extend outward in the form of concentric

circles+e temperature in the deep surrounding rocks is notaffected by the decrease in the temperature of the wall faceand maintain the virgin temperature

4 Results and Discussion

41 FiniteElementMethodCalculationResults To ensure theaccuracy of the experimental results the change in thetemperature field in three hours is taken as an example +efinite element method is used to calculate the results for thethree schemes in Table 1 and the obtained results are plottedwith Tecplot software for comparative analysis

As shown in Figure 9 the temperature at the wall surfacedecreases sequentially from (a) to (c) +e wall temperaturein Scheme 1 is approximately 135degC while the wall tem-perature in Scheme 3 is reduced to approximately 7degC Inaddition the temperature disturbance range decreases inturn from (a) to (c) +e temperature disturbance range inScheme 1 is approximately 026m while the disturbancerange of temperature in Scheme 3 is reduced to approxi-mately 021m

+ere is no insulation system in Scheme 1 unlike inScheme 2 and Scheme 3 +e results show that the tem-perature of the wall face and the temperature disturbancerange of the surrounding rocks are greatly reduced due tothe effect of the thermal insulation layer

42 Characteristics of the Temperature Distribution in theRoadway To verify the correctness of the finite elementsimulation results the experimental results of the tem-perature field of the surrounding rocks within 01 hours05 hours 1 hour and 3 hours are selected and comparedwith the simulation results as shown in Figures 9(a)ndash10(d)

Figure 10 shows that the general distribution charac-teristics of the temperature field with the heat insulationlayer (Scheme 2 and Scheme 3) are consistent with those ofthe temperature field without the insulation layer (Scheme

T (degC)20195191851817517165161551514514135

Figure 8 Transient temperature contours

6 Mathematical Problems in Engineering

1) +e temperature gradually increases with increasingdistance in the radial direction At the wall face the walltemperature gradually decreases as the conductivity of theinsulation layer decreases Due to the influence of thethermal insulation layer the temperature of the surroundingrocks with the insulation layer is higher than that of thesurrounding rocks without the insulation layer after anintersection of curves when the curve extends to the internaltemperature field of the surrounding rocks In addition theexperimental values are roughly distributed on the curvecalculated by the finite element method and their resultsvalidate each other

43 Variation Law of the Temperature Gradient in the Tem-perature Field As shown in Figure 11 near the wall face thesmaller the conductivity coefficient of the insulation layer isthe larger the temperature gradient is When the curveextends to a certain position inside the surrounding rocksthe smaller the conductivity coefficient of the insulationlayer is the smaller the temperature gradient is

44 Variation Law of the Temperature of the Wall Face withTime As shown in Figure 12 the wall temperature of theroad under the three schemes shows a decreasing trend tovarying degrees after the start of ventilation +e reductionrange of Scheme 1 is the smallest +e reduction range of thewall temperature increases with the decrease in the con-ductivity coefficient of the insulating layer and its reductionrange reaches a maximum under Scheme 3 Similarly therate of change in the curves of each scheme follows the abovelaw that is this rate is the lowest for Scheme 1 and thehighest for Scheme 3 In addition the experimental resultsare basically consistent with the finite element method re-sults and the trends of both curves are consistent

45 Analysis of the 5ermal Insulation Effect for EngineeringExample Applications +e main purpose of analyzing theheat control mechanism of the surrounding rocks with heatinsulation in the roadway is to reduce the heat dissipationcapacity and control the thermal hazard of the surroundingrocks of the deep roadway Here a circular tunnel with a

Distance to the center of the roadway on the X-axis (m)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

20195191851817517165161551514514135

(a)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

2019181716151413121110

(b)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

0452019181716151413121110

T (degC)

987

(c)

Figure 9 +ree-hour cloud chart (a) Scheme 1 (b) Scheme 2 (c) Scheme 3

Mathematical Problems in Engineering 7

radius of 2m is taken as an example to illustrate the heatdissipation law of surrounding rocks +e airflow velocity inthe roadway is 3ms +e excess temperature of the virginrock relative to the airflow temperature is 13degC +e order ofthe structure from the roadway wall is the insulation layerthe concrete layer and the rock stratum +e thermalphysical parameters and calculation scheme of the sur-rounding rocks are shown in Table 4

In this paper the wall temperature of the surroundingrocks of the roadway obtained by the finite elementmethod and the Newton cooling formula is used to cal-culate the thermal dissipation capacity of the surroundingrocks for the insulated roadway +e wall temperaturechanges sharply in the initial heat dissipation stage afterventilation +e heat-dissipating capacity of the

surrounding rocks varies greatly during this unsteadyprocess To improve the calculation accuracy we dividedthe time of the unsteady state process of the temperaturefield into a geometric progression +e whole time is di-vided into n segments and the heat dissipation capacity ofthe surrounding rocks at each time was thus represented asQ1 Q2 Qn +e total time was L and the time of eachperiod was L1 L2 L3

As shown in Figure 13 the thermal dissipation of thesurrounding rocks enters a relatively stable stage after 3 yearsof ventilation +e conductivity coefficient of the insulationlayer decreases successively from Scheme 1 to Scheme 3+eheat dissipation capacity of the surrounding rocks of theroadway is significantly reduced when the heat insulationlayer is as designed in Scheme 3

000 005 010 015 020 025 0306

9

12

15

18

21

Distance to wall surface (m)

Tem

pera

ture

(degC)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(a)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(b)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(c)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(d)

Figure 10 Internal temperature field of surrounding rocks (a) 01H (b) 05H (c) 1H (d) 3H

8 Mathematical Problems in Engineering

005 010 015 020 0250

20

40

60

80

100

120

140

160

Distance to wall surface (m)

Tem

pera

ture

gra

dien

t (degC

middotmndash1

)

Scheme 1

Scheme 2

Scheme 3

Figure 11 Variation law of the temperature gradient

00 05 10 15 20 256

9

12

15

18

21

Tem

pera

ture

(degC)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

Figure 12 Comparison of the variation laws for wall temperature

Table 4 Calculation scheme

Parameters Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of stratum (λ) 264 264 264 W(mmiddotdegC)+ermal diffusivity of stratum (a) 113 113 113 10minus6 (m2s)Conductivity coefficient of the concrete layer (λ) None 151 151 W(mmiddotdegC)+ermal diffusivity of the concrete layer (a) None 07136 07136 10minus6 (m2s)+ickness of concrete layer (L) None 01 01 mConductivity coefficient of insulation layer (λ) 264 076 023 W(mmiddotdegC)+ermal diffusivity of insulation layer (a) 113 04825 04319 10minus6 (m2s)Insulating material None Lime gypsum mortar Coalgangue block + Expanded perlite NoneInsulation layer thickness (L) None 018 018 m

Mathematical Problems in Engineering 9

To accurately calculate the average emission reductionratio under the three schemes we use the weighted averagemethod to calculate the heat dissipation capacity of thesurrounding rocks as shown in

Qm Q1 + Q2( 11138572( 1113857L1 + Q2 + Q3( 11138572( 1113857L2 + middot middot middot + Qn + Qn+1( 11138572( 1113857Ln

L

(12)

Table 5 shows the emission reduction ratios at different timepoints under the two schemes +e designs of Scheme 2 andScheme 3 showed good emission reduction effects+e emissionreduction ratio reaches 8499 in one month of ventilation8761 in one year and 8941 in thirty years when the heatinsulation layer is as designed in Scheme 3 +erefore theconstruction of a heat insulation layer is very effective in re-ducing the heat dissipation capacity of surrounding rocks

5 Conclusions

(1) A mathematical model of surrounding rocks withheat insulation around deep roadways was estab-lished with the finite element method Experimentalresults were used to verify the numerical results andthese results agreed well

(2) +e wall temperature and the disturbance range ofthe temperature of the surrounding rocks are

greatly reduced due to the effect of the thermalinsulation layer Near the wall face the smaller theconductivity coefficient of the insulation layer isthe lower the wall temperature is and the largerthe temperature gradient is Within the sur-rounding rocks far from the wall face the smallerthe conductivity coefficient of the insulation layeris the higher the temperature of the surroundingrocks is and the smaller the temperature gradientis In addition the numerical analysis of thevariation law of the temperature of the wall facewith time shows that the smaller the conductivitycoefficient of the insulation layer is the larger thereduction range of the wall temperature and therate of change in the curves is

(3) +e heat dissipation capacity of the surroundingrocks of the roadway is significantly reduced whenthe heat insulation layer is introduced into the designof the roadway It is explained in detail in this paperthat this heat insulation layer design can cool thesurrounding rock of deep mine roadways

Data Availability

+e data used to support the findings of this study are in-cluded within the article

50 times 104 10 times 105 15 times 105 20 times 105 25 times 105100

101

102

103

104

Diss

ipat

ion

capa

city

(W)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Figure 13 Variation curves of the dissipation capacity of the surrounding rocks with unit length

Table 5 Emission reduction ratio with an insulation layer relative to that with no insulation layer

Time Emission reduction ratio of scheme 2 () Emission reduction ratio of scheme 3 ()1 day 1162 65871 month 5414 84991 year 6095 876110 years 6448 889120 years 6533 892130 years 6589 8941

10 Mathematical Problems in Engineering

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+is work has been financially funded by the Natural ScienceFoundation of China (Grant number 51574249)

Supplementary Materials

+e supplementary material consists of three parts one forrelated data and the other two for related graphics (Sup-plementary Materials)

References

[1] H P Xie H W Zhou D J Xue H W Wang R Zhang andF Gao ldquoResearch and consideration on deep coal mining andcritical mining depthrdquo Journal of China Coal Society vol 37no 4 pp 535ndash542 2012

[2] H Yan F He T Yang L Li S Zhang and J Zhang ldquo+emechanism of bedding separation in roof strata overlying aroadway within a thick coal seam a case study from thePingshuo Coalfield Chinardquo Engineering Failure Analysisvol 62 pp 75ndash92 2016

[3] G E Plessis L Liebenberg and E H Mathews ldquoCase studythe effects of a variable flow energy saving strategy on a deep-mine cooling systemrdquo Applied Energy vol 36 no 1pp 101ndash104 2012

[4] S J Luo X F Wang F Liu L Yan and Y Xie ldquoSome keyproblems and technical countermeasures for deep miningrdquoCoal Technology vol 33 no 11 pp 309ndash311 2014

[5] M Sunkpal P Roghanchi and K C Kocsis ldquoA method toprotect mine workers in hot and humid environmentsrdquo Safetyand Health at Work vol 6 no 11 pp 1ndash10 2017

[6] D J Brake and G P Bates ldquoFluid losses and hydration statusof industrial workers under thermal stress working extendedshiftsrdquo Occupational and Environmental Medicine vol 60no 2 pp 90ndash96 2003

[7] R Pedram K C Kocsis and M Sunkpal ldquoSensitivity analysisof the effect of airflow velocity on the thermal comfort inunderground minesrdquo Journal of Sustainable Mining vol 15no 4 pp 175ndash180 2016

[8] B You C Wu J Li and H Liao ldquoPhysiological responses ofpeople in working faces of deep underground minesrdquo In-ternational Journal of Mining Science and Technology vol 24no 5 pp 683ndash688 2014

[9] M-c He ldquoApplication of HEMS cooling technology in deepmine heat hazard controlrdquo Mining Science and Technology(China) vol 19 no 3 pp 269ndash275 2009

[10] A E Krasnoshtein B P Kazakov and A V ShalimovldquoMathematical modeling of heat exchange between mine airand rock mass during firerdquo Journal of Mining Science vol 42no 3 pp 287ndash295 2006

[11] A P Sasmito J C Kurnia E Birgersson andA S Mujumdar ldquoComputational evaluation of thermalmanagement strategies in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1444ndash1150 2015

[12] R Anderson and E D Souza ldquoHeat stress management inunderground minesrdquo International Journal of Mining Scienceand Technology vol 27 no 4 pp 651ndash655 2017

[13] S P Zhang J Qin and G Chen ldquoHeat transfer analysis ondouble-skin air tube in ventilation of deepmine heading facerdquoProcedia Engineering vol 26 pp 1626ndash1632 2011

[14] A Habibi R B Kramer and A D S Gillies ldquoInvestigating theeffects of heat changes in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1164ndash1171 2015

[15] Y Zhang Z Wan B Gu H Zhang and P Zhou ldquoFinitedifference analysis of transient heat transfer in surroundingrock mass of high geothermal roadwayrdquo MathematicalProblems in Engineering vol 2016 Article ID 89515247 pages 2016

[16] P Duda ldquoFinite element method formulation in polar co-ordinates for transient heat conduction problemsrdquo Journal of5ermal Science vol 25 no 2 pp 188ndash194 2016

[17] J J del Coz Dıaz P J Garcıa Nieto C Betegon Biempica andM B Prendes Gero ldquoAnalysis and optimization of the heat-insulating light concrete hollow brick walls design by the finiteelement methodrdquo Applied5ermal Engineering vol 27 no 8-9 pp 1445ndash1456 2007

[18] C Guo X Nian Y Liu C Qi J Song andW Yu ldquoAnalysis of2D flow and heat transfer modeling in fracture of porousmediardquo Journal of 5ermal Science vol 26 no 4 pp 331ndash3382017

[19] J Kim and H Choi ldquoAn immersed-boundary finite-volumemethod for simulation of heat transfer in complex geome-triesrdquo Ksme International Journal vol 18 no 6pp 1026ndash1035 2004

[20] Q Wu Y P Qin L Guo and Q Y Wu ldquoCalculation of theheat emitting from the wall rock at drifting face with finiteelement methodrdquo China Safety Science Journal vol 12 no 6pp 33ndash36 2002

Mathematical Problems in Engineering 11

To program the calculation program equations (5) (6)and (7) are converted into matrix forms to be expressed as

zJe

zTi

zJe

zTj

zJe

zTm

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

kii kij kim

kji kjj kjm

kmi kmj kmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Ti

Tj

Tm

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭

+

nii nij nim

nji njj njm

nmi nmj nmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

zTi

zτ

zTj

zτ

zTm

zτ

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

(8)

where

kll λ4S

b2l + c

2l1113872 1113873

kln knl λ4S

blbn + clcn( 1113857

nll Sρc

6

nln nnl Sρc

12

(l n i j m lne n)

(9)

When the symbol m is the internal node of the com-putational region the boundary nodes of the element arerepresented by the symbols i and j +erefore the contri-bution of the internal triangular element to any node iscalculated using the above method Similarly the contri-bution of each boundary element to the correspondingboundary node is calculated and represented as a matrix asfollows

θi

θj

⎡⎣ ⎤⎦ uii uij

uji ujj

⎡⎣ ⎤⎦Ti

Tj

⎡⎣ ⎤⎦ +vi

vj

⎡⎣ ⎤⎦ (10)

where

uii ujj hS

3

uij uji hS

6

vi vj hSTf

2

(11)

By solving the above equations the temperature valuesof all the nodes in the discrete region can be calculated andthe temperature field can be obtained Taking the ventilationtime of 3 hours of Scheme 1 in Table 1 as an example thetransient temperature contours obtained by the abovemethods are shown in Figure 7

As shown in Figure 8 the temperature of the wall facebegins to decrease after ventilation begins and the tem-perature contours extend outward in the form of concentric

circles+e temperature in the deep surrounding rocks is notaffected by the decrease in the temperature of the wall faceand maintain the virgin temperature

4 Results and Discussion

41 FiniteElementMethodCalculationResults To ensure theaccuracy of the experimental results the change in thetemperature field in three hours is taken as an example +efinite element method is used to calculate the results for thethree schemes in Table 1 and the obtained results are plottedwith Tecplot software for comparative analysis

As shown in Figure 9 the temperature at the wall surfacedecreases sequentially from (a) to (c) +e wall temperaturein Scheme 1 is approximately 135degC while the wall tem-perature in Scheme 3 is reduced to approximately 7degC Inaddition the temperature disturbance range decreases inturn from (a) to (c) +e temperature disturbance range inScheme 1 is approximately 026m while the disturbancerange of temperature in Scheme 3 is reduced to approxi-mately 021m

+ere is no insulation system in Scheme 1 unlike inScheme 2 and Scheme 3 +e results show that the tem-perature of the wall face and the temperature disturbancerange of the surrounding rocks are greatly reduced due tothe effect of the thermal insulation layer

42 Characteristics of the Temperature Distribution in theRoadway To verify the correctness of the finite elementsimulation results the experimental results of the tem-perature field of the surrounding rocks within 01 hours05 hours 1 hour and 3 hours are selected and comparedwith the simulation results as shown in Figures 9(a)ndash10(d)

Figure 10 shows that the general distribution charac-teristics of the temperature field with the heat insulationlayer (Scheme 2 and Scheme 3) are consistent with those ofthe temperature field without the insulation layer (Scheme

T (degC)20195191851817517165161551514514135

Figure 8 Transient temperature contours

6 Mathematical Problems in Engineering

1) +e temperature gradually increases with increasingdistance in the radial direction At the wall face the walltemperature gradually decreases as the conductivity of theinsulation layer decreases Due to the influence of thethermal insulation layer the temperature of the surroundingrocks with the insulation layer is higher than that of thesurrounding rocks without the insulation layer after anintersection of curves when the curve extends to the internaltemperature field of the surrounding rocks In addition theexperimental values are roughly distributed on the curvecalculated by the finite element method and their resultsvalidate each other

43 Variation Law of the Temperature Gradient in the Tem-perature Field As shown in Figure 11 near the wall face thesmaller the conductivity coefficient of the insulation layer isthe larger the temperature gradient is When the curveextends to a certain position inside the surrounding rocksthe smaller the conductivity coefficient of the insulationlayer is the smaller the temperature gradient is

44 Variation Law of the Temperature of the Wall Face withTime As shown in Figure 12 the wall temperature of theroad under the three schemes shows a decreasing trend tovarying degrees after the start of ventilation +e reductionrange of Scheme 1 is the smallest +e reduction range of thewall temperature increases with the decrease in the con-ductivity coefficient of the insulating layer and its reductionrange reaches a maximum under Scheme 3 Similarly therate of change in the curves of each scheme follows the abovelaw that is this rate is the lowest for Scheme 1 and thehighest for Scheme 3 In addition the experimental resultsare basically consistent with the finite element method re-sults and the trends of both curves are consistent

45 Analysis of the 5ermal Insulation Effect for EngineeringExample Applications +e main purpose of analyzing theheat control mechanism of the surrounding rocks with heatinsulation in the roadway is to reduce the heat dissipationcapacity and control the thermal hazard of the surroundingrocks of the deep roadway Here a circular tunnel with a

Distance to the center of the roadway on the X-axis (m)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

20195191851817517165161551514514135

(a)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

2019181716151413121110

(b)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

0452019181716151413121110

T (degC)

987

(c)

Figure 9 +ree-hour cloud chart (a) Scheme 1 (b) Scheme 2 (c) Scheme 3

Mathematical Problems in Engineering 7

radius of 2m is taken as an example to illustrate the heatdissipation law of surrounding rocks +e airflow velocity inthe roadway is 3ms +e excess temperature of the virginrock relative to the airflow temperature is 13degC +e order ofthe structure from the roadway wall is the insulation layerthe concrete layer and the rock stratum +e thermalphysical parameters and calculation scheme of the sur-rounding rocks are shown in Table 4

In this paper the wall temperature of the surroundingrocks of the roadway obtained by the finite elementmethod and the Newton cooling formula is used to cal-culate the thermal dissipation capacity of the surroundingrocks for the insulated roadway +e wall temperaturechanges sharply in the initial heat dissipation stage afterventilation +e heat-dissipating capacity of the

surrounding rocks varies greatly during this unsteadyprocess To improve the calculation accuracy we dividedthe time of the unsteady state process of the temperaturefield into a geometric progression +e whole time is di-vided into n segments and the heat dissipation capacity ofthe surrounding rocks at each time was thus represented asQ1 Q2 Qn +e total time was L and the time of eachperiod was L1 L2 L3

As shown in Figure 13 the thermal dissipation of thesurrounding rocks enters a relatively stable stage after 3 yearsof ventilation +e conductivity coefficient of the insulationlayer decreases successively from Scheme 1 to Scheme 3+eheat dissipation capacity of the surrounding rocks of theroadway is significantly reduced when the heat insulationlayer is as designed in Scheme 3

000 005 010 015 020 025 0306

9

12

15

18

21

Distance to wall surface (m)

Tem

pera

ture

(degC)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(a)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(b)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(c)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(d)

Figure 10 Internal temperature field of surrounding rocks (a) 01H (b) 05H (c) 1H (d) 3H

8 Mathematical Problems in Engineering

005 010 015 020 0250

20

40

60

80

100

120

140

160

Distance to wall surface (m)

Tem

pera

ture

gra

dien

t (degC

middotmndash1

)

Scheme 1

Scheme 2

Scheme 3

Figure 11 Variation law of the temperature gradient

00 05 10 15 20 256

9

12

15

18

21

Tem

pera

ture

(degC)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

Figure 12 Comparison of the variation laws for wall temperature

Table 4 Calculation scheme

Parameters Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of stratum (λ) 264 264 264 W(mmiddotdegC)+ermal diffusivity of stratum (a) 113 113 113 10minus6 (m2s)Conductivity coefficient of the concrete layer (λ) None 151 151 W(mmiddotdegC)+ermal diffusivity of the concrete layer (a) None 07136 07136 10minus6 (m2s)+ickness of concrete layer (L) None 01 01 mConductivity coefficient of insulation layer (λ) 264 076 023 W(mmiddotdegC)+ermal diffusivity of insulation layer (a) 113 04825 04319 10minus6 (m2s)Insulating material None Lime gypsum mortar Coalgangue block + Expanded perlite NoneInsulation layer thickness (L) None 018 018 m

Mathematical Problems in Engineering 9

To accurately calculate the average emission reductionratio under the three schemes we use the weighted averagemethod to calculate the heat dissipation capacity of thesurrounding rocks as shown in

Qm Q1 + Q2( 11138572( 1113857L1 + Q2 + Q3( 11138572( 1113857L2 + middot middot middot + Qn + Qn+1( 11138572( 1113857Ln

L

(12)

Table 5 shows the emission reduction ratios at different timepoints under the two schemes +e designs of Scheme 2 andScheme 3 showed good emission reduction effects+e emissionreduction ratio reaches 8499 in one month of ventilation8761 in one year and 8941 in thirty years when the heatinsulation layer is as designed in Scheme 3 +erefore theconstruction of a heat insulation layer is very effective in re-ducing the heat dissipation capacity of surrounding rocks

5 Conclusions

(1) A mathematical model of surrounding rocks withheat insulation around deep roadways was estab-lished with the finite element method Experimentalresults were used to verify the numerical results andthese results agreed well

(2) +e wall temperature and the disturbance range ofthe temperature of the surrounding rocks are

greatly reduced due to the effect of the thermalinsulation layer Near the wall face the smaller theconductivity coefficient of the insulation layer isthe lower the wall temperature is and the largerthe temperature gradient is Within the sur-rounding rocks far from the wall face the smallerthe conductivity coefficient of the insulation layeris the higher the temperature of the surroundingrocks is and the smaller the temperature gradientis In addition the numerical analysis of thevariation law of the temperature of the wall facewith time shows that the smaller the conductivitycoefficient of the insulation layer is the larger thereduction range of the wall temperature and therate of change in the curves is

(3) +e heat dissipation capacity of the surroundingrocks of the roadway is significantly reduced whenthe heat insulation layer is introduced into the designof the roadway It is explained in detail in this paperthat this heat insulation layer design can cool thesurrounding rock of deep mine roadways

Data Availability

+e data used to support the findings of this study are in-cluded within the article

50 times 104 10 times 105 15 times 105 20 times 105 25 times 105100

101

102

103

104

Diss

ipat

ion

capa

city

(W)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Figure 13 Variation curves of the dissipation capacity of the surrounding rocks with unit length

Table 5 Emission reduction ratio with an insulation layer relative to that with no insulation layer

Time Emission reduction ratio of scheme 2 () Emission reduction ratio of scheme 3 ()1 day 1162 65871 month 5414 84991 year 6095 876110 years 6448 889120 years 6533 892130 years 6589 8941

10 Mathematical Problems in Engineering

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+is work has been financially funded by the Natural ScienceFoundation of China (Grant number 51574249)

Supplementary Materials

+e supplementary material consists of three parts one forrelated data and the other two for related graphics (Sup-plementary Materials)

References

[1] H P Xie H W Zhou D J Xue H W Wang R Zhang andF Gao ldquoResearch and consideration on deep coal mining andcritical mining depthrdquo Journal of China Coal Society vol 37no 4 pp 535ndash542 2012

[2] H Yan F He T Yang L Li S Zhang and J Zhang ldquo+emechanism of bedding separation in roof strata overlying aroadway within a thick coal seam a case study from thePingshuo Coalfield Chinardquo Engineering Failure Analysisvol 62 pp 75ndash92 2016

[3] G E Plessis L Liebenberg and E H Mathews ldquoCase studythe effects of a variable flow energy saving strategy on a deep-mine cooling systemrdquo Applied Energy vol 36 no 1pp 101ndash104 2012

[4] S J Luo X F Wang F Liu L Yan and Y Xie ldquoSome keyproblems and technical countermeasures for deep miningrdquoCoal Technology vol 33 no 11 pp 309ndash311 2014

[5] M Sunkpal P Roghanchi and K C Kocsis ldquoA method toprotect mine workers in hot and humid environmentsrdquo Safetyand Health at Work vol 6 no 11 pp 1ndash10 2017

[6] D J Brake and G P Bates ldquoFluid losses and hydration statusof industrial workers under thermal stress working extendedshiftsrdquo Occupational and Environmental Medicine vol 60no 2 pp 90ndash96 2003

[7] R Pedram K C Kocsis and M Sunkpal ldquoSensitivity analysisof the effect of airflow velocity on the thermal comfort inunderground minesrdquo Journal of Sustainable Mining vol 15no 4 pp 175ndash180 2016

[8] B You C Wu J Li and H Liao ldquoPhysiological responses ofpeople in working faces of deep underground minesrdquo In-ternational Journal of Mining Science and Technology vol 24no 5 pp 683ndash688 2014

[9] M-c He ldquoApplication of HEMS cooling technology in deepmine heat hazard controlrdquo Mining Science and Technology(China) vol 19 no 3 pp 269ndash275 2009

[10] A E Krasnoshtein B P Kazakov and A V ShalimovldquoMathematical modeling of heat exchange between mine airand rock mass during firerdquo Journal of Mining Science vol 42no 3 pp 287ndash295 2006

[11] A P Sasmito J C Kurnia E Birgersson andA S Mujumdar ldquoComputational evaluation of thermalmanagement strategies in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1444ndash1150 2015

[12] R Anderson and E D Souza ldquoHeat stress management inunderground minesrdquo International Journal of Mining Scienceand Technology vol 27 no 4 pp 651ndash655 2017

[13] S P Zhang J Qin and G Chen ldquoHeat transfer analysis ondouble-skin air tube in ventilation of deepmine heading facerdquoProcedia Engineering vol 26 pp 1626ndash1632 2011

[14] A Habibi R B Kramer and A D S Gillies ldquoInvestigating theeffects of heat changes in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1164ndash1171 2015

[15] Y Zhang Z Wan B Gu H Zhang and P Zhou ldquoFinitedifference analysis of transient heat transfer in surroundingrock mass of high geothermal roadwayrdquo MathematicalProblems in Engineering vol 2016 Article ID 89515247 pages 2016

[16] P Duda ldquoFinite element method formulation in polar co-ordinates for transient heat conduction problemsrdquo Journal of5ermal Science vol 25 no 2 pp 188ndash194 2016

[17] J J del Coz Dıaz P J Garcıa Nieto C Betegon Biempica andM B Prendes Gero ldquoAnalysis and optimization of the heat-insulating light concrete hollow brick walls design by the finiteelement methodrdquo Applied5ermal Engineering vol 27 no 8-9 pp 1445ndash1456 2007

[18] C Guo X Nian Y Liu C Qi J Song andW Yu ldquoAnalysis of2D flow and heat transfer modeling in fracture of porousmediardquo Journal of 5ermal Science vol 26 no 4 pp 331ndash3382017

[19] J Kim and H Choi ldquoAn immersed-boundary finite-volumemethod for simulation of heat transfer in complex geome-triesrdquo Ksme International Journal vol 18 no 6pp 1026ndash1035 2004

[20] Q Wu Y P Qin L Guo and Q Y Wu ldquoCalculation of theheat emitting from the wall rock at drifting face with finiteelement methodrdquo China Safety Science Journal vol 12 no 6pp 33ndash36 2002

Mathematical Problems in Engineering 11

1) +e temperature gradually increases with increasingdistance in the radial direction At the wall face the walltemperature gradually decreases as the conductivity of theinsulation layer decreases Due to the influence of thethermal insulation layer the temperature of the surroundingrocks with the insulation layer is higher than that of thesurrounding rocks without the insulation layer after anintersection of curves when the curve extends to the internaltemperature field of the surrounding rocks In addition theexperimental values are roughly distributed on the curvecalculated by the finite element method and their resultsvalidate each other

43 Variation Law of the Temperature Gradient in the Tem-perature Field As shown in Figure 11 near the wall face thesmaller the conductivity coefficient of the insulation layer isthe larger the temperature gradient is When the curveextends to a certain position inside the surrounding rocksthe smaller the conductivity coefficient of the insulationlayer is the smaller the temperature gradient is

44 Variation Law of the Temperature of the Wall Face withTime As shown in Figure 12 the wall temperature of theroad under the three schemes shows a decreasing trend tovarying degrees after the start of ventilation +e reductionrange of Scheme 1 is the smallest +e reduction range of thewall temperature increases with the decrease in the con-ductivity coefficient of the insulating layer and its reductionrange reaches a maximum under Scheme 3 Similarly therate of change in the curves of each scheme follows the abovelaw that is this rate is the lowest for Scheme 1 and thehighest for Scheme 3 In addition the experimental resultsare basically consistent with the finite element method re-sults and the trends of both curves are consistent

45 Analysis of the 5ermal Insulation Effect for EngineeringExample Applications +e main purpose of analyzing theheat control mechanism of the surrounding rocks with heatinsulation in the roadway is to reduce the heat dissipationcapacity and control the thermal hazard of the surroundingrocks of the deep roadway Here a circular tunnel with a

Distance to the center of the roadway on the X-axis (m)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

20195191851817517165161551514514135

(a)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

045T (degC)

2019181716151413121110

(b)

Dist

ance

to th

e cen

ter o

fth

e roa

dway

on

the Y

-axi

s (m

)

Distance to the center of the roadway on the X-axis (m)

0 005 01 015 02 025 03 035 04 0450

005

01

015

02

025

03

035

04

0452019181716151413121110

T (degC)

987

(c)

Figure 9 +ree-hour cloud chart (a) Scheme 1 (b) Scheme 2 (c) Scheme 3

Mathematical Problems in Engineering 7

radius of 2m is taken as an example to illustrate the heatdissipation law of surrounding rocks +e airflow velocity inthe roadway is 3ms +e excess temperature of the virginrock relative to the airflow temperature is 13degC +e order ofthe structure from the roadway wall is the insulation layerthe concrete layer and the rock stratum +e thermalphysical parameters and calculation scheme of the sur-rounding rocks are shown in Table 4

In this paper the wall temperature of the surroundingrocks of the roadway obtained by the finite elementmethod and the Newton cooling formula is used to cal-culate the thermal dissipation capacity of the surroundingrocks for the insulated roadway +e wall temperaturechanges sharply in the initial heat dissipation stage afterventilation +e heat-dissipating capacity of the

surrounding rocks varies greatly during this unsteadyprocess To improve the calculation accuracy we dividedthe time of the unsteady state process of the temperaturefield into a geometric progression +e whole time is di-vided into n segments and the heat dissipation capacity ofthe surrounding rocks at each time was thus represented asQ1 Q2 Qn +e total time was L and the time of eachperiod was L1 L2 L3

As shown in Figure 13 the thermal dissipation of thesurrounding rocks enters a relatively stable stage after 3 yearsof ventilation +e conductivity coefficient of the insulationlayer decreases successively from Scheme 1 to Scheme 3+eheat dissipation capacity of the surrounding rocks of theroadway is significantly reduced when the heat insulationlayer is as designed in Scheme 3

000 005 010 015 020 025 0306

9

12

15

18

21

Distance to wall surface (m)

Tem

pera

ture

(degC)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(a)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(b)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(c)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(d)

Figure 10 Internal temperature field of surrounding rocks (a) 01H (b) 05H (c) 1H (d) 3H

8 Mathematical Problems in Engineering

005 010 015 020 0250

20

40

60

80

100

120

140

160

Distance to wall surface (m)

Tem

pera

ture

gra

dien

t (degC

middotmndash1

)

Scheme 1

Scheme 2

Scheme 3

Figure 11 Variation law of the temperature gradient

00 05 10 15 20 256

9

12

15

18

21

Tem

pera

ture

(degC)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

Figure 12 Comparison of the variation laws for wall temperature

Table 4 Calculation scheme

Parameters Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of stratum (λ) 264 264 264 W(mmiddotdegC)+ermal diffusivity of stratum (a) 113 113 113 10minus6 (m2s)Conductivity coefficient of the concrete layer (λ) None 151 151 W(mmiddotdegC)+ermal diffusivity of the concrete layer (a) None 07136 07136 10minus6 (m2s)+ickness of concrete layer (L) None 01 01 mConductivity coefficient of insulation layer (λ) 264 076 023 W(mmiddotdegC)+ermal diffusivity of insulation layer (a) 113 04825 04319 10minus6 (m2s)Insulating material None Lime gypsum mortar Coalgangue block + Expanded perlite NoneInsulation layer thickness (L) None 018 018 m

Mathematical Problems in Engineering 9

To accurately calculate the average emission reductionratio under the three schemes we use the weighted averagemethod to calculate the heat dissipation capacity of thesurrounding rocks as shown in

Qm Q1 + Q2( 11138572( 1113857L1 + Q2 + Q3( 11138572( 1113857L2 + middot middot middot + Qn + Qn+1( 11138572( 1113857Ln

L

(12)

Table 5 shows the emission reduction ratios at different timepoints under the two schemes +e designs of Scheme 2 andScheme 3 showed good emission reduction effects+e emissionreduction ratio reaches 8499 in one month of ventilation8761 in one year and 8941 in thirty years when the heatinsulation layer is as designed in Scheme 3 +erefore theconstruction of a heat insulation layer is very effective in re-ducing the heat dissipation capacity of surrounding rocks

5 Conclusions

(1) A mathematical model of surrounding rocks withheat insulation around deep roadways was estab-lished with the finite element method Experimentalresults were used to verify the numerical results andthese results agreed well

(2) +e wall temperature and the disturbance range ofthe temperature of the surrounding rocks are

greatly reduced due to the effect of the thermalinsulation layer Near the wall face the smaller theconductivity coefficient of the insulation layer isthe lower the wall temperature is and the largerthe temperature gradient is Within the sur-rounding rocks far from the wall face the smallerthe conductivity coefficient of the insulation layeris the higher the temperature of the surroundingrocks is and the smaller the temperature gradientis In addition the numerical analysis of thevariation law of the temperature of the wall facewith time shows that the smaller the conductivitycoefficient of the insulation layer is the larger thereduction range of the wall temperature and therate of change in the curves is

(3) +e heat dissipation capacity of the surroundingrocks of the roadway is significantly reduced whenthe heat insulation layer is introduced into the designof the roadway It is explained in detail in this paperthat this heat insulation layer design can cool thesurrounding rock of deep mine roadways

Data Availability

+e data used to support the findings of this study are in-cluded within the article

50 times 104 10 times 105 15 times 105 20 times 105 25 times 105100

101

102

103

104

Diss

ipat

ion

capa

city

(W)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Figure 13 Variation curves of the dissipation capacity of the surrounding rocks with unit length

Table 5 Emission reduction ratio with an insulation layer relative to that with no insulation layer

Time Emission reduction ratio of scheme 2 () Emission reduction ratio of scheme 3 ()1 day 1162 65871 month 5414 84991 year 6095 876110 years 6448 889120 years 6533 892130 years 6589 8941

10 Mathematical Problems in Engineering

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+is work has been financially funded by the Natural ScienceFoundation of China (Grant number 51574249)

Supplementary Materials

+e supplementary material consists of three parts one forrelated data and the other two for related graphics (Sup-plementary Materials)

References

[1] H P Xie H W Zhou D J Xue H W Wang R Zhang andF Gao ldquoResearch and consideration on deep coal mining andcritical mining depthrdquo Journal of China Coal Society vol 37no 4 pp 535ndash542 2012

[2] H Yan F He T Yang L Li S Zhang and J Zhang ldquo+emechanism of bedding separation in roof strata overlying aroadway within a thick coal seam a case study from thePingshuo Coalfield Chinardquo Engineering Failure Analysisvol 62 pp 75ndash92 2016

[3] G E Plessis L Liebenberg and E H Mathews ldquoCase studythe effects of a variable flow energy saving strategy on a deep-mine cooling systemrdquo Applied Energy vol 36 no 1pp 101ndash104 2012

[4] S J Luo X F Wang F Liu L Yan and Y Xie ldquoSome keyproblems and technical countermeasures for deep miningrdquoCoal Technology vol 33 no 11 pp 309ndash311 2014

[5] M Sunkpal P Roghanchi and K C Kocsis ldquoA method toprotect mine workers in hot and humid environmentsrdquo Safetyand Health at Work vol 6 no 11 pp 1ndash10 2017

[6] D J Brake and G P Bates ldquoFluid losses and hydration statusof industrial workers under thermal stress working extendedshiftsrdquo Occupational and Environmental Medicine vol 60no 2 pp 90ndash96 2003

[7] R Pedram K C Kocsis and M Sunkpal ldquoSensitivity analysisof the effect of airflow velocity on the thermal comfort inunderground minesrdquo Journal of Sustainable Mining vol 15no 4 pp 175ndash180 2016

[8] B You C Wu J Li and H Liao ldquoPhysiological responses ofpeople in working faces of deep underground minesrdquo In-ternational Journal of Mining Science and Technology vol 24no 5 pp 683ndash688 2014

[9] M-c He ldquoApplication of HEMS cooling technology in deepmine heat hazard controlrdquo Mining Science and Technology(China) vol 19 no 3 pp 269ndash275 2009

[10] A E Krasnoshtein B P Kazakov and A V ShalimovldquoMathematical modeling of heat exchange between mine airand rock mass during firerdquo Journal of Mining Science vol 42no 3 pp 287ndash295 2006

[11] A P Sasmito J C Kurnia E Birgersson andA S Mujumdar ldquoComputational evaluation of thermalmanagement strategies in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1444ndash1150 2015

[12] R Anderson and E D Souza ldquoHeat stress management inunderground minesrdquo International Journal of Mining Scienceand Technology vol 27 no 4 pp 651ndash655 2017

[13] S P Zhang J Qin and G Chen ldquoHeat transfer analysis ondouble-skin air tube in ventilation of deepmine heading facerdquoProcedia Engineering vol 26 pp 1626ndash1632 2011

[14] A Habibi R B Kramer and A D S Gillies ldquoInvestigating theeffects of heat changes in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1164ndash1171 2015

[15] Y Zhang Z Wan B Gu H Zhang and P Zhou ldquoFinitedifference analysis of transient heat transfer in surroundingrock mass of high geothermal roadwayrdquo MathematicalProblems in Engineering vol 2016 Article ID 89515247 pages 2016

[16] P Duda ldquoFinite element method formulation in polar co-ordinates for transient heat conduction problemsrdquo Journal of5ermal Science vol 25 no 2 pp 188ndash194 2016

[17] J J del Coz Dıaz P J Garcıa Nieto C Betegon Biempica andM B Prendes Gero ldquoAnalysis and optimization of the heat-insulating light concrete hollow brick walls design by the finiteelement methodrdquo Applied5ermal Engineering vol 27 no 8-9 pp 1445ndash1456 2007

[18] C Guo X Nian Y Liu C Qi J Song andW Yu ldquoAnalysis of2D flow and heat transfer modeling in fracture of porousmediardquo Journal of 5ermal Science vol 26 no 4 pp 331ndash3382017

[19] J Kim and H Choi ldquoAn immersed-boundary finite-volumemethod for simulation of heat transfer in complex geome-triesrdquo Ksme International Journal vol 18 no 6pp 1026ndash1035 2004

[20] Q Wu Y P Qin L Guo and Q Y Wu ldquoCalculation of theheat emitting from the wall rock at drifting face with finiteelement methodrdquo China Safety Science Journal vol 12 no 6pp 33ndash36 2002

Mathematical Problems in Engineering 11

radius of 2m is taken as an example to illustrate the heatdissipation law of surrounding rocks +e airflow velocity inthe roadway is 3ms +e excess temperature of the virginrock relative to the airflow temperature is 13degC +e order ofthe structure from the roadway wall is the insulation layerthe concrete layer and the rock stratum +e thermalphysical parameters and calculation scheme of the sur-rounding rocks are shown in Table 4

In this paper the wall temperature of the surroundingrocks of the roadway obtained by the finite elementmethod and the Newton cooling formula is used to cal-culate the thermal dissipation capacity of the surroundingrocks for the insulated roadway +e wall temperaturechanges sharply in the initial heat dissipation stage afterventilation +e heat-dissipating capacity of the

surrounding rocks varies greatly during this unsteadyprocess To improve the calculation accuracy we dividedthe time of the unsteady state process of the temperaturefield into a geometric progression +e whole time is di-vided into n segments and the heat dissipation capacity ofthe surrounding rocks at each time was thus represented asQ1 Q2 Qn +e total time was L and the time of eachperiod was L1 L2 L3

As shown in Figure 13 the thermal dissipation of thesurrounding rocks enters a relatively stable stage after 3 yearsof ventilation +e conductivity coefficient of the insulationlayer decreases successively from Scheme 1 to Scheme 3+eheat dissipation capacity of the surrounding rocks of theroadway is significantly reduced when the heat insulationlayer is as designed in Scheme 3

000 005 010 015 020 025 0306

9

12

15

18

21

Distance to wall surface (m)

Tem

pera

ture

(degC)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(a)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(b)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(c)

Distance to wall surface (m)

Tem

pera

ture

(degC)

000 005 010 015 020 025 0306

9

12

15

18

21

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

(d)

Figure 10 Internal temperature field of surrounding rocks (a) 01H (b) 05H (c) 1H (d) 3H

8 Mathematical Problems in Engineering

005 010 015 020 0250

20

40

60

80

100

120

140

160

Distance to wall surface (m)

Tem

pera

ture

gra

dien

t (degC

middotmndash1

)

Scheme 1

Scheme 2

Scheme 3

Figure 11 Variation law of the temperature gradient

00 05 10 15 20 256

9

12

15

18

21

Tem

pera

ture

(degC)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

Figure 12 Comparison of the variation laws for wall temperature

Table 4 Calculation scheme

Parameters Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of stratum (λ) 264 264 264 W(mmiddotdegC)+ermal diffusivity of stratum (a) 113 113 113 10minus6 (m2s)Conductivity coefficient of the concrete layer (λ) None 151 151 W(mmiddotdegC)+ermal diffusivity of the concrete layer (a) None 07136 07136 10minus6 (m2s)+ickness of concrete layer (L) None 01 01 mConductivity coefficient of insulation layer (λ) 264 076 023 W(mmiddotdegC)+ermal diffusivity of insulation layer (a) 113 04825 04319 10minus6 (m2s)Insulating material None Lime gypsum mortar Coalgangue block + Expanded perlite NoneInsulation layer thickness (L) None 018 018 m

Mathematical Problems in Engineering 9

To accurately calculate the average emission reductionratio under the three schemes we use the weighted averagemethod to calculate the heat dissipation capacity of thesurrounding rocks as shown in

Qm Q1 + Q2( 11138572( 1113857L1 + Q2 + Q3( 11138572( 1113857L2 + middot middot middot + Qn + Qn+1( 11138572( 1113857Ln

L

(12)

Table 5 shows the emission reduction ratios at different timepoints under the two schemes +e designs of Scheme 2 andScheme 3 showed good emission reduction effects+e emissionreduction ratio reaches 8499 in one month of ventilation8761 in one year and 8941 in thirty years when the heatinsulation layer is as designed in Scheme 3 +erefore theconstruction of a heat insulation layer is very effective in re-ducing the heat dissipation capacity of surrounding rocks

5 Conclusions

(1) A mathematical model of surrounding rocks withheat insulation around deep roadways was estab-lished with the finite element method Experimentalresults were used to verify the numerical results andthese results agreed well

(2) +e wall temperature and the disturbance range ofthe temperature of the surrounding rocks are

greatly reduced due to the effect of the thermalinsulation layer Near the wall face the smaller theconductivity coefficient of the insulation layer isthe lower the wall temperature is and the largerthe temperature gradient is Within the sur-rounding rocks far from the wall face the smallerthe conductivity coefficient of the insulation layeris the higher the temperature of the surroundingrocks is and the smaller the temperature gradientis In addition the numerical analysis of thevariation law of the temperature of the wall facewith time shows that the smaller the conductivitycoefficient of the insulation layer is the larger thereduction range of the wall temperature and therate of change in the curves is

(3) +e heat dissipation capacity of the surroundingrocks of the roadway is significantly reduced whenthe heat insulation layer is introduced into the designof the roadway It is explained in detail in this paperthat this heat insulation layer design can cool thesurrounding rock of deep mine roadways

Data Availability

+e data used to support the findings of this study are in-cluded within the article

50 times 104 10 times 105 15 times 105 20 times 105 25 times 105100

101

102

103

104

Diss

ipat

ion

capa

city

(W)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Figure 13 Variation curves of the dissipation capacity of the surrounding rocks with unit length

Table 5 Emission reduction ratio with an insulation layer relative to that with no insulation layer

Time Emission reduction ratio of scheme 2 () Emission reduction ratio of scheme 3 ()1 day 1162 65871 month 5414 84991 year 6095 876110 years 6448 889120 years 6533 892130 years 6589 8941

10 Mathematical Problems in Engineering

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+is work has been financially funded by the Natural ScienceFoundation of China (Grant number 51574249)

Supplementary Materials

+e supplementary material consists of three parts one forrelated data and the other two for related graphics (Sup-plementary Materials)

References

[1] H P Xie H W Zhou D J Xue H W Wang R Zhang andF Gao ldquoResearch and consideration on deep coal mining andcritical mining depthrdquo Journal of China Coal Society vol 37no 4 pp 535ndash542 2012

[2] H Yan F He T Yang L Li S Zhang and J Zhang ldquo+emechanism of bedding separation in roof strata overlying aroadway within a thick coal seam a case study from thePingshuo Coalfield Chinardquo Engineering Failure Analysisvol 62 pp 75ndash92 2016

[3] G E Plessis L Liebenberg and E H Mathews ldquoCase studythe effects of a variable flow energy saving strategy on a deep-mine cooling systemrdquo Applied Energy vol 36 no 1pp 101ndash104 2012

[4] S J Luo X F Wang F Liu L Yan and Y Xie ldquoSome keyproblems and technical countermeasures for deep miningrdquoCoal Technology vol 33 no 11 pp 309ndash311 2014

[5] M Sunkpal P Roghanchi and K C Kocsis ldquoA method toprotect mine workers in hot and humid environmentsrdquo Safetyand Health at Work vol 6 no 11 pp 1ndash10 2017

[6] D J Brake and G P Bates ldquoFluid losses and hydration statusof industrial workers under thermal stress working extendedshiftsrdquo Occupational and Environmental Medicine vol 60no 2 pp 90ndash96 2003

[7] R Pedram K C Kocsis and M Sunkpal ldquoSensitivity analysisof the effect of airflow velocity on the thermal comfort inunderground minesrdquo Journal of Sustainable Mining vol 15no 4 pp 175ndash180 2016

[8] B You C Wu J Li and H Liao ldquoPhysiological responses ofpeople in working faces of deep underground minesrdquo In-ternational Journal of Mining Science and Technology vol 24no 5 pp 683ndash688 2014

[9] M-c He ldquoApplication of HEMS cooling technology in deepmine heat hazard controlrdquo Mining Science and Technology(China) vol 19 no 3 pp 269ndash275 2009

[10] A E Krasnoshtein B P Kazakov and A V ShalimovldquoMathematical modeling of heat exchange between mine airand rock mass during firerdquo Journal of Mining Science vol 42no 3 pp 287ndash295 2006

[11] A P Sasmito J C Kurnia E Birgersson andA S Mujumdar ldquoComputational evaluation of thermalmanagement strategies in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1444ndash1150 2015

[12] R Anderson and E D Souza ldquoHeat stress management inunderground minesrdquo International Journal of Mining Scienceand Technology vol 27 no 4 pp 651ndash655 2017

[13] S P Zhang J Qin and G Chen ldquoHeat transfer analysis ondouble-skin air tube in ventilation of deepmine heading facerdquoProcedia Engineering vol 26 pp 1626ndash1632 2011

[14] A Habibi R B Kramer and A D S Gillies ldquoInvestigating theeffects of heat changes in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1164ndash1171 2015

[15] Y Zhang Z Wan B Gu H Zhang and P Zhou ldquoFinitedifference analysis of transient heat transfer in surroundingrock mass of high geothermal roadwayrdquo MathematicalProblems in Engineering vol 2016 Article ID 89515247 pages 2016

[16] P Duda ldquoFinite element method formulation in polar co-ordinates for transient heat conduction problemsrdquo Journal of5ermal Science vol 25 no 2 pp 188ndash194 2016

[17] J J del Coz Dıaz P J Garcıa Nieto C Betegon Biempica andM B Prendes Gero ldquoAnalysis and optimization of the heat-insulating light concrete hollow brick walls design by the finiteelement methodrdquo Applied5ermal Engineering vol 27 no 8-9 pp 1445ndash1456 2007

[18] C Guo X Nian Y Liu C Qi J Song andW Yu ldquoAnalysis of2D flow and heat transfer modeling in fracture of porousmediardquo Journal of 5ermal Science vol 26 no 4 pp 331ndash3382017

[19] J Kim and H Choi ldquoAn immersed-boundary finite-volumemethod for simulation of heat transfer in complex geome-triesrdquo Ksme International Journal vol 18 no 6pp 1026ndash1035 2004

[20] Q Wu Y P Qin L Guo and Q Y Wu ldquoCalculation of theheat emitting from the wall rock at drifting face with finiteelement methodrdquo China Safety Science Journal vol 12 no 6pp 33ndash36 2002

Mathematical Problems in Engineering 11

005 010 015 020 0250

20

40

60

80

100

120

140

160

Distance to wall surface (m)

Tem

pera

ture

gra

dien

t (degC

middotmndash1

)

Scheme 1

Scheme 2

Scheme 3

Figure 11 Variation law of the temperature gradient

00 05 10 15 20 256

9

12

15

18

21

Tem

pera

ture

(degC)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Experimental data

Scheme 1

Scheme 2

Scheme 3

Numerical results

Figure 12 Comparison of the variation laws for wall temperature

Table 4 Calculation scheme

Parameters Scheme 1 Scheme 2 Scheme 3 UnitConductivity coefficient of stratum (λ) 264 264 264 W(mmiddotdegC)+ermal diffusivity of stratum (a) 113 113 113 10minus6 (m2s)Conductivity coefficient of the concrete layer (λ) None 151 151 W(mmiddotdegC)+ermal diffusivity of the concrete layer (a) None 07136 07136 10minus6 (m2s)+ickness of concrete layer (L) None 01 01 mConductivity coefficient of insulation layer (λ) 264 076 023 W(mmiddotdegC)+ermal diffusivity of insulation layer (a) 113 04825 04319 10minus6 (m2s)Insulating material None Lime gypsum mortar Coalgangue block + Expanded perlite NoneInsulation layer thickness (L) None 018 018 m

Mathematical Problems in Engineering 9

To accurately calculate the average emission reductionratio under the three schemes we use the weighted averagemethod to calculate the heat dissipation capacity of thesurrounding rocks as shown in

Qm Q1 + Q2( 11138572( 1113857L1 + Q2 + Q3( 11138572( 1113857L2 + middot middot middot + Qn + Qn+1( 11138572( 1113857Ln

L

(12)

Table 5 shows the emission reduction ratios at different timepoints under the two schemes +e designs of Scheme 2 andScheme 3 showed good emission reduction effects+e emissionreduction ratio reaches 8499 in one month of ventilation8761 in one year and 8941 in thirty years when the heatinsulation layer is as designed in Scheme 3 +erefore theconstruction of a heat insulation layer is very effective in re-ducing the heat dissipation capacity of surrounding rocks

5 Conclusions

(1) A mathematical model of surrounding rocks withheat insulation around deep roadways was estab-lished with the finite element method Experimentalresults were used to verify the numerical results andthese results agreed well

(2) +e wall temperature and the disturbance range ofthe temperature of the surrounding rocks are

greatly reduced due to the effect of the thermalinsulation layer Near the wall face the smaller theconductivity coefficient of the insulation layer isthe lower the wall temperature is and the largerthe temperature gradient is Within the sur-rounding rocks far from the wall face the smallerthe conductivity coefficient of the insulation layeris the higher the temperature of the surroundingrocks is and the smaller the temperature gradientis In addition the numerical analysis of thevariation law of the temperature of the wall facewith time shows that the smaller the conductivitycoefficient of the insulation layer is the larger thereduction range of the wall temperature and therate of change in the curves is

(3) +e heat dissipation capacity of the surroundingrocks of the roadway is significantly reduced whenthe heat insulation layer is introduced into the designof the roadway It is explained in detail in this paperthat this heat insulation layer design can cool thesurrounding rock of deep mine roadways

Data Availability

+e data used to support the findings of this study are in-cluded within the article

50 times 104 10 times 105 15 times 105 20 times 105 25 times 105100

101

102

103

104

Diss

ipat

ion

capa

city

(W)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Figure 13 Variation curves of the dissipation capacity of the surrounding rocks with unit length

Table 5 Emission reduction ratio with an insulation layer relative to that with no insulation layer

Time Emission reduction ratio of scheme 2 () Emission reduction ratio of scheme 3 ()1 day 1162 65871 month 5414 84991 year 6095 876110 years 6448 889120 years 6533 892130 years 6589 8941

10 Mathematical Problems in Engineering

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+is work has been financially funded by the Natural ScienceFoundation of China (Grant number 51574249)

Supplementary Materials

+e supplementary material consists of three parts one forrelated data and the other two for related graphics (Sup-plementary Materials)

References

[1] H P Xie H W Zhou D J Xue H W Wang R Zhang andF Gao ldquoResearch and consideration on deep coal mining andcritical mining depthrdquo Journal of China Coal Society vol 37no 4 pp 535ndash542 2012

[2] H Yan F He T Yang L Li S Zhang and J Zhang ldquo+emechanism of bedding separation in roof strata overlying aroadway within a thick coal seam a case study from thePingshuo Coalfield Chinardquo Engineering Failure Analysisvol 62 pp 75ndash92 2016

[3] G E Plessis L Liebenberg and E H Mathews ldquoCase studythe effects of a variable flow energy saving strategy on a deep-mine cooling systemrdquo Applied Energy vol 36 no 1pp 101ndash104 2012

[4] S J Luo X F Wang F Liu L Yan and Y Xie ldquoSome keyproblems and technical countermeasures for deep miningrdquoCoal Technology vol 33 no 11 pp 309ndash311 2014

[5] M Sunkpal P Roghanchi and K C Kocsis ldquoA method toprotect mine workers in hot and humid environmentsrdquo Safetyand Health at Work vol 6 no 11 pp 1ndash10 2017

[6] D J Brake and G P Bates ldquoFluid losses and hydration statusof industrial workers under thermal stress working extendedshiftsrdquo Occupational and Environmental Medicine vol 60no 2 pp 90ndash96 2003

[7] R Pedram K C Kocsis and M Sunkpal ldquoSensitivity analysisof the effect of airflow velocity on the thermal comfort inunderground minesrdquo Journal of Sustainable Mining vol 15no 4 pp 175ndash180 2016

[8] B You C Wu J Li and H Liao ldquoPhysiological responses ofpeople in working faces of deep underground minesrdquo In-ternational Journal of Mining Science and Technology vol 24no 5 pp 683ndash688 2014

[9] M-c He ldquoApplication of HEMS cooling technology in deepmine heat hazard controlrdquo Mining Science and Technology(China) vol 19 no 3 pp 269ndash275 2009

[10] A E Krasnoshtein B P Kazakov and A V ShalimovldquoMathematical modeling of heat exchange between mine airand rock mass during firerdquo Journal of Mining Science vol 42no 3 pp 287ndash295 2006

[11] A P Sasmito J C Kurnia E Birgersson andA S Mujumdar ldquoComputational evaluation of thermalmanagement strategies in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1444ndash1150 2015

[12] R Anderson and E D Souza ldquoHeat stress management inunderground minesrdquo International Journal of Mining Scienceand Technology vol 27 no 4 pp 651ndash655 2017

[13] S P Zhang J Qin and G Chen ldquoHeat transfer analysis ondouble-skin air tube in ventilation of deepmine heading facerdquoProcedia Engineering vol 26 pp 1626ndash1632 2011

[14] A Habibi R B Kramer and A D S Gillies ldquoInvestigating theeffects of heat changes in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1164ndash1171 2015

[15] Y Zhang Z Wan B Gu H Zhang and P Zhou ldquoFinitedifference analysis of transient heat transfer in surroundingrock mass of high geothermal roadwayrdquo MathematicalProblems in Engineering vol 2016 Article ID 89515247 pages 2016

[16] P Duda ldquoFinite element method formulation in polar co-ordinates for transient heat conduction problemsrdquo Journal of5ermal Science vol 25 no 2 pp 188ndash194 2016

[17] J J del Coz Dıaz P J Garcıa Nieto C Betegon Biempica andM B Prendes Gero ldquoAnalysis and optimization of the heat-insulating light concrete hollow brick walls design by the finiteelement methodrdquo Applied5ermal Engineering vol 27 no 8-9 pp 1445ndash1456 2007

[18] C Guo X Nian Y Liu C Qi J Song andW Yu ldquoAnalysis of2D flow and heat transfer modeling in fracture of porousmediardquo Journal of 5ermal Science vol 26 no 4 pp 331ndash3382017

[19] J Kim and H Choi ldquoAn immersed-boundary finite-volumemethod for simulation of heat transfer in complex geome-triesrdquo Ksme International Journal vol 18 no 6pp 1026ndash1035 2004

[20] Q Wu Y P Qin L Guo and Q Y Wu ldquoCalculation of theheat emitting from the wall rock at drifting face with finiteelement methodrdquo China Safety Science Journal vol 12 no 6pp 33ndash36 2002

Mathematical Problems in Engineering 11

To accurately calculate the average emission reductionratio under the three schemes we use the weighted averagemethod to calculate the heat dissipation capacity of thesurrounding rocks as shown in

Qm Q1 + Q2( 11138572( 1113857L1 + Q2 + Q3( 11138572( 1113857L2 + middot middot middot + Qn + Qn+1( 11138572( 1113857Ln

L

(12)

Table 5 shows the emission reduction ratios at different timepoints under the two schemes +e designs of Scheme 2 andScheme 3 showed good emission reduction effects+e emissionreduction ratio reaches 8499 in one month of ventilation8761 in one year and 8941 in thirty years when the heatinsulation layer is as designed in Scheme 3 +erefore theconstruction of a heat insulation layer is very effective in re-ducing the heat dissipation capacity of surrounding rocks

5 Conclusions

(1) A mathematical model of surrounding rocks withheat insulation around deep roadways was estab-lished with the finite element method Experimentalresults were used to verify the numerical results andthese results agreed well

(2) +e wall temperature and the disturbance range ofthe temperature of the surrounding rocks are

greatly reduced due to the effect of the thermalinsulation layer Near the wall face the smaller theconductivity coefficient of the insulation layer isthe lower the wall temperature is and the largerthe temperature gradient is Within the sur-rounding rocks far from the wall face the smallerthe conductivity coefficient of the insulation layeris the higher the temperature of the surroundingrocks is and the smaller the temperature gradientis In addition the numerical analysis of thevariation law of the temperature of the wall facewith time shows that the smaller the conductivitycoefficient of the insulation layer is the larger thereduction range of the wall temperature and therate of change in the curves is

(3) +e heat dissipation capacity of the surroundingrocks of the roadway is significantly reduced whenthe heat insulation layer is introduced into the designof the roadway It is explained in detail in this paperthat this heat insulation layer design can cool thesurrounding rock of deep mine roadways

Data Availability

+e data used to support the findings of this study are in-cluded within the article

50 times 104 10 times 105 15 times 105 20 times 105 25 times 105100

101

102

103

104

Diss

ipat

ion

capa

city

(W)

Time (h)

Scheme 1

Scheme 2

Scheme 3

Figure 13 Variation curves of the dissipation capacity of the surrounding rocks with unit length

Table 5 Emission reduction ratio with an insulation layer relative to that with no insulation layer

Time Emission reduction ratio of scheme 2 () Emission reduction ratio of scheme 3 ()1 day 1162 65871 month 5414 84991 year 6095 876110 years 6448 889120 years 6533 892130 years 6589 8941

10 Mathematical Problems in Engineering

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+is work has been financially funded by the Natural ScienceFoundation of China (Grant number 51574249)

Supplementary Materials

+e supplementary material consists of three parts one forrelated data and the other two for related graphics (Sup-plementary Materials)

References

[1] H P Xie H W Zhou D J Xue H W Wang R Zhang andF Gao ldquoResearch and consideration on deep coal mining andcritical mining depthrdquo Journal of China Coal Society vol 37no 4 pp 535ndash542 2012

[2] H Yan F He T Yang L Li S Zhang and J Zhang ldquo+emechanism of bedding separation in roof strata overlying aroadway within a thick coal seam a case study from thePingshuo Coalfield Chinardquo Engineering Failure Analysisvol 62 pp 75ndash92 2016

[3] G E Plessis L Liebenberg and E H Mathews ldquoCase studythe effects of a variable flow energy saving strategy on a deep-mine cooling systemrdquo Applied Energy vol 36 no 1pp 101ndash104 2012

[4] S J Luo X F Wang F Liu L Yan and Y Xie ldquoSome keyproblems and technical countermeasures for deep miningrdquoCoal Technology vol 33 no 11 pp 309ndash311 2014

[5] M Sunkpal P Roghanchi and K C Kocsis ldquoA method toprotect mine workers in hot and humid environmentsrdquo Safetyand Health at Work vol 6 no 11 pp 1ndash10 2017

[6] D J Brake and G P Bates ldquoFluid losses and hydration statusof industrial workers under thermal stress working extendedshiftsrdquo Occupational and Environmental Medicine vol 60no 2 pp 90ndash96 2003

[7] R Pedram K C Kocsis and M Sunkpal ldquoSensitivity analysisof the effect of airflow velocity on the thermal comfort inunderground minesrdquo Journal of Sustainable Mining vol 15no 4 pp 175ndash180 2016

[8] B You C Wu J Li and H Liao ldquoPhysiological responses ofpeople in working faces of deep underground minesrdquo In-ternational Journal of Mining Science and Technology vol 24no 5 pp 683ndash688 2014

[9] M-c He ldquoApplication of HEMS cooling technology in deepmine heat hazard controlrdquo Mining Science and Technology(China) vol 19 no 3 pp 269ndash275 2009

[10] A E Krasnoshtein B P Kazakov and A V ShalimovldquoMathematical modeling of heat exchange between mine airand rock mass during firerdquo Journal of Mining Science vol 42no 3 pp 287ndash295 2006

[11] A P Sasmito J C Kurnia E Birgersson andA S Mujumdar ldquoComputational evaluation of thermalmanagement strategies in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1444ndash1150 2015

[12] R Anderson and E D Souza ldquoHeat stress management inunderground minesrdquo International Journal of Mining Scienceand Technology vol 27 no 4 pp 651ndash655 2017

[13] S P Zhang J Qin and G Chen ldquoHeat transfer analysis ondouble-skin air tube in ventilation of deepmine heading facerdquoProcedia Engineering vol 26 pp 1626ndash1632 2011

[14] A Habibi R B Kramer and A D S Gillies ldquoInvestigating theeffects of heat changes in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1164ndash1171 2015

[15] Y Zhang Z Wan B Gu H Zhang and P Zhou ldquoFinitedifference analysis of transient heat transfer in surroundingrock mass of high geothermal roadwayrdquo MathematicalProblems in Engineering vol 2016 Article ID 89515247 pages 2016

[16] P Duda ldquoFinite element method formulation in polar co-ordinates for transient heat conduction problemsrdquo Journal of5ermal Science vol 25 no 2 pp 188ndash194 2016

[17] J J del Coz Dıaz P J Garcıa Nieto C Betegon Biempica andM B Prendes Gero ldquoAnalysis and optimization of the heat-insulating light concrete hollow brick walls design by the finiteelement methodrdquo Applied5ermal Engineering vol 27 no 8-9 pp 1445ndash1456 2007

[18] C Guo X Nian Y Liu C Qi J Song andW Yu ldquoAnalysis of2D flow and heat transfer modeling in fracture of porousmediardquo Journal of 5ermal Science vol 26 no 4 pp 331ndash3382017

[19] J Kim and H Choi ldquoAn immersed-boundary finite-volumemethod for simulation of heat transfer in complex geome-triesrdquo Ksme International Journal vol 18 no 6pp 1026ndash1035 2004

[20] Q Wu Y P Qin L Guo and Q Y Wu ldquoCalculation of theheat emitting from the wall rock at drifting face with finiteelement methodrdquo China Safety Science Journal vol 12 no 6pp 33ndash36 2002

Mathematical Problems in Engineering 11

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+is work has been financially funded by the Natural ScienceFoundation of China (Grant number 51574249)

Supplementary Materials

+e supplementary material consists of three parts one forrelated data and the other two for related graphics (Sup-plementary Materials)

References

[1] H P Xie H W Zhou D J Xue H W Wang R Zhang andF Gao ldquoResearch and consideration on deep coal mining andcritical mining depthrdquo Journal of China Coal Society vol 37no 4 pp 535ndash542 2012

[2] H Yan F He T Yang L Li S Zhang and J Zhang ldquo+emechanism of bedding separation in roof strata overlying aroadway within a thick coal seam a case study from thePingshuo Coalfield Chinardquo Engineering Failure Analysisvol 62 pp 75ndash92 2016

[3] G E Plessis L Liebenberg and E H Mathews ldquoCase studythe effects of a variable flow energy saving strategy on a deep-mine cooling systemrdquo Applied Energy vol 36 no 1pp 101ndash104 2012

[4] S J Luo X F Wang F Liu L Yan and Y Xie ldquoSome keyproblems and technical countermeasures for deep miningrdquoCoal Technology vol 33 no 11 pp 309ndash311 2014

[5] M Sunkpal P Roghanchi and K C Kocsis ldquoA method toprotect mine workers in hot and humid environmentsrdquo Safetyand Health at Work vol 6 no 11 pp 1ndash10 2017

[6] D J Brake and G P Bates ldquoFluid losses and hydration statusof industrial workers under thermal stress working extendedshiftsrdquo Occupational and Environmental Medicine vol 60no 2 pp 90ndash96 2003

[7] R Pedram K C Kocsis and M Sunkpal ldquoSensitivity analysisof the effect of airflow velocity on the thermal comfort inunderground minesrdquo Journal of Sustainable Mining vol 15no 4 pp 175ndash180 2016

[8] B You C Wu J Li and H Liao ldquoPhysiological responses ofpeople in working faces of deep underground minesrdquo In-ternational Journal of Mining Science and Technology vol 24no 5 pp 683ndash688 2014

[9] M-c He ldquoApplication of HEMS cooling technology in deepmine heat hazard controlrdquo Mining Science and Technology(China) vol 19 no 3 pp 269ndash275 2009

[10] A E Krasnoshtein B P Kazakov and A V ShalimovldquoMathematical modeling of heat exchange between mine airand rock mass during firerdquo Journal of Mining Science vol 42no 3 pp 287ndash295 2006

[11] A P Sasmito J C Kurnia E Birgersson andA S Mujumdar ldquoComputational evaluation of thermalmanagement strategies in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1444ndash1150 2015

[12] R Anderson and E D Souza ldquoHeat stress management inunderground minesrdquo International Journal of Mining Scienceand Technology vol 27 no 4 pp 651ndash655 2017

[13] S P Zhang J Qin and G Chen ldquoHeat transfer analysis ondouble-skin air tube in ventilation of deepmine heading facerdquoProcedia Engineering vol 26 pp 1626ndash1632 2011

[14] A Habibi R B Kramer and A D S Gillies ldquoInvestigating theeffects of heat changes in an underground minerdquo Applied5ermal Engineering vol 90 no 5 pp 1164ndash1171 2015

[15] Y Zhang Z Wan B Gu H Zhang and P Zhou ldquoFinitedifference analysis of transient heat transfer in surroundingrock mass of high geothermal roadwayrdquo MathematicalProblems in Engineering vol 2016 Article ID 89515247 pages 2016

[16] P Duda ldquoFinite element method formulation in polar co-ordinates for transient heat conduction problemsrdquo Journal of5ermal Science vol 25 no 2 pp 188ndash194 2016

[17] J J del Coz Dıaz P J Garcıa Nieto C Betegon Biempica andM B Prendes Gero ldquoAnalysis and optimization of the heat-insulating light concrete hollow brick walls design by the finiteelement methodrdquo Applied5ermal Engineering vol 27 no 8-9 pp 1445ndash1456 2007

[18] C Guo X Nian Y Liu C Qi J Song andW Yu ldquoAnalysis of2D flow and heat transfer modeling in fracture of porousmediardquo Journal of 5ermal Science vol 26 no 4 pp 331ndash3382017

[19] J Kim and H Choi ldquoAn immersed-boundary finite-volumemethod for simulation of heat transfer in complex geome-triesrdquo Ksme International Journal vol 18 no 6pp 1026ndash1035 2004

[20] Q Wu Y P Qin L Guo and Q Y Wu ldquoCalculation of theheat emitting from the wall rock at drifting face with finiteelement methodrdquo China Safety Science Journal vol 12 no 6pp 33ndash36 2002

Mathematical Problems in Engineering 11