AnalysisoftheThermalCharacteristicsofSurroundingRockin ...downloads.hindawi.com/journals/ace/2019/2130943.pdf · temperature, 15°C; inlet air relative humidity, 80%;and inlet airow

Research ArticleAnalysis of the Thermal Characteristics of Surrounding Rock inDeep Underground Space

Liu Chen Jiangbo Li Fei Han Yu Zhang Lang Liu and Bo Zhang

Energy School Xirsquoan University of Science and Technology Yanta Road Xirsquoan 710054 China

Correspondence should be addressed to Lang Liu liulangxusteducn

Received 20 September 2018 Accepted 11 December 2018 Published 16 January 2019

Guest Editor Zhanguo Ma

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

With the development of society the economy and national security the exploitation of deep underground space has become aninevitable trend in human society However high-temperature-related problems occur in deep underground spaces )e hightemperature of deep underground space is essentially influenced by the thermal characteristics of the surrounding rockAccording to the mathematical model of heat transfer of the surrounding rock in deep underground space similar criterianumbers are established Experiments were carried out to investigate the thermal characteristics of the surrounding rock )edistribution characteristics of temperature were determined by the Fourier number (Fo) and Biot number (Bi) and the effects ofheat transfer time airflow velocities and air temperature and radial displacement on the distribution characteristics of tem-perature were studied )e results indicate that the surrounding rock temperature decreases with long heat transfer times highairflow velocities and low air temperatures

1 Introduction

As an important part of urban space resources undergroundspace is an important way to promote urban sustainabledevelopment ability [1 2] )ese uses of underground spaceinclude the installation of transportation infrastructurepublic utilities disposal of waste energy utilization facilitystorage of substances and exploitation of minerals [3ndash9]Resources in shallow underground spaces have graduallybecome exhausted )erefore exploiting deep undergroundspace is becoming increasingly important [10]

)e challenges associated with deep underground spacesinclude high temperatures which are harmful to humanhealth and decreased production efficiency [11 12] In deepunderground space the major source of high temperatures isgeothermal energy Geothermal energy continuouslytransfers from surrounding rocks to deep undergroundspaces It is essential to understand the thermal character-istics of surrounding rock in deep underground spacesMany researchers have examined the thermal characteristicsof surrounding rock by theoretical experimental and

numerical modelling approaches)e unsteady heat transferequation of the rocks surrounding deep roadways withconstant air volume was solved using a variable separationapproach)e solution was an infinite series including Besselfunctions [13] Numerical simulation was utilized to studythe effect of heat generated after burying radioactive wasteon the stability of underground space and the surroundingrock strata for 16 years at a constant heat flux [14] )erandom temperature fields of a tunnel in a cold region wereobtained by numerical simulation and analysed with sto-chastic boundary conditions and random rock properties[15] )e steady heat transfer of surrounding rocks inroadway ventilation was numerically analysed )e heat fluxwas approximately uniformly distributed in a ring shape)e heat flux of the rock near the roadway wall was greaterthan that in the far side roadway wall [16]

)e heat characteristics of the surrounding rock insubway tunnels were analysed by experimental testing for 17years)e heat characteristics of the surrounding rock variedwith depth and heat storage and release are noted [17] Heattransfer characteristics in a single rock fracture were

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 2130943 9 pageshttpsdoiorg10115520192130943

investigated )e experimental results indicated that theroughness of rock improves overall heat transfer whereaslithology has little influence on heat transfer [18]

Although extensive research on the heat characteristicsof surrounding rock in deep underground spaces has beenconducted using theoretical numerical and field testmethods there are only a few experimental studies most ofwhich are focused on steady heat transfer rather than un-steady heat transfer

)is study aims at experimentally investigating theunsteady thermal characteristics of surrounding rock indeep underground space )e thermal properties of sur-rounding rocks and boundary conditions of different deepunderground spaces have significant differences Similarityexperiments were carried out to investigate the thermalcharacteristics of surrounding rock and the effects of themain parameters on the temperature distribution charac-teristics are discussed

2 Heat Transfer Model and Similar Criteria ofSurrounding Rock in DeepUnderground Space

21 Basic Assumptions To model the heat transfer of sur-rounding rock in deep underground space the followingsimplified assumptions are made

(1) )e inner boundary of the surrounding rock is ahollow cylinder with an infinite outer diameter

(2) )e surrounding rock mass is homogeneous andisotropic

(3) )e seepage effect of water in the surrounding rock isnegligible

(4) )e initial temperature of the surrounding rock isequivalent to its original rock temperature

22 Mathematical Model Based on the above assumptionswhich conform to one-dimensional unsteady thermalconduction the mathematical description of cylindricalcoordinate form regardless of the variation in the axialtemperature of the surrounding rock is adopted

)e mathematical equations governing the heat transferof surrounding rock in deep underground space are shownas follows

zTzτ

az2T

zr2+1r

zT

zr1113888 1113889 (1)

Initial condition

T(r τ)|τ0 T0 (2)

Boundary condition

λzT

zr rr0

11138681113868111386811138681113868 h TminusTf( 1113857

T r⟶infin T01113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

τ gt 0 (3)

23 Similarity Analysis Dimensionless equation (1) is ob-tained where θ0 T0minusTf is selected as the temperaturemeasuring scale the radial radius r0 is selected as the lengthmeasuring scale r02α0 is selected as the time measuringscale the average thermal conductivity coefficient λ0 is se-lected as the thermal conductivity coefficient measuringscale the average thermal diffusivity α0 is selected as thermaldiffusivity measuring scale and the average convective heattransfer coefficient h0 is selected as the convective heattransfer coefficient of surrounding rock and the airflowmeasuring scale

Dimensionless equation (4) can be expressed as follows

θ0r20a0

z θθ0( 1113857

z a0τr20( 1113857 a0

a

a0

1r0

1r1r0

θ0r0

z θθ0( 1113857

z rr0( 1113857+θ0r20

z2 θθ0( 1113857

z rr0( 11138572

⎡⎣ ⎤⎦

(4)

)e dimensionless temperature dimensionless radiusand dimensionless thermal diffusion coefficient are given asfollows

Θ θθ0

R r

r0

A a

a0

(5)

Ignoring the change of thermal properties of sur-rounding rocks with temperature A is equal to 1 thenEquation (4) can be converted into

a0

θ0

zΘz a0τr20( 1113857

a0θ0r20

1R

zΘzR

+z2ΘzR21113888 1113889 (6)

)e initial conditions can be converted as follows

a0τr02

0

Θ 1

(7)

)e boundary conditions can be converted to

R 1 λ0θ0r0

zΘzR

h0θ0Θ

R⟶infinzΘzR

0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

a0τr20gt 0 (8)

)e dimensionless equations governing the heat transferof surrounding rock in deep underground space are shownas follows

zΘz Fo( 1113857

1R

zΘzR

+z2ΘzR2 (9)

)e dimensionless initial condition is as follows

2 Advances in Civil Engineering

Fo 0

Θ 1(10)

)e dimensionless boundary condition is as follows

R 1zΘzR

BiΘ

R⟶infinzΘzR

0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

Fo gt 0 (11)

From the derivation of the above dimensionless Equa-tion (9) the dimensionless initial condition (12) and thedimensionless boundary conditions (11) it can be seen thatthe dimensionless temperature Θ of surrounding rock is afunction of Fo Bi and R that is

Θ f Fo Bi R( 1113857 (12)

)erefore the conclusion is obtained as follows theFourier number Fo and Biot number Bi are the similarcriteria numbers of surrounding rock in deep undergroundspace

3 Experimental Method

31 Prototype and Model Surrounding rock in a deep un-derground tunnel was taken as the prototype )e depth ofthe deep underground tunnel centre is 965m Taking therock surrounding a tunnel as a three-dimensional model itwas simplified as cuboids )e tunnel space is located in themiddle of the surrounding rock and the equivalent diameterof the tunnel is 5m)e surrounding rock of the prototype is25m long 25m wide and 625m high A 1 25 scale modelwas built to carry out small-scale model experiments toinvestigate the thermal characteristics of surrounding rockin deep underground space

32 Experimental Device Figure 1 shows the schematicdiagram of the experimental set up )e experimental set upconsists of a surrounding rock model a space model airconditioning equipment a thermal boundary system and adata acquisition system )e surrounding rock model isenclosed by stainless steel and covered with an insulatinglayer to ensure a constant boundary temperature )e air-conditioning equipment which consisted of cooling coil anelectric heater a steam humidifier and a process fan is ableto supply air under various conditions to the space modelFigure 2 is a photograph of the air conditioning equipment)e thermal boundary system is composed of a heating beltand a temperature controller that are uniformly attached tothe outer wall of the surrounding rock to guarantee the fixedthermal boundary temperature requirements were satisfied)e data acquisition system collects and controls the airtemperature air humidity air speed and internal temper-ature of the surrounding rock )ere are arranged tem-perature measuring points in the surrounding rock )elayout of the measuring points in the surrounding rockmodel is shown in Figure 3 Each temperature in radius

displacement r is taken from the average of the vertical andhorizontal direction temperature )e photograph of theexperimental set up is shown in Figure 4

)e measurement parameters used for the experimentalset up and the type and accuracy of the sensor are shown inTable 1 )e sensor position is shown in Figures 1 and 3

33ExperimentalDesign )e experimental model should beguaranteed to be equal to Fourier number Fo Biot number Biand the single value condition of the prototype )e singlevalue condition is the initial rock temperature the constanttemperature boundary of the infinite surrounding rock andthe convection heat transfer boundary of the space )einitial rock temperature and boundary temperature of themodel are the same as those of the prototype the inlet airtemperature and inlet air humidity )e humidity in deepunderground space is generally high accordingly the rel-ative humidity of the inlet air of space in this experiment isconstant at 80 Air enters the space model from the air-conditioning equipment through a section of horizontalpipe and the length of the horizontal pipe is 40 times thediameter of the space so it can be considered that the air inthe underground space model is in the fully developed areaof flow [19]

34 2ermal Properties of Surrounding Rocks )e thermalproperties of the surrounding rock in deep undergroundspace are less affected by pressure variations and temper-ature variations so the thermal properties of the sur-rounding rock can be considered constant A similarsurrounding rock material with a mixture of cement ex-panded perlite quartz sand aluminium powder and waterwas formed )e thermal properties of the surroundingrocks measured by the apparatus in the experiment areshown in Table 2

As shown in Table 2 the thermal properties of thesurrounding rock in the experimental model are smallerthan the properties of the artificial rock )is is because r inthe experimental model is small compared to r in theprototype so with Fo being equal smaller thermal con-ductivity is used in the experimental model

35 ConvectiveHeat Transfer Coefficient In this experimentthe convective heat transfer coefficient was calculated )efollowing method was used to calculate the convective heattransfer coefficient

)e heat gain of air in space is as follows

Q1 G i2 minus i1( 1113857 (13)

)e convective heat transfer between the wall surface ofthe space and the air is as follows

Q2 h Tw minusTp1113872 1113873A1 (14)

Ignoring the heat loss from airflowQ1 should be equal toQ2 )e convective heat transfer coefficient h of the wallsurface of the space and the air can be obtained as follows

Advances in Civil Engineering 3

h G i2 minus i1( 1113857

A Tw minusTp1113872 1113873 (15)

4 Results and Discussion

41 Fourier Number Folowast )e experimental conditions wereas follows original rock temperature 50degC inlet air tem-perature 12degC inlet air relative humidity 80 and inletairflow velocity 35ms )e dimensionless temperaturedistribution of the surrounding rock was tested by varyingFoprime from 0 to 04

Figure 5 shows that the higher the Folowast is the lower the Θis When Folowast is greater than 03 the dimensionless tem-perature of the surrounding rock remained substantiallyconstant As shown in Figure 5 three stages can be dis-tinguished in terms of change in the dimensionless tem-perature initial stage (Folowast 0ndash015) transition stage(Folowast 015ndash03) and stabilization stage (Folowast gt 03) )e in-fluence of Folowast on Θ mainly occurs in the initial stage whileFolowast has an influence in the stabilization stage )is indicatesthat when Folowast is greater than 03 the dimensionless

temperature distribution of the surrounding rock dependson R and Bi independently of Folowast )erefore when Folowast isgreater than 03 the unsteady heat transfer model ofsurrounding rock in deep underground space could besimplified to a steady heat transfer model for simplificationof the calculations

42 Biot Number Bi )e experimental conditions were asfollows original rock temperature 30degC inlet air

Heating belt

Outlet airAir conditioning equipment

Space model

Inlet air

Computer

Humidity sensor

Data acquisition device

Surrounding rock model

Temperature sensor Flow rate sensorT H F

Figure 1 Schematic diagram of the experimental set up

Cooling coil Steam humidifier Electric heater

Figure 2 Photograph of the air-conditioning equipment

Heating belt

Insulating layer


Temperature measuring point

Space model

5cm 5cm

02cm

5cm

5 5 5 5 5 5 5555555

5cm

5cm

555555

5 5 5 5 5

Figure 3 Layout of measuring points in the surrounding rockmodel


temperature 15degC inlet air relative humidity 80 and inletairow velocity 35ms (Bi 987) and 60ms (Bi 152) e dimensionless temperature distribution of the sur-rounding rock was tested by varying Fo

As shown in Figure 6 comparing the dimensionless tem-peratures under two dierent Bi the results show that Θ de-creases with increasing Bi but the inuence of Bi decreases withincreasing dimensionless displacement R A major reason forthe decrease in Θ is that higher Bi leads to a thinner boundarylayer Since convective heat transfer between the internal surfaceof surrounding rock and air was strengthened the closer themeasuring point to the internal surface is the lower the Θ is

It can be seen in Figure 6 that there is little eect onΘ as Foincreases and when Fo is greater than 0355 Bi has no sub-stantial eect onΘ Furthermore as a result when Fo is greaterthan 0355 the unsteady heat transfer model of surroundingrock in deep underground space is signicantly not inuencedby convection heat transfer boundary conditions

43 Radial Displacement R e experimental conditionswere as follows original rock temperature 50degC inlet airtemperature 12degC inlet air relative humidity 80 and inletairow velocity 35ms e dimensionless temperaturedistribution of the surrounding rock was tested by varying R

Figure 7 shows that when Fo is equal to 0 the heat transferstarts and the temperature of the surrounding rockmaintainsthe original rock temperature in all radial displacements eresults veried the accuracy of the experiment

Figure 7 shows the trends of Θ against R When Rchanges from 15 to 45Θ increases e greater the Fo is thehigher the temperature dierence between measured pointsor the temperature gradient is Θ remains almost constantand equal to 1 when R is equal to 45 A major reason for theincrease in Θ is that the original temperature eld of thesurrounding rock is disturbed by air from near R to far R e wall surface near the underground space (R 15) isaected by the ventilation of the deep underground spaceand the temperature is slightly lower while the bottom of thesurrounding rock (R 45) is aected by the original rocktemperature and the temperature is higher

As shown in Figure 7 the temperature gradient de-creases with increasing R that is the heat ux density de-creases with increasing R according to Fourierrsquos law is isbecause the geothermal heat in the deep part of the sur-rounding rock continuously transfers to deep undergroundspace while the airow passes e airow has not yet beenable to disturb the temperature eld there or the heat carriedby the airow is less than the heat transmitted to it that isthe temperature range of the surrounding rock that can bespread into the underground space is from near R to far R

As shown in Figure 7 the curve of an Fo value of 0403and the curve of an Fo value of 0470 nearly overlap eresults show that when Fo is more than 0403 the di-mensionless temperature distribution tends to be stable asdoes the heat ux density distribution

44 Inlet Air Temperature Tf e experimental conditionswere as follows original rock temperature 40degC inlet airrelative humidity 80 and inlet airow velocity 5ms edimensionless temperature distribution of the surroundingrock was tested by varying the inlet air temperature from16degC to 25degC

Computer

Temperature controller


Space model

Figure 4 Photograph of the experimental set up

Table 1 Measured parameters

Measured parameter Type Measurement range AccuracyTemperature PT 100 minus40degCsim150degC plusmn05degCRelative humidity Capacitive 0sim100 RH plusmn2Airow velocity Hot wire 0mssim15ms plusmn02ms

Table 2 ermal properties of surrounding rocks

Density (kgm3) Specic heat capacity(kJ(kgmiddotk))

ermal conductivityW(mmiddotK)

772 0804 0139

100

095

090

085

080

075

0700 100 200

Folowast (times10ndash3)

300 400

Θ

Figure 5 Eect of Folowast on Θ


100

090

080

070

060

050

04015 20 25 30

R35 40

Bi = 987Bi = 152

45

Θ

(a)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(b)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(c)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(d)

Figure 6 Eect of Bi on Θ (a) Fo 0067 (b) Fo 0201 (c) Fo 0268 (d) Fo 0355

105

R

Fo = 0Fo = 0067Fo = 0134

Fo = 0201Fo = 0268Fo = 0335

Fo = 0403Fo = 0470

100095090085080075070065060

050055

15 20 25 30 35 40 45

Θ

Figure 7 Eect of R on Θ


Figure 8 shows the trends of Θ against Tf When Tfchanges from 16degC to 25degC Θ increases A major reason forthe increase in Θ is that higher Tf leads to a smaller tem-perature dierence between the internal surface of sur-rounding rock and air which decreases heat convection

As shown in Figure 8 Tf aected the closer measuringpoints more than the further measuring points When R wasequal to 45 Θ was nearly equivalent to 10 with any value ofFo is also indicates that the inuence of air temperatureon the heat transfer range is negligible

5 Conclusions

(a) e heat transfer between surrounding rock anddeep underground space is a complicated non-stationary process A 1-dimensional nonstationaryheat transfer model was established to model theheat transfer of surrounding rock and deep

underground space e temperature distribution ofthe surrounding rock was a function of the radialdisplacement (R) Biot number (Bi) and Fouriernumber (Fo) by dimensional analysis

(b) Experiments were carried out to investigate thethermal characteristics of the surrounding rock Inthis experiment Fourier number (Fo) and Biotnumber (Bi) were adopted as the criteria of similarityand the model was made at a 125 geometric scale rough simulation experiments the temperatureeld of the surrounding rock is obtained and theeects of Fo Bi R and Tf on Θ are analysed

(c) e experimental results indicate that three stagescan be distinguished in terms of change in di-mensionless temperature initial stage (Foprime 0ndash015)transition stage (Foprime 015ndash03) and stabilizationstage (Foprime gt 03) To facilitate engineering applica-tions the nonstationary heat transfer of surrounding

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(a)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(b)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(c)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(d)

Figure 8 Eect of tf on Θ (a) Fo 0067 (b) Fo 0201 (c) Fo 0268 (d) Fo 0355


rock in deep underground space could be simplifiedas stationary heat transfer in the stabilization stageWhen R is less than or equal to 40 the higher the Foand Bi are the lower the dimensionless temperaturewith the same R is while the higher the Tf is thehigher the dimensionless temperature with the sameR is When R is equal to 45Θ is nearly equivalent to10 with any value of Fo Bi and Tf )us when Fo isless than or equal to 047 and R is greater thanor equal to 45 and the temperature field of thesurrounding rock is less affected by the undergroundspace

Nomenclature

A Dimensionless thermal diffusivity (αα0)A1 Internal surface area of surrounding rock (m2)Bi Biot number (hr0λ)Fo Fourier number with the feature size of r0 (ατr02)Folowast Fourier number with the feature size of r (ατr2)G Air mass flow rate (kgs)h Convective heat transfer coefficient (W(m2middotK))h0 Average convective heat transfer coefficient (W

(m2middotK))i Enthalpy (kJkg)Q Heat gain (kW)R Dimensionless radial displacement (rr0)r Radius displacement (m)r0 Space radius (m)T Temperature (degC)Tf Air temperature (degC)T0 Initial temperature (degC)Tw Wall temperature (degC)Tp Average temperature of the air ((T2minusT1)2) (degC)

Greek Symbols

Θ Dimensionless temperature ((TminusTf )(T0minusTf ))α )ermal diffusivity (m2s)α0 Average thermal diffusivity (m2s)θ0 Temperature measuring scale (T0minusTf ) (degC)λ )ermal conductivity (W(mmiddotK))λ0 Average thermal conductivity (W(mmiddotK))τ Time (s)

Subscript

1 Inlet air2 Outlet air

Data Availability

All the original data used to support the findings of thisstudy are shown in the figures

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is study was supported by the National Natural ScienceFoundations of China (Nos 51404191 51504182 51674188and 51774229) Shaanxi Innovative Talents CultivateProgram-New-Star Plan of Science and Technology(2018KJXX-083) Natural Science Basic Research Plan ofShaanxi Province of China (No 2015JQ5187) ScientificResearch Program funded by the Shaanxi Provincial Edu-cation Department (No 15JK1466) China PostdoctoralScience Foundation (No 2015M582685) and OutstandingYouth Science Fund of Xirsquoan University of Science andTechnology (No 2018YQ2-01)

References

[1] X Wang F Zhen X Huang M Zhang and Z Liu ldquoFactorsinfluencing the development potential of urban undergroundspace structural equation model approachrdquo Tunnelling andUnderground Space Technology vol 38 no 3 pp 235ndash2432013

[2] B Uliasz-Misiak and A Przybycin ldquoPresent and future statusof the underground space use in Polandrdquo EnvironmentalEarth Sciences vol 75 no 22 p 1430 2016

[3] MWang L Liu L Chen X Zhang B Zhang and C Ji ldquoColdload and storage functional backfill for cooling deep minerdquoAdvances in Civil Engineering vol 2018 Article ID 54352148 pages 2018

[4] D Evans M Stephenson and R Shaw ldquo)e present andfuture use of rsquolandrsquo below groundrdquo Land Use Policy vol 26pp S302ndashS316 2009

[5] N Bobylev ldquoMainstreaming sustainable development into acityrsquos master plan a case of urban underground space userdquoLand Use Policy vol 26 no 4 pp 1128ndash1137 2009

[6] C D F Rogers H Parker R Sterling et al ldquoSustainabilityissues for underground space in urban areasrdquoUrban Design ampPlanning vol 165 no 4 pp 241ndash254 2012

[7] S A Alkaff S C Sim and M N Ervina Efzan ldquoA review ofunderground building towards thermal energy efficiency andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 60 pp 692ndash713 2016

[8] Z Yujiao L Ruoyao J Changfa H Chao Z Bo and L LangldquoParametric study and design of an earth-air heat exchangerusing model experiment for memorial heating and coolingrdquoApplied 2ermal Engineering vol 148 no 2 pp 838ndash8452019

[9] L Lang F Zhiyu Q Chongchong Z Bo G Lijie andK I-I L Song ldquoNumerical study on the pipe flow charac-teristics of the cemented paste backfill slurry consideringhydration effectsrdquo Powder Technology vol 343 pp 454ndash4642019

[10] P G Ranjith J Zhao M Ju R V S De SilvaT D Rathnaweera and A K M S Bandara ldquoOpportunitiesand challenges in deep mining a brief reviewrdquo Engineeringvol 3 no 4 pp 546ndash551 2017

[11] F Winde F Kaiser and E Erasmus ldquoExploring the use ofdeep level gold mines in South Africa for undergroundpumped hydroelectric energy storage schemesrdquo Renewableand Sustainable Energy Reviews vol 78 pp 668ndash682 2017

[12] F H V Glehn R Hemp and R C Funnell ldquoNumericalmodelling of heat flow in minesrdquo South African Journal ofScience vol 98 no 9 pp 485ndash490 2002


[13] Y Wang G Zhou L Wu Y Zhou and Y Lu ldquoAn analyticalstudy of unsteady heat transfer in the rock surrounding a deepairwayrdquo International Journal of Mining Science and Tech-nology vol 22 no 3 pp 411ndash415 2012

[14] A K Verma P Gautam T N Singh and R K BajpaildquoNumerical simulation of high level radioactive waste fordisposal in deep underground tunnelrdquo in Engineering Geologyfor Society and Territory Volume 1 Springer InternationalPublishing Berlin Germany 2015

[15] T Wang G Zhou J Wang and X Zhao ldquoStochastic analysisfor the uncertain temperature field of tunnel in cold regionsrdquoTunnelling and Underground Space Technology vol 59pp 7ndash15 2016

[16] C Du and M Bian ldquoNumerical simulation of fluid solidcoupling heat transfer in tunnelrdquo Case Studies in 2ermalEngineering vol 12 pp 117ndash125 2018

[17] LWang X Zou H Tao J Song and Y Zheng ldquoExperimentalstudy on evolution characteristics of the heat storage ofsurrounding soil in subway tunnelsrdquo Procedia Engineeringvol 205 pp 2728ndash2735 2017

[18] Z W Li X T Feng Y J Zhang C Zhang T F Xu andY S Wang ldquoExperimental research on the convection heattransfer characteristics of distilled water in manmade smoothand rough rock fracturesrdquo Energy vol 133 pp 206ndash208 2017

[19] F Kreith R M Manglik and M S Bohn Principles of HeatTransfer )omson Learning Boston MA USA 1965


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investigated )e experimental results indicated that theroughness of rock improves overall heat transfer whereaslithology has little influence on heat transfer [18]

Although extensive research on the heat characteristicsof surrounding rock in deep underground spaces has beenconducted using theoretical numerical and field testmethods there are only a few experimental studies most ofwhich are focused on steady heat transfer rather than un-steady heat transfer

)is study aims at experimentally investigating theunsteady thermal characteristics of surrounding rock indeep underground space )e thermal properties of sur-rounding rocks and boundary conditions of different deepunderground spaces have significant differences Similarityexperiments were carried out to investigate the thermalcharacteristics of surrounding rock and the effects of themain parameters on the temperature distribution charac-teristics are discussed

2 Heat Transfer Model and Similar Criteria ofSurrounding Rock in DeepUnderground Space

21 Basic Assumptions To model the heat transfer of sur-rounding rock in deep underground space the followingsimplified assumptions are made

(1) )e inner boundary of the surrounding rock is ahollow cylinder with an infinite outer diameter

(2) )e surrounding rock mass is homogeneous andisotropic

(3) )e seepage effect of water in the surrounding rock isnegligible

(4) )e initial temperature of the surrounding rock isequivalent to its original rock temperature

22 Mathematical Model Based on the above assumptionswhich conform to one-dimensional unsteady thermalconduction the mathematical description of cylindricalcoordinate form regardless of the variation in the axialtemperature of the surrounding rock is adopted

)e mathematical equations governing the heat transferof surrounding rock in deep underground space are shownas follows

zTzτ

az2T

zr2+1r

zT

zr1113888 1113889 (1)

Initial condition

T(r τ)|τ0 T0 (2)

Boundary condition

λzT

zr rr0

11138681113868111386811138681113868 h TminusTf( 1113857

T r⟶infin T01113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

τ gt 0 (3)

23 Similarity Analysis Dimensionless equation (1) is ob-tained where θ0 T0minusTf is selected as the temperaturemeasuring scale the radial radius r0 is selected as the lengthmeasuring scale r02α0 is selected as the time measuringscale the average thermal conductivity coefficient λ0 is se-lected as the thermal conductivity coefficient measuringscale the average thermal diffusivity α0 is selected as thermaldiffusivity measuring scale and the average convective heattransfer coefficient h0 is selected as the convective heattransfer coefficient of surrounding rock and the airflowmeasuring scale

Dimensionless equation (4) can be expressed as follows

θ0r20a0

z θθ0( 1113857

z a0τr20( 1113857 a0

a

a0

1r0

1r1r0

θ0r0

z θθ0( 1113857

z rr0( 1113857+θ0r20

z2 θθ0( 1113857

z rr0( 11138572

⎡⎣ ⎤⎦

(4)

)e dimensionless temperature dimensionless radiusand dimensionless thermal diffusion coefficient are given asfollows

Θ θθ0

R r

r0

A a

a0

(5)

Ignoring the change of thermal properties of sur-rounding rocks with temperature A is equal to 1 thenEquation (4) can be converted into

a0

θ0

zΘz a0τr20( 1113857

a0θ0r20

1R

zΘzR

+z2ΘzR21113888 1113889 (6)

)e initial conditions can be converted as follows

a0τr02

0

Θ 1

(7)

)e boundary conditions can be converted to

R 1 λ0θ0r0

zΘzR

h0θ0Θ

R⟶infinzΘzR

0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

a0τr20gt 0 (8)

)e dimensionless equations governing the heat transferof surrounding rock in deep underground space are shownas follows

zΘz Fo( 1113857

1R

zΘzR

+z2ΘzR2 (9)

)e dimensionless initial condition is as follows


Fo 0

Θ 1(10)


R 1zΘzR

BiΘ

R⟶infinzΘzR

0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

Fo gt 0 (11)


Θ f Fo Bi R( 1113857 (12)












Q1 G i2 minus i1( 1113857 (13)


Q2 h Tw minusTp1113872 1113873A1 (14)



h G i2 minus i1( 1113857

A Tw minusTp1113872 1113873 (15)






Heating belt


Space model

Inlet air

Computer

Humidity sensor







Heating belt

Insulating layer



Space model

5cm 5cm

02cm

5cm

5 5 5 5 5 5 5555555

5cm

5cm

555555

5 5 5 5 5












Computer



Space model







772 0804 0139

100

095

090

085

080

075

0700 100 200


300 400

Θ



100

090

080

070

060

050

04015 20 25 30

R35 40

Bi = 987Bi = 152

45

Θ

(a)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(b)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(c)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(d)


105

R

Fo = 0Fo = 0067Fo = 0134

Fo = 0201Fo = 0268Fo = 0335

Fo = 0403Fo = 0470

100095090085080075070065060

050055

15 20 25 30 35 40 45

Θ





5 Conclusions





105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(a)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(b)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(c)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(d)




Nomenclature



Greek Symbols


Subscript


Data Availability




Acknowledgments


References
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Fo 0

Θ 1(10)


R 1zΘzR

BiΘ

R⟶infinzΘzR

0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

Fo gt 0 (11)


Θ f Fo Bi R( 1113857 (12)












Q1 G i2 minus i1( 1113857 (13)


Q2 h Tw minusTp1113872 1113873A1 (14)



h G i2 minus i1( 1113857

A Tw minusTp1113872 1113873 (15)






Heating belt


Space model

Inlet air

Computer

Humidity sensor







Heating belt

Insulating layer



Space model

5cm 5cm

02cm

5cm

5 5 5 5 5 5 5555555

5cm

5cm

555555

5 5 5 5 5












Computer



Space model







772 0804 0139

100

095

090

085

080

075

0700 100 200


300 400

Θ



100

090

080

070

060

050

04015 20 25 30

R35 40

Bi = 987Bi = 152

45

Θ

(a)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(b)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(c)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(d)


105

R

Fo = 0Fo = 0067Fo = 0134

Fo = 0201Fo = 0268Fo = 0335

Fo = 0403Fo = 0470

100095090085080075070065060

050055

15 20 25 30 35 40 45

Θ





5 Conclusions





105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(a)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(b)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(c)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(d)




Nomenclature



Greek Symbols


Subscript


Data Availability




Acknowledgments


References
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


h G i2 minus i1( 1113857

A Tw minusTp1113872 1113873 (15)






Heating belt


Space model

Inlet air

Computer

Humidity sensor







Heating belt

Insulating layer



Space model

5cm 5cm

02cm

5cm

5 5 5 5 5 5 5555555

5cm

5cm

555555

5 5 5 5 5












Computer



Space model







772 0804 0139

100

095

090

085

080

075

0700 100 200


300 400

Θ



100

090

080

070

060

050

04015 20 25 30

R35 40

Bi = 987Bi = 152

45

Θ

(a)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(b)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(c)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(d)


105

R

Fo = 0Fo = 0067Fo = 0134

Fo = 0201Fo = 0268Fo = 0335

Fo = 0403Fo = 0470

100095090085080075070065060

050055

15 20 25 30 35 40 45

Θ





5 Conclusions





105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(a)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(b)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(c)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(d)




Nomenclature



Greek Symbols


Subscript


Data Availability




Acknowledgments


References
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











Computer



Space model







772 0804 0139

100

095

090

085

080

075

0700 100 200


300 400

Θ



100

090

080

070

060

050

04015 20 25 30

R35 40

Bi = 987Bi = 152

45

Θ

(a)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(b)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(c)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(d)


105

R

Fo = 0Fo = 0067Fo = 0134

Fo = 0201Fo = 0268Fo = 0335

Fo = 0403Fo = 0470

100095090085080075070065060

050055

15 20 25 30 35 40 45

Θ





5 Conclusions





105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(a)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(b)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(c)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(d)




Nomenclature



Greek Symbols


Subscript


Data Availability




Acknowledgments


References
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


100

090

080

070

060

050

04015 20 25 30

R35 40

Bi = 987Bi = 152

45

Θ

(a)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(b)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(c)

Bi = 987Bi = 152

100

090

080

070

060

050

04015 20 25 30

R35 40 45

Θ

(d)


105

R

Fo = 0Fo = 0067Fo = 0134

Fo = 0201Fo = 0268Fo = 0335

Fo = 0403Fo = 0470

100095090085080075070065060

050055

15 20 25 30 35 40 45

Θ





5 Conclusions





105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(a)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(b)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(c)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(d)




Nomenclature



Greek Symbols


Subscript


Data Availability




Acknowledgments


References
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




5 Conclusions





105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(a)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(b)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(c)

105

100

095

090

085

080

075

070

065

060

05515 20 25 30 35 40 45

R

Θ

16degC19degC

22degC25degC

(d)




Nomenclature



Greek Symbols


Subscript


Data Availability




Acknowledgments


References
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Nomenclature



Greek Symbols


Subscript


Data Availability




Acknowledgments


References
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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