analysisofthethermalcharacteristicsofsurroundingrockin ...temperature, 15 c; inlet air relative...

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, Xi’an University of Science and Technology, Yanta Road, Xi’an 710054, China

Correspondence should be addressed to Lang Liu; [email protected]

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

Guest Editor: Zhanguo Ma

Copyright © 2019 Liu Chen et al. )is is an open access article distributed under the Creative Commons Attribution License,which 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 rock.According 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 infrastructure,public utilities, disposal of waste, energy utilization facility,storage of substances, and exploitation of minerals [3–9].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 spaces.Many 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 pageshttps://doi.org/10.1155/2019/2130943

mailto:[email protected]://orcid.org/0000-0001-9536-0508http://orcid.org/0000-0002-7332-081Xhttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2019/2130943

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

2.1. 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

2.2. Mathematical Model. Based on the above assumptions,which 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

zr . (1)

Initial condition:

T(r, τ)|τ�0 � T0. (2)

Boundary condition:

λzT

zr r�r0

� h T−Tf( ,

T r⟶∞ � T0 ,

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

τ > 0. (3)

2.3. Similarity Analysis. Dimensionless equation (1) is ob-tained where θ0 �T0−Tf is selected as the temperaturemeasuring scale, the radial radius r0 is selected as the lengthmeasuring scale, r02/α0 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:

θ0r20/a0

z θ/θ0( z a0τ/r20(

� a0a

a0

1r0

1/r1/r0

θ0r0

z θ/θ0( z r/r0(

+θ0r20

z2 θ/θ0( z r/r0(

2⎡⎣ ⎤⎦.

(4)

)e dimensionless temperature, dimensionless radius,and 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 a0τ/r20(

�a0θ0r20

1R

zΘzR

+z2ΘzR2

. (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⟶∞zΘzR

� 0,

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

a0τr20> 0. (8)

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

zΘz Fo(

�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 � 1,zΘzR

� BiΘ,

R⟶∞,zΘzR

� 0,

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

Fo > 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( . (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

3.1. 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 62.5m high. A 1 : 25 scale modelwas built to carry out small-scale model experiments toinvestigate the thermal characteristics of surrounding rockin deep underground space.

3.2. 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 model.Figure 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.

3.3.ExperimentalDesign. )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].

3.4. 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.

3.5. ConvectiveHeat Transfer Coefficient. In this experiment,the 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 − i1( . (13)

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

Q2 � h Tw −Tp A1. (14)

Ignoring the heat loss from airflow,Q1 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 − i1(

A Tw −Tp . (15)

4. Results and Discussion

4.1. Fourier Number Fo∗. )e experimental conditions wereas follows: original rock temperature, 50°C; inlet air tem-perature, 12°C; inlet air relative humidity, 80%; and inletairflow velocity, 3.5m/s. )e dimensionless temperaturedistribution of the surrounding rock was tested by varyingFo′ from 0 to 0.4.

Figure 5 shows that the higher the Fo∗ is, the lower the Θis. When Fo∗ is greater than 0.3, 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 (Fo∗� 0–0.15), transition stage(Fo∗� 0.15–0.3), and stabilization stage (Fo∗ > 0.3). )e in-fluence of Fo∗ on Θ mainly occurs in the initial stage, whileFo∗ has an influence in the stabilization stage. )is indicatesthat when Fo∗ is greater than 0.3, the dimensionless

temperature distribution of the surrounding rock dependson R and Bi independently of Fo∗. )erefore, when Fo∗ isgreater than 0.3, the unsteady heat transfer model ofsurrounding rock in deep underground space could besimplified to a steady heat transfer model for simplificationof the calculations.

4.2. Biot Number Bi. )e experimental conditions were asfollows: original rock temperature, 30°C; 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

0.2cm

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, 15°C; inlet air relative humidity, 80%; and inletair�ow velocity, 3.5m/s (Bi� 9.87) and 6.0m/s (Bi� 15.2). 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 in�uence 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 0.355, Bi has no sub-stantial eect onΘ. Furthermore, as a result, when Fo is greaterthan 0.355, the unsteady heat transfer model of surroundingrock in deep underground space is signicantly not in�uencedby convection heat transfer boundary conditions.

4.3. Radial Displacement R. e experimental conditionswere as follows: original rock temperature, 50°C; inlet airtemperature, 12°C; inlet air relative humidity, 80%; and inletair�ow velocity, 3.5m/s. 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 1.5 to 4.5,Θ 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 4.5. 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� 1.5) isaected by the ventilation of the deep underground space,and the temperature is slightly lower, while the bottom of thesurrounding rock (R� 4.5) 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 Fourier’s law. is isbecause the geothermal heat in the deep part of the sur-rounding rock continuously transfers to deep undergroundspace while the air�ow passes. e air�ow has not yet beenable to disturb the temperature eld there, or the heat carriedby the air�ow is less than the heat transmitted to it; that is,the 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 0.403and the curve of an Fo value of 0.470 nearly overlap. eresults show that when Fo is more than 0.403, the di-mensionless temperature distribution tends to be stable, asdoes the heat �ux density distribution.

4.4. Inlet Air Temperature Tf. e experimental conditionswere as follows: original rock temperature, 40°C; inlet airrelative humidity, 80%; and inlet air�ow velocity, 5m/s. edimensionless temperature distribution of the surroundingrock was tested by varying the inlet air temperature from16°C to 25°C.

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 −40°C∼150°C ±0.5°CRelative humidity Capacitive 0%∼100% RH ±2%Air�ow velocity Hot wire 0m/s∼15m/s ±0.2m/s

Table 2: ermal properties of surrounding rocks.

Density (kg/m3) Specic heat capacity(kJ/(kg·k)) ermal conductivity

W/(m·K)772 0.804 0.139

1.00

0.95

0.90

0.85

0.80

0.75

0.700 100 200

Fo∗ (×10–3)300 400

Θ

Figure 5: Eect of Fo∗ on Θ.


1.00

0.90

0.80

0.70

0.60

0.50

0.401.5 2.0 2.5 3.0

R3.5 4.0

Bi = 9.87Bi = 15.2

4.5

Θ

(a)

Bi = 9.87Bi = 15.2

1.00

0.90

0.80

0.70

0.60

0.50

0.401.5 2.0 2.5 3.0

R3.5 4.0 4.5

Θ

(b)

Bi = 9.87Bi = 15.2

1.00

0.90

0.80

0.70

0.60

0.50

0.401.5 2.0 2.5 3.0

R3.5 4.0 4.5

Θ

(c)

Bi = 9.87Bi = 15.2

1.00

0.90

0.80

0.70

0.60

0.50

0.401.5 2.0 2.5 3.0

R3.5 4.0 4.5

Θ

(d)

Figure 6: Eect of Bi on Θ. (a) Fo� 0.067. (b) Fo� 0.201. (c) Fo� 0.268. (d) Fo� 0.355.

1.05

R

Fo = 0Fo = 0.067Fo = 0.134

Fo = 0.201Fo = 0.268Fo = 0.335

Fo = 0.403Fo = 0.470

1.000.950.900.850.800.750.700.650.60

0.500.55

1.5 2.0 2.5 3.0 3.5 4.0 4.5

Θ

Figure 7: Eect of R on Θ.


Figure 8 shows the trends of Θ against Tf. When Tfchanges from 16°C to 25°C, 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 4.5, Θ was nearly equivalent to 1.0 with any value ofFo. is also indicates that the in�uence 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 similarity,and the model was made at a 1/25 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 (Fo′� 0–0.15),transition stage (Fo′� 0.15–0.3), and stabilizationstage (Fo′ > 0.3). To facilitate engineering applica-tions, the nonstationary heat transfer of surrounding

1.05

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.551.5 2.0 2.5 3.0 3.5 4.0 4.5

R

Θ

16°C19°C

22°C25°C

(a)

1.05

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.551.5 2.0 2.5 3.0 3.5 4.0 4.5

R

Θ

16°C19°C

22°C25°C

(b)

1.05

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.551.5 2.0 2.5 3.0 3.5 4.0 4.5

R

Θ

16°C19°C

22°C25°C

(c)

1.05

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.551.5 2.0 2.5 3.0 3.5 4.0 4.5

R

Θ

16°C19°C

22°C25°C

(d)

Figure 8: Eect of tf on Θ. (a) Fo� 0.067. (b) Fo� 0.201. (c) Fo� 0.268. (d) Fo� 0.355.


rock in deep underground space could be simplifiedas stationary heat transfer in the stabilization stage.When R is less than or equal to 4.0, 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 4.5,Θ is nearly equivalent to1.0 with any value of Fo, Bi, and Tf. )us, when Fo isless than or equal to 0.47, and R is greater thanor equal to 4.5, and the temperature field of thesurrounding rock is less affected by the undergroundspace.

Nomenclature

A: Dimensionless thermal diffusivity (α/α0)A1: Internal surface area of surrounding rock (m2)Bi: Biot number (hr0/λ)Fo: Fourier number with the feature size of r0 (ατ/r02)Fo∗: Fourier number with the feature size of r (ατ/r2)G: Air mass flow rate (kg/s)h: Convective heat transfer coefficient (W/(m2·K))h0: Average convective heat transfer coefficient (W/

(m2·K))i: Enthalpy (kJ/kg)Q: Heat gain (kW)R: Dimensionless radial displacement (r/r0)r: Radius displacement (m)r0: Space radius (m)T: Temperature (°C)Tf: Air temperature (°C)T0: Initial temperature (°C)Tw: Wall temperature (°C)Tp: Average temperature of the air ((T2−T1)/2) (°C)

Greek Symbols

Θ: Dimensionless temperature ((T−Tf )/(T0−Tf ))α: )ermal diffusivity (m2/s)α0: Average thermal diffusivity (m2/s)θ0: Temperature measuring scale (T0−Tf ) (°C)λ: )ermal conductivity (W/(m·K))λ0: Average thermal conductivity (W/(m·K))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, 51674188,and 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 Xi’an University of Science andTechnology (No. 2018YQ2-01).

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