Analysis of the Thermal Characteristics of Surrounding Rock in Deep Underground Space

With the development of society, the economy, and national security, the exploitation of deep underground space has become an inevitable trend in human society. However, high-temperature-related problems occur in deep underground spaces. )e high temperature 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 criteria numbers are established. Experiments were carried out to investigate the thermal characteristics of the surrounding rock. )e distribution characteristics of temperature were determined by the Fourier number (Fo) and Biot number (Bi), and the effects of heat transfer time, airflow velocities, and air temperature and radial displacement on the distribution characteristics of temperature were studied. )e results indicate that the surrounding rock temperature decreases with long heat transfer times, high airflow velocities, and low air temperatures.


Introduction
As an important part of urban space resources, underground space is an important way to promote urban sustainable development ability [1,2]. ese uses of underground space include the installation of transportation infrastructure, public utilities, disposal of waste, energy utilization facility, storage of substances, and exploitation of minerals [3][4][5][6][7][8][9]. Resources in shallow underground spaces have gradually become exhausted. erefore, exploiting deep underground space is becoming increasingly important [10]. e challenges associated with deep underground spaces include high temperatures, which are harmful to human health, and decreased production efficiency [11,12]. In deep underground space, the major source of high temperatures is geothermal energy. Geothermal energy continuously transfers from surrounding rocks to deep underground spaces. It is essential to understand the thermal characteristics of surrounding rock in deep underground spaces. Many researchers have examined the thermal characteristics of surrounding rock by theoretical, experimental, and numerical modelling approaches. e unsteady heat transfer equation of the rocks surrounding deep roadways with constant air volume was solved using a variable separation approach. e solution was an infinite series including Bessel functions [13]. Numerical simulation was utilized to study the effect of heat generated after burying radioactive waste on the stability of underground space and the surrounding rock strata for 16 years at a constant heat flux [14]. e random temperature fields of a tunnel in a cold region were obtained by numerical simulation and analysed with stochastic boundary conditions and random rock properties [15]. e steady heat transfer of surrounding rocks in roadway ventilation was numerically analysed. e heat flux was approximately uniformly distributed in a ring shape. e heat flux of the rock near the roadway wall was greater than that in the far side roadway wall [16]. e heat characteristics of the surrounding rock in subway tunnels were analysed by experimental testing for 17 years. e heat characteristics of the surrounding rock varied with depth, and heat storage and release are noted [17]. Heat transfer characteristics in a single rock fracture were investigated. e experimental results indicated that the roughness of rock improves overall heat transfer, whereas lithology has little influence on heat transfer [18].
Although extensive research on the heat characteristics of surrounding rock in deep underground spaces has been conducted using theoretical, numerical, and field test methods, there are only a few experimental studies, most of which are focused on steady heat transfer rather than unsteady heat transfer.
is study aims at experimentally investigating the unsteady thermal characteristics of surrounding rock in deep underground space. e thermal properties of surrounding rocks and boundary conditions of different deep underground spaces have significant differences. Similarity experiments were carried out to investigate the thermal characteristics of surrounding rock, and the effects of the main parameters on the temperature distribution characteristics are discussed. (1) e inner boundary of the surrounding rock is a hollow cylinder with an infinite outer diameter (2) e surrounding rock mass is homogeneous and isotropic (3) e seepage effect of water in the surrounding rock is negligible (4) e initial temperature of the surrounding rock is equivalent to its original rock temperature 2.2. Mathematical Model. Based on the above assumptions, which conform to one-dimensional unsteady thermal conduction, the mathematical description of cylindrical coordinate form regardless of the variation in the axial temperature of the surrounding rock is adopted. e mathematical equations governing the heat transfer of surrounding rock in deep underground space are shown as follows:

Heat Transfer Model and Similar
Initial condition: Boundary condition: (1) is obtained where θ 0 � T 0 − T f is selected as the temperature measuring scale, the radial radius r 0 is selected as the length measuring scale, r 0 2 /α 0 is selected as the time measuring scale, the average thermal conductivity coefficient λ 0 is selected as the thermal conductivity coefficient measuring scale, the average thermal diffusivity α 0 is selected as thermal diffusivity measuring scale, and the average convective heat transfer coefficient h 0 is selected as the convective heat transfer coefficient of surrounding rock and the airflow measuring scale.

Similarity Analysis. Dimensionless equation
Dimensionless equation (4) can be expressed as follows: e dimensionless temperature, dimensionless radius, and dimensionless thermal diffusion coefficient are given as follows: Ignoring the change of thermal properties of surrounding rocks with temperature, A is equal to 1; then Equation (4) can be converted into e initial conditions can be converted as follows: e boundary conditions can be converted to e dimensionless equations governing the heat transfer of surrounding rock in deep underground space are shown as follows: e dimensionless initial condition is as follows: 2 Advances in Civil Engineering e dimensionless boundary condition is as follows: From the derivation of the above dimensionless Equation (9), the dimensionless initial condition (12), and the dimensionless boundary conditions (11), it can be seen that the dimensionless temperature Θ of surrounding rock is a function of F o , B i , and R, that is, erefore, the conclusion is obtained as follows: the Fourier number F o and Biot number B i are the similar criteria numbers of surrounding rock in deep underground space.

Prototype and Model.
Surrounding rock in a deep underground tunnel was taken as the prototype. e depth of the deep underground tunnel centre is 965 m. Taking the rock surrounding a tunnel as a three-dimensional model, it was simplified as cuboids. e tunnel space is located in the middle of the surrounding rock, and the equivalent diameter of the tunnel is 5 m. e surrounding rock of the prototype is 25 m long, 25 m wide, and 62.5 m high. A 1 : 25 scale model was built to carry out small-scale model experiments to investigate the thermal characteristics of surrounding rock in deep underground space. Figure 1 shows the schematic diagram of the experimental set up. e experimental set up consists of a surrounding rock model, a space model, air conditioning equipment, a thermal boundary system, and a data acquisition system. e surrounding rock model is enclosed by stainless steel and covered with an insulating layer to ensure a constant boundary temperature. e airconditioning equipment, which consisted of cooling coil, an electric heater, a steam humidifier, and a process fan, is able to 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 belt and a temperature controller that are uniformly attached to the outer wall of the surrounding rock to guarantee the fixed thermal boundary temperature requirements were satisfied. e data acquisition system collects and controls the air temperature, air humidity, air speed, and internal temperature of the surrounding rock.

Experimental Device.
ere are arranged temperature measuring points in the surrounding rock. e layout of the measuring points in the surrounding rock model is shown in Figure 3. Each temperature in radius displacement r is taken from the average of the vertical and horizontal direction temperature. e photograph of the experimental set up is shown in Figure 4. e measurement parameters used for the experimental set up and the type and accuracy of the sensor are shown in Table 1. e sensor position is shown in Figures 1 and 3.

Experimental Design.
e experimental model should be guaranteed to be equal to Fourier number F o , Biot number B i and the single value condition of the prototype. e single value condition is the initial rock temperature, the constant temperature boundary of the infinite surrounding rock, and the convection heat transfer boundary of the space. e initial rock temperature and boundary temperature of the model are the same as those of the prototype, the inlet air temperature, and inlet air humidity. e humidity in deep underground space is generally high; accordingly, the relative humidity of the inlet air of space in this experiment is constant at 80%. Air enters the space model from the airconditioning equipment through a section of horizontal pipe, and the length of the horizontal pipe is 40 times the diameter of the space, so it can be considered that the air in the underground space model is in the fully developed area of flow [19].

ermal Properties of Surrounding Rocks.
e thermal properties of the surrounding rock in deep underground space are less affected by pressure variations and temperature variations, so the thermal properties of the surrounding rock can be considered constant. A similar surrounding rock material with a mixture of cement, expanded perlite, quartz sand, aluminium powder, and water was formed. e thermal properties of the surrounding rocks measured by the apparatus in the experiment are shown in Table 2.
As shown in Table 2, the thermal properties of the surrounding rock in the experimental model are smaller than the properties of the artificial rock. is is because r in the experimental model is small compared to r in the prototype, so with F o being equal, smaller thermal conductivity is used in the experimental model.

Convective Heat Transfer Coefficient.
In this experiment, the convective heat transfer coefficient was calculated. e following method was used to calculate the convective heat transfer coefficient. e heat gain of air in space is as follows: e convective heat transfer between the wall surface of the space and the air is as follows: Ignoring the heat loss from airflow, Q 1 should be equal to Q 2 . e convective heat transfer coefficient h of the wall surface of the space and the air can be obtained as follows:

Fourier Number F o
* . e experimental conditions were as follows: original rock temperature, 50°C; inlet air temperature, 12°C; inlet air relative humidity, 80%; and inlet airflow velocity, 3.5 m/s. e dimensionless temperature distribution of the surrounding rock was tested by varying F o ′ from 0 to 0.4. Figure 5 shows that the higher the F o * is, the lower the Θ is. When F o * is greater than 0.3, the dimensionless temperature of the surrounding rock remained substantially constant. As shown in Figure 5, three stages can be distinguished in terms of change in the dimensionless temperature: initial stage (F o * � 0-0. 15  As shown in Figure 6, comparing the dimensionless temperatures under two di erent B i , the results show that Θ decreases with increasing B i , but the in uence of B i decreases with increasing dimensionless displacement R. A major reason for the decrease in Θ is that higher B i leads to a thinner boundary layer. Since convective heat transfer between the internal surface of surrounding rock and air was strengthened, the closer the measuring point to the internal surface is, the lower the Θ is.
It can be seen in Figure 6 that there is little e ect on Θ as F o increases, and when F o is greater than 0.355, B i has no substantial e ect on Θ. Furthermore, as a result, when F o is greater than 0.355, the unsteady heat transfer model of surrounding rock in deep underground space is signi cantly not in uenced by convection heat transfer boundary conditions.

Radial Displacement R.
e experimental conditions were as follows: original rock temperature, 50°C; inlet air temperature, 12°C; inlet air relative humidity, 80%; and inlet air ow velocity, 3.5 m/s. e dimensionless temperature distribution of the surrounding rock was tested by varying R. Figure 7 shows that when F o is equal to 0, the heat transfer starts, and the temperature of the surrounding rock maintains the original rock temperature in all radial displacements. e results veri ed the accuracy of the experiment. Figure 7 shows the trends of Θ against R. When R changes from 1.5 to 4.5, Θ increases. e greater the F o is, the higher the temperature di erence between measured points or the temperature gradient is. Θ remains almost constant and equal to 1 when R is equal to 4.5. A major reason for the increase in Θ is that the original temperature eld of the surrounding rock is disturbed by air from near R to far R. e wall surface near the underground space (R 1.5) is a ected by the ventilation of the deep underground space, and the temperature is slightly lower, while the bottom of the surrounding rock (R 4.5) is a ected by the original rock temperature, and the temperature is higher.
As shown in Figure 7, the temperature gradient decreases with increasing R; that is, the heat ux density decreases with increasing R according to Fourier's law. is is because the geothermal heat in the deep part of the surrounding rock continuously transfers to deep underground space while the air ow passes. e air ow has not yet been able to disturb the temperature eld there, or the heat carried by the air ow is less than the heat transmitted to it; that is, the temperature range of the surrounding rock that can be spread into the underground space is from near R to far R.
As shown in Figure 7, the curve of an F o value of 0.403 and the curve of an F o value of 0.470 nearly overlap. e results show that when F o is more than 0.403, the dimensionless temperature distribution tends to be stable, as does the heat ux density distribution.

Inlet Air Temperature T f .
e experimental conditions were as follows: original rock temperature, 40°C; inlet air relative humidity, 80%; and inlet air ow velocity, 5 m/s. e dimensionless temperature distribution of the surrounding rock was tested by varying the inlet air temperature from 16°C to 25°C.     6 Advances in Civil Engineering Figure 8 shows the trends of Θ against T f . When T f changes from 16°C to 25°C, Θ increases. A major reason for the increase in Θ is that higher T f leads to a smaller temperature di erence between the internal surface of surrounding rock and air, which decreases heat convection.
As shown in Figure 8, T f a ected the closer measuring points more than the further measuring points. When R was equal to 4.5, Θ was nearly equivalent to 1.0 with any value of F o . is also indicates that the in uence of air temperature on the heat transfer range is negligible.   Advances in Civil Engineering rock in deep underground space could be simplified as stationary heat transfer in the stabilization stage. When R is less than or equal to 4.0, the higher the F o and B i are, the lower the dimensionless temperature with the same R is, while the higher the T f is, the higher the dimensionless temperature with the same R is. When R is equal to 4.5, Θ is nearly equivalent to 1.0 with any value of F o , B i , and T f . us, when F o is less than or equal to 0.47, and R is greater than or equal to 4.5, and the temperature field of the surrounding rock is less affected by the underground space.

Data Availability
All the original data used to support the findings of this study are shown in the figures.

Conflicts of Interest
e authors declare that they have no conflicts of interest.