International Journal of Advanced Computer Science, Vol. 2, No. 2, Pp. 70-72, Feb. 2012.

Manuscript Received: 7, Jun., 2011

Revised:

19,Sep. 2011

Accepted:

19,Jan., 2012

Published: 15,Mar.,2012

Keywords

surrounding

rock,

fluid-solid

coupling,

mathematical

model,

numerical

simulation,

temperature

field,

seepage,

heat

exchange

Abstract In order to analyze the effect

of Seepage on temperature field in tunnel

Surrounding Rock, thermo-hydro coupling

mathematical model of heat-transfer is

developed. Temperature field and seepage

field distribution of fracture rock is described

by using heat-transfer and seepage

differential equations. Combined with

hydrogeological conditions of Panxi Coal, the

numerical solution is obtained by using

numerical software. The research results

show that heat exchange will occur in the

interaction section Because of the

temperature difference between fluid and

rock. Under the effect of seepage, isotherm

skewing occurs in surrounding rock. At the

same time, skewing value will enlarge along

with the seepage speed increasing. Because

fluid temperature is lower than surrounding

rock. For the left rock of the tunnel, effect of

seepage on distribution of temperature field is

large. The situation has improved with the

rising temperature of fluid the right rock of

the tunnel.

1. Introduction

The aberrant temperature of groundwater often occurs in

deep water-bearing formation, and its water migration often

goes along with obvious heat-transfer. Research of

temperature field in this area is vital to controlling heat

damage and exploiting geothermal resources, and numerical

procedure is developed by coupling fluid flow with heat

transfer [1]-[3].

The scholars have achieved research on numerical model

for thermo-hydro-mechanical coupling in fractured rock [4].

At present, fully-coupled model is built to analyze fluid flow,

heat transfer, and deformation in fractured rock in [5] and

[6]. Three-dimensional analysis of coupled problem is used

to study heat transfer in the surrounding rock and heat

convection between the air and the surrounding rock in

[7]-[9]. For numerical calculation, the boundary layer theory

in [10], equation discretization in [11], and transient

heat-transfer or steady heat-transfer are used. Above research

makes known the heat-exchange mechanism in rock.

This work was supported by the National Natural Science Foundation of

China (No. 50804021).

Shuguang Zhang and Qioulong Zhou are with China Liaoning Technical

University, Department of Civil Engineering

(zh.angshuguang168@163.com; fx.5152@126.com)

The paper is aimed at that China coal mines have been

mining the deep coal layers and is threatened by high

temperature and heat harm. So the deeper of mining depth

becomes, the more heat-harm is in deep mining. Coal

production and geology condition is various. The existence

of water-bearing formation is a popular phenomenon and it

will affect seepage field and temperature field. This research

is carried out based on these understandings. The research's

main aim is to study temperature feature in surrounding rock

of tunnel with water-bearing formation. Thereby, it has

certain guiding significance to solve hot problems caused by

high temperature in deep mining pit.

2. Coupling Mathematical Model

The existence of fracture has a remarkable influence on

the seepage and it determines the seepage feature of

formation. For water-bearing formation, solution of

transient temperature field is not only difficult, but also has

little significance to the project.

For steady temperature field under Hydro-Thermo coupling, seepage control equation is

2 22 2

2 2 2 20w w

T

T TH HK D

x y x y

(Equ. 1)

Where K is coefficient Permeability; H is the distribution

of pressure head; Tw is water temperature; DT is water

diffusivity under the different temperature. Fluid temperature equation is

2 2

2 2( ) ( ) ( ) 0w w w w r

w w w f r w

T T T TH Hc K T T

x y x x y y

(Equ. 2)

Where λw is the water of thermal conductivity; λr is the

rock of thermal conductivity; cw is water of specific heat;

ρw is water density; kf is coefficient Permeability; H is the

distribution of pressure head; Tw is water temperature;

Tr is the edge temperature of fracture rock. The heat-transfer equation is

2 2

2 20r rT T

x y

(Equ.3)

Where Tr is the temperature of rock. By associating the Equ.1~ Equ.3, the coupling

mathematical model of stable temperature in surrounding

rock is obtained.

Effect of Seepage on Temperature Field of Tunnel

Surrounding Rock in Water-bearing Formation Shuguang Zhang & Qiulong Zhou

International Journal of Advanced Computer Science, Vol. 2, No. 2, Pp. 70-72, Feb. 2012.

International Journal Publishers Group (IJPG)©

2

2 22 2

2 2 2 2

2 2

2 2

2 2

2 2

0

( ) ( ) ( ) 0

0

w wT

w w rw w w f r w

r r

T TH HK D

x y x y

T T H T H Tc K T T

x y x x y y

T T

x y

(Equ.4)

Combined with boundary and initial condition, the

model is solved by using the iterative approach.

3. Numerical Simulation

COMSOL Multiphysics software is used to numerical

simulation. COMSOL Multiphysics software is a powerful

finite element FEM partial differential equation PDE

solution engine. Its environment facilitates all steps in the

modeling process − defining your geometry, meshing,

specifying your physics, solving, and then visualizing your

results. Model set-up is quick, thanks to a number of

predefined physics interfaces for applications ranging from

fluid flow and heat transfer to structural mechanics and

electromagnetic analyses. Material properties, source terms

and boundary conditions can all be arbitrary functions of the

dependent variables. Predefined multiphysics application

templates solve many common problem types.

The research region is selected by 50m×25m. The

cross section of surrounding rock is the semicircle arch,

which the sectional width is 8.0m, the straight wall and the

rise of arch are 4m, the vertical width of fault zone is 1m,

and the vertical height from arch to the fault zone is 6m.

The model was divided by the three-node triangular unit.

The model have 1677 nodes and 3216 triangle units.

Computational grid model was showed in Fig. 1.

Fig. 1. Mesh generation of solid element.

(1) Calculation parameter

The surrounding rock in the - 740 tunnel of Panxi coal

mine is the sandstone. Density of rock is 2650 kg/m3,

specific heat is 0.69kJ/(kg·K) and thermal conductivity is

2.035 W/(m·K). The density of water is 1000 kg/m3,

viscosity of water movement 0.001pa·s, thermal

conductivity of water is 0.6 W/(m·K), water diffusivity

under the different temperature is 1.03e-11m/(s·K) and

coefficient Permeability is 1.15e-9 m/s.

(2) Boundary condition

Seepage boundary: The left margin is regarded as the

boundary of head 60m and the right head 20m. The upper

and lower boundaries are selected as the zero flux.

Temperature boundary: The upper boundary which is

calculated by temperature gradient is regarded as the

thermal boundary and density of heat flow is -0.0338665

W/m2. The lower boundary temperature is 50℃, and water

temperature of Initial seepage is 20 ℃ . The contact

boundary is supposed by the continuous boundary, and

other boundary condition for convection flux boundary

condition.

Initial condition: The head of seepage field is zero,

initial temperature of seepage 18℃ and rock 31.5℃.

(3) Simulation Results

For model with water-bearing formation, simulation

results of temperature are showed in Fig.2 when seepage

speed is 8e-8 m/s. To study the effect of seepage speed,

when seepage speed increases to 8e-7 m/s, simulation

results is showed in Fig.3.

Fig. 2. Temperature distribution when seepage speed is 8e-8 m/s.

Fig. 3. Temperature distribution when seepage speed is 8e-7 m/s.

In order to check reliability of model and parameters,

comparing results are listed in table 1 between test data and

simulation results. Table 1: Comparison of test data and simulation results

In addition, geometric model is built to analyze the

influence of water-bearing formation to temperature field.

Using the same calculation condition, simulation result

without water-bearing formation is illustrated in Fig. 4. Its

isotherm is smooth around tunnel, and temperature vectors

show in diffusion surrounding tunnel center.

Test Site Test data /℃ Simulation result /℃

Point 103 35.96 33.28

Point 104 37.53 36.07

Point 105 40.02 38.99

Point 204 37.08 36.26

Point 207 35.83 34.57

Shuguang Zhang et al.: Effect of Seepage on Temperature Field of Tunnel Surrounding Rock in Water-bearing Formation.

International Journal Publishers Group (IJPG)©

3

Fig. 4. Temperature distribution without water-bearing formation.

4. Conclusion

Through analyzing the simulation of the temperature

distribution in surrounding rock of Panxi coal, seeing from

influence on temperature distribution under the seepage, we

can show that the temperature field belongs to type of

transfer-convection. In this temperature field, heat transfer

occurs between rock and fluid. Fluid can absorb or release

heat from rock, which results in the change of temperature

field.

By analyzing of simulation result in Fig.2, Fig.3 and

Fig.4, water-bearing formation plays an important part in

the process of heat transfer. Seepage in water-bearing

formation change Symmetrical state of temperature field. In

Fig.4, the temperature of groundwater is lower than

surrounding rock, so the heat of surrounding rock transmits

to the groundwater. Under the action of heat exchange, the

temperature of fluid gradually increases along the flow

direction. Above phenomenon also appears around

water-bearing formation in Fig.2 and Fig.3.

In Fig.2 and Fig.3, under the effect of seepage,

isotherm skewing occurs in surrounding rock. At the same

time, skewing value will enlarge along with the seepage

speed increasing. Because fluid temperature is lower than

surrounding rock, local temperature reduction area appears

in the upper left. For the left rock of the tunnel, effect of

seepage on distribution of temperature field is large. The

situation has improved with the rising temperature of fluid

the right rock of the tunnel.

In Table 1, the results of simulation is basic anastomotic

with the test. Therefore, simulation results show the

effectiveness of the proposed technique.

5. References

[1] Zhao jian, "Study of flow rock heat transfer in rock

fractures," (1999) Chinese journal of rock mechanics and

engineering, vol.18, no.2, pp.119-123.

[2] Zhao Yangsheng, Yang Dong, & Feng Zengchao, "Multi-

Field Coupling Theory of Porous Media and its Applications

to Resources and Energy Engineering," (2008) Chinese

journal of rock mechanics and engineering, vol.27, no.7,

pp.1321-1328.

[3] Shaik Abdul Ravoof, Rahman Sheik S., & Tran Nam H.,

"Numerical simulation of Fluid-Rock coupling heat transfer

in naturally fractured geothermal system," (2011) Applied

Thermal Engineering, vol.31, no.10, pp.1600-1606.

[4] K.M. Bower & G. Zyvoloski, "A numerical model for

thermo-hydro-mechanical coupling in fractured rock," (1997)

International journal of rock mechanics and mining sciences

& geomechanics abstracts, vol.34, no.8, pp.1201-1211.

[5] Podgorney Robert, Huang Hai, & Gaston Derek, "A

fully-coupled, implicit, finite element model for

simultaneously solving multiphase fluid flow, heat transport,

and rock deformation," (2010) Transactions-Geothermal

Resources Council, vol.34, no.1, pp.395-400.

[6] J. Rutqvist, Y.S. Wu, & C.F. Tsang, " A modeling approach

for analysis of coupled multiphase fluid flow, heat transfer,

and deformation in fractured porous rock," (2002)

International Journal of Rock Mechanics and Mining

Sciences, vol.39, no.4, pp.429-442.

[7] Yuanming Lai, Xuefu Zhang, & Wenbing Yu, "Three-

dimensional nonlinear analysis for the coupled problem of

the heat transfer of the surrounding rock and the heat

convection between the air and the surrounding rock in

cold-region tunnel," (2005) Tunnelling and Underground

Space Technology, vol.20, no.4, pp.323-332.

[8] Xuefu Zhang, Wenbing Yu, Cheng Wang, & Zhiqiang Liu,

"Three-dimensional nonlinear analysis of coupled problem

of heat transfer in the surrounding rock and heat convection

between the air and the surrounding rock in the Fenghuo

mountain tunnel," (2006) Cold Regions Science and

Technology, vol.44, no.1, pp.38-51.

[9] Zhang Yujun "3D finite element simulation for influence of

thermo-hydro-mechanical coupling on migration in

geological disposal of nuclear waste," (2009) Rock and Soil

Mechanics, vol.30, no.7, pp. 2126-2132.

[10] Chen Xingzhou, Li Baoguo, & Dong Yuan, "Analysis of

water-rock heat transfer in fractured rock mass," (2007)

Northwest hydropower, no.3, pp.18-20.

[11] Sasaki Takeshi & Nagai Fumio, "Thermo-mechanical

consolidation coupling analysis and its discretization on

jointed rock mass by finite element method," (1994) Doboku

Gakkai Rombun-Hokokushu/Proceedings of the Japan

Society of Civil Engineers, no.493, pp.11-20.

[12] Wang Rubin, "A Coupled Model for Steady Heat and Fluid

Flow in Single Rock Fracture and Its Numerical Solution,"

(2006) Disaster and Control Engineering, no.1, pp.65-70.

Shuguang Zhang was born in Shandong,

China, in 1974. He received the M.E. And

D.E. degrees from Liaoning Technical

University (LNTU) in 2001 and 2004,

respectively. He is the author or coauthor

of more than sixty national and

international papers and also collaborated

more than twenty research projects. He

currently is the professor. Since 1996 he

has been with the Department of Civil Engineering at LNTU. His

research interests include geoenvironmental engineering and

underground engineering.

Qiuling Zhou was born in Jiangsu,

China, in 1988. He received the B.E.

degree in civil engineering from LNTU in

2010. He is the author or coauthor of

more than ten national and international

papers and also collaborated in several

research projects. His current research

interests is geoenvironmental engineering.

He is currently pursuing his M.E. degree

in LNTU.