^{1}

^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

Hydraulic-thermal coupling is a key problem in rock mass engineering, especially in the disposal of nuclear wastes in deep rock mass. To accurately describe the coupling action of rock mass when under the interaction of hydraulic stress and thermal, the hydraulic-thermal coupling solving methods were proposed in this paper; in addition, the corresponding hydraulic-thermal coupling program FRHT3D was complied. Consequently, the numerical simulation was performed, it can be concluded that the flow speed is faster when the coupling effect is considered at the unstable seepage stage, and the seepage coupling solution is larger than that of uncoupling. Furthermore, when the coupling effects are considered, the permeable water head solution is much larger than that of the uncoupling solution at the unstable seepage stage. The proposed hydraulic-thermal coupling solving methods and programs can be applied to rock mass engineering practice.

Hydraulic-thermal coupling is one of the most important subsystems of the thermal-hydraulic-mechanical (THM) system; it is a new research area with wide application. The thermal-hydraulic coupling process and mechanism of rock mass are conducive to petroleum excavation, natural gas excavation, underground water excavation, geothermal resource development, and disposal of nuclear wastes in deep rock mass. Besides, there exist problems in large water conservation and hydropower project in the river and gorge; the related study is critically important for the stability of water conservation and hydropower project. At present, the study on the hydraulic-thermal coupling mechanism of rock mass with fissures is mainly based on the continuum and equivalent continuum seepage theory. With regard to the study of THM coupling, how to simulate the process of hydraulic-thermal coupling of rock mass with fissures with noncontinuum theory has become a hot topic.

McDermott et al. [

Though some numerical simulation software, such as FLAC and 3DEC, can simulate the THM coupling, this coupling is one-way coupling, which only considered the influence of the thermal field to the seepage field. Meanwhile, the heat transform coefficient, heat conductivity coefficient, and width of cracks are constant; however, many researches proved that the heat transform coefficient

In this paper, the fluid mechanics and boundary layer theory of heat conductivity theory were applied to the study of water-rock heat transform, and the heat transform between single fissure interface and water fluid was analyzed, its hydraulic-thermal model was established, and the effect of hydraulic-thermal coupling was systematically studied.

The seepage field and thermal field of discrete fissure net interact. On the one hand, the variation of fissure seepage of rock mass could influence the transmitting and exchange of water fluid and fissure interface, which further changes the distribution of the thermal field; on the other hand, the variation of the thermal field could change the fluid viscosity and density, influencing the distribution of the crack seepage field. For convenience of establishing the noncontinuum hydraulic-thermal coupling model of rock mass, some basic assumptions are as follows.

Rock mass consists of impermeable rock and rock fissures; the fissure is the channel of rock mass seepage

The fluid in fissure seepage cannot be compressed, and it obeys Darcy’s law and cubic law

The heat in rock is transmitted by heat conduction; the heat of water can be transmitted by heat conduction and thermal convection, which occurs on the interface of rock and water

Hydraulic-thermal analysis systems of noncontinuum rock mass include thermal field analysis of rock-fissure water, seepage field of fissures, and hydraulic-thermal coupling parameter transmitting analysis.

Heat transmission of thermal field analysis of rock seepage can be summarized: fluid-fluid heat transmission, thermal convection of fluid-fluid, and thermal convection of rock-fluid, which is displayed in Figure

Heat equilibrium of fluid in fissure for a calculation unit.

As regard to thermal convection of fluid-fluid, the heat flux variation of unit thickness on the

The heat flux variation is

The heat flux variation of rock-fluid thermal convection can be expressed as

Heat conduction coefficient

Figure

It obeys Darcy’s law in fissure fluid, which can be expressed as

Adopting the

The heat in rock is transmitted by the way of heat conduction; the heat theory can be expressed as follows:

Based on the law of conservation of mass, the conservation of mass of any unit controlled by fissure can be determined by the following equation:

With respect to the fluid-thermal coupling analysis of noncontinuum, the main coupling parameters, such as fluid density

The fluid-thermal mathematical model of noncontinuum rock is a nonlinear three-dimensional parabola equation, these equations consist of many coupling parameters and variables, they are hard to be solved even for a one-dimensional problem, and we complied the numerical simulation program FRHT3D of fluid-coupling of noncontinuum rock mass. A planar four-node unit was used for the planar fissure; eight nodes in space are used for the rock. The solving systems contain two subsystems: fissure seepage and rock system and thermal seepage field system. The main solving procedure is illustrated in Figure

Procedure of fluid-thermal coupling.

To study the hydrothermal coupling effect of noncontinuum rocks, the calculation example is established in Figure

Numerical simulation model.

The initial and boundary condition of seepage is that the fissure is kept with the state of saturation, its initial water head is

The initial temperature condition is

The basic mechanical parameters of the hydraulic-thermal coupling model are listed in Table

Basic parameters of the fluid-thermal coupling numerical model.

Medium | Density (kg/m^{3}) | Thermal conductivity (W/m/K) | Heat absorption capacity coefficient (J/kg/K) | Initial permeable coefficient (m/s) | Hydraulic opening ( | Specific water storage coefficient (m^{-1}) |
---|---|---|---|---|---|---|

Rock | 2.58 | |||||

Fluid | 1000 | 0.6 | 50 | 0.007 |

To study the hydraulic-thermal coupling effect of noncontinuum rock mass, the coupling and uncoupling numerical simulation would be analyzed; the uncoupling parameters are listed in Table

Calculation parameters of the numerical model without considering hydraulic-thermal coupling.

Water temperature (K) | Density (kg/m^{3}) | Viscosity (m^{2}/s) | Permeable coefficient (m/s) | Heat transform coefficient (W/m^{2}/K) |
---|---|---|---|---|

293 |

The coupling effect of the thermal field to the seepage field is mainly due to the fact that fluid density, viscosity, and permeable coefficient are the function of fluid temperature; the variation of fluid temperature leads to the variation of seepage control equations, which influence the distribution of the fluid field. Figure

Isometric line of the seepage field in the fissure interface.

Figure

Water head evolution at the nodes 2#, 4#, and 7# in the fissure interface.

The temperature of injected water (

Comparison of the thermal field in

The coupling parameters of hydraulic-thermal coupling of noncontinuum rock mass and the main coupling parameters include fluid density

As regards heat conductivity

Heat conductivity

The hydraulic-thermal coupling phenomenon is widely existing in rock mass engineering,to better predict the rock mass engineering stability, the hydraulic-thermal coupling solving methods were proposed, based on the methods, the corresponding program was complied; finally, the numerical simulation of hydraulic-thermal coupling was performed. The results of this paper can be summarized as below.

The influence between the seepage field and the thermal field was analyzed; meanwhile, the corresponding theory was applied to implement the influence between the seepage field and the thermal field. Meanwhile, the fortran program FRHT3 was complied to simulate the hydraulic-thermal coupling

Through the numerical simulation, it can be concluded that the flow speed is faster when the coupling effect is considered at the unstable seepage stage, and the seepage coupling solution is larger than that of uncoupling. Furthermore, when the coupling effects are considered, the permeable water head solution is much larger than that of the uncoupling solution at the unstable seepage stage

All data and models generated or used during the study appear in the submitted article.

The authors declare that they have no conflicts of interest.

This research is supported by the National Natural Science Foundation of China (Nos. 51774131 and 51274097). The authors are thankful for all of the support for this basic research.