Thermo-hydro-mechanical Coupling Research Articles

A semi‐analytical model for coupled THM consolidation of saturated clays improved by PVTD considering thermal contraction

AbstractPrevious studies have demonstrated that saturated normally consolidated and lightly over‐consolidated clays undergo contraction when heated due to a reduction in preconsolidation pressure. A linear constitutive model is proposed to describe the thermal contraction, with this model, governing equations are developed for the coupled thermo‐hydro‐mechanical (THM) consolidation induced by a prefabricated vertical thermo‐drain (PVTD). Corresponding semi‐analytical solutions are derived employing the Laplace transform and validated via comparison with experimental results, existing numerical model, and custom finite element method (FEM) model. Subsequently, comprehensive parametric analyses are carried out to investigate the THM coupling consolidation behaviors of the clays. Outcomes show that aside from surcharge load, generation of excess pore water pressure in soils can also be induced by thermal contraction, difference in thermal expansibility between pore water and soil grains, and thermo‐osmosis, where the influence of thermal contraction on the excess pore water pressure is the most prominent among the three factors.

Transversely isotropic effects on the coupled thermo‐hydro‐mechanical performance for layered saturated media

AbstractIn this manuscript, a novel transformed differential quadrature solution to the coupled thermo‐hydro‐mechanical (THM) problem of layered transversely isotropic (TI) saturated media is proposed, accompanied by a sensitivity analysis of pertinent parameters. Initially, the THM governing equations that encompass the transverse isotropy characteristics of thermal, permeable, and mechanical properties are introduced. Subsequently, utilizing the transformed differential quadrature method (TDQM), the discretized algebraic equations in the transformed domain are derived. Boundary conditions related to stresses, displacements, and temperatures are defined leveraging integral transform techniques and the stress‐strain relationship, while algebraic equations for continuity conditions across adjacent layers are incorporated. The global matrix equation is assembled and solved. After verifying the proposed TDQM solution, a sensitivity analysis on the complex transversely isotropic parameters is conducted to identify the principal factors influencing THM coupling behaviors, thereby simplifying the parameters for discussion in practical engineering applications.

A thermo-hydromechanical damage model and its application to a deep geological radioactive repository

This study conducts a numerical analysis of long-term thermo-hydromechanical (THM) processes, with a particular focus on deep geological disposal of radioactive waste. It emphasizes the modeling of damage zones resulting from excavation activities, as well as changes in pore pressure and temperature. The numerical model presented in this paper delineates the fundamental relations of thermo-poro-elasticity. It also introduces a double phase field model specifically formulated for rock materials under compressive stress, taking into account THM coupling and time-dependent behavior. The proposed model has been implemented in a finite element code and applied to numerical analysis of short and long terms responses around a horizontal borehole in the context of the French High-Level Waste (HLW) disposal concept. In particular, displacements, temperature changes, pore fluid pressure variations as well as evolution of induced damage zones are presented and analyzed for different periods including excavation, operation and post-closure. It is found that the occurrence of damage zones is clearly related to the spacing distance between two neighboring disposal boreholes. The time-dependent deformation of host rock plays an significant role in the long-term responses.

The stability issue of fractured rock mass slope under the influences of freeze–thaw cycle

Freeze–thaw failure of frozen rock slope often occurs during engineering construction and mining in cold area, which poses a great threat to engineering construction and people's life safety. The properties of rock mass in cold region will change with the periodic change of temperature, which makes it difficult to accurately evaluate the stability of slope under the action of freeze–thaw cycle by conventional methods. Based on field investigation and literature review, this paper discusses the characteristics of frozen rock mass and the failure mechanism of frozen rock slope, and gives the types and failure modes of frozen rock slope. Then, the research status of frozen rock slope is analyzed. It is pointed out that the failure of frozen rock slope is the result of thermo-hydro-mechanical (THM) coupling. It is considered that freeze–thaw cycle, rainfall infiltration and fracture propagation have significant effects on the stability of frozen rock slope, and numerical simulation is used to demonstrate. The research shows that the safety factor of frozen rock slope changes dynamically with the surface temperature, and the safety factor of slope decreases year by year with the increase of freeze–thaw cycles, and the fracture expansion will significantly reduce the safety factor. Based on the above knowledge, a time-varying evaluation method of frozen rock slope stability based on THM coupling theory is proposed. This paper can deepen scholars' understanding of rock fracture slope in cold area and promote related research work.

THM model of rock tunnels in cold regions and numerical simulation

The freezing damage of rock tunnels in cold region involves ice-water phase change and complicated interaction of Thermo–Hydro–Mechanical (THM) field. Taking the fractured rock mass of cold region tunnels as research subject, the THM coupling model of cold region tunnels was established, which is based on the seepage mechanics, heat transfer theory, damage mechanics and equivalent continuum theory. This model could reflect the anisotropic properties of deformation, water migration and heat transfer caused by the initial fracture of rock mass. The construction and operation processes of a rock tunnel in cold region were simulated, and results were compared with the measured value and predecessor’s achievements. It shows that proposed model could reflect the anisotropic property of surrounding rock and the simulated deformation and stress are not symmetrical. Compared with the literature, the calculated results in this paper are closer to the measured values. The insulating layer has a significant effect on the stress of the supporting structures. The maximum tension stress of the lining is 4.5 times as that without insulating layer, and the lining will be destroyed for the overlarge tension stress.

Development of a Scalable Parallel Compositional Simulator for Thermo-Hydromechanical Coupling in Fractured Rocks Using an Embedded Discrete Fracture Model

Summary Numerical simulation of thermo-hydromechanical (THM) coupling in practical complex fractured rocks is an essential but challenging issue for the evaluation and optimization of underground energy production. In this study, we present our work on a scalable parallel compositional simulator for THM coupling, which is suitable for massive 3D polygonal fractures. In addition, we also present the improvements, parallel implementation, and optimization of an embedded discrete fracture model (EDFM). A unified cell-centered grid system based on the finite volume method (FVM) is used for all governing equations, and an extended stencil is adopted for mechanical equations to resolve the low-resolution defect of the traditional FVM. The deformation of both matrix rock and fractures is considered. A sequential fully implicit (SFI) method is adopted to solve THM coupling. This simulator is validated against three analytical solution models. Finally, we apply the simulator to two cases including a multilayered shale gas reservoir with massive natural fractures and a fractured geothermal model using CO2 as a working fluid. We also test the performance and parallel scalability on 1,024 CPU cores with up to 50 million matrix gridblocks and 5.5 million fracture gridblocks. The results show that this simulator can efficiently solve the THM coupling problem in practical massive fractures.

Thermo-hydro-mechanical modelling of geothermal energy extraction in deep mines in spatially heterogeneous settings

With the increasing demand for mineral and alternative energy resources, as well as the gradual depletion of shallow resources, the exploitation and utilization of mineral resources and geothermal energy in deep strata is an effective way to solve the problem of resource shortage [1]. In recent years, as a new type of resource mining mode, the co-mining of deep mineral and geothermal energy has developed rapidly [2, 3]. This method can make use of the original equipment of the mine for geothermal exploitation. However, the deep co-mining system faces two significant challenges: the first is the significant uncertainty inherent in subsurface properties, while the second is the high levels of geostress and temperature associated with deep mining. These challenges are adding some constraints on the practicality of exploiting such systems and limit the feasibility of deep resource co-mining, so that modelling efforts are needed for actual risk assessment.
 Consequently, we developed a Thermo-Hydro-Mechanical (THM) coupling framework for geothermal energy exploitation in deep mines using COMSOL to quantitatively characterize the temperature field of the geothermal system and predict the stress field of the mining system, considering the joint effects of large uncertainties and THM coupling. Through SGeMS, the uncertainty and spatial heterogeneity distribution of porosity are first generated. Then, the uncertainty of the hydraulic parameter [4] (permeability), mechanical parameter [5] (elastic modulus), and thermal parameter [6] (heat capacity and heat conductivity) was derived from the porosity. 500 samples were generated within a given uncertainty range, by means of Monte Carlo simulations. The spatial and temporal distributions of the temperature field of the geothermal system, and the stress field of the mining system were simulated, for each sample with COMSOL. Using the distance-based global sensitivity analysis [6], the most sensitive parameters for deep mining are identified, the heat storage capacity of the system and evolution of the maximum stress ratio are evaluated, including uncertainty.

Numerical simulation of frost heave of saturated soil considering thermo‐hydro‐mechanical coupling

AbstractFrost heave can lead to both the ground uplifting and frost heave pressure under different circumstances, and cause many engineering problems. To describe the characteristics of frost heave under various thermo‐hydro‐mechanical (THM) coupling conditions and calculate both the frost heave amount and the frost heave pressure, the coupled THM process, as well as the phase change of the pore water, should be considered for freezing soil. In this paper, thermodynamic equilibrium conditions in saturated freezing soil were derived to account for the mechanical effect on the cryogenic suction and unfrozen saturation of pore water during phase transition. Then the governing equations were developed considering the water flow, heat transfer, stress equilibrium, phase change, ice segregation, and their complex interactions. Based on that, a numerical model considering fully THM coupling is presented within the framework of finite element provided by COMSOL. Both frost heave amount tests and frost heave pressure tests were simulated to verify the proposed model. Then the model was applied to subgrades with different types of soil and different boundary conditions, to reveal the characteristics of frost heave amount and frost heave pressure under different conditions, and at the same time to demonstrate the model's applicative prospect.

A framework to model the hydraulic fracturing with thermo-hydro-mechanical coupling based on the variational phase-field approach

In this research, a numerical framework for hydraulic fracturing has been formulated, incorporating thermo-hydro-mechanical (THM) coupled effects. While previous studies have reported various hydraulic fracturing models based on the phase-field method, a THM coupling scheme grounded in the variational phase-field approach remains unexplored. The THM coupling is of paramount importance for understanding underground fracture propagation. This study’s principal innovation lies in its extension of the variational phase field model, introducing it to a thermoporoelastic medium, thereby integrating fluid flow and heat transfer elements in fractured materials. In our advanced model, the fluid flow and heat transfer in the matrix and fracture are modeled independently. Subsequently, employing a set of reasonable assumptions, we introduce unified flow and heat transfer equations derived from phase-field calculus. A pivotal contribution of our work is the development of an iterative solution algorithm based on the fixed stress method, pivotal for tackling the THM coupled system. The proposed equations are discretized employing the FEM. Additionally, to address the numerical oscillations in advection-dominant issues that manifest in the heat transfer model, we have applied a generalized Streamline Upwind Petrov Galerkin method for 8-node elements. The accuracy of fracture propagation was assessed by comparing the numerical results of the evolution of fracture length, fracture width at the injection point, and the injection pressure under the K regime with the corresponding analytical solution. Furthermore, the process of heat transfer within a fractured domain, often referred to as the Barends problem, has been studied by proposed model. Additionally, some numerical experiments were conducted to gain insights into the intricate interplay between the thermal–hydraulic–mechanical system during hydraulic fracturing, thereby further emphasizing the significance of our advanced model.

Embedded discrete fracture network method for numerical estimation of long-term performance of CO2-EGS under THM coupled framework

In enhanced geothermal system (EGS), the artificial fracture networks created by hydraulic fracturing provide highly conductive channel for heat extraction. Very complicated thermo-hydro-mechanical (THM) coupled processes will be involved during cold CO2 injection into the hot fractured reservoir. In this work, a new THM coupled approach is proposed for simulating the long-term performance of CO2-EGS based on embedded discrete fracture networks (DFNs). Due to significant temperature difference between the injection fluid and surrounding, the heat flow in fractures is governed by local thermal non-equilibrium theory. The THM coupling process is achieved by coupling the mechanical simulator FLAC3D and hydraulic-thermal simulator TOUGH2MP. The feasibility of proposed approach is verified and validated through comparing it with analytical solution and other method. The CO2 injection into a reservoir with stochastically generated DFNs is simulated for a period of 20 years, to study the flow behavior, fracture deformation, and thermal performance. The channeling flow is observed by streamlines of fluid and heat flow. The thermal stress due to temperature drop will enhance the fracture width, further decreasing the injection pressure, which shows the significance of incorporating the THM coupling effect in such high temperature reservoirs. This approach also enriches the tools for CO2-EGS simulation.

Study on the Periodic Collapse of Suspended Sandstone Interlayer under Coupled Thermo–Hydro–Mechanical Environment

In the process of in situ heat injection mining of coal seams, a circular combustion chamber will gradually be formed. However, for the interlayer coal seam, the interlayer will gradually suspend in the combustion chamber. When the critical distance is reached, the initial collapse and periodic collapse will occur, which will affect the flow field distribution and extraction efficiency of combustion gas. In order to study the initial and periodic collapse steps of interlayer in real-time high temperature and high-pressure thermo–hydro–mechanical (THM) coupling environments, sandstone specimens were collected from the field, and the macroscopic mechanical parameters of sandstone interlayer were tested using a self-developed thermo–hydro–mechanical coupling tester. The mechanical parameters (e.g., triaxial compressive strength, elastic modulus, Poisson’s ratio) of sandstone under different stress conditions were obtained. Then, based on the elastic thin plate theory, the mechanical modeling of the annular sandstone interlayer is carried out and the preceding mechanical parameters are brought into the generated analysis equation. Thus, the periodic collapse step of the suspended circular sandstone interlayer is obtained. The study results show that: (1) the macroscopic physicomechanical parameters of the sandstone interlayer do not vary monotonically with temperature—a slight increase in macroscopic parameters occurs at 400°C; and (2) the periodic caving pace of the sandstone interlayer decreases with the increase in the number of collapses. With the increase of temperature, the periodic caving pace of the sandstone interlayer decreases first, then increases, and then decreases. It gradually decreases with the increase of surrounding pressure. The research results of this paper can provide theoretical guidance and technical support for in situ heat injection mining technology.

A Novel Numerical Method for Geothermal Reservoirs Embedded with Fracture Networks and Parameter Optimization for Power Generation

Geothermal recovery involves a coupled thermo-hydro-mechanical (THM) process in fractured rocks. A fluid transient equilibrium equation, considering thermal conduction, convection, and heat exchange, is established. The evolution of the reservoir permeability and the variance in the fracture aperture due to a change in the stress field are derived simultaneously. THM coupling is accomplished through iterative hydromechanical and thermo-hydro processes. To overcome the difficulty of geometric discretization, a three-dimensional THM coupler model embedded with discrete fracture networks, using a zero-thickness surface and line elements to simulate fractures and injection/production wells, is established to evaluate the geothermal production. The reliability of the method is verified by a case study. Then, this method is applied to evaluate the influence of the geometric topological characteristics of fracture networks and the fracture aperture on the reservoir temperature evolution and heat extraction effectiveness. The results show that the power generation efficiency and geothermal depletion rate are significantly affected by the injection–production pressure. Injection wells and production wells with pressures higher than the initial fluid pressure in the fractures can be used to significantly increase power generation, but the consumption of geothermal energy and loss of efficiency are significant and rapid. To achieve better benefits for the geothermal recovery system, an optimization algorithm based on simultaneous perturbation stochastic approximation (SPSA) is proposed; it takes the power generation efficiency as the objective function, and the corresponding program is developed using MATLAB to optimize the position and pressure values for each production well. The results show that the heat transfer for the entire EGS reservoir becomes more uniform after optimization, and the heat transfer efficiency is greatly improved.

Fault friction under thermal pressurization during large seismic-slip: Numerical analyses and extension of the model of frictional slip

Earthquake faults are the result of severe strain localization in rocks deep down in the earth’s crust. This localized deformation is controlled by the size of the microstructure and various Thermo-Hydro-Mechanical (THM) couplings, whose modeling is central for understanding earthquake nucleation and seismic energy release. We model this challenging system using the Cosserat theory and by considering large shear deformations during seismic slip. Our numerical results justify the rate and state friction law (Dieterich, 1992; Ruina, 1983a), which describes empirically the fault tribology. This shows the importance of the underlying physics of our model for fault friction. In our analyses traveling shear bands along the thickness of the fault are present, leading to oscillations in the fault’s frictional response. Existing numerical analyses presented in Rattez et al. (2018a, 2018b, 2018c) do not capture this behavior, which goes beyond the established models of uniform shear (Lachenbruch, 1980) and shear on a mathematical plane (Rice, 2006a). Recent experimental results, that insulate thermal pressurization from other weakening mechanisms (Badt et al., 2020), corroborate our numerical results. Our results motivate us to extend the classical model of thermal pressurization in Mase & Smith (1987) and Rice (2006b) to incorporate different strain localization modes, temperature and pore fluid pressure boundary conditions.In particular, we start our analysis by using the normalized coupled system of partial differential equations that include the THM couplings for the case of a Cosserat continuum. We then perform a bifurcation analysis, which indicates that traveling shear bands are possible inside the fault gouge. Next, we derive our non linear mesh independent numerical results accounting for the influence of large displacements by using and Adaptive Lagrangian Eulerian (ALE) procedure. We introduce viscosity in our numerical analyses for the rate and state phenomenology to emerge. We corroborate our numerical results comparing them to similar laboratory experiments. Furthermore, we modify the Volterra integral equation of the classical model of thermal pressurization in Mase & Smith (1987) and Rice (2006b), which we solve by a semi analytical procedure, in order to capture the effect of isothermal drained boundary conditions and traveling shear bands. Our results reappraise and extend the established models of frictional weakening due to thermal pressurization during coseismic slip.

A fully coupled thermo-hydro-mechanical model for fractured rock masses in cold regions

Freezing-thawing disasters are caused by the coupling effect of thermo-hydro-mechanical (THM) activity in rock masses at low temperatures, which seriously threatens the safety of rock mass engineering in cold regions. The accuracy of the coupled THM model is controlled by coupling parameters, such as the migration velocity of unfrozen water, equivalent thermal conductivity, and freezing point. The main difference in the THM coupling process between the frozen rock mass and frozen soil is the anisotropy caused by fractures, and the main difference between the frozen rock mass and normal rock mass is the existence of the ice-water phase transitions. In this paper, the governing equations for THM coupling of fractured rock masses at low temperatures are established, including the mechanical equilibrium equation, continuity equation and energy conservation equation. These equations include the effect of fractures, ice-water phase transitions, water migration and thermal expansion and contraction, which can also be degenerated to equations for rock masses without fractures. Then, the main parameters for the THM analysis are studied. The migration velocity of unfrozen water is closely related to the fractures, temperature, pressure, and phase transitions. Based on the energy conservation law, the expression of the equivalent thermal conductivity is proposed, which is a function of the geometric parameters of fractures, the thermal conductivity of each component, and the content of unfrozen water. Finally, the correctness of the proposed model are validated by Neaupane's experiment and an actual open-pit slope.

An evaluation framework for production performance of high-temperature fractured and karstified geothermal reservoirs: Production mechanism, sensitivity study, and key parameters ranking

High-temperature (>150 °C) geothermal resources have great potential for sustainable power generation. These geothermal resources can be exploited efficiently through highly permeable geological structures, i.e. tectonic fractures and dissolution caves, which thus are categorized as fractured and karstified geothermal reservoirs. However, the study of long-term cold fluids injection into these high-temperature geothermal systems is faced with significant unsolved challenges, i.e. the simulation of coupled porous media flow and free flow in multiscale and heterogeneous fracture-cave networks with distinct thermo-hydro-mechanical (THM) coupling effects. To address these challenges, we develop a novel coupled THM model based on the discrete fracture-cave network approach. We then apply this model to perform the analysis of THM coupling mechanism, sensitivity study, and key parameters ranking to identify the development characteristics of high-temperature geothermal reservoirs. Results show that with respect to coupled THM processes, the fluid flow and heat transfer are dominated by connected fracture clusters and are strongly influenced by the inclusion of caves. However, the behavior of solid deformation is governed by the distribution of caves. As to the reservoir thermal performance under different working fluids, i.e. water and CO2, the water-based geothermal reservoir exhibits longer service life, greater global thermal power, and higher heat extraction rate than the CO2-based one. Regarding sensitivity analysis and key factors ranking, fracture attributes (fracture length and density) are the two most important parameters in regulating the geothermal extraction performance. Caves fall out as the third most significant parameter. However, the operating parameters (i.e. injection temperature, injection pressure, production pressure, well length, and well distance) play a limited role in influencing thermal performance compared with geometrical parameters of fractures and caves. The developed model and insights obtained from our research have crucial implications for understanding and optimizing the thermal production of high-temperature fractured and karstified geothermal reservoirs.

Fully coupled thermo-hydro-mechanical modeling and simulation of a fluid-saturated porous medium under local thermal non-equilibrium condition

• Fully coupled THM model of porous media under LTNE condition is presented. • T s is always higher than T f due to the LTNE effect. • Dependences of multi-physical fields on the pertinent parameters are investigated. This paper presents a fully coupled thermo-hydro-mechanical (THM) model of a fluid-saturated and compressible porous medium under local thermal non-equilibrium (LTNE) condition and carries out the corresponding numerical simulation. First, the coupling among the temperature field, the pore fluid pressure field, and the solid stress/displacement field is fulfilled by means of strong explicit coupling of governing equations in this study. Then, the presented model is applied to the THM coupling problem in an infinite porous medium with a cylindrical borehole subjected to uniform fluid pressure and temperature at the borehole boundary. Subsequently, the partial differential equations (PDEs) module in COMSOL Multiphysics software is employed to numerically solve the studied problem. Consequently, the finite element solutions of the pore fluid pressure field, the strain/stress fields and the two temperature fields of pore fluid and skeleton solid are obtained, and the spatial-temporal distribution characteristics of the above multi-physical fields are investigated. Finally, the corresponding parametric studies are carried out. The numerical results show that the stress decreases with the increase of the bulk volumetric thermal expansion coefficient of porous media. And the pore pressure decreases when the pore fluid mobility increases. Meanwhile, it is found in this work that the solid temperature is always higher than that of pore fluid due to the LTNE effect. Besides, with increasing the specific solid–fluid interfacial heat transfer coefficient, the solid temperature decreases, while the temperature of pore fluid increases. Accordingly, the temperature difference between the solid and the pore fluid diminishes. In addition, the thermal conductivity of solid grains has a greater impact on the solid temperature but has a limited impact on the temperature of pore fluid, and vice versa. The findings in this work are of benefit to obtain in-depth understanding of THM fully coupling mechanism and LTNE effect in a fluid-saturated porous medium.

Thermo-Hydro-Mechanical Coupling Numerical Simulation on Mechanical Heterogeneity of Coal Rock

Coal rock is a porous medium composed of organic matter and inorganic minerals, and it is very complex and highly heterogeneous. Coal bed methane (CBM) production is a thermo-hydro-mechanical (THM) coupling process in heterogeneous coal rock. THM coupling numerical simulation on the coal rock by considering the effect of mechanical heterogeneity is rarely reported. We use Weibull’s probability density distribution function to characterize the heterogeneity in elastic modulus of the coal rock, establish a THM coupling 3D finite element model of the coal rock by considering the variation in pore pressure caused by methane desorption, the linear thermal expansion effect, and coal rock skeleton shrinkage and deformation, and analyze variation in permeability, porosity, stress, temperature, and pore pressure within the coal rock representative elementary volume (REV) of variable mechanical heterogeneity with the cross-coupling correlation between permeability and porosity, and thermal field, stress field, and pressure field. The results show that the evolution of porosity and permeability in the coal rock is a THM coupling process related to mechanical heterogeneity, thermal expansion effect, pore pressure change caused by CBM desorption, and stressed deformation in the coal rock skeleton. The permeability and porosity fluctuate within the heterogeneous coal rock. The permeability and porosity fluctuate more frequently in the coal rock with stronger mechanical heterogeneity. The mechanical heterogeneity promotes local stress concentration. The time for variation in the stress through the whole the coal rock REV and the value of the first principal stress increase when the coal rock heterogeneity is enhanced. Under the THM coupling effect, the strong heterogeneity of the coal rock causes fluctuation in the thermal field. The evolution of coal porosity and permeability is a THM coupling process. This study provides theoretical guidance for CBM exploitation.

Thermohydromechanical coupling analysis and engineering verification of gravel pile groups for strengthening permafrost marshland highway foundations

Thermohydromechanical coupling analysis and engineering verification of gravel pile groups for strengthening permafrost marshland highway foundations

Thermo-Hydro-Mechanical Coupling Model of Unsaturated Soil Based on Modified VG Model and Numerical Analysis

A modified VG model considering both pore ratio and temperature effect is constructed. Based on the wet-thermal elasticity theory and mixture theory, coupled thermo-hydro-mechanical (THM) equations for moisture migration, heat transfer, and deformation in unsaturated soil are derived. The numerical implementation of the coupled theory was implemented by secondary development in the finite element platform. The validity of the established theoretical equation was verified by comparing it with the experimental data. Then the THM coupling response characteristics and internal mechanism of axisymmetric soil samples were numerically analyzed. Study shows that the water in unsaturated soil migrates from high-temperature zone to low-temperature zone under temperature load, and the permeability will change during the process of moisture absorption and dehydration. Particular attention should pay to the reasonable determination of the parameters in the modified VG model for the warming and cooling process of different measurement points during the numerical calculation. The higher the heat source temperature, the greater the saturation at the specific measurement point of the soil sample at thermal stability. The lower the heat source temperature, the shorter the time required for the saturation to stabilize at the specific measuring point. The volumetric strain of unsaturated soil results from a combination of wet expansion and thermal expansion, which is dominated by wet expansion near the heat source and mainly by thermal expansion far from the heat source. The change of the total displacement with time is dominated by the z-direction displacement, and its change trend along the radial direction is similar to that in the r-direction. The peak of the total displacement curve keeps moving backward with time.

A 3D fully thermo–hydro–mechanical coupling model for saturated poroelastic medium

Thermo–hydro–mechanical (THM) coupling prevails in all sorts of underground activities, and numerical simulation is an effective tool to understand THM coupling. The essence of performing THM coupling simulation lies in solving a system of partial differential equations (PDEs) with displacements (U), pore pressure (P) and temperature (T) as the primary variables. In previous studies, only the UPT and U-PT schemes are reported to solve the system PDEs. Another promising scheme UP-T was rarely explored. In addition, although multiple solution schemes are theoretically possible, the performance thereof varies. Few studies have ever compared the performance of different solution schemes. Moreover, the rock mass in hydrothermal fields is highly permeable wherein heat advection dominates. Advection-dominated heat transfer may lead to numerical oscillation, but how to stabilize the simulation in the 3D case was inadequately reported. In this study, we developed a new THM coupling simulator HENGYI in the context of the finite element method. The UP-T solution scheme was verified to be robust enough to simulate large engineering problems. The Streamline Upwind Petrov Galerkin method was generalized to 3D and applied to HENGYI to address the advection-dominated heat transfer. The performance of the UPT, UP-T and U-PT schemes was compared and the applicability of different solution schemes was found to be highly associated with the degree of coupling between primary variables. Great details are provided regarding the development of HENGYI. Thus HENGYI not only bridges the research gaps mentioned above but also provides a comprehensive understanding of THM coupling simulation techniques.