Heterogeneous granite temperature-dependent compression-shear dual-phase field simulation method

Abstract

The invention relates to a heterogeneous granite temperature-dependent compression-shear dual-phase field simulation method. The method comprises the following steps: establishing a heterogeneous thermal-mechanical coupling geometric model; building displacement, temperature and fracture control equations in a solid solution domain of the heterogeneous thermal-mechanical coupling geometric model on the basis of material parameters which are endowed with temperature change by minerals; establishing a temperature-dependent compression-shear two-phase field model; based on displacement, temperature and fracture control equations, solving the temperature-dependent compression-shear dual-phase field model by using a separated iterative algorithm to obtain temperature field characteristics, stress field characteristics and phase field distribution; and under the condition that the temperature field characteristics, the stress field characteristics and the phase field distribution precision are verified to meet preset conditions through standard examples and experimental data, temperature-dependent compression-shear dual-phase field simulation of the heterogeneous granite is completed. The method has the beneficial effects that the accuracy of simulating the fracture behavior of the heterogeneous granite under thermal-mechanical coupling is improved, and the influence of a granite microcosmic mineral structure on the mechanical and fracture characteristics of the granite microcosmic mineral structure is effectively represented.

Description

Technical Field

[0001] This invention relates to the field of rock thermo-coupling phase field model research technology, and in particular to a method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite. Background Technology

[0002] Deep hot dry rock is representative of clean and renewable geothermal resources. Hot dry rock is a high-temperature, dense rock mass with a temperature of 180℃ to 650℃, a burial depth of 3km to 10km, and containing little or no internal fluid. Granite, as the main bedrock of hot dry rock reservoirs, has been extensively studied in many countries. The physical, mechanical, and fracture characteristics of rocks at high temperatures differ significantly from those at room temperature. Typically, at high temperatures, due to temperature gradients and the non-uniform thermal expansion of minerals, rocks are highly susceptible to thermal cracking. Therefore, elucidating the physical, mechanical, and fracture mechanisms of granite under thermo-mechanical coupling is of great significance for the safe and efficient development of deep geothermal resources.

[0003] The physical and mechanical properties of rocks exhibit a strong temperature dependence, significantly influencing their thermal cracking characteristics. Extensive experimental research has been conducted on the mechanical and thermophysical properties of granite at high temperatures. Mechanical studies primarily focus on the strength, deformation, and failure characteristics of rocks at high temperatures. Thermophysical studies mainly investigate the thermal conductivity, specific heat capacity, and coefficient of thermal expansion of rocks at high temperatures. Furthermore, numerical simulation has become an important method for revealing the problems of thermo-mechanical coupling fracture in rocks and has achieved significant research progress. However, existing numerical simulation methods suffer from high computational costs, and there are relatively few thermal cracking models that consider temperature dependence.

[0004] The fracture phase-field method, which characterizes crack propagation through a continuous damage field, provides a new approach for studying thermo-coupled fracture. This method, incorporating criteria such as the Mohr-Coulomb model, can simulate combined compression and shear failure in rocks. The two-phase-field model can also distinguish between tensile and shear crack morphologies, and experimental verification demonstrates its high accuracy. However, existing two-phase-field models mostly use statistical distributions to describe material heterogeneity, making it difficult to accurately reflect the microscopic mineral effects and thermal expansion differences of quartz, feldspar, and mica in granite. Grain models can characterize the fine structure of minerals, but their application in thermally fractured phase-field models requires further investigation.

[0005] Based on the above research, it can be found that traditional thermo-coupled phase-field models have the following shortcomings: 1) In terms of temperature coupling mechanism, the thermophysical parameters mostly adopt linearization assumptions and do not consider the influence of temperature-related parameters on the results; 2) In terms of heterogeneous thermal cracking, most existing models are statistically distributed and are single-phase field models, which cannot simultaneously consider the tensile / shear cracking of granite mineral crystal structure at high temperatures. Summary of the Invention

[0006] Technical problems to be solved

[0007] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite, which solves the technical problem of how to improve the accuracy of simulating the fracture behavior of heterogeneous granite under thermo-coupling.

[0008] Technical solution

[0009] To achieve the above objectives, the main technical solutions adopted by the present invention include:

[0010] This invention provides a method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite, comprising:

[0011] Based on the mineral composition parameters of the target granite, material parameters that vary with temperature are assigned to each mineral, and a heterogeneous thermo-mechanical coupling geometric model is established using a Thiessen polygon mesh.

[0012] Based on the temperature-dependent material parameters imparted by minerals, displacement, temperature, and fracture control equations are established in the solid solution domain of a heterogeneous thermo-mechanical coupled geometric model.

[0013] The elastic strain energy is decomposed into tensile and compressive components, which drive the evolution of the tensile phase field and the shear phase field respectively, thus establishing a temperature-dependent compression-shear two-phase field model.

[0014] Based on displacement, temperature, and fracture control equations, a temperature-dependent compression-shear two-phase field model is solved using a separate iterative algorithm to obtain temperature field characteristics, stress field characteristics, and phase field distribution.

[0015] By verifying that the temperature field characteristics, stress field characteristics, and phase field distribution accuracy meet the preset conditions through standard calculation examples and experimental data, the temperature-dependent compression-shear two-phase field simulation of heterogeneous granite was completed.

[0016] Optionally, based on the mineral composition parameters of the target granite, a heterogeneous thermo-coupled geometric model is established using a Thiessen polygon mesh, including:

[0017] Based on the mineral composition parameters of the target granite, the Thiessen polygon mesh module of the open-source software Neper was used to input the thermal parameters of the target granite and set the material fracture properties of each mineral block as a function of temperature. The critical energy release rate was determined by nanoindentation to establish a heterogeneous thermo-mechanical coupling geometric model.

[0018] Optionally,

[0019] Based on the temperature-dependent material parameters imparted by minerals, displacement, temperature, and fracture governing equations are established in the solid solution domain of a heterogeneous thermo-mechanical coupled geometric model, including:

[0020] A normalization method was used to establish the functional relationship between material parameters and temperature;

[0021] Based on the functional relationship and combined with the dispersion crack regularization, the temperature, displacement and phase field variables in the solid solution domain of the heterogeneous thermo-mechanical coupling geometric model under the applied initial conditions are obtained;

[0022] Based on the rock heterogeneity characterized by the grain method and the material parameters of the rock as it evolves with temperature, displacement, and phase field variables are combined to establish displacement, temperature, and fracture control equations in the solid solution domain of a heterogeneous thermo-mechanical coupled geometric model.

[0023] Optionally, the displacement, temperature, and fracture control equations in the solid solution domain of the heterogeneous thermo-coupled geometric model are as follows:

[0024] Displacement field:

[0025] ▽·σ+f=0inΩ

[0026]

[0027] Temperature field:

[0028]

[0029] Fracture phase field:

[0030]

[0031] d α =1on A Γ ;

[0032] In the displacement field, σ is the stress tensor, f is the body force term, and Ω is the solution domain. This represents the displacement boundary; in the temperature field, ρ is the material density, and c is the specific heat capacity. Let ν be the rate of change of the temperature field, q be the heat flux, n be the normal vector, and γ be the internal heat source. For heat flux boundary conditions, For temperature boundary conditions, For heat flux boundary, Temperature boundary; h in the fracture phase field t ′(d t ) is the tensile damage function, h s ′(d s ) is the shear damage function. For the stretching driving energy, Shear driving energy, To stretch the critical energy release rate. l is the critical shear energy release rate. d d is the characteristic width of the phase field. t For the tensile damage phase field, d s For the shear damage phase field, ▽dt For the tensile damage phase field gradient, ▽d s Shear damage phase field gradient, ▽d α The superscript in A indicates stretching or shearing. Γ This represents the boundary of the fracture crack.

[0033] Optionally, based on displacement, temperature, and fracture control equations, a separate iterative algorithm is used to solve the temperature-dependent compression-shear two-phase field model to obtain temperature field characteristics, stress field characteristics, and phase field distribution:

[0034] Temperature field elements, displacement field elements, and phase field elements are layered and covered on the same element;

[0035] The temperature field elements are written using UMAT elements and the common block is used to transmit iteration information between different elements.

[0036] The Newton-Raphson algorithm is used to update the stiffness matrix and residual force matrix at each iteration step until the convergence criterion is met, thereby obtaining the temperature field characteristics, stress field characteristics and phase field distribution.

[0037] Optionally, after verifying that the temperature field characteristics, stress field characteristics, and phase field distribution accuracy meet the preset conditions through standard calculation examples and experimental data, a temperature-dependent compression-shear two-phase field simulation of heterogeneous granite is completed, including:

[0038] The accuracy of the temperature field evolution over time is verified through a transient heat transfer example of a rectangular thin plate.

[0039] The accuracy of the stress field was verified using a steady-state thermo-mechanical coupling example of a thick-walled cylinder.

[0040] The feasibility of the phase field model was verified by thermo-coupling conventional triaxial compression experiments on heterogeneous rocks.

[0041] Optionally, the accuracy of the temperature field evolution over time is verified through a transient heat transfer example of a rectangular thin plate, including:

[0042] A rectangular thin plate model was established, and the boundary temperature and the initial temperature of the model were set. The temperature field cloud map and temperature-time curves at different locations calculated by the temperature-dependent compression-shear two-phase field model were compared with the analytical solution. The simulation results showed that the error between the simulation results and the theoretical solution was ≤3%, which proved the reliability of the model's temperature field evolution calculation.

[0043] Optionally, the accuracy of the stress field is verified using a steady-state thermo-mechanical coupling example of a thick-walled cylinder, including:

[0044] A cylindrical model was constructed to simulate the stress and deformation of a thick-walled cylinder when the inner wall is heated and the outer wall is cooled. The pressure and temperature coupling effect was investigated to verify the consistency between the stress field distribution and the solution of classical mechanics formulas.

[0045] Optionally, the feasibility of the phase-field model is verified through thermo-coupling conventional triaxial compression experiments on heterogeneous rocks, including:

[0046] A heterogeneous granite model was established, and the distribution of minerals such as quartz and feldspar was characterized based on Thiessen polygons. The stress-strain curves and peak intensity decay laws of the simulation and experiment were compared. The propagation characteristics of random thermal tensile fractures and heterogeneous-induced single-slope shear cracks in the phase field distribution were observed. The results were consistent with the indoor experimental phenomena, proving that the model can accurately capture the compression-shear failure mechanism of rocks under thermo-mechanical coupling. Its temperature-dependent parameter settings and two-phase field energy decomposition method have engineering feasibility.

[0047] Beneficial effects

[0048] The beneficial effects of this invention are as follows: This invention provides a temperature-dependent compression-shear two-phase field simulation method for heterogeneous granite, establishing a more practical thermo-coupling model of heterogeneous granite. It considers the temperature dependence of physical parameters and accurately simulates the fracture behavior of heterogeneous granite under thermo-coupling. Currently, the critical energy release rate in the fracture phase field is a key parameter, often selected empirically. This invention uses nanoindentation to measure its critical energy release rate, improving the model's realism. It overcomes the shortcomings of existing models in describing rock heterogeneity, effectively characterizing the influence of granite's micromineral structure on its mechanical and fracture characteristics. It provides accurate model support for the safe and efficient development of hot dry rocks, contributing to the development and utilization of deep geothermal resources. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of a method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite according to an embodiment of the present invention.

[0050] Figure 2 The distribution diagram of thermo-coupled phase field fracture elements provided in the embodiments of the present invention;

[0051] Figure 3 This is a schematic diagram of the steady-state thermo-mechanical coupling simulation results provided in an embodiment of the present invention;

[0052] Figure 4 A transient heat conduction thin plate model diagram provided in an embodiment of the present invention;

[0053] Figure 5 This is a schematic diagram of the transient heat conduction simulation results provided in an embodiment of the present invention;

[0054] Figure 6 A schematic diagram of boundary conditions provided for an embodiment of the present invention;

[0055] Figure 7 This is a schematic diagram of a conventional triaxial compressive stress loading path provided in an embodiment of the present invention;

[0056] Figure 8 This is a schematic diagram of a conventional triaxial compression temperature loading path provided in an embodiment of the present invention;

[0057] Figure 9 A schematic diagram of heating damage provided in an embodiment of the present invention;

[0058] Figure 10 This is a schematic diagram of compression-shear fracture provided in an embodiment of the present invention. Detailed Implementation

[0059] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] This invention provides a model for the temperature dependence and compressive-shear damage fracture behavior of heterogeneous granite under thermo-mechanical coupling. By establishing the displacement, temperature, and phase field fracture control equations in the solid solution domain of the dispersed crack and thermo-mechanical coupling phase field, and by using the elastic strain energy and thermo-mechanical coupling control equations of the rock, a thermo-mechanical coupling phase field model of the heterogeneous rock is established. The model is then discretized using the finite element method, and the temperature field, stress field, and fracture phase field distribution are solved using a separate iterative method. The model is then validated through numerical examples, followed by strength calibration, and finally, numerical model experiments are conducted.

[0061] The established thermo-coupling phase-field model for heterogeneous granite, considering temperature dependence, better aligns with engineering realities. Within the framework of phase-field theory, and considering the compressive-shear nature of thermo-coupling in heterogeneous rocks, a new phase-field model is proposed by decomposing the tensile and compressive driving energies of the phase field. Furthermore, the model considers the temperature dependence of physical parameters. The phase-field model was developed using the UEL platform in Abaqus, and its accuracy and reliability were verified by comparing it with analytical solutions and indoor experimental results.

[0062] Given the current situation, granite is a crystalline material composed of minerals such as quartz, feldspar, and mica. Statistical models cannot characterize the influence of factors such as the composition and proportion of microscopic minerals. Grain models have significant advantages in simulating the microscopic mineral structure of rocks and are currently widely used in numerical simulations of rock compression and shear. Therefore, further research is needed to establish a heterogeneous thermal cracking phase-field model that can consider the microscopic mineral structure of rocks.

[0063] In indoor experiments on granite, the elastic modulus and Poisson's ratio of Gonghe granite were accurately determined using a high-temperature and high-pressure rock testing system; the thermal conductivity, coefficient of thermal expansion, specific heat capacity, and density of Gonghe granite or its mineral components were accurately determined using a rock thermophysical parameter testing system. This improved the reliability of the thermo-coupling numerical model for solving thermo-coupling problems of Gonghe granite.

[0064] Compared to existing technologies, heterogeneous granite simulation models can simulate the propagation and development of cracks after rock mass excavation, and visualize the effects of temperature and pressure on rock mass failure. To better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the accompanying drawings show examples of the present invention...

[0065] These are embodiments; however, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the invention can be understood more clearly and thoroughly, and so as to fully convey the scope of the invention to those skilled in the art.

[0066] Reference Figure 1 This embodiment provides a method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite, including:

[0067] S1, based on the mineral composition parameters of the target granite, sets material parameters for each mineral that vary with temperature, and establishes a heterogeneous thermo-coupling geometric model using a Thiessen polygon mesh.

[0068] The mineral composition and distribution of rocks at the engineering site are determined by XRD analysis and observation using a polarizing microscope to obtain the mineral composition and proportion of the target rocks.

[0069] Thiessen polygonal blocks: Each block is assigned different mechanical and thermodynamic parameters to represent different rock mineral particles and is grouped according to mineral composition. Each polygonal block represents a single mineral particle, and its size, shape, and distribution are determined by statistical results of mineral particle size. The size and distribution of these mineral particles are adjusted to ensure that the model's microstructure is consistent with that of actual rocks. This allows for the simulation of the thermo-mechanical coupling compressive failure characteristics of heterogeneous rocks under external temperature and load.

[0070] Thermodynamic parameters include: elastic modulus, coefficient of thermal expansion, and thermal conductivity. The temperature-mechanical parameter relationships of granite at different temperatures were obtained through laboratory heating experiments.

[0071] S2, based on the material parameters that vary with temperature imparted by minerals, establish the displacement, temperature and fracture control equations in the solid solution domain of the heterogeneous thermo-mechanical coupled geometric model.

[0072] S3 decomposes the elastic strain energy into tensile and compressive components, which drive the evolution of the tensile phase field and the shear phase field respectively, and establishes a temperature-dependent compression-shear two-phase field model.

[0073] S4, based on displacement, temperature and fracture control equations, uses a separate iterative algorithm to solve the temperature-dependent compression-shear two-phase field model, and obtains the temperature field characteristics, stress field characteristics and phase field distribution.

[0074] S5, through standard calculation examples and experimental data, verifies that the temperature field characteristics, stress field characteristics, and phase field distribution accuracy meet the preset conditions, and completes the temperature-dependent compression-shear two-phase field simulation of heterogeneous granite.

[0075] Optionally, based on the mineral composition parameters of the target granite, a heterogeneous thermo-coupled geometric model is established using a Thiessen polygon mesh, including:

[0076] Based on the mineral composition parameters of the target granite, the Thiessen polygon mesh module of the open-source software Neper was used to input the thermal parameters of the target granite and set the material fracture properties of each mineral block as a function of temperature. The critical energy release rate was determined by nanoindentation to establish a heterogeneous thermo-mechanical coupling geometric model.

[0077] Optionally,

[0078] Based on the temperature-dependent material parameters imparted by minerals, displacement, temperature, and fracture governing equations are established in the solid solution domain of a heterogeneous thermo-mechanical coupled geometric model, including:

[0079] A normalization method was used to establish the functional relationship between material parameters and temperature;

[0080] Based on the functional relationship and combined with the dispersion crack regularization, the temperature, displacement and phase field variables in the solid solution domain of the heterogeneous thermo-mechanical coupling geometric model under the applied initial conditions are obtained;

[0081] Based on the rock heterogeneity characterized by the grain method and the material parameters of the rock as it evolves with temperature, displacement, and phase field variables are combined to establish displacement, temperature, and fracture control equations in the solid solution domain of a heterogeneous thermo-mechanical coupled geometric model.

[0082] Optionally, the displacement, temperature, and fracture control equations in the solid solution domain of the heterogeneous thermo-coupled geometric model are as follows:

[0083] Displacement field:

[0084] ▽·σ+f=0inΩ

[0085]

[0086] Temperature field:

[0087]

[0088] Fracture phase field:

[0089]

[0090] d α =1on A Γ ;

[0091] In the displacement field, σ is the stress tensor, f is the body force term, and Ω is the solution domain. This represents the displacement boundary; in the temperature field, ρ is the material density, and c is the specific heat capacity. Let ν be the rate of change of the temperature field, q be the heat flux, n be the normal vector, and γ be the internal heat source. For heat flux boundary conditions, For temperature boundary conditions, For heat flux boundary, Temperature boundary; h in the fracture phase field t ′(d t ) is the tensile damage function, h s ′(d s ) is the shear damage function. For the stretching driving energy, Shear driving energy, To stretch the critical energy release rate. l is the critical shear energy release rate. d d is the characteristic width of the phase field. t For the tensile damage phase field, d s For the shear damage phase field, ▽d t For the tensile damage phase field gradient, ▽d s Shear damage phase field gradient, ▽d α The superscript in A indicates stretching or shearing. Γ This represents the boundary of the fracture crack.

[0092] Optionally, based on displacement, temperature, and fracture control equations, a separate iterative algorithm is used to solve the temperature-dependent compression-shear two-phase field model to obtain temperature field characteristics, stress field characteristics, and phase field distribution:

[0093] Temperature field elements, displacement field elements, and phase field elements are layered and covered on the same element;

[0094] The temperature field elements are written using UMAT elements and the common block is used to transmit iteration information between different elements.

[0095] The Newton-Raphson algorithm is used to update the stiffness matrix and residual force matrix at each iteration step until the convergence criterion is met, thereby obtaining the temperature field characteristics, stress field characteristics and phase field distribution.

[0096] Numerical simulation of thermo-coupled phase-field fracture is implemented based on the User-Defined Interface (UEL) in Abaqus. The core method is to cover temperature field elements, displacement field elements, and phase field elements on the same element in a layered manner (e.g., Figure 2(As shown). Each layer of elements is connected to the same node, but has different degrees of freedom. In the two-dimensional model, the phase field element and temperature field element each have one degree of freedom, while the displacement field element has two degrees of freedom. To visualize the calculation results, the temperature field element is written using UMAT elements, and a common block is used to pass iteration information between different elements. Furthermore, a separate iterative algorithm is used to solve the coupling problem of the displacement field, temperature field, and phase field.

[0097] To achieve the numerical implementation of a thermo-coupled phase-field model, a thermo-coupled two-phase-field model was developed using the Abaqus finite element software platform via the User-Defined Element (UEL) interface. The multiphysics coupling framework model comprises three coupled fields: displacement, temperature, and phase. Subsequently, based on the heat conduction equation, force balance equation, and phase evolution equation, governing equations and boundary conditions were set.

[0098] Optionally, the three-field coupling function includes: displacement field: characterizing rock deformation; temperature field: describing heat conduction and temperature evolution; phase field: dispersing cracks through a continuous scalar field (0-1) to distinguish between tensile and shear damage.

[0099] Optionally, after verifying that the temperature field characteristics, stress field characteristics, and phase field distribution accuracy meet the preset conditions through standard calculation examples and experimental data, a temperature-dependent compression-shear two-phase field simulation of heterogeneous granite is completed, including:

[0100] The accuracy of the temperature field evolution over time is verified through a transient heat transfer example of a rectangular thin plate.

[0101] The accuracy of the stress field was verified using a steady-state thermo-mechanical coupling example of a thick-walled cylinder.

[0102] The feasibility of the phase field model was verified by thermo-coupling conventional triaxial compression experiments on heterogeneous rocks.

[0103] Optionally, the accuracy of the temperature field evolution over time is verified through a transient heat transfer example of a rectangular thin plate, including:

[0104] A rectangular thin plate model was established, and the boundary temperature and the initial temperature of the model were set. The temperature field cloud map and temperature-time curves at different locations calculated by the temperature-dependent compression-shear two-phase field model were compared with the analytical solution. The simulation results showed that the error between the simulation results and the theoretical solution was ≤3%, which proved the reliability of the model's temperature field evolution calculation.

[0105] Optionally, the accuracy of the stress field is verified using a steady-state thermo-mechanical coupling example of a thick-walled cylinder, including:

[0106] A cylindrical model was constructed to simulate the stress and deformation of a thick-walled cylinder when the inner wall is heated and the outer wall is cooled. The pressure and temperature coupling effect was investigated to verify the consistency between the stress field distribution and the solution of classical mechanics formulas.

[0107] Optionally, the feasibility of the phase-field model is verified through thermo-coupling conventional triaxial compression experiments on heterogeneous rocks, including:

[0108] A heterogeneous granite model was established, and the distribution of minerals such as quartz and feldspar was characterized based on Thiessen polygons. The stress-strain curves and peak intensity decay laws of the simulation and experiment were compared. The propagation characteristics of random thermal tensile fractures and heterogeneous-induced single-slope shear cracks in the phase field distribution were observed. The results were consistent with the indoor experimental phenomena, proving that the model can accurately capture the compression-shear failure mechanism of rocks under thermo-mechanical coupling. Its temperature-dependent parameter settings and two-phase field energy decomposition method have engineering feasibility.

[0109] The standard calculation verification method includes transient heat transfer verification and thermo-mechanical coupling verification of a thick-walled cylinder. The accuracy of the temperature and stress fields is verified by transient heat transfer in a rectangular thin plate and steady-state thermo-mechanical coupling in a thick-walled cylinder, with the error controlled within 1.81%. When the model temperature reaches steady state, the distribution of temperature, radial stress, and circumferential stress in the model is as follows: Figure 3 As shown, the simulation results show good agreement with the theoretical solution, verifying the accuracy of the model under thermo-coupling. Through the above testing methods, the results of different tests on the model are analyzed to ensure their consistency with mathematical theory and predictions, thus guaranteeing the reliability of the computer simulation results.

[0110] Standard case studies include transient heat transfer verification and thermo-mechanical coupling verification of a thick-walled cylinder. Transient heat transfer verification involves simulating the heat transfer process of a rectangular thin plate, comparing the numerical solution with the theoretical solution (e.g., error <2%), and confirming the accuracy of the temperature field calculation. The thermo-mechanical coupling verification of the thick-walled cylinder involves simulating the stress and deformation of a thick-walled cylinder during internal heating and external cooling, applying the combined effects of pressure and temperature, and verifying the consistency between the stress field distribution and the solutions provided by classical mechanics formulas.

[0111] Calibration of the mechanical response of heterogeneous rocks includes uniaxial / triaxial compression simulation and Brazilian splitting simulation. The uniaxial / triaxial compression simulation involves adjusting the stiffness ratio, cohesion, and friction angle of the mineral contact surfaces to ensure that the error between the simulated stress-strain curve and experimental data is ≤1.81%. The Brazilian splitting simulation calibrates the tensile strength parameters between mineral grains through tensile strength inversion.

[0112] A suitable constitutive model is selected for the model and various parameters are assigned. Then, simulation experiments are conducted on the model to simulate real-world engineering problems and to assess its engineering applications and safety.

[0113] Simulating real-world high-temperature and high-pressure scenarios, this study predicts the fracture behavior of high-temperature rocks in real-world conditions. Through stability analysis of dry hot rock well walls, simulation of high-temperature heating processes, and pressure loading, and by comparing experimental results, the computer-predicted rock strength and crack modes are compared with actual laboratory test data (error ≤ 1.81%), allowing for further application in practical engineering.

[0114] Optionally, the dry hot rock wellbore stability analysis includes: applying the calibrated model to high temperature (≤650℃) and high confining pressure (≤60MPa) conditions to simulate the compression-shear damage evolution of the wellbore rock and predict the crack initiation location and propagation path.

[0115] Optionally, the parameter sensitivity optimization includes the influence of mineral heterogeneity and the optimization of heating rate. The influence of mineral heterogeneity includes comparing the differences in damage modes under different mineral distribution models (e.g., a 5% increase in mica content); the optimization of heating rate includes analyzing the risk of thermal shock damage at heating rates of 5℃ / min and 10℃ / min, and determining a safety threshold.

[0116] The following describes a method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite, based on a specific embodiment:

[0117] Based on the mineral composition and distribution of rocks at the engineering site, Thiessen polygon meshes are generated using open-source software such as Neper or Abaqus scripts. The geometric model is then imported into finite element software (such as Abaqus), and quadrilateral elements are used for mesh generation, followed by mesh discretization. This invention introduces the concept of diffuse cracking and first presents the displacement, temperature, and fracture control equations in the thermo-coupled phase-field solid solution domain. The heterogeneity of the rock is characterized based on the grain method. Then, a thermo-coupled tensile and shear phase-field energy-driven model of the rock is established to describe the thermal cracking and compressive-shear characteristics of the rock material.

[0118] In this embodiment, the mineral composition and distribution of the rocks at the engineering site are obtained by XRD analysis and observation with a polarizing microscope to determine the mineral composition and proportion of the target rocks.

[0119] In this embodiment, the thermodynamic parameters include: elastic modulus, coefficient of thermal expansion, thermal conductivity, etc. The temperature-mechanical parameter relationship of granite at different temperatures is obtained through laboratory heating experiments.

[0120] Optionally, the Thiessen polygon mesh creation process primarily utilizes software or scripts to randomly distribute control points within a two-dimensional plane, generating Thiessen polygons that match the number of mineral particles. Each block is assigned different mechanical and thermal property parameters to represent different rock mineral particles and is grouped according to mineral composition. Each polygon represents a type of mineral particle, assigned corresponding mechanical parameters (elastic modulus, Poisson's ratio, etc.) and thermal property parameters (thermal conductivity, coefficient of thermal expansion, etc.) to ensure that the model's microstructure is consistent with that of actual rocks. This then simulates the thermo-mechanical coupling compressive failure characteristics of heterogeneous rocks under external temperature and load.

[0121] The regularization of the dispersed crack is based on Griffith's fracture theory and variational principle. It uses the continuous phase field method to model discontinuous cracks in a dispersed manner, thereby achieving a regularized characterization of dispersed cracks.

[0122] The aforementioned rock Thiessen polygon mesh model was imported into the finite element software Abaqus to generate a heterogeneous rock geometric model. In the numerical implementation of the thermo-coupled phase-field model, a thermo-coupled two-phase field model was developed using the User-Defined Element (UEL) interface on the Abaqus platform.

[0123] Optionally, a multiphysics coupling framework is constructed: the model includes three coupled fields: displacement field: characterizing rock deformation; temperature field: describing heat conduction and temperature evolution; fracture phase field: dispersing cracks through a continuous scalar field (0-1) to distinguish between tensile and shear damage. Subsequently, based on the heat conduction equation, force balance equation, and phase field evolution equation, the governing equations and boundary conditions are set.

[0124] Optionally, by using the finite element method to discretize the model, the numerical problems of the displacement field, temperature field and phase field model can be solved by the separate iterative method to obtain the temperature field and stress field.

[0125] To further verify the accuracy of the model, standard calculation examples and calibration verification of the mechanical response of heterogeneous rocks can be used.

[0126] The standard case verification methods include transient heat transfer verification on a rectangular thin plate and thermo-mechanical coupling verification on a thick-walled cylinder. The transient heat transfer verification on the rectangular thin plate verifies the correctness of the temperature field evolution over time. After verifying the accuracy of the temperature field transfer in the model, the accuracy of the model's stress field solution under thermo-mechanical coupling is further verified through steady-state thermo-mechanical coupling on a thick-walled cylinder.

[0127] Optionally, the transient heat transfer verification of the rectangular thin plate includes: establishing a rectangular plate with a length of 2m and a width of 0.5m, with an initial model temperature of 100℃, a left and right boundary temperature of 0℃, and an upper and lower boundary condition of adiabatic. The temperature field contour map calculated by the model and the temperature-time curves at different locations are compared with the analytical solution. Where T is temperature, T out T is the boundary temperature of the thin plate. in Let π be the internal temperature of the thin plate, π be the mathematical constant pi, and t be the heat transfer time. The general term of the summation series is given, where l is the length of the thin plate. The simulation results show good agreement with the theoretical solution, verifying the accuracy of the model. Figure 4 The image shown is a diagram of a transient heat conduction template model. Figure 5 This is a schematic diagram of the transient heat conduction simulation results.

[0128] Optionally, the thermo-mechanical coupling verification of the thick-walled cylinder includes: establishing a thick-walled cylinder model with an inner diameter of 0.5m and an outer diameter of 1.5m, applying boundary conditions of an inner wall temperature of 50℃ and a pressure of 20MPa, and an outer wall temperature of 10℃ and a pressure of 5MPa, simulating the stress and deformation of the thick-walled cylinder when the inner wall is heated and the outer wall is cooled, performing the combined action of pressure and temperature, and verifying the consistency between the stress field distribution and the solution of classical mechanics formulas.

[0129] Optionally, the thermo-coupled heterogeneous rock is subjected to conventional triaxial compression simulation. A 50mm×100mm heterogeneous granite model is established, and the distribution of minerals such as quartz and feldspar is characterized based on Thiessen polygons. A loading path of 40MPa confining pressure and a heating rate of 5℃ / min to 220℃ is set. The stress-strain curves and peak strength decay law of the simulation and experiment are compared (simulation peak strength error ≤1.81%). The random thermal tensile cracks (maximum damage value of 0.28 at 220℃) and the propagation characteristics of heterogeneous induced single-slope shear cracks in the phase field distribution are observed. The results are consistent with the indoor experimental phenomena, proving that the model can accurately capture the compression-shear failure mechanism of rocks under thermo-coupled conditions, and its temperature-dependent parameter settings and two-phase field energy decomposition method are engineering feasible.

[0130] Optionally, the dry hot rock wellbore stability analysis includes: applying the calibrated model to high temperature (≤650℃) and high confining pressure (≤60MPa) conditions to simulate the compression-shear damage evolution of the wellbore rock and predict the crack initiation location and propagation path.

[0131] Optionally, the parameter sensitivity optimization includes the influence of mineral heterogeneity and the optimization of heating rate. The influence of mineral heterogeneity includes comparing the differences in damage modes under different mineral distribution models (e.g., a 5% increase in mica content); the optimization of heating rate includes analyzing the risk of thermal shock damage at heating rates of 5℃ / min and 10℃ / min, and determining a safety threshold.

[0132] To better understand the research method of the temperature-dependent compression-shear two-phase field model for heterogeneous granite, the following explanation is based on a specific application case.

[0133] High-temperature triaxial compression simulation of granite in Gonghe County, Qinghai Province:

[0134] First, on-site sampling and indoor mechanical testing were conducted. Representative granite outcrops were selected in the Gonghe dry-hot rock exploration area of ​​Qinghai Province, and samples were obtained using diamond drill bits. Cylindrical specimens were used, ensuring they were free of obvious cracks or mineral distribution defects. After surface polishing, the specimens underwent systematic mechanical testing using an RTR-2000 high-temperature triaxial testing machine. Experimental results showed that the elastic modulus of granite decreased linearly with increasing temperature.

[0135] Furthermore, to characterize the thermal properties of granite, the coefficient of thermal expansion, thermal conductivity, and specific heat capacity were tested using a ZRPY-1000 thermal expansion meter and an LFA-467 laser thermal conductivity meter to obtain these parameters.

[0136] Based on the mechanical and thermophysical properties obtained from the above experiments, a two-dimensional heterogeneous granite grain model was constructed using the Voronoi algorithm to characterize the spatial distribution differences of mineral components. The specific steps are as follows: first, a geometric model was established; then, the minerals were grouped and their parameters were mapped; finally, strength calibration was performed.

[0137] Specifically, geometric modeling: In Neper software, the model size was set to 50mm × 100mm, with 6000 control points randomly distributed to generate Thiessen polygonal elements. The size of a single mineral was approximately 0.93mm, and the smallest element size was 0.2mm. Mineral grouping: Based on the XRD mineral composition analysis results (quartz 39%, potassium feldspar 41%, sodium feldspar 16%, biotite 4%), different mechanical parameters were assigned to different minerals. For example, the elastic modulus of the quartz element was 79.34 GPa, and that of the biotite element was 45.48 GPa. Parameter mapping: Mineral parameters were batch-imported into the Abaqus model using a Python script to generate .inp files containing material heterogeneity. Figure 6 The diagram shows the boundary conditions.

[0138] Specifically, to verify the accuracy of the heterogeneous model, inverse parameter optimization was carried out based on experimental data. By adjusting the contact stiffness (normal stiffness kn, tangential stiffness ks) and friction coefficient (μ) between the Thiessen polygonal elements, the error between the uniaxial compressive strength of the numerical specimens and the experimental values ​​was made less than 3%.

[0139] The heterogeneous model was imported into Abaqus software and combined with user-defined elements (UEL) to simulate the thermally coupled phase field fracture. Figure 7 The conventional triaxial compression loading path is thermo-coupled. To achieve thermo-coupled loading and numerical simulation, the specific process is as follows: initial stress balancing, temperature loading, and axial loading are performed sequentially.

[0140] Specifically, the initial stress balance includes: Figure 7 As shown in the stress loading path, the y-direction displacement of the bottom edge of the model is fixed, and then a stress of 40MPa is applied inside the model. Finally, a confining pressure of 40MPa is applied at the boundary of the model to achieve initial stress equilibrium.

[0141] Specifically, the temperature loading includes: Figure 8As shown in the temperature loading path, the initial temperature of the heterogeneous rock model is set to 20℃, consistent with the indoor experiment. The model is heated to the target temperature at a rate of 5℃ / min. After the boundary temperature is raised to the target temperature, the model is kept warm to ensure that the entire model is heated to the target temperature.

[0142] Specifically, the axial compression includes: after temperature loading, displacement loading in the σ1 direction is performed at the top of the model with a displacement of Δu = 4 × 10. -3 The displacement boundary is measured in mm until the model fails under compression. The triaxial compression process is simulated while the stress-strain response and crack propagation path are monitored.

[0143] Furthermore, the two-phase field theory (GB-PFM) is used to describe the thermal cracking and compressive-shear failure behavior of rocks:

[0144] Specifically, the coupled calculation of displacement, temperature, and phase fields is achieved through the Abaqus UEL interface. The degrees of freedom of the custom element include: displacement field (U1, U2); temperature field (TEMP); and phase field (PHI). The iterative solution employs the separable Newton-Raphson algorithm, and the stiffness matrix and residual force matrix are updated through code snippets.

[0145] The numerical model research method provided in this embodiment verifies the accuracy of the thermo-mechanical coupling model by comparing simulation results with experimental data, focusing on thermal damage characteristics, compression-shear failure modes, and stress-strain response.

[0146] Specifically, the thermal damage characteristics include: during the heating stage, random tensile cracks occur within the granite due to differences in the thermal expansion coefficients of the minerals. At 220℃, the maximum damage value (dt) at the quartz-feldspar interface reaches 0.28, consistent with indoor thermal cracking observation results. Figure 9 The diagram shown illustrates heat damage.

[0147] Specifically, the compressive-shear failure mode includes: an axial loading stage where the crack propagates along the direction of maximum shear stress, forming a non-local shear band. The failure inclination angle in the numerical simulation is 55°, with an error of less than 4% compared to the shear plane angle of the experimental specimen (53°), verifying the accuracy of the model's compressive-shear response. Figure 10 The diagram shown is a schematic of compression-shear fracture.

[0148] This embodiment establishes a thermo-mechanical coupling model for heterogeneous granite using experimental data-driven and heterogeneous thermo-mechanical coupling experimental-numerical methods, achieving refined prediction of the mechanical behavior of granite at high temperatures. Key advantages include: refined heterogeneous characterization: the Thiessen polygon algorithm combined with mineral parameter mapping accurately reflects the influence of microstructure; temperature-dependent modeling: parameters such as elastic modulus and coefficient of thermal expansion are dynamically corrected with temperature, improving the accuracy of high-temperature predictions; and engineering applicability: the model can accurately predict crack propagation paths after fracturing in hot dry rock wells, providing a basis for reservoir stimulation design.

[0149] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, then this invention should also include these modifications and variations.

[0150] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make modifications, alterations, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite, characterized in that, include: Based on the mineral composition parameters of the target granite, material parameters that vary with temperature are assigned to each mineral, and a heterogeneous thermo-mechanical coupling geometric model is established using a Thiessen polygon mesh. Based on the temperature-dependent material parameters imparted by minerals, displacement, temperature, and fracture control equations are established in the solid solution domain of a heterogeneous thermo-mechanical coupled geometric model. The elastic strain energy is decomposed into tensile and compressive components, which drive the evolution of the tensile phase field and the shear phase field respectively, thus establishing a temperature-dependent compression-shear two-phase field model. Based on displacement, temperature, and fracture control equations, a temperature-dependent compression-shear two-phase field model is solved using a separate iterative algorithm to obtain temperature field characteristics, stress field characteristics, and phase field distribution. By verifying that the temperature field characteristics, stress field characteristics, and phase field distribution accuracy meet the preset conditions through standard calculation examples and experimental data, the temperature-dependent compression-shear two-phase field simulation of heterogeneous granite was completed.

2. The method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite according to claim 1, characterized in that, Based on the mineral composition parameters of the target granite, a heterogeneous thermo-coupled geometric model was established using a Thiessen polygon mesh, including: Based on the mineral composition parameters of the target granite, the Thiessen polygon mesh module of the open-source software Neper was used to input the thermal parameters of the target granite and set the material fracture properties of each mineral block as a function of temperature. The critical energy release rate was determined by nanoindentation to establish a heterogeneous thermo-mechanical coupling geometric model.

3. The method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite according to claim 2, characterized in that, Based on the temperature-dependent material parameters imparted by minerals, displacement, temperature, and fracture governing equations are established in the solid solution domain of a heterogeneous thermo-mechanical coupled geometric model, including: A normalization method was used to establish the functional relationship between material parameters and temperature; Based on the functional relationship and combined with the dispersion crack regularization, the temperature, displacement and phase field variables in the solid solution domain of the heterogeneous thermo-mechanical coupling geometric model under the applied initial conditions are obtained; Based on the rock heterogeneity characterized by the grain method and the material parameters of the rock as it evolves with temperature, displacement, and phase field variables are combined to establish displacement, temperature, and fracture control equations in the solid solution domain of a heterogeneous thermo-mechanical coupled geometric model.

4. The method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite according to claim 3, characterized in that, The displacement, temperature, and fracture control equations in the solid solution domain of the heterogeneous thermo-coupling geometric model are as follows: Displacement field: Temperature field: Fracture phase field: In the displacement field, σ is the stress tensor, f is the body force term, and Ω is the solution domain. This represents the displacement boundary; in the temperature field, ρ is the material density, and c is the specific heat capacity. Let ν be the rate of change of the temperature field, q be the heat flux, n be the normal vector, and γ be the internal heat source. For heat flux boundary conditions, For temperature boundary conditions, For heat flux boundary, Temperature boundary; h in the fracture phase field t ′(d t ) is the tensile damage function, h s ′(d s ) is the shear damage function. For the stretching driving energy, Shear driving energy, To stretch the critical energy release rate. l is the critical shear energy release rate. d d is the characteristic width of the phase field. t For the tensile damage phase field, d s For shear damage phase field, For the phase field gradient of tensile damage, Shear damage phase field gradient, The superscript in A indicates stretching or shearing. Γ This represents the boundary of the fracture crack.

5. The method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite according to claim 4, characterized in that, Based on displacement, temperature, and fracture control equations, a temperature-dependent compression-shear two-phase field model is solved using a separate iterative algorithm to obtain temperature field characteristics, stress field characteristics, and phase field distribution: Temperature field elements, displacement field elements, and phase field elements are layered and covered on the same element; The temperature field elements are written using UMAT elements and the common block is used to transmit iteration information between different elements. The Newton-Raphson algorithm is used to update the stiffness matrix and residual force matrix at each iteration step until the convergence criterion is met, thereby obtaining the temperature field characteristics, stress field characteristics and phase field distribution.

6. The method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite according to claim 5, characterized in that, By verifying, through standard calculation examples and experimental data, that the temperature field characteristics, stress field characteristics, and phase field distribution accuracy meet the preset conditions, a temperature-dependent compression-shear two-phase field simulation of heterogeneous granite is completed, including: The accuracy of the temperature field evolution over time is verified through a transient heat transfer example of a rectangular thin plate. The accuracy of the stress field was verified using a steady-state thermo-mechanical coupling example of a thick-walled cylinder. The feasibility of the phase field model was verified by thermo-coupling conventional triaxial compression experiments on heterogeneous rocks.

7. The method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite according to claim 6, characterized in that, The accuracy of the temperature field evolution over time is verified through a transient heat transfer example using a rectangular thin plate, including: A rectangular thin plate model was established, and the temperature field contour plots and temperature-time curves at different locations were compared with the temperature field curves and analytical solutions calculated by the temperature-dependent compression-shear two-phase field model. The simulation results showed an error of ≤3% between the simulation results and the theoretical solutions, proving the reliability of the model's temperature field evolution calculation.

8. The method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite according to claim 7, characterized in that, The accuracy of the stress field is verified using a steady-state thermo-mechanical coupling example of a thick-walled cylinder, including: A cylindrical model was constructed to simulate the stress and deformation of a thick-walled cylinder when the inner wall is heated and the outer wall is cooled. The pressure and temperature coupling effect was investigated to verify the consistency between the stress field distribution and the solution of classical mechanics formulas.

9. The method for simulating the temperature-dependent compression-shear two-phase field of heterogeneous granite according to claim 8, characterized in that, The feasibility of the phase-field model was verified through thermo-coupled conventional triaxial compression experiments on heterogeneous rocks, including: A heterogeneous granite model was established, and the distribution of minerals such as quartz and feldspar was characterized based on Thiessen polygons. The stress-strain curves and peak intensity decay laws of the simulation and experiment were compared. The propagation characteristics of random thermal tensile fractures and heterogeneous-induced single-slope shear cracks in the phase field distribution were observed. The results were consistent with the indoor experimental phenomena, proving that the model can accurately capture the compression-shear failure mechanism of rocks under thermo-mechanical coupling. Its temperature-dependent parameter settings and two-phase field energy decomposition method have engineering feasibility.

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