A Rock Continuous-Discontinuous Thermodynamic Coupling Simulation Method Based on 3D Voronoi Block

Abstract

This invention relates to the field of numerical simulation technology in rock mechanics, and discloses a continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks. It aims to solve the problems of poor accuracy, insufficient thermo-mechanical coupling integrity, and lack of true triaxial stress adaptability in existing methods. The main solutions include: generating a set of three-dimensional Voronoi blocks; forming fractable blocks through surface-to-volume cutting Boolean operations and internally tetrahedralizing them; assigning different mechanical parameters to the block boundaries and internal tetrahedral boundaries respectively; simulating heat transfer after fracture using point-to-point, point-to-surface, and surface-to-surface contacts in the heating and cooling simulation; extracting the fracture surface coordinates and subtracting the displacement to obtain thermally induced cracks; and mapping the thermally induced cracks back to the model and applying true triaxial loading to evaluate rock strength. This invention achieves simulation of transgranular-intergranular composite fracture, dynamic preservation of heat transfer after fracture, and true triaxial stress adaptability, significantly improving simulation realism and engineering applicability.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology of rock mechanics, and specifically to a continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks. Background Technology

[0002] With the rapid development of underground engineering projects such as deep tunnels, mines, geothermal development, and nuclear waste disposal, the surrounding rock is generally in a state of strong coupling between high ground stress and high temperature environment. Temperature changes the mechanical properties of rocks through thermal expansion, thermal softening, and thermal fracturing. This, combined with tectonic stress and excavation unloading, easily induces disasters such as rock bursts and large deformations. Accurately simulating the fracturing process of rocks under thermo-mechanical coupling is of great significance for engineering design and disaster prevention.

[0003] Currently, numerical simulations of rock mechanics are mainly divided into continuous and discontinuous methods. Continuous methods (such as finite element method and finite difference method) have high computational efficiency and are suitable for analyzing stress and temperature fields at the engineering scale, but they are difficult to describe the initiation, propagation, and penetration of cracks, and their simulation of discontinuous processes such as block slip and thermal cracking after rock fracture is distorted. Discontinuous methods (such as discrete element method and block element method) can simulate cracks, joints, and block movement, but they have high computational costs, complex contact criteria, and the temperature field is difficult to stably propagate on the discontinuous surface after fracture, resulting in insufficient accuracy of thermo-mechanical coupling.

[0004] Application publication number CN118036384A discloses a thermo-mechanical coupling numerical simulation method and apparatus based on the FDEM-Voronoi particle model. The method includes the following steps: establishing a numerical model of the microstructure of rock using the Voronoi particle model; heating and cooling a first rock sample model to obtain microscopic thermal cracks generated by the heating-cooling cycle; importing the thermal crack coordinate information into a second rock sample model and performing geometric reconstruction to give the second rock sample model the presence of thermal cracks; and conducting a uniaxial compression simulation test on the reconstructed model. This method uses the Voronoi particle model to characterize the microstructure of rocks, thus depicting the continuous-discontinuous fracture process of rocks to a certain extent and reproducing the weakening effect of temperature on rocks.

[0005] However, the aforementioned existing technologies still have significant drawbacks. First, the scheme is based on a two-dimensional Voronoi particle model, where the particles are indestructible. In this case, cracks can only propagate along the interfaces between particles, meaning it can only simulate intergranular fracture and cannot simulate transgranular fracture where cracks penetrate the interior of particles. This does not match the actual intergranular-transgranular composite fracture mechanism of rocks, leading to distortion in the simulation of fracture paths and failure modes. Second, the scheme only obtains hot cracks during heating-cooling cycles and then maps the coordinates of the hot cracks to a new model for mechanical testing. Hot cracks are treated as static geometric defects and cannot simulate the heat transfer process between rock fragments through point-to-point, point-to-surface, and surface-to-surface contacts after rock fracture. This disrupts the continuity of thermo-mechanical coupling and makes it difficult to reflect the dynamic impact of changes in thermal conductivity on the temperature and stress fields after fracture. Third, the scheme only conducts uniaxial compression simulation tests on the reconstructed model, ignoring the constraint and strengthening effect of the intermediate principal stress on rock strength under true triaxial stress conditions. This cannot realistically reflect the three-dimensional high-stress environment of the surrounding rock in deeply buried underground engineering projects. Summary of the Invention

[0006] This invention aims to address the problems of poor accuracy, insufficient thermo-mechanical coupling integrity, and lack of true triaxial stress adaptability in existing numerical simulation methods for rock mechanics. It proposes a continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows: In a first aspect, the present invention provides a method for continuous-discontinuous thermo-mechanical coupling simulation of rocks based on three-dimensional Voronoi blocks, the method comprising: A three-dimensional block mesh is constructed using the duality relationship between Delaunay tetrahedral partitioning and Voronoi diagrams, resulting in a three-dimensional Voronoi block set; Perform a face-to-volume cutting Boolean operation on the surfaces of all three-dimensional Voronoi blocks in the three-dimensional Voronoi block set to form breakable blocks, and then perform tetrahedral element meshing on the interior of the blocks to obtain a three-dimensional Voronoi breakable block tetrahedral model; wherein, the tetrahedral elements inside each block constitute the breakable elements of the block, and the interface between adjacent blocks is defined as the block boundary. The three-dimensional Voronoi fractable block tetrahedral model was imported into a continuous-discontinuous numerical simulation program. Two sets of mechanical parameters were used to assign values ​​to the tetrahedral element boundaries of the block boundary and the interior of the block, respectively, with the mechanical properties of the interior of the block being higher than those of the block boundary. A temperature field was set to simulate heating and cooling. During the simulation, the block boundary included point-to-point contact, point-to-surface contact, and surface-to-surface contact to simulate heat transfer between blocks after rock fracturing. After the simulation, the coordinate information of the fracture surface was extracted, and the current coordinates of each point on the fracture surface were subtracted from the displacement corresponding to that point to obtain the initial coordinate information of the thermally induced crack. The initial coordinate information of all thermally induced cracks is mapped onto the three-dimensional Voronoi fractable block tetrahedron model to obtain the numerical model of the rock sample after heat treatment. A true triaxial load is applied to the numerical model of the heated rock sample, that is, stress or displacement boundary conditions are applied independently in three mutually perpendicular directions of the numerical model of the rock sample until the rock sample fails, and the rock strength is evaluated based on the stress state at the time of failure.

[0008] Furthermore, the three-dimensional Voronoi block is an irregular polyhedral block, and its geometry is controlled by random seed points to restore the heterogeneous distribution of rock grains, rock bridges and natural joints.

[0009] Furthermore, the tetrahedral element meshing adopts an unstructured mesh, and the meshed model data includes the node coordinates of the tetrahedral elements, the element connection relationships, and the contact information of the block boundaries.

[0010] Furthermore, the two sets of mechanical parameters specifically include: A first set of mechanical parameters is assigned to the boundary of the block, and a second set of mechanical parameters is assigned to the boundary of the tetrahedral unit inside the block. The first set of mechanical parameters includes the first tensile strength, first cohesion, first friction angle, and first thermal conductivity of the block boundary. The second set of mechanical parameters includes the second tensile strength, second cohesion, second friction angle, and second thermal conductivity of the boundary of the tetrahedral unit inside the block. The second tensile strength is greater than the first tensile strength, and the second cohesion is greater than the first cohesion.

[0011] Furthermore, the heating and cooling simulation employs a uniform heating method to heat the three-dimensional Voronoi breakable tetrahedral block model to the target temperature and then hold it at that temperature, followed by a uniform cooling method to cool it to room temperature. The heating temperature range is from room temperature to 300°C.

[0012] Furthermore, the extraction of fracture surface coordinate information specifically includes: Identify adjacent tetrahedral element pairs that have cracked, obtain the current coordinates of the vertices of the triangular elements on the cracked surface, and form a triangular mesh of the cracked surface.

[0013] Furthermore, the initial coordinate information of all thermally induced cracks is mapped onto the three-dimensional Voronoi fractable block tetrahedral model, specifically including: The node coordinates in the initial coordinate information of the thermally induced crack are matched with the node coordinates in the three-dimensional Voronoi fractable block tetrahedral model, and the boundary of the tetrahedral element where the successfully matched node is located is set as the crack element.

[0014] Furthermore, the true triaxial loading specifically includes: Minimum principal stresses are applied to the left and right surfaces of the numerical model of the rock sample, intermediate principal stresses are applied to the front and rear surfaces of the numerical model of the rock sample, and constant compression is applied to the upper and lower surfaces of the numerical model of the rock sample; the tetrahedral elements inside the block are based on an elastoplastic constitutive model, and the thermally induced cracks are based on a contact model with no tensile strength and a residual friction angle.

[0015] Furthermore, the continuous-discontinuous numerical simulation program is a numerical simulation program based on the finite element-discrete element coupling method.

[0016] Furthermore, the rock strength is assessed based on the stress state at the time of failure, specifically including: Record the maximum principal stress value at which the rock specimen fails, and use this maximum principal stress value as the rock strength of the rock specimen under the currently applied minimum principal stress and intermediate principal stress conditions.

[0017] The beneficial effects of this invention are as follows: The continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks provided by this invention, by using fractable three-dimensional Voronoi blocks and dividing the interior of the blocks into tetrahedral elements, allows cracks to propagate along the block interface and also to undergo transgranular fracture through the interior of the blocks, realistically reproducing the complex fracture mechanism of rocks and improving the accuracy of the fracture process simulation; by setting the block boundaries to point-to-point, point-to-surface, and surface-to-surface contact and participating in the dynamic calculation of the entire process of heating, cooling, and subsequent loading, the heat transfer simulation between blocks after rock fracture is realized, ensuring the continuity of thermo-mechanical coupling and avoiding the defect of treating thermal cracks only as static geometric defects; by applying true triaxial loading and independently controlling stress or displacement boundary conditions in three mutually perpendicular directions, the constraint effect of the intermediate principal stress on rock strength can be reflected, which is closer to the three-dimensional high-stress environment of deeply buried underground engineering. Attached Figure Description

[0018] Figure 1 A schematic diagram of the process for a continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks, provided for an embodiment; Figure 2A schematic diagram of the structure of a three-dimensional Voronoi block provided for an embodiment; Figure 3 A schematic diagram of the structure of a three-dimensional Voronoi breakable block tetrahedron model provided for an embodiment; Figure 4 The following is a schematic diagram of the block boundary structure provided in the embodiment; wherein, (a) is a block boundary with point-to-point contact, (b) is a block boundary with point-to-surface contact, and (c) is a block boundary with surface-to-surface contact; Figure 5 The following is a schematic diagram of crack surface coordinate information extraction provided in the embodiment; wherein, (a) is a schematic diagram of adjacent tetrahedral element pairs where cracking occurs, 2, 3, and 4 represent the three vertices of the crack surface, (b) is a schematic diagram of the current coordinates of the crack surface after heating, A, B, and C represent the three vertices of the crack surface after heating, and (c) is a schematic diagram of the initial coordinates of the thermally induced crack after subtracting the displacement, 6, 7, and 8 represent the three initial vertices of the thermally induced crack; Figure 6 A schematic diagram of the structure of thermally induced cracks provided in the embodiment; Figure 7 A schematic diagram of the true triaxial compressive stress-strain curve of the rock sample provided in the embodiment; Figure 8 A schematic diagram of the structure of the numerical model of the damaged rock sample provided in the example. Detailed Implementation

[0019] Existing technologies employ a thermo-mechanical coupling simulation method based on the FDEM-Voronoi particle model. This method generates thermal cracks through heating and cooling, which are then mapped onto a new model for uniaxial compression tests. However, in the two-dimensional Voronoi particle model, the particles are indestructible, resulting in the simulation of intergranular fracture rather than transgranular fracture. Furthermore, thermally induced cracks are treated as static defects and do not participate in heat transfer after fracture. Additionally, uniaxial loading ignores the intermediate principal stress effect. Therefore, the simulation of the continuous-discontinuous thermo-mechanical coupling fracture process of rocks under deep-buried, high-stress, and high-temperature environments is not realistic, lacks thermo-mechanical coupling integrity, and lacks three-dimensional stress adaptability.

[0020] Based on this, the technical solution of the present invention is proposed. In the present invention, firstly, a three-dimensional Voronoi block is used and Boolean operations and tetrahedral element subdivision are performed to make each block contain breakable tetrahedral elements. Cracks can propagate along the block interface (intergranular fracture) and also penetrate the block interior to cause cracking (transgranular fracture), thus realistically reproducing the complex fracture mechanism of rock. Secondly, throughout the heating, cooling and subsequent loading process, the block boundaries are set to point-to-point, point-to-surface, and surface-to-surface contacts and dynamically participate in heat transfer calculations. Even after the rock fractures, the blocks can still exchange heat through the contact interface, ensuring the continuity of thermal coupling from continuous to discontinuous states and avoiding the limitation of treating thermal cracks only as static geometric defects. Finally, a true triaxial loading method is adopted to independently control stress or displacement boundary conditions in three mutually perpendicular directions, which can quantify the constraint and strengthening effect of the intermediate principal stress on the rock strength. In the above process, the fractured block provides a realistic physical basis for fracture, heat transfer after fracture maintains the dynamic integrity of thermo-mechanical coupling, and true triaxial loading restores the three-dimensional high ground stress environment. Together, these three elements achieve a high-fidelity simulation of the entire process of thermo-mechanical coupling fracture of deeply buried rocks.

[0021] The technical solutions in this embodiment will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0022] Figure 1 A flowchart illustrating a continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks is shown. Please refer to [link / reference]. Figure 1 The method includes the following steps: Step 1: Generate a 3D Voronoi block set: A three-dimensional block mesh is constructed using the duality between Delaunay tetrahedral partitioning and Voronoi diagrams, resulting in a three-dimensional Voronoi block set.

[0023] Specifically, a set of seed points is first generated in three-dimensional space. The number and distribution of seed points determine the size and shape of the three-dimensional Voronoi block. To simulate the heterogeneity of the rock, the positions of the seed points can be randomly distributed or set according to the grain size distribution obtained statistically from actual rock thin sections.

[0024] Then, using the seed point as the vertex, a Delaunay tetrahedral partition is performed to obtain a set of non-overlapping tetrahedral elements. Next, the circumcenter of each tetrahedral element is taken, and the circumcenters of adjacent tetrahedral elements are connected to obtain the 3D Voronoi block corresponding to each seed point. (See also...) Figure 2Each three-dimensional Voronoi block is a convex polyhedron, and all three-dimensional Voronoi blocks together constitute a set of three-dimensional Voronoi blocks.

[0025] The above process can be implemented using the open-source software package TetGen. TetGen takes the seed point coordinates as input and outputs a tetrahedral mesh and the corresponding Voronoi diagram information. By extracting the vertex coordinates and face connectivity of each 3D Voronoi block using a custom script, a set of 3D Voronoi blocks can be obtained.

[0026] Three-dimensional Voronoi blocks are irregular polyhedra whose geometry is controlled by random seed points, enabling the reproduction of the heterogeneous distribution of rock grains, rock bridges, and natural joints. Compared to two-dimensional Voronoi polygons, three-dimensional Voronoi blocks can realistically represent the three-dimensional stress redistribution and spatial failure morphology of rock masses, providing a more rigorous geometric basis for subsequent continuous-discontinuous simulations.

[0027] Step 2: Construct a 3D Voronoi fractable tetrahedral model: Perform a face-to-volume Boolean operation on the surfaces of all three-dimensional Voronoi blocks in the three-dimensional Voronoi block set to form breakable blocks, and then mesh the interior of the blocks with tetrahedral elements to obtain a three-dimensional Voronoi breakable block tetrahedral model; wherein, the tetrahedral elements inside each block constitute the breakable elements of the block, and the interface between adjacent blocks is defined as the block boundary.

[0028] It can be understood that in the set of three-dimensional Voronoi blocks obtained in step 1, each three-dimensional Voronoi block is a convex polyhedron surrounded by multiple polygonal faces. The three-dimensional Voronoi blocks are adjacent to each other, and the common face between the three-dimensional Voronoi blocks is the potential fracture surface. In order to simulate the cracking inside the rock block (i.e., transgranular fracture), each three-dimensional Voronoi block needs to be further subdivided into smaller basic units so that the crack can propagate through the interior of the block.

[0029] Specifically, this step uses a face-to-volume cutting Boolean operation to achieve the above objective. First, extract the surfaces of all 3D Voronoi blocks from the 3D Voronoi block set; these surfaces form a closed set of faces. Create a cube whose boundaries completely cover the outer contours of all block surfaces, meaning the cube encloses all 3D Voronoi blocks. Then, using this cube as the base entity, and using the surfaces of all 3D Voronoi blocks as cutting tools, perform a face-to-volume cutting Boolean operation on the cube. After the calculation, the cube is divided into several independent 3D regions by the block surfaces, each region corresponding to a block.

[0030] After completing the face-to-volume cutting, the interior of each block is meshed using tetrahedral elements. The tetrahedral meshing uses an unstructured mesh, meaning the interior of each block is discretized into several non-overlapping tetrahedral elements. The shape and size of the tetrahedral elements can be controlled according to computational accuracy and efficiency requirements, and are typically generated using the Delaunay tetrahedral meshing algorithm.

[0031] After the above processing, a three-dimensional Voronoi fractable tetrahedral model of the block is obtained. In this model, the tetrahedral elements inside each block constitute the fractable elements of that block. When the external force or thermal stress is large enough, cracks can occur at the boundaries between the tetrahedral elements. Cracks can propagate not only at the interfaces between different blocks (i.e., block boundaries) but also between tetrahedral elements within the same block, thus simulating transgranular fracture. The interfaces between adjacent blocks are defined as block boundaries. In subsequent simulations, block boundaries serve as potential intergranular fracture surfaces and bear the functions of contact and heat transfer between blocks after fracture.

[0032] After meshing, the model data of the 3D Voronoi fractable block tetrahedron is exported as an INP file. The INP file contains the node coordinates of the tetrahedral elements, element connection relationships, and contact information of the block boundaries. This INP file can be read by continuous-discontinuous numerical simulation programs for subsequent thermo-mechanical coupling calculations.

[0033] Step 3: Generating and extracting thermally induced cracks: The three-dimensional Voronoi fractable block tetrahedral model was imported into a continuous-discontinuous numerical simulation program. Two sets of mechanical parameters were used to assign values ​​to the tetrahedral element boundaries of the block boundary and the block interior, respectively, with the mechanical properties inside the block being higher than those of the block boundary. A temperature field was set to simulate heating and cooling. During the simulation, the block boundary included point-to-point contact, point-to-surface contact, and surface-to-surface contact to simulate heat transfer between blocks after rock fracturing. After the simulation, the coordinate information of the fracture surface was extracted, and the current coordinates of each point on the fracture surface were subtracted from the displacement corresponding to that point to obtain the initial coordinate information of the thermally induced crack.

[0034] Specifically, this step imports the three-dimensional Voronoi fractable block tetrahedron model obtained in step 2 into a continuous-discontinuous numerical simulation program; wherein, the continuous-discontinuous numerical simulation program can be a numerical simulation program based on the finite element-discrete element coupling method.

[0035] In practical applications, firstly, mechanical parameters are assigned to two different interfaces in the three-dimensional Voronoi fractable tetrahedral block model: a first set of mechanical parameters is assigned to the block boundaries between adjacent blocks, including a first tensile strength, a first cohesive force, a first friction angle, and a first thermal conductivity; a second set of mechanical parameters is assigned to the boundaries of tetrahedral elements within each block, including a second tensile strength, a second cohesive force, a second friction angle, and a second thermal conductivity, wherein the second tensile strength is greater than the first tensile strength, and the second cohesive force is greater than the first cohesive force. The tetrahedral elements themselves adopt an elastic constitutive model, and failure only occurs at the element boundaries.

[0036] Then, the initial temperature was set to room temperature, and the 3D Voronoi fractable tetrahedral model was uniformly heated to the target temperature (room temperature to 300°C), held at that temperature, and then uniformly cooled to room temperature. Throughout the heating and cooling process, the block boundaries maintained heat transfer capability, and the contact types included point-to-point contact, point-to-surface contact, and surface-to-surface contact. Please refer to [link to relevant documentation]. Figure 4 , Figure 4 (a) shows a block boundary with point-to-point contact; Figure 4 (b) shows a block boundary with point-to-surface contact; Figure 4 (c) illustrates a block boundary with surface-to-surface contact. Even if adjacent blocks crack and separate due to thermal stress, the contact interface between the blocks can still dynamically calculate heat exchange, simulating heat transfer between blocks after rock fracture.

[0037] After the simulation, all adjacent tetrahedral element pairs that cracked were identified, and the current coordinates of the vertices of the triangles on each cracked surface were extracted as the crack surface coordinate information. Since the model expanded and deformed during heating and cooling, the crack surface coordinate information needed to be restored to its undeformed state: the total displacement of each vertex at the end of the simulation was obtained, and the current coordinates of that vertex were subtracted from its corresponding displacement to obtain the initial coordinate information of that vertex before deformation. This operation was performed on all cracked surface vertices to obtain the initial coordinate information of each crack surface. The crack surface represented by the initial coordinate information is the thermally induced crack. (See also...) Figure 5 , Figure 5 (a) shows a schematic diagram of a pair of adjacent tetrahedral elements that have cracked, where the two tetrahedral elements share a common triangular face. The three vertices of the triangular face are numbered 2, 3, and 4 in the current coordinate system. This triangular face is a crack surface. Figure 5 (b) shows a schematic diagram of the current coordinates of the fracture surface after heating. The fracture surface is extracted separately, and its three vertices are renumbered as A, B, and C. The coordinates at this time record the current position of the fracture surface after heating and cooling. Figure 5(c) shows a schematic diagram of the initial coordinates of the thermally induced crack after subtracting the displacement. By subtracting the corresponding displacement from the current coordinates of points A, B, and C, three new points 6, 7, and 8 are obtained. The triangle formed by points 6, 7, and 8 represents the initial position and shape of the crack surface before any deformation occurs, i.e., the initial coordinate information of the thermally induced crack. Finally, for all extracted thermally induced cracks, please refer to [link to relevant documentation]. Figure 6 .

[0038] Step 4: Construct a numerical model of the rock sample with thermally induced cracks: The initial coordinate information of all thermally induced cracks is mapped onto the three-dimensional Voronoi fractable block tetrahedron model to obtain the numerical model of the heated rock sample.

[0039] Specifically, this step maps the initial coordinate information of all thermally induced cracks obtained in step 3 to the three-dimensional Voronoi fractable block tetrahedral model obtained in step 2, and constructs a numerical model of the heated rock sample.

[0040] In practical applications, the mapping process is as follows: First, extract the node coordinates of the triangle vertices on each crack surface from the initial coordinate information of the thermally induced crack. Then, match these node coordinates one by one with the node coordinates of all nodes in the 3D Voronoi fractable block tetrahedral model to find the corresponding nodes with overlapping positions. For each successfully matched node, locate the boundary of the tetrahedral element to which the node belongs. Finally, set the tetrahedral element boundary as the crack element, that is, mark it as the interface that allows cracking and slippage during subsequent mechanical loading.

[0041] Through the above mapping, all element boundaries corresponding to the geometric locations of thermally induced cracks in the original three-dimensional Voronoi fractable block tetrahedral model are converted into crack elements, while the other parts of the model (the block boundaries unaffected by thermally induced cracks and the boundaries of internal tetrahedral elements) retain their original mechanical parameters. This results in a new model that simultaneously incorporates the original block structure and the distribution of thermally induced cracks—a numerical model of the heated rock sample. This model retains the geometric shape and mechanical layering characteristics of the original model from step 2, while also incorporating the realistic spatial distribution of thermal cracks generated through heating and cooling simulation in step 3, providing an accurate initial state for subsequent true triaxial strength assessment.

[0042] Step 5: True triaxial simulation evaluation of rock strength under three-dimensional thermo-mechanical coupling conditions: A true triaxial load is applied to the numerical model of the heated rock sample, that is, stress or displacement boundary conditions are applied independently in three mutually perpendicular directions of the numerical model of the rock sample until the rock sample fails, and the rock strength is evaluated based on the stress state at the time of failure.

[0043] In practical applications, the specific loading method is as follows: Minimum principal stresses are applied to the left and right surfaces of the numerical model of the rock sample to simulate the constraint of the minimum principal stress direction in deep rock masses; intermediate principal stresses are applied to the front and rear surfaces of the numerical model of the rock sample to simulate the constraint of the intermediate principal stress direction; and constant-velocity compression is applied to the upper and lower surfaces of the numerical model of the rock sample to simulate loading in the direction of the maximum principal stress. The compression rate should meet the static loading conditions to avoid inertial effects.

[0044] Different constitutive models are used for different components within the numerical model of the rock sample: for the rock matrix (i.e., tetrahedral elements inside a three-dimensional Voronoi block), an elastoplastic constitutive model is used to describe its continuous deformation behavior; for the thermally induced crack (i.e., the crack elements set in step 4), a contact model without tensile strength but with residual friction angle is used to simulate the mechanical properties of shear force transmission solely through friction after crack opening. For block boundaries that have not cracked and element boundaries that have not been activated, either the first or second set of mechanical parameters from step 3 is still used.

[0045] During the simulation, the reaction force and displacement of the loading plate are recorded in real time, and stress-strain curves are plotted. Rock specimen failure is defined as the point where internal cracks penetrate and the bearing capacity decreases sharply within the numerical model of the rock specimen. The maximum principal stress value at failure is recorded and used as the rock strength under the applied minimum and intermediate principal stresses. For example, if the applied minimum principal stress (confining pressure) is 5 MPa, and the maximum principal stress at failure is 33 MPa, then the rock strength under this stress state is 33 MPa. By changing the combination of the minimum and intermediate principal stresses, the true triaxial strength envelope of the rock can also be plotted, providing complete strength parameters for underground engineering design.

[0046] Figure 7 A schematic diagram of a true triaxial compressive stress-strain curve for a rock specimen is shown, where the horizontal axis represents axial strain (%) and the vertical axis represents axial stress (MPa). The curve illustrates the complete stress-strain response process of the rock specimen under true triaxial loading conditions, from... Figure 7 As can be seen, in the initial loading stage, stress increases linearly with strain, and the slope of the curve represents the elastic modulus of the rock. When the axial strain reaches approximately 0.12%, the stress reaches its peak value of approximately 33 MPa, which is the peak strength of the rock. Subsequently, the curve drops sharply, indicating that the rock undergoes macroscopic failure and its bearing capacity decreases rapidly. For the numerical model of the failed rock sample, please refer to [link to model]. Figure 8 .

[0047] In summary, the continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks provided in this embodiment, by employing fractable three-dimensional Voronoi blocks and dividing the block interior into tetrahedral elements, allows cracks to propagate along the block interface and also penetrate the block interior to undergo transgranular fracture, realistically reproducing the intergranular-transgranular composite fracture mechanism of rocks and improving the accuracy of the fracture process simulation; by setting point-to-point, point-to-surface, and surface-to-surface contacts at the block boundaries and participating in the dynamic calculation of the entire heating, cooling, and subsequent loading process, rock fracture is realized. The simulation of heat transfer between the blocks ensures the continuity of thermo-mechanical coupling from continuous to discontinuous states, avoiding the limitation of treating thermal cracks merely as static geometric defects. By applying true triaxial loading and independently controlling stress or displacement boundary conditions in three mutually perpendicular directions, the constraint effect of the intermediate principal stress on rock strength can be reflected, more closely resembling the three-dimensional high-stress environment of deeply buried underground engineering. Furthermore, compared with two-dimensional models, three-dimensional Voronoi blocks can realistically reproduce the spatial heterogeneity of rock mass and three-dimensional stress redistribution, providing a more rigorous mechanical basis for surrounding rock stability evaluation. In summary, this invention effectively solves the problems of poor simulation realism, incomplete thermo-mechanical coupling, and insufficient adaptability to stress states in existing technologies, providing a reliable numerical simulation tool for disaster prevention and support design in deep rock engineering.

Claims

1. A continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks, characterized in that, The method includes: A three-dimensional block mesh is constructed using the duality relationship between Delaunay tetrahedral partitioning and Voronoi diagrams, resulting in a three-dimensional Voronoi block set; Perform a face-to-volume cutting Boolean operation on the surfaces of all three-dimensional Voronoi blocks in the three-dimensional Voronoi block set to form breakable blocks, and then perform tetrahedral element meshing on the interior of the blocks to obtain a three-dimensional Voronoi breakable block tetrahedral model; wherein, the tetrahedral elements inside each block constitute the breakable elements of the block, and the interface between adjacent blocks is defined as the block boundary. The three-dimensional Voronoi fractable block tetrahedral model was imported into a continuous-discontinuous numerical simulation program. Two sets of mechanical parameters were used to assign values ​​to the tetrahedral element boundaries of the block boundary and the interior of the block, respectively, with the mechanical properties of the interior of the block being higher than those of the block boundary. A temperature field was set to simulate heating and cooling. During the simulation, the block boundary included point-to-point contact, point-to-surface contact, and surface-to-surface contact to simulate heat transfer between blocks after rock fracturing. After the simulation, the coordinate information of the fracture surface was extracted, and the current coordinates of each point on the fracture surface were subtracted from the displacement corresponding to that point to obtain the initial coordinate information of the thermally induced crack. The initial coordinate information of all thermally induced cracks is mapped onto the three-dimensional Voronoi fractable block tetrahedron model to obtain the numerical model of the rock sample after heat treatment. A true triaxial load is applied to the numerical model of the heated rock sample, that is, stress or displacement boundary conditions are applied independently in three mutually perpendicular directions of the numerical model of the rock sample until the rock sample fails, and the rock strength is evaluated based on the stress state at the time of failure.

2. The continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks according to claim 1, characterized in that, The three-dimensional Voronoi block is an irregular polyhedral block whose geometry is controlled by random seed points, used to reconstruct the heterogeneous distribution of rock grains, rock bridges and natural joints.

3. The continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks according to claim 1, characterized in that, The tetrahedral element meshing uses an unstructured mesh, and the meshed model data includes the node coordinates of the tetrahedral elements, the element connection relationships, and the contact information of the block boundaries.

4. The continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks according to claim 1, characterized in that, The two sets of mechanical parameters specifically include: A first set of mechanical parameters is assigned to the boundary of the block, and a second set of mechanical parameters is assigned to the boundary of the tetrahedral unit inside the block. The first set of mechanical parameters includes the first tensile strength, first cohesion, first friction angle, and first thermal conductivity of the block boundary. The second set of mechanical parameters includes the second tensile strength, second cohesion, second friction angle, and second thermal conductivity of the boundary of the tetrahedral unit inside the block. The second tensile strength is greater than the first tensile strength, and the second cohesion is greater than the first cohesion.

5. The continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks according to claim 1, characterized in that, The heating and cooling simulation uses a uniform heating method to heat the three-dimensional Voronoi breakable tetrahedral block model to the target temperature and then hold it at that temperature. Then, a uniform cooling method is used to cool it to room temperature. The heating temperature range is from room temperature to 300°C.

6. The continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks according to claim 1, characterized in that, The extraction of fracture surface coordinate information specifically includes: Identify adjacent tetrahedral element pairs that have cracked, obtain the current coordinates of the vertices of the triangular elements on the cracked surface, and form a triangular mesh of the cracked surface.

7. The continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks according to claim 1, characterized in that, Mapping the initial coordinate information of all thermally induced cracks onto the three-dimensional Voronoi fractable block tetrahedron model specifically includes: The node coordinates in the initial coordinate information of the thermally induced crack are matched with the node coordinates in the three-dimensional Voronoi fractable block tetrahedral model, and the boundary of the tetrahedral element where the successfully matched node is located is set as the crack element.

8. The continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks according to claim 1, characterized in that, The true triaxial loading specifically includes: Minimum principal stresses are applied to the left and right surfaces of the numerical model of the rock sample, intermediate principal stresses are applied to the front and rear surfaces of the numerical model of the rock sample, and constant compression is applied to the upper and lower surfaces of the numerical model of the rock sample; the tetrahedral elements inside the block are based on an elastoplastic constitutive model, and the thermally induced cracks are based on a contact model with no tensile strength and a residual friction angle.

9. The continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks according to claim 1, characterized in that, The continuous-discontinuous numerical simulation program is a numerical simulation program based on the finite element-discrete element coupling method.

10. The continuous-discontinuous thermo-mechanical coupling simulation method for rocks based on three-dimensional Voronoi blocks according to claim 1, characterized in that, Assessing rock strength based on the stress state at the time of failure includes: Record the maximum principal stress value at which the rock specimen fails, and use this maximum principal stress value as the rock strength of the rock specimen under the currently applied minimum principal stress and intermediate principal stress conditions.

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