A seepage-stress nonlinear coupling analysis method based on finite volume-finite element framework

Abstract

A nonlinear coupling analysis method for seepage and stress based on a finite volume-finite element framework is presented, belonging to the field of hydraulic and hydropower technology. First, a three-dimensional mesh model and a three-dimensional seepage calculation model are established. Second, based on the three-dimensional seepage calculation model, the total head and hydraulic gradient distribution results are obtained and converted into corresponding loads, which are then transferred to the finite element stress-deformation solver through field variable mapping or a common-node mode. Third, based on the three-dimensional mesh model and corresponding loads, the stress, displacement, and volumetric strain results of the earth-rock dam are obtained to evaluate the dam's state, dynamically update the dam's porosity, and thus correct the dam's permeability coefficient. Finally, the volumetric seepage solver is invoked again to obtain the changes in total head and displacement, and convergence is determined. This invention employs an iterative coupling strategy, enabling dynamic coupling analysis of seepage and stress, and improving the accuracy and reliability of numerical simulation of soil in multi-physics coupling processes.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy and hydropower technology, and relates to a nonlinear coupling analysis method for seepage and stress based on a finite volume-finite element framework. Background Technology

[0002] In recent years, soil-water coupling problems have increasingly highlighted their importance in the engineering field, becoming a research hotspot of common concern in both academia and engineering. A series of typical engineering problems, such as deep overburden erosion, tunnel water and mud inrush disasters, underground cavern erosion and damage, landslide-debris flow geological hazards, and seepage deformation and instability of earth-rock dams, all reflect the complexity and harmfulness of this coupling effect. These engineering problems not only directly threaten the safe operation of major infrastructure, but may also trigger chain reactions of economic losses and far-reaching social impacts. In-depth analysis of these problems reveals that their essence involves the complex interaction mechanism between the seepage field and the stress-strain field of the soil and rock mass. For this reason, the study of seepage-stress coupling mechanism has become one of the most challenging frontier topics in the field of geotechnical engineering, and its research results have important theoretical guiding value and practical significance for engineering safety prevention and control.

[0003] As research deepens, the academic community's understanding of the soil-water coupling mechanism continues to grow. Studies show that the seepage field directly affects the soil stress state by altering the pore water pressure distribution, inducing soil deformation and changing its pore structure; conversely, changes in the stress field react upon the seepage field, creating dynamic feedback by adjusting soil permeability. This two-way coupling significantly alters the mechanical and permeability properties of the soil, thus affecting the overall stability of engineering structures. Traditional single-field analysis methods struggle to accurately describe this complex process, making seepage-stress coupling analysis an essential choice for engineering practice. For example, Chinese invention patent 2024110199496 provides a grid-based simulation analysis method and system for the hydraulic coupling stability of earth-rock dams. By constructing a network simulation model, a seepage-stress coupling model, and a local mesh refinement model, it achieves stability assessment of the hydraulic coupling of earth-rock dams. Chinese invention patent 2023108867377 provides a method for constructing a rock seepage-stress coupling damage constitutive model. By analyzing the porosity variation characteristics of the rock's internal structure, it establishes the relationship between seepage-stress coupling variables and damage and plastic deformation. Existing technologies improve resolution through local mesh refinement, but fail to address the lack of mass conservation in the seepage field-stress field iteration process, leading to oscillations in calculation results in high hydraulic gradient zones, and neglecting the impact of soil wetting on dam deformation.

[0004] The seepage-stress coupling problem, due to its strong nonlinear characteristics, suffers from technical bottlenecks in numerical solutions, such as poor computational convergence and insufficient accuracy. To address this challenge, this invention innovatively proposes a finite volume-finite element coupled analysis framework. By introducing a wetting deformation constitutive model, it achieves high-precision coupled calculations of the seepage and stress fields. This method overcomes the limitations of traditional analysis techniques, improving the computational accuracy of the interaction between soil wetting deformation and seepage processes by establishing a dynamic coupling mechanism between seepage and deformation, thus providing a novel technical means for engineering safety assessment. Summary of the Invention

[0005] This invention addresses the problem of analytical distortion caused by the inability to accurately reflect the seepage-deformation interaction in soil-water coupled simulations in the geotechnical field. It provides a nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework. To achieve high-precision bidirectional coupling calculations of the seepage and stress fields, this method constructs a dedicated data interaction and coupling calculation architecture. This architecture provides two data transfer mechanisms: one is an interpolation transfer mode based on field variable mapping, and the other is a common-node transfer mode based on unified spatial discretization. Through this architecture, real-time, bidirectional, and nonlinear interaction of physical quantities (such as pore water pressure and displacement) between the seepage analysis module and the stress analysis module can be achieved, thereby accurately simulating the entire process of seepage deformation of geotechnical structures under seepage.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework is proposed, comprising the following steps: S1. Establish a three-dimensional geometric model of the key structures of the dam, perform high-precision mesh discretization, and set the initial permeability coefficient and upstream and downstream water level boundaries to obtain a three-dimensional mesh model and a three-dimensional seepage calculation model. Specifically: S1.1, based on the actual engineering characteristics of earth-rock dams (panel, core wall, dam shell, dam foundation, etc.), completes the three-dimensional geometric model of the key dam structure in the computational domain, obtains the three-dimensional geometric model, and uses unstructured mesh technology to complete the spatial discretization of the computational domain to obtain the three-dimensional mesh model, ensuring the accurate geometric representation of complex dam structures.

[0007] S1.2, based on geological surveys and similar projects, assign corresponding initial permeability coefficients to each material zone of the earth-rock dam; at the same time, based on actual hydrological conditions, set initial upstream and downstream water level boundary conditions to obtain a three-dimensional seepage calculation model.

[0008] S2, based on the three-dimensional seepage calculation model obtained in S1, uses a three-dimensional high-performance finite volume seepage solver for numerical calculation to obtain the total head and hydraulic gradient distribution results. Specifically: S2.1, Based on the three-dimensional seepage calculation model obtained in S1, the three-dimensional high-performance finite volume seepage solver is invoked, and the head convergence accuracy is set to 1.0 × 10⁻⁶. -5 The three-dimensional seepage calculation of the dam body was completed.

[0009] S2.2, organize the seepage calculation results of S2.1, and obtain the total head and hydraulic gradient distribution results under the given initial permeability coefficient of the earth-rock dam.

[0010] S3 converts the total head and hydraulic gradient results obtained in S2 into seepage pressure loads and seepage volumetric force loads, respectively, and then transfers them to the finite element stress-deformation solver through field variable mapping or common-node mode. Specifically: S3.1 converts the total head obtained in S2 into a seepage pressure load. p for: (1) in, Indicates the specific gravity of water; Indicates the total head distribution; Indicates the location elevation.

[0011] S3.2, convert the hydraulic gradient obtained in S2 into a seepage volume force load, which is: (2) in, This represents the volumetric force load from seepage in the x-direction; This represents the volumetric force load of seepage in the y-direction; This represents the volumetric force load of seepage in the z-direction; This represents the hydraulic gradient in the x-direction; This represents the hydraulic gradient in the y-direction; This represents the hydraulic gradient in the z-direction; Indicates the specific gravity of water; x In Cartesian coordinate system x direction; y In Cartesian coordinate system y Direction; z represents the Cartesian coordinate system. z direction; express x Directional hydraulic gradient; express y Directional hydraulic gradient; express z Directional hydraulic gradient.

[0012] S3.3 treats the seepage water pressure load and seepage volume force load as external load conditions, and transfers them to the finite element stress-deformation analysis solver through the field variable mapping mode or the common node mode; specifically: (1) Field variable mapping mode: Seepage analysis and stress analysis are discretized and solved using their respective independent mesh systems. The two mesh systems are independent of each other in terms of geometric topology and node distribution, enabling independent calculation of seepage and stress processes, and facilitating bidirectional data transfer between physical quantities through a field variable mapping method. Details are as follows: 1) Traverse the mesh nodes of seepage analysis and stress analysis, and obtain the mapping relationship between mesh nodes and mesh; 2) Using the grid nodes and their corresponding grid nodes, divide the grid into three small triangles and calculate the area of ​​each small triangle; 3) The physical quantity of the grid node is obtained by weighting the grid node value with the proportion of its corresponding area to the total grid area, thus completing the interpolation process.

[0013] (2) Shared node transmission mode: Seepage analysis and stress analysis are coupled and calculated using the same spatial discrete mesh. Both share the same node coordinates and indexing system, achieving strict consistency in the geometric space. In this mode, seepage analysis and stress analysis can achieve direct data transmission through shared nodes, effectively ensuring numerical consistency and computational efficiency in the solution process.

[0014] S4: Based on the 3D mesh model obtained in S1, the constitutive parameters of the earth-rock dam material are set. The seepage water pressure load and seepage volumetric force load obtained in S3 are used as external load conditions. The finite element stress-deformation solver is called to obtain the stress, displacement, and volumetric strain results of the earth-rock dam. Specifically: S4.1 Based on the three-dimensional mesh model obtained in S1, set the constitutive model of each material zone of the earth-rock dam, assign calculation parameters, and set the parameters of the finite element stress-deformation solver.

[0015] S4.2 uses the seepage water pressure load and seepage volume force load obtained in S3 as external load conditions, and calls the finite element stress-deformation solver to obtain the stress, displacement and volume strain results of the earth-rock dam.

[0016] S5 assesses the dam's condition based on the stress and displacement results obtained in S4, dynamically updates the dam's porosity based on the strain values ​​obtained in S4, and then corrects the dam's permeability coefficient based on the new porosity. Specifically: S5.1, Update porosity based on strain values ​​of the earth-rock dam body: (3) In the formula: The initial porosity, Porosity For the body to adapt to strain.

[0017] S5.2, Correct the permeability coefficient of earth-rock dams based on the new porosity: (4) In the formula: K s The corrected permeability coefficient for earth-rock dams; The initial absolute permeability of the earth-rock dam; The dynamic viscosity coefficient of water; The density of water; This is the acceleration due to gravity.

[0018] In step S6, based on the corrected permeability coefficient of the earth-rock dam obtained in S5, the three-dimensional high-performance finite volume seepage solver is invoked again to obtain new total head and hydraulic gradient distribution results. The process is then returned to steps S3-S5 to complete one bidirectional coupled iterative calculation of the seepage field and stress field, obtaining the changes in total head and displacement. Specifically: The total head change: (5) In the formula: This represents the total head change between two iterations. and The first m Second and m The total head value of +1 iteration steps.

[0019] The displacement change: (6) In the formula: This represents the displacement change between two iterations; and Representing the first m Second and m The displacement value of +1 iteration step.

[0020] S7 determines whether the total head change and displacement change obtained in S6 meet the convergence criteria. If they do, the seepage-stress two-way iterative coupled calculation is completed; otherwise, the process returns to step S2 and restarts the calculation. Specifically: The convergence criteria for the total head change and displacement change are shown in the following formula: (7) In the formula: This represents the total head convergence standard, with a value of 1.0 × 10⁻⁶. -4 ; The displacement convergence criterion is represented by a value of 1.0 × 10⁻⁶. -4 .

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention simulates the seepage-stress coupling effect based on the finite volume-finite element coupling framework, providing a scientific basis for safety assessment and optimization design of actual engineering projects.

[0022] (2) By introducing a dynamic update mechanism of porosity-permeability coefficient, this invention effectively improves the calculation accuracy of soil in the coupling effect of stress deformation and seepage process.

[0023] (3) This invention realizes the combined application of a three-dimensional high-performance finite volume flow solver and a finite element stress-deformation solver, providing multiple data interaction modes. All numerical tools are independently developed, the system has strong controllability, and is easy to promote and apply.

[0024] In summary, this invention employs an iterative coupling strategy, achieving dynamic coupling analysis of seepage and stress through the collaborative calculation of the finite volume method and the finite element method. The built-in dynamic update mechanism for porosity and permeability coefficient improves the accuracy and reliability of numerical simulations of soil in multiphysics coupling processes. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the main process of the method of the present invention; Figure 2 Geometric model diagram of a homogeneous earth-rock dam Figure 3 Grid division diagram for a homogeneous earth-rock dam; Figure 4 This is a contour map of horizontal displacement from the AutoBANK software. Figure 5 This is a contour map of the horizontal displacement of the present invention; Figure 6 This is a contour map of vertical displacement from the AutoBANK software. Figure 7 This is a contour map of the vertical displacement of the present invention; Figure 8 This is a contour map of the principal stresses in AutoBANK software. Figure 9 This is a contour map of the major principal stresses of this invention; Figure 10 This is a contour map of minor principal stresses from the AutoBANK software. Figure 11 This is a contour map of the minor principal stresses of this invention.

[0026] In the diagram: H1 represents the dam height; H2 represents the upstream water level; a1 represents the upstream and downstream slope ratio; L1 represents the dam crest width. Detailed Implementation

[0027] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0028] See Figure 1 A nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework, taking the seepage deformation of an earth-rock dam as an example, includes the following steps: S1. Establish a three-dimensional geometric model of the key structure of the dam, perform high-precision mesh discretization, and set the initial permeability coefficient and upstream and downstream water level boundaries to obtain a three-dimensional mesh model and a three-dimensional seepage calculation model.

[0029] S2, based on the three-dimensional seepage calculation model obtained in S1, uses a three-dimensional high-performance finite volume seepage solver for numerical calculation to obtain the total head and hydraulic gradient distribution results.

[0030] S3 converts the total head and hydraulic gradient results obtained in S2 into seepage pressure load and seepage volume force load, respectively, and then transfers them to the finite element stress-deformation solver through field variable mapping or common node mode.

[0031] S4. Based on the three-dimensional mesh model obtained in S1, set the constitutive parameters of the earth-rock dam material, take the seepage water pressure load and seepage volume force load obtained in S3 as external load conditions, call the finite element stress-deformation solver, and obtain the stress, displacement and volume strain results of the earth-rock dam.

[0032] S5 assesses the state of the earth-rock dam body based on the stress and displacement results obtained in S4, and dynamically updates the porosity of the earth-rock dam body based on the strain values ​​obtained in S4, and then corrects the permeability coefficient of the earth-rock dam body based on the new porosity.

[0033] In S6, based on the corrected permeability coefficient of the earth-rock dam obtained in S5, the three-dimensional high-performance finite volume seepage solver is called again to obtain new total head and hydraulic gradient distribution results. Then, the process returns to S3~S5 to complete a two-way coupled iterative calculation of seepage field-stress field and obtain the total head change and displacement change.

[0034] S7. Determine whether the total head change and displacement change obtained in S6 meet the convergence criteria. If they meet the convergence criteria, complete the seepage-stress bidirectional iterative coupling calculation. If they do not meet the convergence criteria, return to step S2 and start the calculation again.

[0035] Example 1: Deformation problem of homogeneous earth-rock dam under seepage-stress coupling; S1. Establish a three-dimensional geometric model of the key structures of the dam, perform high-precision mesh discretization, and set the initial permeability coefficient and upstream and downstream water level boundaries to obtain a three-dimensional mesh model and a three-dimensional seepage calculation model. Specifically: S1.1, Figure 2 This is a geometric model of a homogeneous earth-rock dam, with a dam height H1 of 50.0m and a crest width L1 of 10.0m. Figure 2 The upstream and downstream slope ratios are the same, a1=1:2.0, and the upstream water level H2 is 45.0m. The earth-rock dam is constructed in 10 uniformly compacted layers, each layer being 5.0m high; refer to Figure 2 In the geometric model, a finite element mesh is created, such as... Figure 3 As shown.

[0036] S1.2, Set soil material parameters, with a soil permeability coefficient of 1.0 × 10⁻⁶. -6 m / s, the unsaturated characteristics are based on the VanGenuchten model, and the parameters are detailed in Table 1.

[0037] Table 1: Unsaturated Characteristic Parameters

[0038] S2, based on the three-dimensional seepage calculation model obtained in S1, calls the three-dimensional high-performance finite volume seepage solver to perform numerical calculations and obtain the total head and hydraulic gradient distribution results.

[0039] S2.1, Based on the three-dimensional seepage calculation model obtained in S1, the three-dimensional high-performance finite volume seepage solver is invoked, and the head convergence accuracy is set to 1.0 × 10⁻⁶. -5 Complete the three-dimensional seepage calculation of the dam body; S2.2, organize the seepage calculation results of S2.1, and obtain the total head and hydraulic gradient distribution results under the given initial permeability coefficient of the earth-rock dam.

[0040] S3 converts the total head and hydraulic gradient results obtained in S2 into seepage pressure load and seepage volume force load, and then transfers them to the finite element stress-deformation solver through field variable mapping or common node transfer mechanism.

[0041] S4: Based on the 3D mesh model obtained in S1, the constitutive parameters of the earth-rock dam material are set. The seepage water pressure load and seepage volumetric force load obtained in S3 are used as load conditions. The finite element stress-deformation solver is called to obtain the stress, displacement, and volumetric strain results of the earth-rock dam. Specifically: S4.1, the deformation constitutive model of the earth-rock dam adopts a linear elastic model with an elastic modulus of 2.0 × 10⁷ Pa, a Poisson's ratio of 0.3, and a unit weight of 20 kN / m³. 3 S4.2 uses the seepage water pressure load and seepage volume force load obtained in S3 as external load conditions, and calls the finite element stress-deformation solver to obtain the stress, displacement and volume strain results of the earth-rock dam.

[0042] S5 assesses the state of the earth-rock dam body based on the stress and displacement results obtained in S4, and dynamically updates the porosity of the earth-rock dam body based on the strain values ​​obtained in S4, and then corrects the permeability coefficient of the earth-rock dam body based on the new porosity.

[0043] S6, based on the corrected permeability coefficient obtained in S5, calls the seepage solver again to obtain new total head and hydraulic gradient distribution results, and returns to S3~S5 to complete a two-way coupled iterative calculation of seepage field-stress field, and obtains the total head change and displacement change.

[0044] S7. Determine whether the total head change and displacement change obtained in S6 meet the convergence criteria. If they meet the convergence criteria, complete the seepage-stress bidirectional iterative coupling calculation. If they do not meet the convergence criteria, return to step S2 and start the calculation again.

[0045] Based on this invention and the commercial software AutoBANK, the deformation of a homogeneous earth-rock dam under seepage-stress coupling was analyzed, and contour maps of displacement and stress distribution were obtained, as shown below. Figures 5-8 As shown in Table 2 below, the displacement and stress extrema calculation results of the two methods are compared.

[0046] Table 2: Comparison of Calculation Results between the Invention and AutoBANK

[0047] Specifically, Figure 4 and Figure 5 Contour maps of horizontal displacement obtained by two methods under seepage-stress coupling conditions are presented. Figure 6 and Figure 7 This shows the vertical displacement contour maps obtained by the two methods; Figure 8 and Figure 9 Contour maps of major principal stresses obtained by the two methods under seepage-stress coupling conditions are presented respectively. Figure 10 and Figure 11 This shows the contour maps of minor principal stresses obtained by the two methods.

[0048] from Figures 4-11 The contour maps and the comparison results in Table 2 show that the results calculated by the present invention are in good agreement with those of the commercial software AutoBANK, and have high accuracy. This indicates that the present invention can be effectively applied to the analysis of seepage-stress coupling problems in engineering practice.

[0049] The above description describes a more feasible specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, improvements, or adaptive adjustments made within the technical concept and core principles disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework, characterized in that, The aforementioned seepage-stress nonlinear coupling analysis method includes the following steps: S1. Establish a three-dimensional geometric model of the key structure of the dam, perform high-precision mesh discretization, and set the initial permeability coefficient and upstream and downstream water level boundaries to obtain a three-dimensional mesh model and a three-dimensional seepage calculation model. S2, based on the three-dimensional seepage calculation model obtained in S1, numerical calculation is performed using a three-dimensional high-performance finite volume seepage solver to obtain the total head and hydraulic gradient distribution results. S3 converts the total head and hydraulic gradient results obtained in S2 into seepage pressure load and seepage volume force load, respectively, and then transfers them to the finite element stress-deformation solver through field variable mapping or common node mode. S4. Based on the three-dimensional mesh model obtained in S1, set the constitutive parameters of the earth-rock dam material, take the seepage water pressure load and seepage volume force load obtained in S3 as external load conditions, call the finite element stress-deformation solver, and obtain the stress, displacement and volume strain results of the earth-rock dam. S5 assesses the state of the earth-rock dam body based on the stress and displacement results obtained in S4, and dynamically updates the porosity of the earth-rock dam body based on the strain values ​​obtained in S4, and then corrects the permeability coefficient of the earth-rock dam body based on the new porosity. S6, based on the corrected permeability coefficient of the earth-rock dam obtained in S5, the three-dimensional high-performance finite volume seepage solver is called again to obtain new total head and hydraulic gradient distribution results, and returns to S3~S5 to complete a two-way coupled iterative calculation of seepage field-stress field, and obtain the total head change and displacement change. S7. Determine whether the total head change and displacement change obtained in S6 meet the convergence criteria. If they meet the convergence criteria, complete the seepage-stress bidirectional iterative coupling calculation. If they do not meet the convergence criteria, return to step S2 and start the calculation again.

2. The nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework according to claim 1, characterized in that, Specifically, S1 refers to: S1.1 Based on the actual engineering characteristics of earth-rock dams, three-dimensional geometric modeling of key dam structures is completed in the computational domain to obtain a three-dimensional geometric model. Unstructured mesh technology is used to complete the spatial discretization of the computational domain to obtain a three-dimensional mesh model. S1.2, based on geological surveys and similar projects, assign corresponding initial permeability coefficients to each material zone of the earth-rock dam; at the same time, based on actual hydrological conditions, set initial upstream and downstream water level boundary conditions to obtain a three-dimensional seepage calculation model.

3. The nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework according to claim 2, characterized in that, Specifically, S2 is: S2.1, Based on the three-dimensional seepage calculation model obtained in S1, the three-dimensional high-performance finite volume seepage solver is invoked, and the head convergence accuracy is set to 1.0 × 10⁻⁶. -5 Complete the three-dimensional seepage calculation of the dam body; S2.2, organize the seepage calculation results of S2.1, and obtain the total head and hydraulic gradient distribution results under the given initial permeability coefficient of the earth-rock dam.

4. The nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework according to claim 3, characterized in that, Specifically, S3 is: S3.1 converts the total head obtained in S2 into a seepage pressure load. p for: （1） in, Indicates the specific gravity of water; Indicates the total head distribution; Indicates location elevation; S3.2, convert the hydraulic gradient obtained in S2 into a seepage volume force load, which is: （2） in, This represents the volumetric force load from seepage in the x-direction; This represents the volumetric force load of seepage in the y-direction; This represents the volumetric force load of seepage in the z-direction; This represents the hydraulic gradient in the x-direction; This represents the hydraulic gradient in the y-direction; This represents the hydraulic gradient in the z-direction; Indicates the specific gravity of water; x In Cartesian coordinate system x direction; y In Cartesian coordinate system y Direction; z represents the Cartesian coordinate system. z direction; express x Directional hydraulic gradient; express y Directional hydraulic gradient; express z Directional hydraulic gradient; S3.3 uses the seepage water pressure load and seepage volume force load as external load conditions, and transfers them to the finite element stress-deformation analysis solver through the field variable mapping mode or the common node mode.

5. The nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework according to claim 4, characterized in that, In S3.3, the field variable mapping mode is specifically as follows: Seepage analysis and stress analysis are discretized and solved using their respective independent grid systems. The two grid systems are independent of each other in terms of geometric topology and node distribution, enabling independent calculation of seepage and stress processes. Furthermore, a field variable mapping method facilitates bidirectional data transfer between physical quantities. Details are as follows: 1) Traverse the mesh nodes of seepage analysis and stress analysis, and obtain the mapping relationship between mesh nodes and mesh; 2) Using the grid nodes and their corresponding grid nodes, divide the grid into three small triangles and calculate the area of ​​each small triangle; 3) The physical quantity of the grid node is obtained by weighting the grid node value with the proportion of its corresponding area to the total grid area, thus completing the interpolation process.

6. The nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework according to claim 4, characterized in that, In S3.3, the common node transmission mode is specifically as follows: Seepage analysis and stress analysis are coupled calculations based on the same set of spatial discrete meshes. They share the same node coordinates and indexing system, achieving strict consistency in geometric space. In this mode, seepage analysis and stress analysis can achieve direct data transmission through shared nodes, ensuring numerical consistency and computational efficiency in the solution process.

7. The nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework according to claim 4, characterized in that, Specifically, S4 is: S4.1 Based on the three-dimensional mesh model obtained in S1, set the constitutive model of each material zone of the earth-rock dam, assign calculation parameters, and set the parameters of the finite element stress-deformation solver. S4.2 uses the seepage water pressure load and seepage volume force load obtained in S3 as external load conditions, and calls the finite element stress-deformation solver to obtain the stress, displacement and volume strain results of the earth-rock dam.

8. The nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework according to claim 7, characterized in that, Specifically, S5 is: S5.1, Update porosity based on strain values ​​of the earth-rock dam body: （3） In the formula: The initial porosity, Porosity For the body strain; S5.2, Correct the permeability coefficient of earth-rock dams based on the new porosity: （4） In the formula: K s The corrected permeability coefficient for earth-rock dams; The initial absolute permeability of the earth-rock dam; The dynamic viscosity coefficient of water; The density of water; This is the acceleration due to gravity.

9. The nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework according to claim 8, characterized in that, In S6 as described above: The total head change: （5） In the formula: This represents the total head change between two iterations. and The first m Second and m The total head value of +1 iteration steps; The displacement change: （6） In the formula: This represents the displacement change between two iterations; and Representing the first m Second and m The displacement value of +1 iteration step.

10. The nonlinear coupling analysis method for seepage-stress based on a finite volume-finite element framework according to claim 9, characterized in that, In S7: The convergence criteria for the total head change and displacement change are shown in the following formula: （7） In the formula: This represents the total head convergence standard, with a value of 1.0 × 10⁻⁶. -4 ; The displacement convergence criterion is represented by a value of 1.0 × 10⁻⁶. -4 .

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