Dam foundation cover layer nonlinear seepage fine calculation method and system

Abstract

The application relates to the technical field of water conservancy and hydropower engineering, and discloses a dam foundation covering layer nonlinear seepage fine calculation method and system, which aims to solve the problem of poor accuracy and fineness of the existing method, and mainly comprises the following steps: constructing a seepage wall geometric model containing defects based on field drilling data and dividing the grid; based on the physical property parameters of the covering layer soil, the Darcy seepage coefficient and the Forchheimer seepage coefficient under the Darcy-Forchheimer model are calculated by using the Ergun formula; boundary conditions, fluid parameters and solution control parameters are configured, and the nonlinear seepage characteristic parameters of the covering layer soil and the seepage wall defects are specified to construct a fine analysis model; the seepage field numerical calculation is carried out based on the RANS equation and the Darcy-Forchheimer model by using a finite volume method solver; and the calculation results are extracted to obtain the nonlinear seepage field distribution containing the covering layer soil and the seepage wall defects. The application improves the accuracy and fineness of the dam foundation seepage calculation containing the seepage wall, and is suitable for two-dimensional seepage analysis or three-dimensional seepage analysis.

Description

Technical Field

[0001] This invention relates to the field of water conservancy and hydropower engineering technology, specifically to a method and system for refined calculation of nonlinear seepage in dam foundation overburden. Background Technology

[0002] A core challenge in earth-rock dam engineering is the seepage stability of the dam foundation, specifically whether water flow through the foundation will lead to soil erosion or structural damage. To control seepage, cutoff walls (underground vertical walls) are commonly used, embedded in the overburden layer (the loose soil and rock layer above the bedrock) of the dam foundation to act as a water barrier. However, as a concealed engineering structure, cutoff walls face complex construction and operation environments, making them prone to defects such as cracks, voids, or poor joints.

[0003] When a cutoff wall has defects, water will preferentially seep through these weak points, potentially causing localized scouring or even overall seepage failure. Because cutoff walls are buried deep underground, direct sampling or observation is extremely difficult. Therefore, engineering practices mainly rely on numerical simulation techniques to analyze their seepage safety.

[0004] Currently, the main technical limitations for seepage calculations in dam foundations containing cutoff walls are as follows:

[0005] First, regarding seepage theory, traditional methods typically assume that the movement of water in the dam foundation overburden follows Darcy's law, meaning that the flow velocity is linearly related to the hydraulic gradient. However, for overburden composed of coarse-grained soils such as gravel and crushed stone, especially under high water head, the water velocity is high, and seepage often exhibits significant nonlinear characteristics, rendering Darcy's law inapplicable. Second, in terms of model construction, existing methods significantly simplify the defect morphology of the cutoff wall. For example, wall defects are simply replaced with areas having the same parameters as the surrounding soil, or cracks are idealized as smooth, straight single fissures. This simplification ignores the true morphology of defects (such as crack roughness and the irregularity of pores) and their complex interactions with the surrounding soil, making it difficult to reflect actual local high-speed seepage conditions. Third, in terms of computational conditions, most methods are based on the steady-state assumption, assuming that the water head and water pressure do not change over time. This cannot simulate the transient seepage process during rapid rises and falls in reservoir water levels (such as flood season impoundment or sudden drops in water level), potentially leading to distorted assessments of the most dangerous conditions. Furthermore, from a computational perspective, traditional seepage analysis often employs the finite element method. For seepage problems centered on fluid mass (such as water) transport, the finite element method, based on the weighted residual method or variational principle, mathematically pursues the continuity and approximate optimality of nodal physical quantities. However, physically, it does not strictly guarantee the conservation of mass (i.e., water flow) within each computational unit. This leads to mass errors when dealing with seepage problems centered on mass transport and exhibiting strong nonlinear characteristics. Moreover, the flux calculation accuracy for key areas (such as defects in the anti-seepage wall) is insufficient, making it difficult to accurately capture the true physical process of local high-speed seepage.

[0006] In summary, existing technologies are insufficient to accurately and precisely assess the actual seepage state and safety of dam foundations with defective cutoff walls under complex hydraulic conditions. Summary of the Invention

[0007] This invention aims to address the problem of poor accuracy and precision in existing methods for calculating seepage in dam foundations containing cutoff walls, and proposes a refined calculation method and system for nonlinear seepage in dam foundation overburden layers.

[0008] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0009] In a first aspect, the present invention provides a method for refined calculation of nonlinear seepage in dam foundation overburden layers, the method comprising:

[0010] Based on the field drilling data, a geometric model of the seepage barrier wall including defects was constructed, and a model file was generated;

[0011] The computational domain mesh is divided based on the geometric model of the cutoff wall. The computational domain mesh includes the mesh of the dam foundation overburden soil and the mesh at the defects of the cutoff wall.

[0012] Based on the physical property parameters of the dam foundation overburden soil, the nonlinear seepage characteristic parameters of the dam foundation overburden soil and the seepage barrier defect under the Darcy-Forchheimer model are calculated using the empirical formula for porous media. The nonlinear seepage characteristic parameters include the Darcy seepage coefficient and the Forchheimer seepage coefficient.

[0013] Based on the computational domain grid, the boundary conditions, fluid parameters, turbulence model, discretization scheme, solver algorithm parameters and time step parameters in the computation process are configured, and the nonlinear seepage characteristic parameters at the defects of the dam foundation overburden soil and the anti-seepage wall are specified to construct a refined analysis model.

[0014] Numerical calculations of the seepage field were performed on the refined analysis model using the finite volume method solver, based on the RANS equations and the Darcy-Forchheimer model.

[0015] The numerical calculation results of the seepage field are extracted to obtain the nonlinear seepage field distribution at the defects in the dam foundation overburden soil and the anti-seepage wall.

[0016] Furthermore, the expression for the RANS equation is as follows:

[0017] ;

[0018] ;

[0019] in, In the Cartesian coordinate system, the first... Velocity components in each coordinate direction , In the Cartesian coordinate system, the first... Coordinates in each coordinate direction, Indicates fluid density, Indicates fluid pressure. In the Cartesian coordinate system, the first... Gravitational acceleration components in each coordinate direction In the Cartesian coordinate system, the first... Coordinates in each coordinate direction, , Indicates the effective viscosity of the fluid. , Indicates the dynamic viscosity of a fluid. Indicates eddy current viscosity; Indicates that other external forces are in the first... Components in each coordinate direction, Indicates time, It represents a partial differential.

[0020] Furthermore, the Darcy seepage coefficient and Forchheimer seepage coefficient are calculated based on the Ergun formula, as follows:

[0021] ;

[0022] ;

[0023] ;

[0024] in, Indicates the hydraulic gradient. This represents the Darcy flow coefficient. This represents the Forchheimer seepage coefficient. Indicates the dynamic viscosity of a fluid. This indicates the porosity of the soil at the corresponding location in the dam foundation overburden layer. Indicates the equivalent diameter of the particles. Indicates fluid density, This indicates the seepage velocity.

[0025] Furthermore, the equivalent diameter of the particles The calculation was obtained based on the particle size distribution of the dam foundation overburden soil, and the calculation formula is as follows:

[0026] ;

[0027] ;

[0028] in, Represents the shape factor. This represents the average diameter of Sauter. Indicates the first Mass fraction of each particle size range Indicates the first The average particle size of each particle size range.

[0029] Furthermore, the boundary conditions, fluid parameters, turbulence model, discretization scheme, solver algorithm parameters, and time step parameters in the configuration calculation process include:

[0030] Set boundary conditions: including inflow boundary, outflow boundary and wall boundary, wherein the inflow boundary can be set with water pressure that varies with time according to the water storage process;

[0031] Set fluid parameters: including fluid density and kinematic viscosity;

[0032] Set the turbulence model: Select either the laminar flow model or the k-epsilon model;

[0033] Set the discretization scheme: Set the corresponding numerical discretization scheme for each term in the RANS equation;

[0034] Set solver algorithm parameters: Specify the linear solver for the pressure and velocity terms and the residual convergence criterion;

[0035] Set time step parameters: Set the total computation time, the initial computation step size, and the number of CFLs used to control the adaptive time step size;

[0036] The nonlinear seepage characteristic parameters specified at the defects in the dam foundation overburden soil and the cutoff wall include: specifying the dam foundation overburden soil region and the cutoff wall defect region in the calculation domain, and assigning the corresponding Darcy seepage coefficient and Forchheimer seepage coefficient.

[0037] Furthermore, the types of defects in the impermeable wall include through cracks, honeycomb pitting or holes on the surface of the impermeable wall.

[0038] Furthermore, the model file is in .stl format and is constructed using SolidWorks or AutoCAD software.

[0039] Furthermore, the computational domain mesh can be generated using OpenFOAM's built-in mesh generation tool, Gmsh, Fluent, or ICEM software.

[0040] Furthermore, the method is applicable to two-dimensional or three-dimensional seepage analysis.

[0041] Secondly, the present invention provides a refined calculation system for the nonlinear seepage characteristics of a dam foundation overburden layer, used to implement the refined calculation method for the nonlinear seepage characteristics of a dam foundation overburden layer as described in the first aspect, the system comprising:

[0042] The model building module is used to construct a geometric model of the cutoff wall, including defects, based on field drilling data, and generate model files;

[0043] The mesh generation module is used to perform computational domain mesh generation based on the geometric model of the cutoff wall. The computational domain mesh includes the mesh of the dam foundation overburden soil and the mesh at the defects of the cutoff wall.

[0044] The parameter calculation module is used to calculate the nonlinear seepage characteristic parameters of the dam foundation overburden soil and the defects of the anti-seepage wall under the Darcy-Forchheimer model based on the physical property parameters of the dam foundation overburden soil and using the empirical formula of porous media. The nonlinear seepage characteristic parameters include the Darcy seepage coefficient and the Forchheimer seepage coefficient.

[0045] The preprocessing configuration module is used to configure the boundary conditions, fluid parameters, turbulence model, discretization scheme, solver algorithm parameters and time step parameters in the calculation process based on the computational domain grid, and to specify the nonlinear seepage characteristic parameters of the dam foundation overburden soil and the defects of the anti-seepage wall, so as to construct a refined analysis model.

[0046] The numerical solution module is used to perform numerical calculations of the seepage field on the refined analysis model using the finite volume method solver, based on the RANS equations and the Darcy-Forchheimer model.

[0047] The post-processing evaluation module is used to extract the numerical calculation results of the seepage field and obtain the nonlinear seepage field distribution including the defects of the dam foundation overburden soil and the anti-seepage wall.

[0048] The beneficial effects of this invention are as follows: The nonlinear seepage refinement calculation method and system for dam foundation overburden provided by this invention model the defective anti-seepage wall and the surrounding dam foundation overburden as a whole system, which truly reflects the actual path of water flow from the soil into the cracks. At the same time, by introducing a nonlinear seepage model into the calculation and determining key parameters based on the physically meaningful Ergun formula, it overcomes the limitation of traditional methods that ignore the nonlinear characteristics of water flow in coarse-grained soil. On this basis, this invention uses the finite volume method with strict physical conservation properties for transient solution, which can accurately capture the high-speed seepage process under complex working conditions such as reservoir water level changes, thus providing a more scientific and reliable calculation method for evaluating the seepage stability of dam foundation and guiding the design of anti-seepage engineering. Attached Figure Description

[0049] Figure 1 A flowchart illustrating the refined calculation method for nonlinear seepage in the dam foundation overburden layer provided in this embodiment;

[0050] Figure 2 A schematic diagram of a geometric model of a cutoff wall containing cracks, provided for an embodiment;

[0051] Figure 3 A schematic diagram of the seepage calculation grid for the dam foundation overburden layer considering defects in the cutoff wall is provided for the embodiment.

[0052] Figure 4 A schematic diagram of the seepage velocity distribution in the dam foundation overburden soil and the cracks in the anti-seepage wall, provided for an embodiment;

[0053] Figure 5 A schematic diagram of the pressure distribution in the dam foundation overburden soil and the cracks in the anti-seepage wall, provided for an embodiment;

[0054] Figure 6 A schematic diagram of the structure of the refined calculation system for nonlinear seepage in the dam foundation overburden layer provided in the embodiment;

[0055] Explanation of reference numerals in the attached figures:

[0056] 1-Impervious wall; 2-Impervious wall cracks; 3-Grid of overburden soil; 4-Grid of impervious wall cracks. Detailed Implementation

[0057] Existing technologies, due to their use of linear seepage theory, oversimplified defect models, and steady-state assumptions, cannot accurately assess the actual seepage stability of cutoff wall and dam foundation cover layer systems containing real defects under complex hydraulic conditions. Therefore, this invention proposes a technical solution.

[0058] In this invention, a geometric model of the cutoff wall containing the actual defect morphology is first constructed and meshed to lay the geometric foundation for refined analysis. Then, based on the measured physical properties of the overburden soil, the Darcy and Forchheimer seepage coefficients, which characterize nonlinear seepage, are calculated using the Ergun formula. On this basis, the overburden soil region and the cutoff wall defect region in the computational domain are assigned the above-mentioned nonlinear seepage parameters, and corresponding boundary conditions and solution control parameters are configured to construct a refined analysis model that can simultaneously describe the seepage behavior at the overburden and cutoff wall defects. Finally, a solver based on the finite volume method is used to numerically solve the RANS equation coupled with the Darcy-Forchheimer model, ultimately obtaining the nonlinear seepage field distribution that can truly reflect the interaction between the cutoff wall defects and the overburden soil.

[0059] 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.

[0060] Figure 1 A flowchart illustrating a refined calculation method for nonlinear seepage in dam foundation overburden is shown. Please refer to [link / reference]. Figure 1 The method includes the following steps:

[0061] Step 1: Based on the field drilling data, construct a geometric model of the cutoff wall including defects and generate a model file.

[0062] Specifically, this step aims to establish a geometric basis that can accurately reflect the actual shape of the cutoff wall for subsequent seepage calculations.

[0063] In practical applications, the first step is to collect and organize the on-site borehole survey data of the target dam foundation. From this data, the geometric dimensions (such as thickness, depth, and orientation) and spatial location of the cutoff wall, as well as the types, locations, and geometric characteristics of defects present in the wall, are extracted. Defects in the cutoff wall can take the form of through cracks, honeycomb pitting, or voids. For example, for typical crack defects, its aperture (e.g., 2 cm), extension length, and roughness (e.g., JRC16~18 roughness coefficient) need to be determined based on the survey results to replace the assumption of smooth cracks used in traditional methods.

[0064] Then, using commercial computer-aided design software such as SolidWorks or AutoCAD, a precise three-dimensional geometric model of the seepage barrier wall, including its defects, is constructed based on the aforementioned survey data. During the modeling process, it is essential to ensure that the geometry of the wall and defects closely matches the actual site conditions. Figure 2 A schematic diagram of a geometric model of a cutoff wall containing cracks is shown, where cutoff wall sections 1 contain cutoff wall cracks 2. After the model is built, it is exported as a standard .stl file. This .stl file will serve as the geometric basis for subsequent steps in meshing the computational domain, ensuring that the computational model can accurately reproduce the complex geometric features at the defects in the cutoff wall.

[0065] Step 2: Based on the geometric model of the cutoff wall, perform computational domain meshing. The computational domain mesh includes the mesh of the dam foundation overburden soil and the mesh at the defects of the cutoff wall.

[0066] Specifically, this step aims to discretize the geometric model constructed in step 1 into mesh cells that can be used for numerical solutions.

[0067] In practical applications, the .stl format geometry file containing the defective cutoff wall generated in step 1 is first imported into a mesh generation tool. In this embodiment, mesh generation can be achieved using various tools, such as the open-source mesh generation tools blockMesh and snappyHexMesh included with OpenFOAM, or other professional software such as Gmsh, Fluent, ICEM, etc. The meshing strategy requires simultaneously generating meshes in the computational domain for both the area containing the dam foundation overburden soil and the area inside and near the defects in the cutoff wall.

[0068] To ensure computational accuracy, local mesh refinement is required for areas with defects in the cutoff wall (such as areas with complex geometries like cracks and pores, or areas where high-speed seepage is expected) to accurately characterize the flow characteristics at those locations. For areas with overburden soil, a relatively sparse mesh can be used to improve computational efficiency, depending on the computational requirements.

[0069] After mesh generation, a complete discrete mesh of the computational domain, including the overburden soil and the defective impermeable wall, is obtained, such as... Figure 3As shown, the gray area represents the cutoff wall 1, and the remaining areas are the overburden soil mesh 3 and the mesh 4 at the cracks in the cutoff wall. This mesh file will serve as the basis for defining physical properties, applying boundary conditions, and performing numerical solutions in subsequent steps.

[0070] Step 3: Based on the physical property parameters of the dam foundation overburden soil, the nonlinear seepage characteristic parameters of the dam foundation overburden soil and the seepage barrier defect under the Darcy-Forchheimer model are calculated using the empirical formula for porous media. The nonlinear seepage characteristic parameters include the Darcy seepage coefficient and the Forchheimer seepage coefficient.

[0071] Specifically, this step aims to transform the macroscopic physical properties of the overburden soil into seepage model parameters required for numerical calculations.

[0072] In practical applications, it is first necessary to obtain the basic physical properties of the soil in the dam foundation overburden layer, mainly including the porosity of the soil at the corresponding location in the dam foundation overburden layer. And the particle size distribution. To accurately characterize the geometric features of the particles, it is necessary to calculate the Sauter average diameter based on the particle size distribution. In specific calculations, the mass fraction of each particle size range is... Divide by the average particle size of that range Summing and taking the reciprocal will give you the result. ,Right now: ; then, Multiply by the shape factor, which reflects the degree of particle irregularity. The equivalent diameter of the particles was obtained. ,Right now: This parameter is used to uniformly characterize the overall size of soil particles.

[0073] After obtaining the aforementioned basic parameters, the Ergun formula is used to calculate the nonlinear seepage characteristic parameters. The Ergun formula expresses the nonlinear relationship between the hydraulic gradient and the seepage velocity. Based on this formula, the Darcy seepage coefficient can be extracted. and Forchheimer permeability coefficient The specific expression for Ergun's formula is as follows:

[0074] ;

[0075] ;

[0076] ;

[0077] in, Indicates the hydraulic gradient. This represents the Darcy flow coefficient. This represents the Forchheimer seepage coefficient. Indicates the dynamic viscosity of a fluid. This indicates the porosity of the soil at the corresponding location in the dam foundation overburden layer. Indicates the equivalent diameter of the particles. Indicates fluid density, This indicates the seepage velocity.

[0078] In the above formula, Darcy's permeability coefficient and Forchheimer permeability coefficient These two coefficients together constitute the core parameters of the Darcy-Forchheimer model: the Darcy seepage coefficient. The linear resistance term reflecting the porous medium's resistance to seepage corresponds to viscous dissipation at low flow velocities; the Forchheimer seepage coefficient. This reflects the nonlinear resistance term, corresponding to inertial dissipation at high flow velocities. During the calculation, not only the dam foundation overburden soil region needs to be assigned the above parameters, but defects in the cutoff wall (such as cracks and pores) are also considered as porous media regions and assigned the same or modified parameters based on the defect characteristics. and These coefficients are used to uniformly describe the nonlinear seepage behavior of water flow in soil particle gaps and wall defects. The calculated coefficients will serve as key input parameters for the refined analysis model in step 4.

[0079] Step 4: Based on the computational domain grid, configure the boundary conditions, fluid parameters, turbulence model, discretization scheme, solver algorithm parameters and time step parameters in the computation process, and specify the nonlinear seepage characteristic parameters of the dam foundation overburden soil and the defects of the anti-seepage wall to construct a refined analysis model.

[0080] Specifically, this step aims to combine the mesh model generated in step 2 with the physical parameters calculated in step 3, and through a complete pre-computation configuration, construct a computational analysis model that can be recognized and run by the solver.

[0081] In practical applications, based on the computational domain mesh that has been divided in step 2, the following key parameters need to be configured sequentially:

[0082] Step 41: Set boundary conditions. Specify different types of boundaries for the computational domain based on the hydraulic boundaries of the actual project. For example, set the upstream side as the inflow boundary, applying a linearly increasing water pressure over time according to the reservoir impoundment process; set the downstream side as the outflow boundary, typically specifying a fixed pressure (such as zero pressure or hydrostatic pressure); and set all other interfaces that do not exchange water with the outside (such as the surface of the cutoff wall, the bottom of the model, and both sides) as wall boundaries.

[0083] Step 42: Set fluid parameters. Specify the fluid density (e.g., based on the actual physical properties of the water body) ) and kinematic viscosity (e.g. ).

[0084] Step 43: Set up the turbulence model. Select an appropriate turbulence model based on the flow characteristics of the seepage field. For cases with low flow velocity and stable flow, a laminar flow model can be selected; for cases where local high-speed flow or turbulence may occur, a two-equation turbulence model such as k-epsilon can be selected to simulate turbulence effects.

[0085] Step 44: Set the discretization scheme. Based on the discretization requirements of the finite volume method, set appropriate numerical discretization schemes for each term in the RANS equations (such as the time term, gradient term, divergence term, and Laplace term). For example, the gradient term can use the Gausslinear scheme to ensure the accuracy and stability of the calculation.

[0086] Step 45: Set the solver algorithm parameters. Specify the linear solver type and residual convergence criteria for each key physical quantity (such as fluid pressure and velocity) during the solution process. For example, the pressure equation can use the GAMG (Geometric Algebraic Multigrid) solver to improve the convergence speed.

[0087] Step 46, set the time step parameters. Since this embodiment involves transient seepage calculations, it is necessary to set the total calculation time (the actual physical time being simulated) and the initial calculation step size (e.g., ...). (seconds) and the number of CFLs (e.g., 0.1) used to control the adaptive time step to ensure the stability and efficiency of the computation process.

[0088] Step 47: Specify nonlinear seepage characteristic parameters. This requires accurately identifying and specifying the areas of the dam foundation overburden soil and the areas with defects in the cutoff wall within the computational domain, and using the Darcy seepage coefficient calculated in Step 3. and Forchheimer permeability coefficient These regions were then assigned specific roles. In this way, the Darcy-Forchheimer model was successfully incorporated into the flow control equations for the overburden soil and the defects in the impermeable wall.

[0089] After completing all the above configurations, a refined analytical model that can be used for subsequent numerical calculations is constructed. This model includes the actual geometry of the defective cutoff wall, the nonlinear seepage characteristics of the overburden soil, and the transient boundary conditions reflecting changes in reservoir water level.

[0090] Step 5: Using the finite volume method solver, based on the RANS equations and the Darcy-Forchheimer model, perform numerical calculations of the seepage field on the refined analysis model.

[0091] In this embodiment, the expression of the RANS equation is as follows:

[0092] ;

[0093] ;

[0094] in, In the Cartesian coordinate system, the first... Velocity components in each coordinate direction , In the Cartesian coordinate system, the first... Coordinates in each coordinate direction, Indicates fluid density, Indicates fluid pressure. In the Cartesian coordinate system, the first... Gravitational acceleration components in each coordinate direction In the Cartesian coordinate system, the first... Coordinates in each coordinate direction, , Indicates the effective viscosity of the fluid. , Indicates the dynamic viscosity of a fluid. Indicates eddy current viscosity; Indicates that other external forces are in the first... Components in each coordinate direction, Indicates time, It represents a partial differential.

[0095] Specifically, this step aims to calculate the refined analysis model constructed in step 4 using a numerical solver, thereby obtaining the seepage field distribution at the defects in the dam foundation cover layer and the anti-seepage wall.

[0096] In practical applications, pimpleFoam, the transient solver in OpenFOAM, an open-source computational fluid dynamics software based on the finite volume method, is selected as the core for numerical calculation. pimpleFoam can solve the RANS equations for transient incompressible flows and supports the introduction of porous media drag source terms through the Darcy-Forchheimer model.

[0097] Before starting the calculation, ensure that all parameters configured in step 4 (including mesh, boundary conditions, fluid properties, turbulence model, discretization scheme, solver algorithm, time step, and Darcy seepage coefficient at defects in the overburden soil and cutoff wall) are correct. With Forchheimer permeability coefficient The input data has been correctly written to the corresponding input file. Then, run the pimpleFoam solver in the terminal or command-line interface. The solver will begin iteratively solving the RANS equations time-step by time.

[0098] Within each time step, the solver iteratively solves the momentum and continuity equations using a pressure-velocity coupled algorithm (PIMPLE algorithm, i.e., a combined PISO-SIMPLE algorithm) until the preset residual convergence criterion is met. During this process, the Darcy seepage coefficient calculated in step 3... With Forchheimer permeability coefficient It is added to the right-hand side of the RANS equation in the form of a momentum source term (i.e. This allows for a precise description of the linear and nonlinear resistance encountered by water as it flows through the pores of the overburden soil and the defects of the impermeable wall.

[0099] The calculation will continue until the total calculation time set in step 47 is reached, thus fully simulating the entire transient seepage process from the initial state to a predetermined time (e.g., a moment after the reservoir water level has risen). During the calculation, the solver will output residual information of key physical quantities (such as pressure and velocity) in real time for the user to monitor the convergence and stability of the calculation. After the calculation is completed, the solver will generate a calculation result file containing seepage field data for each time step. The calculation result file includes the velocity components of all grid cells in the computational domain (e.g., pressure, velocity). ), fluid pressure Turbulent kinetic energy and dissipation rate The calculation results include physical quantities such as the seepage velocity vector and pressure gradient distribution. This result file will serve as the basis for post-processing and results analysis in step 6.

[0100] Step 6: Extract the numerical calculation results of the seepage field to obtain the nonlinear seepage field distribution including the soil of the dam foundation cover layer and the defects of the anti-seepage wall.

[0101] Specifically, this step aims to visualize and comprehensively analyze the results generated in step 5, so as to intuitively present the seepage characteristics of the dam foundation cover layer and the defective anti-seepage wall system.

[0102] In practical applications, the result file after the calculation in step 5 can be read using the paraFoam post-processing tool (a parallel visualization software based on VTK technology) that comes with OpenFOAM or other third-party post-processing software that supports the OpenFOAM data format.

[0103] In post-processing, the computational domain grid and physical field data for each time step are loaded first. Then, by setting visualization methods such as slicing, isosurfaces, and streamlines, seepage information in key areas (especially the interior of the dam foundation overburden soil and defects in the cutoff wall) is extracted. The focus is primarily on the distribution of two core physical quantities: the velocity field, used to analyze the seepage path, velocity magnitude, and direction, particularly whether localized high-velocity seepage occurs at cutoff wall defects, such as... Figure 4 As shown; secondly, the pressure field, used to analyze the head distribution, pressure gradient, and water-blocking effect of the cutoff wall, such as... Figure 5 As shown.

[0104] By comparing the calculation results at different time steps, the dynamic evolution of the seepage field during reservoir water level changes can be further analyzed. Finally, these visualization results are output as cloud maps, vector maps, or line graphs, forming a complete nonlinear seepage field distribution map. This result can be used to evaluate the impact of defects in the cutoff wall on the seepage stability of the dam foundation, providing a scientific basis for engineering design.

[0105] This method is applicable to both two-dimensional and three-dimensional seepage analysis. In practical engineering applications, the choice between two-dimensional or three-dimensional modeling can be made based on the specific analytical requirements and computational resources. For cases with clear profile features, relatively regular morphologies of cutoff wall defects (such as through cracks), and where the focus is primarily on seepage characteristics along a specific direction, a two-dimensional analysis model can be used to simplify the computational domain into a planar problem, thereby improving computational efficiency. For engineering problems with complex cutoff wall defect morphologies (such as localized voids or honeycomb-like surfaces), or where precise depiction of the three-dimensional spatial seepage path and local flow characteristics around the defects is required, a three-dimensional analysis model should be used to fully reflect the distribution of the seepage field in all spatial directions. Regardless of whether the analysis is two-dimensional or three-dimensional, the core steps of this invention—geometric modeling of the cutoff wall with defects, calculation of nonlinear seepage parameters of the overburden soil, configuration of Darcy-Forchheimer model parameters, and transient solution based on the finite volume method—are all applicable, requiring only adjustments to the corresponding dimensions during mesh generation and boundary condition settings.

[0106] In summary, this embodiment models the seepage barrier defects with realistic roughness and geometry, along with the dam foundation overburden soil, as a whole system. Based on the Ergun formula, it calculates the physically meaningful Darcy and Forchheimer seepage coefficients, thus accurately characterizing the high-speed nonlinear seepage features at the overburden and defects in the Darcy-Forchheimer model. Furthermore, it employs the finite volume method, which has strict physical conservation properties, for transient solutions. This method can precisely capture the local high-speed seepage process at the defect location under varying reservoir water levels. It overcomes the limitations of traditional methods, which rely on linear seepage theory, simplified defect morphology, and steady-state assumptions, making it difficult to accurately evaluate seepage stability under complex hydraulic conditions. This provides a scientifically reliable and easily applicable refined calculation method for the design and safety assessment of dam foundation seepage barriers.

[0107] Based on the above technical solution, this embodiment also proposes a refined calculation system for the nonlinear seepage characteristics of the dam foundation overburden layer, used to implement the refined calculation method for the nonlinear seepage characteristics of the dam foundation overburden layer as described in the embodiment. Please refer to [link to relevant documentation]. Figure 6 The system includes:

[0108] The model building module is used to construct a geometric model of the cutoff wall, including defects, based on field drilling data, and generate model files;

[0109] The mesh generation module is used to perform computational domain mesh generation based on the geometric model of the cutoff wall. The computational domain mesh includes the mesh of the dam foundation overburden soil and the mesh at the defects of the cutoff wall.

[0110] The parameter calculation module is used to calculate the nonlinear seepage characteristic parameters of the dam foundation overburden soil and the defects of the anti-seepage wall under the Darcy-Forchheimer model based on the physical property parameters of the dam foundation overburden soil and using the empirical formula of porous media. The nonlinear seepage characteristic parameters include the Darcy seepage coefficient and the Forchheimer seepage coefficient.

[0111] The preprocessing configuration module is used to configure the boundary conditions, fluid parameters, turbulence model, discretization scheme, solver algorithm parameters and time step parameters in the calculation process based on the computational domain grid, and to specify the nonlinear seepage characteristic parameters of the dam foundation overburden soil and the defects of the anti-seepage wall, so as to construct a refined analysis model.

[0112] The numerical solution module is used to perform numerical calculations of the seepage field on the refined analysis model using the finite volume method solver, based on the RANS equations and the Darcy-Forchheimer model.

[0113] The post-processing evaluation module is used to extract the numerical calculation results of the seepage field and obtain the nonlinear seepage field distribution including the defects of the dam foundation overburden soil and the anti-seepage wall.

[0114] It is understood that the refined calculation system for nonlinear seepage characteristics of dam foundation overburden described in this embodiment is a system for implementing the refined calculation method for nonlinear seepage characteristics of dam foundation overburden described in the embodiment. As the system disclosed in the embodiment corresponds to the method disclosed in the embodiment, the description is relatively simple. For relevant parts, please refer to the description of the method. It will not be repeated here.

Claims

1. A refined calculation method for nonlinear seepage in dam foundation overburden, characterized in that, The method includes: Based on the field drilling data, a geometric model of the seepage barrier wall including defects was constructed, and a model file was generated; The computational domain mesh is divided based on the geometric model of the cutoff wall. The computational domain mesh includes the mesh of the dam foundation overburden soil and the mesh at the defects of the cutoff wall. Based on the physical property parameters of the dam foundation overburden soil, the nonlinear seepage characteristic parameters of the dam foundation overburden soil and the seepage barrier defect under the Darcy-Forchheimer model are calculated using the empirical formula for porous media. The nonlinear seepage characteristic parameters include the Darcy seepage coefficient and the Forchheimer seepage coefficient. Based on the computational domain grid, the boundary conditions, fluid parameters, turbulence model, discretization scheme, solver algorithm parameters and time step parameters in the computation process are configured, and the nonlinear seepage characteristic parameters at the defects of the dam foundation overburden soil and the anti-seepage wall are specified to construct a refined analysis model. Numerical calculations of the seepage field were performed on the refined analysis model using the finite volume method solver, based on the RANS equations and the Darcy-Forchheimer model. The numerical calculation results of the seepage field are extracted to obtain the nonlinear seepage field distribution at the defects in the dam foundation overburden soil and the anti-seepage wall.

2. The refined calculation method for nonlinear seepage characteristics of dam foundation overburden as described in claim 1, characterized in that, The expression for the RANS equation is as follows: ； ； in, In the Cartesian coordinate system, the first... Velocity components in each coordinate direction , In the Cartesian coordinate system, the first... Coordinates in each coordinate direction, Indicates fluid density, Indicates fluid pressure. In the Cartesian coordinate system, the first... Gravitational acceleration components in each coordinate direction In the Cartesian coordinate system, the first... Coordinates in each coordinate direction, , Indicates the effective viscosity of the fluid. , Indicates the dynamic viscosity of a fluid. Indicates eddy current viscosity; Indicates that other external forces are in the first... Components in each coordinate direction, Indicates time, It represents a partial differential.

3. The refined calculation method for nonlinear seepage characteristics of dam foundation overburden layer according to claim 1, characterized in that, The Darcy and Forchheimer seepage coefficients were calculated based on the Ergun formula, as follows: ； ； ； in, Indicates the hydraulic gradient. This represents the Darcy flow coefficient. This represents the Forchheimer seepage coefficient. Indicates the dynamic viscosity of a fluid. This indicates the porosity of the soil at the corresponding location in the dam foundation overburden layer. Indicates the equivalent diameter of the particles. Indicates fluid density, This indicates the seepage velocity.

4. The refined calculation method for nonlinear seepage characteristics of dam foundation overburden layer according to claim 3, characterized in that, The particle equivalent diameter The calculation was obtained based on the particle size distribution of the dam foundation overburden soil, and the calculation formula is as follows: ； ； in, Represents the shape factor. This represents the average diameter of Sauter. Indicates the first Mass fraction of each particle size range Indicates the first The average particle size of each particle size range.

5. The refined calculation method for nonlinear seepage characteristics of dam foundation overburden layer according to claim 1, characterized in that, The boundary conditions, fluid parameters, turbulence model, discretization scheme, solver algorithm parameters, and time step parameters in the configuration calculation process include: Set boundary conditions: including inflow boundary, outflow boundary and wall boundary, wherein the inflow boundary can be set with water pressure that varies with time according to the water storage process; Set fluid parameters: including fluid density and kinematic viscosity; Set the turbulence model: Select either the laminar flow model or the k-epsilon model; Set the discretization scheme: Set the corresponding numerical discretization scheme for each term in the RANS equation; Set solver algorithm parameters: Specify the linear solver for the pressure and velocity terms and the residual convergence criterion; Set time step parameters: Set the total computation time, the initial computation step size, and the number of CFLs used to control the adaptive time step size; The nonlinear seepage characteristic parameters specified at the defects in the dam foundation overburden soil and the cutoff wall include: specifying the dam foundation overburden soil region and the cutoff wall defect region in the calculation domain, and assigning the corresponding Darcy seepage coefficient and Forchheimer seepage coefficient.

6. The refined calculation method for nonlinear seepage characteristics of dam foundation overburden as described in claim 1, characterized in that, The types of defects in the cutoff wall include through cracks, honeycomb pitting or holes on the surface of the cutoff wall.

7. The refined calculation method for nonlinear seepage characteristics of dam foundation overburden layer according to claim 1, characterized in that, The model file is in .stl format and is built using SolidWorks or AutoCAD software.

8. The refined calculation method for nonlinear seepage characteristics of dam foundation overburden layer according to claim 1, characterized in that, The computational domain mesh can be generated using OpenFOAM's built-in mesh generation tool, Gmsh, Fluent, or ICEM software.

9. The refined calculation method for nonlinear seepage characteristics of dam foundation overburden layer according to claim 1, characterized in that, The method is applicable to two-dimensional or three-dimensional seepage analysis.

10. A refined calculation system for the nonlinear seepage characteristics of a dam foundation overburden layer, characterized in that, The system is used to implement the refined calculation method for the nonlinear seepage characteristics of the dam foundation overburden layer as described in any one of claims 1 to 9, the system comprising: The model building module is used to construct a geometric model of the cutoff wall, including defects, based on field drilling data, and generate model files; The mesh generation module is used to perform computational domain mesh generation based on the geometric model of the cutoff wall. The computational domain mesh includes the mesh of the dam foundation overburden soil and the mesh at the defects of the cutoff wall. The parameter calculation module is used to calculate the nonlinear seepage characteristic parameters of the dam foundation overburden soil and the defects of the anti-seepage wall under the Darcy-Forchheimer model based on the physical property parameters of the dam foundation overburden soil and using the empirical formula of porous media. The nonlinear seepage characteristic parameters include the Darcy seepage coefficient and the Forchheimer seepage coefficient. The preprocessing configuration module is used to configure the boundary conditions, fluid parameters, turbulence model, discretization scheme, solver algorithm parameters and time step parameters in the calculation process based on the computational domain grid, and to specify the nonlinear seepage characteristic parameters of the dam foundation overburden soil and the defects of the anti-seepage wall, so as to construct a refined analysis model. The numerical solution module is used to perform numerical calculations of the seepage field on the refined analysis model using the finite volume method solver, based on the RANS equations and the Darcy-Forchheimer model. The post-processing evaluation module is used to extract the numerical calculation results of the seepage field and obtain the nonlinear seepage field distribution including the defects of the dam foundation overburden soil and the anti-seepage wall.

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