A two-dimensional seepage simulation method based on the particle discrete element method

Abstract

The present invention discloses a two-dimensional seepage simulation method based on particle discrete element, which relates to the technical field of two-dimensional seepage. It includes: establishing a discrete seepage model, and endowing the particle material parameters, geometric parameters and particle-fluid property parameters; conducting particle-particle contact pair retrieval and particle-boundary contact pair retrieval, generating a virtual seepage channel, and obtaining the particle coordination number; judging whether seepage can occur in the particle-particle contact pair and the particle-boundary contact pair, conducting seepage-related variable calculation, and obtaining the calculation result; updating the pore pressure and the total head at the coupled particle positions according to the calculation result; realizing seepage simulation. The present invention can generate a particle seepage conduction model applicable to both steady-state and transient seepage phenomena of continuous media. At the same time, the macroscopic seepage coefficient of the material does not need to be additionally corrected or calibrated and can be directly applied to the seepage model.

Description

Technical Field

[0001] The present invention relates to the technical field of two-dimensional seepage, and in particular to a two-dimensional seepage simulation method based on particle discrete element method. Background Art

[0002] The flow of groundwater has an important impact on aspects such as the stability of geological structures, the management of groundwater resources, and environmental protection. Studying the problem of groundwater seepage has always been an important research topic in the fields of geotechnical engineering and geological science. Therefore, it is of great theoretical and practical significance to conduct in-depth research on the unconfined seepage behavior in homogeneous materials.

[0003] Numerical analysis methods have the characteristics of low cost and accurate calculation, and have been widely used in the fields of geotechnical engineering and geology in recent years. Currently, the numerical analysis methods commonly used for seepage problems are mainly the finite element method, the boundary element method, the finite difference method, the finite volume method, the numerical manifold method, and the hybrid methods combining these methods. The finite element method mainly includes the adaptive grid method and the fixed grid method. The adaptive grid method needs to continuously update the grid during the calculation process. When the calculation process of the free surface changes greatly, it may lead to grid deformation. Moreover, in non-uniform or complex structures, the adaptive grid will change the medium boundary and it is difficult to obtain a stable solution. Since Neuman proposed the Galperin method with an invariant network, under the research of domestic and foreign scholars, methods such as the residual flow method, the virtual element method, and the unit permeability matrix adjustment method have emerged. In recent years, the continuous development of computer technology has provided many calculation software for domestic and foreign scholars. Currently, the software for calculating unconfined seepage problems mainly includes Midas GTS NX, ABAQUS, COMSOL, etc. Most of these software are based on the finite element method and iterate to calculate the free surface in the element grid.

[0004] With the continuous update and iteration of simulation algorithms, the seepage simulation method based on computer simulation has gradually become a development trend. However, the existing two-dimensional seepage simulation methods still face many challenges. For example, how to simulate the transient and steady-state seepage of seepage, how to efficiently solve the position of the free surface, and how to ensure the stability and accuracy of the solution while ensuring the seepage solution efficiency.

[0005] Therefore, in order to promote the development of two-dimensional seepage simulation technology, proposing a two-dimensional seepage simulation method based on particle discrete element method to solve the difficulties existing in the prior art is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a two-dimensional seepage simulation method based on particle discrete element method, which can generate a particle seepage conduction model applicable to both the steady-state and transient seepage phenomena of continuous media. At the same time, the macroscopic seepage coefficient of the material does not need to be additionally corrected or calibrated and can be directly applied to the seepage model.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A two-dimensional seepage simulation method based on the particle discrete element method, comprising the following steps:

[0009] S1. Establish a discrete seepage model, and assign particle material parameters, geometric parameters, and particle-fluid property parameters;

[0010] S2. Conduct a search for particle-particle contact pairs and particle-boundary contact pairs, generate a virtual seepage channel, and obtain the particle coordination number;

[0011] S3. Determine whether seepage can occur in the particle-particle contact pairs and particle-boundary contact pairs, calculate seepage-related variables, and obtain the calculation results;

[0012] S4. Update the pore pressure and total head at the coupled particle positions according to the calculation results of S3;

[0013] S5. Repeat S3 - S4 until the calculation results are stable to achieve seepage simulation.

[0014] In the above method, optionally, the particle material parameters assigned in S1 are particle density , the geometric parameters include particle position coordinates, particle shape, and solid volume , and the particle-fluid property parameters include the pore pressure of the particle, permeability , and bulk modulus .

[0015] In the above method, optionally, the correction coefficient of the virtual seepage channel generated in S2 is as follows:

[0016] ;

[0017] In the formula, represents the coordination number of the corresponding particle, represents the volume fraction of the particle.

[0018] In the above method, optionally, the specific content of determining whether seepage can occur in the particle-particle contact pairs and particle-boundary contact pairs in S3, calculating seepage-related variables, and obtaining the calculation results is as follows:

[0019] In the particle-particle contact pairs, the calculation of seepage-related variables is as follows:

[0020] ;

[0021] In the formula, and are the total heads of particles and particles respectively, is the correction coefficient used to correct the cross-sectional area of the seepage channel, is the bulk modulus of the fluid, is the time step calculated by the discrete element program, is the unit weight of the fluid, are the particles volume, is the permeability coefficient of the seepage channel for particle-to-particle contact, is the length of the seepage channel, is the cross-sectional area of the seepage channel, is the total head change of particles calculated from the seepage flow between particles, is related to particles the number of particle-to-particle contact pairs.

[0022] For the above method, optionally, in the particle-to-boundary contact pairs, the calculation of seepage-related variables is as shown in the following formula:

[0023] ;

[0024] In the formula, and are the total heads of the boundary and particles respectively, is the permeability coefficient of the seepage channel for particle-to-boundary contact, is the length of the seepage channel, is the cross-sectional area of the seepage channel, is related to particles the number of particle-to-wall contact pairs.

[0025] For the above method, optionally, the specific content of updating the pore pressure and total head at the coupled particle position according to the calculation result of S3 in S4 is:

[0026] The calculation formulas for updating the total head and pore pressure at the coupled particle position are:

[0027] ;

[0028] ;

[0029] Among them, is the pore pressure after updating of particles , is the total head after updating of particles , are the particles The y - coordinate of the centroid is the unit weight of water.

[0030] In the above - mentioned method, optionally, in the discrete seepage model, two types of head boundaries are set as the constant - head boundary and the seepage - head boundary respectively.

[0031] As can be seen from the above - mentioned technical solutions, compared with the prior art, the present invention provides a two - dimensional seepage simulation method based on particle discrete element, which has the following beneficial effects: The present invention can generate a particle seepage conduction model applicable to both steady - state and transient seepage phenomena of continuous media. At the same time, the macroscopic seepage coefficient of the material does not require additional correction or calibration and can be directly applied to the seepage model. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on the provided drawings.

[0033] Figure 1 is a flowchart of a two - dimensional seepage simulation method based on particle discrete element provided by the present invention;

[0034] Figure 2 is a schematic diagram of the discrete seepage model provided by the present invention;

[0035] Figure 3 is a schematic diagram of the seepage model and parameter settings between particles provided by the present invention;

[0036] Figure 4 is a schematic diagram of the seepage model and parameter settings between particles and boundaries provided by the present invention;

[0037] Figure 5 is a schematic diagram of a particle represented by a regular pentagon element provided by the present invention;

[0038] Figure 6 is a schematic diagram of the free - surface seepage problem provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0039] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0040] Refer to Figure 1 As shown, the present invention discloses a two-dimensional seepage simulation method based on particle discrete element, including the following steps:

[0041] S1. Establish a discrete seepage model, and endow the particle material parameters, geometric parameters and particle fluid property parameters;

[0042] S2. Conduct retrieval of particle-particle contact pairs and particle-boundary contact pairs, generate a virtual seepage channel, and obtain the particle coordination number;

[0043] S3. Judge whether seepage can occur in the particle-particle contact pairs and particle-boundary contact pairs, calculate the seepage-related variables, and obtain the calculation result;

[0044] S4. Update the pore pressure and total head at the coupled particle positions according to the calculation result of S3;

[0045] S5. Repeat S3 - S4 until the calculation result is stable to achieve seepage simulation.

[0046] Further, the particle material parameters endowed in S1 are particle density , the geometric parameters include particle position coordinates, particle shape, solid volume , and the particle fluid property parameters include the pore pressure , permeability , bulk modulus .

[0047] Further, the correction coefficient of the virtual seepage channel generated in S2 is as shown in the following formula:

[0048] ;

[0049] In the formula, represents the coordination number of the corresponding particle, represents the volume fraction of the particle.

[0050] Further, the specific content of judging whether seepage can occur in the particle-particle contact pairs and particle-boundary contact pairs in S3, calculating the seepage-related variables, and obtaining the calculation result is:

[0051] In the particle-particle contact pairs, the calculation of the seepage-related variables is as shown in the following formula:

[0052] ;

[0053] In the formula, and are the total heads of particle and particle respectively, is the correction coefficient, used to correct the cross-sectional area of the seepage channel, is the bulk modulus of the fluid, is the time step calculated by the discrete element program, is the unit weight of the fluid, is the particle volume, is the permeability coefficient of the seepage channel for particle-to-particle contact, is the length of the seepage channel, is the seepage channel area, is the total head change of the particle calculated from the seepage flow between particles, is related to the particle number of particle-to-particle contact pairs.

[0054] Furthermore, in the particle-to-boundary contact pairs, the calculation of seepage-related variables is as shown in the following formula:

[0055] ;

[0056] In the formula, and are the total heads of the boundary and the particle respectively, is the permeability coefficient of the seepage channel for particle-to-boundary contact, is the length of the seepage channel, is the seepage channel area, is related to the particle number of particle-to-wall contact pairs.

[0057] Furthermore, the specific content of updating the pore pressure and total head at the coupled particle position according to the calculation result of S3 in S4 is:

[0058] The calculation formulas for updating the total head and pore pressure at the coupled particle position are:

[0059] ;

[0060] ;

[0061] Among them, is the updated pore pressure of the particle , is the updated total head of the particle , is the centroid y-coordinate of the particle , is the specific weight of water.

[0062] Further, in the discrete seepage model, two types of head boundaries are set as the constant head boundary and the seepage head boundary respectively.

[0063] Specifically, when the change value of the head between two adjacent steps in S6 is less than 10 -6 the calculation end condition is satisfied, and seepage simulation is realized.

[0064] In a specific embodiment, it includes the following content:

[0065] To establish a discrete seepage model, based on the discrete element method (DEM), the properties of the liquid originally existing between the gaps of geotechnical particles are assigned to discrete particles, and the seepage in the geotechnical body is transmitted through particle contact pairs. The specific assumptions are as follows:

[0066] 1) Assign the properties of the fluid to the particles in the discrete element model. For example, Figure 2 This is a schematic diagram of the discrete seepage model provided by the present invention. Among them, a is a simplified model of the porous medium in the project, b is a schematic diagram of the particle-to-particle contact pair in the discrete seepage model, and c is a schematic diagram of the particle-to-boundary contact pair in the discrete seepage model; the continuous porous medium model in the project is simplified into particles of different sizes arranged densely, and the flow of the fluid in the pores between the particles is simplified to the transmission of the fluid properties of the particles themselves. The fluid properties of the particles (pore pressure p, seepage flow rate q, etc.) are transmitted through the particle-to-particle contact pairs or the particle-to-boundary contact pairs. Two basic contact pairs in the model are shown in b and c, namely the particle-to-particle contact pair and the particle-to-boundary contact pair;

[0067] 2) Fluid transfer conditions between particles: There is a pore pressure difference between adjacent particles, and the direction of fluid transfer is always the same as the direction of the pore pressure drop;

[0068] 3) The flow of the fluid in the continuous medium follows Darcy's law, and the relationship between the fluid seepage flow rate and the hydraulic gradient can be known as shown in the following formula:

[0069]

[0070] In the formula, is the fluid flow rate, is the permeability, is the cross-sectional area in the seepage direction, is the total head loss, is the total head, is the seepage path length. In the seepage problem, the total head is expressed as the sum of the position head and the pressure head, and the expression is as shown in the following formula:

[0071]

[0072] In the formula, is the height above the reference datum plane, is the pore pressure, is the unit weight of the fluid.

[0073] 4) Assume a fluid increment , flowing into a given volume , the change in pore pressure within the volume is shown by the following equation:

[0074]

[0075] wherein, is the bulk modulus of the fluid.

[0076] 5) In the discrete seepage model, consider the fluid flowing from particle to particle , where the radii of particles and are and 。 As shown in Figure 3 , the seepage channel is a rectangle. The length of the seepage channel is taken as the distance between the centers of particles and particle . The cross-section of the seepage channel can be roughly regarded as the average value of the diameters of the two particles . In the two-dimensional plane, since a seepage particle may be in contact with several different particles, at this time, the cross-sectional area of the seepage channel needs to be corrected, and the correction coefficient is .

[0077] The permeability coefficient of the channel is defined as the minimum value of the permeability coefficients of the two particles, that is , where and are the permeability coefficients of particle and particle 。

[0078] Therefore, the fluid exchange volume between particle and its surrounding particles is shown by the following equation:

[0079]

[0080] Therefore, the change amount of the pore pressure of particle caused by the fluid exchange volume is shown by the following equation:

[0081]

[0082] In the formula, and are the total water heads of particle and particle respectively, which are used to correct the cross-sectional area of the seepage channel.

[0083] Since the position of the particle does not change, the change in the total water head at the position of the particle only depends on the pressure head, and the relationship is shown in the following formula:

[0084]

[0085] In the formula, , , represent the total water head value, the height value above the reference datum plane, and the pore pressure value of particle at time step respectively. Therefore, the change in the water head caused by the inflow of the surrounding particle fluid into particle

[0086] is shown in the following formula:

[0087]

[0088] The seepage occurring in the particle-boundary contact pair is very similar to that in the particle-particle contact pair. Assume that particle is in contact with the boundary , and the end points of the boundary model are the line segment of and , as shown in Figure 4 . When there are different boundaries causing fluid exchange in particle within a time step , the amount of fluid exchange can be calculated by the following formula:

[0089]

[0090] Therefore, the change in the total water head at the position of the particle caused by the fluid exchange of the boundary pair with the particle is shown in the following formula:

[0091]

[0092] In summary, the calculation formula for updating the water head of the particle in the model can be obtained as:

[0093]

[0094] 6) In the discrete seepage model, there are mainly three seepage parameters of the particle: the volume of the coupled particle , the bulk modulus and the permeability coefficient . Among them, the latter two parameters are set to the values of the physical medium. When representing a continuous medium with particles, the volume of the particles needs to correspond to the physical medium. Introducing the volume fraction, the calculated volume of the coupled particles should be adjusted as shown in the following formula:

[0095]

[0096] In the formula, is the volume of the particle, is the volume fraction of the particle system.

[0097] In the model, the coordination number (CN) is a measure of the average number of other particles in contact with each particle. Usually, the coordination number only considers adjacent particles in contact with each other. If two particles are adjacent, a fluid channel can be generated. Therefore, the average number of fluid channels in the whole system depends on the coordination number. To make the model better conform to the actual situation, the cross-sectional area of the particle seepage channel is corrected. Consider a particle p with a radius of R and relate it to a regular CN-sided polygon e. The particle is the inscribed circle of the regular CN-sided polygon. CN may not be an integer, but in the model, it can be regarded as the average of multiple particles. So in the particle, the polygon matching the particle can also be regarded as the average of multiple regular polygons.

[0098] To intuitively explain the principle of the correction, a regular pentagon is used to explain the principle. Let represent the side length of the polygon e. Through Figure 5 the expression of the volume fraction can be obtained as shown in the following formula:

[0099]

[0100] Particle The uncorrected seepage channel area is the sum of CN pipes, , and actually the seepage channel area of the regular CN-sided polygon is According to the relationship of the same seepage area, we can get , and then we can get The expression of

[0101]

[0102] 7) In fluid mechanics, the free surface refers to the interface between a liquid and air or other fluids. In the discrete seepage model, when simulating unconfined seepage problems, the free surface is defined as the demarcation line where the coupled particle pore water pressure is greater than or less than. Specifically, the pore pressure of the coupled particles above the free surface is zero, that is, the total head of the coupled particles above the free surface is equal to the elevation head. In the present invention, there is no need to adjust the free surface additionally. After setting the interface conditions, the generation of the free surface is automatic.

[0103] For the convenience of description, Figure 6 is a schematic diagram of the free surface seepage problem, which involves the downstream and the upstream . For such seepage problems, in the discrete seepage model, only two types of head boundaries need to be set, namely the constant head boundary and the seepage head boundary. For the constant head boundary, the AB boundary adopts the downstream head boundary condition , and the DE boundary adopts the upstream head . In addition, an additional seepage boundary BC is required to simulate the situation of real fluid seepage. This boundary adopts a linear boundary condition where the boundary head is equal to the elevation head. An impervious layer is set on AE, and no boundaries are set for other parts of the model.

[0104] The various embodiments in this specification are described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, refer to the description in the method section.

[0105] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features disclosed herein.

Claims

1. A two-dimensional seepage simulation method based on particle discrete elements, characterized in that: The following steps are involved: S1. Establish a discrete seepage model and assign particle material parameters, geometric parameters and particle fluid property parameters; S2, searching for contact pairs between particles and between particles and boundaries, generating virtual percolation channels, and obtaining particle coordination numbers; S3, judging whether seepage can occur between particle-particle contact pairs and between particle and boundary contact pairs, calculating seepage-related variables, and obtaining calculation results; S4, updating the pore pressure and total water head at the coupled particle position according to the calculation results of S3; S5, repeat S3-S4 until the calculation results are stable and the seepage simulation is realized; In S3, it is determined whether the contact pairs between particles and between particles and boundaries can seep, and the seepage-related variables are calculated. The specific contents of the calculation results are as follows: In the contact between particles, the calculation of seepage related variables is shown as follows: In the formula, and are the total water heads of particles i and j, respectively; α is the correction coefficient used to correct the cross-sectional area of ​​the seepage channel; k v is the bulk modulus of the fluid, Δt is the time step of the discrete element program calculation, γ is the specific gravity of the fluid, V i is the volume of particle i, k ij is the permeability coefficient of the particle-particle contact to the seepage channel, L ij is the length of the seepage channel, S ij is the permeation channel area, is the total head change of particle i calculated from the interparticle seepage, n is the number of particle-particle contact pairs associated with particle i; In the contact pair between particles and boundaries, the calculation of seepage related variables is shown as follows: In the formula, and are the total hydraulic head of boundary w and particle i, k iw is the permeability coefficient of the particle-boundary contact to the seepage channel, L iw is the length of the seepage channel, S iw is the permeable channel area, and m is the number of contact pairs between particle i and the wall.

2. A two-dimensional seepage simulation method based on particle discrete element according to claim 1, characterized in that: The particle material parameters assigned in S1 are particle density ρ, geometric parameters include particle position coordinates, particle shape, solid volume V, and particle fluid property parameters include particle pore pressure p, permeability k, and bulk modulus k v .

3. The two-dimensional seepage simulation method based on particle discrete element according to claim 1, characterized in that: The correction coefficient α of the virtual seepage channel generated in S2 is as follows: In the formula, CN represents the coordination number of the corresponding particle, f v represents the volume fraction of particles.

4. The two-dimensional seepage simulation method based on particle discrete element according to claim 1, characterized in that: The specific content of updating the pore pressure and total water head at the coupled particle position according to the calculation results of S3 in S4 is: The calculation formulas for the total water head and pore pressure at the updated coupled particle position are: Among them, P i is the updated pore pressure of particle i, is the updated total water head of particle i, y i is the y coordinate of the centroid of particle i, and λ is the density of water.

5. The two-dimensional seepage simulation method based on particle discrete element according to claim 1, characterized in that: In the discrete seepage model, the free surface is defined as the boundary where the pore water pressure of the coupled particles is greater than or less than, and two types of head boundaries are set: constant head boundary and seepage head boundary.

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