A three-dimensional explicit granular discrete element method for seepage simulation

Abstract

This invention discloses a three-dimensional explicit particle discrete element seepage simulation method, which relates to the field of computer numerical simulation technology. The method comprises the following steps: assigning particle material parameters based on a three-dimensional particle discrete seepage model; performing contact searches between particles and between particles and boundaries within the three-dimensional particle discrete seepage model based on the material parameters, determining the corresponding coordination numbers of the particles, and establishing virtual seepage channels; calculating the seepage rate per unit time between particles and between particles and boundaries based on the total head difference; and updating the total head value and pore pressure using an explicit solution based on the total flow rate obtained for each particle within a time step. This invention solves the problem of simulating steady-state and transient seepage in three-dimensional continuous media.

Description

Technical Field

[0001] The present invention relates to the technical field of computer numerical simulation, and more particularly to a three-dimensional explicit particle discrete element seepage simulation method. Background Art

[0002] Traditional continuum methods (such as the finite element method and the finite volume method) are commonly used to study fluid distribution and seepage behavior in continuous media. However, these methods often struggle to accurately simulate the actual flow paths of fluids in complex pore structures. In contrast, the discrete element method (DEM), based on discontinuous methods, can more accurately describe the flow behavior of fluids in granular media. Explicit DEM flow simulations, because their calculations do not rely on iterative convergence, offer high computational efficiency. They can analyze and simulate transient seepage problems in porous granular systems and are suitable for simulating large-scale three-dimensional seepage problems. The advantage of explicit methods lies in their simplified computational process and high accuracy, thus meeting the requirements of complex seepage environments. Numerous researchers have contributed to the study of three-dimensional seepage simulations, but this work still suffers from shortcomings, such as inaccuracies in accuracy and efficiency.

[0003] Therefore, a three-dimensional explicit particle discrete element seepage simulation method is proposed to solve the difficulties existing in the existing technology, which is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0004] In view of this, the present invention provides a three-dimensional explicit particle discrete element seepage simulation method, which solves the problem of simulating steady-state seepage and transient seepage in three-dimensional continuous media.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A three-dimensional explicit granular discrete element seepage simulation method includes the following steps:

[0007] Assign granular material parameters based on a three-dimensional granular discrete seepage model;

[0008] In the three-dimensional discrete particle percolation model, the contact between particles and between particles and boundaries is retrieved based on material parameters, the corresponding coordination number of the particles is determined, and a virtual percolation channel is established;

[0009] Calculate the seepage rate per unit time between particles and between particles and boundaries based on the total hydraulic head difference;

[0010] Based on the total flow rate obtained for each particle within one time step, the total head value and pore pressure are updated using an explicit solution.

[0011] Optionally, a three-dimensional particle discrete seepage model is to establish polygons according to the actual shape and size of the model, and import the shape information of the polygons into the matrix operation system as the model boundary, and establish a model composed of a finite number of randomly or regularly closely arranged discrete particles and walls based on the polygons.

[0012] Optionally, the particle material parameters include geometric parameters and seepage parameters.

[0013] Optionally, the virtual channels for percolation established between particles and between particles and boundaries are cubes.

[0014] Optionally, the percolation rate per unit time between particles and between particles and boundaries is calculated as follows:

[0015] The transmission surface of the virtual seepage channel is a rectangle, and the area of ​​the rectangle is defined as the length of the particle j and particles i The average value of the diameter square area, the transmission area of ​​the seepage virtual channel is S ij is defined as:

[0016] ;

[0017] in, R j For particles j The radius, R i For particles i radius;

[0018] particles j and particles i Distance between centers L ij The calculation is as follows:

[0019] ;

[0020] Among them, particles i The center coordinates of in three dimensions are , particles j The center coordinates of in three dimensions are ;

[0021] Define the permeability coefficient of the seepage virtual channel k ij For particles j and particles i Harmonic mean of permeability coefficient:

[0022] ;

[0023] in, ki and k j Particles i With particles j The permeability coefficient;

[0024] According to Darcy's law, the linear relationship between seepage velocity and hydraulic gradient is obtained. j Flow particles i The percolation rate per unit time It is expressed by the following formula:

[0025] ;

[0026] in, and Particles i With particles j Total head; A correction coefficient is introduced to correct the transmission area of ​​the virtual seepage channel. The value is calculated by the following formula:

[0027] ;

[0028] Among them, the coordination number CN is a measure of the average number of neighboring particles for each particle, f v is the volume fraction of the particle aggregate.

[0029] Optionally, the calculation of the percolation rate per unit time between particles and between particles and boundaries also includes:

[0030] particles i and borders w Contact, by the border w Toward particles i The percolation rate per unit time for:

[0031] ;

[0032] in, k iw For particles i and borders w The permeability coefficient between L iw For particles i and borders w The distance between S iw is the transmission area of ​​the virtual channel for water seepage;

[0033] S iw for:

[0034] .

[0035] Optionally, use an explicit solution to update the total head and pore pressure as follows:

[0036] particles i have n adjacent particles and m adjacent boundaries, flowing particles i The total flow is:

[0037] ;

[0038] According to the total flow Q Find the total head increment within a time step, the particle i The total head update is solved explicitly and is calculated as:

[0039] ;

[0040] in, k v is the bulk modulus of the fluid, V i For particles i The volume, is the time step;

[0041] According to Bernoulli's principle, the pore pressure is calculated from the total head value as follows:

[0042] ;

[0043] in, For particles i The pore pressure, For particles i The bulk density.

[0044] Optional, explicit solution time step The analytical expression of is:

[0045] .

[0046] It can be seen from the above technical solution that compared with the existing technology, the present invention provides a three-dimensional explicit particle discrete element seepage simulation method, proposes a simple and efficient explicit calculation scheme, avoids solving complex differential equations, and provides an analytical expression for quickly determining the time step to improve computational efficiency while ensuring the convergence of the computational simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0048] Figure 1 A flow chart of a three-dimensional explicit particle discrete element seepage simulation method provided by the present invention;

[0049] Figure 2 A schematic diagram of seepage between particles through virtual channels provided by the present invention;

[0050] Figure 3 Schematic diagram of seepage between particles and boundaries through virtual channels provided by the present invention;

[0051] Figure 4 A schematic diagram of a three-dimensional inclined core wall earth-rock dam model provided by the present invention;

[0052] Figure 5 A schematic diagram of the pore pressure distribution results of the dam body and foundation provided by the present invention; DETAILED DESCRIPTION

[0053] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0054] The embodiment of the present invention discloses a reference Figure 1 As shown, the present invention discloses a three-dimensional explicit particle discrete element seepage simulation method, comprising the following steps:

[0055] S1. Assign granular material parameters based on a three-dimensional granular discrete seepage model;

[0056] S2. Searching for contacts between particles and between particles and boundaries based on material parameters, determining the coordination numbers corresponding to the particles and establishing virtual channels for percolation;

[0057] S3. Calculate the seepage rate per unit time between particles and between particles and boundaries based on the total head difference;

[0058] S4. Based on the total flow rate obtained for each particle within one time step, the total hydraulic head value and pore pressure are updated using an explicit solution.

[0059] In an optional embodiment, the relevant information of the particles is updated according to the result calculated in S4 and an iterative calculation is performed.

[0060] Furthermore, the three-dimensional particle discrete seepage model in S1 establishes polygons according to the actual shape and size of the model, imports the polygon information into the matrix operation system as the model boundary, and establishes a model composed of a finite number of randomly or regularly closely arranged discrete particles and walls based on the polygons.

[0061] Specifically, the three-dimensional discrete particle seepage model (3DPSM) includes:

[0062] 1) In the discrete element modeling process of continuous media, the study area is discretized into densely packed particles. The contacting particles are connected by a bonded particle model. In 3DPSM, contact forces and seepage only occur between adjacent particles and at the boundaries between adjacent particles. Therefore, the contact mesh of the particles can be regarded as the domain of mechanical and seepage effects.

[0063] 2) The percolation between particles and between particles and boundaries is generated by Figure 2 、 Figure 3 The virtual channels shown are carried out, and the virtual percolation channels between particles and between particles and boundaries are cubic;

[0064] 3) Darcy's law describes the linear relationship between the seepage velocity of water in a medium and the hydraulic gradient:

[0065]

[0066] in, q is the seepage rate per unit time, k is the permeability coefficient, is the head gradient, - (minus sign) indicates that the fluid is conducted from the end with higher total head value to the end with lower total head value;

[0067] Assuming total seepage Q Flow to a given volume V , then the head change of this part can be defined as:

[0068]

[0069] in, k v is the bulk modulus of the fluid;

[0070] Furthermore, the material parameters in S1 include geometric parameters and seepage parameters.

[0071] Specifically, the geometric parameters include particle position coordinate information and particle size , the location and length of the boundary; seepage parameters include the permeability coefficient , head boundary conditions , bulk modulus of the fluid k v , material bulk density γ.

[0072] Furthermore, the virtual channels for percolation established between particles and between particles and boundaries in S2 are cubes.

[0073] Furthermore, the specific content of calculating the seepage between particles in S3 is as follows: the transmission surface of the seepage virtual channel is a rectangle, and the area of ​​the rectangle is defined as the side length of the particle j and particles i The average value of the diameter square area, the transmission area of ​​the seepage virtual channel is S ij is defined as:

[0074]

[0075] in, R j For particles j The radius, R i For particles i radius;

[0076] particles j and particles i Distance between centers L ij The calculation is as follows:

[0077] ;

[0078] Among them, particles i The center coordinates of in three dimensions are , particles j The center coordinates of in three dimensions are ;

[0079] Define the permeability coefficient of the virtual seepage channel k ij For particles j and particles i Harmonic mean of permeability coefficient:

[0080] ;

[0081] in, k i and k j Particles i With particles j The permeability coefficient;

[0082] particles j Flow particles i The percolation rate per unit time It is expressed by the following formula:

[0083] ;

[0084] in, and Particles i With particles j Total head; A correction coefficient is introduced to correct the transmission area of ​​the virtual seepage channel. The value is calculated by the following formula:

[0085] ;

[0086] Among them, the coordination number CN is a measure of the average number of neighboring particles for each particle, f v is the volume fraction of the particle aggregate.

[0087] Furthermore, the specific content of calculating the seepage between particles and boundaries in S3 is: Simplified to a triangle in space, assuming that the particle i and borders w Contact, by the border w Toward particles i The percolation rate per unit time for:

[0088] ;

[0089] in, k iw For particles i and borders w The permeability coefficient between L iw For particles i and borders w The distance between S iw is the transmission area of ​​the virtual channel for water seepage;

[0090] S iw for:

[0091] .

[0092] Furthermore, the specific content of updating the total head value and pore pressure in S4 is:

[0093] In unit time, according to the total flow of particles, the total head change of particles is calculated, and the flow into particles The total flow rate is the total flow rate of all adjacent particles and the flow rate of particles flowing into the adjacent boundaries. The total flow rate, assuming that the particles i have n adjacent particles and m adjacent boundaries, flowing particles i The total flow is:

[0094] ;

[0095] According to the total flow Find the total head increment within a time step, the particle i The total head update is solved explicitly and is calculated as:

[0096] ;

[0097] in, k v is the bulk modulus of the fluid, V i For particles i The volume, is the time step;

[0098] According to Bernoulli's principle, the pore pressure is calculated from the total head value as follows:

[0099] ;

[0100] in, For particles i The pore pressure, For particles i The bulk density.

[0101] Furthermore, for the explicit solution time step The selection of is too large to meet the convergence requirements, and too small will affect the calculation efficiency. In this embodiment, an innovative time step is proposed. The analytical expression is as follows:

[0102] First, when calculating the time step In the process of , the general case is given priority, that is, the particles inside the model do not contact the boundary to simplify the formula. Consider a particle i , with an initial total head , particles i With the surrounding n The total head update algorithm is used to calculate a time step. Afterwards, particles The total water head is ,

[0103]

[0104] To obtain the maximum time step , considering the extreme case, Take the maximum value, that is, around n The total hydraulic head of the contacting particles is set to 0, then Has the following form,

[0105]

[0106] In order to prevent the Inner particles The total head changes sign, The coefficient of needs to be always positive, that is,

[0107]

[0108] From this, the time step can be determined Must be satisfied,

[0109]

[0110] The following uses a three-dimensional inclined core wall earth-rock dam steady-state seepage to verify the effectiveness of the three-dimensional particle discrete seepage model. Figure 4 Figure 1 shows an earth-rock dam with an inclined core and horizontal drainage ditches. The bedding plane is inclined to the horizontal, and the water level on the left side is 15 m high. The core is composed of two materials with permeabilities of 1 m / s and 50 m / s, respectively. The foundation below the dam is slightly permeable with a permeability of 0.01 m / s. The pore pressure distribution of the dam and foundation in the final stable state is obtained as follows: Figure 5 shown.

[0111] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0112] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A three-dimensional explicit particle discrete element seepage simulation method, characterized in that: The following steps are involved: Assign granular material parameters based on a three-dimensional granular discrete seepage model; In the three-dimensional discrete particle percolation model, the contact between particles and between particles and boundaries is retrieved based on material parameters, the corresponding coordination number of the particles is determined, and a virtual percolation channel is established; Calculate the seepage rate per unit time between particles and between particles and boundaries based on the total hydraulic head difference; Based on the total flow rate obtained for each particle within one time step, the total head value and pore pressure are updated using explicit solution; Use explicit solution to update the total head value and pore pressure as follows: Particle i has n adjacent particles and m adjacent boundaries. The total flow into particle i is: The total head increment within a time step is calculated based on the total flow rate Q. The total head update of particle i is solved explicitly and is calculated as: Among them, k v is the bulk modulus of the fluid, V i is the volume of particle i, Δt is the time step, φ i and φ j are the total water heads of particles i and j respectively; α is a correction coefficient introduced to correct the transmission area of ​​the virtual seepage channel, Q j→i is the percolation rate per unit time from particle j to particle i, Q w→i is the percolation rate per unit time from boundary w to particle i, k ij is the permeability coefficient of the virtual seepage channel, k iw is the permeability coefficient between particle i and boundary w, L iw is the distance between particle i and boundary w, L ij is the distance between the centers of particles j and i, S iw is the transmission area of ​​the water seepage virtual channel, S ij is the transmission area of ​​the virtual seepage channel between particles j and i; According to Bernoulli's principle, the pore pressure is calculated from the total head value as follows: P i =(φ i -y i )×γ i ; Among them, P i is the pore pressure of particle i, γ i is the bulk density of particle i; The analytical expression for explicitly solving the time step Δt is:

2. A three-dimensional explicit particle discrete element seepage simulation method according to claim 1, characterized in that: The three-dimensional particle discrete seepage model establishes polygons based on the actual shape and size of the model, and imports the polygon shape information into the matrix operation system as the model boundary. Based on the polygons, a model consisting of a finite number of randomly or regularly closely arranged discrete particles and walls is established.

3. A three-dimensional explicit particle discrete element seepage simulation method according to claim 1, characterized in that: Granular material parameters include geometric parameters and seepage parameters.

4. A three-dimensional explicit particle discrete element seepage simulation method according to claim 1, characterized in that: The virtual channels for percolation between particles and between particles and boundaries are cubes.

5. The three-dimensional explicit particle discrete element seepage simulation method according to claim 1, characterized in that: Calculate the percolation rate per unit time between particles and between particles and boundaries, specifically: The transmission surface of the virtual seepage channel is a rectangle. The area of ​​the rectangle is defined as the average area of ​​the square whose side length is the diameter of particle j and particle i. Then the transmission area S of the virtual seepage channel is ij is defined as: Among them, R j is the radius of particle j, R i is the radius of particle i; The distance L between the centers of particles j and i ij The calculation is as follows: The center coordinates of particle i in three dimensions are (x i ,y i ,z i ), the center coordinate of particle j in three dimensions is (x j ,y j ,z j ); Define the permeability coefficient k of the virtual seepage channel ij is the harmonic mean of the permeability coefficients of particles j and i: Among them, k i and k j are the permeability coefficients of particles i and j, respectively; According to Darcy's law, the linear relationship between seepage velocity and hydraulic gradient is obtained as follows: j→i It is expressed by the following formula: Among them, φ i and φ j are the total water heads of particles i and j respectively; α is a correction coefficient introduced to correct the transmission area of ​​the virtual seepage channel. The value of α can be calculated by the following formula: Among them, the coordination number CN is a measure of the average number of adjacent particles for each particle, f v is the volume fraction of the particle aggregate.

6. A three-dimensional explicit particle discrete element seepage simulation method according to claim 5, characterized in that: Calculation of percolation between particles and between particles and boundaries also includes: Particle i is in contact with boundary w, and the percolation rate per unit time from boundary w to particle i is Q w→i for: Among them, k iw is the permeability coefficient between particle i and boundary w, L iw is the distance between particle i and boundary w, S iw is the transmission area of ​​the virtual channel for water seepage; S iw for: S iw =4R i 2 。

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