CN117094171A - Numerical simulation method for solid-fluid conversion movement of rock debris - Google Patents
Numerical simulation method for solid-fluid conversion movement of rock debris Download PDFInfo
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Abstract
The invention relates to the technical field of numerical simulation, and particularly discloses a numerical simulation method for solid-liquid conversion movement of rock fragments, which comprises the following steps: establishing a simulation model of the target research object based on an MPS method; calculating a particle count density based on all of the determined particle positions; determining yield stress of the chip body in different states based on the strain; calculating dynamic viscosity coefficients of the chip body in different states based on the obtained yield stress; discretizing a control equation by using a Laplace model and a gradient model based on the MPS, and calculating an external force and a viscosity term; calculating the pressure born by the particles by adopting a pressure poisson equation, and then dispersing pressure gradient items based on a gradient model; and correcting the speed and the position of the particles based on the obtained result to obtain a numerical simulation result of the solid-liquid conversion movement of the rock debris. The invention considers the solid-fluid conversion motion state of the ice-rock fragments, and the simulation result is more fit for the actual situation.
Description
Technical Field
The invention relates to the technical field of numerical simulation, in particular to a numerical simulation method for solid-fluid conversion movement of rock fragments.
Background
The ice-rock debris flow is a phenomenon that ice scraps, rock blocks and soil particles formed after landslide, ice collapse or rock collapse and disintegration in steep mountain slope areas in alpine regions flow at a high speed; because ice scraps are wrapped, the ice-rock scraps flow has super-strong mobility and harm, disastrous events which cause the world to frighten are often caused, and the problems of hot spots and fronts of geological disaster research under the global warming background are also caused; therefore, the method has important significance for predicting and controlling related accident disasters by carrying out simulation on the solid-liquid conversion movement of the rock fragments.
In the prior art, a physical test device can be used to simulate the solid-to-fluid conversion motion of the rock debris body, for example, a test system for simulating the solid-to-fluid conversion motion of the rock debris body at a high speed is disclosed in patent CN 116358828A; however, the physical test method has the problems of long period, high cost, difficulty in sample preparation, difficulty in ensuring the consistency of the experimental effect and the on-site fluid, and the like; whereas the rock clastic body solid-to-fluid conversion motion is a complex multi-state conversion motion process, a more elaborate way is needed to actually simulate the rock clastic body solid-to-fluid conversion motion. In the traditional CFD (Computational Fluid Dynamics ) method using grids, generating an "optimal grid" is time consuming and difficult to simulate free surface flow or complex boundary geometries.
Therefore, in order to solve the above-mentioned problems, a numerical simulation method of the solid-to-fluid conversion motion of the rock fragments is needed, which can simulate the solid-to-fluid conversion motion of the rock fragments more truly, so that the simulation result is more fit to the actual situation.
Disclosure of Invention
Therefore, the invention aims to provide a numerical simulation method for the solid-to-fluid conversion movement of the rock debris body, which can simulate the solid-to-fluid conversion movement of the rock debris body more truly, so that the simulation result is more fit with the actual situation.
In order to achieve the above object, the present invention provides a numerical simulation method for solid-fluid conversion movement of an iceberg clastic body, first, an iceberg clastic body simulation model is established according to an MPS method, the iceberg clastic body simulation model includes an MPS fluid domain and MPS particles located in the MPS fluid domain, solid particles in the MPS particles are regarded as fluid particles, and numerical calculation is performed together with the fluid particles; the numerical calculation includes the steps of:
s11: after starting and initializing, calculating the particle count density based on all the determined particle positions;
s12: determining yield stress of the chip body in different states according to the strain;
s13: calculating dynamic viscosity coefficients of the chip body in different states based on the determined yield stress;
s14: discretizing a control equation by adopting a Laplace model and a gradient model, and calculating external force and viscosity items;
s15: updating the particle position;
s16: calculating the particle number density after the position update;
s17: using a laplace model to discretely calculate a pressure poisson equation;
s18: calculating the pressure born by the particles based on a pressure poisson equation, and then calculating a pressure gradient term by adopting a gradient model;
s19: and correcting the speed and the position of the particles based on the obtained result to obtain a numerical simulation result of the solid-liquid conversion movement of the rock debris.
As a further improvement of the above technical solution, in step S19, it is determined whether the number of steps of the simulation time reaches a preset value, if not, the process returns to step S11, otherwise, the simulation is stopped.
As a further improvement to the above solution, in step S11, the positions of all particles are found, and the particle number density is affected by the neighboring particles within the effective radius, and follows a weight function:
wherein w is ij (r ij ) Is a weight function between particle i and particle j,r e is the effective radius;
and then adding all the weights among the particles to obtain the particle number density.
As a further improvement to the above technical solution, in step S12, the relative displacement equation of the particles is discretized to obtain strain;
the resulting strain is then compared to its plastic bias strain in the peak, residual and fluid states to determine whether the crumb body is in a solid, transitional or fluid state.
As a further improvement to the above technical solution, in step S13, velocity gradient tensor is first obtained by discretizing velocity gradient terms based on MPS gradient model, and shear rate is obtained according to the obtained result;
then, the obtained shear rate is carried into a Bingham model, and dynamic viscosity coefficients of the clastic bodies in different states are calculated;
the constitutive relational expression of the Bingham model is as follows:
where τ is the shear stress, μ is the coefficient of viscosity,for shear rate τ y Is the yield shear stress.
As a further improvement to the above technical solution, in step S14, the minimum pressure of all particles in the adjacent areas thereof is calculated first, and then the control equation is discretized by using the laplace model and the gradient model based on the MPS method, so as to obtain the pressure to which the fluid particles are subjected;
the Laplace model is as follows:
wherein,is an arbitrary scalar quantity of particles i, d is a spatial dimension, n 0 Is the initial particle number density;
the gradient model is as follows:
wherein p is pressure.
As a further improvement to the above solution, in step S18, the calculating the pressure to which the particle is subjected based on the poisson equation includes: firstly discretizing the left side of an equation of a pressure poisson equation by using a Laplacian model, wherein the right side of the equation represents the deviation of the particle number density;
the poisson equation is:
wherein ρ is density, Δt is the size of the time step;
the pressure to which the particles are subjected is then obtained by simultaneous equations using a linear symmetric matrix representation and solving with an incomplete Cholesky conjugate gradient method.
As a further improvement to the above-described technical solution, in step S18, a pressure gradient term is calculated using the MPS gradient model.
As a further improvement to the above technical solution, in step S19, the formula for modifying the speed and the position is as follows:
where u is the speed and k is the current time step.
Compared with the prior art, the invention has the following beneficial technical effects:
according to the numerical simulation method for the solid-fluid conversion motion of the rock debris body, the speed and the position of all particles are calculated by adopting a fluid control equation, and the speed and the position are corrected after solving a pressure poisson equation; the simulation result is more fit for the actual situation because of considering the solid-fluid transition motion state of the ice-rock fragments.
Additional aspects of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a flow chart of the numerical calculation of the present invention;
FIG. 2 is a schematic diagram showing the state of the crumb body according to the plastic strain.
Detailed Description
In order to make the technical scheme of the present invention better understood by those skilled in the art, the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments.
Examples
As shown in fig. 1 and 2: the embodiment provides a numerical simulation method for solid-fluid conversion movement of rock fragments.
By way of background, a moving particle semi-implicit (MPS) method and bingham fluid model (Bingham fluid model) will be described first.
The MPS (Moving Particle Semi-implicit) method is a numerical analysis method of incompressible fluid first proposed by Koshizuka S and Oka in 1996, and starts to be mainly applied to nuclear engineering and coastal engineering problems, focusing on the research on fluids; calculating the displacement and the speed of the particles by using a fluid control equation, and correcting the speed and the position of the particles by using a poisson equation; the MPS method is gradually applied to the landslide field in geotechnical engineering by adopting a semi-implicit time calculation algorithm, in each time step, firstly, the viscous term in the momentum equation is explicitly calculated to obtain initial values of the speed and the position of an example, and then the poisson equation is implicitly solved to obtain a corrected value of the speed position; the speed and the position of the particles in the next time step are obtained through corresponding correction calculation; and the flow information of the whole flow field fluid is obtained by tracking the movement rule of each particle in each time step. The MPS method without using a mesh is easy to model and can simulate surface variations and liquid splash phenomena without difficulty.
Bingham fluids (Bingham fluids) were at the earliest proposed viscoelastic non-newtonian fluids with linear flow properties; in the Bingham fluid model, if the shear stress is below the threshold τ y (yield shear stress), no deformation occurs; when the shear stress is greater than tau y Deformation occurs when the material is deformed; and the deformation and shear stressExceeding τ y Is proportional to the extent of (a).
According to the numerical simulation method for the solid-fluid conversion movement of the rock debris body, firstly, a rock debris body simulation model (which can be implemented by taking the rock debris body in reality as a target study object and collecting related physical parameters for modeling) is established according to an MPS method, the rock debris body simulation model comprises an MPS fluid domain and MPS particles located in the MPS fluid domain, and solid particles in the MPS particles are regarded as fluid particles and are subjected to numerical calculation together with the fluid particles.
As shown in fig. 1 (in fig. 1, u represents a velocity, r represents a position, Δt: represents a time step, ×represents a calculation time, and k represents a calculation step), the numerical calculation includes the steps of:
s11: after starting and initializing, calculating the particle count density based on all the determined particle positions;
s12: determining yield stress of the clastic body (namely the simulated model of the clastic body of the rock) in different states according to the strain epsilon;
s13: calculating dynamic viscosity coefficients of the chip body in different states based on the determined yield stress;
s14: discretizing a control equation by adopting a Laplace model and a gradient model, and calculating external force and viscosity items;
s15: updating the particle position;
s16: calculating the particle number density after the position update;
s17: using a laplace model to discretely calculate a pressure poisson equation;
s18: calculating the pressure born by the particles based on a pressure poisson equation, and then calculating a pressure gradient term by adopting a gradient model;
s19: correcting the speed and the position of the particles based on the obtained result to obtain a numerical simulation result of the solid-liquid conversion movement of the rock debris; judging whether the step number of the simulation time reaches a preset value, if not, returning to the step S11, otherwise, stopping simulation.
In the MPS method, the pressure term is calculated using an implicit algorithm and the viscosity and external force terms are calculated using an explicit algorithm. The mass conservation equation and momentum conservation equation for incompressible fluids are as follows:
wherein ρ is the fluid density; u is the fluid velocity; p is the pressure; mu is the dynamic coefficient of viscosity; f is the volumetric force; to the left of the conservation of momentum equation is the Lagrange derivative, which contains the convection term, which is directly calculated by tracking the particle motion; the right side consists of a pressure gradient and an external force item; all terms represented by differential operators should be replaced by interactions of particles.
Wherein, the discrete form of the momentum conservation equation can be written as:
where k is the current number of time steps,is the size of the time step.
Wherein the viscous term is discretized into the following form:
wherein,is the kinematic viscosity coefficient, dynamic viscosity coefficient of particle i at time step k>Is a variable parameterA number; the left Laplace term can be interpreted as the difference between the velocity of a point and the average velocity of a small surrounding volume, which means that the viscosity is a diffusion of momentum.
In the MPS method, the number of particles may be affected by neighboring particles within the effective radius; the effective radius is denoted by re; the weight function is expressed by:
wherein w is ij (r ij ) Is a weight function between particle i and particle j,r e is the effective radius.
When all particle positions are obtained, the particle number density can also be obtained:
strain tensor epsilon d Represented by a relative displacement vector d:
wherein x is a space vector coordinate, and alpha and beta are space indexes; the gradient model of the MPS method is applicable to each term on the right of formula (1); obtaining the strain tensor epsilon of the particle i i The method comprises the steps of carrying out a first treatment on the surface of the Can be summarized by the following formula:
from the above, strain ε is obtained d When the strain is less thanWhen the crumb body is characterised by a solidMechanical behavior; when the strain is greater than->And is less than->When the clastic body is characterized by transitional state mechanical behavior; when the plastic deviation strain of the fluid is greater than + ->When the crumb exhibited perfect rheological properties; determining the magnitude of the yield stress according to the magnitude of the yield stress; the specific formula is as follows:
the dynamic viscosity coefficient of the crumb body in different states (solid, transitional, fluid) can be expressed as:
wherein,the following equation is used to obtain:
here, the MPS gradient model is introduced to discretize the rate of change of velocity in equation (11):
after obtaining the value of the velocity gradient tensor, replacing it to formula (11), and obtaining the value of the shear rate; the viscosity coefficient μ is obtained by substituting the known shear rate into equation (10).
The MPS method discretizes the control equation by using a laplace model and a gradient model:
wherein,minimum pressure for adjacent regions of particle i:
the Laplace operator discretizes into:
wherein:
the pressure was calculated using the poisson equation:
the left side can be discretized by using an MPS Laplace model [ as shown in formula (15) ]; the right side of the equation represents the deviation of the population density; on this basis, simultaneous equations are represented by linear symmetric matrices and can be solved by incomplete Cholesky conjugate gradient method (ICCG).
Furthermore, using the MPS gradient model, the pressure gradient term can be calculated.
The final speed and position modifications are as follows:
in order to keep the simulation stable, the time step t needs to meet the following constraints:
wherein l 0 D is an empirically derived value and should be less than 1.0 for the distance between adjacent particles; in general, D can be set equal to 0.2; under this constraint, when the kinematic viscosity is high, the time step becomes small, resulting in a long simulation time; it is disadvantageous that the time step is too small.
In summary, this embodiment divides one calculation step into two processes; in a first process, the acceleration of the particles of all items except the pressure item is calculated, and the time velocity and position are calculated; the pressure term is calculated in the second process; after solving the pressure poisson equation, the velocity and position are corrected.
In the embodiment, the speed and the position of all particles are calculated by adopting a fluid control equation, and the speed and the position are corrected after solving a pressure poisson equation; the simulation result is more fit for the actual situation because of considering the solid-fluid transition motion state of the ice-rock fragments.
Finally, it is pointed out that the principles and embodiments of the invention have been described herein with reference to specific examples, which are intended to be merely illustrative of the core idea of the invention, and that several improvements and modifications can be made to the invention without departing from the principles of the invention, which also fall within the scope of protection of the invention.
Claims (9)
1. The numerical simulation method for the solid-fluid conversion movement of the ice rock detritus body is characterized by firstly establishing an ice detritus body simulation model according to an MPS method, wherein the ice detritus body simulation model comprises an MPS fluid domain and MPS particles positioned in the MPS fluid domain, and taking solid particles in the MPS particles as fluid particles and carrying out numerical calculation together with the fluid particles; the numerical calculation includes the steps of:
s11: after starting and initializing, calculating the particle count density based on all the determined particle positions;
s12: determining yield stress of the chip body in different states according to the strain;
s13: calculating dynamic viscosity coefficients of the chip body in different states based on the determined yield stress;
s14: discretizing a control equation by adopting a Laplace model and a gradient model, and calculating external force and viscosity items;
s15: updating the particle position;
s16: calculating the particle number density after the position update;
s17: using a laplace model to discretely calculate a pressure poisson equation;
s18: calculating the pressure born by the particles based on a pressure poisson equation, and then calculating a pressure gradient term by adopting a gradient model;
s19: and correcting the speed and the position of the particles based on the obtained result to obtain a numerical simulation result of the solid-liquid conversion movement of the rock debris.
2. The numerical simulation method of the solid-fluid conversion motion of the rock fragments according to claim 1, wherein the method comprises the following steps of:
in step S19, it is determined whether the number of steps of the simulation time reaches a preset value, if not, the process returns to step S11, otherwise, the simulation is stopped.
3. A method for numerical simulation of solid-to-fluid conversion movement of rock fragments according to claim 1 or 2, wherein:
in step S11, the positions of all particles are obtained, the particle number density is affected by the neighboring particles within the effective radius, and the weighting function is followed:
wherein w is ij (r ij ) Is a weight function between particle i and particle j,r e is the effective radius;
and then adding all the weights among the particles to obtain the particle number density.
4. A method for numerical simulation of solid-fluid conversion movement of rock fragments according to claim 3, wherein:
in step S12, the relative displacement equation of the particles is discretized to obtain strain;
the resulting strain is then compared to its plastic bias strain in the peak, residual and fluid states to determine whether the crumb body is in a solid, transitional or fluid state.
5. The numerical simulation method for the solid-fluid conversion motion of the rock fragments according to claim 4, wherein the method comprises the following steps of:
in step S13, first, velocity gradient tensor is obtained by discretizing velocity gradient term based on MPS gradient model, and shear rate is obtained according to the obtained result;
then, the obtained shear rate is carried into a Bingham model, and dynamic viscosity coefficients of the clastic bodies in different states are calculated;
the constitutive relational expression of the Bingham model is as follows:
wherein τ is the shear stress and μ isThe coefficient of viscosity of the adhesive tape,for shear rate τ y Is the yield shear stress.
6. The numerical simulation method for the solid-fluid conversion motion of the rock fragments according to claim 5, wherein the method comprises the following steps of:
in step S14, firstly, calculating the minimum pressure of all particles in the adjacent areas, and then discretizing a control equation by using a laplace model and a gradient model based on an MPS method to obtain the pressure exerted by the fluid particles;
the Laplace model is as follows:
wherein,is an arbitrary scalar quantity of particles i, d is a spatial dimension, n 0 Is the initial particle number density;
the gradient model is as follows:
wherein p is pressure.
7. The numerical simulation method of the solid-fluid conversion motion of the rock fragments according to claim 6, wherein the method comprises the following steps of:
in step S18, the calculating the pressure applied to the particle based on the poisson equation includes: firstly discretizing the left side of an equation of a pressure poisson equation by using a Laplacian model, wherein the right side of the equation represents the deviation of the particle number density;
the poisson equation is:
wherein ρ is density, Δt is the size of the time step;
the pressure to which the particles are subjected is then obtained by simultaneous equations using a linear symmetric matrix representation and solving with an incomplete Cholesky conjugate gradient method.
8. The numerical simulation method of the solid-fluid conversion motion of the rock fragments according to claim 7, wherein the method comprises the following steps of:
in step S18, a pressure gradient term is calculated using the MPS gradient model.
9. The numerical simulation method of the solid-fluid conversion motion of the rock fragments according to claim 8, wherein the method comprises the following steps of:
in step S19, the formula for modifying the speed and position is as follows:
where u is the speed and k is the current time step.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117291060A (en) * | 2023-11-23 | 2023-12-26 | 成都理工大学 | Three-dimensional simulation prediction method for rock burst movement process in consideration of dynamic fragmentation effect |
| CN117473908A (en) * | 2023-12-27 | 2024-01-30 | 中国科学院、水利部成都山地灾害与环境研究所 | Rock ice avalanche motion simulation method based on depth average quasi-multiphase model |
| CN118378571A (en) * | 2024-06-25 | 2024-07-23 | 中国地质科学院地质力学研究所 | Rock mixing and ice water conversion numerical simulation method and device for extremely high mountain debris flow |
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2023
- 2023-09-07 CN CN202311151911.XA patent/CN117094171A/en active Pending
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117291060A (en) * | 2023-11-23 | 2023-12-26 | 成都理工大学 | Three-dimensional simulation prediction method for rock burst movement process in consideration of dynamic fragmentation effect |
| CN117291060B (en) * | 2023-11-23 | 2024-02-27 | 成都理工大学 | Three-dimensional simulation prediction method for rock burst movement process in consideration of dynamic fragmentation effect |
| CN117473908A (en) * | 2023-12-27 | 2024-01-30 | 中国科学院、水利部成都山地灾害与环境研究所 | Rock ice avalanche motion simulation method based on depth average quasi-multiphase model |
| CN117473908B (en) * | 2023-12-27 | 2024-05-03 | 中国科学院、水利部成都山地灾害与环境研究所 | Rock ice avalanche motion simulation method based on depth average quasi-multiphase model |
| CN118378571A (en) * | 2024-06-25 | 2024-07-23 | 中国地质科学院地质力学研究所 | Rock mixing and ice water conversion numerical simulation method and device for extremely high mountain debris flow |
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