CN106055851B - A kind of calculating simulation method of soil body large deformation flowing - Google Patents
A kind of calculating simulation method of soil body large deformation flowing Download PDFInfo
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Abstract
The invention discloses a kind of calculating simulation methods of soil body large deformation flowing, this method is based on molecular dynamics (abbreviation MD) method, using newton's equation of motion as governing equation, it introduces Hertzian type friction formula and Si Duoke formula describes solid-solid particles' interaction and solid-liquid particles' interaction respectively, integral process is solved with Verlet algorithm, establishes the soil body large deformation flowing computation model of solid-liquid coupling.The basic dynamic feature and its characteristics of motion of soil body particle Complex Flows can be presented in the present invention, be conducive to further improve and improve the research level of China's prevention and treatment soil body large deformation flowing disaster, while being also that certain basis is established in extensive use and popularization of the Molecular Dynamics Calculation method in soil body large deformation flowing disaster.
Description
Technical field
The invention belongs to rock-soil mechanics calculating fields, are related to a kind of calculating simulation method of soil body large deformation flowing.
Background technique
Soil body large deformation flowing disaster is mainly shown as all multiforms such as slope instability, foundation pit deformation destruction and surface collapse
Formula seriously threatens human life and property safety.The analysis of soil body large deformation is for engineering design and prevents and reduces natural disasters with important
Meaning, but there is presently no preferably being solved, one of key reason is that numerical value calculates that there is no reflection soil completely
The mechanical characteristics of body large deformation.Deformation process of the soil body under larger stress state belongs to nonlinear large deformation state, becomes
Shape is no longer to meet small deformation theory, and the complete procedure of soil body large deformation can not be simulated in view of conventional numeric calculation method.Therefore,
Seek a kind of effective calculation method is particularly important to simulate soil body large deformation flow process.
Summary of the invention
It is an object of the invention to solve existing numerical computation method can not effectively simulate soil body large deformation flowing disaster
Technical problem, and then propose a kind of calculating simulation method of soil body large deformation flowing, the present invention is by Hertzian type friction formula
Molecular Dynamics Calculation frame is introduced with Si Duoke formula, integral process is solved with Verlet algorithm, establishes solid-liquid coupling
The soil body large deformation flowing computation model, it can be achieved that soil body large deformation flow process simulation.
In order to achieve the above objectives, the present invention adopts the following technical scheme:
A kind of calculating simulation method of soil body large deformation flowing, it is characterised in that: the calculating of the soil body large deformation flowing
Analogy method the following steps are included:
1) particle information file is inputted in molecular dynamics Digital calculation modelling software LAMMPS:
Based on counting system feature, dimension, unit, particle types, the particle radii, perimeter strip of counting system are set first
Part and integral algorithm create analogue unit；Then counting system essential information is set, the counting system essential information includes
But it is not limited to assemblage, the time interval of output, step-length and operation step number；The counting system is Digital calculation modelling to be carried out
Object, the object that carry out Digital calculation modelling is the soil body；The counting system is characterized in that numerical value to be carried out calculates mould
The physico-mechanical properties of quasi- object and locating boundary condition；
2) initial setup module starts, all grains of the molecular dynamics Digital calculation modelling software LAMMPS to counting system
Son assigns initial position and initial velocity, is initialized；It is outer suffered by input model parameter, particle initial density and particle
Power；The particle is molecule, atom and the ion for the object that composition will carry out Digital calculation modelling；
3) simulation control module starting, particle proximity search:
According to the particle radius of influence, carried out with Verlet proximity search method to all particles in particle coverage are calculated
Search, judge one by one ambient particles and calculate particle between spacing and the radius of influence between relationship, determine ambient particles and
It calculates the spacing between particle and is less than the ambient particles of the radius of influence as the proximate particle for calculating particle；Until determining each grain
All proximate particles of son；
The calculating particle is the particle calculated；
The ambient particles are the particles for calculating particle periphery；
The radius of influence is the distance of the grain diameter size setting according to the object that carry out Digital calculation modelling；
4) all proximate particles of each particle are calculated to active force caused by these particles, instantaneous acceleration and wink
Shi Sudu:
It is obtained that external force suffered by model parameter, particle initial density and the particle inputted according to step 2) calculates step 3)
Then all proximate particles of each particle acquire on each particle active force caused by these particles by vector
Suffered resultant force acquires instantaneous acceleration by newton's equation of motion, is solved, is obtained to newton's equation of motion using Verlet integral algorithm
Instantaneous velocity and position to each particle；
All proximate particles of each particle are to use to the calculation of active force caused by these particles
What Hertzian type friction formula and Si Duoke law were calculated,
The Hertzian type friction formula is:
Wherein:
δ is the distance being overlapped between i-th of particle and j-th of particle；
Ri、RjIt is the radius of i-th of particle and j-th of particle respectively；
kn、ktIt is the normal direction coefficient of elasticity and tangential coefficient of elasticity between i-th of particle and j-th of particle respectively；It is described
kt=2/7kn；
γn、γtIt is the normal direction damped coefficient and tangential damped coefficient between i-th of particle and j-th of particle respectively；Institute
State γt=1/2 γn；
meffIt is the effective mass between i-th of particle and j-th of particle, the meff=mimj/(mi+mj)；
mi, mjThe respectively quality of i-th of particle and j-th of particle；
ΔstIt is the tangential displacement vector between i-th of particle and j-th of particle；
nijIt is the unit vector for connecting i-th of particle and j-th of particle centre；
vn、vtIt is the normal component and tangential component of i-th of particle and j-th of particle relative velocity respectively；
T is the time；
I is i-th of particle；
J is all particles in addition to i-th of particle；
The calculation formula of the Si Duoke law is:
F=-3 π η dv
Wherein:
η is the viscosity of hydrone；
D is the partial size of i-th of particle；
V is the movement velocity of i-th of particle；
The calculation formula of the instantaneous velocity of each particle is:
Wherein:
I is i-th of particle, i.e., the particle calculated；
T is the time；
viIt (t) is speed of i-th of particle in t moment；
riIt (t) is i-th of particle in the position of t moment；
Δ t is time interval；
ri(t- Δ t)) is i-th of particle in the position of t- time Δt；
ri(t+ Δ t) is i-th of particle in the position of t+ time Δt；
O((Δt)2) be Δ t second order it is infinitely small；
5) step 4) is repeated, all proximate particles of each particle obtained to step 4) are to caused by these particles
Active force, instantaneous acceleration and instantaneous velocity are updated；
6) calculated result output module starting in real time, physical quantity needed for counting find out in simulation system particle in phase space
Track after, applied statistics physical principle obtains the macroscopic properties and design feature of system；
7) judge whether simulated time is greater than the total time of setting, if simulated time is greater than the total time of setting, step
5) renewal process terminates, program determination；When institute's simulated time is less than the total time of setting, step 5) is repeated until simulated time
Greater than the total time of setting；The simulated time is the product of step-length and operation step number in step 1)；The total time of the setting
It is the product of step-length and operation step number summation in step 1).
Advantages of the present invention is as follows:
(1) in view of the status and conventional numeric calculation method of current soil body large deformation flow field problem numerical simulation study
Limitation, it is accurate without approximation, dynamically track particle trajectory, analog result that the present invention provides one kind, and have link up
Calculating simulation method --- the Molecular Dynamics method of macroscopic properties and microstructure effect, can effectively reproduce soil body large deformation
Flow process solves the challenges such as soil body particle flow bring relative trajectory dynamic change and large deformation, can be anti-
It controls soil body large deformation flowing disaster and related guidance foundation is provided.
(2) Hertzian type friction formula and Si Duoke formula are introduced into MD frame by the present invention for the first time, establish solid-liquid
Computation model is flowed in the soil body large deformation of coupling, which effectively compensates for current soil body large deformation flow simulating essence
The problem of exactness deficiency.
(3) present invention applies Molecular Dynamics method calculating simulation soil body large deformation flow field problem for the first time.Molecular dynamics
Method should not modulus type oversimplification, moreover it is possible to overcome the problems, such as that grid dividing is brought, improve computational efficiency.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is the calculating simulation result that sand flows final configuration.
Specific embodiment
Done with reference to the accompanying drawing with calculating simulation method of the specific embodiment to soil body large deformation flowing of the invention into
The detailed description of one step:
Referring to Fig. 1 and Fig. 2, the present invention provides a kind of calculating simulation method of soil body large deformation flowing, this method packets
Include following steps:
1) particle information file is inputted in molecular dynamics Digital calculation modelling software LAMMPS:
Based on counting system feature, dimension, unit, particle types, the particle radii, perimeter strip of counting system are set first
Part and integral algorithm create analogue unit；Then counting system essential information is set, counting system essential information includes but not
It is limited to assemblage, the time interval of output, step-length and operation step number；Counting system is the object of Digital calculation modelling to be carried out,
The object for carrying out Digital calculation modelling is the soil body；Counting system is characterized in the physical force of the object of Digital calculation modelling to be carried out
Learn property and locating boundary condition；
2) initial setup module starts, all grains of the molecular dynamics Digital calculation modelling software LAMMPS to counting system
Son assigns initial position and initial velocity, is initialized；It is outer suffered by input model parameter, particle initial density and particle
Power；Particle is molecule, atom and the ion for the object that composition will carry out Digital calculation modelling；
3) simulation control module starting, particle proximity search:
According to the particle radius of influence, carried out with Verlet proximity search method to all particles in particle coverage are calculated
Search, judge one by one ambient particles and calculate particle between spacing and the radius of influence between relationship, determine ambient particles and
It calculates the spacing between particle and is less than the ambient particles of the radius of influence as the proximate particle for calculating particle；Until determining each grain
All proximate particles of son；
Calculating particle is the particle calculated；
Ambient particles are the particles for calculating particle periphery；
The radius of influence is the distance of the grain diameter size setting according to the object that carry out Digital calculation modelling；
4) all proximate particles of each particle are calculated to active force caused by these particles, instantaneous acceleration and wink
Shi Sudu:
It is obtained that external force suffered by model parameter, particle initial density and the particle inputted according to step 2) calculates step 3)
Then all proximate particles of each particle acquire on each particle active force caused by these particles by vector
Suffered resultant force acquires instantaneous acceleration by newton's equation of motion, is solved, is obtained to newton's equation of motion using Verlet integral algorithm
Instantaneous velocity and position to each particle；
All proximate particles of each particle are to use to the calculation of active force caused by these particles
What Hertzian type friction formula and Si Duoke law were calculated,
Hertzian type friction formula is:
Wherein:
δ is the distance being overlapped between i-th of particle and j-th of particle；
Ri、RjIt is the radius of i-th of particle and j-th of particle respectively；
kn、ktIt is the normal direction coefficient of elasticity and tangential coefficient of elasticity between i-th of particle and j-th of particle respectively；kt=
2/7kn；
γn、γtIt is the normal direction damped coefficient and tangential damped coefficient between i-th of particle and j-th of particle respectively；
γt=1/2 γn；
meffIt is the effective mass between i-th of particle and j-th of particle, meff=mimj/(mi+mj)；
mi, mjThe respectively quality of i-th of particle and j-th of particle；
ΔstIt is the tangential displacement vector between i-th of particle and j-th of particle；
nijIt is the unit vector for connecting i-th of particle and j-th of particle centre；
vn、vtIt is the normal component and tangential component of i-th of particle and j-th of particle relative velocity respectively；
T is the time；
I is i-th of particle；
J is all particles in addition to i-th of particle；
The calculation formula of Si Duoke law:
F=-3 π η dv
Wherein:
η is the viscosity of hydrone；
D is the partial size of i-th of particle；
V is the movement velocity of i-th of particle；
The calculation formula of the instantaneous velocity of each particle is:
Wherein:
I is i-th of particle, i.e., the particle calculated；
T is the time；
viIt (t) is speed of i-th of particle in t moment；
riIt (t) is i-th of particle in the position of t moment；
Δ t is time interval；
ri(t- Δ t)) is i-th of particle in the position of t- time Δt；
ri(t- Δ t)) is i-th of particle in the position of t+ time Δt；
O((Δt)2) be Δ t second order it is infinitely small；
5) step 4) is repeated, all proximate particles of each particle obtained to step 4) are to caused by these particles
Active force, instantaneous acceleration and instantaneous velocity are updated；
6) calculated result output module starting in real time, physical quantity needed for counting find out in simulation system particle in phase space
Track after, applied statistics physical principle obtains the macroscopic properties and design feature of system；
7) judge whether simulated time is greater than the total time of setting, if simulated time is greater than the total time of setting, step
5) renewal process terminates, program determination；When institute's simulated time is less than the total time of setting, step 5) is repeated until simulated time
Greater than the total time of setting；Simulated time is the product of step-length and operation step number in step 1)；The total time of the setting is step
It is rapid 1) in step-length and operation step number summation product.
Embodiment:
It is horizontal positioned having a size of 40cm × 10cm × 12cm model casing, wherein the effective dimensions of inscribed case be 10cm ×
Common middle sand (partial size 0.25mm-0.5mm) is slowly uniformly charged stopping when 8cm height of inscribed case by 10cm × 10cm
Sand loading, the baffle for quickly taking out inscribed case flow sand.
Using calculation method of the invention, calculating simulation is carried out to sand flowing in model casing, steps are as follows for specific calculating:
(1) when calculating using molecular dynamics software LAMMPS, a length of 40cm in zoning, width 10cm are set, it is a height of
10cm, a length of 10cm of sand sample size, width 10cm, a height of 8cm, the unit that system is arranged is reduction unit (dimensionless), particle
Shape is considered as spheroidal, ignores the particle diameter distribution of sand grains, and boundary condition is fixed boundary, and the left and right sides and downside are the side wall
Boundary, top are contacted with ambient atmosphere, and calculated diameter takes 3 times of about 2mm of partial size desired value.
(2) it is consistent when sand sample initial position installs sand with inscribed case, initial velocity is set as zero.
(3) Verlet proximity search method is used, with 0.3 times of spacing, ambient particles is judged one by one and calculates between particle
Whether spacing is less than the radius of influence, and the particle is proximate particle if being less than, and and so on, determines that each particle is all one by one
Qualified proximate particle, establishes neighbor list.
(4) according to interaction force between particle in formula (1) and (2) counting system, calculating parameter is as shown in table 1, finds out
The suffered resultant force of particle, and then corresponding acceleration is acquired, corresponding speed is acquired further according to formula (3).
(5) step (4) are repeated, updates the position and speed of each step particle one by one.
(6) according to the required corresponding physical quantity of output, such as the instantaneous velocity of each step, acceleration, position, temperature.
(7) when simulated time is greater than the total time of setting, end loop is calculated.Finally export the thermodynamics number of system
According to: kinetic energy, angular momentum, volume, density, time step and calculating speed etc..
1 calculating parameter table of table
| Parameter name | Value |
| Partial size (mm) | 2 |
| Density (g/cm3) | 2.65 |
| Normal direction elasticity modulus (MPa) | 1 |
| Normal direction damped coefficient | 0.01 |
| Viscosity (kPas) | 535 |
| Time step (s) | 0.001 |
| Population | 115298 |
Finally, it is stated that the above examples are only used to illustrate the technical scheme of the present invention and are not limiting, this field it is general
Lead to it will be appreciated by the skilled person that can be with modification or equivalent replacement of the technical solution of the present invention are made, without departing from the present invention
The objective and range of technical solution, are intended to be within the scope of the claims of the invention.
Claims (1)
1. a kind of calculating simulation method of soil body large deformation flowing, it is characterised in that: the calculating mould of the soil body large deformation flowing
Quasi- method the following steps are included:
1) particle information file is inputted in molecular dynamics Digital calculation modelling software LAMMPS:
Based on counting system feature, first the dimension of setting counting system, unit, particle types, particle radii, boundary condition with
And integral algorithm, create analogue unit；Then counting system essential information is set, the counting system essential information includes but not
It is limited to assemblage, the time interval of output, step-length and operation step number；The counting system is pair of Digital calculation modelling to be carried out
As the object that carry out Digital calculation modelling is the soil body；The counting system is characterized in Digital calculation modelling to be carried out
The physico-mechanical properties of object and locating boundary condition；
2) initial setup module starts, and molecular dynamics Digital calculation modelling software LAMMPS assigns all particles of counting system
Initial position and initial velocity are given, is initialized；External force suffered by input model parameter, particle initial density and particle；Institute
State molecule, atom and the ion that particle is the object that composition will carry out Digital calculation modelling；
3) simulation control module starting, particle proximity search:
According to the particle radius of influence, searched with Verlet proximity search method to all particles in particle coverage are calculated
Rope judges ambient particles one by one and calculates the spacing between particle and the relationship between the radius of influence, determines ambient particles and meter
It calculates the spacing between particle and is less than the ambient particles of the radius of influence as the proximate particle for calculating particle；Until determining each particle
All proximate particles；
The calculating particle is the particle calculated；
The ambient particles are the particles for calculating particle periphery；
The radius of influence is the distance of the grain diameter size setting according to the object that carry out Digital calculation modelling；The shadow
Radius≤L/2 is rung, wherein L is the side length of analogue unit cuboid box；
4) all proximate particles of each particle are calculated to active force caused by these particles, instantaneous acceleration and instantaneous speed
Degree:
It is obtained each that external force suffered by model parameter, particle initial density and the particle inputted according to step 2) calculates step 3)
Then all proximate particles of particle acquire suffered on each particle active force caused by these particles by vector
With joint efforts, instantaneous acceleration is acquired by newton's equation of motion, newton's equation of motion is solved using Verlet integral algorithm, is obtained every
The instantaneous velocity of a particle and position；
All proximate particles of each particle are to use to the calculation of active force caused by these particles
What Hertzian type friction formula and Si Duoke law were calculated,
The Hertzian type friction formula is:
Wherein:
δ is the distance being overlapped between i-th of particle and j-th of particle；
Ri、RjIt is the radius of i-th of particle and j-th of particle respectively；
kn、ktIt is the normal direction coefficient of elasticity and tangential coefficient of elasticity between i-th of particle and j-th of particle respectively；The kt=
2/7kn；
γn、γtIt is the normal direction damped coefficient and tangential damped coefficient between i-th of particle and j-th of particle respectively；It is described
γt=1/2 γn；
meffIt is the effective mass between i-th of particle and j-th of particle, the meff=mimj/(mi+mj)；
mi, mjThe respectively quality of i-th of particle and j-th of particle；
ΔstIt is the tangential displacement vector between i-th of particle and j-th of particle；
nijIt is the unit vector for connecting i-th of particle and j-th of particle centre；
vn、vtIt is the normal component and tangential component of i-th of particle and j-th of particle relative velocity respectively；
T is the time；
I is i-th of particle；
J is all particles in addition to i-th of particle；
The calculation formula of the Si Duoke law is:
F=-3 π η dv
Wherein:
η is the viscosity of hydrone；
D is the partial size of i-th of particle；
V is the movement velocity of i-th of particle；
The calculation formula of the instantaneous velocity of each particle is:
Wherein:
I is i-th of particle, i.e., the particle calculated；
T is the time；
viIt (t) is speed of i-th of particle in t moment；
riIt (t) is i-th of particle in the position of t moment；
Δ t is time interval；
ri(t- Δ t)) is i-th of particle in the position of t- time Δt；
ri(t+ Δ t) is i-th of particle in the position of t+ time Δt；
O((Δt)2) be Δ t second order it is infinitely small；
5) step 4) is repeated, all proximate particles of each particle obtained to step 4) are to effect caused by these particles
Power, instantaneous acceleration and instantaneous velocity are updated；
6) calculated result output module starting in real time, physical quantity needed for counting find out in simulation system all particles in phase space
Track after, applied statistics physical principle obtains the macroscopic properties and design feature of counting system；
7) judge whether simulated time is greater than the total time of setting, if simulated time is greater than the total time of setting, step 5)
Renewal process terminates, program determination；When institute's simulated time is less than the total time of setting, step 5) is repeated until simulated time is greater than
The total time of setting；The simulated time is the product of step-length and operation step number in step 1)；The total time of the setting is step
It is rapid 1) in step-length and operation step number summation product.
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| CN103147451A (en) * | 2013-03-07 | 2013-06-12 | 山东省水利科学研究院 | Method of forming flow control interface of underground flow media |
| CN103678752A (en) * | 2012-08-31 | 2014-03-26 | 住友橡胶工业株式会社 | Method for simulating polymer material |
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