CN103425898B - Cement paste microcosmic digital model generating algorithm - Google Patents

Abstract

The invention provides a cement paste microcosmic digital model generating algorithm which aims at meeting the requirements for current cement-based material hydration reaction research and early-phase material performance prediction and achieving the purposes of being reasonable, clear in concept and high in fitting rate. The grain sizes and the centroid positions of all kinds of microcosmic particles in cement paste are generated according to the Monte Carlo method, cell unit attribute identification can be achieved according to the occupied area exclusion method, and a cyclic boundary is used for simulating a real boundary environment of a digital model. According to the cement paste microcosmic digital model generating algorithm, the microcosmic digital model suitable for cement-based hydration reaction research and early-phase material performance prediction can be built. The cement paste microcosmic digital model generating algorithm is simple, capable of enabling the identification method to be rapid and convenient, high in model fitting rate, clear in concept, and capable of being easily mastered and expanded by a user.

Description

A kind of cement paste microcosmic mathematical model generating algorithm

Technical field

The invention belongs to concrete microcosmic numerical experiment pretreatment technology field, be specially one and based on loop boundary and account for The concrete micromodel generating algorithm of region scalping method, the model generated can be used for the emulation of concrete hydrating process value.

Background technology

Concrete is a kind of heterogeneous multiple dimensioned heterogeneous material, by the little cement granules to micron level and several centimetres, Tens Centimeter Level other coarse aggregate compositions, internal structure is extremely complex.In hydration process, inside concrete can produce nanoscale Other hydrated calcium silicate gel and glue intergranular pore, above solid, liquid, gas three-phase coexistence is in cement-based material, and in disorder distribution State.Concrete is idealized as homogeneous continuous media body by tradition research, have ignored concrete microcosmic level and macro property Internal relation.But research shows: the microstructure of material has decisive role to its molar behavior, for given match ratio The development of cement-based material, intensity and elastic performance is maintained close ties with the development of its internal microstructure.Therefore to cement matrix The research of material should take into account macro property research and microcosmic Mechanism Analysis, starts to recognize cement-based material from hydrated cementitious internal micro- The evolutionary process of microscopical structure, understands cement-based material process of physicochemical change within the whole phase in service life, illustrates water Cement-based material fine sight Structure formation mechanism and and macroscopic view thermal property, relation between mechanical property and deformation performance, ability Fundamentally explain the change of concrete performance, and then lay the foundation for improving the properties of concrete.

Cement paste Study on Microstructure is the basis of concrete microexamination, and wherein numerical experiment is a kind of effective Method, can clearly show the cement paste microstructure real-time change at hydration process, it is provided that hydrated product, distribution of pores All information, beneficially cement paste microstructure formation mechanism study.For obtaining the first requirement of numerical experiment result accurately Set up a rational cement paste 3D microcosmic mathematical model, by four big mineral constituent (C in the given ratio of mud and cement₃S、C₂S、 C₃A and C₄AF granule) volume ratio correctly carries out microscopic particles input and grid cell attribute identification.Only reasonably cement paste Microcosmic mathematical model is being effectively ensured of cement hydration process microexamination.

Therefore find a kind of clear concept, consider comprehensively, can be used for that the cement paste microcosmic of common Project Computer is digital The modeling method of model, to realizing concrete microcosmic numerical experiment, carries out concrete microstructure formation mechanism study, sets up mixed Solidifying soil macro-mechanical property and microstructure connect each other and are of great practical significance.

Summary of the invention

It is an object of the invention to provide a kind of cement paste microcosmic mathematical model generating algorithm, to meet current cement based The needs of the research of material hydration reaction and in early days Optimization of Material Property, reach rationally, purpose that clear concept, qualified rates of fitting are high.

For achieving the above object, the present invention is by the following technical solutions:

A kind of cement paste microcosmic mathematical model generating algorithm, use that Monte Carlo method generates in cement paste is all kinds of micro- See particle diameter and the position of form center of granule, use territory, occupied area scalping method to realize grid cell attribute identification, use loop boundary simulation The real border environment of mathematical model.

When using territory, occupied area scalping method to realize grid cell attribute identification, only the unit centre of form is in (x_i-R_i～x_i+R_i, y_i-R_i～y_i+R_i, z_i-R_i～z_i+R_iGrid cell in the range of) carries out attribute identification and material properties is initial value (Pro- Water) grid cell carries out material properties identification, can increase substantially recognition efficiency, particularly with the numeral examination surpassing million Test Model Identification efficiency to be obviously improved.

When using the real border of loop boundary simulation mathematical model, replace whole description model micro unit true with local Boundary condition, accurately throws in all kinds of mineral constituents, the original state of matching cement mix moment according to cement granules composition.

The cube that cement paste micromodel is length of side L μm mentioned in the present invention, the projection on 3-D walls and floor Scope is (0～L μm, 0～L μm, 0～L μm), and model meshes unit size is 1 μm；The ratio of mud w/c of given model of fit, water Volume ratio v of four big mineral constituents in mud_iAnd particle size rangeFour big mineral constituent material properties are designated as Pro_i。

Being described further below for the inventive method, particular content is as follows:

(1) microscopic particles particle diameter and position of form center are generated

Propose to use Monte Carlo method to complete the input of four big mineral constituent microscopic particles in cement.First basis gives Known conditions calculates the volume V of cement granules_cementVolume V with four big mineral constituents_i, it is shown below:

V_cement=L³/(w/c+1) (1)

V_i=v_i×V_cement (2)

Then use mixed congruence method in a series of pseudo random number μ of [0,1] interval generation₁～μ_j, simple declaration the below The launch process of i kind mineral constituent granule, first obtains this mineral constituent the first by formula (3) Suo Shi in its particle size range The particle diameter of grain:

$R_1=R_i^{\min }+(R_i^{\max }-R_i^{\min }){\mathrm{\μ}}_1---\left(3\right)$

Calculate the volume of this granuleAfter, if V_p1> (1+5%) V_iThen show that this grain diameter is wrong, need weight New input；Otherwise, the relevant information of first granule of record, enter the input of second granule；Second granule is thrown in same Formula (3) is used to generate particle diameter R₂, calculate the volume of this granuleThis volume is added to first granule On volume $V_i^{\mathrm{tol}}=V_{p1}+V_{p2};$

IfV_iThen show that particle overall volume has reached this mineral constituent given volume, then show this granule Particle diameter is wrong, need to again throw in；Otherwise, record the relevant information of this granule, enter the input of next granule, until granule is total VolumeShow that this mineral constituent granule is thrown in complete, enter lower a kind of mineral constituent granule Throw in；

Finally, after completing the input of all cement minerals component particles, to all grain diameters by order from big to small It is ranked up.

(2) model each grid cell attribute identification

Use territory, occupied area scalping method to complete model each grid cell attribute identification, all grid cell initial attributes are set For water, it is designated as Pro-water, briefly describes the identification of grid cell attribute in the range of certain granule i below:

Use mixed congruence method to generate a series of pseudo random number [0,1] is interval, use method as shown in formula (3) with Machine generates the centre of form coordinate (x of granule i_i, y_i, z_i).Then the unit centre of form is in (x_i-R_i～x_i+R_i, y_i-R_i～y_i+R_i, z_i- R_i～z_i+R_iGrid cell in the range of) carries out attribute identification, if the centre of form of certain unit is positioned in the range of granule i (such as Fig. 3 (a) Shown in), then it is assumed that this grid cell attribute is Pro_iOtherwise, do not change this grid cell attribute (as shown in Fig. 3 (b))；

$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}\≤R_i$ In the range of granule i (4)

During identifying, every run into the grid cell that material properties is not equal to Pro-water, then it is assumed that this grid list Unit is belonging to certain mineral constituent, it is no longer necessary to carry out material properties identification decision, here it is territory, occupied area scalping method.Employing accounts for Region scalping method can be greatly improved grid cell recognition efficiency.

(3) loop boundary definition

The sub-fraction of actual cement slurry it is only, it is therefore desirable to use loop boundary as this in view of model micro unit The boundary condition of micromodel in invention, i.e. utilizes boundary condition to substitute the selected portion (system) shadow by periphery (environment) Ringing, concrete grammar is as follows:

For granule i, work as x_i-R_i< when 0, the unit scope of cell attribute identification need to be carried out and include following two parts:

(0～x_i+R_i, y_i-R_i～y_i+R_i, z_i-R_i～z_i+R_i) and (x_i-R_i+ L～L, y_i-R_i～y_i+R_i, z_i-R_i～z_i+R_i)

Decision condition should be respectively defined as:

$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}\&le;R_i$ In the range of granule i (5)

$\sqrt{{(x-(x_i+L))}^2+{(y-y_i)}^2+{(z-z_i)}^2}\&le;R_i$

In formula, x, y, z is the centre of form coordinate of recognition unit；

Work as x_i+R_i> L time, the unit scope of cell attribute identification need to be carried out and include following two parts:

(x_i-R_i～L, y_i-R_i～y_i+R_i, z_i-R_i～z_i+R_i) and (0～x_i+R_i-L, y_i-R_i～y_i+R_i, z_i-R_i～z_i+R_i)

Decision condition should be respectively defined as:

$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}\&le;R_i$ In the range of granule i (6)

$\sqrt{{(x-(x_i-L))}^2+{(y-y_i)}^2+{(z-z_i)}^2}\&le;R_i$

When granulometric range exceeds border in y, z-axis, use loop boundary equally, with reference to formula (5), formula (6) Method be analyzed, as shown in formula (7)～(10):

$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}\&le;R_i$ In the range of granule i (7)

$\sqrt{{(x-x_i)}^2+{(y-(y_i+L))}^2+{(z-z_i)}^2}\&le;R_i$

$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}\&le;R_i$ In the range of granule i (8)

$\sqrt{{(x-x_i)}^2+{(y-(y_i-L))}^2+{(z-z_i)}^2}\&le;R_i$

$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}\&le;R_i$ In the range of granule i (9)

$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-(z_i+L))}^2}\&le;R_i$

$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}\&le;R_i$ In the range of granule i (10)

$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-(z_i-L))}^2}\&le;R_i$

The invention has the beneficial effects as follows: the present invention can build and be applicable to the research of cement based hydration reaction and early stage material property The microcosmic mathematical model of prediction, the algorithm of the present invention is simple, recognition methods is quick, models fitting rate height, clear concept, be prone to make User grasps and extension.

Accompanying drawing explanation

Fig. 1 cement paste microcosmic mathematical model product process figure；

Fig. 2 a is concrete scroll schematic diagram in cement paste microcosmic mathematical model

Fig. 2 b is C in cement paste microcosmic mathematical model₃S showing particle distribution；

Fig. 2 c is C in cement paste microcosmic mathematical model₂S showing particle distribution；

Fig. 2 d is C in cement paste microcosmic mathematical model₃A showing particle distribution；

Fig. 2 e is C in cement paste microcosmic mathematical model₄AF showing particle distribution；

Fig. 3 a is grid cell attribute identification schematic diagram (in the range of the centre of form of unit is positioned at granule i)；

Fig. 3 b is grid cell attribute identification schematic diagram (it is outer that the centre of form of unit is positioned at granule i scope).

Detailed description of the invention

Below in conjunction with detailed description of the invention, the present invention will be further described.

Key step flow chart of the present invention is as it is shown in figure 1, the specific embodiment party of the accompanying drawings present invention in detail below Method:

Step 1, setting up the length of side is L μm cement paste microcosmic cube model, and unit grids size is equal to 1 μm；

Step 2, reads in the ratio of mud of simulation cement paste, four big mineral constituent content and particle diameter distribution thereof；

Step 3, calculates cement granules volume by formula (1)；

Step 4, to four class mineral constituent circulations, calculates the volume V of this mineral constituent_i, and depend on by its size distribution profile The particle diameter (unit μm, round) of each granule of this mineral constituent of secondary generation:

Step 5, it is determined whether proceed this mineral constituent granule and throw in

(1) the cumulative volume V of granule has been generated when this mineral constituent_i ^tol< (1-5%) V_iTime, proceed this mineral constituent Grain is thrown in, and adds up this mineral constituent and has generated total number and the cumulative volume of granule；

(2) cumulative volume (1-5%) V of granule has been generated when this mineral constituent_i≤V_i ^tol≤ (1+5%) V_iTime, terminate this ore deposit Thing component particles is thrown in, and adds up this mineral constituent and has generated total number and the cumulative volume of granule；

(3) the cumulative volume V of granule has been generated when this mineral constituent_i ^tol> (1+5%) V_iTime, current input granule mistake, need Regenerate particle diameter, return step 4；

All granules are circulated by step 6, the position of form center x of stochastic generation granule i_i, y_i, z_i；

Step 7, carries out grid cell attribute identification；

(1) if x_i-R_i>=0, enter step 8；

(2) otherwise, then to (0～x_i+R_i, y_i-R_i～y_i+R_i, z_i-R_i～z_i+R_i) and (x_i-R_i+ L～L, y_i-R_i～y_i+ R_i, z_i-R_i～z_i+R_iUnit traveling material properties identification in the range of), if all unit material attributes meeting formula (5) condition are equal For Pro-water, then show that this particle position is reasonable, give the material properties that above unit is new；Otherwise, then this granule position is shown Putting mistake, return step 6, impressions adds up 1；

Step 8, (1) if x_i+R_i≤ L, enters step 9；

(2) otherwise, then to (x_i-R_i～L, y_i-R_i～y_i+R_i, z_i-R_i～z_i+R_i) and (0～x_i+R_i-L, y_i-R_i～y_i+ R_i, z_i-R_i～z_i+R_iUnit traveling material properties identification in the range of), if all unit material attributes meeting formula (6) condition are equal For Pro-water, then show that this particle position is reasonable, give the material properties that above unit is new；Otherwise, then this granule position is shown Putting mistake, return step 6, impressions adds up 1；

Step 9, (1) if y_i-R_i>=0, enter step 10；

(2) otherwise, then to (x_i-R_i～x_i+R_i, 0～y_i+R_i, z_i-R_i～z_i+R_i) and (x_i-R_i～x_i+R_i, y_i-R_i+ L～ L, z_i-R_i～z_i+R_iUnit traveling material properties identification in the range of), if all unit material attributes meeting formula (7) condition are equal For Pro-water, then show that this particle position is reasonable, give the material properties that above unit is new；Otherwise, then this granule position is shown Putting mistake, return step 6, impressions adds up 1；

Step 10, (1) if y_i+R_i≤ L, enters step 11；

(2) otherwise, then to (x_i-R_i～x_i+R_i, y_i-R_i～L, z_i-R_i～z_i+R_i) and (x_i-R_i～x_i+R_i, 0～y_i+R_i- L, z_i-R_i～z_i+R_iUnit traveling material properties identification in the range of), if all unit material attributes meeting formula (8) condition are equal For Pro-water, then show that this particle position is reasonable, give the material properties that above unit is new；Otherwise, then this granule position is shown Putting mistake, return step 6, impressions adds up 1；

Step 11, (1) if z_i-R_i>=0, enter step 12；

(2) otherwise, then to (x_i-R_i～x_i+R_i, y_i-R_i～y_i+R_i, 0～z_i+R_i) and (x_i-R_i～x_i+R_i, y_i-R_i～y_i+ R_i, z_i-R_i+ L～L) in the range of unit traveling material properties identification, if all unit material attributes meeting formula (9) condition are Pro-water, then show that this particle position is reasonable, give the material properties that above unit is new；Otherwise, then this particle position is shown Mistake, returns step 6, and impressions adds up 1；

Step 12, (1) if z_i+R_i≤ L, enters step 13；

(2) otherwise, then to (x_i-R_i～x_i+R_i, y_i-R_i～y_i+R_i, z_i-R_i～L) and (x_i-R_i～x_i+R_i, y_i-R_i～y_i+ R_i, 0～z_i+R_i-L) in the range of unit traveling material properties identification, if all unit material attributes meeting formula (8) condition are Pro-water, then show that this particle position is reasonable, give the material properties that above unit is new；Otherwise, then this particle position is shown Mistake, returns step 6, and impressions adds up 1；

Step 12, then to (x_i-R_i～x_i+R_i, y_i-R_i～y_i+R_i, z_i-R_i～z_i+R_iUnit traveling material properties in the range of) Identify, if all unit material attributes meeting formula (4) condition are Pro-water, then show that this particle position is reasonable, give The material properties that above unit is new；Otherwise, then showing this particle position mistake, return step 6, impressions adds up 1；

Step 13, repeats step 6～12 until unit identification in completing all granulometric ranges, if impressions exceedes 10000 times, show to complete granule and throw in and unsuccessfully return step 3 and regenerate new a collection of microscopic particles particle diameter distribution.

Step 14, exports the material properties of all unit.

Little wild field three-dimensional cement paste microcosmic mathematical model, cube size 100 μ m 100 μm is built according to above step × 100 μm, unit grid size 1 μm, unit sum 1000000, throw in through cement granules and after grid cell identification, obtain Result shown in accompanying drawing 2, in micromodel, cement granules and four big mineral constituent distribution of particles are reasonable, and models fitting rate is high, available In the research of cement-based material hydration reaction and Optimization of Material Property emulation in early days.

Claims (5)

1. a cement paste three-dimensional microcosmic model generation algorithm, it is characterised in that: use Monte Carlo method to generate cement paste In the particle diameter of all kinds of microscopic particles and position of form center, use territory, occupied area scalping method to realize grid cell attribute identification, use circulation The real border of boundary condition simulation mathematical model；Monte Carlo method is used to generate microscopic particles particle diameter and the concrete steps of position of form center For:

Propose to use Monte Carlo method to complete the input of four big mineral constituent microscopic particles in cement, first known according to give Condition calculates the volume V of cement granules_cementVolume V with four big mineral constituents_i, it is shown below:

V_cement=L³/(w/c+1) (1)

V_i=v_i×V_cement (2)

Then use mixed congruence method in a series of pseudo random number μ of [0,1] interval generation₁～μ_j, i-th kind of mineral constituent granule Launch process: first by the particle diameter obtaining this first granule of mineral constituent formula (3) Suo Shi in its particle size range:

$R_1=R_i^{\min }+(R_i^{\max }-R_i^{\min }){\mathrm{\&mu;}}_1---\left(3\right)$

Calculate the volume of this granuleAfter, if V_p1＞ (1+5%) V_iThen show that this grain diameter is wrong, need again Throw in；Otherwise, the relevant information of first granule of record, enter the input of second granule；Second granule is thrown in and is adopted equally Particle diameter R is generated with formula (3)₂, calculate the volume of this granuleThis volume is added to the body of first granule Long-pending upper V_i ^tol=V_p1+V_p2；

If V_i ^tol＞ (1+5%) V_iThen show that particle overall volume has reached this mineral constituent given volume, then show this grain diameter Wrong, need to again throw in；Otherwise, record the relevant information of this granule, enter the input of next granule, until particle overall volume (1-5%) V_i≤V_i ^tol≤ (1+5%) V_i, show that this mineral constituent granule is thrown in complete, enter lower a kind of mineral constituent granule and throw Put；

Finally, after completing the input of all cement minerals component particles, all grain diameters are carried out by order from big to small Sequence；

Meaning of parameters illustrates: cement paste micromodel is the cube of length of side L μm, and the drop shadow spread on 3-D walls and floor is (0～L μm, 0～L μm, 0～L μm), model meshes unit size is 1 μm；The ratio of mud w/c of given model of fit, in cement four Volume ratio v of big mineral constituent_iAnd particle size rangeFour big mineral constituent material properties are designated as Pro_i。

2. cement paste three-dimensional microcosmic model generation algorithm as claimed in claim 1, it is characterised in that: use territory, occupied area to reject When method realizes grid cell attribute identification, only the unit centre of form is in (x_i-R_i～x_i+R_i,y_i-R_i～y_i+R_i,z_i-R_i～z_i+R_i) In the range of grid cell carry out attribute identification and the grid cell that material properties is initial value carries out material properties identification, this is first Initial value i.e. Pro-water.

3. cement paste three-dimensional microcosmic model generation algorithm as claimed in claim 2, it is characterised in that: use territory, occupied area to reject Method realizes concretely comprising the following steps of grid cell attribute identification:

Use territory, occupied area scalping method to complete model each grid cell attribute identification, all grid cell initial attributes are set as Water, is designated as Pro-water, the identification of grid cell attribute in the range of certain granule i:

Use mixed congruence method in a series of pseudo random number of [0,1] interval generation, use the method as shown in formula (3) to give birth at random Become the centre of form coordinate (x of granule i_i,y_i,z_i), then the unit centre of form is in (x_i-R_i～x_i+R_i,y_i-R_i～y_i+R_i,z_i-R_i～z_i +R_iGrid cell in the range of) carries out attribute identification, if in the range of the centre of form of certain unit is positioned at granule i, then it is assumed that this grid list Meta-attribute is Pro_iOtherwise, do not change this grid cell attribute；

$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}\&le;R_i$ In the range of granule i (4)

During identifying, every run into the grid cell that material properties is not equal to Pro-water, then it is assumed that this grid cell is Belong to certain mineral constituent, it is no longer necessary to carry out material properties identification decision, here it is territory, occupied area scalping method.

4. cement paste three-dimensional microcosmic model generation algorithm as claimed in claim 1, it is characterised in that: use loop boundary mould When intending the real border of mathematical model, replace whole description model micro unit real border condition with local.

5. cement paste three-dimensional microcosmic model generation algorithm as claimed in claim 4, it is characterised in that: use loop boundary mould The real border body intending mathematical model uses following steps to realize:

For granule i, work as x_i-R_iDuring ＜ 0, the unit scope of cell attribute identification need to be carried out and include following two parts:

(0～x_i+R_i,y_i-R_i～y_i+R_i,z_i-R_i～z_i+R_i) and (x_i-R_i+ L～L, y_i-R_i～y_i+R_i,z_i-R_i～z_i+R_i)

Decision condition should be respectively defined as:

In formula, x, y, z is the centre of form coordinate of recognition unit；

Work as x_i+R_iDuring ＞ L, the unit scope of cell attribute identification need to be carried out and include following two parts:

(x_i-R_i～L, y_i-R_i～y_i+R_i,z_i-R_i～z_i+R_i) and (0～x_i+R_i-L,y_i-R_i～y_i+R_i,z_i-R_i～z_i+R_i)

Decision condition should be respectively defined as:

When granulometric range exceeds border in y, z-axis, use loop boundary equally, with reference to formula (5), the side of formula (6) Method is analyzed, as shown in formula (7)～(10):

Step 1, (1) if x_i-R_i>=0, enter step 2；

(2) otherwise, then to (0～x_i+R_i,y_i-R_i～y_i+R_i,z_i-R_i～z_i+R_i)

(x_i-R_i+ L～L, y_i-R_i～y_i+R_i,z_i-R_i～z_i+R_iUnit traveling material properties identification in the range of), meets if all The unit material attribute of formula (5) condition is Pro-water, then show that this particle position is reasonable, give the material that above unit is new Material attribute；Otherwise, then this particle position mistake is shown；

Step 2, (1) if x_i+R_i≤ L, enters step 3；

(2) otherwise, then to (x_i-R_i～L, y_i-R_i～y_i+R_i,z_i-R_i～z_i+R_i)

(0～x_i+R_i-L,y_i-R_i～y_i+R_i,z_i-R_i～z_i+R_iUnit traveling material properties identification in the range of), meets if all The unit material attribute of formula (6) condition is Pro-water, then show that this particle position is reasonable, give the material that above unit is new Material attribute；Otherwise, then this particle position mistake is shown；

Step 3, (1) if y_i-R_i>=0, enter step 4；

(2) otherwise, then to (x_i-R_i～x_i+R_i, 0～y_i+R_i,z_i-R_i～z_i+R_i)

(x_i-R_i～x_i+R_i,y_i-R_i+ L～L, z_i-R_i～z_i+R_iUnit traveling material properties identification in the range of), meets if all The unit material attribute of formula (7) condition is Pro-water, then show that this particle position is reasonable, give the material that above unit is new Material attribute；Otherwise, then this particle position mistake is shown；

Step 4, (1) if y_i+R_i≤ L, enters step 5；

(2) otherwise, then to (x_i-R_i～x_i+R_i,y_i-R_i～L, z_i-R_i～z_i+R_i) and (x_i-R_i～x_i+R_i, 0～y_i+R_i-L,z_i- R_i～z_i+R_iUnit traveling material properties identification in the range of), if all unit material attributes meeting formula (8) condition are Pro- Water, then show that this particle position is reasonable, give the material properties that above unit is new；Otherwise, then show that this particle position is wrong By mistake；

Step 5, (1) if z_i-R_i>=0, enter step 6；

(2) otherwise, then to (x_i-R_i～x_i+R_i,y_i-R_i～y_i+R_i, 0～z_i+R_i) and (x_i-R_i～x_i+R_i,y_i-R_i～y_i+R_i,z_i- R_i+ L～L) in the range of unit traveling material properties identification, if all unit material attributes meeting formula (9) condition are Pro- Water, then show that this particle position is reasonable, give the material properties that above unit is new；Otherwise, then show that this particle position is wrong By mistake；

Step 6, (1) if z_i+R_i≤ L, enters step 7；

(2) otherwise, then to (x_i-R_i～x_i+R_i,y_i-R_i～y_i+R_i,z_i-R_i～L) and (x_i-R_i～x_i+R_i,y_i-R_i～y_i+R_i,0 ～z_i+R_i-L) in the range of unit traveling material properties identification, if all unit material attributes meeting formula (8) condition are Pro- Water, then show that this particle position is reasonable, give the material properties that above unit is new；Otherwise, then show that this particle position is wrong By mistake；

Step 7, then to (x_i-R_i～x_i+R_i,y_i-R_i～y_i+R_i,z_i-R_i～z_i+R_iUnit traveling material properties identification in the range of), If all unit material attributes meeting formula (4) condition are Pro-water, then show that this particle position is reasonable, more than imparting The material properties that unit is new；Otherwise, then this particle position mistake is shown.