CN104931400A - Quantitative test and image analysis method of particle material pore fabric - Google Patents

Abstract

A quantitative test and image analysis method of a particle material pore fabric comprises following steps: step 1, performing theoretical definition on a tensor of the particle material pore fabric; step 2, standardizing test steps of the particle material pore fabric; step 3, compiling an image processing and image analysis program according to the theoretical definition of the tensor of the particle material pore fabric, wherein the quantitative test and image analysis of the particle material pore fabric mean that a material microscomic image is collected by experiments, and orthotropy of particle material pore special distribution is described by using the image processing and analysis technology. A theoretical frame of the material pore fabric is described based on a morphology principle, a new quantitative description method for orthotropy pore tensor of sand soil is provided, in the method, the three dimensional orthotropy pore distribution is described by any two amplitude values on an orthogonal surface, and transverse isotropy pore distribution is described by one amplitude value parameter.

Description

The quantitative test of particulate material hole group structure and image analysis method

Technical field:

The grand mesomechanics that the present invention relates to particulate material, friction material and mushy material calculates its constitutive relation research, particularly a kind of quantitative test of particulate material hole group structure and image analysis method.

Background technology:

Void ratio controls one of soil body mechanical response most critical, most widely used physical characteristics of materials parameter.In critical state soil mechanics, it describes the unique Material Physics parameter of critical conditions.Recently, Li and Dafalias (2012), Zhao and Guo (2013), Abouzar etc. (2014) research confirms due to the anisotropic existence of the soil body carefully sight group structure, its critical conditions line is not unique, namely the relation of critical conditions void ratio and hydrostatic force is not unique, and this uniqueness to soil mechanics critical conditions line hypothesis is a challenge.Although the substantial effect of group structure to soil body mechanical property is rooted in the hearts of the people, but relatively lag behind owing to carefully seeing measuring technology, test and description theory development, the shortcoming causing hole group structure description theory to be familiar with, seriously constrains the grand thin research seeing its mechanical characteristic of contact description.

Hilliard (1967) sets up the mathematical framework of morphology principle quantitative test soil body hole tensor the earliest, with p-wire in Different Plane, space quantitative measurement distribution of pores.Afterwards, Kanatani (1984,1985) Hilliard method is extended to the form of Cartesian coordinates tensor, and first the Hilliard method solving different problem being unified into unique mathematical framework---Buffon converts, the inverse transformation of Buffon of having derived conversion, it directly can use p-wire intersection point determination fabric tensor.Kuo and Frost (1996,1997), Kuo etc. (1998) and Jang and Frost (1999,2000), based on stereometry combining image analytical technology, provide a kind of powerful fabric tensor analytical approach.Domestic image technique experimental study aspect: loud, high-pitched sound etc. (2005) measure soil test with structure interface in thin sight of sand grains move.The SEM image three-dimensional visualization of Wang Baojun etc. (2008) etc. and the research of weak soil porosity calculation; The Changing Pattern research of the clay microscopic void that Zhang Xianwei etc. (2012) test based on SEM and MIP; Nearest Xu celebrating waits (2015) based on the weak soil porosimeter calculation and Analysis of SEM image; These experimental study achievements are for having done Beneficial by the thin micromechanism of the image technique research soil body.

But in existing hole group structure describing method, there is description process all in various degree and exist and artificial to judge and operation, or have that assay method is easy not and physical significance is unintelligible waits deficiency.

Summary of the invention:

In view of this, quantitative test and image analysis method that a kind of particulate material hole group structure is provided is necessary.The present invention is based on the theoretical frame of morphology principle quantitative description hole group structure, propose a kind of description new method of sand orthotropy hole tensor.The method adopts normalized thought to redefine hole tensor, and the mark perseverance of definition tensor is one, and the theory greatly facilitating it is determined.The tensor of new definition is based on mathematical probabilities statistical method, and the discrete feature of hole is converted into the group structure characteristic parameter surveyed in the plane, its physical significance is clear.

The quantitative test of particulate material hole group structure and an image analysis method, is characterized in that: particulate material hole group structure quantitative test and image analysis method following steps: step one, carries out theoretical definition to particulate material hole fabric tensor; Step 2, carries out specification to particulate material hole group structure determination step; Step 3, according to the theoretical definition of particulate material hole fabric tensor, writes the program of image procossing and graphical analysis;

The quantitative measurement of particulate material hole group structure and graphical analysis, refer to and adopt experiment to gather image, describe the orthotropy of particulate material pore space distribution with image procossing and image analysis technology.

Image procossing and image analysis program are image procossing Matlab program and graphical analysis Matlab program.

The idiographic flow of image procossing and image analysis program is: particulate material solidifies and meso-cracking Image Acquisition, gather the thin sight picture of particulate material, the thin sight picture collection of particulate material needs to be cured particulate material sample with hardening agent, then through cutting, grinding, polishing, metal spraying process, obtain the thin sight image of particulate material, gather picture with SEM again, picture is used for image procossing and graphical analysis, image procossing, the picture gathered with SEM, through gray-scale pixels, denoising, level and smooth, equalization, medium filtering, binaryzation, optimized treatment method, finally obtains the image for sample particulate material distribution of pores, the determination of mean porosities, the key element of morphology principle particle tested material hole group structure is p-wire, what particulate material hole was added up is pixel shared by binary image mesoporosity, namely porosity is the ratio of hole pixel summation and p-wire pixel, in image analysis program, particulate material sample image process figure carries out AND operation, the image that acquisition p-wire and sample hole occur simultaneously, extract hole data, the mean porosities of image hole is obtained by graphical analysis Matlab program and image procossing Matlab program computation, comprehensive multiple picture obtains the mean porosities of particulate material sample, the plane distribution of porosity is determined, in order to obtain particulate material plane distribution of pores rule, uses annular p-wire form, measures the plane distribution situation of circle ring area endoparticle material hole with annular p-wire.

Adopt the orthotropy of the pore space distribution of morphology principles illustrated particulate material, the theoretical definition of particulate material hole fabric tensor is for shown in formula one:

Formula one: $M_{i_1{i}_2...i_m}=\frac{{\∫}_{\mathrm{\Ω}}{n}_{i_1{i}_2...i_m}{n}_{\mathrm{im}}{L}_L(\mathrm{\α},\mathrm{\β})d\stackrel{\→}{n}}{{\∫}_{\mathrm{\Ω}}{L}_L(\mathrm{\α},\mathrm{\β})d\stackrel{\→}{n}}$

In formula one: for the generalized definition of particulate material hole fabric tensor; for the durection component of m rank particulate material hole fabric tensor, L _l(α, β) is distribution of pores function, and its value is the ratio of p-wire and hole; value is tensor unit direction vector; Ω is integrating range; Second order particulate material hole fabric tensor is for shown in formula two:

Formula two: $M_{\mathrm{ij}}=\frac{{\∫L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)n_i{n}_{j}d\stackrel{\→}{n}}{{\∫L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)d\stackrel{\→}{n}}$

In formula two: M _ijfor Second-order Symmetric particulate material hole fabric tensor, n _in _jfor the durection component of second order granular material hole fabric tensor, in image analysis program, adopt formula three:

Formula three: $M_{\mathrm{ij}}=\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}\frac{L_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)n_i{n}_j}{N}}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}\frac{L_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}{N}}=\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)n_i{n}_j}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}$

F ₁-F ₃space, formula four:

Formula four: $\left.\begin{array}{c}{b}_1=\sqrt{J_2}=\sqrt{\frac{1}{2}{(M_{11}-M_{33})}^2+{M_{13}}^2}\\ {\mathrm{\θ}}_1=\frac{1}{2}\arctan \frac{2M_{13}}{M_{11}-M_{33}}\end{array}\right\}$

F ₁-F ₂space, formula five:

Formula five: $\left.\begin{array}{c}{b}_2=\sqrt{J_2}=\sqrt{\frac{1}{4}{(M_{11}-M_{22})}^2+{M_{12}}^2}\\ {\mathrm{\θ}}_2=\frac{1}{2}\arctan \frac{2M_{12}}{M_{11}-M_{22}}\end{array}\right\}$

F ₂-F ₃space, formula six:

Formula six: $\left.\begin{array}{c}{b}_3=\sqrt{J_2}=\sqrt{\frac{1}{4}{(M_{22}-M_{33})}^2+{M_{23}}^2}\\ {\mathrm{\θ}}_3=\frac{1}{2}\arctan \frac{2M_{23}}{M_{22}-M_{33}}\end{array}\right\}$

Formula four, formula five are with formula six: F ₁-F ₃space, F ₁-F ₂space and F ₂-F ₃space is three different spaces of particulate material, M _ij(i, j=1,2,3) are the component of second order particulate material hole group structure in formula three; b _i(i=1,2,3) are the hole amplitude parameter on three normal surfaces, are invariants, and be also the scalar of reflection anisotropic degree, its theoretical span is 0 to 1, works as b _iwhen=0, porous nickel distributes, and sample is isotropy; Work as b _iwhen=1, sample imporosity; θ _i=0 is a point measuring angle, reflects anisotropic orientation;

After plane hole amplitude parameter size and Orientation is determined, its plane distribution function is for shown in formula seven:

Formula seven: N (n _i, θ) and=n _i(1+b _icos2 (θ-θ _i))

In formula: N (n _i, θ) and be plane distribution of pores function; n _i(i=1,2,3) are the mean porosities on three normal surfaces; θ planimetric coordinates parameter.

Owing to defining particulate material orthotropy particulate material hole fabric tensor, the transverse isotropy tensor of three different conditions, the mark perseverance of the particulate material hole fabric tensor of definition is 1, two are only had in above definition three amplitude parameter independent variation amounts, therefore only any two parameters in three normal surfaces of particulate material need be measured, its hole orthotropy particulate material hole fabric tensor can uniquely be determined, its concrete formula is as follows:

B ₁with b ₂the fabric tensor 1 that hole parameter is determined,

Formula eight: $M_{\mathrm{ij}}=\frac{1}{3+b_1+b_2-b_1{b}_2}\left[\begin{array}{ccc}1+b_1+b_2+b_1{b}_2& & \\ & 1+b_1-b_2-b_1{b}_2& \\ & & 1-b_1+b_2-b_1{b}_2\end{array}\right]$

B ₁with b ₃the fabric tensor 2 that hole parameter is determined,

Formula nine: $M_{\mathrm{ij}}=\frac{1}{3-b_1-b_3-b_1{b}_3}\left[\begin{array}{ccc}1+b_1-b_3-b_1{b}_3& & \\ & 1-b_1+b_3-b_1{b}_{2=3}& \\ & & 1-b_1-b_3+b_1{b}_3\end{array}\right]$

B ₃with b ₂the fabric tensor 3 that hole parameter is determined,

Formula ten: $M_{\mathrm{ij}}=\frac{1}{3-b_2+b_3+b_2{b}_3}\left[\begin{array}{ccc}1+b_2+b_3+b_2{b}_3& & \\ & 1-b_2+b_3-b_2{b}_3& \\ & & 1-b_2-b_3+b_2{b}_3\end{array}\right]$

Two principal components in particulate material hole fabric tensor are equal, so for Axial symmetric anisotropy sample, only need a scalar parameter just corresponding fabric tensor of definable;

In formula four and formula five, work as β _m=π/4, sin β _m=cos β _m, then b ₁=b ₂, this both direction hole parameter is equal, and so material shows as transverse isotropy, and formula eight deteriorates to transverse isotropy three-dimensional group configuration formula:

Formula 11: $M_{\mathrm{ij}}=\frac{1}{3-b}\left[\begin{array}{ccc}1+b& 0& 0\\ 0& 1-b& 0\\ 0& 0& 1-b\end{array}\right]$

In formula:

Formula 12: $b=\sqrt{{\left[\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)({\cos }^2{\mathrm{\α}}_m-\frac{1}{2}{\sin }^2{\mathrm{\α}}_m)}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right]}^2+\frac{1}{2}{\left(\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)\sin 2{\mathrm{\α}}_m}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right)}^2}$

In formula 12: b is the amplitude parameter of transverse isotropy hole tensor, obtain plane hole fabric tensor invariant according to any one face in two same sex faces and obtain, b ₁=b ₂=b shows that the hole tensor invariant of these two planes is equal, and formula eight can describe the transverse isotropy of particulate material hole with an amplitude parameter, may be used for the transverse isotropy characteristic describing topsoil; In like manner, as α in formula four _m=pi/2, and β in formula six _mwhen=0, then b ₁=b ₃, formula nine also can deteriorate to the form of transverse isotropy such as formula shown in 13:

Formula 13: $M_{\mathrm{ij}}=\frac{1}{3+b}\left[\begin{array}{ccc}1+b& 0& 0\\ 0& 1+b& 0\\ 0& 0& 1-b\end{array}\right]$

In formula:

Formula 14: $b=\sqrt{{\left[\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)\cos 2{\mathrm{\α}}_m}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right]}^2+\frac{1}{2}{\left(\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)\sin 2{\mathrm{\α}}_m}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right)}^2}$

In formula 14: b transverse isotropy hole parameter, in formula five, as β in formula six _mduring=pi/2, then b ₂=b ₃, formula ten also can deteriorate to:

Formula 15: $M_{\mathrm{ij}}=\frac{1}{3+b^2}\left[\begin{array}{ccc}{(1+b)}^2& 0& 0\\ 0& 1-b^2& 0\\ 0& 0& {(1-b)}^2\end{array}\right]$

In formula 15: the expression formula of b is identical with formula 14 form, and formula 15 remains orthotropic form.

The sample of particulate material hole group structure quantitative test and graphical analysis adopts sand sample, and the picture that SEM gathers is Tengger desert aeolian sand undisturbed, and enlargement factor is 150 times.

Collection, the making of sample use cuboid sample.

In image procossing, the binaryzation of the picture gathered with SEM comprises: Two-peak method, OTSU method, empty completion method, adhesion granule morphology, adhesion particle watershed algorithm are split.

Particulate material, due to the existence of its hole, causes its solid, liquids and gases three-phase medium composition, also result in the mechanical characteristic of its complexity.The most complicated three-dimensional orthogonal hole is carefully seen characteristic and is calculated demarcation by theoretical and test method by the present invention, quantitative measurement can go out the changes in spatial distribution rule of multiple particulate material meso-cracking group structure, draw corresponding hole magnitude parameters, for various underground engineering design, construction provide theoretic prediction methods.The present invention adopts normalized thought to redefine particulate material hole fabric tensor, and the mark perseverance of definition tensor is one, and the theory greatly facilitating it is determined.The method that the particulate material hole fabric tensor of new definition is added up based on mathematical probabilities, discrete pore characteristic is converted into the group structure characteristic parameter surveyed in the plane, its physical significance is clear.

Accompanying drawing illustrates:

Fig. 1 is particulate material hole group structure quantitative test process flow diagram.

In figure: particulate material hole group structure quantitative test step s1 ~ s8.

Embodiment:

Particulate material hole group structure is carefully seen measuring technology and is decided by its theoretical definition.At present main measuring technology has two classes: one is the method for hole fabric theory based on Oda (1976), Bhatia and Soliman (1990) tests by the method, Al-Shibli (2001) also extracts hole directional spreding direction by the method, and contrast with the method for Oda, the method artificially judges and operation because relating to the link needs such as particle center of gravity, polygon, process is loaded down with trivial details, measures difficulty; Two is the hole group structure defining method by morphology principle, and the method is based on the work of (1984,1985) such as Kanatani, and Kuo etc. (1996,1997) have done the quantitative detection of sand hole tensor.The present invention adopts the second theoretical method---and morphology principle, redefines particulate material hole fabric tensor, and exploitation process analysis calculates.

Because void ratio describes the unique Material Physics parameter of critical state soil mechanics, in current soil mechanics, soil body-shield machine system theory is also relatively immature, and many mechanical characteristics of the soil body all cannot describe.In addition, the inherent mechanism of soil body mechanical characteristic is that it carefully sees characteristic, therefore the present invention proposes quantitative description particulate material meso-cracking characteristic, and the thin sight mechanism description for its macro-mechanical characters has been established theoretical foundation and proposed concrete test method.Soil mechanics theory immature, building, traffic, water conservancy and mineral exploration and exploitation etc. is made to relate to the design and construction overwhelming majority dependence experience of underground works, theoretical application is considerably less, and therefore reasonable application of the present invention, the theoretical prediction that can be the damage of soil body mechanism related in underground works lays the foundation.

Present embodiment provides a kind of preferred embodiment one:

Embodiment one: according to the Theoretical Determination of the particulate material hole fabric tensor that inventor proposes, develop graphical analysis and the image procossing Matlab program of the theory of particulate material hole fabric tensor, main-process stream as shown in Figure 1, give the mensuration main-process stream of whole meso-cracking group structure in Fig. 1, concrete steps are:

Step s1, sample, grinding, polishing, metal spraying are cut in sand sample solidification, cube;

Step s2, the SEM obtaining three normal surfaces carefully sees image;

Step s3, image procossing;

Step s4, draws parallel testing line and annular p-wire;

Step s5, graphical analysis, calculating obtain distribution of pores function;

Step s6, Calculation Plane tensor;

Step s7, calculates amplitude parameter and direction;

Step s8, calculates and obtains three-dimensional pore space fabric tensor.

Because the fundamental purpose of research is the orthotropy measuring hole tensor, therefore sample collection, make and need to use cuboid sample.

In Fig. 1, exploitation program is made up of two parts, and one is image procossing Matlab program, its objective is reduce environmental factor interference, obtain clearly binary picture so that graphical analysis.Two is graphical analysis Matlab programs, is the part of most critical in flow process.New method is the probability statistics rule of description three orthogonal directions distribution of pores, and therefore, program needs to do statistical computation to the distribution of pores of all p-wires of single picture and equidirectional different picture, and two loop structures in Fig. 1 mainly complete this task.Just can calculate hole amplitude parameter, direction and three-dimensional pore space tensor by the hole plane distribution information that graphical analysis is extracted, the invariant of three-dimensional pore space tensor feasible planes hole tensor describes, and its physical significance is clear.Whole flow process is primarily of following four part compositions:

One, material cured and meso-cracking Image Acquisition:

Thin sight picture collection needs to solidify sand sample with hardening agent such as epoxy resin, then through processes such as cutting, grinding, polishing, metal sprayings, can obtain carefully seeing image clearly, then use SEM (scanning electron microscope) to gather picture, namely such picture can be used for image procossing and analysis.

Two, image procossing:

SEM picture directly carefully can not see distribution with extraction hole, must advanced row relax.Colour picture, through the disposal route such as gray-scale pixels, denoising, level and smooth, equalization, medium filtering, binaryzation (comprising: Two-peak method, OTSU method (maximum variance between clusters), empty completion method), adhesion granule morphology, the segmentation of adhesion particle watershed algorithm, optimization, finally obtains the image that can be used for sample distribution of pores.Image procossing object is the disturbing factor removed by image processing techniques in picture.

Three, the determination of mean porosities:

The key element of morphology principle test hole group structure is p-wire.What hole was added up is pixel shared by binary image mesoporosity, and namely porosity is the ratio of hole pixel summation and p-wire pixel.In image analysis program, sample image process figure carries out AND operation.The image that acquisition p-wire and sample hole occur simultaneously, extracts hole data.Just can be obtained the mean porosities of image hole by exploitation program computation, comprehensive multiple picture just available parallel testing line obtains the mean porosities of sand sample.

Four, the plane distribution of porosity is determined:

In order to obtain plane distribution of pores rule, annular p-wire form must be used.The plane distribution situation of sand hole in circle ring area is measured with annular p-wire.

The present embodiment adopts the hole orthotropy of morphology principles illustrated mushy material, and the theoretical definition of hole tensor of the present invention is for shown in formula one:

Formula one: $M_{i_1{i}_2...i_m}=\frac{{\∫}_{\mathrm{\Ω}}{n}_{i_1{i}_2...i_m}{n}_{\mathrm{im}}{L}_L(\mathrm{\α},\mathrm{\β})d\stackrel{\→}{n}}{{\∫}_{\mathrm{\Ω}}{L}_L(\mathrm{\α},\mathrm{\β})d\stackrel{\→}{n}}$

In formula one: for the generalized definition of particulate material hole fabric tensor; for the durection component of m rank particulate material hole fabric tensor, L _l(α, β) is distribution of pores function, and its value is the ratio of p-wire and hole; value is tensor unit direction vector; Ω is integrating range.In general application, second order hole fabric tensor just can meet General Requirements, therefore ignores the impact of high-order hole fabric tensor, and the second order particulate material hole fabric tensor that formula one describes is for shown in formula two:

Formula two: $M_{\mathrm{ij}}=\frac{{\∫L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)n_i{n}_{j}d\stackrel{\→}{n}}{{\∫L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)d\stackrel{\→}{n}}$

In formula two: M _ijfor Second-order Symmetric particulate material hole fabric tensor, n _in _jfor the durection component of second order granular material hole fabric tensor.Formula three is adopted in image analysis program:

Formula three: $M_{\mathrm{ij}}=\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}\frac{L_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)n_i{n}_j}{N}}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}\frac{L_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}{N}}=\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)n_i{n}_j}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}$

F ₁-F ₃space, formula four:

Formula four: $\left.\begin{array}{c}{b}_1=\sqrt{J_2}=\sqrt{\frac{1}{2}{(M_{11}-M_{33})}^2+{M_{13}}^2}\\ {\mathrm{\θ}}_1=\frac{1}{2}\arctan \frac{2M_{13}}{M_{11}-M_{33}}\end{array}\right\}$

F ₁-F ₂space, formula five:

Formula five: $\left.\begin{array}{c}{b}_2=\sqrt{J_2}=\sqrt{\frac{1}{4}{(M_{11}-M_{22})}^2+{M_{12}}^2}\\ {\mathrm{\θ}}_2=\frac{1}{2}\arctan \frac{2M_{12}}{M_{11}-M_{22}}\end{array}\right\}$

F ₂-F ₃space, formula six:

Formula six: $\left.\begin{array}{c}{b}_3=\sqrt{J_2}=\sqrt{\frac{1}{4}{(M_{22}-M_{33})}^2+{M_{23}}^2}\\ {\mathrm{\θ}}_3=\frac{1}{2}\arctan \frac{2M_{23}}{M_{22}-M_{33}}\end{array}\right\}$

Formula four, formula five are with formula six: F ₁-F ₃space, F ₁-F ₂space and F ₂-F ₃space is three different spaces of particulate material, M _ij(i, j=1,2,3) are the component of second order particulate material hole group structure in formula three; b _i(i=1,2,3) are the hole amplitude parameter on three normal surfaces, are invariants, and be also the scalar of reflection anisotropic degree, its theoretical span is 0 to 1, works as b _iwhen=0, porous nickel distributes, and sample is isotropy; Work as b _iwhen=1, sample imporosity; θ _i=0 is a point measuring angle, reflects anisotropic orientation.

After plane hole amplitude parameter size and Orientation is determined, its plane distribution function is for shown in formula seven:

Formula seven: N (n _i, θ) and=n _i(1+b _icos2 (θ-θ _i))

In formula: N (n _i, θ) and be plane distribution of pores function; n _i(i=1,2,3) are the mean porosities on three normal surfaces; θ planimetric coordinates parameter.

The present invention better can measure the plane distribution situation of sand hole, and determines that dirigibility is large, and physical significance is clear.

The mark perseverance of the hole tensor of the present invention's definition is 1, and so in above definition three amplitude parameters, independent variation amount only has two, and therefore only need measure any two parameters in three normal surfaces, its hole orthotropy fabric tensor just can uniquely be determined.Its concrete formula is as follows:

B ₁with b ₂the fabric tensor 1 that hole parameter is determined,

Formula eight: $M_{\mathrm{ij}}=\frac{1}{3+b_1+b_2-b_1{b}_2}\left[\begin{array}{ccc}1+b_1+b_2+b_1{b}_2& & \\ & 1+b_1-b_2-b_1{b}_2& \\ & & 1-b_1+b_2-b_1{b}_2\end{array}\right]$

B ₁with b ₃the fabric tensor 2 that hole parameter is determined,

Formula nine: $M_{\mathrm{ij}}=\frac{1}{3-b_1-b_3-b_1{b}_3}\left[\begin{array}{ccc}1+b_1-b_3-b_1{b}_3& & \\ & 1-b_1+b_3-b_1{b}_{2=3}& \\ & & 1-b_1-b_3+b_1{b}_3\end{array}\right]$

B ₃with b ₂the fabric tensor 3 that hole parameter is determined,

Formula ten: $M_{\mathrm{ij}}=\frac{1}{3-b_2+b_3+b_2{b}_3}\left[\begin{array}{ccc}1+b_2+b_3+b_2{b}_3& & \\ & 1-b_2+b_3-b_2{b}_3& \\ & & 1-b_2-b_3+b_2{b}_3\end{array}\right]$

It is generally acknowledged that soil is the material of transverse isotropy, so two principal components in fabric tensor are equal, so for Axial symmetric anisotropy sample, only need a scalar parameter just corresponding fabric tensor of definable.

In formula four and formula five, work as β _m=π/4, sin β _m=cos β _m, then b ₁=b ₂, this both direction hole parameter is equal, and so material shows as transverse isotropy, and formula eight deteriorates to transverse isotropy three-dimensional group configuration formula:

Formula 11: $M_{\mathrm{ij}}=\frac{1}{3-b}\left[\begin{array}{ccc}1+b& 0& 0\\ 0& 1-b& 0\\ 0& 0& 1-b\end{array}\right]$

In formula:

Formula 12: $b=\sqrt{{\left[\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)({\cos }^2{\mathrm{\α}}_m-\frac{1}{2}{\sin }^2{\mathrm{\α}}_m)}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right]}^2+\frac{1}{2}{\left(\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)\sin 2{\mathrm{\α}}_m}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right)}^2}$

In formula 12: b is the amplitude parameter of transverse isotropy hole tensor, obtain plane hole fabric tensor invariant according to any one face in two same sex faces and obtain.B ₁=b ₂=b shows that the hole tensor invariant of these two planes is equal, and formula eight can describe the transverse isotropy of particulate material hole with an amplitude parameter, may be used for the transverse isotropy characteristic describing topsoil.

In like manner, as α in formula four _m=pi/2, and β in formula six _mwhen=0, then b ₁=b ₃, formula nine also can deteriorate to the form of transverse isotropy such as formula shown in 13:

Formula 13: $M_{\mathrm{ij}}=\frac{1}{3+b}\left[\begin{array}{ccc}1+b& 0& 0\\ 0& 1+b& 0\\ 0& 0& 1-b\end{array}\right]$

In formula:

Formula 14: $b=\sqrt{{\left[\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)\cos 2{\mathrm{\α}}_m}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right]}^2+\frac{1}{2}{\left(\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)\sin 2{\mathrm{\α}}_m}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right)}^2}$

In formula 14: b transverse isotropy hole amplitude parameter, in formula five, as β in formula six _mduring=pi/2, then b ₂=b ₃, formula ten also can deteriorate to:

Formula 15: $M_{\mathrm{ij}}=\frac{1}{3+b^2}\left[\begin{array}{ccc}{(1+b)}^2& 0& 0\\ 0& 1-b^2& 0\\ 0& 0& {(1-b)}^2\end{array}\right]$

In formula 15: the expression formula of b is identical with formula 14 form, formula 15 remains orthotropic form, tranversely isotropic material can not be described, but, under certain simplified condition, whether it also can need to study checking further by the orthotropy that an amplitude parameter describes material.

Particulate material, due to the existence of its hole, causes its solid, liquids and gases three-phase medium composition, also result in the mechanical characteristic of its complexity.The most complicated three-dimensional orthogonal hole is carefully seen characteristic and is calculated demarcation by theoretical and test method by the present invention, mushy material macro-mechanical characters and thin sight group structure is made to be combined into possibility, the soil body is as typical mushy material, the thin Study on Microcosmic Mechanism that can be it provides foundation, for soil body rational approach provides support, for various underground engineering design, construction provide theoretic prediction methods.

Claims (9)

1. the quantitative test of a particulate material hole group structure and image analysis method, it is characterized in that: particulate material hole group structure quantitative test and image analysis method are made up of following three step process: step one, carry out theoretical definition to particulate material hole fabric tensor; Step 2, carries out specification to particulate material hole group structure determination step; Step 3, according to the theoretical definition of particulate material hole fabric tensor, writes the program of image procossing and graphical analysis;

The quantitative test of particulate material hole group structure and graphical analysis, refer to and adopt experiment capturing material image, measure the orthotropy of particulate material pore space distribution with image procossing and image analysis technology.

2. the quantitative test of particulate material hole group structure as claimed in claim 1 and image analysis method, is characterized in that: image procossing and image analysis program are graphical analysis Matlab program and image procossing Matlab program.

3. the quantitative test of particulate material hole group structure as claimed in claim 1 and image analysis method, it is characterized in that: the specification determination step of hole group structure, the idiographic flow of image procossing and image analysis program is: particulate material solidifies and meso-cracking Image Acquisition, gather the thin sight picture of particulate material, the thin sight picture collection of particulate material needs to be cured particulate material sample with hardening agent, then through cutting, grinding, polishing, metal spraying process, obtain the thin sight image of particulate material, picture is gathered again with SEM, picture is used for image procossing and graphical analysis, image procossing, the picture gathered with SEM, through gray-scale pixels, denoising, level and smooth, equalization, medium filtering, binaryzation, optimized treatment method, finally obtains the image for sample particulate material distribution of pores, the determination of mean porosities, the key element of morphology principle particle tested material hole group structure is p-wire, what particulate material hole was added up is pixel shared by binary image mesoporosity, namely porosity is the ratio of hole pixel summation and p-wire pixel, namely porosity is the probability of distribution of pores, image processing program needs to do statistical computation to all p-wires of single picture of SEM collection and the distribution of pores of equidirectional different picture, in image analysis program, particulate material sample image process figure carries out AND operation, the image that acquisition p-wire and sample hole occur simultaneously, extract hole data, the mean porosities of image hole is obtained by graphical analysis Matlab program and image procossing Matlab program computation, comprehensive multiple picture parallel testing line obtains the mean porosities of particulate material sample, the plane distribution of porosity is determined, in order to obtain particulate material plane distribution of pores rule, uses annular p-wire form, measures the plane distribution situation of circle ring area endoparticle material hole with annular p-wire.

4. the quantitative test of particulate material hole group structure as claimed in claim 3 and image analysis method, it is characterized in that: the mensuration main-process stream of hole group structure, concrete steps are: sample, grinding, polishing, metal spraying are cut in sand sample solidification, cube; The SEM obtaining three normal surfaces carefully sees image; Image procossing; Draw parallel testing line and annular p-wire; Graphical analysis, calculating obtain distribution of pores function; Calculation Plane tensor; Calculate amplitude parameter and direction; Calculate and obtain three-dimensional pore space fabric tensor.

5. the quantitative test of particulate material hole group structure as claimed in claim 3 and image analysis method, it is characterized in that: the orthotropy adopting the pore space distribution of morphology principles illustrated particulate material, the theoretical definition of particulate material hole fabric tensor is for shown in formula one:

Formula one: $M_{i_1{i}_2...i_m}=\frac{{\∫}_{\mathrm{\Ω}}{n}_{i_1{i}_2...i_m}{n}_{\mathrm{im}}{L}_L(\mathrm{\α},\mathrm{\β})d\stackrel{\→}{n}}{{\∫}_{\mathrm{\Ω}}{L}_L(\mathrm{\α},\mathrm{\β})d\stackrel{\→}{n}}$

In formula one: for the generalized definition of particulate material hole fabric tensor; for the durection component of m rank particulate material hole fabric tensor, L _l(α, β) is distribution of pores function, and its value is the ratio of p-wire and hole; value is tensor unit direction vector; Ω is integrating range; Second order particulate material hole fabric tensor is for shown in formula two:

Formula two: $M_{\mathrm{ij}}=\frac{{\∫L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)n_i{n}_{j}d\stackrel{\→}{n}}{\∫L_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)d\stackrel{\→}{n}}$

In formula two: M _ijfor Second-order Symmetric particulate material hole fabric tensor, n _in _jfor the durection component of second order granular material hole fabric tensor, in image analysis program, adopt formula three:

Formula three: $M_{\mathrm{ij}}=\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}\frac{L_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)n_i{n}_j}{N}}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}\frac{L_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}{N}}=\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)n_i{n}_j}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}$

F ₁-F ₃space, formula four:

Formula four: $\left.\begin{array}{c}{b}_1=\sqrt{J_2}=\sqrt{\frac{1}{4}{(M_{11}-M_{33})}^2+{M_{13}}^2}\\ {\mathrm{\θ}}_1=\frac{1}{2}\arctan \frac{2M_{13}}{M_{11}-M_{33}}\end{array}\right\}$

F ₁-F ₂space, formula five:

Formula five: $\left.\begin{array}{c}{b}_2=\sqrt{J_2}=\sqrt{\frac{1}{4}{(M_{11}-M_{22})}^2+{M_{12}}^2}\\ {\mathrm{\θ}}_2=\frac{1}{2}\arctan \frac{2M_{12}}{M_{11}-M_{22}}\end{array}\right\}$

F ₂-F ₃space, formula six:

Formula six: $\left.\begin{array}{c}{b}_3=\sqrt{J_2}=\sqrt{\frac{1}{4}{(M_{22}-M_{33})}^2+{M_{23}}^2}\\ {\mathrm{\θ}}_3=\frac{1}{2}\arctan \frac{2M_{23}}{M_{22}-M_{33}}\end{array}\right\}$

Formula four, formula five are with formula six: F ₁-F ₃space, F ₁-F ₂space and F ₂-F ₃space is three normal surfaces of particulate material, M _ij(i, j=1,2,3) are the component of second order particulate material hole group structure in formula three; b _i(i=1,2,3) are the hole amplitude parameter on three normal surfaces, are invariants, and be also the scalar of reflection anisotropic degree, its theoretical span is 0 to 1, works as b _iwhen=0, porous nickel distributes, and sample is isotropy; Work as b _iwhen=1, sample imporosity; θ _i=0 is a point measuring angle, reflects anisotropic orientation;

After plane hole amplitude parameter size and Orientation is determined, its plane distribution function is for shown in formula seven:

Formula seven: N (n _i, θ) and=n _i(1+b _icos2 (θ-θ _i))

In formula: N (n _i, θ) and be plane distribution of pores function; n _i(i=1,2,3) are the mean porosities on three normal surfaces; θ planimetric coordinates parameter.

6. the quantitative test of particulate material hole group structure as claimed in claim 5 and image analysis method, is characterized in that: define particulate material orthotropy particulate material hole fabric tensor, the transverse isotropy tensor under three different conditions.The mark perseverance of the particulate material hole fabric tensor of definition is 1, three amplitude parameter independent variation amounts of definition only have two, therefore only any two parameters in three normal surfaces of particulate material need be measured, its hole orthotropy particulate material hole fabric tensor can uniquely be determined, its concrete formula is as follows:

B ₁with b ₂the fabric tensor 1 that hole parameter is determined,

Formula eight: $M_{\mathrm{ij}}=\frac{1}{3+b_1+b_2-b_1{b}_2}\left[\begin{array}{ccc}1+b_1+b_2+b_1{b}_2& & \\ & 1+b_1-b_2-b_1{b}_2& \\ & & 1-b_1+b_2-b_1{b}_2\end{array}\right]$

B ₁with b ₃the fabric tensor 2 that hole parameter is determined,

Formula nine: $M_{\mathrm{ij}}=\frac{1}{3-b_1-b_3-b_1{b}_3}\left[\begin{array}{ccc}1+b_1-b_3-b_1{b}_3& & \\ & 1-b_1+b_3-b_1{b}_3& \\ & & 1-b_1-b_3+b_1{b}_3\end{array}\right]$ B ₂with b ₃the fabric tensor 3 that hole parameter is determined,

Formula ten: $M_{\mathrm{ij}}=\frac{1}{3-b_2+b_3+b_2{b}_3}\left[\begin{array}{ccc}1+b_2+b_3+b_2{b}_3& & \\ & 1-b_2+b_3-b_2{b}_3& \\ & & 1-b_2-b_3+b_2{b}_3\end{array}\right]$

If two principal components in particulate material hole fabric tensor are equal, material is transverse isotropy, only needs a scalar parameter just corresponding fabric tensor of definable;

In formula four and formula five, work as β _m=π/4, sin β _m=cos β _m, then b ₁=b ₂, this both direction hole parameter is equal, and so material shows as transverse isotropy, and formula eight deteriorates to transverse isotropy three-dimensional group configuration formula:

Formula 11: $M_{\mathrm{ij}}=\frac{1}{3-b}\left[\begin{array}{ccc}1+b& 0& 0\\ 0& 1-b& 0\\ 0& 0& 1-b\end{array}\right]$

In formula:

Formula 12: $b=\sqrt{{\left[\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)({\cos }^2{\mathrm{\α}}_m-\frac{1}{2}{\sin }^2{\mathrm{\α}}_m)}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right]}^2+\frac{1}{2}{\left(\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)\sin 2{\mathrm{\α}}_m}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right)}^2}$ In formula 12: b is the amplitude parameter of transverse isotropy hole tensor, obtain plane hole fabric tensor invariant according to any one face in two same sex faces and obtain, b ₁=b ₂=b shows that the hole tensor invariant of these two planes is equal, and formula eight can describe the transverse isotropy of particulate material hole with an amplitude parameter, may be used for the transverse isotropy characteristic describing topsoil; In like manner, as α in formula four _m=pi/2, and β in formula six _mwhen=0, then b ₁=b ₃, formula nine also can deteriorate to the form of transverse isotropy such as formula shown in 13:

Formula 13: $M_{\mathrm{ij}}=\frac{1}{3+b}\left[\begin{array}{ccc}1+b& 0& 0\\ 0& 1+b& 0\\ 0& 0& 1-b\end{array}\right]$

In formula:

Formula 14: $b=\sqrt{{\left[\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)\cos 2{\mathrm{\α}}_m}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right]}^2+\frac{1}{2}{\left(\frac{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)\sin 2{\mathrm{\α}}_m}{\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{L}_L({\mathrm{\α}}_m,{\mathrm{\β}}_m)}\right)}^2}$

In formula 14: b transverse isotropy hole parameter, in formula five, as β in formula six _mduring=pi/2, then b ₂=b ₃, formula ten also can deteriorate to:

Formula 15: $M_{\mathrm{ij}}=\frac{1}{3+b^2}\left[\begin{array}{ccc}{(1+b)}^2& 0& 0\\ 0& 1-b^2& 0\\ 0& 0& {(1-b)}^2\end{array}\right]$

In formula 15: the expression formula of b is identical with formula 14 form, and formula 15 remains orthotropic form.

7. the quantitative test of particulate material hole group structure as claimed in claim 3 and image analysis method, it is characterized in that: the sample of particulate material hole group structure quantitative test and graphical analysis adopts sand to be sample, the picture that SEM gathers is Tengger desert aeolian sand undisturbed, and enlargement factor is 150 times.

8. the quantitative test of particulate material hole group structure as claimed in claim 3 and image analysis method, is characterized in that: the collection of sample, make and use cuboid sample.

9. the quantitative test of particulate material hole group structure as claimed in claim 3 and image analysis method, it is characterized in that: in image procossing, the binaryzation of the picture gathered with SEM comprises: Two-peak method, OTSU method, empty completion method, adhesion granule morphology, adhesion particle watershed algorithm are split.