CN104764679A - Microfabric quantitative test and analysis method for orthogonal anisotropy of granular material - Google Patents

Abstract

The invention relates to computational mechanics and constitutive modeling of granular material, and particularly to a microfabric quantitative test and analysis method for orthogonal anisotropy of granular material. The method is characterized by comprising the following steps: (1) curing the initial internal structure of granular material; (2) slicing a cured granular material sample, and milling and polishing the surface of a slice; and (3) observing and analyzing the microstructure on the surface of the slice by a scanning electron microscope, and performing quantitative test and analysis on the microfabric of orthogonal anisotropy of the granular material. Trial of the method shows that, by the method, the initial internal structure of the granular material can be fixed well, after the initial internal structure is maintained and cured elaborately and the surface of the slice is milled and polished, the internal structure of the granular material can be observed clearly in the scanning electron microscope, and on the basis, accurate execution of following analysis work is facilitated, and mechanical behaviors under complex conditions, such as granular material anisotropy and stress anisotropy, can be simulated accurately.

Description

The orthotropic thin sight group structure quantitative test of particulate material and analytical approach

Technical field

The present invention relates to particulate material Computational Mechanics and constitutive modeling, the orthotropic thin sight group structure quantitative test of especially a kind of particulate material and analytical approach.

Background technology

Gillott (1970) and Yoshinaka and Kazama (1973) measures with X-ray.The method that Moegenstern and Tchalenko (1967) have employed optics to the particle studying clay towards.Kanatani (1984) has found that turning round of tensor form cuts density function.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.Arulamamdan and Dafalias (1979) and Anandarajah and Kuganenthira (1995) parameter assess the electric conductivity of sand.Hohai University ginger Jingshan mountain etc. adopt computer picture measuring and analysis system multi-model test picture to analyze, and can analyze the change of the displacement of particle in coarse particle process of the test, corner, the orientation of major axis, coordination number and Zhi Xiangliang quantitatively.Tsing-Hua University Zhang Jianmin etc. adopt the biaxial compression test system of independent research, and form two-dimentional accumulation body for subjects with metal club-shaped material that is circular and ellipse cross section, the method forming material inner structure by manual alignment carries out correlative study.ODA is simplified formula by hypothesis, is not considering that branch length and coordination number are on the impact of grain fabric tensor, under only considering the impact in particle direction, and the grain fabric tensor F be simplified _ij.

Above method respectively has relative merits, but each method all has certain limitation, for the group structure anisotropy of certain material or the qualitative acquisition particulate material of certain test method, can only can describe the horizontal sight anisotropy group structure of particulate material, cannot orthotropy be described.Because the macro-mechanical characters of group structure anisotropy to material of particulate material has considerable influence, therefore in the urgent need to proposing the orthotropy of a set of particulate material to the quantitative test of the macro-mechanical characters of material and analytical approach, the method facilitates and has universality.

Summary of the invention

The object of this invention is to provide the orthotropic thin sight group structure quantitative test of a kind of new particulate material and analytical approach, the method can go out the change of different types of particulate material carefully sight group structure by quantitatively calibrating, draws corresponding rill evolution.

A kind of orthotropic thin sight group structure quantitative test of particulate material and analytical approach, its special feature is, comprises the steps:

(1) solidification of the initial inner structure of particulate material;

(2) to solidification after particulate material sample section, and slice surface is milled, polishing;

(3) analyze the microscopical structure of slice surface with scanning electron microscopic observation, quantitative test and analysis are carried out to the orthotropic thin sight group structure of particulate material.

In step (3), quantitative test and analysis are carried out to the orthotropic thin sight group structure of particulate material, specifically refer to adopt reflection particle towards geometrical statistic parameter to represent the orthotropy of sand sample, it is defined as:

(1), F ₁-F ₃space

$a_1=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}({\cos }^2{{\mathrm{\θ}}_1}^{\left(k\right)}-{\sin }^2{{\mathrm{\θ}}_1}^{\left(k\right)}{\cos }^2{\mathrm{\α}}^{\left(k\right)})\right)}^2+{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\sin 2{{\mathrm{\θ}}_1}^{\left(k\right)}\cos {\mathrm{\α}}^{\left(k\right)}\right)}^2}---\left(1\right);$

(2), F ₁-F ₂space

$a_2=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}({\cos }^2{{\mathrm{\θ}}_1}^{\left(k\right)}-{\sin }^2{{\mathrm{\θ}}_1}^{\left(k\right)}{\sin }^2{\mathrm{\α}}^{\left(k\right)})\right)}^2+{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\sin 2{{\mathrm{\θ}}_1}^{\left(k\right)}\sin {\mathrm{\α}}^{\left(k\right)}\right)}^2}---\left(2\right);$

(3), F ₂-F ₃space

$a_3=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\left({\sin }^2{{\mathrm{\θ}}_1}^{\left(k\right)}\cos {2\mathrm{\α}}^{\left(k\right)}\right)\right)}^2+{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}s{\mathrm{in}}^2{{\mathrm{\θ}}_1}^{\left(k\right)}\sin 2{\mathrm{\α}}^{\left(k\right)}\right)}^2}---\left(3\right);$

θ in formula ₁ ^(K)the projection in the vertical direction of particle major axis and the F of a kth particle in cell cube ₁the angle of axle; α ^(k)that the particle major axis of a kth particle projects and F in the horizontal plane ₃the angle of axle; F _i(i=1,2,3) are three orthogonal main directions of group structure; a _i(i=1,2,3) are the anisotropy amplitude parameter on three normal surfaces, and its theoretical span is 0 to 1, works as a _iwhen=0, particle towards being uniformly distributed, sample inner structure isotropy; Work as a _iwhen=1, particle be anisotropy towards concentrating entirely on surface level, N represents all amounts of particles in detecting unit body;

According to above-mentioned formula (1), formula (2) and formula (3) determine the thin sight anisotropy amplitude parameter of three planes respectively, then just can determine an orthotropy fabric tensor completely with any two parameters wherein, the particulate material orthotropy namely under definable three different conditions carefully sees fabric tensor.

Further, the particulate material orthotropy defined under three different conditions carefully sees fabric tensor and F _ijspecific as follows:

(1), F is used ₁-F ₃with F ₁-F ₂the fabric tensor 1 that the parameter of plane is determined

$F_{\mathrm{ij}}=\frac{1}{3+a_1+a_2-a_1{a}_2}\left[\begin{array}{ccc}1+a_1+a_2+a_1{a}_2& & \\ & 1+a_1-a_2-a_1{a}_2& \\ & & 1-a_1+a_2-a_1{a}_2\end{array}\right]---\left(4\right);$

(2), F ₁-F ₂with F ₂-F ₃the fabric tensor 2 that the parameter of plane is determined

$F_{\mathrm{ij}}=\frac{1}{3-a_1-a_3-a_1{a}_3}\left[\begin{array}{ccc}1+a_1-a_3-a_1{a}_3& & \\ & 1-a_1+a_3-a_1{a}_3& \\ & & 1-a_1-a_3+a_1{a}_3\end{array}\right]---\left(5\right);$

(3), F ₁-F ₃with F ₂-F ₃the fabric tensor 3 that the parameter of plane is determined

$F_{\mathrm{ij}}=\frac{1}{3-a_2+a_3+a_2{a}_3}\left[\begin{array}{ccc}1+a_2+a_3+a_2{a}_3& & \\ & 1-a_2+a_3-a_2{a}_3& \\ & & 1-a_1-a_3+a_2{a}_3\end{array}\right]---\left(6\right);$

In formula (1) and formula (2), work as α ^(k)=π/4, sin α ^(k)=cos α ^(k), then a ₁=a ₂, the amplitude parameter of horizontal direction two vertical planes is equal, and so material shows as transverse isotropy, and formula (6) deteriorates to transverse isotropy three-dimensional group configuration formula:

$F_{\mathrm{ij}}=\frac{1}{3-a}\left[\begin{array}{ccc}1+a& 0& 0\\ 0& 1-a& 0\\ 0& 0& 1-a\end{array}\right]---\left(7\right)$

In formula

$a=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}({\cos }^2{\mathrm{\θ}}_1^{\left(k\right)}-\frac{{\sin }^2{\mathrm{\θ}}_1^{\left(k\right)}}{2})\right)}^2+\frac{1}{2}{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\sin 2{\mathrm{\θ}}_1^{\left(k\right)}\right)}^2}---\left(8\right)$

In formula, a is transverse isotropy amplitude parameter, and its span remains [0,1].

Solidification in step (1) specifically refers to the air pressure of applying 15 ~ 25kpa, is slowly injected in particulate material sample by epoxy resin, then maintenance particulate material sample makes it solidify completely.

Through probationary certificate, adopt said method, can the initial inner structure of immobilized particles material well, through meticulously curing, in the process of slice surface grinding and polishing, under scanning electron microscope, the inner structure of particulate material clearly can be observed, on this basis, be conducive to subsequent analysis work to carry out exactly, with the mechanical behavior of the complex conditions such as accurate simulation particulate material anisotropy and stress anisotropy.

Accompanying drawing explanation

Fig. 1 is the method for making sample schematic diagram of embodiment 1;

Fig. 2 is the soil body orthotropy group structure schematic diagram of embodiment 1;

Fig. 3 is embodiment 1 sand sample group structure amplitude parameter a ₃determination;

Fig. 4 is embodiment 1 sand sample group structure amplitude parameter a ₂determination;

Fig. 5 is embodiment 1 sand sample group structure amplitude parameter a ₁determination;

Fig. 6 is the electron-microscope scanning image of the Ningxia Tengger desert sand sample section of the amplification 150 times of embodiment 1;

Fig. 7 is the metaloscope image of the Ningxia Tengger desert sand sample section of the amplification 50 times of embodiment 1;

Fig. 8 is the binary black white image obtained through image procossing Fig. 4;

Fig. 9 is the particle orthotropy amplitude parameter a of embodiment 1 ₁result of calculation;

Figure 10 is the particle orthotropy amplitude parameter a of embodiment 1 ₂result of calculation;

Figure 11 is the particle orthotropy amplitude parameter a of embodiment 1 ₃result of calculation.

Embodiment

At present, can the expression formula that Oda in 1972 be only had to propose of quantitative description particulate material space arrangement fabric tensor.Domestic and international many experts and scholars adopt the expression formula of Oda carefully to see quantitative test and theoretical analysis, are widely applied.But the expression formula of Oda proposes based on transverse isotropy hypothesis, can describe the group structure character of a part of horizontal sight anisotropy soil body, can not describe the orthotropy of the soil body.The present invention directly defines its three-dimensional expression formula by fabric theory, according to particle arrangement geometry physical relation, retrogression of nature is to the form of transverse isotropy, it can describe the orthotropy that the arrangement of various particle is formed, the transverse isotropy of the soil body under various condition can be described, therefore have more ubiquity.

The soil body-shield machine system theory of current soil mechanics is relatively immature, and many mechanical characteristics of the soil body all cannot describe, and the failure mechanism of the soil body is also unpredictable.Inherent mechanism due to soil body mechanical characteristic is that it carefully sees characteristic, therefore the present invention proposes the thin sight characteristic that arrangement carefully seen by quantitative description particulate material, thin sight mechanism description for particulate material macro-mechanical characters has been established theoretical foundation and has been proposed concrete test method, for explaining the failure mechanism supplying method of the soil body.Immature due to soil mechanics theory, 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, 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.

Embodiment 1:

1, the solidifying of particulate material orthotropy group structure:

The method for making sample shown in Fig. 1 is adopted to manufacture the sand sample of various orthotropy group structure.Fig. 1 is the method for making sample reinventing sand.Fixed by sand sample mould by die frame 1, die frame can be adjusted to different angles, and sand falls into mould from sander 2, layering sample preparation (wet smash the unnecessary moisture of method sample preparation can be discharged by conduit 3); After sand sample reaches sample preparation height, remove unnecessary sand sample, the sand 4 of die top first retains; Installation mold side plate 5, fixing, turnover mould frame 1, removed by unnecessary sand 6, sand sample completes.

For solidifying sand sample completely, reducing the impact of sand group structure, being put down gently by mould solidifies in room in sand sample, solidify indoor and be full of epoxy resin, mould can be covered, 15 ~ 25kpa back-pressure (vacuum) dry air is passed at sand sample die top (escape pipe), die side plate has equally distributed ventilative pore, and epoxy resin can enter mould by pore, is solidified by sand sample.

It is pointed out that epoxy resin bond effect is in humid conditions poor.If containing moisture in sample, need first soil sample to be dried, make water cut lower than 3%, absorb moisture.

After injection ring epoxy resins, need maintenance sample to make it harden completely, just can cut into slices.Under room temperature, maintenance just can ensure that the particulate material of epoxy gluing has sufficient intensity for 18 hours.

2, cured granulate material surface slicing treatment:

Scanning electron microscope (Scanning Electronic Microscope is called for short SEM) is higher to the requirement of particulate material section.First the particulate material of solidification is cut roughly, then cut surface is ground and polishing, to obtain the tangent plane of better quality.In grinding and polishing process, fine scratches can fade away, and particle can brighten gradually.Relative to epoxy resin-base, the effect of polishing to particulate material is more obvious.Contrast through polishing section is comparatively large, makes the image procossing of follow-up microscopical structure become possibility.

3, the acquisition of particulate material inner structure and quantification are expressed:

For the concrete steps that anisotropy is expressed accurately are described, the application is described for sand sample, and other species of particle MATERIALS METHODS are similar, are described as follows.

Through cutting, mill and polishing (cutting method is shown in Fig. 2), the determination of the amplitude parameter of three normal surfaces is as Fig. 3, Fig. 4 and Fig. 5.The microscopical structure of available scanning electron microscopic observation analysis section.Fig. 6 is the electron-microscope scanning image of the typical sand sample section of amplification 150 times, and Fig. 7 is the electric metaloscope image of amplification 50 times, and Fig. 8 is through the binary black white image that image procossing obtains.

In soil test, the preparation method of sand sample sample mainly contains two kinds, one is knockout method (DryDeposit, be called for short DD), another kind wets to smash method (Moist Temping, be called for short MT) it has been generally acknowledged that, by the impact of preparation method, two kinds of sand samples have distinct microscopical structure and macroscopic anisotropy mechanical characteristic.For the anisotropic mechanical characteristic of quantitative examination sand, meso-scopic structure analysis need be carried out to the sand sample prepared by above-mentioned two kinds of methods.

The present embodiment adopt reflection particle towards geometrical statistic parameter represent the anisotropy of sand sample, it is defined as:

(1), F ₁-F ₃space

$a_1=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}({\cos }^2{{\mathrm{\θ}}_1}^{\left(k\right)}-{\sin }^2{{\mathrm{\θ}}_1}^{\left(k\right)}{\cos }^2{\mathrm{\α}}^{\left(k\right)})\right)}^2+{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\sin 2{{\mathrm{\θ}}_1}^{\left(k\right)}\cos {\mathrm{\α}}^{\left(k\right)}\right)}^2}---\left(1\right)$

(2), F ₁-F ₂space

$a_2=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}({\cos }^2{{\mathrm{\θ}}_1}^{\left(k\right)}-{\sin }^2{{\mathrm{\θ}}_1}^{\left(k\right)}{\sin }^2{\mathrm{\α}}^{\left(k\right)})\right)}^2+{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\sin 2{{\mathrm{\θ}}_1}^{\left(k\right)}\sin {\mathrm{\α}}^{\left(k\right)}\right)}^2}---\left(2\right)$

(3), F ₂-F ₃space

$a_3=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\left({\sin }^2{{\mathrm{\θ}}_1}^{\left(k\right)}\cos {2\mathrm{\α}}^{\left(k\right)}\right)\right)}^2+{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}s{\mathrm{in}}^2{{\mathrm{\θ}}_1}^{\left(k\right)}\sin 2{\mathrm{\α}}^{\left(k\right)}\right)}^2}---\left(3\right)$

θ in formula ₁ ^(K)the projection in the vertical direction of particle major axis and the F of a kth particle in cell cube ₁the angle of axle; α ^(k)that the particle major axis of a kth particle projects and F in the horizontal plane ₃the angle of axle; F _i(i=1,2,3) are three orthogonal main directions of group structure; a _i(i=1,2,3) are the anisotropy amplitude parameter on three normal surfaces, and its theoretical span is 0 to 1, works as a _iwhen=0, particle towards being uniformly distributed, sample inner structure isotropy; Work as a _iwhen=1, particle be anisotropy towards concentrating entirely on surface level, N represents all amounts of particles in detecting unit body.

Fig. 9, Figure 10 and Figure 11 provide sand particle α and θ in three orthogonal planes ₁the statistics at angle.Obviously, the distributional difference of particle in three planes is very large, shows obvious orthotropy.Anisotropic parameters a _ijust the particle statistic arrangement regulation reflecting three normal surfaces of value.

It is each as follows to fabric tensor that ODA defines:

$F_{\mathrm{ij}}=\frac{1}{2N}\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}{n^k}_i{n_j}^k$

Wherein, N represents the number of measurement volumes particle, n _i ^k, n _j ^krepresent the component of particle major axis normal vector on axle i and axle j respectively.Therefore, only two angle θ are needed ₁ ^kand α ^kjust can calculate the expression formula of its three-dimensional group structure.

F _ijdirection vector n be:

n＝{cosθ ₁ ^(k)， sinθ ₁ ^(k)sinα ^(k)， sinθ ₁ ^(k)cosα ^(k)}

Fabric tensor is:

$F_{\mathrm{ij}}=\left[\begin{array}{ccc}{F}_{11}& F_{12}& F_{13}\\ F_{21}& F_{22}& F_{23}\\ F_{31}& F_{32}& F_{33}\end{array}\right]$

F in formula _ij(i, j=1,2,3) are component of tensor.

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.

(1), F ₁-F ₃with F ₁-F ₂the fabric tensor 1 that the parameter of plane is determined

$F_{\mathrm{ij}}=\frac{1}{3+a_1+a_2-a_1{a}_2}\left[\begin{array}{ccc}1+a_1+a_2+a_1{a}_2& & \\ & 1+a_1-a_2-a_1{a}_2& \\ & & 1-a_1+a_2-a_1{a}_2\end{array}\right]---\left(4\right)$

(2), F ₁-F ₂with F ₂-F ₃the fabric tensor 2 that the parameter of plane is determined

$F_{\mathrm{ij}}=\frac{1}{3-a_1-a_3-a_1{a}_3}\left[\begin{array}{ccc}1+a_1-a_3-a_1{a}_3& & \\ & 1-a_1+a_3-a_1{a}_3& \\ & & 1-a_1-a_3+a_1{a}_3\end{array}\right]---\left(5\right)$

(3), F ₁-F ₃with F ₂-F ₃the fabric tensor 3 that the parameter of plane is determined

$F_{\mathrm{ij}}=\frac{1}{3-a_2+a_3+a_2{a}_3}\left[\begin{array}{ccc}1+a_2+a_3+a_2{a}_3& & \\ & 1-a_2+a_3-a_2{a}_3& \\ & & 1-a_1-a_3+a_2{a}_3\end{array}\right]---\left(6\right)$

A wherein ₁, a ₂, a ₃it is exactly aforesaid anisotropic parameters.With regard to knockout method and the wet a smashing method ₁, a ₂, a ₃value substitutes into above formula respectively, can obtain the fabric tensor describing respective samples anisotropic degree.

In formula (1) and formula (2), work as α ^(k)=π/4, sin α ^(k)=cos α ^(k), then a ₁=a ₂, the amplitude parameter of horizontal direction two vertical planes is equal, and so material shows as transverse isotropy, and formula (6) deteriorates to transverse isotropy three-dimensional group configuration formula:

$F_{\mathrm{ij}}=\frac{1}{3-a}\left[\begin{array}{ccc}1+a& 0& 0\\ 0& 1-a& 0\\ 0& 0& 1-a\end{array}\right]---\left(7\right)$

In formula

$a=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}({\cos }^2{\mathrm{\θ}}_1^{\left(k\right)}-\frac{{\sin }^2{\mathrm{\θ}}_1^{\left(k\right)}}{2})\right)}^2+\frac{1}{2}{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\sin 2{\mathrm{\θ}}_1^{\left(k\right)}\right)}^2}---\left(8\right)$

In formula, a is transverse isotropy amplitude parameter, and its span remains [0,1].Formula (6) is according to fabric tensor theoretical definition, and degenerate when aspherical particle arrangement meets transverse isotropy condition, degenerative process nature, geometry and physical meanings are clear.Because natural rock-filled has showed obvious transverse isotropy in natural sediment process, therefore, formula (7) has wider using value.

Natural rock-filled is the three-phase medium composition of solid, liquids and gases, causes the mechanical characteristic of its complexity.The most complicated three-dimensional orthogonal soil body particle is carefully seen characteristic and is calculated demarcation by theoretical and test method by the present invention, as the result of calculation of Fig. 9, Figure 10 and Figure 11, macro-mechanical characters and the thin sight group structure of the soil body are combined into possibility, for the thin Study on Microcosmic Mechanism of soil body mechanical property provides foundation, for damage of soil body study mechanism provides support, for various engineering designs, the construction relating to soil body Mechanics Calculation provides theoretic prediction methods.

Claims (4)

1. the orthotropic thin sight group structure quantitative test of particulate material and an analytical approach, is characterized in that, comprise the steps:

(1) solidification of the initial inner structure of particulate material;

(2) to solidification after particulate material sample section, and slice surface is milled, polishing;

(3) analyze the microscopical structure of slice surface with scanning electron microscopic observation, quantitative test and analysis are carried out to the orthotropic thin sight group structure of particulate material.

2. the orthotropic thin sight group structure quantitative test of particulate material as claimed in claim 1 and analytical approach, is characterized in that:

In step (3), quantitative test and analysis are carried out to the orthotropic thin sight group structure of particulate material, specifically refer to adopt reflection particle towards geometrical statistic parameter to represent the orthotropy of sand sample, it is defined as:

(1), F ₁-F ₃space

$a_1=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}({\cos }^2{{\mathrm{\θ}}_1}^{\left(k\right)}-{\sin }^2{{\mathrm{\θ}}_1}^{\left(k\right)}{\cos }^2{\mathrm{\α}}^{\left(k\right)})\right)}^2+{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\sin 2{{\mathrm{\θ}}_1}^{\left(k\right)}\cos {\mathrm{\α}}^{\left(k\right)}\right)}^2}---\left(1\right);$

(2), F ₁-F ₂space

$a_2=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}({\cos }^2{{\mathrm{\θ}}_1}^{\left(k\right)}-{\sin }^2{{\mathrm{\θ}}_1}^{\left(k\right)}{\sin }^2{\mathrm{\α}}^{\left(k\right)})\right)}^2+{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\sin 2{{\mathrm{\θ}}_1}^{\left(k\right)}\sin {\mathrm{\α}}^{\left(k\right)}\right)}^2}---\left(2\right);$

(3), F ₂-F ₃space

$a_3=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}({\sin }^2{{\mathrm{\θ}}_1}^{\left(k\right)}-\cos 2{\mathrm{\α}}^{\left(k\right)})\right)}^2+{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}{\sin }^2{{\mathrm{\θ}}_1}^{\left(k\right)}\sin 2{\mathrm{\α}}^{\left(k\right)}\right)}^2}---\left(3\right);$

In formula the projection in the vertical direction of particle major axis and the F of a kth particle in cell cube ₁the angle of axle; α ^(k)that the particle major axis of a kth particle projects and F in the horizontal plane ₃the angle of axle;

F _i(i=1,2,3) are three orthogonal main directions of group structure; a _i(i=1,2,3) are the anisotropy amplitude parameter on three normal surfaces, and its theoretical span is 0 to 1, works as a _iwhen=0, particle towards being uniformly distributed, sample inner structure isotropy; Work as a _iwhen=1, particle be anisotropy towards concentrating entirely on surface level, N represents all amounts of particles in detecting unit body;

According to above-mentioned formula (1), formula (2) and formula (3) determine the thin sight anisotropy amplitude parameter of three planes respectively, then just can determine an orthotropy fabric tensor completely with any two parameters wherein, the particulate material orthotropy namely under definable three different conditions carefully sees fabric tensor.

3. the orthotropic thin sight group structure quantitative test of particulate material as claimed in claim 2 and analytical approach, is characterized in that: the particulate material orthotropy defined under three different conditions carefully sees fabric tensor and F _ijspecific as follows:

(1), F is used ₁-F ₃with F ₁-F ₂the fabric tensor 1 that the parameter of plane is determined

$F_{\mathrm{ij}}=\frac{1}{3+a_1+a_2-a_1{a}_{\text{2}}}\left[\begin{array}{ccc}1+a_1+a_2+a_1{a}_2& & \\ & 1+a_1-a_2-a_1{a}_2& \\ & & 1-a_1+a_2-a_1{a}_2\end{array}\right]---\left(4\right);$ (2), F ₁-F ₂with F ₂-F ₃the fabric tensor 2 that the parameter of plane is determined

$F_{\mathrm{ij}}=\frac{1}{3-a_1-a_3-a_1{a}_{\text{3}}}\left[\begin{array}{ccc}1+a_1-a_3-a_1{a}_3& & \\ & 1-a_1+a_3-a_1{a}_3& \\ & & 1-a_1-a_3+a_1{a}_3\end{array}\right]---\left(5\right);$

(3), F ₁-F ₃with F ₂-F ₃the fabric tensor 3 that the parameter of plane is determined

$F_{\mathrm{ij}}=\frac{1}{3-a_2+a_3+a_2{a}_{\text{3}}}\left[\begin{array}{ccc}1+a_2+a_3+a_2{a}_3& & \\ & 1-a_1+a_3-a_2{a}_3& \\ & & 1-a_2-a_3+a_2{a}_3\end{array}\right]---\left(6\right);$

In formula (1) and formula (2), work as α ^(k)=π/4, sin α ^(k)=cos α ^(k), then a ₁=a ₂, the amplitude parameter of horizontal direction two vertical planes is equal, and so material shows as transverse isotropy, and formula (6) deteriorates to transverse isotropy three-dimensional group configuration formula:

$F_{\mathrm{ij}}=\frac{1}{3-a}\left[\begin{array}{ccc}1+a& 0& 0\\ 0& 1-a& 0\\ 0& 0& 1-a\end{array}\right]---\left(7\right)$

In formula

$a=\frac{1}{2N}\sqrt{{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}({\cos }^2{\mathrm{\θ}}_1^{\left(k\right)}-\frac{{\sin }^2{\mathrm{\θ}}_1^{\left(k\right)}}{2})\right)}^2+\frac{1}{2}{\left(\underset{k=1}{\overset{2N}{\mathrm{\Σ}}}\sin 2{\mathrm{\θ}}_1^{\left(k\right)}\right)}^2}---\left(8\right)$

In formula, a is transverse isotropy amplitude parameter, and its span remains [0,1].

4. the orthotropic thin sight group structure quantitative test of particulate material as claimed in claim 1 and analytical approach, it is characterized in that: the solidification in step (1) specifically refers to the air pressure of applying 15 ~ 25kpa, epoxy resin is slowly injected in particulate material sample, then maintenance particulate material sample makes it solidify completely.