CN105160050A - Loaded coal and rock damage constitutive equation building method based on CT scanning - Google Patents

Abstract

The invention discloses a loaded coal and rock damage constitutive equation building method based on CT (Computed Tomography) scanning. According to the method, a CT scanning loading system is used for performing loading scanning processing on a coal and rock test specimen to obtain a two-dimensional gray-level image; by using MATLAB software and the two-dimensional gray-level image, the three-dimensional reconstruction of the coal and rock test specimen is performed through median filtering, threshold segmentation, image cutting, median interpolation, data compression and volume rendering flow process to obtain a three-dimensional reconstruction model; the MATLAB software is used again for extracting a destruction domain model from the three-dimensional rebuilding model; the destruction domain model is processed by a three-dimensional fractal box counting dimension method to obtain a general grid model and a destruction domain grid model; corresponding data statistics is performed to draw a size dimension table and a stress dimension table, and summarization is performed to obtain a corresponding mechanical formula; and a constitutive equation is deduced through the mechanical formula. The goals of quantificationally analyzing the expansion and evolution process and the final destruction degree of cracks in the coal and rock test specimen loaded deformation and cracking process, and accurately reflecting the crack spatial fractal features are achieved.

Description

A kind of loaded coal rock damage Constitutive Equation construction method based on CT scan

Technical field

The invention belongs to mathematic calculation field, relate to coal petrography damage Constitutive Equation construction method, particularly relate to a kind of loaded coal rock damage Constitutive Equation construction method based on CT scan.

Background technology

China is in one and builds stage of develop rapidly, various engineering project all in construction, as civil engineering work, railway traffic engineering, coal mining projects etc. have all related to the discussion about problems such as rock crannies.Because crack rock multiform is formed in special geologic condition, make it have stronger nonuniformity and anisotropy.The deformation and failure occurred under different stress condition obviously can affect quality and the security of all relevant workses with it.

But for a long time the aspects such as its macroscopic property are mainly concentrated on to the research of coal and rock, owing to being subject to the restriction of detection method means, less to the research of fine sight change mechanism, can not carry out in conjunction with the actual of coal and rock interior change veritably, therefore much study all with certain supposition or Utopian pattern.But in engineering reality, these supposition or Utopian pattern are difficult to set up.The internal rupture process of raw coal rock mass under various effect of stress is difficult to observation, indoor rock CT is utilized to test, the crack initiation of crackle, expansion and even to the whole process of breaking can be observed, but be in most cases qualitative analysis for crack developmental state in coal and rock.Based on above-mentioned situation, simple and reliable in the urgent need to one, effectively can improve coal petrography inside and split the loaded coal rock damage Constitutive Equation construction method based on CT scan characterizing precision, reach the expansion evolutionary process of crackle in the distortion of quantitative test coal petrography sample stand under load and rupture process and final destructiveness, accurately the object of reflection crackle spatial fractal.

Summary of the invention

The present invention utilizes CT scan loading system to carry out loading scan process to coal rock specimen and obtains 2-D gray image, 2-D gray image is utilized and through medium filtering by MATLAB software, threshold segmentation, image cut, intermediate value interpolation, data compression, the three-dimensional reconstruction that volume drawing flow process carries out coal rock specimen obtains Three-dimension Reconstruction Model, again utilize MATLAB software from Three-dimension Reconstruction Model, extract destruction domain model, utilize three-dimensional fractal package topology to carry out process to destruction domain model obtain overall trellis model and destroy territory grid model, carry out corresponding data statistics to draw size dimension table and stress dimension table and sum up and draw corresponding force equation, constitutive equation is derived finally by force equation, reach the expansion evolutionary process of crackle in the distortion of quantitative test coal petrography sample stand under load and rupture process and final destructiveness, the object of accurate reflection crackle spatial fractal.To achieve these goals, the present invention adopts following technical scheme:

Based on a loaded coal rock damage Constitutive Equation construction method for CT scan, it is characterized in that, comprise the steps:

(1) preparing experiment standard coal rock specimen, utilizes CT scan loading system load coal rock specimen and scan, and obtains the 2-D gray image of coal rock specimen internal crack expansion developmental condition under different loads.

(2) utilize MATLAB software to carry out medium filtering, threshold segmentation, image cut process to the 2-D gray image obtained in experiment, and utilize intermediate value interpolation, data compression, volume drawing flow process to carry out three-dimensional reconstruction to the 2-D gray image processed and obtain Three-dimension Reconstruction Model.

(3) utilize MATLAB software from Three-dimension Reconstruction Model, obtain crackle growth destruction region to obtain destroying domain model, three-dimensional fractal package topology is utilized to process destruction domain model, obtain covering the overall trellis model destroying domain model and the destruction territory grid model destroying grid occupied by domain model, and count the variable destroying territory grid model, i.e. grid number N, grid length of side L, wherein unit grids is small cubes.

(4) utilize MATLAB software that the variable data N counted, L are depicted as size dimension table, and return out formula lgN _(L)=-DlgL+lgk, wherein D value is required three-dimensional average fractal dimension, draws out stress dimension table, draw fractal dimension and external applied load relation equation in conjunction with the load that loads corresponding in CT scan loading system

$D=\left\{\begin{array}{cc}{C}_1+C_2\mathrm{\σ}/{\mathrm{\σ}}_c& {\mathrm{\σ}}_0>\mathrm{\σ}>0\\ C_3+C_4\mathrm{\σ}/{\mathrm{\σ}}_c& {\mathrm{\σ}}_c>\mathrm{\σ}>{\mathrm{\σ}}_0\end{array}\right..$

(5) isotropic elastoplastic damage variable is defined anisotropic damage variable and in conjunction with formula lgN _(L)=-DlgL+lgk, $D=\left\{\begin{array}{cc}{C}_1+C_2\mathrm{\σ}/{\mathrm{\σ}}_c& {\mathrm{\σ}}_0>\mathrm{\σ}>0\\ C_3+C_4\mathrm{\σ}/{\mathrm{\σ}}_c& {\mathrm{\σ}}_c>\mathrm{\σ}>{\mathrm{\σ}}_0\end{array}\right.,$ σ _ij＝K _ijklε _kl、 $K_{\mathrm{ijkl}}=K_{\mathrm{ijkl}}^0+K_{\mathrm{ijkl}}^I+K_{\mathrm{ijkl}}^{\mathrm{II}},K_{\mathrm{ijkl}}^0={\mathrm{\λ}}_0{\mathrm{\δ}}_{\mathrm{ij}}{\mathrm{\δ}}_{\mathrm{kl}}+2{\mathrm{\μ}}_0{\mathrm{\δ}}_{\mathrm{ik}}{\mathrm{\δ}}_{\mathrm{jl}},K_{\mathrm{ijkl}}^I={\mathrm{\Σ}}_{\mathrm{\γ}=1}^{\∞}({\mathrm{\λ}}_{\mathrm{\γ}}{\mathrm{\δ}}_{\mathrm{ij}}{\mathrm{\δ}}_{\mathrm{kl}}+2{\mathrm{\μ}}_{\mathrm{\γ\λ}}{\mathrm{\δ}}_{\mathrm{ik}}{\mathrm{\δ}}_{\mathrm{jl}}){\mathrm{\ω}}_0^{\mathrm{\γ}},$ $K_{\mathrm{ijkl}}^{\mathrm{II}}=C_1({\mathrm{\δ}}_{\mathrm{ij}}{\mathrm{\ω}}_{\mathrm{kl}}+{\mathrm{\δ}}_{\mathrm{kl}}{\mathrm{\ω}}_{\mathrm{ij}})+C_2({\mathrm{\δ}}_{\mathrm{ik}}{\mathrm{\ω}}_{\mathrm{jl}}+{\mathrm{\δ}}_{\mathrm{il}}{\mathrm{\ω}}_{\mathrm{jk}}+{\mathrm{\δ}}_{\mathrm{il}}{\mathrm{\ω}}_{\mathrm{ik}}+{\mathrm{\δ}}_{\mathrm{jk}}{\mathrm{\ω}}_{\mathrm{il}}),$ Finally draw constitutive equation ${{\mathrm{\σ}}^{\′}}_{\mathrm{ij}}=K_{\mathrm{ijkl}}{{\mathrm{\ϵ}}^{\′}}_{\mathrm{kl}}+K_{\mathrm{ijkl}}^{\′}{\mathrm{\ϵ}}_{\mathrm{kl}}.$

Compared with existing correlation technique, tool of the present invention has the following advantages:

The invention provides a kind of new coal petrography damage Constitutive Equation construction method, can the expansion evolutionary process of crackle and final destructiveness, accurately reflection crackle spatial fractal in the distortion of quantitative test coal petrography sample stand under load and rupture process; Utilize CT scan loading system process coal petrography sample to obtain 2-D gray image, utilize MATLAB to obtain Three-dimension Reconstruction Model and respective formula in conjunction with three-dimensional box counting dimension method, draw constitutive equation finally by the derivation of equation.

Accompanying drawing explanation

Fig. 1 is Three-dimension Reconstruction Model procedure chart of the present invention;

Fig. 2 is destruction domain model leaching process figure of the present invention;

Fig. 3 is constitutive equation building process figure of the present invention;

Fig. 4 is Three-dimension Reconstruction Model stand under load destructive process figure of the present invention;

Fig. 5 is stand under load destructive process sectional view of the present invention.

In figure: 1-coal rock specimen; 2-CT scans loading system; 3-2-D gray image; 4-MATLAB; 5-Three-dimension Reconstruction Model; 6-destroys domain model; 7-overall trellis model; 8-destroys territory grid model; 9-size dimension table; 10-stress dimension table; 11-formula; 12-constitutive equation.

Embodiment

Composition graphs 1, Fig. 2, Fig. 3, shown in Fig. 4, a kind of loaded coal rock damage Constitutive Equation construction method based on CT scan, comprises coal petrography sample 1, CT scan loading system 2, 2-D gray image 3, MATLAB4, Three-dimension Reconstruction Model 5, destroy domain model 6, overall trellis model 7, destroy territory grid model 8, size dimension table 9, stress dimension table 10, formula 11, constitutive equation 12, utilizes CT scan loading system 2 pairs of coal rock specimens 1 to carry out loading scan process and obtains 2-D gray image 3, utilizes 2-D gray image 3 and through medium filtering by MATLAB4 software, threshold segmentation, image cut, intermediate value interpolation, data compression, the three-dimensional reconstruction that volume drawing flow process carries out coal rock specimen 1 obtains Three-dimension Reconstruction Model 5, again utilize MATLAB4 software to extract from Three-dimension Reconstruction Model 5 and destroy domain model 6, utilize three-dimensional fractal package topology to carry out process to destruction domain model 6 obtain overall trellis model 7 and destroy territory grid model 8, carry out corresponding data statistics to draw size dimension table 9 and stress dimension table 10 and sum up and draw corresponding force equation 11, derive constitutive equation 12 finally by force equation 11.

Get certain ore deposit diameter 25mm, the standard coal test specimen model of height 50mm is test specimen, and 0, under 6.7MPa, 8.4MPa, 11.21MPa load, sets forth concrete steps of the present invention as follows:

(1) preparing experiment standard coal rock specimen 1, utilizes CT scan loading system 2 pairs of coal rock specimens 1 load and scan, and obtains the 2-D gray image 3 of coal rock specimen 1 internal crack expansion developmental condition under different loads.

(2) utilize MATLAB4 software to carry out medium filtering, threshold segmentation, image cut process to the 2-D gray image 3 obtained in experiment, and utilize intermediate value interpolation, data compression, volume drawing flow process to carry out three-dimensional reconstruction to the 2-D gray image 3 processed and obtain Three-dimension Reconstruction Model 5.

(3) utilize MATLAB4 software from Three-dimension Reconstruction Model 5, obtain crackle growth destruction region to obtain destroying domain model 6, three-dimensional fractal package topology is utilized to process destruction domain model 6, obtain covering the overall trellis model 7 destroying domain model 6 and the destruction territory grid model 8 destroying grid occupied by domain model 6, and count the variable destroying territory grid model 8, i.e. grid number N, grid length of side L, wherein unit grids is small cubes.

(4) utilize MATLAB4 software that the variable data N counted, L are depicted as size dimension table 9, and return out formula 11lgN _(L)=-DlgL+lgk, wherein D value is required three-dimensional average fractal dimension, draws out stress dimension correlation table as follows in conjunction with loading load corresponding in CT scan loading system 2:

Stress (MPa)	Linear fit result	Fractal dimension D
			0	Y＝-1.8946X+5.3525	1.8946
6.70	Y＝-1.8872X+5.3343	1.8872
			8.40	Y＝-1.8941X+5.3504	1.8941
11.21	Y＝-2.483X+6.4413	2.483

And draw fractal dimension and external applied load relation equation:

$D=\left\{\begin{array}{cc}1.8946-0.0123\mathrm{\σ}/{\mathrm{\σ}}_c& 8.35\mathrm{Mpa}>\mathrm{\σ}>0\\ 0.1337+2.3496\mathrm{\σ}/{\mathrm{\σ}}_c& 11.21\mathrm{Mpa}>\mathrm{\σ}>8.35\mathrm{Mpa}\end{array}\right.$

(5) isotropic elastoplastic damage variable is defined anisotropic damage variable and in conjunction with formula 11lgN _(L)=-DlgL+lgk, $D=\left\{\begin{array}{cc}1.8946-0.0123\mathrm{\σ}/{\mathrm{\σ}}_c& 8.35\mathrm{Mpa}>\mathrm{\σ}>0\\ 0.1337+2.3496\mathrm{\σ}/{\mathrm{\σ}}_c& 11.21\mathrm{Mpa}>\mathrm{\σ}>8.35\mathrm{Mpa}\end{array}\right.,$ σ _ij＝K _ijklε _kl、 $K_{\mathrm{ijkl}}=K_{\mathrm{ijkl}}^0+K_{\mathrm{ijkl}}^I+K_{\mathrm{ijkl}}^{\mathrm{II}},K_{\mathrm{ijkl}}^0={\mathrm{\λ}}_0{\mathrm{\δ}}_{\mathrm{ij}}{\mathrm{\δ}}_{\mathrm{kl}}+2{\mathrm{\μ}}_0{\mathrm{\δ}}_{\mathrm{ik}}{\mathrm{\δ}}_{\mathrm{jl}},K_{\mathrm{ijkl}}^I={\mathrm{\Σ}}_{\mathrm{\γ}=1}^{\∞}({\mathrm{\λ}}_{\mathrm{\γ}}{\mathrm{\δ}}_{\mathrm{ij}}{\mathrm{\δ}}_{\mathrm{kl}}+$ $2{\mathrm{\μ}}_{\mathrm{\γ}}{\mathrm{\δ}}_{\mathrm{ik}}{\mathrm{\δ}}_{\mathrm{jl}}){\mathrm{\ω}}_0^{\mathrm{\γ}},K_{\mathrm{ijkl}}^{\mathrm{II}}=C_1({\mathrm{\δ}}_{\mathrm{ij}}{\mathrm{\ω}}_{\mathrm{kl}}+{\mathrm{\δ}}_{\mathrm{kl}}{\mathrm{\ω}}_{\mathrm{ij}})+C_2({\mathrm{\δ}}_{\mathrm{ik}}{\mathrm{\ω}}_{\mathrm{jl}}+{\mathrm{\δ}}_{\mathrm{il}}{\mathrm{\ω}}_{\mathrm{jk}}+{\mathrm{\δ}}_{\mathrm{il}}{\mathrm{\ω}}_{\mathrm{ik}}+{\mathrm{\δ}}_{\mathrm{jk}}{\mathrm{\ω}}_{\mathrm{il}}),$ Finally draw constitutive equation ${12{\mathrm{\σ}}^{\′}}_{\mathrm{ij}}=K_{\mathrm{ijkl}}{{\mathrm{\ϵ}}^{\′}}_{\mathrm{kl}}+K_{\mathrm{ijkl}}^{\′}{\mathrm{\ϵ}}_{\mathrm{kl}}.$

Certainly; more than illustrate and be only preferred embodiment of the present invention; the present invention is not limited to enumerate above-described embodiment; should be noted that; any those of ordinary skill in the art are under the instruction of this instructions; the all equivalent replacement made, obviously form of distortion, within the essential scope all dropping on this instructions, ought to be subject to protection of the present invention.

Claims (1)

1., based on a loaded coal rock damage Constitutive Equation construction method for CT scan, it is characterized in that, comprise the steps:

(1) preparing experiment standard coal rock specimen, utilizes CT scan loading system load coal rock specimen and scan, and obtains the 2-D gray image of coal rock specimen internal crack expansion developmental condition under different loads.

(2) utilize MATLAB software to carry out medium filtering, threshold segmentation, image cut process to the 2-D gray image obtained in experiment, and utilize intermediate value interpolation, data compression, volume drawing flow process to carry out three-dimensional reconstruction to the 2-D gray image processed and obtain Three-dimension Reconstruction Model.

(3) utilize MATLAB software from Three-dimension Reconstruction Model, obtain crackle growth destruction region to obtain destroying domain model, three-dimensional fractal package topology is utilized to process destruction domain model, obtain covering the overall trellis model destroying domain model and the destruction territory grid model destroying grid occupied by domain model, and count the variable destroying territory grid model, i.e. grid number N, grid length of side L, wherein unit grids is small cubes.

(4) utilize MATLAB software that the variable data N counted, L are depicted as size dimension table, and return out formula lgN _(L)=-DlgL+lgk, wherein D value is required three-dimensional average fractal dimension, draws out stress dimension table, draw fractal dimension and external applied load relation equation in conjunction with the load that loads corresponding in CT scan loading system $D=\left\{\begin{array}{cc}{C}_1+C_2\mathrm{\σ}/{\mathrm{\σ}}_c& {\mathrm{\σ}}_0>\mathrm{\σ}>0\\ C_3+C_4\mathrm{\σ}/{\mathrm{\σ}}_c& {\mathrm{\σ}}_c>\mathrm{\σ}>{\mathrm{\σ}}_0\end{array}\right..$

(5) isotropic elastoplastic damage variable is defined anisotropic damage variable n _j ^(k), and in conjunction with formula lgN _(L)=-DlgL+lgk, $D=\left\{\begin{array}{cc}{C}_1+C_2\mathrm{\σ}/{\mathrm{\σ}}_c& {\mathrm{\σ}}_0>\mathrm{\σ}>0\\ C_3+C_4\mathrm{\σ}/{\mathrm{\σ}}_c& {\mathrm{\σ}}_c>\mathrm{\σ}>{\mathrm{\σ}}_0\end{array}\right.,$ σ _ij＝K _ijklε _kl、 $K_{\mathrm{ijkl}}=K_{\mathrm{ijkl}}^0+K_{\mathrm{ijkl}}^I+k_{\mathrm{ijkl}}^{\mathrm{II}},K_{\mathrm{ijkl}}^0={\mathrm{\λ}}_0{\mathrm{\δ}}_{\mathrm{ij}}{\mathrm{\δ}}_{\mathrm{kl}}+{2\mathrm{\μ}}_0{\mathrm{\δ}}_{\mathrm{ik}}{\mathrm{\δ}}_{\mathrm{jl}},K_{\mathrm{ijkl}}^I={\mathrm{\Σ}}_{\mathrm{\γ}=1}^{\∞}({\mathrm{\λ}}_{\mathrm{\γ}}{\mathrm{\δ}}_{\mathrm{ij}}{\mathrm{\δ}}_{\mathrm{kl}}+{2\mathrm{\μ}}_{\mathrm{\γ}}{\mathrm{\δ}}_{\mathrm{ik}}{\mathrm{\δ}}_{\mathrm{jl}}){\mathrm{\ω}}_0^{\mathrm{\γ}},$ $K_{\mathrm{ijkl}}^{\mathrm{II}}=C_1({\mathrm{\δ}}_{\mathrm{ij}}{\mathrm{\ω}}_{\mathrm{kl}}+{\mathrm{\δ}}_{\mathrm{kl}}{\mathrm{\ω}}_{\mathrm{ij}})+C_2({\mathrm{\δ}}_{\mathrm{ik}}{\mathrm{\ω}}_{\mathrm{jl}}+{\mathrm{\δ}}_{\mathrm{il}}{\mathrm{\ω}}_{\mathrm{jk}}+{\mathrm{\δ}}_{\mathrm{il}}{\mathrm{\ω}}_{\mathrm{ik}}+{\mathrm{\δ}}_{\mathrm{jk}}{\mathrm{\ω}}_{\mathrm{il}}),$ Finally draw constitutive equation $\stackrel{\·}{{\mathrm{\σ}}_{\mathrm{ij}}}=K_{\mathrm{ijkl}}\stackrel{\·}{{\mathrm{\ϵ}}_{\mathrm{kl}}}+K_{\mathrm{ijkl}}^{\·}{\mathrm{\ϵ}}_{\mathrm{kl}}.$