CN116384177A - MATLAB and finite element software combination-based thickness-free disc crack generation method - Google Patents
MATLAB and finite element software combination-based thickness-free disc crack generation method Download PDFInfo
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Abstract
The invention discloses a method for generating a thickness-free disc fracture based on the combination of MATLAB and finite element software, which relates to the field of fracture rock mass seepage calculation, wherein a script file is written by virtue of a finite element software with MATLAB interface, so that a required discrete fracture network model can be directly generated in the finite element software; the probability density function can be directly changed in the script file according to the requirements to generate a discrete fracture network model which accords with the actual situation; when the grid is split, the difficulty of the grid split can be greatly reduced, the crack opening is not required to be considered in pretreatment, the grid discrete difficulty of the model can be reduced, the solving process is simplified, and the numerical dispersion oscillation phenomenon is effectively reduced. The degree of freedom of calculation of the entire model is reduced, thereby reducing the time required for calculation of the model.
Description
Technical Field
The invention belongs to the field of fracture rock mass seepage calculation, and particularly relates to a non-thickness disc fracture generation method based on MATLAB and finite element software combination.
Background
The generation of the existing discrete fracture network model is generally carried out by adopting MATLAB and utilizing a Monte Carlo method. But how the generated fracture network is imported into the mainstream analysis software is a problem. For example, after a disc crack with a thickness is generated by MATLAB, an SCR script file is written by using the space position information of the disc crack and is imported into AUTOCAD for transfer, and the output is imported into finite element software for calculation as a three-dimensional CAD file, but the AUTOCAD has the problems that the micro crack cannot be identified and the calculation is not converged.
At present, when software finite element software is used for seepage and multi-field coupling, random fracture generation can generate a discrete fracture network model by means of software plug-in components, but sometimes when simulation is carried out according to field actual measurement data, parameters obeyed by fracture geometry properties set by plug-in components carried by the software can not be needed by the software, and the software needs to write a proper script by the user to generate the discrete fracture network model which accords with actual conditions.
Disclosure of Invention
The invention aims to provide a method for generating a thickness-free disc crack based on the combination of MATLAB and finite element software, which realizes the seepage analysis of a region by generating the thickness-free disc crack through the combination of MATLAB and finite element software.
The technical solution for realizing the purpose of the invention is as follows:
a method for generating a thickness-free disc crack based on the combination of MATLAB and finite element software comprises the following steps:
Compared with the prior art, the invention has the remarkable advantages that:
(1) Compared with the traditional method for directly generating disc cracks with thickness by utilizing MATLAB, the method can directly generate a required discrete crack network model in finite element software by utilizing the finite element software with MATLAB, does not need to transfer by utilizing AUTOCAD and other software, and does not have the conditions of calculation non-convergence and the like which are easy to occur when the grid model is directly imported;
(2) Compared with the traditional disc fracture with the thickness, the difficulty of grid subdivision can be greatly reduced when the grid is split, the fracture opening is not required to be considered during pretreatment, the grid discrete difficulty of a model can be reduced, the solving process is simplified, and the numerical dispersion oscillation phenomenon is effectively reduced. The calculation freedom degree of the whole model is reduced, so that the time required by model calculation is reduced;
(3) The probability density function obeyed by the fracture geometry parameter distribution can be changed according to the own requirements. Compared with a discrete fracture network model generated by directly using finite element software, FRACMAN and other software with plug-ins, the probability density function can be directly changed in the script file according to the requirements to generate the discrete fracture network model conforming to the actual situation;
(4) The method can delete the disc fracture with small diameter according to the own needs when generating the disc fracture without thickness, consider the relation between the fracture opening and the trace length in the modeling process, directly determine the value of the opening as a variable aperture according to the relation between the opening and the trace length when generating the disc fracture by utilizing finite element software with MATLAB, and directly input aperture when calculating the permeability by utilizing the opening subsequently, so that the permeability can be automatically calculated. And after the disc fracture generated by MATLAB is imported into finite element software, assignment of fracture opening is a problem.
Drawings
FIG. 1 is a diagram of a method and technique of research.
Fig. 2 is a scenario diagram of script execution progress.
Fig. 3 is a schematic diagram of a randomly generated spatial point coordinate distribution.
FIG. 4 is a graph of the disc-shaped fracture occurrence parameters in three dimensions.
FIG. 5 is a graph of a random discrete fracture network model without thickness generated by the present invention.
FIG. 6 is a plan view of a single disc slot.
Detailed Description
The invention is further described with reference to the drawings and specific embodiments.
The method for generating the thickness-free disc fracture based on the combination of MATLAB and finite element software comprises the following steps:
finite element software and MATLAB are normally installed, the desktop cannot be provided with the finite element software and MATLAB, the finite element software needs to be installed again, MATLAB interfaces are reserved during installation, a user name and a password need to be input when the desktop is used for the first time (the user name and the password are not needed later), the MATLAB can be automatically opened after setting is completed, and a script file is newly built.
First, the following procedure is added to the script:
function out＝random_solid_nosize
clc；clear；
import com. Finite element software model
import com. Finite element software model
model＝ModelUtil.create('Model')；
model.component.create('comp1',true)；
model. Component ('comp 1'). Geom. Create ('geom 1', 3); (three-dimensional research Domain)
model.component('comp1').mesh.create('mesh1')；
model. Component ('comp 1'). Geom ('geom 1'). Selection (). Create ('csel 1', 'cumuloven selection'); % create a new selection set and add the tag csel and the name CumulativeSelect
model.nodeGroup.create('grp1','Definitions','comp1')；
import com. Finite element software model.
ModelUtil. Showprogress (true)% shows progress of fracture disc formation
The file name can be defined, the research domain is three-dimensional, and the progress situation of fracture disc generation is displayed, specifically, the figure 2 is shown.
Step two, inputting (the situation is illustrated according to four groups of cracks) in a script opened by finite element software with MATLAB:
% of the number of groups of co-cracks
count＝3；
% creating a rectangle, and the length, width and height are respectively: c. k, g
c＝20；k＝20；g＝20；
The number of fracture groups and the size of the research domain can be input as required.
Step three, determining the space position parameters of the fracture
The fracture location is the most important distribution parameter in the fracture network, and the most common way is to describe the fracture location using the coordinates of a point (typically the coordinates of a centroid point). There are various ways to generate the fracture spatial distribution, and this embodiment uses a homogeneous poisson distribution model to generate fracture location parameters, taking into account the influence of bulk density first. The bulk density parameter can be obtained by statistical analysis after field investigation, and the fracture bulk density and the following formula are calculated.
In the formula (1): e (lambda) ν ) For the desired value of the space-slit bulk density, bars/m 3 ；E(λ a ) For fracture surface density expectations obtained from field survey statistics by the arranged window method, bars/m 2 The method comprises the steps of carrying out a first treatment on the surface of the E (D) is an expected value of the fracture diameter, m; e (|sin v|) is an expected value of an included angle between a structural plane statistical average direction vector and a exposed surface of the arranged windowed rock mass.
For implementation in a programming statement, reference may be made to the following steps:
a. dividing the study domain D into m sub-regions (a 1 ,A 2 ,…,A i …,A m )。
b. In a sub-area A i In, a series of compliance [0,1 ] is generated]Uniformly distributed random numbers: u (U) 1 ,U 2 …, the generation of the random number U is stopped until the following inequality is established:
at this time k is the current sub-region A i The number of cracks in (A) and the number of crack strips N (A) i ) Obeying parameter mu i ＝λ·v(A i ) Poisson distribution of v (A) i ) For the ith sub-area A i Volume, m 3 The method comprises the steps of carrying out a first treatment on the surface of the Lambda is the space density of the crack, bar/m 3 . And then, uniformly distributing the centroid points of the k cracks to generate x, y and z coordinate components in the three-dimensional space coordinates.
c. Operation b is performed for each sub-region in the study domain.
The sub-regions are generally preferably cube units and have uniform side lengths, and the number of sub-regions is made as large as possible. One simulation result in the above procedure can be seen in FIG. 3, which is an average division of the study area (cube with side length of 5 m) into 125 sub-areas A i And then, simulating corresponding parameters to obtain a three-dimensional coordinate distribution diagram of the space point of the crack centroid (circle center). See figure 3 of the drawings. The specific input cases in the script are:
e_lambda_a= [0.005 0.006 0.004]; expected value of% space fracture bulk density, expected value of fracture surface density obtained by field survey statistics by arranging a window method, bar/m
Ejd= [ 1.2.5 ]; expected value of% fracture diameter
E_sinv= [ 0.5.0.6.8 ]; % angle v is the included angle of the structural plane statistical average direction vector and the exposed head face of the arranged windowed rock mass
for i＝1:count
mu(i)＝log((m(i)^2)/sqrt(v(i)+m(i)^2))；
sigma(i)＝sqrt(log(v(i)/(m(i)^2)+1))；
E_lambda_v (i) =e_lambda_a (i)/e_d (i)/e_sinv (i); % fracture volume Density of each group
mu_total (i) =floor (e_lambda_v (i) c k g); % number of fissure strips of each group
end
Step four, determining fracture size parameters
The fracture size parameter means the size of the fracture and is one of the important factors used to assess fracture connectivity within the rock matrix. For a three-dimensional disc-shaped fracture network model, the representative value becomes the radius of the disc, the fracture size distribution form is nearly similar to the trace length distribution form, the trace length distribution can be used for estimating the size parameter in most cases, the trace length can be considered to be subjected to lognormal distribution in the modeling process, and the same fracture size (the disc-shaped fracture diameter here) also is required to be subjected to lognormal distribution.
Wherein: f (x) is a probability density function. Let y=ln x, then y obeys normal distribution, corresponding mathematical expectation μ y Standard deviation sigma y Desired μ by variable x x Standard deviation sigma x Calculated via the following formula:
the fracture disc diameter is deduced by Wu Faquan estimation formula:
wherein:
(m) is the average value of the crack trace; r and D (m) are the radius and diameter of the slit disk, respectively. When the fracture length and the fracture disc diameter on the dew face all obey the same distribution function f x (x) In the time-course of which the first and second contact surfaces,
in formula (6):
is the long average value of the fracture. The average and variance of the fracture length l can be obtained by:
in the formula (7): sigma (sigma) l Is the standard deviation of the fracture length. Average diameter of fracture disc obtained by combining (4)
Corresponding standard deviation sigma D ：
The corresponding situations to be set in the script are:
trace length of% fissures: log normal distribution
l= [5.01 4 3]; % mean value
sigma_l= [ 2.12.1.5 ]; % variance
dlimit=2; % of the limiting diameter, the fissures smaller than this diameter being to be deleted; if smile is to be removed, the parameter is adjusted to a larger value, such as 1e5.
Step five, determining fracture occurrence parameters
The probability density function of the disc fracture is set according to the Fisher distribution rule:
in formula (6): f (θ) is von-Mises distribution probability density function; mu is the average trend E [0,2 pi ]]θ is the average tilt angle ε [0, pi/2 ]]The method comprises the steps of carrying out a first treatment on the surface of the Kappa is the corresponding discrete coefficient; i 0 (κ) is a modified Bessel function of order 0. The specific three-dimensional disc-shaped fissure morphology is shown in figure 3. The corresponding situations to be set in the script are:
% Fisher distribution where kappa is a discrete coefficient (i.e., fisher constant), with a larger kappa indicating a denser distribution and closer to the dominant group yield center; θ is the included angle between the simulated structural plane vector and the average vector of the fracture surface
k1 = [30 28 25]; the discrete coefficients k1 of the% dip angle are from left to right the discrete coefficients of the first group of cracks and the discrete coefficients of the second group of cracks respectively
k2 = [20 15 26]; the discrete coefficients k2 of% trend are from left to right the discrete coefficients of the first group of cracks and the discrete coefficients of the second group of cracks respectively
qj= [69.07 90 0]; % tilt angle, the same as
Step six, determining the opening degree parameter of the crack
And (3) researching the opening degree of the fracture, and if the conditions allow, first selecting an in-situ test experiment in a field. For matrix rock mass cracks, the accurate acquisition of the opening degree is difficult, and a plurality of students find that a certain relation exists between the opening degree of the crack and the trace length through research, and at present, the crack opening degree and the crack length are considered to be subject to power law distribution as accepted:
in the formula e max To measureMeasuring the maximum opening of the crack;
the average value of the trace length of the corresponding opening degree; alpha is a coefficient constant related to fracture roughness, β is a tension control coefficient. The corresponding situations to be set in the script are: % fracture opening
e＝0.000063*l^0.5；
wp＝['wp',num2str(flag)]；
var＝['var',num2str(flag)]；
bnd＝['geom1_wp',num2str(flag),'_bnd']；
The protruding part of the invention is the generation of the disc fracture without thickness, which is mainly to treat the disc fracture into circles equivalently, convert the thickness into a variable (determined according to the formula (10)) and can be directly called when calculating the permeability. And finally, carrying out segmentation objects and a joint body formation in Boolean operation on the generated cuboid universe and the disc fracture, storing and outputting a model, and then directly opening the mph file to manually add material parameters, physical fields and divide grid calculation. The corresponding settings in the script are:
thickness-free disk fracture model randomly generated with reference to data of table 1
TABLE 1 fracture geometry statistics for certain homogeneous zone models
In summary, the invention realizes the probability density function obeyed by manual change of the fracture geometry parameters, has simple operation, can delete the disc fracture with small diameter according to the own needs when generating the non-thickness disc fracture, can consider the relation between the fracture opening and the trace length in the modeling process, can directly determine the value of the opening as a variable aperture according to the relation between the opening and the trace length when generating the disc fracture by utilizing the finite element software with MATLAB, and can automatically calculate the permeability by directly inputting aperture when calculating the permeability by utilizing the opening subsequently. And after the disc fracture generated by MATLAB is imported into finite element software, assignment of fracture opening is a problem. The discrete fracture network model which is generated by the finite element software and the FRACMAN and other software with plug-ins can be directly used for changing probability density functions in script files according to requirements to generate the discrete fracture network model which accords with actual conditions. The transfer is not needed by software such as AUTOCAD, and the situation that calculation is not converged easily occurs when the grid model is directly imported is avoided. And when the grid is split, the crack opening is not required to be considered in pretreatment, so that the grid discrete difficulty of the model can be reduced, the solving process is simplified, and the numerical dispersion oscillation phenomenon is effectively reduced. The degree of freedom of calculation of the entire model is reduced, thereby reducing the time required for calculation of the model.
Claims (5)
1. A method for generating a thickness-free disc crack based on the combination of MATLAB and finite element software is characterized by comprising the following steps:
step 1, opening finite element software with MATLAB, creating a script file for defining file names, research domains and displaying progress conditions of crack disc generation;
step 2, inputting the fracture group number and the size of a research domain in finite element software with MATLAB;
step 3, determining the spatial position distribution of the cracks: dividing a research domain into a plurality of subdomains, and generating a series of uniformly distributed random numbers in each subdomain to obtain coordinates of circle center points of the disc cracks;
step 4, determining the size of the crack: determining the size of a fracture disc according to the trace length of the fracture measured at the present place through a Wu Faquan estimation formula;
step 5, determining the occurrence distribution of the cracks: determining the inclination angle and the discrete coefficient of the disc fracture according to the Fisher distribution rule;
step 6, determining the opening degree of the crack: and determining the opening degree of the fracture according to the trace length of the fracture and the power law distribution.
2. The method for generating the disc crack without thickness based on the combination of MATLAB and finite element software as claimed in claim 1, wherein the step 3 specifically comprises the following steps:
(1) Dividing the study domain D into m sub-regions (a 1 ,A 2 ,…,A i …,A m )；
(2) In a sub-area A i In, a series of compliance [0,1 ] is generated]Uniformly distributed random numbers: u (U) 1 ,U 2 …, the generation of the random number is stopped until the following inequality is established:
where k is the current sub-region A i The number of cracks in (A) and the number of crack strips N (A) i ) Obeying parameter mu i ＝λ·v(A i ) Poisson distribution of v (A) i ) For the ith sub-area A i Is defined by the volume of (2); lambda is the space bulk density of the crack; then, uniformly distributing centroid points of the k cracks in sequence to generate x, y and z coordinate components in the three-dimensional space coordinates;
c. and (3) executing operation (2) on each sub-area in the research area to obtain the coordinates of the center point of the disc fracture of the whole research area.
3. The method for generating a disc-shaped crack without thickness based on the combination of MATLAB and finite element software according to claim 2, wherein the spatial bulk density of the crack is calculated by the following formula:
wherein: e (lambda) ν ) Is the expected value of the space fracture volume density; e (lambda) a ) The fracture surface density expected value is obtained by the field survey statistics through a window arrangement method; e (D) is an expected value of the fracture diameter; e (|sin v|) is an expected value of an included angle between a structural plane statistical average direction vector and a exposed surface of the arranged windowed rock mass.
4. The method for generating a thickness-free disc fracture based on MATLAB and finite element software combination as recited in claim 1, wherein the fracture disc size comprises a fracture disc diameter average
Corresponding standard deviation sigma D ：
Wherein when the fracture length and the fracture disc diameter on the dew face obey the same distribution function f x (x) When it is available
Is the long average value of the fracture; />
Is the average value of the fracture length; r and D (m) are the radius and diameter of the slit disk, respectively.
5. The method for generating a disc crack without thickness based on the combination of MATLAB and finite element software according to claim 1, wherein the crack opening degree is:
in the formula e max To measure the maximum opening of the fracture;
the average value of the trace length of the corresponding opening degree; alpha is a coefficient constant related to crack roughness, and beta is a tension control coefficient.
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