CN114925583B - Method for determining complex dielectric constant of asphalt concrete - Google Patents
Method for determining complex dielectric constant of asphalt concrete Download PDFInfo
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Abstract
A method for determining the complex dielectric constant of asphalt concrete comprises the following steps: 1: generating an asphalt concrete model according to gradation in discrete element software through an aggregate database; 2: dividing the model into a substrate, coarse aggregate, air and water by adopting a reforming method, and generating a document; 3: establishing an electromagnetic wave frequency domain model in electromagnetic simulation software, constructing a three-dimensional geometry, importing a document, and then performing Boolean operation on a geometric complex; 4: respectively setting material properties for the materials, and respectively endowing the material properties with corresponding three-dimensional geometry; 5: setting an electromagnetic wave port and boundary conditions for the model; 6: carrying out mesh division on the model; 7: setting the starting frequency, the stopping frequency and the step length of a solver to be researched; 8: calculating the research to obtain a curve graph of the S parameter changing along with the frequency, and outputting a complex form of the S parameter; 9: and inversely calculating the complex dielectric constant of the asphalt concrete according to the S parameter.
Description
Technical Field
The invention belongs to the technical field of road engineering analysis, and particularly relates to a method for determining the complex dielectric constant of asphalt concrete.
Background
Microwave heating is the penetration of electromagnetic energy into a medium in the form of waves, causing the medium to lose heat and generate heat without conduction, and without the need for a high temperature medium to transfer heat. Asphalt concrete is a non-magnetic material, and the strength of the microwave energy coupling capacity is determined by the dielectric constant of the asphalt concrete. In forward simulation and inversion imaging of the ground penetrating radar, physical parameters of a background medium and a target body are generally assumed to be uniformly distributed, but actually, dielectric characteristics of each component material are different, volume ratios are different, and particle shapes and distribution forms are different. In order to improve the utilization efficiency of microwave energy in the road maintenance process and improve the detection efficiency and accuracy of a ground penetrating radar, the research on the complex dielectric constant of asphalt concrete is an inevitable trend from a microscopic structure.
Therefore, it is necessary to design a method for determining the complex dielectric constant of asphalt concrete.
Disclosure of Invention
The invention aims to provide a method for determining complex dielectric constant of asphalt concrete, which aims to solve the problems that the microwave energy utilization efficiency in the road maintenance process is influenced and the efficiency and accuracy of ground penetrating radar detection are influenced due to different dielectric properties, unequal volume ratios and different particle shapes and distribution forms of various components in the asphalt concrete in the road maintenance process.
The technical scheme of the invention is that,
a method for determining the complex dielectric constant of asphalt concrete comprises the following steps:
step 1: generating an asphalt concrete model according to gradation in discrete element software through an aggregate database;
step 2: dividing the asphalt concrete model into a matrix, coarse aggregate, air and water by adopting a reforming method, and generating a document;
and step 3: establishing an electromagnetic wave frequency domain model in electromagnetic simulation software, constructing a three-dimensional geometry, importing the document finally generated in the step (2), and then performing Boolean operation on a complex formed by the three-dimensional geometry;
and 4, step 4: respectively setting material properties for different materials in the electromagnetic wave frequency domain model, and respectively endowing the material properties with corresponding three-dimensional geometry;
and 5: setting an electromagnetic wave port and boundary conditions for the electromagnetic wave frequency domain model;
step 6: carrying out grid division on the electromagnetic wave frequency domain model;
and 7: setting initial frequency, stop frequency and step length of a solver for researching the electromagnetic wave frequency domain model in finite element software;
and 8: calculating the research of the electromagnetic wave frequency domain model in finite element software to obtain a curve graph of the S parameter changing along with the frequency, and outputting a complex form of the S parameter;
and step 9: and (5) reversely calculating the complex dielectric constant of the asphalt concrete according to the S parameter obtained in the step 8 by using MATLAB programming codes.
In a specific embodiment, the step 1 specifically includes:
1.1 Randomly selecting N aggregate models from the existing three-dimensional aggregate model library, and numbering from GL-1 to GL-N in sequence;
1.2 Sequentially importing stl files of the numbered three-dimensional aggregate models through PFC3D software to generate a template clump;
1.3 The asphalt concrete is regarded as being composed of four components of coarse aggregate, asphalt concrete matrix, air and water, and a growth C is generated in discrete element software through code programming 1 Width of K 1 High is H 1 The coarse aggregate balls are generated in the cuboid according to the gradation and the oilstone ratio of the asphalt concrete;
1.4 And (3) replacing all the coarse aggregate balls in the step 1.3 by using the template column generated in the step 1.2 by using the template column with the same volume by adopting a diameter equivalent method to generate a coarse aggregate column, wherein the coarse aggregate column is arranged in the cuboid generated in the step 1.3, and the part of the cuboid generated in the step 1.3 except the coarse aggregate column is a mixture consisting of asphalt concrete matrix, air and water.
In a specific embodiment, the step 2 specifically includes:
2.1 In the space range of the cuboid generated in the step 1, small balls with the same size and the diameter of less than or equal to 1mm are generated and uniformly arranged to fill the whole space area;
2.2 Judging whether the centroid coordinate of the small balls is located in the coarse aggregate column or in a mixture consisting of the asphalt concrete matrix, air and water through the codes, and setting the grouping type of the small balls according to the positions of the centroid coordinate of the small balls;
2.3 All aggregate spheres are deleted, and only the uniformly distributed small spheres are reserved;
2.4 The method comprises the steps of randomly adjusting the grouping type of pellets belonging to a mixture consisting of an asphalt concrete matrix, air and water through codes, so that the proportion of the pellets with the grouping type of air and water in the total pellets respectively meets the requirements of the void ratio and the water content of the asphalt concrete;
2.5 And outputting the centroid coordinates of all the small balls and the small ball grouping category as a txt document.
In a particular embodiment of the method of the present invention,
in step 2.2, the grouping category of the small balls with the centroid coordinates in the coarse aggregate column is set as guliao, and the grouping category of the small balls with the centroid coordinates in the mixture of the asphalt concrete matrix, the air and the water is set as jizhi;
in step 2.4, by using MATLAB codes, small balls are randomly selected from small balls with the small ball grouping category of jizhi, and the grouping category is changed into kongxi and shui, so that the void ratio and the water content reach the asphalt concrete grading requirement.
In a specific embodiment, the step 3 specifically includes:
3.1 Opening COMSOL Multiphysics software, selecting a model guide, selecting a three-dimensional model, selecting electromagnetic waves and a frequency domain, researching and selecting the frequency domain, and constructing;
3.2 In COMSOL Multiphysics software, geometry is selected, and long C is constructed in sequence 1 Width of K 1 High is H 3 、H 2 、H 1 、H 2 、H 3 Five cuboids connected with each other;
3.3 Setting the cuboid at the top and the bottom of the model as a perfect matching layer in component definition, and naming the perfect matching layer as PML1 and PML2 in geometry;
3.4 The middle height is H 1 The cuboid is named as microscopic asphalt concrete in geometry, and the rest two are H 2 The cuboids are named as air 1 and air 2 in geometry;
3.5 Calling a COMSOL multi-physics and MATLAB joint simulation interface, importing the txt document generated in the step 2 through codes, and converting the centroid coordinates through the codes;
3.6 Selecting small balls with centroid coordinates located in the coarse aggregate column in the microscopical asphalt concrete cuboid according to the converted coordinates, sequentially constructing cubes with side length being the diameter of the small balls by utilizing coordinate information derived from the small balls, and naming the part of geometry, namely the geometry formed by the cubes with side length being the diameter of the small balls constructed by the small balls with all centroid coordinates located in the coarse aggregate column as coarse aggregate;
3.7 Selecting small balls with the grouping category of kongxi in the microscopic asphalt concrete cuboid according to the converted coordinates, sequentially constructing cubes with the side length being the diameter of the small balls by utilizing coordinate information derived from the small balls, and naming the part of geometry, namely the geometry formed by the cubes with the side length being the diameter of the small balls constructed by all the small balls with the grouping category of kongxi as a gap;
3.8 Selecting small balls with the classification of shui in the microscopic asphalt concrete cuboid according to the converted coordinates, sequentially constructing cubes with the side length of the small balls by utilizing coordinate information derived from the small balls, and naming the part of geometry, namely the geometry formed by the cubes with the side length of the small balls constructed by all the small balls with the classification of shui as water;
3.9 And forming a combination of the geometric PML1, the geometric PML2, the air 1, the air 2, the microscopic asphalt concrete, the coarse aggregate, the water and the gaps, and performing Boolean operation.
In a specific embodiment, the step 4 specifically includes:
4.1 Setting different material attributes, wherein the material attributes are named as an air material, a coarse aggregate material, a matrix material and a water material respectively;
4.2 Setting the real part of the complex dielectric constant of the air material as epsilon kqr Imaginary part set to ε kqi Electrical conductivity of σ kq Endowing the PML1, PML2, air 1, air 2 and the corresponding geometry of the gap with the air material property;
4.3 Setting the real part of the complex dielectric constant of the coarse aggregate material as epsilon gr With imaginary part set to ε gi Electrical conductivity of σ g Endowing the aggregate material attribute with the corresponding geometry of the coarse aggregate; when various coarse aggregate materials with different attributes exist, the different coarse aggregate materials are respectively set and corresponding geometric attributes are given;
4.4 Setting the real part of the complex dielectric constant of the water material as epsilon sr Imaginary part set to ε si Electrical conductivity of σ s Endowing the water material attribute with the corresponding geometry of water;
4.5 Setting the real part of the complex dielectric constant of the matrix material to epsilon jr With imaginary part set to ε ji Electrical conductivity of σ j And endowing the matrix material attribute to the corresponding geometry of the microscopic asphalt concrete.
In a specific embodiment, the step 5 specifically includes:
5.1 Adding two ports in a physical field, wherein the two ports are named as an input port and an output port respectively;
5.2 The input port is chosen to be the top of the air 1, the port type is set to a periodic condition, the port's wave excitation is set to open and activate a slit condition on the internal port, the magnitude of the electric mode field is set to TE 10 The incident elevation angle and azimuth angle are set to 0rad;
5.3 The output port is chosen to be the bottom of air 2, the port type is set to periodic condition, the port's wave excitation is set to off and a slit condition is activated on the internal port, the magnitude of the electric mode field is set to TE 10 The incident elevation angle and azimuth angle are set to 0rad;
5.4 Setting a periodic boundary condition 1, selecting two opposite boundary surfaces in the geometric PML1 and PML2, wherein the total number of the boundary surfaces is 4, setting the periodic types as Floquet periods, and setting k vectors from periodic ports;
5.5 Setting a periodic boundary condition 2, selecting another two opposite boundary surfaces in the geometric PML1 and PML2, wherein the total number of the boundary surfaces is 4, setting the periodic types as Floquet periods, and setting k vectors from periodic ports;
5.6 Setting a periodic boundary condition 3, selecting two opposite boundary surfaces of geometric air 1, air 2 and microscopic asphalt concrete, wherein the total number of the two boundary surfaces is 6, setting periodic types as Floquet periods, and setting k vectors from periodic ports;
5.7 Setting a periodic boundary condition 4, selecting another two opposite boundary surfaces in geometric air 1, air 2 and microscopic asphalt concrete, and setting 6 boundary surfaces in total, wherein the periodic types are all Floquet periods, the Floquet period boundary condition can better simulate the periodicity, the continuous boundary condition and the anti-symmetric boundary condition are only special cases that the Floquet phases are respectively 0 and pi, and k vectors are all from periodic ports, namely wave vectors.
In a particular embodiment of the method of the present invention,
the step 6 specifically includes:
6.1 Controlling the grid by adopting a physical field, wherein the size of grid cells is set to be refined;
6.2 Selecting the maximum grid cell size control parameter as from research and analyzing the wave in the lossy medium;
6.3 Constructing a free tetrahedral grid of the electromagnetic wave frequency domain model;
the step 7 specifically includes:
7.1 set the solver starting frequency for the study to f 1 Setting the solver stopping frequency of the study to be f 2 ；
7.2 Setting the step length of the simulation to f d 。
In a specific embodiment, the step 8 specifically includes:
8.1 Calculating the research to obtain an electric field multi-section schematic diagram of an electromagnetic wave frequency domain model and a one-dimensional schematic diagram of S parameters changing along with frequency, wherein the S parameters comprise a reflection coefficient S11 and a transmission coefficient S21;
8.2 And outputting the complex form of the S parameter to an excel table.
In a specific embodiment, the step 9 specifically includes:
9.1 Importing table data of excel with S parameters generated in the step 8 in MATLAB, and carrying out phase conversion on the S parameters; the phase conversion formula is:
S 11w 、S 21w respectively calculating a reflection coefficient and a transmission coefficient obtained by finite element software;
9.2 Calculating the converted S parameter through codes, and selecting different m values to calculate the complex dielectric constant according to the asphalt concrete with different thicknesses, wherein the calculation formula is as follows:
A 1 =S 21 +S 11
A 2 =S 21 -S 11
ε r =n/Z
Where I is the reflection coefficient, T is the propagation coefficient, θ is the phase, n is the refractive index, k 0 Is the wave vector in vacuum, epsilon r Is the complex dielectric constant of the sample;
9.3 And drawing one-dimensional change curves of the real part and the imaginary part of the complex dielectric constant of the asphalt concrete along with the frequency respectively by using the codes.
The beneficial effects of the invention include:
the invention discloses a three-dimensional model based on real block stones, which is randomly put into a discrete element model according to gradation to establish an asphalt concrete model with a microscopic structure, calculates the S parameter of the asphalt concrete with the microscopic structure by using electromagnetic simulation software through a reforming method, performs code programming by using MATLAB (matrix laboratory), calculates the complex dielectric constant of the asphalt concrete under different conditions, and develops research on the complex dielectric constant of the asphalt concrete from the microscopic structure.
The invention utilizes software simulation to rapidly back calculate the complex dielectric constant of the asphalt concrete aiming at different gradations, adopts a free space method and can be used for measuring the dielectric constant of a large-size material, and the coaxial method and the waveguide method in a laboratory have higher requirements on the size. Meanwhile, the method can clarify the influence on the macro from the viewpoint of the microscopic view, is beneficial to developing the research on the asphalt concrete dielectric constant theoretical model subsequently, promotes the development of the green technology for microwave heating pavement maintenance, and the like.
At present, the research on the dielectric property of asphalt concrete mainly focuses on treating the asphalt concrete as a heterogeneous material, and researches on the influence of the variety and content change of asphalt and aggregate, the change of water content and porosity and the like on the overall dielectric property of the asphalt concrete through tests; the invention is applied to the research on the distribution state of aggregate, asphalt, pore positions and the like in the asphalt concrete.
The invention can set the step length and the initial frequency at will by formula correction and code programming, obtain correct S parameter result, and inversely calculate the complex dielectric constant of the asphalt concrete.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of the position of the coarse aggregate of the asphalt concrete generated in PFC software according to the present invention;
FIG. 3 is a schematic diagram showing the rearrangement of asphalt concrete aggregate in the present invention, wherein (a) is a schematic diagram of irregularly shaped aggregate, (b) is a schematic diagram of a column formed by filling irregular aggregate with pellets, (c) is a schematic diagram of a column of irregular aggregate and pellets with a diameter of 1mm and a centroid of irregular aggregate in the column, and (d) is a schematic diagram of the position of irregular aggregate for reforming pellets with a diameter of 1 mm;
FIG. 4 is a schematic representation of the present invention for the reformation of asphalt concrete;
FIG. 5 is a schematic diagram of the geometric model built in COMSOL software according to the present invention;
FIG. 6 is a schematic diagram of meshing of the geometric model built in COMSOL software according to the present invention;
FIG. 7 is a diagram illustrating a one-dimensional S-parameter curve calculated in COMSOL software according to the present invention;
FIG. 8 is a graph showing the real complex permittivity of asphalt concrete as a function of frequency;
FIG. 9 is a graph illustrating the variation of the imaginary part of the complex dielectric constant of asphalt concrete with frequency.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, and the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
A method for determining the complex dielectric constant of asphalt concrete comprises the following steps:
step 1: generating an asphalt concrete model according to gradation in PFC3D software through an aggregate database;
the step 1 specifically comprises the following steps:
1.1 Randomly selecting 50 aggregate models from the existing three-dimensional aggregate model database, and numbering from GL-1 to GL-50 in sequence;
1.2 Sequentially importing stl files of the numbered three-dimensional aggregate models through PFC5.0 3D software to generate a template column;
1.3 The asphalt concrete is regarded as coarse aggregate (aggregate with the thickness of more than 2.36 mm), asphalt concrete matrix (asphalt and aggregate with the thickness of less than 2.36 mm), air and water, a cuboid with the length of 4cm, the width of 4cm and the height of 3cm is firstly generated in discrete element software (PFC 3D 5.0) through code programming, and coarse aggregate balls are generated in the cuboid according to the gradation AC-16 of the asphalt concrete and the oilstone ratio of 4.5%.
The coarse aggregate is coarse aggregate, the asphalt concrete matrix comprises asphalt and fine aggregate, and the coarse aggregate and the fine aggregate both meet the corresponding requirements in the Highway engineering aggregate test regulations.
And step 1.4, replacing all the coarse aggregate balls in the step 1.3 by various template columns at the same volume by using the template generated in the step 1.2 by adopting a diameter equivalent method to generate all the coarse aggregate columns, wherein the asphalt concrete cuboid contains the coarse aggregate columns, and the cuboid part except the coarse aggregate becomes a mixture consisting of asphalt concrete matrix (FAM), air and water. As shown in fig. 2.
Step 2: dividing the model into a substrate, coarse aggregate, air and water by adopting a reforming method, and generating a document;
the step 2 specifically comprises the following steps:
2.1 In the space range of the cuboid generated in the step 1, generating small balls with the diameter of 1mm, uniformly arranging the small balls and filling the whole space area;
2.2 Judging whether the centroids of the small balls with the diameter of 1mm are positioned in the coarse aggregate or in a mixture consisting of the asphalt concrete matrix, air and water through the codes, and setting the small balls in the coarse aggregate as guliao in a grouping manner; for pellets in a mixture of asphalt concrete matrix, air and water, the pellet grouping category was set to jizhi. As shown in fig. 4.
2.3 All aggregate balls are deleted, and only the uniformly distributed small balls are reserved;
2.4 The method comprises the steps of randomly adjusting the grouping type of pellets belonging to a mixture consisting of an asphalt concrete matrix, air and water through codes, so that the proportion of the pellets in the total pellets in the grouping type of air and water meets the requirements of 6% of void ratio and 1% of water content of asphalt concrete respectively. Specifically, the small balls are randomly selected from the small balls with the small ball grouping category of jizhi through codes, and the grouping category is changed into kongxi and shui, so that the void ratio and the water content reach the asphalt concrete grading requirement.
2.5 And outputting the centroid coordinates and the small sphere grouping categories of all the small spheres as txt documents.
And 3, step 3: establishing a model of 'electromagnetic wave, frequency domain (emw)' in COMSOL Multiphysics, and constructing a three-dimensional geometry;
the step 3 specifically comprises the following steps:
3.1 Opening COMSOL Multiphysics, selecting a model guide, selecting a three-dimensional model, selecting electromagnetic waves and a frequency domain (emw), researching and selecting the frequency domain, and completing construction by clicking;
3.2 Selecting geometry in COMSOL Multiphysics, taking the mesoscopic model generated in the step 1 as an example in the embodiment, and sequentially constructing cuboids with the length of 4cm, the width of 4cm and the height of 4cm, 3cm, 4cm and 4cm which are connected with each other;
3.3 Setting attributes of two cuboids at the top and the bottom of the model as perfect matching layers in component definition, and naming the perfect matching layers as PML1 and PML2 in geometry;
3.4 A cuboid with the middle height of 3cm is named as microscopic asphalt concrete in geometry, and the remaining two cuboids with the height of 4cm are named as air 1 and air 2 in geometry;
3.5 Calling an interface of COMSOL Multiphysics and MATLAB joint simulation, importing the txt document generated in the step 2 through codes, and converting the centroid coordinates through the codes;
3.6 Selecting the small balls with the grouping category of guliao in the microscopic asphalt concrete cuboid according to the converted coordinates, sequentially constructing cubes with the side length of 1mm by utilizing the derived coordinate information of the small balls, and naming the part of geometry, namely the geometry formed by the cubes with the side length of 1mm constructed by all the small balls with the grouping category of guliao as coarse aggregate;
3.7 Selecting the small balls with the grouping category of kongxi in the microscopical asphalt concrete cuboid according to the converted coordinates, sequentially constructing cubes with the side length of 1mm by utilizing derived coordinate information of the small balls, and naming the part of geometry, namely the geometry formed by the cubes with the side length of 1mm constructed by all the small balls with the grouping category of kongxi as a gap;
3.8 Selecting small balls with the grouped category of sui in the microscopic asphalt concrete cuboid according to the converted coordinates, sequentially constructing cubes with the side length being the diameter of the small balls by utilizing coordinate information derived from the small balls, and naming the part of geometry, namely the geometry formed by the cubes with the side length being the diameter of the small balls constructed by all the small balls with the grouped category of sui as water;
3.9 The combination of the geometry PML1, PML2, air 1, air 2, fine asphalt concrete, coarse aggregate, water and voids was subjected to boolean operations as shown in fig. 5.
And 4, step 4: setting different material properties and respectively endowing the geometry with the material properties;
the step 4 specifically comprises the following steps:
4.1 Setting 4 different material attributes, wherein the material attributes are named as air material, coarse aggregate material, water material and matrix material;
4.2 Setting the real part of the complex dielectric constant of the air material as 1, the imaginary part as 0 and the conductivity as 0, and endowing the material with the properties of the corresponding geometry of PML1, PML2, air 1, air 2 and gaps;
4.3 Setting the real part of the complex dielectric constant of the coarse aggregate material as 6, the imaginary part as 0.5 and the conductivity as 0, and endowing the material with the property by the corresponding geometry of the coarse aggregate;
4.4 Setting the real part of the complex dielectric constant of the water material as 80, the imaginary part as 0.1 and the conductivity as 0, and endowing the material with the property by the corresponding geometry of water;
4.5 The real part of the complex dielectric constant of the matrix material is set to be 5, the imaginary part is set to be 0.3, the conductivity is 0, and the material property is given by the corresponding geometry of the microscopic asphalt concrete.
And 5: setting an electromagnetic wave port and boundary conditions for the model;
the step 5 specifically comprises the following steps:
5.1 Adding two ports in a physical field, wherein the two ports are named as an input port and an output port respectively;
5.2 The input port is chosen to be the top of the air 1, the port type is set to periodic condition, the port's wave excitation is set to open and a slit condition is activated on the internal port, the magnitude of the electric mode field is set to TE 10 The incident elevation angle and azimuth angle are set to 0rad;
5.3 The output port is chosen to be the bottom of air 2, the port type is set to periodic condition, the port's wave excitation is set to off and a slit condition is activated on the internal port, the magnitude of the electric mode field is set to TE 10 In addition toThe elevation angle and the azimuth angle are set to be 0rad;
5.4 Setting a periodic boundary condition 1, selecting two opposite boundary surfaces of a geometric PML1 and a geometric PML2, wherein the number of the boundary surfaces is 4, and enabling periodic types to be Floquet periods and k vectors to be from periodic ports;
5.5 Setting a periodic boundary condition 2, selecting another two opposite boundary surfaces of the geometric PML1 and the geometric PML2, wherein the other two boundary surfaces are 4 boundary surfaces, and the periodic types are Floquet periods, and k vectors are from periodic ports;
5.6 Setting a periodic boundary condition 3, selecting two opposite boundary surfaces of geometric air 1, air 2 and microscopic asphalt concrete, wherein the total number of the two boundary surfaces is 6, and enabling periodic types to be Floquet periods, and enabling k vectors to come from periodic ports;
5.7 Setting a periodic boundary condition 4, selecting another two opposite boundary surfaces of geometric air 1, air 2 and microscopic asphalt concrete, wherein the other two boundary surfaces are 6 boundary surfaces, the periodic types are Floquet periods, and k vectors are from periodic ports;
and 6: carrying out mesh division on the model;
the step 6 specifically comprises:
6.1 Controlling the grid by adopting a physical field, wherein the size of grid cells is set to be refined;
6.2 Selecting the maximum grid cell size control parameter as from research and analyzing the wave in the lossy medium;
6.3 Constructing a free tetrahedral mesh of the model; as shown in fig. 6.
And 7: setting the starting frequency and the stopping frequency of a solver to be researched and the step length;
the step 7 specifically comprises the following steps:
7.1 setting the starting frequency of a solver for research to be 2GHz and the stopping frequency to be 4GHz;
7.2 The step size of the simulation was set to 0.1GHz.
And 8: calculating the research to obtain a curve graph of the S parameter changing along with the frequency, and outputting a complex form of the S parameter;
the step 8 specifically comprises:
8.1 Calculating the research to obtain an electric field multi-section schematic diagram of an electromagnetic wave frequency domain model and a one-dimensional schematic diagram of S parameters changing along with frequency, wherein the S parameters comprise a reflection coefficient S11 and a transmission coefficient S21;
8.2 And outputting the complex form of the S parameter to an excel table.
And step 9: and (5) reversely calculating the complex dielectric constant of the asphalt concrete according to the S parameter obtained in the step 8 by using MATLAB programming codes.
The step 9 specifically comprises:
9.1 In MATLAB, the table data of excel of the S parameter generated in step 8 is imported, and the S parameter is subjected to phase conversion. Phase conversion formula:
S 11w 、S 21w respectively, the reflection coefficient and the transmission coefficient are obtained by finite element software calculation.
9.2 Calculating the converted S parameter through codes, and selecting different m values to calculate the complex dielectric constant according to the asphalt concrete with different thicknesses, wherein the calculation formula is as follows:
A 1 =S 21 +S 11
A 2 =S 21 -S 11
ε r =n/Z
Wherein the reflection coefficient is I, the propagation coefficient is T, theta is phase, n is refractive index, k 0 Is a wave vector in vacuum, ε r Is the complex dielectric constant of the sample.
9.3 And drawing one-dimensional change curves of the real part and the imaginary part of the complex dielectric constant of the asphalt concrete along with the frequency respectively by using the codes.
As shown in fig. 8 and 9.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions and substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (6)
1. A method for determining the complex dielectric constant of asphalt concrete is characterized by comprising the following steps:
step 1: generating an asphalt concrete model according to gradation in discrete element software through an aggregate database; in the step 1, the method specifically comprises the following steps:
1.1 randomly selecting N aggregate models from an existing three-dimensional aggregate model library, and numbering from GL-1 to GL-N in sequence;
1.2 sequentially importing stl files of the numbered three-dimensional aggregate models through PFC3D software to generate a template column;
1.3 treating the asphalt concrete as coarse aggregate, asphalt concrete matrix, air and water, and generating a growth C in discrete element software by code programming 1 Width of K 1 High is H 1 The coarse aggregate balls are generated in the cuboid according to the gradation and the oilstone ratio of the asphalt concrete;
1.4, by adopting a diameter equivalent method, utilizing the template column generated in the step 1.2, replacing all the coarse aggregate balls in the step 1.3 by various template columns at the same volume to generate coarse aggregate columns, wherein the coarse aggregate columns are arranged in the cuboid generated in the step 1.3, and the part of the cuboid generated in the step 1.3 except the coarse aggregate columns is set to be a mixture consisting of asphalt concrete matrix, air and water;
step 2: dividing the asphalt concrete model into a matrix, coarse aggregate, air and water by adopting a reforming method, and generating a document; the step 2 specifically comprises the following steps:
2.1, in the space range of the cuboid generated in the step 1, generating small balls with the same size and the diameter of less than or equal to 1mm, uniformly arranging the small balls and filling the whole space area;
2.2 judging whether the centroid coordinate of the small balls is positioned in the coarse aggregate column or in the mixture consisting of the asphalt concrete matrix, the air and the water through the code, and setting the grouping category of the small balls according to the position of the centroid coordinate of the small balls;
in step 2.2, the grouping category of the small balls with the centroid coordinates in the coarse aggregate column is set as guliao, and the grouping category of the small balls with the centroid coordinates in the mixture of the asphalt concrete matrix, the air and the water is set as jizhi;
2.3 deleting all aggregate balls, and only keeping the uniformly distributed balls;
2.4, randomly adjusting the grouping type to be air and water by the code, so that the proportion of the balls in the total balls in the grouping type to be air and water meets the requirements of the void ratio and the water content of the asphalt concrete respectively;
in step 2.4, randomly selecting the small balls in the small balls with the small ball grouping category of jizhi through MATLAB codes, and changing the grouping category into kongxi and shui to enable the void ratio and the water content to meet the asphalt concrete grading requirement;
2.5, outputting the centroid coordinates of all the small balls and the small ball grouping categories as txt documents;
and step 3: establishing an electromagnetic wave frequency domain model in electromagnetic simulation software, constructing a three-dimensional geometry, importing the document finally generated in the step (2), and then performing Boolean operation on a complex formed by the three-dimensional geometry;
the step 3 specifically comprises the following steps:
3.1 opening COMSOL Multiphysics software, selecting a model guide, selecting a three-dimensional model, selecting electromagnetic waves and a frequency domain, researching and selecting the frequency domain, and constructing;
3.2 in COMSOL Multiphysics software, choosing geometry, constructing Long C in sequence 1 Width of K 1 High is H 3 、H 2 、H 1 、H 2 、H 3 Five connected cuboids;
3.3 setting the attributes of the cuboids at the top and the bottom of the model as perfect matching layers in component definition, and naming the perfect matching layers as PML1 and PML2 in geometry;
3.4 the height of the middle part is H 1 The cuboid is named as microscopic asphalt concrete in geometry, and the rest two are H 2 Is longThe cubes are named as air 1 and air 2 in geometry;
3.5 calling a COMSOL Multiphysics and MATLAB joint simulation interface, importing the txt document generated in the step 2 through codes, and converting the centroid coordinates through the codes;
3.6 selecting small balls with centroid coordinates in the coarse aggregate column in the microscopical asphalt concrete cuboid according to the converted coordinates, sequentially constructing cubes with side length being the diameter of the small balls by utilizing coordinate information derived from the small balls, and naming the part of geometry, namely the geometry formed by the cubes with side length being the diameter of the small balls constructed by the small balls with all centroid coordinates in the coarse aggregate column as coarse aggregate;
3.7 selecting the small balls with the grouping category of kongxi in the microscopic asphalt concrete cuboid according to the converted coordinates, sequentially constructing cubes with the side length being the diameter of the small balls by utilizing the coordinate information derived from the small balls, and naming the part of geometry, namely the geometry formed by the cubes with the side length being the diameter of the small balls constructed by all the small balls with the grouping category of kongxi as a gap;
3.8 selecting small balls with the classification of shui in the microscopic asphalt concrete cuboid according to the converted coordinates, sequentially constructing cubes with the side length of the small balls by utilizing the coordinate information derived from the small balls, and naming the part of geometry, namely the geometry formed by the cubes with the side length of the small balls constructed by all the small balls with the classification of shui as water;
3.9 forming a union body by the geometric PML1, the PML2, the air 1, the air 2, the microscopic asphalt concrete, the coarse aggregate, the water and the gaps, and performing Boolean operation;
and 4, step 4: respectively setting material properties for different materials in the electromagnetic wave frequency domain model, and respectively endowing the material properties with corresponding three-dimensional geometry; different materials in the electromagnetic wave frequency domain model comprise a substrate, coarse aggregate, air and water;
and 5: setting an electromagnetic wave port and boundary conditions for the electromagnetic wave frequency domain model;
step 6: carrying out grid division on the electromagnetic wave frequency domain model;
and 7: setting initial frequency, stop frequency and step length of a solver for researching the electromagnetic wave frequency domain model in finite element software;
and 8: calculating the research of the electromagnetic wave frequency domain model in finite element software to obtain a curve graph of the S parameter changing along with the frequency, and outputting a complex form of the S parameter;
and step 9: and (5) inversely calculating the complex dielectric constant of the asphalt concrete according to the S parameter obtained in the step 8 by using MATLAB programming codes.
2. The method for determining the complex permittivity of the asphalt concrete according to claim 1, wherein the step 4 specifically comprises:
4.1 setting different material attributes, wherein the material attributes are named as an air material, a coarse aggregate material, a matrix material and a water material respectively;
4.2 setting the real part of the complex permittivity of the air material to ε kqr With imaginary part set to ε kqi Electrical conductivity of σ kq Endowing the PML1, PML2, air 1, air 2 and the corresponding geometry of the gap with the air material property;
4.3 setting the real part of the complex permittivity of the coarse aggregate material to ε gr With imaginary part set to ε gi Electrical conductivity of σ g Endowing the properties of the coarse aggregate material to the corresponding geometry of the coarse aggregate; when various coarse aggregate materials with different attributes exist, the different coarse aggregate materials are respectively set and corresponding geometric attributes are given;
4.4 setting the real part of the complex permittivity of the water material to ε sr With imaginary part set to ε si Electrical conductivity of σ s Endowing the water material attribute with the corresponding geometry of water;
4.5 setting the real part of the complex permittivity of the matrix material to ε jr With imaginary part set to ε ji Electrical conductivity of σ j And endowing the matrix material attribute to the corresponding geometry of the microscopic asphalt concrete.
3. The method for determining the complex permittivity of the asphalt concrete according to claim 1, wherein the step 5 specifically comprises:
5.1 adding two ports in the physical field, named as input port and output port respectively;
5.2 input port selected as the top of air 1, port type set to periodic condition, port excitation set to open and slit condition activated on internal port, electric mode field size set to TE 10 The incident elevation angle and azimuth angle are set to 0rad;
5.3 output port selected as bottom of air 2, port type set to periodic condition, port excitation set to off and slit condition activated on internal port, electric mode field size set to TE 10 The incident elevation angle and azimuth angle are set to 0rad;
5.4 setting a periodic boundary condition 1, selecting two opposite boundary surfaces in the geometric PML1 and PML2, wherein 4 boundary surfaces are selected, setting periodic types as Floquet periods, and setting k vectors from periodic ports, namely wave vectors;
5.5, setting a periodic boundary condition 2, selecting another two opposite boundary surfaces in the geometric PML1 and PML2, wherein the other two boundary surfaces are 4 boundary surfaces, setting periodic types as Floquet periods, and setting k vectors from periodic ports;
5.6 setting a periodic boundary condition 3, selecting two opposite boundary surfaces of geometric air 1, air 2 and microscopic asphalt concrete, wherein 6 boundary surfaces are selected, the periodic types are set as Floquet periods, and k vectors are from periodic ports;
and 5.7, setting a periodic boundary condition 4, selecting another two opposite boundary surfaces of the geometric air 1, the air 2 and the microscopic asphalt concrete, and setting periodic types as Floquet periods, wherein k vectors are from periodic ports, wherein the total number of the other two boundary surfaces is 6.
4. The method for determining complex permittivity of asphalt concrete according to claim 1,
the step 6 specifically includes:
6.1, controlling the grid by adopting a physical field, and setting the size of grid cells as refinement;
6.2 selecting the control parameter of the maximum grid unit size as from research and analyzing the wave in the loss medium;
6.3 constructing a free tetrahedral mesh of the electromagnetic wave frequency domain model;
the step 7 specifically includes:
7.1 set the solver starting frequency for the study to f 1 Setting the solver stopping frequency of the study to be f 2 ；
7.2 setting the step size of the simulation to f d 。
5. The method for determining the complex permittivity of the asphalt concrete according to claim 1, wherein the step 8 specifically includes:
8.1, calculating the research to obtain an electric field multi-section schematic diagram of an electromagnetic wave frequency domain model and a one-dimensional schematic diagram of S parameters changing along with frequency, wherein the S parameters comprise a reflection coefficient S11 and a transmission coefficient S21;
8.2 output the complex form of the S parameter into an excel table.
6. The method for determining the complex permittivity of the asphalt concrete according to claim 1, wherein the step 9 specifically includes:
9.1 importing the table data of the excel of the S parameter generated in the step 8 in MATLAB, and carrying out phase conversion on the S parameter; the phase conversion formula is:
S 11 ＝S 11w exp(2γ 0 l 1 )
S 21 ＝S 21w exp(2γ 0 l 2 )
S 11w 、S 21w respectively calculating a reflection coefficient and a transmission coefficient obtained by finite element software;
γ 0 is a constant of propagation in the air and,
wherein lambda 0=c/f lambda 0 Is the wavelength of free space, c is the speed of light, f is the frequency; l 1 、l 2 The length of air areas on two sides of the material to be detected;
9.2, calculating the converted S parameter through codes, and selecting different m values to calculate the complex dielectric constant according to the asphalt concretes with different thicknesses, wherein the calculation formula is as follows:
A 1 ＝S 21 +S 11
A 2 ＝S 21 -S 11
ln (T) = ln (| T |) + j (theta + -2 m π), m is an integer
ε r ＝n/Z
Where I is the reflection coefficient, T is the propagation coefficient, θ is the phase, n is the refractive index, k 0 Is the wave vector in vacuum, epsilon r Is the complex dielectric constant of the sample;
and 9.3, drawing one-dimensional change curves of the real part and the imaginary part of the complex dielectric constant of the asphalt concrete along with the frequency by using the codes.
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