CN115586073A - Method for analyzing microstructure mechanics of asphalt mixture based on three-dimensional local homogenization model - Google Patents
Method for analyzing microstructure mechanics of asphalt mixture based on three-dimensional local homogenization model Download PDFInfo
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Abstract
The invention relates to a method for performing mechanical analysis on a microscopic structure of an asphalt mixture based on a three-dimensional local homogenization model, and belongs to the technical field of microscopic mechanical analysis. According to the invention, by means of an image topological principle and a mesoscopic mechanics theory, a mesoscopic structure model is divided into a plurality of local areas based on the distribution condition of aggregates in the asphalt mixture, then local area homogenization model parameters are calculated according to the properties of the aggregates and mortar matrix materials, and finally a numerical analysis frame for the mesoscopic multi-scale coupling of the asphalt pavement macro and the asphalt mixture is constructed, so that the analysis of the mesoscopic structure mechanics of the asphalt mixture is realized under the background of the macroscopic stress of the pavement structure, the internal mechanism and the evolution rule of the mechanical behavior of the asphalt mixture and even the asphalt pavement are revealed, and a foundation is provided for the establishment of a future pavement structure digital platform.
Description
Technical Field
The invention relates to a method for performing microscopic structure mechanical analysis on an asphalt mixture based on a three-dimensional local homogenization model, and belongs to the technical field of microscopic mechanical analysis.
Background
The mechanical behavior of the asphalt pavement is mainly determined by the microscopic structure in the asphalt mixture. At present, the mechanical analysis of the asphalt mixture mainly comprises two methods of mechanical test and numerical simulation. The test method regards the inhomogeneous mixture as the homogeneous material, summarizes and summarizes the mechanical properties of the mixture from the experimental data by using the phenomenological theory, and provides reference and basis for future pavement structure analysis, so that the test method ignores the microscopic structure of the mixture, and cannot accurately represent the microscopic mechanical behavior of different mixture structures.
The numerical simulation method realizes the establishment of a non-uniform microscopic structure model and mechanical simulation through grid division and the definition of different material parameters, explains the mechanical mechanisms of different mixtures on microscopic scales, thereby improving the prediction and analysis level of pavement mechanical behavior and improving the pavement structure design method.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for analyzing the microstructure mechanics of asphalt mixture based on a three-dimensional local homogenization model, which divides the microstructure model into a plurality of local areas based on the distribution condition of aggregate in the asphalt mixture by means of an image topological principle and a microstructure mechanics theory, then calculates the parameters of the homogenization model of the local areas according to the properties of the aggregate and mortar base materials, finally constructs a numerical analysis frame for the macroscopic and microscopic multi-scale coupling of asphalt pavement, realizes the analysis of the microstructure mechanics of the asphalt mixture under the background of the macroscopic stress of the pavement structure, reveals the internal mechanism and the evolution law of the mechanical behavior of the asphalt mixture and even the asphalt pavement, and provides a foundation for the establishment of a future pavement structure digital platform.
The technical scheme of the invention is as follows:
a method for carrying out mechanical analysis on a microstructure of an asphalt mixture based on a three-dimensional local homogenization model comprises the following steps:
(1) According to the structural design requirements of different types of asphalt pavements, selecting an aggregate grading scheme of the asphalt mixture, and determining an aggregate grading curve (such as AC-13, AC-16, SMA-13 and the like) corresponding to the grading scheme;
(2) Taking coarse aggregate distribution as a main body, constructing a random microscopic structure model of the asphalt mixture:
firstly, calculating the mass fraction of each grain size aggregate in an aggregate grading curve and the density parameters of the aggregate and asphalt to obtain the volume fraction of the aggregate, wherein the density parameters of the aggregate and the asphalt can be determined by indoor tests or literature reference, then, assuming the coarse aggregates with the same grain size grade (for example, the grain size is 4.75mm-9.5mm, the grain size grade can be divided according to the actual situation by referring to the prior art) as spherical particles with the same size, and calculating the required feeding number of each grain size coarse aggregate according to the volume fraction; randomly distributing the calculated coarse aggregates in an asphalt mixture model space by using a random putting method, preliminarily generating an asphalt mixture random microscopic structure model, and recording the central position coordinates and the particle size information of each coarse aggregate in the microscopic structure model;
coarse aggregate is defined as aggregate having a particle size of not less than 2.36 mm; fine aggregate is defined as aggregate having a particle size of less than 2.36mm and the matrix of the asphalt mortar formed by mixing the fine aggregate with asphalt can be considered a homogeneous material.
(3) Carrying out local area space division:
taking the central point of each coarse aggregate as a control point, taking the particle size of the coarse aggregate as a weight, and adopting a weighted Voronoi method to perform space division on the asphalt mixture, so as to divide the model space into a plurality of local areas taking the distribution of the coarse aggregates as the center; the local areas are adjacent to each other and fill the whole space; meanwhile, each local area contains coarse aggregate particles with specific particle sizes and a mortar matrix containing fine aggregates and asphalt, and finally a geometric model of a continuous and non-uniform microscopic structure of the asphalt mixture is formed; as the distribution of the coarse aggregates with different grain sizes in the model is random, the shape of a local area containing each coarse aggregate is an irregular polyhedron; in order to subsequently construct a microscopic structure model and calculate homogenization parameters of local regions, reading and recording the volume of each local region of the microscopic model, the geometrical coordinate information of a vertex and the particle size information of the contained coarse aggregate;
(4) Respectively constructing a geometric model and a constitutive model;
(5) Writing the viscoelasticity parameters corresponding to each local area in the constitutive model into an input file of the finite element model according to the serial number sequence of the geometric model, and then constructing the finite element model by using a file import mode;
(6) And (3) constraining the boundary of the microscopic structure model by using the macroscopic structure of the asphalt pavement, and then equivalently inputting the macroscopic vehicle load to finish analyzing the microscopic mechanical response in the asphalt mixture on the premise of considering the macroscopic stress load of the pavement structure. The cross-scale coupling analysis of the mechanical behaviors of the pavement structure and the mixture structure is realized, the internal mechanism of the mechanical performance of the asphalt pavement is disclosed, the influence of different microscopic structures on the mechanical behaviors of the pavement is explained from a microscopic level, and the future performance prediction of the pavement structure is carried out.
The invention mainly constructs a macro-micro scale coupled numerical analysis system of the asphalt pavement structure based on an image topological weighting Voronoi method and a mesomechanics Mori-Tanaka method, and realizes deep exploration on the mesomechanics mechanism of the asphalt pavement structure. The invention can realize the following functions: and determining the mixture mesostructure distribution condition according to the aggregate grading information, and dividing the model into a plurality of local areas according to the mesostructure distribution by using a weighted Voronoi algorithm. Each local region contains partial mesostructure information (such as aggregate content, aggregate shape, etc.) to characterize the mix non-uniform structural features on a macro-scale. On the microscopic scale, equivalently assuming each local area as a homogenized structure, calculating the homogenized model parameters of the local area by using a microscopic mechanics Mori-Tanaka method based on the aggregate quantity, volume content, shape, mechanical properties and other factors in the area, and constraining the boundary part of the finished microscopic structure by using the macroscopic structure of the asphalt pavement, thereby constructing a coupled asphalt pavement multi-scale numerical simulation system frame and performing the multi-scale analysis of the microscopic mechanics behavior of the asphalt pavement.
Preferably, the random delivery method in step (2) includes:
(1) firstly, assuming coarse aggregates with the same particle size as spherical particles with the same size, and sequencing all coarse aggregate information according to the particle size;
(2) all the coarse aggregates are sequentially and randomly put in sequence, and the particles are prevented from overlapping and exceeding the boundary in the putting process;
(3) after all the particles are put in, a fine structure model of the asphalt mixture based on the coarse aggregate framework is initially established, and then the sphere center position and the particle size information of each coarse aggregate sphere in the space are recorded.
Preferably, the weighted Voronoi method in the step (3) includes:
A. distributing the central points of the coarse aggregates in space;
B. converting the vector file with the space coordinate information into a raster file to distribute weight information;
C. calculating Euclidean distances among the central points of the coarse aggregates in the grid file;
D. applying the weight information to the euclidean distance, typically dividing the euclidean distance by the weight;
E. calculating pixel points in space based on Euclidean distances considering weights, and allocating the pixel points to the most appropriate aggregate central points, wherein the most appropriate aggregate central points generally refer to central points with the Euclidean distances divided by the weight values, for example, the Euclidean distances between a certain pixel point and two central points are both 6, but the weight of a central point is 2, and the weight of b central point is 4, so that the Euclidean distances divided by the weights are 3 and 1.5 respectively, and the pixel points should be allocated to b central points;
F. and after all the pixel points are distributed, converting the raster file into a vector coordinate graph.
Preferably, the geometric model in step (4) is constructed by:
a. reading the geometrical coordinate information of the vertexes of all local regions of the mesoscopic model, carrying out parametric modeling by utilizing a python secondary development interface of commercial finite element software, constructing a finite element geometrical model according to the sequence of point-line-surface-body, and numbering all local regions in the model according to aggregate particle size arrangement;
b. and dividing the model by adopting a free mesh mode, generating an input file containing model information after the mesh division is finished, wherein in the file, the model and the local area information are represented by nodes and units with numbers and correspondingly represent different aggregate distribution information.
Preferably, the construction process of the constitutive model in step (4) is as follows:
i. the method can be used for analyzing the viscoelasticity behavior of the asphalt mixture, wherein in the asphalt mixture, an asphalt mortar matrix is defined as a viscoelasticity material, and coarse aggregates contained in a model are defined as a linear elasticity material;
ii. For an asphalt mortar matrix, determining a viscoelasticity index of the asphalt mortar by adopting an indoor dynamic shear rheological experiment method, wherein the viscoelasticity index comprises parameters such as dynamic modulus, phase angle and the like; then, establishing a viscoelastic main curve of the asphalt mortar by means of a main curve fitting method, wherein a common main curve model comprises a sigmoidal model, a generalized Maxwell model, a generalized voigt model, a 2S2P1D model, a HN model and the like, the viscoelastic main curve comprises expressions of viscoelastic information (the viscoelastic information is the dynamic modulus and the phase angle) under a frequency domain coordinate system, and a stiffness matrix of the asphalt mortar matrix is calculated through the Poisson ratio of the asphalt mortar matrix;
iii, determining the elastic modulus and Poisson ratio parameters of the coarse aggregate by adopting an indoor test or consulting documents, calculating a rigidity matrix of the coarse aggregate, recording the rigidity matrix of the asphalt mortar matrix and the rigidity matrix of the aggregate as basic mechanical input parameters, and taking the subsequent calculation of homogenization mechanical parameters as a basis;
iv, reading structural information (information such as the volume of a local area, the number of particles of the coarse aggregate contained, the particle size and the like) of the geometric model, wherein each local area corresponds to the particle size of the coarse aggregate under specific gradation, assuming the coarse aggregate as an ellipsoid in order to consider different shapes of the coarse aggregate, randomly appointing the three-axis length of the ellipsoid on the basis of the determined particle size of the coarse aggregate, calculating the volume of the coarse aggregate on the basis of the information such as the three-axis length and the like, and calculating the volume content of the coarse aggregate in the local area according to the volume information of the local area;
v, synthesizing local area volume information, matrix viscoelasticity parameters, coarse aggregate elastic modulus, volume content, three-axis length of an ellipsoid and other factors, calculating local area homogenization mechanical parameters by using a Mori-Tanaka mesomechanics method, namely a local area homogenization rigidity matrix, calculating local area homogenization dynamic modulus and Poisson ratio parameters through the local area homogenization rigidity matrix (the rigidity matrix contains all parameter information), and enabling the homogenization mechanical parameters to correspond to the models one by one;
and vi, converting the dynamic modulus in the frequency domain into the dynamic modulus in the time domain by using a Laplace inverse transformation method so as to meet the requirement of numerical simulation calculation.
Preferably, the local area is calculated by using a Mori-Tanaka mesomechanics methodUniformized stiffness matrix L hom The process comprises the following steps:
G r ＝[I+S r ∶(L * (ω)) -1 ∶(L r -L * (ω))] -1
wherein L is * (omega) and L r (ω) stiffness matrices of the bitumen mortar matrix and the r-th coarse aggregate in the local area, c 0 And c n The volume contents S of the matrix and the nth coarse aggregate particles in a local area r The Eshelby tensor, which is the coarse aggregate particle, represents the shape characteristics of the coarse aggregate particle, M represents the total number of coarse aggregates contained in the region, I represents the identity matrix, G n The local strain concentration tensor representing the nth coarse aggregate.
Preferably, in step vi, the Laplace inverse transformation operation formula is,
wherein f (t) is a function expression of the dynamic modulus in the time domain; f (omega) is a function expression of the dynamic modulus in the frequency domain; l is Laplace operation symbol, j represents imaginary unit, j 2 = 1, β represents the real part of the complex laplace variable, and ω represents the frequency variable.
Where the invention is not described in detail, reference is made to the prior art.
The invention has the beneficial effects that:
(1) The invention divides a mesoscopic structure model into a plurality of local areas based on the aggregate distribution condition in the asphalt mixture by means of an image topological principle and a mesoscopic mechanics theory, and then calculates the homogenization model parameters of the local areas according to the properties of the aggregates and the mortar matrix material. The model effectively represents the characteristics of the non-uniform microscopic structure in the asphalt mixture in a macroscopic scale based on a local area based on aggregate distribution, and ensures the accuracy of microscopic mechanical analysis of the asphalt mixture; meanwhile, on the microscopic scale, the local area is of a uniform structure, and the continuity and effectiveness of the microscopic model are guaranteed. Finally, a numerical analysis frame for the microscopic multi-scale coupling of the asphalt pavement macro and the asphalt mixture is constructed, the analysis on the microscopic structure mechanics of the asphalt mixture is realized under the background of the pavement structure macro stress, the internal mechanism and the evolution law of the asphalt mixture and even the asphalt pavement mechanics behavior are disclosed, and a foundation is provided for the establishment of a future pavement structure digital platform.
(2) According to the invention, the spherical particles are used for randomly putting aggregates in the mixture, so that the modeling analysis of the random asphalt mixture structure is realized; in the process of calculating the homogenization parameters, different ellipsoid aggregate axial lengths are defined in a parameter form, so that different particle shapes are analyzed.
(3) The invention is divided into a plurality of local areas on the basis of coarse aggregate distribution in the macro scale, thereby ensuring the accuracy of mesoscopic numerical simulation. And each local area is of a uniform structure under the microscopic scale, and the local areas are of continuous structures, so that the grid division difficulty is reduced, the unit number is reduced, and the effective operation of the numerical analysis process is ensured.
(4) By means of a topological method and a mesoscopic mechanical method, aggregate grading information in the mixture can be effectively fused into a macroscopic non-uniform model and mesoscopic uniform mechanical parameters, so that the model calculation convergence is improved, the application scene of a mesoscopic structure model is expanded, and the multi-scale analysis capability is improved; the method has strong openness, local homogenization mechanical parameters can be defined as linear elasticity, linear viscoelasticity, nonlinear viscoelasticity, viscoplasticity and the like according to engineering practice, and the microscopic mechanical analysis of different mixed materials is realized.
(5) The local homogenization structure of the invention effectively improves the grid division quality of the model and reduces the calculation time and the resource occupation. And finally, the boundary of the mixture micro-structure model is constrained by using the asphalt pavement macro-structure, so that the cross-scale coupling analysis of the asphalt pavement macro-structure is realized.
Drawings
FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention;
FIG. 2 is a three-dimensional stochastic structure model created according to an embodiment of the present invention;
FIG. 3 is a mesh partitioning of a model established in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of a viscoelastic principal curve used in accordance with one embodiment of the present invention;
FIG. 5 illustrates a road macrostructure boundary condition established according to an embodiment of the present invention;
FIG. 6 shows the loading results of the model according to an embodiment of the present invention.
The specific implementation mode is as follows:
in order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific examples, but not limited thereto, and the present invention is not described in detail and is in accordance with the conventional techniques in the art.
Example 1
A method for performing mechanical analysis on a microstructure of an asphalt mixture based on a three-dimensional local homogenization model is shown in figure 1 and comprises the following steps:
(1) After comprehensive investigation on the requirements of use function, traffic volume, load and the like of a certain road is assumed, the AC-13 graded asphalt mixture is determined to be used as a road surface material, and the AC-13 mixture needs to be subjected to microscopic numerical simulation to analyze and predict the mechanical property of the future road in a service state. Inquiring literature data to determine an AC-13 mixture gradation curve;
(2) Taking coarse aggregate distribution as a main body, constructing a random microscopic structure model of the asphalt mixture:
and calculating the volume fraction of each particle size aggregate in the grading curve according to the mass fraction of each particle size aggregate in the AC-13 mixture grading curve and by referring to the aggregate density parameter. And (3) calculating the volume content of the aggregate in the mixture under each particle size by referring to the design requirement of 5% of porosity and combining the density numerical values of the asphalt and the aggregate.
In the above calculations, the density parameters of the aggregate and bitumen can be determined by laboratory tests, and also by consulting relevant literature. In this example, the bitumen density parameter is about 1.1g/cm3 and the limestone aggregate density is about 2.7g/cm3. And then, the coarse aggregate distribution is used as a framework to carry out primary construction of the asphalt mixture microstructure. The fine aggregate and the asphalt are mixed to form the asphalt mortar matrix, and the material mechanics parameters of the asphalt mortar matrix can be determined in an experimental mode in subsequent work if the asphalt mortar matrix is assumed to be a uniform material. Aggregates having an aggregate particle size of 2.36mm or more are assumed to be coarse aggregates, and aggregates having a particle size of 2.36mm or less are assumed to be fine aggregates. And determining the distribution of the coarse aggregate in the asphalt mixture by using a random feeding method by utilizing program programming software. The following steps are random releasing steps:
(1) firstly, assuming coarse aggregates with the same particle size as spherical particles with the same size, and sequencing all coarse aggregate information according to the particle size;
(2) sequentially and randomly putting all coarse aggregates in sequence, wherein in the putting process, attention is paid to avoiding overlapping of particles and avoiding the particles from exceeding the boundary;
(3) after all the particles are put in, a fine structure model of the asphalt mixture based on the coarse aggregate framework is initially established, and then the sphere center position and the particle size information of each coarse aggregate sphere in the space are recorded.
(3) Carrying out local area space division:
the mixture mesoscopic structure model established above is stored in data formats such as a sphere center coordinate, a particle size and the like, then the sphere center coordinate of the coarse aggregate is taken as a control point, the particle size of the coarse aggregate is taken as a weight, weighted Voronoi space division is carried out by means of a python computer programming language, and the weighted Voronoi method comprises the following steps:
A. distributing the central points of the coarse aggregates in space;
B. converting the vector file with the space coordinate information into a raster file to distribute weight information;
C. calculating Euclidean distances among the central points of the coarse aggregates in the grid file;
D. applying the weight information to the euclidean distance, typically dividing the euclidean distance by the weight;
E. calculating the pixel points in the space based on the Euclidean distance considering the weight, and allocating the pixel points to the central point with the Euclidean distance divided by the weight value being the minimum, for example, the Euclidean distance between a certain pixel point and two central points is 6, but the weight of the central point a is 2, and the weight of the central point b is 4, so that the Euclidean distance divided by the weight is 3 and 1.5 respectively, and the pixel points should be allocated to the central point b;
F. and after all the pixel points are distributed, converting the raster file into a vector coordinate graph.
After the weighted Voronoi space division, each partial Voronoi space contains one coarse aggregate particle. The divided local spaces are irregular polyhedrons which are mutually adjacent and fill the whole model space, and the division result data contains the volume of each local space, the position coordinates of all vertexes, the coordinates of the center point of coarse aggregates, the particle size of the coarse aggregates and other information. And storing all the information as json files for later calling to establish a finite element model. The method has higher flexibility and openness, can distribute the space according to the requirements of engineering precision, scale and computing power, can contain a plurality of coarse aggregate particles in each local space, and can also consider the particle size information of the fine aggregate in the space division process.
(4) Respectively constructing a geometric model and a constitutive model;
the construction process of the geometric model comprises the following steps:
a. reading the geometrical coordinate information of the vertexes of all local areas of the mesoscopic model, reading the spatial information by means of a python parametric modeling interface of finite element software, constructing a finite element geometrical model according to the sequence of point-line-surface-body, and numbering all local areas in the model by referring to aggregate grain size arrangement; in the model, only the geometric information of the asphalt mixture mesostructure distribution is included, and the modulus, poisson ratio and other material mechanics information of the aggregate and the asphalt are determined in the following work by means of material tests or reference documents, and the like, and the finite element model is shown in fig. 2.
b. And dividing the model by adopting a free mesh mode, generating an input file containing model information after the mesh division is finished, wherein in the file, the model and the local area information are represented by nodes and units with numbers and correspondingly represent different aggregate distribution information.
The local homogenization model established by the method forms a continuous structure in the model space, so that the grid size can be increased, the unit number can be reduced and the mesoscopic numerical simulation calculation efficiency can be increased on the premise of ensuring the grid division quality. FIG. 3 is a mesh partition diagram of a local homogenization model. After the meshing is finished, classifying the units and the nodes according to the local regions to which the units and the nodes belong, and writing the information of the units and the nodes into a finite element input operation file.
The construction process of the constitutive model comprises the following steps:
i. the method can be used for analyzing the viscoelasticity behavior of the asphalt mixture, wherein in the asphalt mixture, an asphalt mortar matrix is defined as a viscoelasticity material, and coarse aggregates contained in a model are defined as a linear elasticity material;
ii. For the asphalt mortar matrix, in the example, the mechanical parameters of the asphalt mortar material are determined by adopting an indoor test method, and the viscoelasticity index of the asphalt mortar is determined by adopting an indoor dynamic shear rheological test method, wherein the viscoelasticity index comprises parameters such as dynamic modulus, phase angle and the like;
firstly, preparing an asphalt mortar test piece in a laboratory, and then determining the viscoelastic property of the asphalt mortar by adopting a frequency scanning experiment. In this embodiment, the loading frequency of the frequency sweep experiment is 10, 6.31, 3.98, 2.51, 1.58, 1, 0.631, 0.398, 0.251, 0.158, 0.1Hz, and the loading temperature is 0, 10, 20, 30 ℃.
Finally, at each specific frequency and at a specific temperature, a dynamic modulus and a phase angle containing viscoelastic information can be obtained. The dynamic modulus data represents the ratio of stress to strain of the asphalt mortar at different frequencies and temperatures, and the phase angle data represents the phase difference of the stress and strain of the asphalt mortar at different frequencies and temperatures. And constructing a main curve of the viscoelasticity dynamic modulus of the asphalt mortar by means of a 2S2P1D model. As shown in fig. 4, the main dynamic modulus curve has angular frequency as abscissa and dynamic modulus value as ordinate, and contains all the dynamic modulus information of the asphalt mortar at the service temperature and the loading frequency (or time). In addition, the phase angle master curve can also be constructed by means of a 2S2P1D model, which uses frequency as an abscissa and a phase angle value as an ordinate, and contains all phase angle information of the asphalt mortar at the service temperature and the loading frequency (or time), and no image display is performed here.
The dynamic modulus main curve contains the dynamic modulus information of the asphalt mortar in a frequency domain coordinate system, and is expressed by | E × (ω) |, and the reference determines that the poisson ratio of the asphalt mortar is 0.35. Therefore, the rigidity matrix of the asphalt mortar material can be calculated as follows:
iii, for coarse aggregate, the Young's modulus of elasticity of the limestone aggregate obtained by the reference is 55GPa, the Poisson ratio is 0.2, and similarly, the rigidity matrix of the coarse aggregate is calculated to be
Making the rigidity matrix L of the asphalt mortar material * (ω) and the stiffness matrix L of the aggregate are recorded as basic mechanical input parameters.
iv, reading structural information (information such as the volume of a local area, the number of the contained coarse aggregate particles, the particle size and the like) of the geometric model, then performing traversal calculation on mechanical parameters of each local space in programming software, wherein each local area corresponds to the particle size of the coarse aggregate under specific gradation, randomly defining coarse aggregate spherical particles as ellipsoid particles in each local space based on the particle size of the coarse aggregate spherical particles so as to consider the distribution of the coarse aggregates with different shapes, calculating the volume of the coarse aggregate based on information such as triaxial length and the like, and calculating the volume content of the coarse aggregate in the local area according to the volume information of the local area;
v, synthesizing local area volume information, matrix viscoelasticity parameters, coarse aggregate elastic modulus, volume content, three-axis length of an ellipsoid and other factors, calculating local area homogenization mechanical parameters by using a Mori-Tanaka mesoscopic mechanics method, namely a local area homogenization rigidity matrix, calculating local area homogenization dynamic modulus and Poisson ratio parameters through the local area homogenization rigidity matrix (the rigidity matrix contains all parameter information), and enabling the homogenization mechanical parameters to correspond to the models one by one;
calculating local area homogenization rigidity matrix L by using Mori-Tanaka mesomechanics method hom The process comprises the following steps:
G r ＝[I+S r ∶(L * (ω)) -1 ∶(L r -L * (ω))] -1
wherein L is * (omega) and L r (ω) stiffness matrices of the bitumen mortar matrix and the r-th coarse aggregate in the local area, c 0 And c n The volume contents of the matrix and the nth coarse aggregate particles in a local area respectively, M represents the total number of coarse aggregates contained in the area, I represents an identity matrix, G n A local strain concentration tensor representing the nth coarse aggregate.
S r The Eshelby tensor, which is the Eshelby tensor for the coarse aggregate particles, which characterizes the shape of the coarse aggregate particles, depends on the shape of the coarse aggregate particles and on the material properties of the asphalt mortar matrix. In this example, the asphalt mortar is an isotropic material, and therefore the Eshelby tensor for each coarse aggregate particle can be determined by the ellipse integral. For ellipsoidal particles, the Eshelby tensor expression is as follows,
S ijkl ＝S jikl ＝S ijlk
in the above formula, a 1 >a 2 >a 3 Is the three-axis length of an ellipsoid; upsilon is the poisson ratio of the asphalt mortar matrix; i is 1 、I 2 、I 3 、I 11 、I 12 、I 13 Etc. are constants that can be calculated from the elliptic integral. All the non-zero components can be obtained by (1, 2, 3) cyclic arrangement, and (1, 2, 3) respectively represent coordinate axis directions corresponding to three axes of the ellipsoid. Other components being zero, e.g. S 1112 ＝S 1223 ＝S 1232 ＝0。
In the above formula, S ijkl 、S jikl 、S ijlk The components in the tensor are subjected to symmetrical transformation;
finally, the homogenization mechanical rigidity matrix L of each local area is obtained through calculation hom (ω)，L hom (ω) can be further decomposed into:
the homogenization dynamic modulus | E of the local area can be calculated from the homogenization mechanical stiffness matrix hom (ω) | and Poisson ratio parameter upsilon hom 。
vi, the dynamic modulus is an expression in a frequency domain, the dynamic modulus needs to be converted into an expression in a time domain by using a Laplace inverse transformation method so as to meet the requirement of numerical simulation, and the dynamic modulus in the frequency domain is converted into the dynamic modulus in the time domain by using the Laplace inverse transformation method so as to meet the requirement of numerical simulation calculation;
the inverse Laplace transform has the following operation formula,
wherein f (t) is a function expression of the dynamic modulus in the time domain; f (omega) is a function expression of the dynamic modulus in the frequency domain; l is Laplace operation symbol, j represents imaginary unit, j 2 = 1, β represents the real part of the complex laplace variable, and ω represents the frequency variable.
(5) And the model parameters obtained by the calculation correspond to the local areas one by one, and then the model parameters are written into an input file. And importing an input file in finite element software to establish a model.
(6) Reasonable model boundary conditions are applied to the established model. In this embodiment, a road structure macroscopic model with a length, width and height of 6m × 3m is established, wherein the topmost layer is an asphalt mixture surface layer and the thickness is 5cm; secondly, a semi-rigid cement stabilized macadam foundation layer is arranged, and the thickness is 30cm; the bottommost layer is a soil base layer and is 265cm in thickness. Due to the fact that the size of the mixture macro model is too large, in order to save operation time, only the structure with the geometric size of 30cm 5cm is selected at the middle position of the mixture surface layer to be subjected to scratching and removing treatment, then the micro structure local homogenization model is embedded into the asphalt mixture surface layer, and the macro pavement structure is used for applying constraint on the boundary of the micro structure model, so that cross-scale coupling analysis of the macro and micro structure of the asphalt pavement is achieved. The surface layer, the base layer and the soil base layer of the rest of the mixture are all of uniform structures. In order to simulate the real stress condition of the pavement structure, rigid constraint conditions are applied to the side surface boundary and the lower bottom surface boundary of the macrostructure. The road macrostructure and boundary conditions are shown in fig. 5.
(7) The upper surface of the macroscopic model does not exert any constraint, and the simulated road surface bears the load of the vehicle. In the vehicle load simulation process, the contact surface of a vehicle tire and a road surface is assumed to be a circle with the diameter of 20cm, the wheel load is 700kPa, and the moving speed of the vehicle is 60km/h. Therefore, a circular surface load with the diameter of 20cm can be defined on the road surface in the model, the surface load is 700kPa, and meanwhile, the surface load moves at a constant speed on the surface of the model at the speed of 16.667m/s so as to simulate the loading behavior of the dynamic vehicle.
Fig. 6 shows the partial simulation result of the mesostructure model. The model can be seen to show the stress characteristic of the asphalt pavement structure on the macroscopic scale; at the same time, there are very obvious non-uniform stress concentration phenomena (the dotted circle in fig. 6) on the microscopic scale, and the stress concentration phenomena are mainly caused by the non-uniform microscopic structure in the mixture. Therefore, the proposed local homogenization model numerical analysis method can reasonably represent the inhomogeneous microscopic mechanical response in the asphalt mixture on the premise of considering the macroscopic mechanical characteristics of the pavement structure. Moreover, the boundary of the microscopic structure model is constrained by the macroscopic structure of the asphalt pavement, so that the macroscopic and microscopic cross-scale coupling research of the asphalt pavement is realized. The internal mesomechanics performance and the evolution mechanism of the pavement structure are revealed on the premise of bearing the vehicle load. The method lays a foundation for future scientific research personnel to carry out pavement structure optimization design, pavement service performance prediction and intelligent pavement maintenance system construction.
While the foregoing is directed to the preferred embodiment of the present invention, it will be appreciated by those skilled in the art that various changes and modifications may be made therein without departing from the principles of the invention as set forth in the appended claims.
Claims (7)
1. A method for carrying out mechanical analysis on a microstructure of an asphalt mixture based on a three-dimensional local homogenization model is characterized by comprising the following steps:
(1) According to the structural design requirements of different types of asphalt pavements, selecting an aggregate grading scheme of the asphalt mixture, and determining an aggregate grading curve corresponding to the grading scheme;
(2) Taking coarse aggregate distribution as a main body, constructing a random microscopic structure model of the asphalt mixture:
firstly, calculating the volume fraction of aggregate according to the mass fraction of aggregate with each particle size in an aggregate grading curve and the density parameters of the aggregate and asphalt, then, assuming the coarse aggregate with the same particle size grade as spherical particles with the same size, and calculating the required feeding number of the coarse aggregate with each particle size according to the volume fraction; randomly distributing the calculated coarse aggregates in an asphalt mixture model space by using a random putting method, preliminarily generating an asphalt mixture random microscopic structure model, and recording the central position coordinates and the particle size information of each coarse aggregate in the microscopic structure model;
(3) Carrying out local area space division:
taking the central point of each coarse aggregate as a control point, taking the particle size of the coarse aggregate as a weight, and adopting a weighted Voronoi method to perform space division on the asphalt mixture, so as to divide the model space into a plurality of local areas taking the distribution of the coarse aggregates as the center; the local areas are adjacent to each other and fill the whole space; meanwhile, each local area contains coarse aggregate particles with specific particle sizes and a mortar matrix containing fine aggregates and asphalt, and finally a continuous non-uniform microscopic structure geometric model of the asphalt mixture is formed; as the coarse aggregates with different grain diameters are distributed randomly in the model, the shape of a local area containing each coarse aggregate is an irregular polyhedron, and the volume of each local area of the microscopical model, the geometrical coordinate information of a vertex and the grain diameter information of the contained coarse aggregates are read and recorded;
(4) Respectively constructing a geometric model and a constitutive model;
(5) Writing the viscoelasticity parameters corresponding to each local area in the constitutive model into a finite element model input file according to the serial number sequence of the geometric model, and then constructing the finite element model by using a file import mode;
(6) And (3) constraining the boundary of the microscopic structure model by using the macroscopic structure of the asphalt pavement, and then equivalently inputting the macroscopic vehicle load to finish analyzing the microscopic mechanical response in the asphalt mixture on the premise of considering the macroscopic stress load of the pavement structure.
2. The method for conducting mechanical analysis on the asphalt mixture microstructure based on the three-dimensional local homogenization model according to claim 1, wherein the random feeding method in the step (2) comprises:
(1) firstly, assuming coarse aggregates with the same particle size as spherical particles with the same size, and sequencing all coarse aggregate information according to the particle size;
(2) sequentially and randomly putting all coarse aggregates in sequence, wherein in the putting process, attention is paid to avoiding overlapping of particles and avoiding the particles from exceeding the boundary;
(3) after all the particles are put in, a fine structure model of the asphalt mixture based on the coarse aggregate framework is initially established, and then the sphere center position and the particle size information of each coarse aggregate sphere in the space are recorded.
3. The method for conducting mechanical analysis on the asphalt mixture mesostructure based on the three-dimensional local homogenization model as claimed in claim 1, wherein the weighted Voronoi method in the step (3) comprises the following steps:
A. distributing the central points of the coarse aggregates in space;
B. converting the vector file with the space coordinate information into a raster file to distribute weight information;
C. calculating Euclidean distances among the central points of the coarse aggregates in the grid file;
D. applying the weight information to the euclidean distance, dividing the euclidean distance by the weight;
E. calculating pixel points in the space based on the Euclidean distance considering the weight, and allocating the pixel points to the most appropriate aggregate central point, wherein the most appropriate aggregate central point is the central point with the minimum weight value divided by the Euclidean distance;
F. and after all the pixel points are distributed, converting the raster file into a vector coordinate graph.
4. The method for conducting mechanical analysis on the asphalt mixture microstructure based on the three-dimensional local homogenization model according to claim 1, wherein the geometric model in the step (4) is constructed through the following process:
a. reading the geometrical coordinate information of the vertexes of all local areas of the mesoscopic model, carrying out parametric modeling by utilizing a python secondary development interface of commercial finite element software, constructing a finite element geometrical model according to the sequence of point-line-surface-body, and numbering all local areas in the model by referring to aggregate grain size arrangement;
b. and dividing the model by adopting a free mesh mode, generating an input file containing model information after the mesh division is finished, wherein in the file, the model and the local area information are represented by nodes and units with numbers and correspondingly represent different aggregate distribution information.
5. The method for conducting mechanical analysis on the asphalt mixture microstructure based on the three-dimensional local homogenization model as recited in claim 4, wherein the constitutive model in the step (4) is constructed by the following steps:
i. in the asphalt mixture, defining an asphalt mortar matrix as a viscoelastic material, and defining coarse aggregate contained in a model as a linear elastic material;
ii. For an asphalt mortar matrix, determining a viscoelastic index of the asphalt mortar by adopting an indoor dynamic shear rheological experiment method, wherein the viscoelastic index comprises a dynamic modulus and a phase angle; then, establishing a viscoelasticity main curve of the asphalt mortar by means of a main curve fitting method, wherein the viscoelasticity main curve comprises the expression of viscoelasticity information under a frequency domain coordinate system, and calculating to obtain a rigidity matrix of the asphalt mortar matrix through the Poisson ratio of the asphalt mortar matrix;
iii, determining the elastic modulus and Poisson ratio parameters of the coarse aggregate by adopting an indoor test or consulting documents, calculating a rigidity matrix of the coarse aggregate, and recording the rigidity matrix of the asphalt mortar matrix and the rigidity matrix of the aggregate as basic mechanical input parameters;
iv, reading the structural information of the geometric model, wherein each local area corresponds to the particle size of the coarse aggregate under the specific gradation, assuming the coarse aggregate as an ellipsoid, randomly appointing the three-axis length of the ellipsoid on the basis of the determined particle size of the coarse aggregate, calculating the volume of the coarse aggregate based on the three-axis length information, and calculating the volume content of the coarse aggregate in the local area according to the volume information of the local area;
v, integrating the volume information of the local area, the viscoelasticity parameter of the matrix, the elastic modulus of the coarse aggregate, the volume content and the three-axis length factors of the ellipsoid, calculating the homogenization mechanical parameters of the local area by using a Mori-Tanaka mesoscopic mechanics method, namely a local area homogenization rigidity matrix, calculating the local area homogenization dynamic modulus and the Poisson ratio parameter through the local area homogenization rigidity matrix, and corresponding the homogenization mechanical parameters to the models one to one;
and vi, converting the dynamic modulus in the frequency domain into the dynamic modulus in the time domain by using a Laplace inverse transformation method so as to meet the requirement of numerical simulation calculation.
6. The method for conducting mechanical analysis on asphalt mixture mesostructure based on three-dimensional local homogenization model according to claim 5, wherein the local area homogenization rigidity matrix L is calculated by utilizing Mori-Tanaka mesomechanics method hom The process comprises the following steps:
G r ＝[I+S r ∶(L * (ω)) -1 ∶(L r -L * (ω))] -1
wherein L is * (omega) and L r (ω) stiffness matrices of the bitumen mortar matrix and the r-th coarse aggregate in the local area, c 0 And c n The volume contents S of the matrix and the nth coarse aggregate particles in a local area r The Eshelby tensor, which is the coarse aggregate particle, represents the shape characteristics of the coarse aggregate particle, M represents the total number of coarse aggregates contained in the region, I represents the identity matrix, and G represents the number of coarse aggregates in the region n A local strain concentration tensor representing the nth coarse aggregate.
7. The method for performing mechanical analysis on the fine structure of the asphalt mixture based on the three-dimensional local homogenization model as recited in claim 5, wherein in the step vi, the inverse Laplace transform operation formula is,
wherein f (t) is a function expression of the dynamic modulus in the time domain; f (omega) is a function expression of the dynamic modulus in the frequency domain; l is Laplace operation symbol, j represents imaginary unit, j 2 = 1, β represents the real part of the complex laplace variable, and ω represents the frequency variable.
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