A method for establishing a numerical model of spatial variability of mechanical parameters of asphalt mixture

Abstract

The application discloses a numerical model establishing method for spatial variability of asphalt mixture mechanical parameters, and specifically implements the following steps: 1. determining relevant distances based on discrete data of asphalt mixture mechanical parameters at different positions λ ; 2. establishing an asphalt pavement structure model and performing grid division; 3. based on the grid unit of the asphalt mixture surface layer in step 2, acquiring relevant discrete random fields by using a random field theory; and 4. based on the discrete random field in step 3, assigning the random field to the grid unit in step 2 and inputting into finite element software, thereby establishing a random finite element model considering spatial variability of asphalt mixture material mechanical parameters. The method can provide an accurate, effective and more practical numerical model, and can be combined with existing commercial finite element software to study the influence of spatial random fields of asphalt mixture mechanical parameters on the mechanical behavior of the asphalt pavement.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of numerical simulation methods of asphalt mixture, and particularly relates to a numerical model establishment method for spatial variability of mechanical parameters of asphalt mixture. BACKGROUND

[0002] The main challenges faced by pavement mechanical behavior analysis and pavement structure design are attributed to the complexity and uncertainty of the constituent materials and future traffic loads, as well as multiple failure mechanisms. Asphalt mixture, as a constituent material of asphalt pavement, is a multiphase composite material composed of asphalt, aggregate and voids. Due to the differences in the mesostructure between local parts of the asphalt mixture, the asphalt mixture presents certain heterogeneity at the macro level, and the mechanical parameters of the asphalt mixture have variability. And in the process of pavement construction, due to the non-uniformity of construction quality, the mechanical parameters of the asphalt mixture have spatial variability, but this spatial variability is not purely random, but has random and structural characteristics, and should be regarded as a spatial random field.

[0003] In the process of pavement mechanics design, the elastic layered system theory and the finite element numerical analysis method are usually used to predict the response of the pavement structure. Although the deterministic and probabilistic analysis of pavement design based on the elastic layered system theory has high calculation efficiency, the simplification assumption of uniform and homogeneous linear material layer used in the elastic layered system theory will lead to inaccurate analysis of the actual pavement structure, such as the inability to simulate the nonlinear material behavior in the actual pavement structure, multiple site damage, asymmetric traffic load and non-uniform layer thickness. However, in the finite element numerical analysis model, the defects of the elastic layered system theory modeling can be solved by considering the heterogeneity of the pavement material system, the random spatial variation of the pavement layer thickness, and other uncertainties in the external load, pavement geometry, failure mechanism and environmental conditions. Therefore, to accurately analyze the mechanical response of the actual pavement structure, it is necessary to study the influence of the variability of the mechanical parameters of the asphalt mixture on the response of the pavement structure by means of the finite element analysis method, which requires the establishment of a numerical model finite element numerical model considering the spatial variability of the mechanical parameters of the asphalt mixture.

[0004] Currently, the methods to simulate the influence of the variability of asphalt mixture mechanical parameters on its structural response are: (a) using Monte Carlo simulation to randomly sample the mechanical parameters and assign them to the finite element model to calculate the structural response; (b) discretizing the pavement into a finite number of grid elements, simulating the spatial variability of material parameters by assigning different mechanical parameters to the grid elements, and assuming that the material parameters of different grid elements follow a certain probability distribution, such as Weibull distribution, lognormal distribution, etc. The first method calculates the mean and variance of the structural response by simulating multiple homogeneous linear material layers, and analyzes the random behavior of the pavement response; the second method can reflect the random distribution of material parameters in space, but does not consider the spatial correlation of material parameters, i.e. the mechanical parameters of adjacent positions (adjacent elements) are purely random. In fact, the mechanical parameters of adjacent positions (elements) do not change abruptly, and usually have a certain degree of positive correlation. Therefore, the current numerical model does not consider this spatial correlation, resulting in unreasonable situations where the mechanical parameters of adjacent elements differ greatly.

[0005] The prior art is as follows:

[0006] Comparison with the technology of patent CN108629111A, CN108629111B "A simulation method for spatial variability of material parameters of concrete gravity dam"

[0007] The simulation method for spatial variability of material parameters of concrete gravity dam provided in patent CN108629111A and CN108629111B establishes a two-dimensional random model of the gravity dam. What we provide is a simulation method for spatial variability of asphalt mixture on the road, considering a three-dimensional random finite element model of the road pavement.

[0008] The patent CN108629111A and CN108629111B do not provide the related distance used in the spatial variability of mechanical parameters, while we provide a way to obtain the related distance based on real roads, further improving the reliability of the established finite element model.

[0009] The random matrix in patent CN108629111A and CN108629111B is randomly sampled, while we are based on the Latin hypercube sampling method, which can reduce the number of sampling points as much as possible while ensuring uniform distribution of sample points, thereby improving computational efficiency.

[0010] Comparison with the technology of patent CN116245001A "A simulation method and system for spatial variability of concrete based on random discrete elements"

[0011] The space variability simulation method of the concrete mesoscopic discrete element provided in the patent CN116245001A is a simulation method considering parameter variability from the mesoscopic scale, which is suitable for the simulation of small-sized concrete test pieces; and the simulation method of the space variability of the asphalt mixture at the road macroscopic scale provided by us is a simulation method considering the three-dimensional pavement random finite element model of the road, which is suitable for the analysis of the pavement structure design and the mechanical response of the pavement.

[0012] Comparison with the technology of the patent CN113886933A "Airport pavement evaluation method based on cement soil space variability"

[0013] The patent CN116245001A provides an evaluation method of the space variability of the cement soil on the airport pavement. The patent only collects the related parameters of the sand soil and the cement soil, and does not point out the implementation method of the space variability. The invention provides the implementation method of the space variability.

[0014] Comparison with the technologies of the patents CN114330072A, CN115166198A and CN114004117A

[0015] The patents CN114330072A, CN115166198A and CN114004117A and other patents consider the probability distribution method of the soil body variability on the pipeline impact and the soil body slope slip, and the patent belongs to the road field, and the soil body structure is inconsistent with the structure of the asphalt road constructed by the invention.

[0016] The patents CN114330072A, CN115166198A and CN114004117A do not provide the related distance used in the space variability of the mechanical parameters, and the invention provides the method of obtaining the related distance based on the real road, and further improves the reliability of the established finite element model. SUMMARY

[0017] In order to solve the problems in the establishment of the above-mentioned random finite element model considering the space correlation, the invention provides a numerical model establishment method of the space variability of the asphalt mixture mechanical parameters, considers the numerical model of the space variability of the asphalt mixture mechanical parameters (such as the resilient modulus, the long-term equilibrium modulus, the viscoelasticity, the tensile strength, the fracture energy and the like), the method can provide the numerical model which is accurate, effective and more consistent with the engineering practice, and can be combined with the existing commercial finite element software to study the influence of the space random field of the asphalt mixture mechanical parameters on the mechanical behavior of the asphalt pavement.

[0018] To achieve the above-mentioned purpose, the technical scheme adopted by the invention is:

[0019] A numerical model establishment method of spatial variability of asphalt mixture mechanical parameters, comprising the following steps:

[0020] Step (1): based on the discrete data of the collected mechanical parameters of asphalt mixture at different positions, the correlation distance λ is determined according to the spatial recursive method;

[0021] Step (2): an asphalt pavement structure model is established in the finite element software and the model is meshed;

[0022] Step (3): based on the asphalt mixture surface layer grid element in step (2), the same grid as the finite element calculation is used to simulate the spatial variability of the mechanical parameters of the asphalt mixture, and the related random field is obtained;

[0023] Step (4): based on the discrete random field in step (3), the random field is assigned to the grid element according to the grid element number, and is input into the finite element software, so that a random finite element model considering the spatial variability of the mechanical parameters of the asphalt mixture material is established.

[0024] As a further improvement of the application, the correlation distance λ is solved according to the spatial recursive method in step (1), comprising the following steps:

[0025] Step (1.1): the several discrete samples of the test mechanical parameters are obtained by coring at a certain distance based on the road site, the distance between each sample is Δl, the mean value E(x) and the variance σ 2 of all discrete samples of the mechanical parameters are calculated;

[0026] Step (1.2): a group of data is formed by the mean values of the adjacent two sample points, at this time n=2, the mean value and the variance D 2 (2) of the group of data are solved, and Γ 2 (2)=D 2 (2) / σ 2 is calculated;

[0027] Step (1.3): the point is plotted on the nΔlΓ 2 (2)~nΔl graph;

[0028] Step (1.4): similarly, n=3, 4, 5, … are taken respectively, steps (1.2) and (1.3) are repeated, and the nΔlΓ 2 (n)~nΔl graph is plotted;

[0029] Step (1.5): the maximum value of nΔlΓ 2 (n) is found, and the point value is taken as the correlation distance λ.

[0030] As a further improvement of the application, the step (2) of establishing the asphalt pavement structure model in the finite element software and meshing the model comprises the following steps:

[0031] Step (2.1): Establishing the finite element model of the asphalt pavement by using the finite element software, and the pavement structure adopts the form of four-layer structure combination, and from bottom to top, the soil base, the cement stabilized soil base layer, the cement stabilized macadam base layer and the asphalt surface layer are sequentially arranged;

[0032] Step (2.2): The finite element meshing is performed on each structure layer of the pavement structure in step (2.1) by using eight-node hexahedral elements, and a plurality of grid elements are obtained.

[0033] As a further improvement of the application, the step (3) of obtaining the relevant random field comprises the following steps:

[0034] Step (3.1): Numbering each element of the asphalt surface layer in step (2), and calculating the center point coordinate value matrix of each element:

[0035]

[0036] Wherein, i, i=1, 2, …, N is the element number of the asphalt surface layer, x ij , j=1, 2, …, 8 is the horizontal coordinate value of the jth node of the ith element, y ij is the vertical coordinate value of the jth node of the ith element, z ij is the vertical coordinate value of the jth node of the ith element, x i , y i and z i are the horizontal coordinate value, vertical coordinate value and vertical coordinate value of the center point of the ith element, respectively;

[0037] Step (3.2): Based on the center point coordinate values of each element obtained in step (3.1), the autocorrelation function and the correlation distance λ determined in step (1), the autocorrelation coefficient matrix M ρ between each element in space is determined:

[0038]

[0039] Wherein, ρ kl represents the correlation coefficient between the kth element and the lth element;

[0040] Step (3.3): Cholesky decomposition is performed on the correlation coefficient matrix M ρ in step (3.2) to obtain an upper triangular matrix L N×N , that is;

[0041]

[0042] wherein, L N×N is an upper triangular matrix;

[0043] Step (3.4): using Latin hypercube sampling method to obtain a sample matrix Z composed of m sample sequences of N-dimensional standard normal distribution random variables m×N ;

[0044] Step (3.5): using the upper triangular matrix L N×N of step (3.3) to linearly transform the sample matrix Z m×N of step (3.4) to obtain a relevant random distribution sample matrix H of m sample sequences m×N , i.e.

[0045] H m×N = Z m×N · L N×N

[0046] Step (3.6): considering the non-negativity of the mechanical parameters, taking the exponential of the matrix H m×N in step (3.5) to obtain a sample matrix X of relevant lognormal random discrete fields m×N , i.e.

[0047]

[0048] As a further improvement of the present application, the step (4) of establishing a random finite element model considering the spatial variability of the mechanical parameters of the asphalt mixture material comprises the following steps:

[0049] Step (4.1): according to the matrix X m×N obtained in step (3), taking m=1, i.e. assigning the N samples in the first row of the matrix to the corresponding finite element grid number N according to the value of N, and inputting it into the finite element software, thereby constructing a random finite element model considering the spatial variability of the mechanical parameters of the asphalt mixture material, and then completing the finite element calculation of the model in the finite element software.

[0050] Step (4.2): similarly, taking m=2, 3, …, respectively, repeating step (4.1), thereby realizing m times of random finite element calculation of the random finite element model considering the spatial variability of the mechanical parameters of the asphalt mixture material.

[0051] As a further improvement of the present application, the autocorrelation function in step (3.2) is a negative exponential autocorrelation function or a Gaussian autocorrelation function or an exponential autocorrelation function or a second-order autoregressive autocorrelation function or an exponential cosine autocorrelation function or a triangular autocorrelation function.

[0052] Compared with the prior art, the present application has the following beneficial effects:

[0053] The present application is based on the random field theory, and uses the autocorrelation function to consider the spatial correlation of the asphalt mixture material parameters, and then proposes a random numerical simulation method based on the spatial variability and meeting the known correlation relationship. The numerical model establishment method described in the present application is more in line with the engineering practice, and can provide more accurate data support for the road design and service process prediction; the simulation method can be combined with the existing commercial finite element software to study the influence of the spatial variability of the material parameters in the asphalt pavement on the mechanical behavior of the asphalt pavement, and provide support for the analysis considering the spatial variability of the material parameters. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 Flow chart for numerical model establishment of the present application

[0055] Figure 2 nΔlΓ for the recursive spatial method 2 (n)~nΔl diagram

[0056] Figure 3 Asphalt pavement finite element model

[0057] Figure 4 Random field distribution diagram of the mechanical parameters of the asphalt pavement surface layer

[0058] Figure 5 Asphalt pavement surface layer model in the finite element software DETAILED DESCRIPTION

[0059] The present application will be described in detail below in combination with the drawings and specific embodiments.

[0060] As Figure 1 shown, a numerical model establishment method of the spatial variability of the mechanical parameters of asphalt mixture, wherein the model of the asphalt pavement surface layer in the finite element software is as Figure 5 shown, comprising the following steps:

[0061] Step (1): based on the discrete data of the mechanical parameters of the asphalt mixture collected at different positions, the correlation distance λ is determined according to the spatial recursive method:

[0062] Step (1.1): the several discrete samples of the mechanical parameters are obtained based on the road site according to a certain distance coring, the distance between each sample is Δl, the mean value E(x) and the variance σ 2 of all the discrete samples of the mechanical parameters are calculated, considering the non-negativity of the mechanical parameters, it is assumed that the mechanical parameters meet the logarithmic normal distribution;

[0063] Step (1.2): the mean values of the adjacent two sample points form a group of data, at this time let n=2, the mean value and the variance D 2 (2) of the group of data are solved, and Γ 2(2) = D 2 (2) / σ 2 ;

[0064] Step (1.3): On the nΔlΓ 2 (2)~nΔl graph, the point is plotted;

[0065] Step (1.4): Similarly, taking n = 3, 4, 5, …, respectively, repeat steps (1.2) and (1.3), draw the nΔlΓ 2 (n)~nΔl graph;

[0066] Step (1.5): Find the maximum value of nΔlΓ 2 (n), take the point value as the correlation distance λ.

[0067] Step (2): Establish an asphalt pavement structure model in the finite element software and mesh the model;

[0068] Step (2.1): Establish an asphalt pavement finite element model using finite element software, and the pavement structure adopts a four-layer structure combination, from bottom to top, it is soil base, cement stabilized soil base layer, cement stabilized macadam base and asphalt surface;

[0069] Step (2.2): Each structure layer of the pavement structure in step (2.1) is meshed by eight-node hexahedral elements to obtain a plurality of grid elements.

[0070] Step (3): Based on the asphalt mixture surface layer grid element in step (2), the same grid as the random field simulation and finite element calculation is used to disperse the asphalt mixture mechanical parameter random field, and the correlation random field is obtained:

[0071] Step (3.1): Number each element of the asphalt surface layer in step 2, and calculate the center point coordinate value matrix

[0072]

[0073] Wherein, i (i = 1, 2, …, N) is the unit number of the asphalt surface layer, x ij (j = 1, 2, …, 8) is the horizontal coordinate value of the jth node of the ith element, y ij is the vertical coordinate value of the jth node of the ith element, z ij is the vertical coordinate value of the jth node of the ith element, x i , y i and z i are the horizontal coordinate value, vertical coordinate value and vertical coordinate value of the center point of the ith element, respectively.

[0074] Step (3.2): Based on the centroid point coordinate values of each unit, the autocorrelation function obtained in step (3.1) and the correlation distance λ determined in step (1), the autocorrelation coefficient matrix M between each unit in space is determined ρ :

[0075]

[0076] wherein ρ kl represents the correlation coefficient between the kth unit and the lth unit. The autocorrelation function can be any one of a negative exponential autocorrelation function, a Gaussian autocorrelation function, an exponential autocorrelation function, a second-order autoregressive autocorrelation function, an exponential cosine autocorrelation function, a triangular autocorrelation function, etc.

[0077] Step (3.3): Cholesky decomposition is performed on the correlation coefficient matrix M ρ in step (3.2) to obtain an upper triangular matrix L N×N , i.e.

[0078]

[0079] wherein L N×N is an upper triangular matrix.

[0080] Step (3.4): Latin hypercube sampling method is used to obtain a sample matrix Z m×N composed of m sampling sequences of N-dimensional standard normal distribution random variables;

[0081] Step (3.5): The upper triangular matrix L N×N in step (3.3) is used to linearly transform the sample matrix Z m×N in step (3.4) to obtain a correlation random distribution sample matrix H m×N of the m sampling sequences, i.e.

[0082] H m×N = Z m×N · L N×N

[0083] Step (3.6): Considering the non-negativity of the mechanical parameters, the matrix H m×N in step (3.5) is taken as an exponential, thereby obtaining a sample matrix X m×N of the correlated lognormal random discrete field, i.e.

[0084]

[0085] Step (4): Based on the discrete random field in step (3), the random field is assigned to the grid units according to the grid unit number, and is input into the finite element software:

[0086] Step (4.1); according to the matrix X obtained in step (3) m×N , take m = 1, that is, assign the N samples in the first row of the matrix to the corresponding finite element grid number N according to the value of N, and input it into the finite element software, thereby constructing a random finite element model considering the spatial variability of the mechanical parameters of asphalt mixture materials, and then completing the finite element calculation of the model in the finite element software.

[0087] Step (4.2); similarly, take m = 2, 3, …, respectively, repeat step (4.1), thereby realizing the m times of random finite element calculation of the random finite element model considering the spatial variability of the mechanical parameters of asphalt mixture materials.

[0088] Embodiment:

[0089] This embodiment takes the resilience modulus of asphalt mixture as an example to illustrate the method for establishing the numerical model of the spatial variability of the mechanical parameters, and the specific steps are as follows:

[0090] Step (1): based on the discrete data of the mechanical parameters of asphalt mixture collected at different positions, determine the correlation distance λ according to the spatial recursive method:

[0091] Step (1.1): take core every 5m in the actual road transversely or longitudinally, the sample number is 50, perform the compression resilience modulus test according to the specification JTGE20-2011, and calculate the resilience modulus, calculate the mean value E(x) of all discrete samples mechanical parameters as 1252MPa, and the variance σ 2 is 137MPa;

[0092] Step (1.2): a group of data is formed by the mean values of the adjacent two sample points, at this time let n = 2, the mean value and variance D 2 (2) of the group of data are calculated, and Γ 2 (2) = D 2 (2) / σ 2 ;

[0093] Step (1.3): plot the point on the nΔlΓ 2 (2)~nΔl graph, as shown in Figure 2 ;

[0094] Step (1.4): similarly, take n = 3, 4, 5, …, respectively, repeat steps (1.2) and (1.3), draw the nΔlΓ 2 (n)~nΔl graph, as shown in Figure 2 ;

[0095] Step (1.5): find the maximum value of nΔlΓ 2 (n), take the point value as the correlation distance λ, as shown in Figure 2The relevant distance λ = 15.95 m at this time.

[0096] Step (2): Establishing an asphalt pavement structure model in a finite element software and meshing the model, as shown in Figure 3 The steps are as follows:

[0097] Step (2.1): The finite element model of the road has a lateral direction of 6.0 m, a longitudinal direction of 6.0 m, and a depth of 3.0 m, and the pavement structure adopts a four-layer structure combination form from bottom to top, that is, a soil base, a cement stabilized soil base layer, a cement stabilized macadam base layer, and an asphalt surface layer, with thicknesses of 2.3 m, 0.2 m, 0.15 m, and 0.35 m, respectively.

[0098] Step (2.2): Each structure layer of the pavement structure is meshed by eight-node hexahedral elements for finite element meshing, obtaining 8316 mesh elements, of which the number of mesh elements of the asphalt surface layer is 756.

[0099] Step (3): Based on the mesh elements of the asphalt mixture surface layer in step (2), the same grid as the finite element calculation is used for random field simulation to disperse the mechanical parameters of the asphalt mixture, and the relevant random field is obtained:

[0100] Step (3.1): The 756 elements of the asphalt surface layer in step 2 are numbered in the finite element software, and the center point coordinate value matrix of each element is calculated as:

[0101]

[0102] The first column is the element number, the second column is the center point horizontal coordinate value, the third column is the center point longitudinal coordinate value, and the fourth column is the center point vertical coordinate value.

[0103] Step (3.2): Based on the center point coordinate values of each element obtained in step (3.1), the autocorrelation function, and the relevant distance λ determined in step (1), the autocorrelation coefficient matrix M of each element in space is determined ρ . The autocorrelation function can be any one of a negative exponential autocorrelation function, a Gaussian autocorrelation function, an exponential autocorrelation function, a second-order autoregressive autocorrelation function, an exponential cosine autocorrelation function, and a triangular autocorrelation function. In this embodiment, the negative exponential autocorrelation function is used to describe the autocorrelation of the spatial points, which is expressed as

[0104]

[0105] Wherein, λ x , λ y , and λ z are the relevant distances of the asphalt mixture in the horizontal, longitudinal, and vertical coordinate directions, respectively, and in this embodiment, λ x = λy = λ z = 15.95 m; x i , y i , z i are the horizontal, vertical and vertical coordinate values of the centroid of the i-th element; x j , y j , z j are the horizontal, vertical and vertical coordinate values of the centroid of the j-th element; by calculating the autocorrelation coefficient matrix M ρ between each element

[0106]

[0107] Step (3.3): Cholesky decomposition is performed on the correlation coefficient matrix M ρ in step (3.2) to obtain an upper triangular matrix L 756×756

[0108]

[0109] Step (3.4): Latin hypercube sampling method is used for random sampling to obtain a sample matrix Z 100×756 composed of 100 sampling sequences of standard normal distribution random variables;

[0110]

[0111] Step (3.5): Linear transformation of the sample matrix Z 756×756 in step (3.4) using the upper triangular matrix L 100×756 in step (3.3) obtains a correlation random distribution sample matrix H 100×756 of 100 sampling sequences, that is

[0112]

[0113] Step (3.6): Considering the non-negativity of the mechanical parameters, the matrix H 100×756 in step (3.5) is taken as an exponential, thereby obtaining a sample matrix X 100×756 of a correlated lognormal random discrete field

[0114]

[0115] Step (4): Based on the discrete random field of step (3), the random field is assigned to the grid element according to the grid element number, and input into the finite element software:

[0116] Step (4.1): According to the matrix X 100×756 obtained in step (3), take m = 1, that is, the matrix X 100×756 ​The 756 samples in the first row are assigned to the corresponding finite element grid number N according to the value of N, as shown in Figure 3 The input is input into the finite element software, thereby constructing a random finite element model considering the spatial variability of the mechanical parameters of the asphalt mixture material, as shown in Figure 4 The finite element calculation of the model is completed in the finite element software.

[0117] Step (4.2); similarly, taking m = 2, 3, … 100 respectively, repeating step (4.1), thereby achieving 100 random finite element calculations of the random finite element model considering the spatial variability of the mechanical parameters of the asphalt mixture material.

[0118] The above is only a preferred embodiment of the present application, not any other form of limitation on the present application, and any modification or equivalent change made according to the technical essence of the present application still falls within the scope of the present application.

Claims

1. A method for establishing a numerical model of the spatial variability of mechanical parameters of asphalt mixtures, characterized in that: The steps include the following: Step (1): Based on the discrete data of mechanical parameters of asphalt mixtures collected at different locations, determine the relevant distance λ according to the spatial recursion method; Step (1) involves solving for the relevant distance λ using a spatial recursion method, including the following steps: Step (1.1): Several discrete samples for testing mechanical parameters are obtained by core sampling at certain intervals from the road site. The distance between each sample is Δl. The mean E(x) and variance σ of the mechanical parameters of all discrete samples are calculated. 2 ; Step (1.2): Use the means of two adjacent sample points to form a data set. Let n=2, and calculate the mean and variance D of this data set. 2 (2), and calculate Γ 2 (2) = D 2 (2) / σ 2 ; Step (1.3): In nΔlΓ 2 (2) Plot the point on the nΔl graph; Step (1.4): Similarly, take n=3,4,5,… and repeat steps (1.2) and (1.3) to plot nΔlΓ. 2 (n) ~ nΔl diagram; Step (1.5): Find nΔlΓ 2 The maximum value of (n) is used as the relevant distance λ. Step (2): Establish an asphalt pavement structure model in finite element software and mesh the model; Step (3): Based on the asphalt mixture surface layer mesh unit in step (2), the mechanical parameters of the asphalt mixture are discretized using the same mesh as the random field simulation and finite element calculation to obtain the relevant random field; Step (3) involves obtaining the relevant random field, including the following steps: Step (3.1): Number each unit of the asphalt surface layer in step (2) and calculate the center point coordinate matrix of each unit. ； Where i, i=1,2,…,N are the unit numbers of the asphalt surface layer, x ij j=1,2,…,8 is the x-coordinate of the j-th node in the i-th unit, y ij Let z be the ordinate value of the j-th node in the i-th unit. ij Let x be the vertical coordinate value of the j-th node in the i-th unit. i y i and z i These are the x-coordinate, y-coordinate, and vertical coordinates of the center point of the i-th unit, respectively. Step (3.2): Based on the coordinates of the centroids of each element obtained in step (3.1), the autocorrelation function, and the correlation distance λ determined in step (1), determine the autocorrelation coefficient matrix M between each element in space. ρ : ； Where, ρ kl This represents the correlation coefficient between the k-th unit and the l-th unit; Step (3.3): For the correlation coefficient matrix M in step (3.2) ρ Cholesky decomposition yields the upper triangular matrix L. N×N ,Right now; ； Among them, L N×N It is an upper triangular matrix; Step (3.4): Use the Latin hypercube sampling method to obtain the sample matrix Z, which consists of m sampling sequences of an N-dimensional standard normal distributed random variable. m×N ; Step (3.5): Using the upper triangular matrix L from step (3.3) N×N For the sample matrix Z in step (3.4) m×N A linear transformation yields the correlated random distribution sample matrix H of m sampling sequences. m×N ,Right now ； Step (3.6): Considering the non-negativity of the mechanical parameters, the matrix H in step (3.5) is... m×N Taking the exponent, we obtain the sample matrix X of the correlated log-normal random discrete field. m×N ,Right now ； Step (4): Based on the discrete random field in step (3), the random field is assigned to the grid cells according to the grid cell number and then input into the finite element software, thereby establishing a stochastic finite element model that considers the spatial variability of the mechanical parameters of asphalt mixture materials.

2. The method for establishing a numerical model of the spatial variability of mechanical parameters of asphalt mixtures according to claim 1, characterized in that: Step (2) involves establishing an asphalt pavement structure model in finite element software and meshing the model, including the following steps: Step (2.1): Use finite element software to establish a finite element model of asphalt pavement. The pavement structure adopts a four-layer structure combination, from bottom to top: subgrade, cement-stabilized soil base, cement-stabilized crushed stone base and asphalt surface layer. Step (2.2): For each structural layer of the pavement structure in step (2.1), finite element meshing is performed using eight-node hexahedral elements to obtain several mesh elements.

3. The method for establishing a numerical model of the spatial variability of mechanical parameters of asphalt mixtures according to claim 1, characterized in that: The autocorrelation function mentioned in step (3.2) is a negative exponential autocorrelation function, a Gaussian autocorrelation function, an exponential autocorrelation function, a second-order autoregressive autocorrelation function, an exponential cosine autocorrelation function, or a trigonometric autocorrelation function.

4. The method for establishing a numerical model of the spatial variability of mechanical parameters of asphalt mixtures according to claim 1, characterized in that: Step (4) establishes a stochastic finite element model that considers the spatial variability of the mechanical parameters of asphalt mixtures, including the following steps: Step (4.1); Based on the matrix X obtained in step (3) m×N Taking m=1, the N samples in the first row of the matrix are assigned to the corresponding finite element mesh number N according to the value of N, and then input into the finite element software, thereby constructing a stochastic finite element model that considers the spatial variability of the mechanical parameters of asphalt mixture materials, and then completing the finite element calculation of the model in the finite element software. Step (4.2); Similarly, take m=2,3,… respectively, and repeat step (4.1), thereby realizing m-times stochastic finite element calculation of the stochastic finite element model considering the spatial variability of the mechanical parameters of asphalt mixture materials.

Images