Asphalt mixture dynamic modulus prediction method and system and storage medium

Abstract

The invention discloses an asphalt mixture dynamic modulus prediction method and system and a storage medium, and the method comprises the following steps: S1, obtaining a fractal dimension of a coarse aggregate through the grading screening fitting of an asphalt mixture, and building a probability density function of the particle size distribution of the coarse aggregate according to the fractal dimension; s2, calculating the dynamic complex modulus by using the energy storage modulus and the loss modulus of the asphalt mortar; s3, dispersing the coarse aggregate into a plurality of particle size intervals, calculating the volume fraction of each particle size interval according to a probability density function, and calculating the equivalent inclusion modulus of the coarse aggregate in combination with the dynamic complex modulus; and S4, taking the equivalent inclusion modulus as a new inclusion phase, taking the asphalt mortar as a basic item, and solving the dynamic modulus of the asphalt mixture through a self-consistent method. The equivalent inclusion modulus is used as a new inclusion phase, the asphalt mortar is used as a basic item, and the dynamic modulus of the asphalt mixture is solved through a self-consistent method. According to the method, a physical mechanism can be truly restored, and the dynamic modulus of the asphalt mixture can be accurately predicted.

Description

Technical Field

[0001] This invention relates to road engineering materials, and in particular to a method, system, and storage medium for predicting the dynamic modulus of asphalt mixtures. Background Technology

[0002] The dynamic modulus of asphalt mixtures is a core parameter in pavement structure design, and its accurate prediction is crucial for road service life. Existing prediction methods include the Witczak model, the ANN model, and the Hirsch model. However, these methods do not consider the influence of coarse aggregate size on the dynamic modulus, and most also fail to account for the frequency dependence of asphalt mortar, using only linear elastic modulus to replace complex modulus. These shortcomings result in low accuracy in predicting the dynamic modulus of asphalt mixtures.

[0003] These methods fail to consider the influence of coarse aggregate size on the dynamic modulus, i.e., they homogenize the coarse aggregate and ignore the fractal characteristics of the gradation, thus ignoring the stress distribution distortion caused by the heterogeneity of the gradation. At the same time, most methods do not consider the frequency dependence of asphalt mortar, and only use the linear elastic modulus to replace the complex modulus, which makes it impossible to reflect the temperature-load coupling effect, i.e., it cannot characterize the modulus jump caused by temperature or frequency changes. These defects make the prediction of the dynamic modulus of asphalt mixtures deviate from the real physical mechanism, making it impossible for existing methods to accurately predict the dynamic modulus of asphalt mixtures. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a method, system, and storage medium for predicting the dynamic modulus of asphalt mixtures that can accurately predict the physical mechanism.

[0005] Technical solution: The present invention provides a method for predicting the dynamic modulus of asphalt mixtures, comprising the following steps:

[0006] S1. The fractal dimension of coarse aggregate is obtained by fitting the gradation of asphalt mixture through sieve analysis, and the probability density function of coarse aggregate particle size distribution is established accordingly.

[0007] S2. Based on the principle of elastic-viscoelastic correspondence, calculate the dynamic complex modulus of asphalt mortar using its storage modulus and loss modulus.

[0008] S3. Disperse the coarse aggregate into multiple particle size intervals according to the fractal distribution of the coarse aggregate, and calculate the volume fraction of each particle size interval according to the probability density function; calculate the Eshelby tensor and dynamic Poisson's ratio of the coarse aggregate in each particle size interval according to the dynamic complex modulus, and calculate the strain lumped tensor and interaction tensor of the coarse aggregate in each particle size interval accordingly; calculate the equivalent inclusion modulus of the coarse aggregate according to the dynamic complex modulus, the volume fraction of each particle size interval, the strain lumped tensor and the interaction tensor.

[0009] S4. The equivalent inclusion modulus is taken as the new inclusion phase, and asphalt mortar is taken as the basic term. The dynamic modulus of the asphalt mixture is solved by the self-consistent method.

[0010] Step S1, based on fractal theory, obtains the fractal dimension of coarse aggregate by fitting experimental data from asphalt mixture gradation sieving, and establishes the probability density function of coarse aggregate particle size distribution. This accurately characterizes the gradation fractal characteristics of coarse aggregate and avoids stress distribution distortion caused by neglecting gradation fractal characteristics. Step S2, based on the elastic-viscoelastic correspondence principle, uses a dynamic shear rheometer to measure the storage modulus and loss modulus of asphalt mortar, calculates the complex modulus, and replaces the traditional linear elastic modulus. This reflects the temperature-frequency coupling effect and solves the problem of being unable to characterize modulus jumps. In step S3, the volume fraction is calculated using a probability density function to reflect differences in particle size distribution. The aggregate-mortar interface interaction is quantified using the Eshelby tensor and dynamic Poisson's ratio to obtain the strain condensation tensor and interaction tensor. These are then combined with the probability density function, strain condensation tensor, and interaction tensor to calculate the equivalent inclusion modulus of the coarse aggregate, which characterizes the viscoelastic behavior of asphalt mortar, output from step S2. This effectively simplifies the complex coarse aggregate into a new, virtual inclusion phase, considering the multi-size effect of coarse aggregate and the frequency dependence of mortar. Step S4 calculates the dynamic modulus using the equivalent inclusion modulus, thus completing the cross-scale coupling between coarse aggregate and mixture. Steps S3 and S4 achieve a complete physical coupling from mortar viscoelasticity to aggregate size effect to mixture modulus, ensuring the prediction conforms to the physical mechanism. Based on the actual physical mechanism, the dynamic modulus of asphalt mixtures under various conditions can be predicted with high accuracy.

[0011] Preferably, the f k The calculation formula is:

[0012]

[0013] Among them, P(D) k (D) represents the particle size. k The probability density of coarse aggregate, D k Let ΔD be the coarse aggregate particle size in the k-th particle size range; k V is the interval length of the k-th particle size interval; agg This represents the total integral of the coarse aggregate.

[0014] A k and T k The calculation formulas are respectively

[0015] A k =[1+S k (E k / E * m -1)]-1

[0016] T k =[1+S k (1+E k / E * m )] -1

[0017] Among them, E k S represents the elastic modulus of coarse aggregate in the k-th particle size range; k Let be the Eshelby tensor of coarse aggregate in the k-th particle size range.

[0018] By calculating the volume fraction of each particle size range using fractal discretization as a weight, the contribution of large-sized and small-sized coarse aggregates to the equivalent inclusion modulus is differentiated, thus restoring the size effect of the true gradation. The strain concentration tensor and interaction tensor are calculated using the elastic modulus, Eshelby tensor, and dynamic Poisson's ratio of the coarse aggregate, which accurately quantifies the interaction between the aggregate and mortar interface. Compared with the traditional model that simplifies the aggregate-mortar interface to rigid contact, this model can more accurately reflect the stress field distortion.

[0019] Preferably, the S k The calculation is based on the assumption that the coarse aggregate is spherical and isotropic, and one non-zero component is taken. The specific calculation formula is as follows:

[0020]

[0021] Among them, v m The dynamic Poisson's ratio of asphalt mortar;

[0022] v m The calculation formula is:

[0023]

[0024] in, and These are the storage modulus and loss modulus of asphalt mortar, respectively.

[0025] The coarse aggregate is simplified into spherical isotropic inclusions, and the non-zero component is taken as S. k The value of significantly reduces the computational complexity of tensors, while maintaining accuracy through dynamic Poisson ratio, thus balancing efficiency and accuracy.

[0026] The dynamic modulus prediction system for asphalt mixtures of the present invention includes:

[0027] Particle size distribution confirmation module: used to obtain the fractal dimension of coarse aggregate by asphalt mixture gradation sieve fitting, and to establish the probability density function of coarse aggregate particle size distribution accordingly;

[0028] Complex modulus verification module: used to calculate the dynamic complex modulus of asphalt mortar using the storage modulus and loss modulus based on the elastic-viscoelastic correspondence principle;

[0029] Inclusion modulus calculation module: This module disperses coarse aggregate into multiple particle size ranges according to its fractal distribution, calculates the volume fraction of each particle size range based on the probability density function, calculates the Eshelby tensor and dynamic Poisson's ratio of the coarse aggregate in each particle size range based on the dynamic complex modulus, and then calculates the strain lumped tensor and interaction tensor of the coarse aggregate in each particle size range accordingly. Finally, it calculates the equivalent inclusion modulus of the coarse aggregate based on the dynamic complex modulus, the volume fraction of each particle size range, the strain lumped tensor, and the interaction tensor.

[0030] Solver module: Used to solve the dynamic modulus of asphalt mixture by taking the equivalent inclusion modulus as a new inclusion phase and asphalt mortar as the basic term.

[0031] The computer-readable storage medium for storing one or more programs according to the present invention includes one or more programs comprising instructions that, when executed by a computing device, cause the computing device to perform any of the methods described above.

[0032] Beneficial effects: The probability density function of coarse aggregate accurately characterizes the gradation fractal characteristics of coarse aggregate, avoiding stress distribution distortion caused by ignoring gradation fractal characteristics; the storage modulus and loss modulus are used to characterize the dynamic complex modulus of asphalt mortar, which can reflect the temperature-frequency coupling effect and solve the problem of the inability to characterize modulus jumps; based on these, the equivalent inclusion modulus is calculated, which simplifies coarse aggregates at different particle size scales into a whole, and the dynamic modulus prediction value of asphalt mixture is calculated in accordance with the real physical mechanism, with high prediction accuracy. Attached Figure Description

[0033] Figure 1 A schematic diagram showing the results of the gradation sieve analysis test of AC-13 asphalt mixture;

[0034] Figure 2 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0035] As shown in the figure, the method for predicting the dynamic modulus of asphalt mixtures according to the present invention includes the following steps:

[0036] S1. Based on fractal theory, a sieve test was conducted on the gradation of asphalt mixture to obtain the cumulative passing rate under each particle size sieve opening. The fractal dimension of coarse aggregate was obtained by fitting the cumulative passing rate under each particle size sieve opening, and the probability density function of coarse aggregate particle size distribution was established accordingly.

[0037]

[0038] Where P(D) is the probability density of coarse aggregate with particle size D; d f D is the fractal dimension. max This represents the maximum particle size of the coarse aggregate.

[0039] S2. Based on the principle of elastic-viscoelastic correspondence, calculate the dynamic complex modulus of asphalt mortar using its storage modulus and loss modulus.

[0040] Storage modulus and loss modulus can be directly measured by instruments, or frequency scanning tests can be conducted on asphalt mortar using a dynamic shear rheometer. The frequency range is 0.1-100Hz, and the temperature range is -10℃ to 50℃. The complex modulus and phase angle at different frequencies can be obtained, and the storage modulus and loss modulus can be calculated from the complex modulus and phase angle. The frequency and temperature range of the dynamic shear rheometer scanning test can be selected according to actual needs.

[0041] The formula for calculating the dynamic complex modulus is:

[0042]

[0043] in, The dynamic complex modulus of asphalt mortar. and These are the storage modulus and loss modulus of asphalt mortar, respectively.

[0044] S3. Disperse the coarse aggregate into multiple particle size intervals according to the fractal distribution of the coarse aggregate, and calculate the volume fraction of each particle size interval according to the probability density function; calculate the Eshelby tensor and dynamic Poisson's ratio of the coarse aggregate in each particle size interval according to the dynamic complex modulus, and calculate the strain condensation tensor and interaction tensor of the coarse aggregate in each particle size interval accordingly; calculate the equivalent inclusion modulus of the coarse aggregate according to the dynamic complex modulus, the volume fraction of each particle size interval, the strain condensation tensor and the interaction tensor.

[0045] Considering the fractal distribution of coarse aggregate, the coarse aggregate is discretized into multiple particle size intervals, where the particle size of the k-th interval is D. k The formula for calculating the volume fraction of each particle size range is as follows:

[0046]

[0047] Among them, P(D) k (D) represents the particle size. k The probability density of coarse aggregate, D k Let ΔD be the coarse aggregate particle size in the k-th particle size range; k V represents the interval length of the k-th particle size interval; the interval length of each particle size interval can be different. agg ΔD represents the total integral of the coarse aggregate; n represents the total number of particle size ranges for the volume discretization of the coarse aggregate.k And n is set randomly.

[0048] For each particle size range, calculate its inclusion interaction tensor, which is the strain concentration tensor A. k and interaction tensor T k :

[0049] A k =[1+S k (E k / E * m -1)] -1

[0050] T k =[1+S k (1+E k / E * m )] -1

[0051] Among them, E k S represents the elastic modulus of coarse aggregate in the k-th particle size range; k Let be the Eshelby tensor of coarse aggregate in the k-th particle size range.

[0052] S k The calculation formula is:

[0053]

[0054] Where ij represents the two directions of the far field, kl represents the two directions of the mixed field, and θ represents the angle of the far field direction. ω represents the direction angle of the mixed field, and ω represents the angular frequency of the load.

[0055] In this invention, coarse aggregate is simplified to a spherical and isotropic shape, and S is calculated accordingly. k The non-zero components are

[0056]

[0057]

[0058] We take S 1111 As S k The value of is shown in the experiment, which proves that the accuracy of the prediction is still relatively high after this simplification;

[0059] That is, S k The calculation formula is simplified to

[0060]

[0061] Among them, v m The dynamic Poisson's ratio of asphalt mortar.

[0062] ν m The calculation formula is:

[0063]

[0064] in, and These are the storage modulus and loss modulus of asphalt mortar, respectively.

[0065] The equivalent inclusion modulus is calculated based on the above parameters. The specific calculation formula is as follows:

[0066]

[0067] in, This represents the equivalent inclusion modulus of asphalt mixtures. f is the dynamic complex modulus of asphalt mortar. k A represents the volume fraction of the k-th particle size range in the discretized coarse aggregate. k and T k These are the strain condensation tensor and interaction tensor of the coarse aggregate in the k-th particle size range, respectively.

[0068] S4. Using the equivalent inclusion modulus as the new inclusion phase and asphalt mortar as the base term, solve for the dynamic modulus of the asphalt mixture using the self-consistent method.

[0069] The volume fraction of the new inclusion phase is the total integral of the coarse aggregate, V. agg The corresponding volume fraction of asphalt mortar is 1-V agg Specifically, the dynamic modulus of asphalt mixtures is solved using the self-consistent method based on the following formula.

[0070]

[0071] in, This is the dynamic modulus of asphalt mixture.

[0072] The dynamic modulus prediction system for asphalt mixtures of the present invention includes:

[0073] Particle size distribution confirmation module: used to obtain the fractal dimension of coarse aggregate by asphalt mixture gradation sieve fitting, and to establish the probability density function of coarse aggregate particle size distribution accordingly;

[0074] Complex modulus verification module: used to calculate the dynamic complex modulus of asphalt mortar using the storage modulus and loss modulus based on the elastic-viscoelastic correspondence principle;

[0075] Inclusion modulus calculation module: This module disperses coarse aggregate into multiple particle size ranges according to its fractal distribution, calculates the volume fraction of each particle size range based on the probability density function, calculates the Eshelby tensor and dynamic Poisson's ratio of the coarse aggregate in each particle size range based on the dynamic complex modulus, and then calculates the strain lumped tensor and interaction tensor of the coarse aggregate in each particle size range accordingly. Finally, it calculates the equivalent inclusion modulus of the coarse aggregate based on the dynamic complex modulus, the volume fraction of each particle size range, the strain lumped tensor, and the interaction tensor.

[0076] Solver module: Used to solve the dynamic modulus of asphalt mixture by taking the equivalent inclusion modulus as a new inclusion phase and asphalt mortar as the basic term.

[0077] The computer-readable storage medium for storing one or more programs according to the present invention includes one or more programs comprising instructions that, when executed by a computing device, cause the computing device to perform any of the methods described above.

[0078] The method of the present invention will be further described below with reference to an embodiment:

[0079] Taking AC-13 asphalt mixture as an example, the asphalt is SBS modified asphalt.

[0080] The gradation of AC-13 aggregate is shown in Table 1.

[0081] Table 1. Schematic diagram of aggregate gradation in dense-graded asphalt mixture (AC-13)

[0082]

[0083] The passing rate corresponding to each sieve aperture is the probability density of coarse aggregate at that particle size. Using fractal theory, the logarithm of both sides of the probability density function formula for coarse aggregate is taken, and then a linear fit is used to obtain the slope of the fitted curve for the gradation, which is 3-df. Figure 1 As shown.

[0084] The curve slope obtained by fitting is k = 0.76, therefore the fractal dimension df = 3 - k = 2.24

[0085] The storage modulus of asphalt mortar was measured using a DSR instrument (Dynamic Shear Rheometer). The strength is 3125 MPa, and the loss modulus is... It is 410 MPa.

[0086] Calculate the probability density function of the coarse aggregate particle size distribution:

[0087]

[0088] The coarse aggregate was discretized into seven intervals: 2.36-4.75 mm, 4.75-6.7 mm, 6.7-8.0 mm, 8.0-9.5 mm, 9.5-11.2 mm, 11.2-12.5 mm, and 12.5-13.2 mm. The volume fraction f for each interval was calculated. k V agg Take 0.42.

[0089] Taking the range of 2.36-4.75 as an example:

[0090] ∫P(D)dD=∫0.1070D -0.24 dD

[0091]

[0092] Volume fraction f for each particle size range k As shown in the table below:

[0093] Table 2 Volume fraction for each particle size range

[0094]

[0095] Calculate the dynamic Poisson's ratio:

[0096]

[0097] Assuming the aggregate is spherical and isotropic, and considering only the axial component, calculate the spherical inclusion component of the Eshelby tensor. Here, S is mainly used. 1111 Quantity:

[0098]

[0099] The equivalent inclusion modulus was calculated using an improved equivalent continuum model, and the strain concentration tensor A was calculated for each grain size range. k and interaction tensor T k Because E in all intervals k Same, E k It can be determined experimentally, or the relevant manual can be consulted directly based on the material of the aggregate. Furthermore, because the Eshelby tensor in this embodiment is uniformly taken as the S-value of a spherical and isotropic aggregate... 1111 The component makes it independent of particle size, therefore all intervals A k and T k They are all the same, that is, A in different intervals. k They are all the same, just different intervals of T. k They are all the same, which requires that the Eshelby tensor takes the same value. If the Eshelby tensor is not valued according to the method of this embodiment, then A in different intervals will be different. k and Tk They are also different; however, A in each of the same intervals k ≠T k The results below are for the range 2.36-4.75.

[0100]

[0101] Calculate the equivalent inclusion modulus

[0102]

[0103] The dynamic modulus was calculated using the self-consistent method (SCM).

[0104]

[0105] The calculation was performed using the Newton-Raphson iterative method, and the result was: E * hom =8249MPa.

[0106] The actual dynamic modulus of the asphalt mixture was measured to be 8123 MPa, which deviated from the predicted value of 7980 MPa by 1.6%, indicating that the method used to predict the dynamic modulus of asphalt mixture has high accuracy.

Claims

1. A method for predicting the dynamic modulus of asphalt mixtures, characterized in that, Includes the following steps: S1. The fractal dimension of coarse aggregate is obtained by fitting the gradation of asphalt mixture through sieve analysis, and the probability density function of coarse aggregate particle size distribution is established accordingly. S2. Based on the principle of elastic-viscoelastic correspondence, calculate the dynamic complex modulus of asphalt mortar using its storage modulus and loss modulus. S3. Disperse the coarse aggregate into multiple particle size intervals according to the fractal distribution of the coarse aggregate, and calculate the volume fraction of each particle size interval according to the probability density function; calculate the Eshelby tensor and dynamic Poisson's ratio of the coarse aggregate in each particle size interval according to the dynamic complex modulus, and calculate the strain condensation tensor and interaction tensor of the coarse aggregate in each particle size interval accordingly. The equivalent inclusion modulus of coarse aggregates is calculated based on the dynamic complex modulus, the volume fraction of each particle size range, the strain condensation tensor, and the interaction tensor. S4. Using the equivalent inclusion modulus as the new inclusion phase and asphalt mortar as the base term, solve for the dynamic modulus of the asphalt mixture using the self-consistent method.

2. The method according to claim 1, characterized in that: The probability density function of the coarse aggregate particle size distribution in step S1 is: Where P(D) is the probability density of coarse aggregate with particle size D; d f D is the fractal dimension. max This represents the maximum particle size of the coarse aggregate.

3. The method according to claim 1, characterized in that: The formula for calculating the dynamic complex modulus in step S2 is as follows: in, The dynamic complex modulus of asphalt mortar. and These are the storage modulus and loss modulus of asphalt mortar, respectively.

4. The method according to claim 1, characterized in that: The formula for calculating the equivalent inclusion modulus in step S3 is as follows: in, This represents the equivalent inclusion modulus of asphalt mixtures. f is the dynamic complex modulus of asphalt mortar. k A represents the volume fraction of the k-th particle size range in the discretized coarse aggregate. k and T k are the strain condensation tensor and interaction tensor of the coarse aggregate in the k-th particle size range, respectively, where n is the total number of particle size ranges for volume discretization of the coarse aggregate.

5. The method according to claim 4, characterized in that: The f k The calculation formula is: Among them, P(D) k (D) represents the particle size. k The probability density of coarse aggregate, D k Let ΔD be the coarse aggregate particle size in the k-th particle size range; k V is the interval length of the k-th particle size interval; agg This represents the total integral of the coarse aggregate. A k and T k The calculation formulas are respectively Among them, E k S represents the elastic modulus of coarse aggregate in the k-th particle size range; k Let be the Eshelby tensor of coarse aggregate in the k-th particle size range.

6. The method according to claim 5, characterized in that: The S k The calculation is based on the assumption that the coarse aggregate is spherical and isotropic, and one non-zero component is taken. The specific calculation formula is as follows: Among them, v m The dynamic Poisson's ratio of asphalt mortar; v m The calculation formula is: in, and These are the storage modulus and loss modulus of asphalt mortar, respectively.

7. The method according to claim 5, characterized in that: Step S4 calculates the dynamic modulus of the asphalt mixture using the self-consistent method according to the following formula. in, This is the dynamic modulus of asphalt mixture.

8. The method according to claim 1, characterized in that: In step S2, the storage modulus and loss modulus are obtained by frequency scanning of the asphalt mixture using a dynamic shear rheometer to calculate the dynamic complex modulus and phase angle at different frequencies.

9. A dynamic modulus prediction system for asphalt mixtures, characterized in that, The system includes: Particle size distribution confirmation module: used to obtain the fractal dimension of coarse aggregate by asphalt mixture gradation sieve fitting, and to establish the probability density function of coarse aggregate particle size distribution accordingly; Complex modulus verification module: used to calculate the dynamic complex modulus of asphalt mortar using the storage modulus and loss modulus based on the elastic-viscoelastic correspondence principle; Inclusion modulus calculation module: This module disperses coarse aggregate into multiple particle size ranges according to its fractal distribution, calculates the volume fraction of each particle size range based on the probability density function, calculates the Eshelby tensor and dynamic Poisson's ratio of coarse aggregate in each particle size range based on the dynamic complex modulus, and calculates the strain condensation tensor and interaction tensor of coarse aggregate in each particle size range accordingly. Finally, it calculates the equivalent inclusion modulus of coarse aggregate based on the dynamic complex modulus, the volume fraction of each particle size range, the strain condensation tensor, and the interaction tensor.

10. Solver Module: Used to solve the dynamic modulus of asphalt mixtures by taking the equivalent inclusion modulus as a new inclusion phase and asphalt mortar as the base term, using the self-consistent method. A computer-readable storage medium for storing one or more programs, characterized in that: The program includes one or more instructions that, when executed by a computing device, cause the computing device to perform any of the methods according to claims 1 to 8.

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