A hierarchical recursive prediction method for dielectric constant of asphalt mixture based on mesoscopic level features

Abstract

The application discloses a kind of based on mesoscopic level features asphalt mixture dielectric constant stratified recursive prediction method, including obtaining the dielectric constant measured data of each component in asphalt mixture multistage dispersion system, asphalt mixture is characterized as the three-phase composite medium consisting of asphalt, aggregate and air, and the volume fraction of each phase medium is calculated;According to the composition relationship of mesoscopic level, asphalt mixture is divided into mortar layer, mortar layer and mixture layer from bottom to top, based on the dielectric constant measured data of each component and the volume fraction of three-phase composite medium, the dielectric constant estimation equation of mortar layer, mortar layer and mixture layer is established respectively, and the index parameter and high dielectric phase critical volume fraction in the estimation equation are solved, so as to obtain the dielectric constant estimation model of each level;Further, the recursive way from bottom to top is used to obtain the composite dielectric constant prediction value of asphalt mixture.The application can improve the stability and precision of asphalt mixture dielectric constant prediction, and provide reliable parameter support for engineering detection results such as ground penetrating radar.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic parameter testing technology for road engineering materials, and in particular to a hierarchical recursive prediction method for the dielectric constant of asphalt mixtures based on microscopic hierarchical characteristics. Background Technology

[0002] The dielectric constant of asphalt mixtures is a key parameter characterizing their electromagnetic properties. It is used in non-destructive testing of roads, such as ground-penetrating radar, for processes like dielectric property inversion, layer identification, and thickness conversion. Asphalt mixtures are composed of single-phase materials such as asphalt, aggregates, mineral powder, and pore air. Their dielectric constant is significantly affected by factors such as material composition, mix proportions, and external environmental conditions, exhibiting considerable uncertainty. In engineering practice, thickness inversion algorithms or total internal reflection methods are commonly used to calibrate the dielectric constant of pavement structural layers. However, these methods are often based on the assumption of layered homogeneity, which deviates from the heterogeneity of actual pavement materials, thus affecting the accuracy of dielectric constant calibration and value determination.

[0003] The dielectric model of asphalt mixtures is a mathematical model describing the relationship between the dielectric constants and volume fractions of each single-phase material and the overall dielectric constant of the composite material. It can be used to supplement or correct ground-penetrating radar calibration results, making them closer to the true values. Therefore, clarifying the relationship between the dielectric constants of each component and the macroscopic dielectric constant of the asphalt mixture is an important way to improve the accuracy of obtaining the dielectric constant of asphalt mixtures. Currently, various composite dielectric models have been proposed for predicting the dielectric constant of asphalt mixtures. Among them, the linear model, root mean square model, cube root model, and Rayleigh model based on the Lichtenecker–Rother (LR) equation are widely used in engineering. Other models include the Böttcher model and the Bruggeman–Hanai (BH) model. Given the volume fractions and dielectric constants of each component, these models can be used to estimate the dielectric constant of asphalt mixtures. However, most models do not adequately consider the compositional characteristics of asphalt mixtures. They often assume that the material components are uniformly distributed or treat asphalt mixtures as a simple collection of single-phase materials, ignoring the multi-stage forming mechanism and micro-hierarchical structural characteristics of asphalt mixtures. They cannot reflect the influence of the internal structural effects of materials on macroscopic dielectric properties, resulting in poor model adaptability to asphalt mixtures with different gradations, different powder-to-binder ratios, and different porosities. The prediction results are not stable enough, and the prediction results often need to be further corrected based on measured values. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a hierarchical recursive prediction method for the dielectric constant of asphalt mixtures based on micro-level characteristics, thereby improving the stability and accuracy of dielectric constant prediction for asphalt mixtures.

[0005] Technical Solution: To achieve the above objectives, the present invention provides a hierarchical recursive prediction method for the dielectric constant of asphalt mixtures based on micro-level characteristics, comprising: dividing the asphalt mixture into a three-level structure from bottom to top: a first-level adhesive layer, a second-level mortar layer, and a third-level mixture layer; based on an improved generalized effective medium equation, constructing a dielectric constant prediction model for the adhesive layer, a dielectric constant prediction model for the mortar layer, and a dielectric constant prediction model for the mixture layer using a hierarchical recursive method; the dielectric constant prediction model for the mortar layer outputs a predicted dielectric constant value for the asphalt mortar based on the predicted dielectric constant value of the asphalt adhesive layer output by the dielectric constant prediction model for the dielectric constant of the adhesive layer, and the dielectric constant prediction model for the mixture layer outputs a predicted composite dielectric constant value for the asphalt mixture based on the predicted dielectric constant value of the asphalt mortar.

[0006] Preferably, the adhesive layer is a micro-dispersion system with mineral powder as the dispersed phase and asphalt as the continuous phase; the mortar layer is a finely dispersed system with fine aggregate as the dispersed phase and asphalt adhesive from the adhesive layer as the continuous phase; and the mixture layer is a coarsely dispersed system with coarse aggregate as the dispersed phase and asphalt mortar from the mortar layer as the continuous phase.

[0007] Preferably, the improved generalized effective medium prediction equation is expressed as:

[0008] ;

[0009] In the formula, F and M are dimensionless parameters F and M, , , , , These represent high dielectric constant material phases, low dielectric constant material phases, and composite dielectric constant material phases, respectively. For the volume fraction of the high dielectric constant phase, For low dielectric constant phase volume fraction, This represents the critical volume fraction of the high dielectric constant phase in the composite material. For exponential parameters.

[0010] Preferably, the dielectric constant prediction model for the asphalt layer uses asphalt as a low dielectric constant material phase, mineral powder as a high dielectric constant material phase, and asphalt asphalt mortar as a composite dielectric constant material phase, and incorporates measured data of the asphalt dielectric constant. Measured data of dielectric constant of mineral powder As a dielectric constant input, the volume fraction of mineral powder As the volume fraction of the high dielectric constant phase is used as input, the measured data of the dielectric constant of asphalt mastic are... As constraints, a model for predicting the dielectric constant of the mortar layer is established by solving the exponential parameter and the critical volume fraction of the high-dielectric phase in the improved generalized effective dielectric equation through nonlinear programming iteration.

[0011] ,

[0012] In the formula, The critical volume fraction of the high dielectric phase in the adhesive layer; For the adhesive layer index parameter; , .

[0013] Preferably, the dielectric constant prediction model for the mortar layer uses asphalt mastic as the low dielectric constant material phase, fine aggregate as the high dielectric constant material phase, and asphalt mortar as the composite dielectric constant material phase, and incorporates measured data of the dielectric constant of asphalt mastic. Measured data of dielectric constant of fine aggregates As a dielectric constant input, the volume fraction of fine aggregates As a high dielectric constant phase volume fraction input, the measured data of asphalt mortar dielectric constant. As constraints, an improved generalized effective dielectric equation exponential parameter and high dielectric phase critical volume fraction are solved through nonlinear programming iteration to establish a model for predicting the dielectric constant of mortar layers.

[0014] ,

[0015] In the formula, The critical volume fraction of high dielectric phase in the mortar layer; For mortar layer index parameters; , .

[0016] Preferably, the dielectric constant prediction model for the mixture layer uses asphalt mortar as the low dielectric constant material phase, coarse aggregate as the high dielectric constant material phase, and asphalt mixture as the composite dielectric constant material phase, and incorporates measured data of the dielectric constant of asphalt mortar. Measured data of dielectric constant of coarse aggregate As a dielectric constant input, the volume fraction of coarse aggregate is used. As input for the volume fraction of the high dielectric constant phase, the measured data of the dielectric constant of asphalt mixture. As constraints, an improved generalized effective dielectric equation exponential parameter and high-dielectric phase critical volume fraction are solved through nonlinear programming iteration to establish a model for predicting the dielectric constant of the mixed material layer.

[0017] ,

[0018] In the formula, The critical volume fraction of the high dielectric phase in the mixture layer; For the mixture bed index parameter; ,

[0019] Preferably, the step of solving the exponential parameter and the critical volume fraction of the high-dielectric phase in the improved generalized effective dielectric equation through nonlinear programming iteration includes: [the step involves] refining the exponential parameter in the improved generalized effective dielectric equation... and the critical volume fraction of high dielectric phase The objective function is constructed with the following parameters set as variables to be optimized: The objective function is to minimize the error between the measured equivalent dielectric constant of asphalt mastic, asphalt mortar, or asphalt mixture and the corresponding model-predicted equivalent dielectric constant.

[0020] ,

[0021] In the formula, The objective function is... For the i-th sample in the parameters and The predicted equivalent dielectric constant is calculated from the simplified generalized effective dielectric equation. is the measured equivalent dielectric constant of the corresponding sample; N is the total number of samples participating in the parameter inversion of the current level;

[0022] Set constraints, where the exponent parameter >0, critical volume fraction of high dielectric phase Satisfy 0 < <1; Under the constraints, a nonlinear programming algorithm is used to iteratively search the objective function, continuously updating the values ​​of the exponential parameter and the critical volume fraction of the high dielectric phase, and recalculating the predicted equivalent dielectric constant and corresponding error after each iteration; during the iterative solution process, multiple sets of candidate parameters are generated. Using goodness of fit as the screening criterion, the set of parameters with the highest goodness of fit is selected, and the optimal parameter set is substituted into the improved generalized effective dielectric equation to obtain the dielectric constant prediction model of the corresponding level.

[0023] Preferably, the volume fraction of mineral powder, fine aggregate, or coarse aggregate is obtained by decomposing the aggregate phase volume fraction, wherein the aggregate phase volume fraction is:

[0024] ,

[0025]

[0026] In the formula, This represents the volume fraction of asphalt. Asphalt content; Gross density of the mixture; The density of asphalt; This represents the volume fraction of the aggregate. Porosity.

[0027] Preferably, the generalized effective medium prediction equation is an improvement based on the generalized effective medium equation, which introduces dimensionless parameters F and M, and is derived by combining the boundary constraints of the two-phase composite medium under the limiting volume fraction condition.

[0028] The generalized effective medium equation is expressed as:

[0029] ;

[0030] The boundary constraints are: Specifically, when the volume fraction of the high-dielectric phase is 0, the equivalent dielectric constant of the composite material degenerates to the dielectric constant of the low-dielectric phase; when the volume fraction of the high-dielectric phase is 1, the equivalent dielectric constant of the composite material degenerates to the dielectric constant of the high-dielectric phase.

[0031] Preferably, the prediction of the composite dielectric constant of the asphalt mixture includes: first, inputting the measured dielectric constant data of asphalt and mineral powder into the dielectric constant prediction model of the mortar layer, and outputting the predicted value of the dielectric constant of the asphalt mortar; then, inputting the predicted value of the dielectric constant of the asphalt mortar and the measured dielectric constant data of the fine aggregate into the dielectric constant prediction model of the mortar layer, and outputting the predicted value of the dielectric constant of the asphalt mortar; finally, inputting the predicted value of the dielectric constant of the asphalt mortar and the measured dielectric constant data of the coarse aggregate into the dielectric constant prediction model of the mixture layer, and outputting the predicted value of the composite dielectric constant of the asphalt mixture.

[0032] Beneficial effects: The present invention has the following advantages:

[0033] 1. Based on the cementitious material theory, this invention treats asphalt mixtures as a multi-level dispersion system and constructs a three-level recursive dielectric constant prediction model consisting of a cementitious material layer, a mortar layer, and a mixture layer. The predicted value of the composite dielectric constant of asphalt mixtures is obtained by using a bottom-up recursive method, which reflects the influence of the internal structure effect of the material on the macroscopic dielectric properties, thereby improving the adaptability and prediction stability of asphalt mixtures with different gradations, different powder-to-binder ratios, and different porosities.

[0034] 2. Based on the theory of generalized effective media, this invention constructs appropriate generalized effective media prediction equations for three different levels of two-phase dispersion systems, and inversely obtains the unknown parameters and critical volume fraction of the high dielectric phase at each level. This is different from the conventional operation of directly applying the general GEM equation and fitting the parameters uniformly across the entire domain in the existing technology. It achieves accurate matching of the dielectric response law at different levels and improves the accuracy of dielectric constant prediction.

[0035] 3. This invention uses appropriate indoor high-frequency dielectric parameter testing methods to obtain dielectric constants for different forms of materials such as mineral powder and aggregates, asphalt and asphalt mortar, asphalt mortar and asphalt mixture, and uniformly selects test values ​​under fixed room temperature and frequency conditions as model inputs. This reduces the sample preparation difficulties, insufficient frequency band adaptation and data dispersion caused by single testing methods, and improves the consistency and repeatability of input parameters. Attached Figure Description

[0036] Figure 1 This is a flowchart of a hierarchical recursive prediction method for the dielectric constant of asphalt mixtures based on micro-level features, provided in an embodiment of the present invention.

[0037] Figure 2 This is a schematic diagram of the multi-level spatial network structure of asphalt mixture in an embodiment of the present invention;

[0038] Figure 3 This illustrates the relationship between the volume fraction of mineral powder and the dielectric constant of the binder in this embodiment of the invention.

[0039] Figure 4 These are calculation results from various dielectric models in the embodiments of the present invention;

[0040] Figure 5 This refers to the relative errors of various dielectric models in the embodiments of the present invention. Detailed Implementation

[0041] The technical solution of the present invention will be described in detail below with reference to the embodiments and accompanying drawings.

[0042] Example 1

[0043] like Figure 1 This embodiment provides a hierarchical recursive prediction method for the dielectric constant of asphalt mixtures based on mesoscopic hierarchical characteristics, including the following steps:

[0044] S1. Obtain measured data of dielectric constants of each component in the multi-stage dispersion system of asphalt mixture, wherein the components include asphalt, mineral powder, fine aggregate, coarse aggregate, asphalt mastic, asphalt mortar and asphalt mixture.

[0045] In this embodiment, under the uniform selection of preset room temperature and fixed frequency, the measured data of dielectric constant of each component are obtained by high-frequency dielectric testing method. Specifically, the dielectric constant of mineral powder, fine aggregate and coarse aggregate is tested by transmission line method; the dielectric constant of asphalt and asphalt mortar is tested by waveguide cavity method; and the dielectric constant of asphalt mortar and asphalt mixture is tested by coaxial probe method.

[0046] The preset room temperature can be set to 20℃, and the fixed frequency can be set to 2GHz. The real part of the dielectric constant, i.e., the relative dielectric constant, is selected as the standardized input parameter for subsequent steps.

[0047] S2. The asphalt mixture is characterized as a three-phase composite medium composed of asphalt phase, aggregate phase and air phase, and the volume fraction of each phase composite medium is calculated, including the volume fraction of asphalt, aggregate and air. According to the aggregate gradation composition, the volume fraction of the aggregate phase is further decomposed into the volume fraction of mineral powder, fine aggregate and coarse aggregate.

[0048] The volume fraction of each phase of the composite medium is calculated based on the asphalt content, bulk density, porosity, and asphalt density parameters of the asphalt mixture using a preset conversion equation. The conversion equation is as follows:

[0049]

[0050]

[0051]

[0052] In the formula, This represents the volume fraction of asphalt. Asphalt content; Gross density of the mixture; The density of asphalt; This represents the volume fraction of the aggregate. Porosity; This represents the air volume fraction.

[0053] S3. Divide the asphalt mixture into a three-level recursive structure from bottom to top, including the first level of the adhesive layer, the second level of the mortar layer, and the third level of the mixture layer.

[0054] The adhesive layer is a micro-dispersion system with mineral powder as the dispersed phase and asphalt as the continuous phase; the mortar layer is a finely dispersed system with fine aggregate as the dispersed phase and asphalt adhesive from the adhesive layer as the continuous phase; the mixture layer is a coarsely dispersed system with coarse aggregate as the dispersed phase and asphalt mortar from the mortar layer as the continuous phase.

[0055] The three-level structure is divided based on the forming mechanism and microscopic multi-level dispersed structure characteristics of asphalt mixtures. The output of the next level serves as the input of the next level, forming a layer-by-layer recursive prediction architecture.

[0056] S4. Based on the improved generalized effective medium equation and the data from S1 and S2, dielectric constant prediction models for the adhesive layer, mortar layer, and mixture layer are constructed respectively.

[0057] S401. Based on the theory of generalized effective media, each layer of composite material is regarded as a two-phase composite medium composed of a high dielectric constant phase and a low dielectric constant phase. The equation of generalized effective media is simplified to obtain the improved equation of generalized effective media.

[0058] This embodiment is based on the generalized effective medium theory, specifically as follows:

[0059]

[0060] In the formula, , , These represent high dielectric constant material phases, low dielectric constant material phases, and composite dielectric constant material phases, respectively. For the volume fraction of the high dielectric constant phase, For low dielectric constant phase volume fraction, This represents the critical volume fraction of the high dielectric constant phase in the composite material. For exponential parameters.

[0061] The generalized effective medium prediction equation is improved as follows:

[0062] Introduce dimensionless parameters F and M, where,

[0063]

[0064]

[0065] The simplified equation is derived from formula (4) combined with the boundary constraints of the two-phase composite medium under the limiting volume fraction condition:

[0066]

[0067]

[0068] Wherein, when the volume fraction of the high-dielectric phase is 0, the equivalent dielectric constant of the composite material degenerates to the dielectric constant of the low-dielectric phase; when the volume fraction of the high-dielectric phase is 1, the equivalent dielectric constant of the composite material degenerates to the dielectric constant of the high-dielectric phase. Equation (5), combined with boundary conditions, yields the improved generalized effective dielectric prediction equation:

[0069]

[0070] S402, Based on the Improved Generalized Effective Medium Equation A model for predicting the dielectric constant of the adhesive layer is constructed, specifically as follows:

[0071] Based on the improved generalized effective medium equation in S5 Using the dielectric constants and volume fractions of asphalt and mineral powder as inputs, and the measured equivalent dielectric constant of asphalt mastic as constraints, the exponential parameters of the mastic layer (denoted as ) are solved through nonlinear programming iterative inversion. ) and the critical volume fraction of the high dielectric constant phase in the composite material (denoted as ) This process obtains a model for predicting the dielectric constant of the asphalt mortar layer and outputs the composite dielectric constant of the asphalt mortar, specifically including:

[0072] Asphalt was used as the low dielectric constant material phase, mineral powder as the high dielectric constant material phase, and asphalt mastic as the composite dielectric constant material phase. The dielectric constant of asphalt measured in S1 (denoted as...) ) and the dielectric constant of mineral powder (denoted as The volume fraction of mineral powder calculated in S2 (denoted as ) is used as the dielectric constant input. ) is used as the volume fraction input of the high dielectric constant phase, and the measured equivalent dielectric constant of the asphalt mortar measured in S1 (denoted as ) is used as the input. Using this as a constraint, the exponential parameter in the improved generalized effective medium equation of the mortar layer is solved through nonlinear programming iterative inversion. and the critical volume fraction of high dielectric phase A model for predicting the dielectric constant of the adhesive layer is established, specifically as follows:

[0073]

[0074] In the formula, This represents the relative volume fraction of mineral powder. The critical volume fraction of the high dielectric phase in the adhesive layer; For the adhesive layer index parameter; , .

[0075] The nonlinear programming iterative inversion solution process includes: resolving the exponential parameters in the improved generalized effective medium equation. and the critical volume fraction of high dielectric phase The measured equivalent dielectric constant of asphalt mortar is set as the variable to be optimized. The objective function is constructed with the goal of minimizing the error between the model's predicted equivalent dielectric constant and the actual dielectric constant.

[0076]

[0077] In the formula, The objective function is... For the i-th sample in the parameters and The predicted equivalent dielectric constant is calculated from the simplified generalized effective dielectric equation. is the measured equivalent dielectric constant of the corresponding sample; N is the total number of samples participating in the parameter inversion of the current level.

[0078] Constraints are set based on the physical meaning of the parameters, among which the exponential parameter... >0, critical volume fraction of high dielectric phase Satisfy 0 < <1; Under the constraints, a nonlinear programming algorithm is used to iteratively search the objective function, continuously updating the values ​​of the exponential parameter and the critical volume fraction of the high dielectric phase, and recalculating the predicted equivalent dielectric constant and corresponding error after each iteration; during the iterative solution process, multiple sets of candidate parameters are generated. Using goodness of fit as the screening criterion, the set of parameters with the highest goodness of fit is selected, and the optimal parameter set is substituted into the simplified generalized effective dielectric equation to obtain the dielectric constant prediction model of the corresponding level.

[0079] S403, Based on the Improved Generalized Effective Medium Equation A model for predicting the dielectric constant of the mortar layer is constructed, specifically as follows:

[0080] Based on the improved generalized effective medium equation in S5, this method uses the dielectric constants and volume fractions of asphalt mortar and fine aggregate as inputs, and the measured equivalent dielectric constant of asphalt mortar as a constraint. The solution for the mortar layer is obtained through nonlinear programming iterative inversion. and A model for predicting the dielectric constant of the mortar layer is obtained, and the composite dielectric constant of the asphalt mortar is output, specifically including:

[0081] Asphalt mastic is used as the low dielectric constant material phase, fine aggregate as the high dielectric constant material phase, and asphalt mortar as the composite dielectric constant material phase. The composite dielectric constant of the asphalt mastic output by S6 (denoted as...) The dielectric constant of the fine aggregate measured in S1 (denoted as ) and S1. ) is used as the dielectric parameter input, and the fine aggregate volume fraction calculated in S3 (denoted as ) is used as the dielectric parameter input. ) is used as the volume fraction input of the high dielectric constant phase, and the measured equivalent dielectric constant of the asphalt mortar measured in S1 (denoted as ) is used as the input. Using this as a constraint, the exponential parameter in the improved generalized effective medium equation of the mortar layer is solved through nonlinear programming iterative inversion. and the critical volume fraction of high dielectric phase A model for predicting the dielectric constant of the mortar layer is established, specifically as follows:

[0082]

[0083] In the formula, This represents the relative volume fraction of mineral powder. The critical volume fraction of high dielectric phase in the mortar layer; For mortar layer index parameters; , The nonlinear programming iterative inversion solution process is the same as that for the adhesive layer.

[0084] S404, Based on the Improved Generalized Effective Medium Equation A model for predicting the dielectric constant of the mixture layer is constructed, specifically as follows:

[0085] Based on the improved generalized effective medium equation in S5, this method uses the dielectric constants and volume fractions of asphalt mortar and coarse aggregate as inputs, and the measured equivalent dielectric constant of asphalt mixture as a constraint. The solution for the mortar layer is obtained through nonlinear programming iterative inversion. and The model for predicting the dielectric constant of the asphalt mixture layer is obtained, and the composite dielectric constant of the asphalt mixture is output, specifically including:

[0086] Asphalt mortar is used as the low dielectric constant material phase, coarse aggregate as the high dielectric constant material phase, and asphalt mixture as the composite dielectric constant material phase. The composite dielectric constant of asphalt mortar output by S7 (denoted as...) The dielectric constant of the coarse aggregate measured in S1 (denoted as ) and S1. ) is used as the dielectric parameter input, and the coarse aggregate volume fraction calculated in S3 (denoted as ) is used as the dielectric parameter input. The volume fraction of the high dielectric constant phase is used as the input, and the measured equivalent dielectric constant of the asphalt mixture measured in S1 (denoted as ) is used as the input. Using this as a constraint, the exponential parameter in the improved generalized effective medium equation of the mortar layer is solved through nonlinear programming iterative inversion. and the critical volume fraction of high dielectric phase A model for predicting the dielectric constant of the mixture layer is established, specifically as follows:

[0087]

[0088] In the formula, This represents the relative volume fraction of mineral powder. The critical volume fraction of the high dielectric phase in the mixture layer; For the mixture bed index parameter; , The nonlinear programming iterative inversion solution process is the same as that for the adhesive layer.

[0089] S5. Based on the dielectric constant prediction models for the adhesive layer, mortar layer, and mixture layer, a bottom-up recursive approach is used to predict the composite dielectric constant of asphalt mixtures. This includes:

[0090] First, the measured dielectric constant data of asphalt and mineral powder are input into the dielectric constant prediction model of the mortar layer, and the predicted value of the dielectric constant of the asphalt mortar is output. Then, the predicted value of the dielectric constant of the asphalt mortar and the measured dielectric constant data of the fine aggregate are input into the dielectric constant prediction model of the mortar layer, and the predicted value of the dielectric constant of the asphalt mortar is output. Finally, the predicted value of the dielectric constant of the asphalt mortar and the measured dielectric constant data of the coarse aggregate are input into the dielectric constant prediction model of the mixture layer, and the predicted value of the composite dielectric constant of the asphalt mixture is output.

[0091] This embodiment further compares the predicted value of the composite dielectric constant of asphalt mixture with the results predicted using linear models, root mean square models, cube root models, and Rayleigh models, and evaluates the prediction accuracy using relative error. In this embodiment, the four comparison models treat asphalt mixture as a three-phase composite medium composed of asphalt phase, aggregate phase, and air phase, and use the volume fraction of each phase material calculated by S2 as the model input to achieve the inversion calculation of dielectric constant.

[0092] Example 2

[0093] This embodiment uses AC-13 type asphalt mixture as an example. Figure 2 As shown, the predicted composite dielectric constant of the asphalt mixture was obtained using the method described in Example 1, as follows:

[0094] 1. The dielectric constants of mineral powder and aggregates were measured.

[0095] This embodiment uses the transmission line method to test the dielectric constant of mineral powder and aggregate separately. Specifically, samples of mineral powder and aggregate are first taken and sieved to obtain samples with a particle size of less than 0.15 mm. Then, the mineral powder and aggregate samples are prepared into coaxial rings and connected to the constructed transmission line testing system for testing. The coaxial ring dimensions can be selected as an outer diameter of 7 mm, an inner diameter of 3.04 mm, and a thickness of 2 mm; the test frequency range is 2~18 GHz.

[0096] 2. The dielectric constants of asphalt and asphalt mortar were measured.

[0097] Both asphalt and asphalt mortar are solid at room temperature, but it is difficult to prepare samples into coaxial rings. Therefore, this embodiment uses the waveguide cavity method to test the dielectric constant of asphalt and asphalt mortar. Specifically, asphalt and asphalt mortar composed of asphalt and different powder-to-mortar ratios are cast into molds, then frozen. After the materials become brittle, the specimens are cut according to the waveguide cavity dimensions. The waveguide cavity selected in this embodiment has dimensions of 47.54 mm in length and 22.12 mm in width, with a frequency range of 1.74~3 GHz.

[0098] 3. The dielectric constant of asphalt mortar and asphalt mixture was measured.

[0099] This embodiment uses the coaxial probe method to test the dielectric constant of asphalt mortar and asphalt mixture respectively. The testing system used in this embodiment includes a flat coaxial probe, a cable, and a vector network analyzer. The flat coaxial probe is connected to the vector network analyzer via an SMA interface and is in contact with the asphalt mortar and asphalt mixture specimens. After obtaining the reflection coefficient by the vector network analyzer, the dielectric constant of the asphalt mortar and asphalt mixture can be further calculated using Formula 15:

[0100]

[0101] In the formula, , and Given the dielectric constant of the material, It is the dielectric constant of the material being tested; , and The reflectance coefficient of the known material is... It is the reflection coefficient of the material under test.

[0102] In this embodiment, the known materials are ethanol, distilled water and air. The materials to be tested are asphalt mortar and asphalt mixture, respectively. The reflectance coefficients of asphalt mortar and asphalt mixture, as well as the dielectric constants and reflectance coefficients of ethanol, distilled water and air, are substituted into formula (14) to obtain the dielectric constants of asphalt mortar and asphalt mixture.

[0103] Test temperature and frequency can cause dielectric constant loss to some extent. Within the frequency range of 0.8-3 GHz, the change in dielectric constant is relatively small. Therefore, to eliminate the influence of factors such as frequency on the model prediction accuracy, the dielectric constant of all materials in this embodiment is measured at 2 GHz at room temperature (20°C) as the input variable of the prediction model. The input variables are summarized in Table 1.

[0104] Table 1 Summary of Model Input Variables

[0105]

[0106] Based on the mix proportion of AC-13, its powder-to-binder ratio was calculated to be 0.465. The volume fraction of mineral powder in the binder portion was 21.35%, the volume fraction of fine aggregate in the mortar portion was 15.4%, and the volume fraction of coarse aggregate in the mixture portion was 9.6%. Substituting the dielectric constants of asphalt and mineral powder, and the volume fraction of mineral powder, into formula (10), the results were obtained through iterative nonlinear programming. Figure 3 The calculation results for the asphalt mortar shown include the parameters. Critical volume fraction .Depend on Figure 3It can be seen that the volume fraction of the high-dielectric phase is generally positively correlated with the dielectric constant of the asphalt mortar. When the critical volume fraction of 0.735 is reached, the dielectric constant of the mortar increases sharply to about 4.2, and then slowly increases with the volume fraction to reach the highest value. This phenomenon indicates that when the volume fraction of mineral powder reaches 73.5%, the dielectric constant of the asphalt mortar will undergo a sudden change.

[0107] Table 2 Accuracy of Asphalt Mash Prediction Model

[0108]

[0109] Table 2 presents the model's predicted dielectric constant of asphalt binder and compares it with the measured values. Although the model's accuracy decreases slightly with increasing mineral powder to asphalt ratio, it remains within an acceptable range overall. In actual engineering projects, the powder-to-binder ratio generally does not exceed 1.4. Therefore, the model's prediction accuracy in the low powder-to-binder ratio range has certain reference value.

[0110] Substituting the dielectric constants of asphalt and mineral powder in AC-13 asphalt mixture, and the volume fraction of mineral powder, into the estimation model, the dielectric constant of the asphalt mastic is calculated to be 2.795. Substituting the calculated mastic dielectric constant (2.795) and aggregate dielectric constant (4.704) into formula (12) to solve for the unknown parameters, the aforementioned calculation steps are repeated. The equation parameters for the mortar are calculated as follows: , Estimated dielectric constant of asphalt mortar The relative error between the measured value of 5.744 and the actual value is 6.3%. Substituting the dielectric constants of the mortar and aggregate into formula (13) again, the equation parameters are obtained as follows: , Predicted dielectric constant of asphalt mixture The relative error between the measured dielectric constant of 6.301 and the actual value is 1.9%.

[0111] In summary, this method uses a three-level layered calculation to sequentially determine the dielectric constants of asphalt binder, asphalt mortar, and asphalt mixture.

[0112] Example 3:

[0113] To verify the prediction effect of the layered recursive prediction method for dielectric constant of asphalt mixture based on micro-level characteristics in Example 1, this example tested asphalt mixture specimens with six gradations: SUP-13, SMA-13, AC-13, SUP-20, SUP-25, and AC-25, and compared the prediction results with those of the linear model, root mean square model, cube root model, and Rayleigh model.

[0114] (1) Linear model

[0115] When layered single-phase materials are randomly arranged to form composite materials, c = -1 is taken; if the electrodes of the electric field are perpendicular to the layer, then c = +1 is taken; at this time, the model is called a linear model, and the expression is shown in (15):

[0116]

[0117] In the formula, ε is the dielectric constant of the composite material; v1, v2, v3…vn are the volume percentages of each component of the composite material. , , … denoted as , where is the dielectric constant of each component in the composite material.

[0118] (2) Root Mean Square Model

[0119] When c takes the value of 1 / 2, the model is called the root mean square model, and its expression is shown in (16):

[0120]

[0121] (3) Cube root model

[0122] When c takes the value of 1 / 3, the model is called the cube root model (Looyenga model), and its expression is shown in (17):

[0123]

[0124] (4) Rayleigh model

[0125] The Rayleigh model is applicable to multiphase composite materials, and its expression is shown in (18):

[0126]

[0127] Table 3 lists the basic parameters of the six asphalt mixtures with different mix proportions involved in this embodiment, and they are numbered accordingly.

[0128] Table 3 Basic Parameters of Asphalt Mixture

[0129]

[0130] The volume fractions of asphalt, aggregate, and air are calculated using formulas (1)-(3). Then, the dielectric constant of the asphalt mixture is calculated by combining the dielectric constants of the raw materials listed in Table 1. To make the calculation process more intuitive, the data are summarized in Table 4.

[0131] Table 4 Basic Parameters of Asphalt Mixture

[0132]

[0133] Based on the above data, the estimated dielectric constants for each model are calculated. Figure 4 The results show the dielectric constant calculations based on various dielectric models. Figure 4 It can be seen that the linear model, root mean square model, and cube root model follow the same trend, but their values ​​decrease sequentially. Overall, the predicted values ​​of all three models are higher than the measured values. The Rayleigh model is relatively close to the measured values, but its prediction accuracy for SUP-20 and SUP-25 is relatively low. Among the six mixtures, the predicted values ​​of the proposed models are close to and slightly higher than the measured values.

[0134] To more intuitively evaluate the prediction accuracy of each dielectric model, the relative errors are summarized into... Figure 5 .Depend on Figure 5 It can be seen that the linear model and the root mean square (RMS) model have poor prediction accuracy, with relative errors ranging from 5% to 15% in the six groups of mixture dielectric constant predictions. In contrast, the cubic root (CUB) model (i.e., when the geometric parameter c=1 / 3) performs better in predicting the mixture, indicating that the physical meaning contained in the cubic root model is more consistent with the actual internal conditions of asphalt mixtures. The Rayleigh model and the model proposed in this paper both have small relative errors and achieve good prediction results, indicating that they also have high application potential in engineering practice.

[0135] Overall, the cubic root model, Rayleigh model, and the recommended model all achieved good prediction results, with relative errors controlled within 9%, 4%, and 2%, respectively. While the proposed model has high prediction accuracy, its calculation method is more complex than the classical model, with more parameters in its expression and greater difficulty in derivation. In contrast, the cubic root model and the Rayleigh model have simpler mathematical expressions and can ensure that the relative error is within an acceptable range. Therefore, the model proposed in this embodiment can be used for predicting the dielectric constant of asphalt mixtures, while the Rayleigh model and the cubic root model can be used to derive electromagnetic mixing models, thereby achieving non-destructive testing of engineering parameters such as the asphalt-aggregate ratio.

[0136] The examples described herein are merely preferred embodiments of the invention and are not intended to limit the concept and scope of the invention. Any modifications and improvements made by those skilled in the art to the technical solutions of the invention without departing from the design concept of the invention should fall within the protection scope of the invention.

Claims

1. A hierarchical recursive prediction method for the dielectric constant of asphalt mixtures based on mesoscopic hierarchical characteristics, characterized in that, include: The asphalt mixture is divided into three layers from bottom to top: the first layer is the adhesive layer, the second layer is the mortar layer, and the third layer is the mixture layer. Based on the improved generalized effective medium equation, a hierarchical recursive method is used to construct dielectric constant prediction models for the asphalt mortar layer, the mortar layer, and the mixture layer, respectively. The mortar layer dielectric constant prediction model outputs the predicted dielectric constant of the asphalt mortar based on the predicted dielectric constant of the asphalt mortar output by the asphalt mortar layer dielectric constant prediction model, and the mixture layer dielectric constant prediction model outputs the predicted composite dielectric constant of the asphalt mixture based on the predicted dielectric constant of the asphalt mortar.

2. The method for predicting the dielectric constant of asphalt mixtures according to claim 1, characterized in that, The adhesive layer is a micro-dispersion system with mineral powder as the dispersed phase and asphalt as the continuous phase; the mortar layer is a finely dispersed system with fine aggregate as the dispersed phase and asphalt adhesive from the adhesive layer as the continuous phase; the mixture layer is a coarsely dispersed system with coarse aggregate as the dispersed phase and asphalt mortar from the mortar layer as the continuous phase.

3. The method for predicting the dielectric constant of asphalt mixtures according to claim 1, characterized in that, The improved generalized effective medium prediction equation is expressed as: ； In the formula, F and M are dimensionless parameters F and M, , , , , These represent high dielectric constant material phases, low dielectric constant material phases, and composite dielectric constant material phases, respectively. For the volume fraction of the high dielectric constant phase, For low dielectric constant phase volume fraction, This represents the critical volume fraction of the high dielectric constant phase in the composite material. For exponential parameters.

4. The method for predicting the dielectric constant of asphalt mixtures according to claim 3, characterized in that, The dielectric constant prediction model for the asphalt mortar layer uses asphalt as a low dielectric constant material phase, mineral powder as a high dielectric constant material phase, and asphalt mortar as a composite dielectric constant material phase, and incorporates measured asphalt dielectric constant data. Measured data of dielectric constant of mineral powder As a dielectric constant input, the volume fraction of mineral powder As the volume fraction of the high dielectric constant phase is used as input, the measured data of the dielectric constant of asphalt mastic are... As constraints, a model for predicting the dielectric constant of the mortar layer is established by iteratively solving the exponential parameter and the critical volume fraction of the high-dielectric phase in the improved generalized effective dielectric equation through nonlinear programming, as follows: ， In the formula, The critical volume fraction of the high dielectric phase in the adhesive layer; For the adhesive layer index parameter; , .

5. The method for predicting the dielectric constant of asphalt mixtures according to claim 3, characterized in that, The dielectric constant prediction model for the mortar layer uses asphalt mastic as the low dielectric constant material phase, fine aggregate as the high dielectric constant material phase, and asphalt mortar as the composite dielectric constant material phase. The measured dielectric constant data of the asphalt mastic are used as the basis for this model. Measured data of dielectric constant of fine aggregates As a dielectric constant input, the volume fraction of fine aggregates As a high dielectric constant phase volume fraction input, the measured data of asphalt mortar dielectric constant. As constraints, a model for predicting the dielectric constant of mortar layers is established by iteratively solving the exponential parameter and the critical volume fraction of the high-dielectric phase in the improved generalized effective dielectric equation through nonlinear programming, as follows: ， In the formula, The critical volume fraction of high dielectric phase in the mortar layer; For mortar layer index parameters; , .

6. The method for predicting the dielectric constant of asphalt mixtures according to claim 3, characterized in that, The dielectric constant prediction model for the mixture layer uses asphalt mortar as the low dielectric constant material phase, coarse aggregate as the high dielectric constant material phase, and asphalt mixture as the composite dielectric constant material phase, based on the measured dielectric constant data of asphalt mortar. Measured data of dielectric constant of coarse aggregate As a dielectric constant input, the volume fraction of coarse aggregate is used. As input for the volume fraction of the high dielectric constant phase, the measured data of the dielectric constant of asphalt mixture. As constraints, a model for predicting the dielectric constant of the mixture layer is established by iteratively solving the exponential parameter and the critical volume fraction of the high-dielectric phase in the improved generalized effective dielectric equation through nonlinear programming, as follows: ， In the formula, The critical volume fraction of the high dielectric phase in the mixture layer; For the mixture bed index parameter; , 7. The method for predicting the dielectric constant of asphalt mixtures according to any one of claims 4 to 6, characterized in that, The method of solving the exponential parameters and critical volume fraction of the high-dielectric phase in the improved generalized effective dielectric equation through nonlinear programming iteration includes: [The text abruptly ends here, so the translation stops.] and the critical volume fraction of high dielectric phase The objective function is constructed with the following parameters set as variables to be optimized: The objective function is to minimize the error between the measured equivalent dielectric constant of asphalt mastic, asphalt mortar, or asphalt mixture and the corresponding model-predicted equivalent dielectric constant. ， In the formula, The objective function is... For the i-th sample in the parameters and The predicted equivalent dielectric constant is calculated from the simplified generalized effective dielectric equation. is the measured equivalent dielectric constant of the corresponding sample; N is the total number of samples participating in the parameter inversion of the current level; Set constraints, where the exponent parameter >0, critical volume fraction of high dielectric phase Satisfy 0 < <1; Under the constraints, a nonlinear programming algorithm is used to iteratively search the objective function, continuously updating the values ​​of the exponential parameter and the critical volume fraction of the high dielectric phase, and recalculating the predicted equivalent dielectric constant and corresponding error after each iteration; during the iterative solution process, multiple sets of candidate parameters are generated. Using goodness of fit as the screening criterion, the set of parameters with the highest goodness of fit is selected, and the optimal parameter set is substituted into the improved generalized effective dielectric equation to obtain the dielectric constant prediction model of the corresponding level.

8. The method for predicting the dielectric constant of asphalt mixtures according to any one of claims 4 to 6, characterized in that, The volume fraction of mineral powder, fine aggregate, or coarse aggregate is obtained by decomposing the aggregate phase volume fraction, which is: ， ， In the formula, This represents the volume fraction of asphalt. Asphalt content; Gross density of the mixture; The density of asphalt; This represents the volume fraction of the aggregate. Porosity.

9. The method for predicting the dielectric constant of asphalt mixtures according to claim 3, characterized in that, The generalized effective medium prediction equation is an improvement based on the generalized effective medium equation, which introduces dimensionless parameters F and M and is derived by combining the boundary constraints of the two-phase composite medium under the limiting volume fraction condition. The generalized effective medium equation is expressed as: ； The boundary constraints are: Specifically, when the volume fraction of the high-dielectric phase is 0, the equivalent dielectric constant of the composite material degenerates to the dielectric constant of the low-dielectric phase; when the volume fraction of the high-dielectric phase is 1, the equivalent dielectric constant of the composite material degenerates to the dielectric constant of the high-dielectric phase.

10. The method for predicting the dielectric constant of asphalt mixtures according to claim 1, characterized in that, The prediction of the composite dielectric constant of the asphalt mixture includes: first, inputting the measured dielectric constant data of asphalt and mineral powder into the dielectric constant prediction model of the mortar layer, and outputting the predicted value of the dielectric constant of the asphalt mortar; then, inputting the predicted value of the dielectric constant of the asphalt mortar and the measured dielectric constant data of the fine aggregate into the dielectric constant prediction model of the mortar layer, and outputting the predicted value of the dielectric constant of the asphalt mortar; finally, inputting the predicted value of the dielectric constant of the asphalt mortar and the measured dielectric constant data of the coarse aggregate into the dielectric constant prediction model of the mixture layer, and outputting the predicted value of the composite dielectric constant of the asphalt mixture.

Images