A prediction method for thermal conductivity of asphalt mixture

Abstract

The present invention discloses a method for predicting the thermal conductivity of asphalt mixtures. The method comprises the following steps: setting asphalt, aggregate, and air to form two new materials in parallel and series, respectively, the two new materials forming the asphalt mixture, setting parameters to represent the volume fractions of the two materials, establishing a parallel-serial-geometricmean model, introducing the influence of a thermal conductivity chain, establishing a preliminary prediction model, determining the parameters in the preliminary prediction model through a small number of experiments, and establishing functional relationships between the parameters and the volume fractions of asphalt and aggregate, as well as between moisture content and the difference in thermal conductivity. Finally, the established functional relationships are introduced into the preliminary prediction model to obtain a final prediction model for the thermal conductivity of the asphalt mixture. The present invention simplifies the asphalt mixture from three phases to two phases and takes into account the influence of moisture content and the thermal conductivity chain, making the model more consistent with the actual conditions of asphalt pavement and more accurate in prediction.

Description

Technical Field

[0001] The invention relates to the field of mechanical properties of materials, and in particular to a method for predicting the thermal conductivity of asphalt mixtures. Background Art

[0002] Asphalt mixture, as a road construction material, is widely used in airports, highways, parking lots and other fields. Due to the viscoelastic properties of asphalt binder, the thermal stability of asphalt mixture will affect its mechanical properties. The thermal conductivity of asphalt mixture is an important thermophysical parameter. It affects the heating rate within the pavement layer, thereby affecting the thermal stability of the asphalt pavement. Therefore, accurately predicting the thermal conductivity of asphalt mixture is crucial to pavement design.

[0003] Currently, researchers have adopted various methods to determine the thermal conductivity coefficient. One method is to measure directly through experiments. This operation is cumbersome and the experiment has limitations. It cannot accurately evaluate the thermal conductivity coefficient of asphalt mixture in all aspects. Another method is to explore the influence of various factors on the thermal conductivity of asphalt mixture through software simulation. However, software simulation has high requirements for users, who need to understand the relevant software and have a high level of modeling skills.

[0004] In addition to experimental measurements and software simulations, mathematical models of composite materials used to calculate thermal conductivity have also attracted widespread attention from researchers due to their advantages of simple operation, low cost and high efficiency. Many mathematical models have been developed to predict the thermal conductivity of composite materials, but these mathematical models are not applicable to three-phase composite materials containing voids, and most models only consider thermal conductivity at low filling rates. More importantly, neither software modeling nor mathematical models consider the influence of water on the thermal conductivity of asphalt mixtures.

[0005] Therefore, for the thermal conductivity of asphalt mixture, not only factors such as the type of asphalt and aggregate in the asphalt mixture, the gradation and shape of the aggregate, and the void content must be considered; the effect of water penetration into asphalt pavement on the thermal conductivity of the asphalt mixture also needs to be considered; and when the volume fraction of aggregate in the asphalt mixture is above 75%, direct contact between aggregate particles will form a thermal chain, affecting the thermal conductivity, and the existing mathematical model is not applicable.

[0006] The present invention establishes a thermal conductivity prediction model based on the parallel model, series model and geometric mean model formulas, which can more comprehensively consider the influence of asphalt, aggregate and voids, as well as the influence of moisture content caused by pavement seepage on thermal conductivity. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for predicting the thermal conductivity of asphalt mixture. Compared with the traditional thermal conductivity prediction model, the prediction model established by the present invention can more comprehensively consider the influence of asphalt, aggregate and voids, as well as the influence of moisture content caused by pavement seepage on the thermal conductivity. Based on the parallel model, series model and geometric mean formula, a new hypothesis is proposed. In addition, the influence of the thermal conductivity chain is also considered, and the effect of the thermal conductivity chain in the composite material is introduced into the model in an exponential form to obtain the final prediction model of the thermal conductivity of the asphalt mixture, so that the prediction result is more in line with the characteristics of the asphalt mixture and more accurate.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] A method for predicting the thermal conductivity of asphalt mixtures is proposed. Asphalt mixtures are three-phase composite materials consisting of asphalt, aggregate, and air. Based on theoretical assumptions and experimental data, a thermal conductivity prediction model for asphalt mixtures under different aggregate gradations, asphalt-to-stone ratios, compaction levels, and moisture contents is established. The steps for establishing the thermal conductivity prediction model are as follows:

[0010] S1: Assume that asphalt, aggregate, and air are arranged parallel to the direction of heat flow to form a three-phase parallel material A, and the three components are arranged perpendicular to the direction of heat flow to form a series material B. Material A and material B together constitute an asphalt mixture. Based on the parallel thermal conductivity model and series thermal conductivity model of composite materials, the parallel thermal conductivity coefficient model of material A and the series thermal conductivity coefficient model of material B are derived;

[0011] S2: Assuming the volume fraction of material A in the asphalt mixture is k, the volume fraction of material B in the asphalt mixture is 1-k. At the same time, k and 1-k also represent the degree of influence of parallel arrangement and series arrangement on the thermal conductivity of asphalt mixture respectively;

[0012] Substitute the parameters k and 1-k in S2 into the parallel and serial thermal conductivity models of the asphalt mixture in step S1, respectively, and establish the parallel-serial-geometric mean model of the asphalt mixture according to the geometric mean model formula;

[0013] S3: Prepare Marshall specimens with different aggregate gradations, asphalt-to-stone ratios, and compaction levels, and calculate the corresponding volume fractions of asphalt and aggregate in the specimens. The compaction level is simulated by the number of compactions performed by a Marshall electric compactor during specimen preparation.

[0014] S4: Effect of introducing thermal conductivity chain into asphalt mixture

[0015] Based on the Agari model of composite materials, it is deformed to establish an Agari model of asphalt mixture based on the serial and parallel thermal conductivity models. In step S3, several groups of specimens with almost zero void ratio are used to conduct experiments. The thermal conductivity of the dry asphalt mixture specimens is tested using the steady-state method, and a functional relationship between the thermal conductivity and the aggregate volume fraction is established. The effect of the thermal conductivity chain in the composite material is then introduced into the parallel-serial-geometric mean model of the asphalt mixture in an exponential form, and a preliminary prediction model for the thermal conductivity of the asphalt mixture is derived.

[0016] S5: Take some of the Marshall specimens in step S3 and measure their corresponding thermal conductivity. After deforming the preliminary prediction model of the thermal conductivity of the asphalt mixture containing the parameter k value in step S5, an expression for the k value is obtained. Then, the expression for the k value is substituted into the above experimental data for calculation. Finally, the k value is fitted with the volume fractions of asphalt and aggregate through multiple linear regression to obtain a functional relationship between the k value and the volume fractions of asphalt and aggregate.

[0017] S6: Considering the change in thermal conductivity after water seeps into the voids and the coupling of the three phases of asphalt, aggregate, water, and air, some of the specimens prepared in step S3 are subjected to water immersion experiments. The volume fraction of water in the wet specimens is calculated. By designing an experiment on the effect of moisture content on the thermal conductivity of asphalt mixtures, a functional relationship between the difference in thermal conductivity and moisture content is established.

[0018] S7: Superimpose all the above-mentioned influencing factors, substitute the functional relationship between the k value and the volume fraction of asphalt and aggregate, and the functional relationship between the thermal conductivity difference and the moisture content into the preliminary prediction model of thermal conductivity, and obtain the final prediction model of thermal conductivity of asphalt mixture;

[0019] By performing corresponding mathematical calculations based on the final prediction model, the thermal conductivity of asphalt mixtures with different aggregate gradations, asphalt-stone ratios, compaction degrees and moisture contents can be predicted.

[0020] Furthermore, according to the parallel thermal conductivity model and series thermal conductivity model formulas of composite materials, the thermal conductivity models of material A and material B in step S1 are respectively as follows (1) and (2):

[0021] λ B =V as λ as +V ag λ ag +V ai λ ai (1)

[0022]

[0023] Where:A —thermal conductivity of material A; λ B —thermal conductivity of material B; λ as —Thermal conductivity of asphalt; λ ag —thermal conductivity of aggregate; λ ai —Thermal conductivity of air; V as —Volume fraction of asphalt; V ag —Volume fraction of aggregate; V ai —Volume fraction of air.

[0024] Furthermore, according to the geometric mean formula, the volume fractions of material A and material B in step S2 are introduced into formulas (1) and (2), and the parallel-serial-geometric mean model of the asphalt mixture in step S3 is the following formula (3):

[0025]

[0026] Where: am —Thermal conductivity of asphalt mixture; k—volume fraction of material A in asphalt mixture; 1-k—volume fraction of material B in asphalt mixture.

[0027] Furthermore, the volume fraction of each specimen is calculated as follows:

[0028] First, weigh the weight m of each specimen, the mass of each component in each specimen, and the mass of asphalt m. as and aggregate mass m ag According to the volume fraction calculation formula of the component materials, the volume fraction calculation formula of asphalt and aggregate is as follows:

[0029]

[0030]

[0031] Where: V as —Volume fraction of asphalt; V ag —Volume fraction of asphalt; V s —Total volume of the specimen; ρ as —density of asphalt; ρ ag —density of aggregate; m as —mass of asphalt; m ag —Quality of aggregate

[0032] Furthermore, the method for determining the Agari model of the asphalt mixture and the parameters in the model in step S4 is as follows:

[0033] S51: The Agari model of composite materials (4) is deformed to establish the Agari model of asphalt mixture as follows (5):

[0034]

[0035]

[0036] Where: λ is the thermal conductivity of the composite material; λ1 is the thermal conductivity of the polymer; λ2 is the thermal conductivity of the filler particles; V is the volume fraction of the filler particles; n is a parameter between -1 and 1; C1 is a parameter related to the crystallinity and grain size of the polymer; C2 is a parameter related to the ability of the filler particles to form thermal conductive chains.

[0037] S52: taking several groups of dry asphalt mixture specimens with a void ratio of almost zero in step S3 and measuring the thermal conductivity of the specimens;

[0038] S53: Draw a graph showing the change in thermal conductivity with the volume fraction of aggregate, and substitute the slope and intercept of the obtained linear relationship graph to obtain the values ​​of parameters C1 and C2 in the Agari model of asphalt mixture; introduce the influencing parameter C2 of the above thermal conductivity chain into the formula (3) of asphalt mixture, and derive the preliminary prediction model of thermal conductivity of asphalt mixture as follows (6):

[0039]

[0040] Furthermore, the functional relationship between the k value and the volume fraction of asphalt and aggregate is calculated as follows:

[0041] S61: The preliminary prediction model of thermal conductivity of asphalt mixture in formula (6) is modified to obtain the expression of k as follows (7):

[0042]

[0043] S62: Substitute the volume fraction of each component in multiple groups of asphalt mixture dry specimens and the measured thermal conductivity into the above expression for k to calculate the k value;

[0044] S63: The fitted data set was imported into Origin software for multivariate linear regression. The k value was fitted with the volume fraction of asphalt and aggregate. The functional relationship between the k value and the volume fraction of asphalt and aggregate was obtained as follows (8):

[0045] k=f(V as ,V ag )=aV as +bV ag +c (8)

[0046] Where: a—parameter in the functional relationship between k value and volume fraction of asphalt; b—parameter in the functional relationship between k value and volume fraction of aggregate; c—constant in the functional relationship;

[0047] Furthermore, by designing an experiment to study the effect of moisture content on the thermal conductivity of asphalt mixture, a function between the thermal conductivity difference and moisture content was established. The specific steps are as follows:

[0048] S71: Select some dry asphalt mixture specimens prepared in step S3, set these specimens as the control group and conduct water immersion test on them. First weigh the weight of the dry sample m d ;

[0049] S72: Before immersing the specimens in water, prepare a polyethylene film and apply a layer of thermal grease of appropriate thickness. Then immerse the dry asphalt mixture specimens in water for different lengths of time. After removing them from the water, wipe the surface and weigh the mass m. w ;

[0050] S73: Wrap the specimen with a polyethylene film coated with thermal grease to isolate the moisture in the specimen from the outside world, thereby obtaining a wet asphalt mixture specimen;

[0051] S74: Measure the thermal conductivity of the immersed specimens using a thermal conductivity meter;

[0052] S75: Calculate the volume fraction of water in the immersed specimen as follows (9):

[0053]

[0054] Where: V wa —Volume fraction of water in the voids; m d —Mass of the dry specimen; m w —The mass of the test piece after immersion in water; ρ w —density of water; V s —Total volume of the test piece;

[0055] The relationship curve between the difference in thermal conductivity and the change in water volume fraction was drawn, and the fitted data set was imported into the Origin software for linear fitting. The functional relationship between the difference in thermal conductivity and water volume fraction was established as the following formula (10):

[0056] Δλ=αV wa (10)

[0057] Where: Δλ is the thermal conductivity difference; α is the undetermined parameter in the functional relationship between the thermal conductivity difference and the water volume fraction.

[0058] Furthermore, combining the above-mentioned influencing factors and formulas (6), (8), and (10), the final prediction model of the thermal conductivity of asphalt mixture is derived as follows (11):

[0059]

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] 1. This paper proposes a parallel-serial-geometric mean model, which associates the number of phases in an asphalt mixture with the arrangement structure of each component. Without neglecting the voids, the asphalt mixture is converted into a two-phase composite material. Then, the geometric mean formula is used to calculate the thermal conductivity of the asphalt mixture. This method provides a new approach for calculating the thermal conductivity of other multiphase composite materials.

[0062] 2. Finally, the present invention proposes a final prediction model for the thermal conductivity of asphalt mixture. This model is an extension and verification of the parallel-serial-geometric mean model. The influence of the thermal conductivity chain is introduced into the parallel-serial-geometric mean model, and the functional relationship between the unknown parameters and the volume fractions of asphalt and aggregate, as well as the functional relationship between the volume fraction of water in the voids and the difference in thermal conductivity are established through linear regression. The above-mentioned influencing factors are combined with the model to make the calculation and analysis results closer to the actual situation and more accurate.

[0063] 3. During the experiment, the present invention selects the number of compaction times, oil-stone ratio and aggregate gradation as experimental parameters, simulates the design conditions of asphalt mixture in actual engineering, and proposes an improved method for measuring wet samples using the steady-state method. The wet sample is wrapped with a polyethylene film coated with thermal grease, and then measured using the steady-state method. The polyethylene film can prevent water loss in the sample, and the thermal grease can reduce the gaps generated in the film folds, so that the film can better fit the sample. This method has little effect on the experimental results and is suitable for steady-state measurement of wet composite materials.

[0064] 4. The present invention can calculate the thermal conductivity of asphalt mixture by applying mathematical models without damaging buildings or roads. Compared with the actual thermal conductivity of the sample obtained by experimental measurement, it does not need to re-prepare the sample for testing every time the material ratio changes. It also saves a lot of repeated experiments required to control the proportion of each component to be the same as the actual road surface when making the test piece. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a flow chart of the prediction method of the present invention;

[0066] Figure 2 Schematic diagram of heat conduction of series model;

[0067] Figure 3 It is a schematic diagram of heat conduction of parallel model;

[0068] Figure 4 This is a schematic diagram of asphalt mixture composed of material A and material B;

[0069] Figure 5 Schematic diagram of the relationship between thermal conductivity and volume fraction of aggregate;

[0070] Figure 6 Schematic diagram of the relationship between k value and asphalt volume fraction;

[0071] Figure 7 Schematic diagram of the relationship between k value and aggregate volume fraction;

[0072] Figure 8 Schematic diagram of the relationship between the thermal conductivity difference and the water volume fraction;

[0073] In the figure: 1—voids; 2—aggregate; 3—asphalt. DETAILED DESCRIPTION

[0074] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0075] A method for predicting the thermal conductivity of asphalt mixtures is provided. Asphalt mixtures are three-phase composite materials consisting of asphalt, aggregate, and air. Based on the three-phase composite asphalt mixture, a thermal conductivity prediction model is established under different aggregate gradations, asphalt-stone ratios, compaction levels, and moisture contents. The method for establishing the thermal conductivity prediction model includes the following steps:

[0076] S1: Assume that in the parallel model and the series model, asphalt, aggregate, and air are arranged in parallel and series respectively. Since parallel and series arrangements exist simultaneously in asphalt mixtures, the actual thermal conductivity is between the theoretical values ​​of the parallel model and the series model. Based on the above analysis, assume that asphalt, aggregate, and air are arranged in parallel to form material A and in series to form material B, and that material A and material B together constitute the asphalt mixture. At this time, the thermal conductivity of material A and material B is the theoretical value of the thermal conductivity under the parallel model and the series model. According to the series and parallel thermal conductivity models of composite materials, the thermal conductivity models of material A and material B are derived as follows (1) and (2):

[0077] λ A =V as λ as +V ag λ ag +V ai λ ai (1)

[0078]

[0079] Where: A —Thermal conductivity of material A (W / (m·K)); λ B —Thermal conductivity of material B (W / (m·K)); λ as —Asphalt thermal conductivity (W / (m·K)); λ ag —Aggregate thermal conductivity (W / (m·K)); λ ai —Thermal conductivity of air (W / (m·K)); V as —Volume fraction of asphalt (%); V ag —Volume fraction of aggregate (%); V ai —Volume fraction of air (%);

[0080] S2: Since the thermal conductivity of materials A and B is related to the thermal conductivity and volume fraction of asphalt, aggregate, and air, assuming the volume fraction of material A is k, the volume fraction of material B is 1-k. At the same time, k and 1-k also represent the degree of influence of parallel arrangement and series arrangement on the thermal conductivity of asphalt mixture, respectively.

[0081] Then, the parameters k and 1-k are introduced into the geometric mean formula based on the parallel and serial asphalt mixture thermal conductivity model. That is, combining equations (1) and (2), the parallel-serial-geometric mean model of asphalt mixture is derived as follows (3):

[0082]

[0083] Where: am —Thermal conductivity of asphalt mixture (W / (m·K)); k—The influence coefficient of material A in asphalt mixture; 1-k—The influence coefficient of material B in asphalt mixture.

[0084] S3: Prepare Marshall specimens with different aggregate gradations, oil-stone ratios, and compaction degrees, and obtain the basic parameters of each specimen. The compaction degree is simulated by the number of compactions using a Marshall electric compactor during specimen preparation.

[0085] Prepare asphalt mixture dry specimens. The specific steps are as follows:

[0086] ① Grading, oil-stone ratio and compaction times were selected as experimental parameters for specimen preparation. Three graded aggregates, AC10, AC16 and AC20, were selected. The coarse and fine aggregates crushed from the sieved limestone were washed with water and then dried.

[0087] ② Place the SBS modified asphalt and the above-screened aggregate in an oven at 180°C and heat until they melt and flow;

[0088] ③ Mix asphalt and aggregate at eight different asphalt-to-aggregate ratios of 5%, 5.5%, 6.0%, 6.5%, 10%, 15%, 20%, and 25% and pour them into a continuously heated mixer and mix thoroughly;

[0089] ④ Pour the asphalt mixture into a cylindrical mold with a diameter of 10.16 cm and compact it on both sides using a Marshall electric compactor according to four different compaction times: 45, 60, 75, and 90:

[0090] ⑤ The molded specimens were placed in a room for 12 hours and then demolded to obtain 28 sets of Marshall specimens, which were marked separately. The parameters of the Marshall specimens are shown in Table 1 below:

[0091] Table 1

[0092]

[0093]

[0094] According to ρ as =1.016g / cm 3 , ρ ag =2.402g / cm 3 And the asphalt mass m corresponding to each specimen in Table 1 as and aggregate mass m ag , substituted into the calculation formula of the volume fraction of asphalt and aggregate, the volume fractions of asphalt and aggregate corresponding to each specimen are obtained as shown in Table 2 below:

[0095] Table 2

[0096]

[0097]

[0098] S4: Considering that the heat conduction chain formed by aggregate particles is also an important factor affecting the thermal conductivity of composite materials, when the filling amount of filler reaches a certain critical value, the fillers will contact each other to form a heat conduction network chain. As the filling amount increases, the heat conduction network chains penetrate each other, and the thermal conductivity of the composite material is significantly improved. Therefore, according to the Agari model of composite materials, the Agari model of asphalt mixture based on the series and parallel models is established.

[0099] The Agari model of the asphalt mixture and the method for determining its parameters are as follows:

[0100] ① The Agari model of composite materials (4) is transformed to establish the Agari model of asphalt mixture based on series and parallel connection as follows (5):

[0101]

[0102] logλ=VC2logλ2+(1-V)log(C1λ1)

[0103]

[0104] Where: λ is the thermal conductivity of the composite material (W / (m·K)); λ1 is the thermal conductivity of the polymer (W / (m·K)); λ2 is the thermal conductivity of the filler particles (W / (m·K)); V is the volume fraction of the filler particles (%); n is a parameter between -1 and 1; C1 is a parameter related to the crystallinity and grain size of the polymer; C2 is a parameter related to the ability of the filler particles to form thermal conductive chains.

[0105] ② Take the four groups of Marshall specimens with almost zero void ratio in step S3, numbered AM25, AM26, AM27, and AM28, and measure the thermal conductivity of the asphalt mixture of these four groups of specimens;

[0106] The thermal conductivity and component ratio of AM25-AM28 specimens are shown in Table 3 below:

[0107] Table 3

[0108]

[0109] ③ Draw an image showing how thermal conductivity changes with aggregate volume fraction, and establish the functional relationship between thermal conductivity and aggregate volume fraction as follows:

[0110] logλ am =1.3157V ag -0.8260

[0111] The goodness of fit R of the above formula 2 is 0.9929, which shows that the functional relationship is reasonable. Then the slope and intercept of the linear relationship line (such as Figure 5 Substituting the above formula (shown in Figure 2), we can obtain the parameters C1=0.6369 and C2=0.9761 in the Agari model.

[0112] The Agari model of asphalt mixture is:

[0113]

[0114] Then, the effect of the heat transfer chain in the composite material is introduced into the parallel-serial-geometric mean model of the asphalt mixture in step S4 in an exponential form, and the preliminary prediction model of the thermal conductivity of the asphalt mixture is derived as follows (6):

[0115]

[0116] S5: Select some Marshall specimens in step S3 to calculate the corresponding volume fraction and measure their thermal conductivity. Combined with the preliminary prediction model of thermal conductivity of asphalt mixture containing parameter k value in step S4, after deformation, the expression of k value is obtained; then the expression of k value is substituted into the experimental data for calculation, such as Figure 6 and 7 The diagram shows the relationship between the k value and the volume fraction of asphalt and aggregate. By observing the image, there may be a linear relationship between them. The software is used to perform multiple linear regression to fit the k value with the volume fraction of asphalt and aggregate, and the functional relationship between the k value and the volume fraction of asphalt and aggregate is obtained.

[0117] ① After deforming the preliminary prediction model of thermal conductivity of asphalt mixture containing parameter k value in step S4, the expression of k is obtained as follows (7):

[0118]

[0119] ② 16 groups of dry asphalt mixture specimens were selected from Tables 1 and 2, numbered AM5-AM20. The volume fractions of each group and the measured thermal conductivity are shown in Table 4 below.

[0120] Table 4:

[0121]

[0122]

[0123] ③Substitute the volume fraction of each of the 16 groups of asphalt mixture dry specimens and the measured thermal conductivity into the above expression (7), and calculate the k value of each group as shown in Table 5 below:

[0124] Table 5

[0125]

[0126] The experimental data in Tables 4 and 5 were fitted with Origin software for multivariate linear regression, and the functional relationship between the k value and the volume fraction of asphalt and aggregate was obtained as follows (8):

[0127] k=f(V as ,Vag )=-0.3764V as +1.0664V ag -0.0740 (8)

[0128] The fitting results show the goodness of fit R 2 It is 0.9245, which shows that the functional relationship is reasonable;

[0129] S6: As the asphalt mixture has the characteristics of high aggregate ratio and high porosity, considering the change of thermal conductivity after water infiltration into the voids, the thermal conductivity of asphalt, aggregate, water and air is coupled. An experiment on the effect of moisture content on the thermal conductivity of asphalt mixture is designed. Some specimens prepared in step S4 are immersed in water to calculate the volume fraction of water in the wet specimens. The volume fraction of water in the immersed specimens is expressed as follows (9):

[0130]

[0131] Where: m d —Mass of dry specimen (g); m w —mass of the specimen after immersion in water (g); ρ w —Density of water (g / cm 3 );V s —Total volume of the specimen (cm 3 );V wa —Volume fraction of water in the voids (%);

[0132] Based on the calculated volume fraction of water in the immersed specimen, the functional relationship between the thermal conductivity difference and the moisture content is established as follows (10):

[0133] Δλ=αV wa (10)

[0134] Where: Δλ is the thermal conductivity difference; α is the undetermined parameter in the functional relationship between the thermal conductivity difference and the water volume fraction.

[0135] The design steps of the experiment on the effect of moisture content on the thermal conductivity of asphalt mixture are as follows:

[0136] ① Set the specimens of group AM17-AM24 in Table 1 as the control group and conduct water immersion test on them. Weigh the weight of the dry sample at this time m d ;

[0137] ② Before immersing the specimens in water, prepare a polyethylene film and apply a layer of thermal conductive silicone grease of appropriate thickness. Then immerse the dry asphalt mixture specimens in water for different lengths of time. After taking them out of the water, wipe the surface and weigh the mass m. w ;

[0138] ③ Wrap the specimen with a polyethylene film coated with thermal grease to isolate the moisture in the specimen from the outside world, and obtain a wet asphalt mixture specimen;

[0139] ④ Use a thermal conductivity meter to measure the thermal conductivity of the immersed specimens;

[0140] ⑤Calculate the volume fraction of water in the immersed specimen.

[0141] Among them: The thermal conductivity and component ratio of AM17-AM24 specimens are shown in Table 6 below:

[0142] Table 6

[0143]

[0144]

[0145] ⑥ Draw the relationship curve of the difference in thermal conductivity with the change of water volume fraction, and use Origin software to import the fitted data set for linear fitting, such as Figure 8 As shown, the value of the undetermined parameter α in the functional relationship between the thermal conductivity difference and the water volume fraction is obtained, and substituted into formula (10) to obtain:

[0146] Δλ=4.6025V wa

[0147] The goodness of fit R 2 It is 0.9775, which shows that the functional relationship is reasonable.

[0148] S7: Introducing the effect of moisture content on the difference in thermal conductivity of asphalt mixture, that is, combining equations (6), (8), and (10), the final prediction model for the thermal conductivity of asphalt mixture is derived as follows (11):

[0149]

[0150] Specific examples:

[0151] In this case, the highway top layer is selected as the main design and calculation object. AC-16C asphalt concrete is selected and the mixed material is spread to form a general highway top layer with a length of 100m, a width of 10m and a thickness of 4cm. Generally, the asphalt-stone ratio of AC-16C is about 4.5%-5.0%. Assuming that the asphalt-stone ratio is 4.5%, the volume of the asphalt mixture is calculated as follows: the volume of the top layer of the road is 40m 3 , after compaction of asphalt mixture, it can generally reach 2400kg / m 3 , then the estimated total mass of the highway is 96t, the asphalt usage is calculated to be 4.32t, and the aggregate usage is 91.68t, of which the apparent density of SBS modified asphalt at 25°C is 1.016g / cm3 , thermal conductivity is 0.2344W / m / K, and the apparent density of limestone aggregate is 2.65g / cm 3 , the thermal conductivity coefficient is 3.175W / m / K. It is calculated that the volume fraction of SBS modified asphalt is 10.6%, the volume fraction of limestone aggregate is 86.5%, and the volume fraction of air is 2.9%. At normal temperature and pressure difference, the thermal conductivity of air is 0.026W / m / K.

[0152] Experimental preparation: Considering the change in thermal conductivity of asphalt, aggregate, water and air after water seeps into the voids, an experiment on the effect of moisture content on the thermal conductivity of asphalt mixture was designed. First, dry asphalt mixture specimens were prepared, and aggregate gradation, oil-stone ratio and compaction times were selected as experimental parameters for specimen preparation. AC-16C graded aggregate was selected, and the coarse aggregate and fine aggregate crushed from limestone were washed with water and then dried. The SBS modified asphalt and the above-mentioned screened aggregate were placed in an oven at 180°C and heated until they melted and flowed. Then, the asphalt and aggregate were mixed with an oil-stone ratio of 4.5% and poured into a continuously heated mixer and mixed well. After mixing, the asphalt mixture was poured into a cylindrical mold with a diameter of 10.16 cm and a height of 4 cm, and then compacted on both sides with a Marshall electric instrument according to the compaction times of 75 times to obtain four groups of Marshall specimens, and the mass m of the dry specimens at this time was weighed respectively. d , and number them, then set these four groups of specimens as their own control group and conduct water immersion experiments on them. Before the specimens are immersed in water, prepare a polyethylene film and apply a layer of thermal conductive silicone grease of appropriate thickness. Then immerse the dry asphalt mixture specimens in water for different lengths of time, take them out of the water, wipe the surface and weigh the mass m w , the specimen was wrapped with a polyethylene film coated with thermal grease to isolate the moisture in the specimen from the outside world, and a wet asphalt mixture specimen was obtained. Finally, the volume fraction of water in the immersed specimen was calculated using the following formula (12):

[0153]

[0154] Where: V wa —Volume fraction of water in the voids (%); m d —Mass of dry specimen (g); m w —mass of the specimen after immersion in water (g); ρ w —Density of water (g / cm 3 );V s —Total volume of the specimen (cm 3 );

[0155] Among them: The parameters of specimens 1 to 4 are shown in Table 7 below:

[0156] Table 7

[0157]

[0158] Calculate the thermal conductivity of the upper layer of the highway as follows:

[0159] Step 1: According to the parallel and series thermal conductivity models of composite materials as shown in equations (1) and (2), the thermal conductivity values ​​of asphalt mixture under the parallel and series models are obtained respectively:

[0160] The thermal conductivity of asphalt mixture under the parallel model is:

[0161] λ A =10.6%×0.2344+86.5%×3.175+2.9%×0.026=3.0(W / m / K)

[0162] The thermal conductivity of asphalt mixture under the series model is:

[0163]

[0164] Step 2: According to the functional relationship between the k value and the volume fraction of asphalt and aggregate (8), the influence coefficients of asphalt, aggregate and voids on asphalt mixture in parallel arrangement and series arrangement are obtained as follows:

[0165] k=f(V as ,V ag )=-0.3764×10.6%+1.0664×86.5%-0.0740=0.81

[0166] 1-k=1-0.81=0.19

[0167] Step 3: Calculate the parallel-serial-geometricmean of the asphalt mixture according to formula (3)

[0168] The thermal conductivity under the model is:

[0169] λ am =3.0 0.81 ×0.54 0.19 =2.17(W / m / K)

[0170] Step 4: The effect of the heat transfer chain in the composite material is introduced into the parallel-serial-geometricmean model of the asphalt mixture in an exponential form. According to formula (6), the preliminary predicted value of the thermal conductivity of the asphalt mixture is calculated as follows:

[0171] λ am =(10.6%×0.2344+86.5%×3.175 0.9761 +2.9%×0.026) 0.81(10.6%×0.2344 -1 +86.5%×3.175 -0.9761 +2.9%×0.026 -1 ) -0.19

[0172] =1.98(W / m / K)

[0173] Step 5: Considering the change in thermal conductivity after water seeps into the voids and the coupling of asphalt, aggregate, water, and air, the average volume fraction of water in the four groups of Marshall specimens in the immersion test is taken as:

[0174] (3.02% + 3.15% + 3.42% + 3.89%) / 4 = 3.37%

[0175] According to formula (10), after considering water seepage into the voids, the change in thermal conductivity of asphalt mixture is:

[0176] Δλ=4.6025×2.69%=0.16(W / m / K)

[0177] Step 6: Superimpose the effect of moisture content on the thermal conductivity difference with the calculated preliminary predicted value of the thermal conductivity of the asphalt mixture. According to formula (11), the thermal conductivity of the asphalt mixture is finally obtained as follows:

[0178] λ am =(10.6%×0.2344+86.5%×3.175 0.9761 +2.9%×0.026) 0.81 (10.6%×0.2344 -1 +86.5%×3.175 -0.9761 +2.9%×0.026 -1 ) -0.19 +0.16

[0179] =2.14(W / m / K)

[0180] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0181] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for predicting the thermal conductivity of asphalt mixture, characterized in that: The mixture is a three-phase composite material consisting of asphalt, aggregate, and air. Based on theoretical assumptions and experimental data, a thermal conductivity prediction model for asphalt mixtures with different aggregate gradations, asphalt-to-stone ratios, compaction levels, and moisture contents was established. The steps for establishing the thermal conductivity prediction model are as follows: S1: Assume that asphalt, aggregate, and air are arranged parallel to the direction of heat flow to form a three-phase parallel material A, and the three components are arranged perpendicular to the direction of heat flow to form a series material B. Material A and material B together constitute an asphalt mixture. Based on the parallel thermal conductivity model and series thermal conductivity model of composite materials, the parallel thermal conductivity coefficient model of material A and the series thermal conductivity coefficient model of material B are derived; S2: Assuming the volume fraction of material A in the asphalt mixture is k, the volume fraction of material B in the asphalt mixture is 1-k. At the same time, k and 1-k also represent the degree of influence of parallel arrangement and series arrangement on the thermal conductivity of asphalt mixture respectively; Substitute the parameters k and 1-k in S2 into the parallel and serial thermal conductivity models of the asphalt mixture in step S1, respectively, and establish the parallel-serial-geometric mean model of the asphalt mixture according to the geometric mean model formula; S3: Prepare Marshall specimens with different aggregate gradations, asphalt-to-stone ratios, and compaction levels, and calculate the corresponding volume fractions of asphalt and aggregate in the specimens. The compaction level is simulated by the number of compactions performed by a Marshall electric compactor during specimen preparation. S4: Effect of introducing thermal conductivity chain into asphalt mixture Based on the Agari model of the composite material, it is deformed to establish an Agari model of asphalt mixture based on the parallel and serial thermal conductivity models. In step S3, several groups of specimens with almost zero void ratio are used to conduct experiments. The thermal conductivity of the dry asphalt mixture specimens is tested by the steady-state method, and a functional relationship between the thermal conductivity and the aggregate volume fraction is established. Then, the effect of the thermal conductivity chain in the composite material is introduced into the parallel-serial-geometric mean model of the asphalt mixture in an exponential form, and a preliminary prediction model for the thermal conductivity of the asphalt mixture is derived. S5: Take some of the Marshall specimens in step S3 and measure their corresponding thermal conductivity. After deforming the preliminary prediction model of the thermal conductivity of the asphalt mixture containing the parameter k value in step S4, an expression for the k value is obtained. Then, the expression for the k value is substituted into the above experimental data for calculation. Finally, the k value is fitted with the volume fractions of asphalt and aggregate through multiple linear regression to obtain a functional relationship between the k value and the volume fractions of asphalt and aggregate. S6: Considering the change in thermal conductivity after water seeps into the voids and the coupling of the three phases of asphalt, aggregate, water, and air, some of the specimens prepared in step S3 are subjected to water immersion experiments. The volume fraction of water in the wet specimens is calculated. By designing an experiment on the effect of moisture content on the thermal conductivity of asphalt mixtures, a functional relationship between the difference in thermal conductivity and moisture content is established. S7: Superimpose all the above-mentioned influencing factors, substitute the functional relationship between the k value and the volume fraction of asphalt and aggregate, and the functional relationship between the thermal conductivity difference and the moisture content into the preliminary prediction model of thermal conductivity, and obtain the final prediction model of thermal conductivity of asphalt mixture; By performing corresponding mathematical calculations based on the final prediction model, the thermal conductivity of asphalt mixtures with different aggregate gradations, asphalt-stone ratios, compaction degrees and moisture contents can be predicted.

2. The method for predicting thermal conductivity of asphalt mixture according to claim 1, characterized in that: According to the parallel thermal conductivity model and series thermal conductivity model formulas of composite materials, the thermal conductivity models of material A and material B in step S1 are respectively as follows (1) and (2): l A =V as l as +V ag l ag +V ai l ai (1) Where: A —thermal conductivity of material A; λ B —thermal conductivity of material B; λ as —Thermal conductivity of asphalt; λ ag —thermal conductivity of aggregate; λ ai —Thermal conductivity of air; V as —Volume fraction of asphalt; V ag —Volume fraction of aggregate; V ai —Volume fraction of air.

3. The method for predicting thermal conductivity of asphalt mixture according to claim 2, characterized in that: According to the geometric mean formula, the volume fractions of material A and material B in step S2 are introduced into formulas (1) and (2), and the parallel-serial-geometric mean model of the asphalt mixture in step S3 is the following formula (3): Where: am —Thermal conductivity of asphalt mixture; k—volume fraction of material A in asphalt mixture; 1-k—volume fraction of material B in asphalt mixture.

4. The method for predicting thermal conductivity of asphalt mixture according to claim 1, characterized in that: The volume fraction of each specimen is calculated as follows: First, weigh the weight m of each specimen, the mass of each component in each specimen, and the mass of asphalt m. as and aggregate mass m ag According to the volume fraction calculation formula of the component materials, the volume fraction calculation formula of asphalt and aggregate is as follows: Where: V as —Volume fraction of asphalt; V ag —Volume fraction of asphalt; V s —Total volume of the specimen; ρ as —density of asphalt; ρ ag —density of aggregate; m as —mass of asphalt; m ag —Quality of aggregate.

5. The method for predicting thermal conductivity of asphalt mixture according to claim 3, characterized in that: The Agari model of asphalt mixture and the method for determining the parameters in the model in step S4 are as follows: S51: The Agari model of composite materials (4) is deformed to establish the Agari model of asphalt mixture as follows (5): logλ am =V ag [C2logλ ag -log(C1λ as )]+log(C1λ as ) (5) Where: λ is the thermal conductivity of the composite material; λ1 is the thermal conductivity of the polymer; λ2 is the thermal conductivity of the filler particles; V is the volume fraction of the filler particles; n is a parameter between -1 and 1; C1 is a parameter related to the crystallinity and grain size of the polymer; C2 is a parameter related to the ability of the filler particles to form thermal conductive chains. S52: taking several groups of dry asphalt mixture specimens with a void ratio of almost zero in step S3 and measuring the thermal conductivity of the specimens; S53: Draw a graph showing the change in thermal conductivity with the volume fraction of aggregate, and substitute the slope and intercept of the obtained linear relationship graph to obtain the values ​​of parameters C1 and C2 in the Agari model of asphalt mixture; introduce the influencing parameter C2 of the above thermal conductivity chain into the formula (3) of asphalt mixture, and derive the preliminary prediction model of thermal conductivity of asphalt mixture as follows (6):

6. The method for predicting thermal conductivity of asphalt mixture according to claim 5, characterized in that: The calculation method of the functional relationship between the k value and the volume fraction of asphalt and aggregate is as follows: S61: The preliminary prediction model of thermal conductivity of asphalt mixture in formula (6) is modified to obtain the expression of k as follows (7): S62: Substitute the volume fraction of each component in multiple groups of asphalt mixture dry specimens and the measured thermal conductivity into the above expression for k to calculate the k value; S63: The fitted data set was imported into Origin software for multivariate linear regression. The k value was fitted with the volume fraction of asphalt and aggregate. The functional relationship between the k value and the volume fraction of asphalt and aggregate was obtained as follows (8): k=f(V as ,V ag )=aV as +bV ag +c (8) Among them: a—parameter in the functional relationship between k value and volume fraction of asphalt; b—parameter in the functional relationship between k value and volume fraction of aggregate; c—constant in the functional relationship.

7. The method for predicting thermal conductivity of asphalt mixture according to claim 1, characterized in that: By designing an experiment on the effect of moisture content on the thermal conductivity of asphalt mixture, a function between the thermal conductivity difference and moisture content is established. The specific steps are as follows: S71: Select some dry asphalt mixture specimens prepared in step S3, set these specimens as the control group and conduct water immersion test on them. First weigh the weight of the dry sample m d ; S72: Before immersing the specimens in water, prepare a polyethylene film and apply a layer of thermal grease of appropriate thickness. Then immerse the dry asphalt mixture specimens in water for different lengths of time. After removing them from the water, wipe the surface and weigh the mass m. w ; S73: Wrap the specimen with a polyethylene film coated with thermal grease to isolate the moisture in the specimen from the outside world, thereby obtaining a wet asphalt mixture specimen; S74: Measure the thermal conductivity of the immersed specimens using a thermal conductivity meter; S75: Calculate the volume fraction of water in the immersed specimen as follows (9): Where: V wa —Volume fraction of water in the voids; m d —Mass of the dry specimen; m w —The mass of the test piece after immersion in water; ρ w —density of water; V s —Total volume of the test piece; ⑥ Draw the relationship curve between the difference in thermal conductivity and the change in water volume fraction, import the fitted data set into Origin software for linear fitting, and establish the functional relationship between the difference in thermal conductivity and water volume fraction as follows (10): Δλ=αV wa (10) Where: Δλ is the thermal conductivity difference; α is the undetermined parameter in the functional relationship between the thermal conductivity difference and the water volume fraction.

8. The method for predicting thermal conductivity of asphalt mixture according to claim 7, characterized in that: Combining the above-mentioned influencing factors and formulas (6), (8), and (10), the final prediction model of the thermal conductivity of asphalt mixture is derived as follows (11):

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