CN114113552A - Quantitative analysis method for asphalt main curve - Google Patents
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Abstract
A quantitative analysis method for an asphalt main curve relates to the field of performance evaluation of road asphalt materials. The invention aims to solve the problem that the asphalt performance analysis lacks data support because quantitative analysis can not be carried out in a divided interval and further quantitative comparison can not be carried out because no specific high-low temperature standard exists when the main curve is used for evaluating the asphalt performance at present. The invention comprises the following steps: obtaining an asphalt sample, and preparing the asphalt sample into a test sample; acquiring a complex modulus, a damage modulus, a storage modulus and a phase angle of a sample; selecting a reference temperature, fitting the complex modulus and the phase angle, planning and solving to obtain a displacement factor, a reduction frequency and a main curve optimal parameter combination, and thus obtaining a main curve parameter set; selecting high and low temperature evaluation indexes, and acquiring a high and low temperature analysis area by using a main curve parameter set; and partitioning and counting the complex modulus, the damage modulus and the storage modulus after coordinate conversion, and evaluating by using a statistical result. The invention is mainly used for evaluating the asphalt performance.
Description
Technical Field
The invention relates to the field of performance evaluation of road asphalt materials, in particular to a quantitative analysis method for an asphalt main curve.
Background
Asphalt is a black-brown complex mixture composed of hydrocarbons with different molecular weights and nonmetallic derivatives thereof, and is one of high-viscosity organic liquids. Asphalt material is a typical viscoelastic material, and in the linear viscoelastic domain, asphalt material has simple thermo-rheological properties, and the stress-strain constitutive relation is usually expressed in the form of integral. Therefore, the research on the viscoelastic characteristics of the pavement material under the load becomes the focus of the research in the field.
Currently, Dynamic Mechanical Analysis (DMA) is commonly used to study the performance of pavement asphalt materials during production, transportation, storage and maintenance. According to the previous research, the mechanical behavior of the viscoelastic material has strong dependence on loading temperature and frequency; however, the loading conditions in the laboratory are limited and fortunately, this problem can be solved in polymer physics-the time-temperature equivalence principle of viscoelastic materials is used to extend the analysis range. This idea stems from the study of dynamic mechanical temperature spectra, and it was found through a number of experiments that the relaxation modulus of the superpolymer at lower temperatures and longer loading times (lower frequencies) exhibits an equivalent substitution law along the time/frequency axis, similar to the relaxation modulus at shorter loading times (higher frequencies) and higher temperatures. The modulus curve obtained at a particular temperature and frequency can be shifted along the time axis and eventually coupled into a smooth curve, i.e., the main curve.
At present, the mode of utilizing the main curve is mainly to qualitatively see the change trend in a large frequency or temperature range, and the complex modulus is considered to be higher at a lower frequency, so that the asphalt material has better high-temperature anti-rutting performance; conversely, asphalt materials with lower complex modulus at higher frequencies have better low temperature crack resistance. However, there is no specific standard for what frequency range represents low temperature and what frequency range represents high temperature, so that quantitative analysis cannot be performed in the divided intervals, and further quantitative comparison cannot be performed, which results in lack of data support for evaluation of asphalt performance analysis.
Disclosure of Invention
The invention aims to solve the problems that quantitative analysis cannot be carried out in a divided interval due to the fact that specific standards of high and low temperatures do not exist when a main curve is used for evaluating the asphalt performance at present, and further quantitative comparison cannot be carried out, so that the asphalt performance analysis lacks data support, and provides a quantitative analysis method for an asphalt main curve.
A quantitative analysis method for an asphalt main curve comprises the following steps:
step one, acquiring n groups of asphalt samples, and preparing the asphalt samples into asphalt slice samples;
wherein n is more than or equal to 3;
step two, obtaining a complex modulus G, a damage modulus G ', a storage modulus G' and a phase angle delta of the asphalt sheet sample;
step three, selecting reference temperature TRAnd at a reference temperature TRAnd fitting the complex modulus G and the phase angle delta obtained in the step two through a CAM model, and planning and solving by using a WLF equation and a planning and solving method to obtain the displacement factor, the reduction frequency omega and the optimal parameter combination of the main curve by taking the minimum sum of the residual squares of the complex modulus G and the phase angle delta as a target
Wherein the content of the first and second substances,
fc、m、k、δm、Rd、fd、md、C1、C2are all undetermined coefficients;
step four, repeating the steps one to three to obtain the main curve parameter combination P of all the asphalt samples1,P2,…,Pn；
Step five, selecting high-temperature and low-temperature evaluation indexes, and obtaining a high-temperature analysis area and a low-temperature analysis area by utilizing all the main curve parameter combinations of the asphalt samples obtained in the step four:
step six, the complex modulus G, the damage modulus G ', the storage modulus G' and the phase angle delta of the asphalt sheet sample obtained in the step two are subjected to coordinate conversion through the displacement factor obtained in the step three, and then the displaced complex modulus is obtained
Phase angle delta1D damage modulus G'1And storage modulus G "1And data, wherein the displaced data falling in the high and low temperature analysis area are subjected to statistical analysis respectively, and the comprehensive properties of the high and low temperature universe of the asphalt material are evaluated by using the analysis result.
The invention has the beneficial effects that:
the invention provides a quantitative analysis region determination method of an asphalt main curve by integrating a rheological analysis method and a mathematical statistic means, and provides a quantitative evaluation means of the asphalt main curve to evaluate the comprehensive properties of the high-temperature/low-temperature universe of asphalt materials; the problem that the asphalt main curve is used as a key technology but lacks an effective quantitative analysis means is solved. The quantitative analysis method for the asphalt main curve provided by the invention can accurately and sensitively distinguish the high-low temperature overall performance of the asphalt material, can perform quantitative analysis in the divided high-low temperature interval, further perform quantitative comparison, and provide powerful data support for the performance analysis of the asphalt.
Drawings
FIG. 1 is a complex modulus master curve after translation using the WLF equation;
FIG. 2 is a principal loss modulus curve after translation using the WLF equation;
FIG. 3 is a main curve of storage modulus after translation using WLF equation;
FIG. 4 is a phase angle master curve after translation using WLF equations;
FIG. 5 is a schematic view of the domain determination process in the pyrometry of example 1.
Detailed Description
The first embodiment is as follows: the quantitative analysis method for the asphalt main curve comprises the following steps:
step one, acquiring n groups of asphalt samples and the aging state of each asphalt sample, and preparing the asphalt samples into asphalt sheet samples according to the aging state in a pouring mode;
the asphalt samples of different groups are different types of asphalt, and if the aging state of the asphalt is to be analyzed, the same asphalt in different aging states can be regarded as two different groups;
the size of the poured test piece is determined according to the type of asphalt: for non-particle effect asphalt, such as base asphalt, SBS modified asphalt and SBR modified asphalt, the test piece size is phi 25mm multiplied by 1 mm; for asphalt with particle effect, such as rubber asphalt and bio-oil modified rubber asphalt, the test piece size is phi 25mm multiplied by 2 mm;
step two, obtaining the complex modulus G, the damage modulus G ', the storage modulus G' and the phase angle delta of the asphalt sheet sample, and comprising the following steps:
step two, frequency scanning is carried out on the asphalt flake sample to obtain f of the asphalt flake sample at various temperatures T and loading frequenciesrShear stress response value of0Strain response value gamma0Phase angle δ:
the asphalt flake sample is subjected to frequency scanning, and a temperature range and a frequency range which are as large as possible are used under the condition of permission of instrument conditions; the loading frequency range is 0.1 Hz-30 Hz; the temperature range is 4-76 ℃;
step two, according to the shear stress response value tau obtained in the step two0Strain response value gamma0The phase angle δ obtains the complex modulus G:
wherein i is an imaginary number and t is a load time;
step two, acquiring a loss modulus G 'and a storage modulus G' according to the complex modulus G obtained in the step two:
G′＝|G*|cosδ (2)
G″＝|G*|sinδ (3)
step three, selectingReference temperature TRAnd at a reference temperature TRAnd fitting the complex modulus G and the phase angle delta obtained in the second step through a CAM model, and simultaneously planning and solving by using a WLF equation and an EXCEL planning and solving functional module to obtain the displacement factor, the reduction frequency omega and the optimal parameter combination of the main curve by taking the minimum sum of the residual squares of the complex modulus G and the phase angle delta as a target
The reference temperature is selected according to requirements, and is usually selected to be 25 ℃ at normal temperature or 60 ℃ at the highest service temperature of a road surface as the reference temperature;
ωr＝ω×αT(T) (7)
wherein f isrIs the loading frequency, I is a constant,
f is a specific frequency, ω is a reduced frequency corresponding to f, ωrIs frCorresponding reduced frequency, alphaT(T) is a displacement factor, T is a frequency sweep temperature,
fc、m、k、δm、Rd、fd、md、C1、C2is the undetermined coefficient;
the sum of the modulus and phase angle residual squared differences is minimal obtained by:
s1, calculating the sum of squares of residuals between the complex modulus G and the calculated value of the formula (4);
s2, calculating the sum of squares of residuals between the phase angle delta and the calculated value of the formula (5);
and S3, adding the residual sum squares obtained in S1 and S2 to obtain the sum of the modulus and phase angle residual sum squares.
Step four, repeating the steps one to three for all the asphalt samples obtained in the step one to obtain the main curve parameter combination P of all the asphalt samples1,P2,…,Pn；
Step five, selecting high-temperature and low-temperature evaluation indexes, and obtaining a high-temperature analysis area or a low-temperature analysis area by utilizing all the main curve parameter combinations of the asphalt samples obtained in the step four:
fifthly, combining all the asphalt sample main curve parameters obtained in the fourth step to obtain a complex modulus and a phase angle under a specific frequency f;
step two, selecting high-temperature and low-temperature evaluation indexes, and carrying out correlation analysis on the complex modulus and the phase angle under the f and the high-temperature and low-temperature evaluation indexes to obtain a correlation coefficient rGAnd rδ
The high-temperature evaluation indexes are as follows: j of rut factor and multiple stress creep recovery test (MSCR) before and after asphalt agingnr0.1、Jnr3.2；
The low-temperature evaluation indexes are as follows: stiffness modulus (Stiffness) and m-value for trabecular bending test (BBR);
step five and step three, according to the correlation coefficient rGAnd rδRespectively obtain rGAnd rδCorrelation coefficient threshold of (2):
fifthly, one, three and one, and carrying out equidistant continuous value taking on logarithmic frequency logf in the frequency f range corresponding to omega to obtain the discrete distribution relation of correlation coefficients, namely rG＝FG(logf) and rδ＝Fδ(logf)；
Wherein, FG()、Fδ() Is a correlation analysis function;
step five, step three, step two, determination of guarantee rate and significance waterFlat alpha ═ P (| rho |)>ρα) According to the degree of freedom n-2, looking up a correlation coefficient critical value table to determine a correlation coefficient threshold value;
the value a is taken as required, and is generally 0.05;
α＝P(|ρ|>ρα) Is a table head formula of a correlation coefficient critical value table.
Step five and four, acquiring the abscissa value f of the modulus and phase angle discrete distribution curve corresponding to the correlation coefficient threshold value by using a trial calculation modeGAnd fδ；
Step five, according to the fGAnd fδObtaining a high temperature analysis region HT ═ { f | f<min(fG,fδ) And a low temperature analysis region LT ═ f | f>max(fG,fδ)}；
Wherein, min () is a function of taking the minimum value, max () is a function of taking the maximum value;
and step six, the complex modulus G, the damage modulus G ', the storage modulus G' and the phase angle delta of the asphalt sheet sample obtained in the step two are subjected to coordinate conversion through the displacement factor obtained in the formula (6), and then the displaced complex modulus is obtained
Phase angle delta1D damage modulus G'1And storage modulus G "1Data, wherein the displaced data falling in the high and low temperature analysis area are respectively subjected to statistical analysis, and the comprehensive properties of the high and low temperature universe of the asphalt material are evaluated by using the analysis result;
the statistical analysis method comprises the following steps: average value, total sum, maximum slope value of the area, and horizontal and vertical coordinate values corresponding to the extreme points of the area.
Example (b): according to the method of the specific embodiment, the high and low temperature performance of the asphalt is analyzed by adopting a three-intermediate experiment, which specifically comprises the following steps:
experiment 1: and (3) determining a high-temperature analysis area by using the original asphalt rutting factor critical temperature as a representative high-temperature evaluation index, and analyzing the high-temperature performance of the asphalt material by using a statistical means.
Experiment 2: after the high-temperature analysis area is determined by adopting the unrecoverable creep compliance (3.2k/Pa) as a representative high-temperature evaluation index, the high-temperature performance of the asphalt material is analyzed by utilizing a statistical means.
Experiment 3: after determining a low-temperature analysis area by adopting a stiffness modulus of a BBR test at-18 ℃ as a representative low-temperature evaluation index, analyzing the low-temperature performance of the asphalt material by utilizing a statistical means.
The key steps for experiments 1-3 are as follows:
the key step 1: selecting asphalt and high and low temperature performance:
the basic properties and high and low temperature properties of 6 bitumens were selected and are shown in table 1.
TABLE 1
The key step 2: frequency sweep test and parameter fitting:
performing frequency scanning tests on six asphalt materials, wherein the frequency range is 0.1 Hz-30 Hz, the recommended temperature range is 4-76 ℃, obtaining modulus and phase angle numerical values under various temperatures and loading frequencies, performing parameter fitting and translation, and fitting a parameter result P1Pn see Table 2, and the data point results after translation are shown in FIGS. 1-4.
TABLE 2 CAM model parameter fitting results
Key step 3: dividing high and low temperature analysis regions:
continuously taking values of logarithmic frequency logf at equal intervals in a frequency range f, and calculating a correlation coefficient r between-5 and 3 for experiments 1 and 3 by taking 0.1 as an intervalGAnd rδAnd curve it with the change of logarithmic frequencyLine rG＝FG(logf) and rδ＝Fδ(logf) was plotted, wherein the results of the specific experiment 1 are shown in FIG. 5, and the results of the other examples are similar and are not repeated.
The guarantee rate is 95% for experiments 1-3, the significance level alpha is 0.05, and the threshold value of the correlation coefficient is 0.8114 by looking up a critical index table according to the degree of freedom n-2 which is 4. By using equations (4) and (5) and a correlation coefficient calculation formula, a logarithmic reduction frequency critical value relative to a complex modulus main curve and a phase angle main curve can be obtained through trial calculation, and the calculation results of experiments 1-3 are shown in table 3.
TABLE 3 results of analysis of the regions
The key step 4: extracting regional statistical characteristics and analyzing high and low temperature performance:
the results of the modulus and phase angle obtained with reference to FIGS. 1 to 4 were statistically analyzed in the analysis regions shown in Table 3, and the results are shown in Table 4, where the mean values were selected for explanation in the present example.
First, referring to the results of experiment 1, according to the complex modulus results in table 4, the high temperature performance in the full high temperature range is ranked as: the results of the sample 2, the sample 3, the sample 6, the sample 4 and the sample 1 are completely different from the results of the original asphalt high-temperature critical temperature (the sample 5, the sample 6, the sample 2, the sample 3, the sample 4 and the sample 1), which indicates that the traditional index can not evaluate the performance of the full high-temperature range, and a quantitative analysis method of the asphalt main curve is required to be developed. Meanwhile, by means of the joint analysis of the phase angle, the loss modulus and the storage modulus, the evaluation and research on the performance of the asphalt material can be more sufficient.
TABLE 4 statistical analysis results in the analysis region
Claims (10)
1. A quantitative analysis method for an asphalt main curve is characterized by comprising the following steps:
step one, acquiring n groups of asphalt samples, and preparing the asphalt samples into asphalt slice samples;
wherein n is more than or equal to 3;
step two, obtaining a complex modulus G, a damage modulus G ', a storage modulus G' and a phase angle delta of the asphalt sheet sample;
step three, selecting reference temperature TRAnd at a reference temperature TRAnd fitting the complex modulus G and the phase angle delta obtained in the step two through a CAM model, and planning and solving by using a WLF equation and a planning and solving functional method to obtain the displacement factor, the reduction frequency omega and the optimal parameter combination of the main curve by taking the minimum sum of the residual squares of the complex modulus G and the phase angle delta as a target
Wherein the content of the first and second substances,
fc、m、k、δm、Rd、fd、md、C1、C2are all undetermined coefficients;
step four, repeating the steps one to three to obtain the main curve parameter combination P of all the asphalt samples1,P2,…,Pn；
Step five, selecting high-temperature and low-temperature evaluation indexes, and obtaining a high-temperature analysis area and a low-temperature analysis area by utilizing all the main curve parameter combinations of the asphalt samples obtained in the step four:
step six, the complex modulus G, the damage modulus G ', the storage modulus G' and the phase angle delta of the obtained asphalt sheet sample obtained in the step two pass through the stepAfter coordinate conversion is carried out on the displacement factors obtained in the third step, the complex modulus after displacement is obtained
Phase angle delta1D damage modulus G'1And storage modulus G ″)1And data, wherein the displaced data falling in the high and low temperature analysis area are respectively subjected to statistical analysis, and the comprehensive properties of the high and low temperature universe of the asphalt material are evaluated by using the analysis results to obtain evaluation results.
2. The quantitative analysis method for the asphalt main curve according to claim 1, characterized in that: in the first step, the asphalt sample is made into an asphalt sheet sample and a pouring mode is adopted;
the size of the poured test piece is determined according to the type of asphalt, and specifically comprises the following steps:
for non-particle effect bitumen: the size of the test piece is phi 25mm multiplied by 1 mm;
for particle effect asphalt: the test piece size was Φ 25mm × 2 mm.
3. The quantitative analysis method for the asphalt main curve according to claim 1 or 2, characterized in that: the second step of obtaining the complex modulus G, the damage modulus G ', the storage modulus G' and the phase angle delta of the asphalt flake sample comprises the following steps:
secondly, performing frequency scanning on the asphalt sheet sample to obtain a shear stress response value tau, a strain response value gamma and a phase angle delta of the asphalt sheet sample in a preset temperature range and a preset loading frequency range;
step two, according to the shear stress response value tau obtained in the step two0Strain response value gamma0The phase angle δ obtains the complex modulus G:
wherein i is an imaginary number and t is a load time;
step two, acquiring a loss modulus G 'and a storage modulus G' according to the complex modulus G obtained in the step two:
G′＝|G*|cosδ (2)
G″＝|G*|sinδ (3)。
4. the quantitative analysis method for the asphalt main curve according to claim 3, characterized in that: the preset temperature range in the second step is as follows: the preset loading frequency range is from 4 ℃ to 76 ℃: 0.1 Hz-30 Hz.
5. The quantitative analysis method for the asphalt main curve according to claim 3, characterized in that: selecting a reference temperature T in the third stepRAnd at a reference temperature TRAnd fitting the complex modulus G and the phase angle delta obtained in the step one through a CAM model, and simultaneously carrying out planning solution by using a WLF equation and an EXCEL planning solution function module to obtain a displacement factor, a reduction frequency omega and a main curve optimal parameter combination by taking the minimum sum of the residual squares of the complex modulus G and the phase angle delta as a target
The formula is as follows:
ωr＝ω×αT(T) (7)
wherein f isrIs the loading frequency, I is a constant，
f is a specific frequency, ω is a reduced frequency corresponding to f, ωrIs frCorresponding reduced frequency, alphaT(T) is a displacement factor, T is a frequency sweep temperature,
fc、m、k、δm、Rd、fd、md、C1、C2is the undetermined coefficient.
6. The quantitative analysis method for the asphalt main curve according to claim 5, characterized in that: the sum of the squares of the modulus and the phase angle residual errors in the three steps is obtained by the following steps:
s1, calculating the sum of squares of residuals between the complex modulus G and the calculated value of the formula (4);
s2, calculating the sum of squares of residuals between the phase angle delta and the calculated value of the formula (5);
and S3, adding the residual sum squares obtained in S1 and S2 to obtain the sum of the modulus and phase angle residual sum squares.
7. The quantitative analysis method for the asphalt main curve according to claim 6, characterized in that: selecting high-temperature and low-temperature evaluation indexes in the fifth step, and obtaining a high-temperature analysis area and a low-temperature analysis area by using all the asphalt sample main curve parameter combinations obtained in the fourth step, wherein the method comprises the following steps:
fifthly, combining all the asphalt sample main curve parameters obtained in the fourth step to obtain a complex modulus and a phase angle under a specific frequency f;
step two, selecting high-temperature and low-temperature evaluation indexes, and carrying out correlation analysis on the complex modulus and the phase angle under the f and the high-temperature evaluation index/low-temperature evaluation index to obtain a correlation coefficient rGAnd rδ；
Step five and step three, according to the correlation coefficient rGAnd rδRespectively obtain rGAnd rδA correlation coefficient threshold of (a);
step five and four, acquiring the abscissa value f of the modulus and phase angle discrete distribution curve corresponding to the correlation coefficient threshold value by using a trial calculation modeGAnd fδ；
Step five, according to the fGAnd fδObtaining a high temperature analysis region HT ═ { f | f<min(fG,fδ) And a low temperature analysis region LT ═ f | f>max(fG,fδ)}。
8. The quantitative analysis method for the asphalt main curve according to claim 7, characterized in that: the high-temperature evaluation indexes in the step five are as follows:
jnr0.1 and Jnr3.2 of rut factors and multiple stress creep recovery tests before and after asphalt aging;
the low-temperature evaluation indexes are as follows: stiffness modulus and m-value for trabecular bending test.
9. The quantitative analysis method for the asphalt main curve according to claim 8, characterized in that: in the fifth step and the third step according to the correlation coefficient rGAnd rδRespectively obtain rGAnd rδThe correlation coefficient threshold value comprises the following steps:
fifthly, one, three and one, and carrying out equidistant continuous value taking on logarithmic frequency logf in the frequency f range corresponding to omega to obtain rGAnd rδIn relation to discrete distribution of correlation coefficients, i.e. rG＝FG(logf) and rδ＝Fδ(logf)；
Wherein, FG()、Fδ() Is a correlation analysis function;
fifthly, determining the guarantee rate and the significance level a, and determining a correlation coefficient threshold value by referring to a correlation coefficient critical value table according to the degree of freedom n-2;
wherein the significance level a is a constant.
10. The quantitative analysis method for the asphalt main curve according to claim 9, characterized in that: in the sixth step, the statistical analysis is performed on the shifted data falling in the high and low temperature analysis region respectively, and the method comprises the following steps: average value, total sum, maximum slope value of the area, and horizontal and vertical coordinate values corresponding to the extreme points of the area.
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| CN115479884A (en) * | 2022-09-01 | 2022-12-16 | 哈尔滨工业大学 | Test and evaluation method considering influence of freeze thawing and aging on asphalt mixture performance |
| US11814506B2 (en) | 2019-07-02 | 2023-11-14 | Marathon Petroleum Company Lp | Modified asphalts with enhanced rheological properties and associated methods |
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| CA2790246A1 (en) * | 2011-09-06 | 2013-03-06 | Ohio University | Method and system for determining properties of an asphalt material |
| CN105067452A (en) * | 2015-08-21 | 2015-11-18 | 哈尔滨工业大学 | Method for acquiring physical hardening property evaluation index of bituminous material |
| CN106950118A (en) * | 2017-03-13 | 2017-07-14 | 山东省交通科学研究院 | A kind of bi tumenf orr oad high temperature, low temperature performance method for quick |
| CN107144683A (en) * | 2017-05-22 | 2017-09-08 | 合肥工业大学 | A kind of construction method of the asphalt principal curve based on Xi Gemode functions |
| CN107462471A (en) * | 2017-09-11 | 2017-12-12 | 交通运输部公路科学研究所 | Method based on section test specimen complex modulus Damage Evaluation stability of asphalt mixture |
| CN110929940A (en) * | 2019-11-26 | 2020-03-27 | 太原理工大学 | Method for predicting dynamic modulus of asphalt mixture and application thereof |
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| US11814506B2 (en) | 2019-07-02 | 2023-11-14 | Marathon Petroleum Company Lp | Modified asphalts with enhanced rheological properties and associated methods |
| CN115479884A (en) * | 2022-09-01 | 2022-12-16 | 哈尔滨工业大学 | Test and evaluation method considering influence of freeze thawing and aging on asphalt mixture performance |
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