CN114113552A - A Quantitative Analysis Method of Asphalt Master Curve - Google Patents

Abstract

A quantitative analysis method of asphalt master curve relates to the field of performance evaluation of road asphalt materials. The present invention is to solve the problem that there is no specific standard of high and low temperature when evaluating asphalt performance by using the master curve at present, which leads to the inability to carry out quantitative analysis in the divided interval and the inability to compare quantitatively, resulting in the lack of data support for asphalt performance analysis. The invention includes: obtaining an asphalt sample, and making the asphalt sample into a sample; obtaining the complex modulus, damage modulus, storage modulus, and phase angle of the sample; selecting a reference temperature, fitting the complex modulus and the phase angle, and combining Perform the planning and solver to obtain the displacement factor, the reduction frequency and the optimal parameter combination of the main curve, so as to obtain the main curve parameter set; select the high and low temperature evaluation index, and use the main curve parameter set to obtain the high and low temperature analysis area; after the coordinates are converted, the complex modulus, damage The modulus and storage modulus are partitioned and counted, and the statistical results are used for evaluation. The present invention is mainly used for the evaluation of asphalt performance.

Description

A Quantitative Analysis Method of Asphalt Master Curve

technical field

The invention relates to the field of performance evaluation of road asphalt materials, in particular to a quantitative analysis method of an asphalt master curve.

Background technique

Asphalt is a dark-brown complex mixture composed of hydrocarbons of different molecular weights and their non-metallic derivatives, and is a kind of high-viscosity organic liquid. Asphalt material is a typical viscoelastic material. In the linear viscoelastic domain, asphalt material has simple thermo-rheological properties, and its stress-strain constitutive relationship is usually expressed in the form of integral. Therefore, studying the viscoelastic properties of pavement materials under load has become the focus of research in this field.

At present, dynamic mechanical analysis (DMA) is usually used to study the performance of pavement asphalt materials during production, transportation, storage and maintenance. According to previous studies, the mechanical behavior of viscoelastic materials has a strong dependence on loading temperature and frequency; however, the loading conditions in the laboratory are limited, and fortunately, this problem can be solved in the context of polymer physics. Find the answer in - using the time-temperature equivalence principle of viscoelastic materials to expand the scope of analysis. This idea stemmed from the study of dynamic mechanical temperature spectra. After extensive experiments, it was found that the relaxation modulus of superpolymers at lower temperature and longer loading time (lower frequency) was significantly different from shorter loading time (higher frequency). frequency) and relaxation moduli at higher temperatures, showing an equivalent substitution law along the time/frequency axis. The modulus curves obtained at a specific temperature and frequency can be shifted along the time axis and finally coupled into a smooth curve, the master curve.

At present, the main method of using the main curve is to qualitatively look at the change trend in a large frequency or temperature range. It is believed that at a lower frequency, the complex modulus is higher, and the asphalt material has better high temperature rutting resistance; Asphalt materials with lower complex modulus at frequency 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. Therefore, quantitative analysis cannot be carried out in the divided interval, and quantitative comparison cannot be carried out, resulting in the lack of data support for the evaluation of asphalt performance analysis.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the problem that there is no specific standard for high and low temperature when evaluating asphalt performance by using the master curve at present, which leads to the inability to carry out quantitative analysis in the divided interval, and thus the inability to quantitatively compare, resulting in the lack of data support for asphalt performance analysis. A quantitative analysis method of asphalt master curve.

A method for quantitative analysis of asphalt master curve comprises the following steps:

Step 1: Obtain n groups of asphalt samples, and make the asphalt samples into asphalt thin slices;

Among them, n≥3;

Step 2: Obtain the complex modulus G*, damage modulus G', storage modulus G", and phase angle δ of the asphalt flake sample;

Step 3: Select the reference temperature _TR , and at the reference temperature _TR , fit the complex modulus G* and phase angle δ obtained in step 2 through the CAM model, and use the complex modulus G* and phase angle δ at the same time. The goal is to minimize the sum of squared residuals. Use the WLF equation and the Solver method to solve the problem to obtain the displacement factor, the reduction frequency ω and the optimal parameter combination of the main curve.

f_c、m、k、δ_m、R_d、f_d、m_d、C₁、C₂均为待定系数；in,

f _c , m, k, δ _m , R _d , f _d , m _d , C ₁ , C ₂ are all undetermined coefficients;

Step 4. Repeat steps 1 to 3 for all asphalt samples obtained in step 1 to obtain the main curve parameter combinations P ₁ , P ₂ , . . . , P _n of all asphalt samples;

Step 5: Select the evaluation indexes of high temperature and low temperature, and obtain the high temperature analysis area and the low temperature analysis area by using the combination of the master curve parameters of all asphalt samples obtained in step 4:

相位角δ₁、损伤模量G’₁和存储模量G”₁数据，将落在高低温分析区域的位移后的数据分别进行统计分析，并利用分析结果对沥青材料高低温全域综合性质进行评价。Step 6. The complex modulus G*, damage modulus G', storage modulus G", and phase angle δ of the asphalt flake sample obtained in step 2 are transformed by the displacement factor obtained in step 3, and then the displacement is obtained. Complex modulus

Phase angle δ ₁ , damage modulus G' ₁ and storage modulus G" ₁ data, the data after the displacement falling in the high and low temperature analysis area are analyzed separately, and the comprehensive properties of the asphalt material at high and low temperature are analyzed by using the analysis results. Evaluation.

The beneficial effects of the present invention are:

The invention integrates the rheological analysis method and the mathematical statistics method, proposes a method for determining the quantitative analysis area of the asphalt master curve, and provides a quantitative evaluation method for the asphalt master curve to evaluate the high-temperature/low-temperature global comprehensive properties of asphalt materials; As a key technology, the master curve lacks effective quantitative analysis methods. The asphalt master curve quantitative analysis method proposed by the invention can accurately and sensitively distinguish the high and low temperature overall performance of the asphalt material, and can carry out quantitative analysis in the divided high and low temperature intervals, and then conduct quantitative comparison, which provides the performance analysis of asphalt. backed by strong data.

Description of drawings

Fig. 1 is the main curve of complex modulus after translation using the WLF equation;

Figure 2 is the main curve of the loss modulus after translation using the WLF equation;

Fig. 3 is the master curve of storage modulus after translation using the WLF equation;

Fig. 4 is the main curve of phase angle after translation using the WLF equation;

FIG. 5 is a schematic diagram of the determination process of the high temperature analysis domain in Example 1. FIG.

Detailed ways

Embodiment 1: A method for quantitative analysis of asphalt master curves in this embodiment includes the following steps:

Step 1: Obtain n≥3 groups of asphalt samples and the aging state of each asphalt sample, and prepare the asphalt samples as asphalt thin slices by pouring according to the aging state;

Asphalt samples of different groups are different types of asphalt. To analyze the aging state of asphalt, the same asphalt under different aging states can be regarded as two different groups;

The size of the poured specimen is determined according to the type of asphalt: for asphalt without particle effect, such as base asphalt, SBS modified asphalt and SBR modified asphalt, the size of the sample is Φ25mm×1mm; for asphalt with particle effect, such as rubber asphalt and bio-oil modified rubber asphalt, the size of the specimen is Φ25mm×2mm;

Step 2: Obtain the complex modulus G*, damage modulus G', storage modulus G", and phase angle δ of the asphalt flake sample, including the following steps:

Step 21. Perform frequency scanning on the asphalt thin sample to obtain the shear stress response value _{τ 0} , the strain response value γ ₀ , and the phase angle δ of the asphalt thin sample fr under each temperature T and loading frequency:

The asphalt thin sample is subjected to frequency scanning, and the temperature range and frequency range should be as large as possible when the instrument conditions allow; the loading frequency range is 0.1Hz～30Hz; the temperature range is 4℃～76℃;

Step 22: Obtain the complex modulus G* according to the shear stress response value τ ₀ , the strain response value γ ₀ , and the phase angle δ obtained in step 21:

where i is an imaginary number and t is the loading time;

Step 23: Obtain the loss modulus G' and the storage modulus G" according to the complex modulus G* obtained in step 22:

G′＝|G ^* |cosδ (2)

G″=|G ^* |sinδ (3)

Step 3: Select the reference temperature _TR , and at the reference temperature _TR , fit the complex modulus G* and phase angle δ obtained in step 2 through the CAM model, and use the complex modulus G* and phase angle δ at the same time. The goal is to minimize the sum of squared residuals. Use WLF equation and EXCEL solver function module to solve the problem to obtain displacement factor, reduction frequency ω and optimal parameter combination of main curve.

The reference temperature is selected according to the needs, usually 25°C at room temperature or 60°C at the maximum service temperature of the road surface as the reference temperature;

ω _r = ω×α _T (T) (7)

f是特定频率，ω是f对应的缩减频率，ω_r是f_r对应的减缩频率，α_T(T)是位移因子，T是频率扫描温度，

f_c、m、k、δ_m、R_d、f_d、m_d、C₁、C₂是待定系数；where _fr is the loading frequency, I is a constant,

f is the specific frequency, ω is the reduced frequency corresponding to f, ω _r is the reduced frequency corresponding to f _r , α _T (T) is the displacement factor, T is the frequency sweep temperature,

f _c , m, k, δ _m , R _d , f _d , m _d , C ₁ , C ₂ are undetermined coefficients;

The modulo and phase angle residual sums of squared minimization are obtained by:

S1. Calculate the residual sum of squares between the complex modulus G* and the calculated value of formula (4);

S2, calculate the residual sum of squares between the phase angle δ and the calculated value of formula (5);

S3. The sum of the squared residuals obtained by S1 and S2 is the sum of the squared residuals of the modulus and the phase angle.

Step 4. Repeat steps 1 to 3 for all asphalt samples obtained in step 1 to obtain the main curve parameter combinations P ₁ , P ₂ , . . . , P _n of all asphalt samples;

Step 5: Select high temperature and low temperature evaluation indicators, and use the combination of all asphalt sample master curve parameters obtained in step 4 to obtain a high temperature analysis area or a low temperature analysis area:

Step 51: Obtain the complex modulus and phase angle at a specific frequency f according to the main curve parameter combination of all asphalt samples obtained in step 4;

Step 52: Select high temperature and low temperature evaluation indexes, and perform correlation analysis between the complex modulus and phase angle under f and the high temperature evaluation index and low temperature evaluation index, and obtain the correlation coefficients r _G and r _δ

The high temperature evaluation index is: rutting factor before and after asphalt aging and J _nr0.1 and J _nr3.2 of the multiple stress creep recovery test (MSCR);

The low temperature evaluation index is: stiffness modulus (Stiffness) and m value of trabecular bending test (BBR);

Step 53: Obtain the correlation coefficient thresholds of r _G and r _δ respectively according to the correlation coefficients r _G and r _δ :

Step 531. Perform continuous values of logarithmic frequency logf at equal intervals within the frequency f range corresponding to ω to obtain the discrete distribution relationship of the correlation coefficient, that is, r _G =F _G (logf) and r _δ =F _δ (logf);

Among them, F _G (), F _δ () are correlation analysis functions;

Step 532: Determine the guarantee rate and the significance level α=P(|ρ|>ρ _α ), and check the correlation coefficient threshold table according to the degree of freedom n-2 to determine the correlation coefficient threshold;

The value of a is taken as needed, generally 0.05;

α=P(|ρ|>ρ _α ) is the header formula of the correlation coefficient critical value table.

Step 54, utilize the trial calculation method to obtain the abscissa values f _G and f _δ of the corresponding modulus of the correlation coefficient threshold and the phase angle discrete distribution curve;

Step 55. Obtain high temperature analysis area HT={f|f<min(f _G ,f _δ )} and low temperature analysis area LT={f|f>max(f _G ,f _δ )} according to f _G and f _δ ;

Among them, min() is the function of taking the minimum value, and max() is the function of taking the maximum value;

相位角δ₁、损伤模量G’₁和存储模量G”₁数据，将落在高低温分析区域的位移后的数据分别进行统计分析，并利用分析结果对沥青材料高低温全域综合性质进行评价；The complex modulus G*, the damage modulus G', the storage modulus G", and the phase angle δ of the asphalt flake samples obtained in step 6 and step 2 are coordinately transformed by the displacement factor obtained by formula (6), and then the displacement is obtained. Complex modulus after

Phase angle δ ₁ , damage modulus G' ₁ and storage modulus G" ₁ data, the data after the displacement falling in the high and low temperature analysis area are analyzed separately, and the comprehensive properties of the asphalt material at high and low temperature are analyzed by using the analysis results. Evaluation;

The statistical analysis sub-methods include: average value, total sum, regional maximum slope value, horizontal and vertical coordinate values corresponding to regional extreme value points, and the like.

Example: According to the method described in the specific embodiment, the high and low temperature performance of asphalt was analyzed by three experiments, as follows:

Experiment 1: After using the original asphalt rutting factor critical temperature as the representative high temperature evaluation index to determine the high temperature analysis area, the high temperature performance of the asphalt material was analyzed by statistical means.

Experiment 2: After using the irreversible creep compliance (3.2k/Pa) as the representative high temperature evaluation index to determine the high temperature analysis area, the high temperature performance of the asphalt material was analyzed by statistical means.

Experiment 3: Using the -18°C BBR test stiffness modulus as a representative low temperature evaluation index to determine the low temperature analysis area, the low temperature performance of the asphalt material was analyzed by statistical means.

The key steps for experiments 1-3 are as follows:

Key step 1: Select asphalt and high and low temperature properties:

In this paper, 6 kinds of asphalt are selected, and their basic properties and high and low temperature properties are shown in Table 1.

Table 1

Key Step 2: Frequency Sweep Experiment and Parameter Fitting:

The frequency sweep test was carried out on six asphalt materials, the frequency range was 0.1Hz～30Hz, and the recommended temperature range was 4℃～76℃. The modulus and phase angle values at each temperature and loading frequency were obtained, and the parameters were fitted and translated. Then, the fitting parameter results P ₁ ~ Pn are shown in Table 2, and the results of the data points after translation are shown in Figure 1-4.

Table 2 CAM model parameter fitting results

Key Step 3: Division of high and low temperature analysis areas:

In the frequency range f, the logarithmic frequency logf is continuously valued at equal intervals. For experiments 1-3, the correlation coefficients r _G and r _δ are calculated between -5 and 3 with an interval of 0.1, and they are changed with the logarithmic frequency. The change curves of r _G =F _G (logf) and r _δ =F _δ (logf) are drawn, and the results of specific experiment 1 are shown in Figure 5. The results of other implementation cases are similar and will not be repeated.

For experiments 1 to 3, the guarantee rate is 95%, and the significance level is α=0.05. According to the degree of freedom n-2=4, the threshold value of the correlation coefficient is determined by referring to the critical index table to be 0.8114. Using equations (4) and (5) and the correlation coefficient calculation formula, the logarithmic reduction frequency critical value relative to the complex modulus master curve and the phase angle master curve can be obtained by trial calculation. The calculation results of experiments 1 to 3 are shown in Table 3. Show.

Table 3 Analysis area results

Key step 4: regional statistical feature extraction and high and low temperature performance analysis:

The modulus and phase angle results obtained from FIGS. 1 to 4 are used for statistical analysis respectively in the analysis areas demarcated in Table 3. In this embodiment, the average value is selected for explanation, and the results are shown in Table 4.

First, let’s look at the results of specific experiment 1. According to the complex modulus results in Table 4, the high temperature performance in the full high temperature range is ranked as follows: Sample 2 > Sample 3 = Sample 5 > Sample 6 > Sample 4 > Sample 1, which is similar to the high temperature critical temperature of the original asphalt. The results (Sample 5>Sample 6>Sample 2=Sample 3>Sample 4>Sample 1) are completely different, which shows that traditional indicators cannot evaluate the performance in the full high temperature range, and it is indeed necessary to develop a quantitative analysis method of asphalt master curve. At the same time, by means of the joint analysis of phase angle, loss modulus and storage modulus, the evaluation and research of asphalt material performance will be more sufficient.

Table 4 Statistical analysis results in the analysis area

Claims (10)

1. a quantitative analysis method of asphalt master curve, is characterized in that described method comprises the following steps: Step 1: Obtain n groups of asphalt samples, and make the asphalt samples into asphalt thin slices; Among them, n≥3; Step 2: Obtain the complex modulus G*, damage modulus G', storage modulus G", and phase angle δ of the asphalt flake sample; Step 3: Select the reference temperature _TR , and at the reference temperature _TR , fit the complex modulus G* and phase angle δ obtained in step 2 through the CAM model, and use the complex modulus G* and phase angle δ at the same time. The goal is to minimize the sum of the squares of the residuals. Use the WLF equation and the Solver function method to solve the problem to obtain the displacement factor, the reduction frequency ω and the optimal parameter combination of the main curve.

in,

f _c , m, k, δ _m , R _d , f _d , m _d , C ₁ , C ₂ are all undetermined coefficients; Step 4. Repeat steps 1 to 3 for all asphalt samples obtained in step 1 to obtain the main curve parameter combinations P ₁ , P ₂ , . . . , P _n of all asphalt samples; Step 5: Select the evaluation indexes of high temperature and low temperature, and obtain the high temperature analysis area and the low temperature analysis area by using the combination of the master curve parameters of all asphalt samples obtained in step 4: Step 6. The complex modulus G*, damage modulus G', storage modulus G", and phase angle δ of the asphalt flake sample obtained in step 2 are transformed by the displacement factor obtained in step 3, and then the displacement is obtained. Complex modulus

The phase angle δ ₁ , damage modulus G′ ₁ and storage modulus G″ ₁ data, the data after the displacement falling in the high and low temperature analysis area are analyzed separately, and the comprehensive properties of the asphalt material at high and low temperature are analyzed by the analysis results. Evaluation obtains evaluation results. 2. A method for quantitative analysis of asphalt master curves according to claim 1, wherein: in the step 1, the asphalt sample is made into an asphalt thin sample by pouring; The size of the poured specimen is determined according to the type of asphalt, specifically: For asphalt without particle effect: the size of the specimen is Φ25mm×1mm; For asphalt with particle effect: the size of the specimen is Φ25mm×2mm. 3. A kind of asphalt master curve quantitative analysis method according to claim 1 and 2, it is characterized in that: in described step 2, obtain the complex modulus G*, damage modulus G', storage modulus of the asphalt thin slice sample G", phase angle δ, including the following steps: Step 21. Perform frequency scanning on the asphalt thin sample to obtain the shear stress response value τ, the strain response value γ, and the phase angle δ of the asphalt thin sample under the preset temperature range and the preset loading frequency range; Step 22: Obtain the complex modulus G* according to the shear stress response value τ ₀ , the strain response value γ ₀ , and the phase angle δ obtained in step 21:

where i is an imaginary number and t is the loading time; Step 23: Obtain the loss modulus G' and the storage modulus G" according to the complex modulus G* obtained in step 22: G′＝|G ^* |cosδ (2) G″=|G ^* |sinδ(3). 4 . The method for quantitative analysis of asphalt master curves according to claim 3 , wherein the preset temperature range in the step 21 is: 4°C to 76°C, and the preset loading frequency range is: 4 . 0.1Hz～30Hz. 5. a kind of asphalt master curve quantitative analysis method according to claim 3, is characterized in that: in described step 3, select reference temperature _TR , and under reference temperature _TR , the complex modulus G obtained in step 1 is * and the phase angle δ are fitted by the CAM model, and at the same time, the WLF equation and the EXCEL solver function module are used to solve the problem to obtain the displacement factor and the reduction frequency with the goal of minimizing the sum of the sum of the squares of the complex modulus G* and the phase angle δ residuals. ω and the main curve optimal parameter combination

The formula is as follows:

ω _r = ω×α _T (T) (7) where _fr is the loading frequency, I is a constant,

f is the specific frequency, ω is the reduced frequency corresponding to f, ω _r is the reduced frequency corresponding to f _r , α _T (T) is the displacement factor, T is the frequency sweep temperature,

f _c , m, k, δ _m , R _d , f _d , m _d , C ₁ , and C ₂ are undetermined coefficients. 6. a kind of asphalt master curve quantitative analysis method according to claim 5 is characterized in that: in described step 3, modulus and phase angle residual sum of squares are obtained in the following manner: S1. Calculate the residual sum of squares between the complex modulus G* and the calculated value of formula (4); S2, calculate the residual sum of squares between the phase angle δ and the calculated value of formula (5); S3. The sum of the squared residuals obtained by S1 and S2 is the sum of the squared residuals of the modulus and the phase angle. 7 . The method for quantitative analysis of asphalt master curves according to claim 6 , wherein the evaluation indexes of high temperature and low temperature are selected in the step 5, and the high temperature analysis area is obtained by using the master curve parameter combination of all asphalt samples obtained in the step 4. 8 . and cryogenic analysis area, including the following steps: Step 51: Obtain the complex modulus and phase angle at a specific frequency f according to the main curve parameter combination of all asphalt samples obtained in step 4; Step 52, select high temperature and low temperature evaluation index, and carry out correlation analysis with complex modulus and phase angle under f and high temperature evaluation index/low temperature evaluation index, obtain correlation coefficient r _G and r _δ ; Step 53: Obtain the correlation coefficient thresholds of r _G and r _δ respectively according to the correlation coefficients r _G and r _δ ; Step 54, utilize the trial calculation method to obtain the abscissa values f _G and f _δ of the corresponding modulus of the correlation coefficient threshold and the phase angle discrete distribution curve; Step 55. Obtain high temperature analysis area HT={f|f<min(f _G ,f _δ )} and low temperature analysis area LT={f|f>max(f _G ,f _δ )} according to f _G and f _δ . 8. a kind of asphalt master curve quantitative analysis method according to claim 7, is characterized in that: the high temperature evaluation index in described step five two is as follows: Rutting factor and multiple stress creep recovery test Jnr0.1, Jnr3.2 before and after asphalt aging; The low temperature evaluation index is: stiffness modulus and m value of trabecular bending test. 9. a kind of asphalt master curve quantitative analysis method according to claim 8, is characterized in that: in described step 53, obtain the correlation coefficient threshold of r _G and r _δ respectively according to correlation coefficient r _G and r _δ , including the following step: Step 531. Perform continuous values of logarithmic frequency logf in the range of frequency f corresponding to ω to obtain the discrete distribution relationship of the correlation coefficient of r _G and r _δ , that is, r _G =F _G (logf) and r _δ = F _δ (logf); Among them, F _G (), F _δ () are correlation analysis functions; Step 532: Determine the guarantee rate and the significance level a, and refer to the correlation coefficient critical value table according to the degree of freedom n-2 to determine the correlation coefficient threshold; where the significance level a is a constant. 10. A method for quantitative analysis of asphalt master curves according to claim 9, wherein in the step 6, statistical analysis is performed on the data after the displacement in the high and low temperature analysis area, including the following methods: averaging value, sum, the maximum slope value of the area, and the abscissa and ordinate values corresponding to the extreme point of the area.

Images