KR101155162B1 - Development of evaluation method to determine the frequency-asphalt modulus curve - Google Patents

Abstract

Method for determining the asphalt elastic modulus for each frequency for determining the master curve according to an embodiment of the present invention, measuring the temperature of the asphalt specimen; Impacting one section of the asphalt specimen to generate a P wave, and then performing a harmonic wavelet transform on the signals obtained through the first and second detectors attached to both ends of the asphalt specimen. step; Determining a dispersion curve indicating a change in P wave velocity (or modulus of elasticity) according to frequency using only a signal in a local region where the signal-to-noise ratio is maximized through the harmonic wavelet transformation. ; Determining the dispersion curve corresponding to each temperature by repeatedly performing the determination of the dispersion curve while changing the temperature of the asphalt specimen; Determining a transfer function using at least three or more dispersion curves of the plurality of dispersion curves; And calculating a horizontal movement distance required to move the dispersion curve corresponding to each temperature to the dispersion curve corresponding to a preset reference temperature through the transition function, and dispersing the temperature corresponding to each temperature based on the horizontal movement distance. Moving a curve to a dispersion curve corresponding to the reference temperature to determine a master curve.

Description

Development of evaluation method to determine the frequency-Asphalt modulus curve}

The present invention relates to a method for determining asphalt elastic modulus by frequency for determining a master curve, and more particularly, to determine a master curve representing a change in asphalt properties according to temperature and frequency change, and a frequency-elastic coefficient curve at an arbitrary site temperature. The present invention relates to a frequency-based asphalt elastic modulus determination method for determining a master curve by using a transition function.

Asphalt mixture is a material exhibiting visco-elastic properties and is subjected to loads having various sizes and loading speeds (frequency) according to various temperature changes according to seasonal changes and types and speeds of vehicles. Viscoelastic materials, such as asphalt, change their properties according to these temperature changes and load loading rates (frequency). Therefore, it is necessary to estimate the physical properties of asphalt materials according to temperature and frequency changes. Asphalt property changes according to temperature and frequency changes are represented by master curves.

The master curve is a frequency-elastic coefficient curve determined at the reference temperature. The frequency-elastic coefficient curve at any field temperature is determined by parallel shifting the master curve using a shifting factor. These master curves are important input data for asphalt pavement design and are very important for maintenance such as fatigue assessment of constructed asphalt pavement.

Test methods for the determination of master curves are given in AASHTO TP62-03 developed by NCHRP Project 9-19. Using asphalt specimens (10 cm diameter, 15 cm high cylinder), five temperatures (-10 ° C, 4.4 ° C, 21.1 ° C, 37.8 ° C, 54.4 ° C) and five excitation frequencies (25, 10.5, 1.0, 0.5, 0.1HZ) Perform the experiment on. The test uses a uniaxial compression tester such as UTM at each temperature, sequentially applying dynamic excitation in the form of a continuous sinusoidal function with five given excitation frequencies and measuring the strain at each frequency using the LVDT. The relationship between is used to determine the modulus of elasticity at the small strain.

Through these experiments, the elastic modulus values for each frequency are determined and then the shifting factor is determined. The horizontal parallel translation of the determined frequency-elastic coefficient curves at each temperature coincides with each other. The transition function indicates that the frequency-elastic coefficient curve obtained at an arbitrary temperature coincides with the frequency-elastic coefficient curve at the reference temperature. The transition function may be determined using data of a region in which elastic modulus determined at different temperatures, such as the rectangular box region of FIG. 1, has the same value.

Once the transition function is determined, all frequency-elastic coefficient curves are shifted to the reference temperature T ₂ to finally complete the master curve. Using the completed master curve and the transition function, it is possible to determine the frequency-elastic coefficient curve at any temperature.

The master curve determination assay given in AASHTO TP62-03 is complex and difficult in the testing process and equipment. The cost of the test is expensive and the test time is also very long. The difficulty of this test is an obstacle to the use of the actual master curve. In particular, in Korea, due to the problem of the experimental equipment, the determination and use of the master curve in the actual field is extremely poor. In order to solve various problems of the existing methods, methods using nondestructive testing using elastic wave propagation characteristics have been studied.

Recent attempts include the use of ultrasonic using non-destructive testing (Ultrasonic test) and impact resonance method (Impact resonance method). This method allows for low-cost, rapid experiments using very simple test equipment consisting of one or two detectors (accelerometers) and one excitation source, but both methods can be used to perform experiments with varying frequencies at a given temperature. It is not possible to determine the elastic modulus at only one frequency.

Therefore, it is not possible to determine the transition function that reflects the change of physical properties with temperature, which is an important factor in the evaluation of asphalt behavior, and it is necessary to assume the transition function when determining the master curve. In addition, since the number of data that can be used for determining the master curve is small, precise master curve determination is difficult.

"Image processing method for the analysis of plastic deformation behavior of asphalt mixture" disclosed in Republic of Korea Patent Registration 10-0564329 relates to a method of measuring the plastic deformation characteristics of asphalt mixtures to determine the movement state of aggregates of asphalt mixture specimens Using the photographed specimens taken in stages, the image processing technique is applied to measure the total amount of deformation occurring on the surface of the test specimen. Through this, it is possible to evaluate the plastic deformation characteristics of the asphalt pavement, but there is a problem that can not reflect the influence of temperature, which is an important factor in the evaluation of asphalt behavior.

In the present invention, HWAW (Harmonic Wavelet Analysis of Waves) method is applied to determine the master curve of asphalt to solve the problems and limitations of the existing methods. The HWAW method was developed to determine the dispersion curve of a wave (frequency-phase velocity curve or frequency-elastic coefficient curve). Therefore, it is possible to apply directly to the determination of the frequency-elastic coefficient curve of asphalt material for the determination of the master curve.

The HWAW method can be quickly tested at low cost by using simple test equipment similar to the existing non-destructive test method, and at the same time, it is possible to determine the elastic modulus at the frequency band instead of one frequency. Therefore, it is possible to determine the transition function by performing experiments by changing the temperature, and it is possible to accurately determine the master curve due to the large number of data that can be used to determine the master curve.

In the present invention, using the Harmonic Wavelet Analysis of Waves (HWAW) method, which is the latest signal processing method recently developed by the present applicant among various non-destructive testing methods, the elastic modulus determination system according to the frequency of asphalt material for determining the master curve is presented. do. The present invention provides an experimental system that can be easily used in the field by using a data analysis technique for determining the elastic modulus according to the frequency of asphalt material and using an automated data acquisition and analysis GUI program. .

The present invention has been made to improve the prior art as described above, the method using the harmonic wavelet (Harmonic Wavelet) transform method using the HWAW method and the phase angle expansion method using the HW-Phase spectrum through two detectors It is an object of the present invention to provide a method for determining asphalt elastic modulus by frequency for determining a master curve which enables the determination of a dispersion curve with reliability by determining a P wave velocity for each frequency of a wave.

In order to achieve the above object and solve the problems of the prior art, the method for determining the asphalt elastic modulus for each frequency for determining the master curve according to an embodiment of the present invention comprises the steps of measuring the temperature of the asphalt specimen; Impacting one section of the asphalt specimen to generate a P wave, and then performing a harmonic wavelet transform on the signals obtained through the first and second detectors attached to both ends of the asphalt specimen. step; Determining a dispersion curve indicating a change in P wave velocity (or modulus of elasticity) according to frequency using only a signal in a local region where the signal-to-noise ratio is maximized through the harmonic wavelet transformation. ; Determining the dispersion curve corresponding to each temperature by repeatedly performing the determination of the dispersion curve while changing the temperature of the asphalt specimen; Determining a transfer function using at least three or more dispersion curves of the plurality of dispersion curves; And calculating a horizontal movement distance required to move the dispersion curve corresponding to each temperature to the dispersion curve corresponding to a preset reference temperature through the transition function, and dispersing the temperature corresponding to each temperature based on the horizontal movement distance. Moving a curve to a dispersion curve corresponding to the reference temperature to determine a master curve.

In addition, the first sensor and the second sensor in the frequency-specific asphalt elastic modulus determination method for determining the master curve according to an embodiment of the present invention is characterized in that the accelerometer.

In addition, in the method for determining the asphalt elastic modulus for each frequency to determine the master curve according to an embodiment of the present invention, only the signal in the local region where the signal to noise ratio is maximized through the harmonic wavelet transformation is selected. Determining a variance curve representing a change in the P wave velocity (or modulus of elasticity) with respect to frequency corresponds to the center frequency ((m + n) π) of the harmonic wavelet function W _{m , n} (ω) Determining a group delay time t _g ¹ , t _g ² and a phase delay time t _ph ¹ , t _ph ² ; Determining the group delay time and phase delay time for the entire frequency band by repeating the determination of the group delay time and the phase delay time; And calculating a group velocity (V _gr ) and a phase velocity (V _ph ) by using the length of the asphalt specimen, the group delay time, and the phase delay time.

In addition, the group corresponding to the center frequency ((m + n) π) of the harmonic wavelet function (W _{m , n} (ω)) in the frequency-specific asphalt elastic modulus determination method for determining the master curve according to an embodiment of the present invention Determining the delay time (t _g ¹ , t _g ² ) and phase delay time (t _ph ¹ , t _ph ² ), the group delay time (t _g ¹ , t in the first and second detectors) _g ² ) is the harmonic wavelet coefficient (a _{m , n} ¹ , a _{m , n} ²⁾ Determining a time at which the size of C) becomes maximum; Determining a phase value θ ₁ corresponding to the group delay time t _g ¹ from phase information of the harmonic wavelet coefficients a _{m and n} ¹ for the first detector; The phase information of the harmonic wavelet coefficient (a _{m , n} ² ) for the second detector is located on the left side of the group delay time (t _g ² ) and has a phase value (θ ₁ ). group delay time (t _g ²⁾ closest to the time (t _L) and the group delay time (t _g ²⁾ the group delay time of several hours on the right side, and with the phase value (θ ₁₎ (t in the determining a time t _R closest to _g ² ); And determine the phase delay time t _ph ¹ for the first detector as the group delay time t _g ¹ for the first detector and the phase delay time t _ph ² for the second detector. Determining a time closer to the group lag time (t _g ² ) for the second detector among the adjacent times (t _L , t _R ).

In addition, in the method for determining the asphalt elastic modulus for each frequency to determine the master curve according to an embodiment of the present invention, only the signal in the local region where the signal to noise ratio is maximized through the harmonic wavelet transformation is selected. Determining a variance curve representing a change in the P wave velocity (or modulus of elasticity) with respect to frequency corresponds to the center frequency ((m + n) π) of the harmonic wavelet function W _{m , n} (ω) The maximum magnitude time (t _max ¹ , t _max ² ) is the harmonic wavelet coefficient (a _{m , n} ¹ , a _{m , n} ² Determining a time at which the size of C) becomes maximum; Determining a phase value (φ ₁ ) corresponding to the maximum size time (t _max ¹ ) from the phase information of the harmonic wavelet coefficients (a _{m , n} ¹ ) for the first detector; Determining a phase value φ ₂ corresponding to the maximum magnitude time t _max ² from phase information of the harmonic wavelet coefficients a _{m and n} ² for the second detector; Determining a time-phase function (φ _Recover ² (t)) of the reconstructed folded form in the second detector using the phase value φ ₂ for the second detector; Determining a phase difference φ _diff (t) corresponding to the center frequency (m + n) π using the time-phase function and the phase value φ ₁ for the first detector; Determining the phase angle spectrum by repeatedly performing the determination of the phase difference φ _diff (t) to determine the phase difference for the entire frequency band; Determining an actual phase difference δ (f) from the phase angle spectrum; And determining a dispersion curve using the actual phase difference.

In addition, in the method for determining the asphalt elastic modulus for each frequency for determining the master curve according to an embodiment of the present invention, the transition function includes at least three dispersion curves and Arenius including P-wave velocity (elastic coefficient) bands overlapping each other. It is characterized by using the Arrenius method.

According to the frequency-specific asphalt elastic modulus determination method for determining the master curve according to an embodiment of the present invention, it is possible to quickly experiment at a low cost by using a simple test equipment and at the same time, unlike the existing non-destructive testing method, one frequency at each given temperature It is possible to determine the modulus of elasticity in the non-frequency band, determine the transition function by performing experiments with varying temperatures, and precisely determine the master curve due to the large number of data available for determining the master curve.

1 is a diagram illustrating the determination of a transition function using a dispersion curve for each temperature.
2 is a diagram illustrating decomposition of a time domain signal through harmonic wavelet transformation.
3 shows determination of phase velocity and group velocity of each frequency component decomposed in the time domain;
4 shows determination of group delay time and phase delay time at an arbitrary frequency (((m + n) π).
Fig. 5 shows the determination of the maximum size time at any frequency (((m + n) π).
6 shows the determination of the time-phase function φ _Recover ² (t) and the phase difference.
7 is a view showing an experimental configuration for implementing the method for determining the asphalt elastic modulus for each frequency for determining the master curve according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

According to one embodiment of the invention, the detectors are located on both ends of the asphalt specimen, and a vertical excitation is applied to the upper surface to generate P waves by using a steel ball. In order to apply a constant energy excitation at a constant position, the drop may be freely dropped using a dropping device.

According to one embodiment of the present invention, as described above, metal beads can be used as the excitation source for generating P waves. The excitation source must be able to generate high energy around natural frequencies. As the diameter of the iron beads increases, more low frequency components are generated, and as the diameter decreases, more high frequency components are generated.

For example, almost all of the wave components generated by a 2 cm diameter ball are concentrated in the low frequency band below the resonant frequency where the error occurs when there is a reflective surface. In contrast, in the case of a 1.5 cm diameter steel ball, almost all energy is concentrated near the resonance frequency.

According to one embodiment of the invention, it is preferable to use as a circle having a 1.5 cm diameter iron ball. The sensor can be a PCB353B15 accelerometer.

 According to one embodiment of the present invention, the P-wave velocity (or modulus of elasticity) curve according to the frequency of the asphalt material is determined using signals in the time domain measured at two measurement positions. In the presence of multiple reflecting surfaces, distortion of the measured signal can occur. Such distortion is not large when the damping is large, such as asphalt, and the degree of distortion is minimized around the natural frequency (or resonance frequency).

According to one embodiment of the invention, volume waves, in particular P waves, are generated and propagated along the interior of the specimen by vertical excitation applied to the asphalt specimen surface. The elastic modulus can be determined via E = (density) × (P wave velocity) ² . Therefore, it is possible to determine the elastic modulus change curve according to the frequency of the asphalt material by determining the P wave velocity change curve according to the frequency.

Detectors are installed on both sides of the asphalt specimen, and one of them can be shocked to generate waves, and then the signals can be measured by the detector and used for speed measurement. At this time, both ends of the specimen serve as reflecting surfaces, and P waves repeat between the two reflecting surfaces. The signal reflected from the reflecting surface is in phase with the input wave incident on the reflecting surface, but the amplitude is doubled, and the wave propagating along the inside of the asphalt specimen is gradually reduced in amplitude by damping as the moving distance increases.

If the attenuation ratio is large, even if the signal is distorted by multiple reflections, the distortion of the signal measured in the wide frequency band around the frequency band corresponding to the natural frequency (wavelength component whose wavelength is around 2 × sample length) is not large. not. Therefore, the velocity of the P wave propagating along the medium between the two end faces of the specimen can be reliably determined using the signals measured by the detectors installed at both end faces.

Even when there are multiple reflecting surfaces, if the damping ratio is large, such as asphalt, the detectors can be installed on both sides of the specimen, and then the signals measured by these two detectors can be used to effectively measure the P-wave velocity (or modulus of elasticity) for each frequency. .

2 and 3 illustrate the basic principle of the HWAW method. FIG. 2 is a diagram illustrating decomposition of a time domain signal through harmonic wavelet transformation, and FIG. 3 is a phase velocity and group velocity of each frequency component resolved in the time domain. The figure which shows the determination of.

The HWAW method determines the phase velocity and group velocity of a wave propagating through a medium and is used to determine the dispersion curve of a wave propagating between two detectors. The HWAW method decomposes the signal obtained from each detector into each frequency component through harmonic wavelet transform, and then localized energy information around the energy-concentrated area in the energy time-frequency map, i.e. the maximum energy line with the highest signal-to-noise ratio. In addition, the dispersion curve is determined using only phase information. Since the HWAW method uses only the energy-intensive local area information, it is very effective to remove the effects of background noise present in the laboratory compared to the existing methods. This feature enables reliable dispersion curve determination using small energy sources.

The process of determining the dispersion curve showing the change of the P wave velocity with the frequency of asphalt material using the HWAW method is as follows.

Measuring the temperature of the asphalt specimen; Performing a harmonic wavelet transform on the signal obtained through the first detector and the second detector; Group lag time (t _g ¹ , t _g ² ) and phase lag time (t _ph ¹ , t _ph ² ) corresponding to the center frequency ((m + n) π) of the harmonic wavelet function (W _{m , n} (ω)) Determining; Determining the group delay time and phase delay time for the entire frequency band by repeating the determination of the group delay time and the phase delay time; And calculating a group velocity (V _gr ) and a phase velocity (V _ph ) by using the length of the asphalt specimen, the group delay time, and the phase delay time.

As shown in (a) and (b) of FIG. 4, the group lag times t _g ¹ and t _g ^{2 in} the first and second detectors are harmonic wavelet coefficients a _{m and n} ^1. , a _{m , n} ² ) Is the maximum time. As shown in (c) of FIG. 4 _, a phase value corresponding to the group delay time t _g ¹ is θ ₁ from the phase information of the harmonic wavelet coefficients a _{m and n} ¹ for the first detector. That Able to know.

As shown in FIG. 4D, t _L and t _R are determined from phase information of the harmonic wavelet coefficients a _{m and n} ² for the second detector. _L t is the closest time to the group delay time (t _g ²⁾ of the number of times having the position and θ ₁ on the left side of the group delay time (t _g ²⁾ a phase value. In addition, t _R is the closest time to the group delay time (t _g ²⁾ of several hours with the position θ _1, and on the right side of the group delay time (t _g ²⁾ a phase value.

The phase lag time t _ph ¹ for the first detector is equal to the group lag time t _g ¹ for the first detector and the phase lag time t _ph ² for the second detector is the closest. The time t _L , t _R is determined to be closer to the group lag time t _g ² for the second detector.

이고 상기 위상속도는

이다.When the length of the asphalt specimen is D, the group velocity is

And the phase velocity is

to be.

The HW-Phase spectrum method is a method developed to determine the phase angle spectrum between two signals. The conventional method of determining the phase angle spectrum using the Fourier transform is difficult to obtain reliable results in the presence of noise such as reflected waves by using the signal for the entire measured time domain, whereas the HW-Phase spectrum method Like the HWAW method, the harmonic wavelet transform can effectively eliminate the effects of noise such as reflected waves because only the signals in the time domain where energy is concentrated in the entire time domain, that is, the signal-to-noise ratio is maximized, are used.

Once the phase angle spectrum is determined by the HW-Phase spectrum method, the speed for each frequency can be easily determined by the phase angle expansion method. Compared with the HWAW method, it is possible to determine the dispersion curve with the same degree of reliability in the presence of noise. The process of determining the dispersion curve showing the change of P wave velocity with frequency of asphalt material using HW-Phase spectrum method is as follows.

Measuring the temperature of the asphalt specimen; Performing a harmonic wavelet transform on the signal obtained through the first detector and the second detector; The maximum magnitude time (t _max ¹ , t _max ² ) corresponding to the center frequency ((m + n) π) of the harmonic wavelet function (W _{m , n} (ω)) is determined by the harmonic wavelet coefficient (a _{m , n} ¹ , a _{m , n} ² Determining a time at which the size of C) becomes maximum; Determining a phase value (φ ₁ ) corresponding to the maximum size time (t _max ¹ ) from the phase information of the harmonic wavelet coefficients (a _{m , n} ¹ ) for the first detector; Determining a phase value φ ₂ corresponding to the maximum magnitude time t _max ² from phase information of the harmonic wavelet coefficients a _{m and n} ² for the second detector; Determining a time-phase function (φ _Recover ² (t)) of the reconstructed folded form in the second detector using the phase value φ ₂ for the second detector; Determining a phase difference φ _diff (t) corresponding to the center frequency (m + n) π using the time-phase function and the phase value φ ₁ for the first detector; Determining the phase angle spectrum by repeatedly performing the determination of the phase difference φ _diff (t) to determine the phase difference for the entire frequency band; Determining an actual phase difference δ (f) from the phase angle spectrum; And determining a dispersion curve using the actual phase difference.

As shown in FIG. 5, the maximum size times t _max ¹ and t _max ² corresponding to the center frequency (m + n) π of the harmonic wavelet function W _{m , n} (ω) are harmonic wavelets. It is time when the magnitude | size of the coefficient (a _{m , n} ¹ , a _{m, n} ² ) becomes the maximum. Fig. 6 shows the determination of the time-phase function φ _Recover ² (t) and the phase difference.

The time-phase function φ _Recover ² (t) of the restored folded form in the second detector may be implemented through Equation 1.

The phase difference φ _diff (t) corresponding to the center frequency (m + n) π may be implemented through Equation 2.

로 구현될 수 있다. 이에, 분산 곡선은 수학식 3을 통해 구현될 수 있다.The phase angle spectrum is in a folded form, and in order to determine a phase angle difference between two detectors, the actual phase difference may be determined by adding 2π of an appropriate number (number of jumps) to the folded phase angle. That is, the actual phase difference δ (f) is

It can be implemented as. Thus, the dispersion curve may be implemented through Equation 3.

The dispersion curve, which shows the properties (wave velocity or modulus) of each asphalt material by frequency, changes with temperature. Therefore, for maintenance and design of asphalt pavement, it is necessary to determine the change of material properties with temperature. In general, asphalt materials have the same modulus of elasticity at high temperature and low excitation frequencies as well as modulus at low temperature and high excitation frequencies. That is, when the dispersion curves determined at the respective temperatures are moved in parallel in the horizontal direction, they coincide with each other.

와 같다. 여기서, a_T는 전이 함수이고, f_T는 온도 T에서의 주파수이며, f_T0은 기준 온도 T₀에서의 주파수이다. 전이 함수는 온도만의 함수로서

와 같은 2차식으로 모사할 수 있다.The transfer function is a function representing the horizontal moving distance (parallel moving distance on the frequency axis) required to move the dispersion curve determined at each individual temperature to the dispersion curve corresponding to the reference temperature. In the present invention, the Arrenius method is used. To determine the transition function. The relationship between travel distance, temperature, and frequency in the horizontal direction

Same as Where a _T is a transition function, f _T is the frequency at temperature T, and f _T0 is the frequency at reference temperature T ₀ . The transition function is a function of temperature only

Can be simulated in quadratic such as

To determine the transition function, a dispersion curve determined at at least three temperatures is required, which must include bands of P-wave velocity (or modulus of elasticity) that overlap each other. Velocity bands that overlap each other are used to determine the amount of horizontal shift required to match the dispersion curve corresponding to the reference temperature (one of the plurality of temperatures with the dispersion curve) and the dispersion curve corresponding to each temperature.

Using these determined values, two unknown A and B values are determined to determine the transition function. Once the transition function is determined, the horizontal distance required to move the dispersion curve determined at any temperature to the dispersion curve at the reference temperature is determined and the master curve is determined through this horizontal parallel movement.

7 is a view showing an experimental configuration for implementing a method for determining the asphalt elastic modulus for each frequency for determining the master curve according to an embodiment of the present invention. As described above, according to the present invention, it is possible to perform a quick experiment at low cost by using a simple test equipment, and at the same time, unlike the existing non-destructive testing method, it is possible to determine the elastic modulus in the frequency band instead of one frequency at each given temperature. We can determine the transition function by performing experiments by changing the number of points, and because of the large number of data that can be used to determine the master curve, precise master curve can be determined.

As described above, the present invention has been described by way of limited embodiments and drawings, but the present invention is not limited to the above-described embodiments, which can be variously modified and modified by those skilled in the art to which the present invention pertains. Modifications are possible. Accordingly, the spirit of the present invention should be understood only in accordance with the following claims, and all equivalents or equivalent variations thereof are included in the scope of the present invention.

Claims (6)

Measuring the temperature of the asphalt specimen;
Impacting one end surface of the asphalt specimen to generate a P wave, and then performing a harmonic wavelet transform on the signals obtained through the first and second detectors attached to both ends of the asphalt specimen. step;
Determining a dispersion curve indicating a change in P wave velocity (or modulus of elasticity) according to frequency using only a signal in a local region where the signal-to-noise ratio is maximized through the harmonic wavelet transformation. ;
Determining the dispersion curve corresponding to each temperature by repeatedly performing the determination of the dispersion curve while changing the temperature of the asphalt specimen;
Determining a transfer function using at least three or more dispersion curves of the plurality of dispersion curves; And
The horizontal curve is required to move the dispersion curve corresponding to each temperature to the dispersion curve corresponding to a preset reference temperature through the transition function, and the dispersion curve corresponding to each temperature is calculated based on the horizontal movement distance. Determining a master curve by moving a to a dispersion curve corresponding to the reference temperature
Including,
The transition function is determined by using at least three dispersion curves including P-wave velocity (elastic coefficient) bands overlapping each other and the Arrenius method. How to decide. The method of claim 1,
The method of determining the asphalt elastic modulus for each frequency for determining the master curve, characterized in that the first detector and the second detector is an accelerometer. The method of claim 1,
Determining a dispersion curve indicating a change in P wave velocity (or modulus of elasticity) according to frequency using only a signal in a local region where the signal-to-noise ratio is maximized through the harmonic wavelet transformation. Is,
Group delay time (t _g ¹ , t _g ² ) and phase delay time (t _ph ¹ , t _ph ² ) corresponding to the center frequency ((m + n) π) of the harmonic wavelet function (W _{m, n} (ω)) Determining;
Determining the group delay time and phase delay time for the entire frequency band by repeating the determination of the group delay time and the phase delay time; And
Calculating a group velocity (V _gr ) and a phase velocity (V _ph ) using the length of the asphalt specimen, the group delay time, and the phase delay time.
Including,
Group delay time (t _g ¹ , t _g ² ) and phase delay time (t _ph ¹ , t _ph ² ) corresponding to the center frequency ((m + n) π) of the harmonic wavelet function W _{m, n} (ω) ) Is determined by
The group delay time (t _g ¹ , t _g ² ) in the first and second detectors is determined as a time at which the magnitude of the harmonic wavelet coefficients (a _{m, n} ¹ , a _{m, n} ² ) becomes maximum. Making;
Determining a phase value θ ₁ corresponding to the group delay time t _g ¹ from phase information of the harmonic wavelet coefficient a _{m, n} ¹ for the first detector;
The phase information of the harmonic wavelet coefficient (a _{m, n} ² ) for the second detector is located on the left side of the group delay time (t _g ² ) and has a phase value (θ ₁ ). group delay time (t _g ²⁾ closest to the time (t _L) and the group delay time (t _g ²⁾ the group delay time of several hours on the right side, and with the phase value (θ ₁₎ (t in the determining a time t _R closest to _g ² ); And
The phase delay time t _ph ¹ for the first detector is determined as the group delay time t _g ¹ for the first detector, and the phase delay time t _ph ² for the second detector is determined to be the closest. Determining a time t _L , t _R that is closer to the group lag time t _g ² for the second detector.
Asphalt elastic modulus determination method for each frequency for determining the master curve comprising a. delete The method of claim 1,
Determining a dispersion curve indicating a change in P wave velocity (or modulus of elasticity) according to frequency using only a signal in a local region where the signal-to-noise ratio is maximized through the harmonic wavelet transformation. Is,
The maximum magnitude time (t _max ¹ , t _max ² ) corresponding to the center frequency ((m + n) π) of the harmonic wavelet function (W _{m , n} (ω)) is determined by the harmonic wavelet coefficient (a _{m , n} ¹ , a _{m , n} ² Determining a time at which the size of C) becomes maximum;
Determining a phase value (φ ₁ ) corresponding to the maximum size time (t _max ¹ ) from the phase information of the harmonic wavelet coefficients (a _{m , n} ¹ ) for the first detector;
Determining a phase value φ ₂ corresponding to the maximum magnitude time t _max ² from phase information of the harmonic wavelet coefficients a _{m and n} ² for the second detector;
Determining a time-phase function (φ _Recover ² (t)) of the reconstructed folded form in the second detector using the phase value φ ₂ for the second detector;
Determining a phase difference φ _diff (t) corresponding to the center frequency (m + n) π using the time-phase function and the phase value φ ₁ for the first detector;
Determining the phase angle spectrum by repeatedly performing the determination of the phase difference φ _diff (t) to determine the phase difference for the entire frequency band;
Determining an actual phase difference δ (f) from the phase angle spectrum; And
Determining a dispersion curve using the actual phase difference
Asphalt elastic modulus determination method for each frequency for determining the master curve comprising a. delete

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