Method for predicting asphalt fatigue crack length based on continuous damage mechanics

Abstract

The invention provides a method for predicting asphalt fatigue crack length based on continuous damage mechanics, and relates to the technical field of road engineering. The method comprises the following steps: preparing an asphalt test piece; selecting test temperature and loading frequency; performing a strain amplitude scanning test to determine a damage critical point of the asphalt test piece; performing a time scanning test, and collecting data of the dynamic shear modulus changing along with the loading period; and predicting the fatigue crack length of the asphalt test piece in a certain loading period according to an asphalt fatigue crack length prediction formula. According to the method, the prediction formula of the asphalt fatigue crack length is deduced by establishing the torque balance equation, the dissipated strain energy balance equation and the reversible strain energy balance equation, and the influence of nonlinearity on the asphalt dynamic shear modulus is considered, so that compared with an existing prediction formula, the length of the asphalt fatigue crack can be predicted more accurately; and a new research thought is provided for deeply exploring the fatigue characteristics of the asphalt material.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of road engineering, and particularly relates to a method for predicting asphalt fatigue crack length based on continuous damage mechanics. BACKGROUND

[0002] Fatigue cracking caused by repeated traffic load is one of the main diseases of asphalt pavement. The appearance of fatigue cracks will lead to uneven load transfer, water intrusion and chemical substance penetration, further leading to deterioration of asphalt pavement condition, thereby affecting the service life of asphalt pavement. Asphalt is one of the main components of asphalt mixture, and accurate evaluation of the fatigue performance of asphalt helps to select the best asphalt at the design stage of asphalt mixture, thereby improving the ability of asphalt mixture to resist fatigue cracking.

[0003] At present, the mainstream test methods for studying asphalt fatigue performance at home and abroad are time scanning test and linear amplitude scanning test, both of which are carried out by dynamic shear rheometer, and the evaluation indexes of the two tests are both fatigue life. Most scholars in the research of asphalt fatigue performance are committed to the definition method and theoretical prediction method of asphalt fatigue life, and lack of in-depth study on the fatigue damage evolution mechanism of asphalt under load.

[0004] The fatigue damage evolution mechanism of asphalt refers to the development law of fatigue cracks of asphalt under load. The research of Hints et al. shows that after being subjected to repeated shear load, the cylindrical asphalt specimen will initially crack at the edge; with the increase of loading period, the fatigue crack will gradually expand to the center of the asphalt specimen, thereby reducing the effective radius of the asphalt specimen. Based on this observation, Hints et al. proposed a prediction formula of asphalt fatigue crack length to characterize the evolution mechanism of asphalt fatigue damage. Subsequently, Zhang et al. established a torque balance equation and a dissipated strain energy balance equation based on continuous damage mechanics, and derived a new prediction formula of fatigue crack length. The research of Zhang et al. shows that the crack length predicted by the equation is smaller than the actual crack length in the later stage of time scanning test. However, when Zhang et al. derived the prediction formula of asphalt fatigue crack length, they only established the dissipated strain energy balance equation, without considering the reversible strain energy prediction formula, and the prediction formula takes the dynamic shear modulus of asphalt in the linear viscoelastic stage as the reference state, without considering the influence of nonlinearity on the dynamic shear modulus of asphalt, so it cannot accurately predict the fatigue crack length of asphalt.

[0005] To address the aforementioned problems, this invention discloses a method for predicting the length of asphalt fatigue cracks based on continuous damage mechanics. This method derives a prediction formula for the length of asphalt fatigue cracks by establishing torque balance equations, dissipated strain energy balance equations, and reversible strain energy balance equations, and considers the influence of nonlinearity on the dynamic shear modulus of asphalt. Therefore, compared with existing prediction formulas, it can predict the length of asphalt fatigue cracks more accurately. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for predicting the length of asphalt fatigue cracks based on continuous damage mechanics. By establishing torque balance equations, dissipated strain energy balance equations, and reversible strain energy balance equations, a prediction formula for the length of asphalt fatigue cracks is derived. Furthermore, the influence of nonlinearity on the dynamic shear modulus of asphalt is considered. Therefore, compared with existing prediction formulas, this method can more accurately predict the length of asphalt fatigue cracks.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for predicting the length of fatigue cracks in asphalt based on continuous damage mechanics, the method comprising the following steps: S1. After heating the asphalt to a flowing state, prepare asphalt specimens; S2. Select the test temperature and loading frequency according to requirements; S3. Using a dynamic shear rheometer, strain amplitude scanning tests are performed on asphalt specimens at the test temperature and loading frequency selected in step S2. Data on the dynamic shear modulus and phase angle as a function of strain amplitude are collected to determine the critical damage point of the asphalt specimens. S4. Based on the critical damage point of the asphalt specimen determined in step S3, select the strain amplitude, and continue to use a dynamic shear rheometer to conduct a strain-controlled time-scan test on the asphalt specimen at the test temperature and loading frequency selected in step S2. Collect data on the changes in dynamic shear modulus and phase angle with the loading cycle to determine the initial dynamic shear modulus of the asphalt specimen. During this period, the fatigue cracks generated in the asphalt specimen are radial cracks, which extend from the edge of the asphalt specimen inward. S5. Substitute the initial dynamic shear modulus determined in step S4 and the dynamic shear modulus of the asphalt specimen in a certain loading cycle into the prediction formula for the fatigue crack length of asphalt, and the fatigue crack length of the asphalt specimen in that loading cycle can be predicted. The prediction formula is as follows: in, N Number of loading cycles; c ( N ) for asphalt specimens at the 1st N The length of fatigue cracks per loading cycle; r 0 represents the initial radius of the asphalt specimen; |G N G is the dynamic shear modulus of the asphalt specimen at the first loading cycle; N G G0 is the initial dynamic shear modulus of the asphalt specimen.

[0008] Preferably, the way of determining the damage critical point of the asphalt specimen in step S3 is that, according to the data of the dynamic shear modulus and the phase angle changing with the strain amplitude, a curve of the dynamic shear modulus changing with the strain amplitude is drawn, and the damage critical point of the asphalt specimen is determined according to the 5% drop of the dynamic shear modulus of the asphalt specimen.

[0009] Preferably, after the time scanning test in step S4 is finished, a curve of the strain amplitude of the asphalt specimen changing with the loading cycle is drawn, and the dynamic shear modulus corresponding to the loading cycle when the strain amplitude of the asphalt specimen reaches the set strain amplitude is selected as the initial dynamic shear modulus of the asphalt specimen.

[0010] Preferably, when the strain amplitude scanning test in step S3 and the time scanning test in step S4 are performed, a parallel plate clamp with a diameter of 8 mm is used, and the distance between the upper and lower parallel plates is set to 2 mm.

[0011] Preferably, the prediction formula in step S5 is derived based on the torque balance equation, the dissipated strain energy balance equation and the reversible strain energy balance equation.

[0012] The present application provides a method for predicting the fatigue crack length of asphalt based on continuous damage mechanics, which has the following advantages compared with the prior art: The present application is based on the theory of continuous damage mechanics, and the prediction formula of the fatigue crack length of asphalt is derived by establishing the torque balance equation, the dissipated strain energy balance equation and the reversible strain energy balance equation. The prediction formula shows that the fatigue crack length of the asphalt specimen at a certain loading cycle is related to the initial dynamic shear modulus of the asphalt specimen and the dynamic shear modulus at the loading cycle. The present application proposes a method for determining the initial dynamic modulus of the asphalt specimen, that is, when the strain amplitude of the asphalt specimen reaches the set strain amplitude, the dynamic shear modulus corresponding to the loading cycle is selected as the initial dynamic shear modulus of the asphalt specimen. Compared with the existing prediction formula of the fatigue crack length, the present application considers the influence of the reversible strain energy and the nonlinear viscoelasticity on the fatigue crack propagation, can more accurately represent the fatigue damage evolution mechanism of asphalt under load, realizes the quantitative analysis of the fatigue cracking process of asphalt, and provides a new research idea for further exploring the fatigue characteristics of asphalt materials. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 The method for selecting the initial modulus of the asphalt specimen of the present application is shown in the figure; Figure 2 ​​The fracture image of the asphalt test piece in Embodiment 1 of the present application; Figure 3 The schematic diagram for calculating the crack length according to the pixel size in Embodiment 1 of the present application; Figure 4 The fracture image of the asphalt test piece in Embodiment 4 of the present application; Figure 5 The schematic diagram for calculating the crack length according to the pixel size in Embodiment 4 of the present application; Figure 6 The relationship diagram between the predicted fatigue fracture length and the actual fatigue fracture length. DETAILED DESCRIPTION

[0014] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in a clear and complete manner in combination with the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0015] Embodiment 1 Method for predicting asphalt fatigue crack length based on continuous damage mechanics: S1, 70# base asphalt is taken as the research object, and the asphalt is sequentially subjected to short-term aging treatment by a rotary thin film oven test and long-term aging treatment by a pressure aging test. The aged 70# base asphalt is heated to a flowing state, and a cylindrical asphalt test piece with a diameter of 8 mm is prepared by using a silica gel mold method. After the asphalt test piece is cooled, it is demolded for standby use; S2, the test temperature and the loading frequency are selected as 20°C and 10 Hz, respectively; S3, a strain amplitude scanning test is performed on the asphalt test piece by using a dynamic shear rheometer at 20°C and 10 Hz, the diameter of the parallel plate clamp is 8 mm, the distance between the upper and lower parallel plates is set to 2 mm, and the data of the dynamic shear modulus and the phase angle changing with the strain amplitude are collected. The curve of the dynamic shear modulus changing with the strain amplitude is drawn, and the damage critical point of the asphalt test piece is determined according to the judgment basis that the dynamic shear modulus of the asphalt test piece decreases by 5%; S4, according to the damage critical point of the asphalt test piece determined in step S3, a strain control time scanning test is performed on the asphalt test piece by using a dynamic shear rheometer at 20°C and 10 Hz, the diameter of the parallel plate clamp is 8 mm, the distance between the upper and lower parallel plates is set to 2 mm, and the data of the dynamic shear modulus and the phase angle changing with the loading period are collected. When the strain amplitude of the asphalt test piece reaches the set strain amplitude, the dynamic shear modulus corresponding to the loading period is selected as the initial dynamic shear modulus of the asphalt test piece, for example,Figure 1 As shown. When the dynamic shear modulus of the asphalt specimen in the current loading cycle decreased by 80% compared with its initial dynamic shear modulus, the test was terminated, and the dynamic shear modulus of the asphalt specimen in the last loading cycle was recorded; S5. Substituting the initial dynamic shear modulus determined in step S4 and the dynamic shear modulus of the last loading cycle into the prediction formula for the fatigue crack length of asphalt, the fatigue crack length of the asphalt specimen at the end of the time scan test can be predicted. This prediction formula is derived based on the torque balance equation, the dissipated strain energy balance equation, and the reversible strain energy balance equation, as shown below: In the formula: N Number of loading cycles; c ( N ) for asphalt specimens at the 1st N The length of fatigue cracks per loading cycle; r 0 represents the initial radius of the asphalt specimen, which is 4 mm; | G *| N The asphalt specimen was in the first N Dynamic shear modulus of each loading cycle; | G *|0 is the initial dynamic shear modulus of the asphalt specimen.

[0016] In this embodiment, parallel tests were conducted on two asphalt specimens. Based on the prediction formula, the lengths of fatigue cracks generated in the two asphalt specimens at the end of the time scan test were predicted to be 1.324 mm and 1.350 mm, respectively.

[0017] To verify the accuracy of the fatigue crack length prediction formula, after the time-scan test, the temperature of the dynamic shear rheometer's environmental chamber was set to 0℃, and the asphalt specimens were kept at 0℃ for 10 minutes. After the heat treatment, the locking mechanism of the dynamic shear rheometer was opened, and the distance between the upper and lower parallel plates was set to 60mm in the software accompanying the dynamic shear rheometer. The upper parallel plate then automatically rose under tension and separated from the lower parallel plate. The asphalt specimen sandwiched between the upper and lower parallel plates was pulled apart, and an asphalt fracture image appeared on the lower plate, as shown in the image. Figure 2 As shown.

[0018] Fracture images of asphalt specimens were captured using digital equipment and imported into Digimizer software for analysis. Given that the radius of the entire asphalt specimen is 4 mm, the radius of the fracture area can be determined by comparing the pixel size between the fracture area and the entire specimen, and the actual fatigue crack length of the asphalt specimen can then be calculated. This embodiment describes the method for estimating the actual fatigue crack length of the asphalt specimen based on pixel size as follows: Figure 3As shown, the actual fatigue crack lengths of the two asphalt test pieces at the end of the time sweep test were 1.344 mm and 1.347 mm, respectively. Therefore, the predicted fatigue crack lengths of the asphalt test pieces were very close to the actual measured values.

[0019] Example 2: The example was substantially the same as Example 1, except that the test was terminated when the dynamic shear modulus of the asphalt test piece at the current loading cycle decreased by 70% compared to the initial dynamic shear modulus.

[0020] In this example, two asphalt test pieces were tested in parallel. According to the formula, the fatigue crack lengths of the two asphalt test pieces at the end of the time sweep test were both 1.040 mm. By analyzing the fracture images of the asphalt test pieces, the actual fatigue crack lengths of the two asphalt test pieces at the end of the time sweep test were 1.043 mm and 0.981 mm, respectively. Therefore, the predicted fatigue crack lengths of the asphalt test pieces were very close to the actual measured values.

[0021] Example 3: The example was substantially the same as Example 1, except that the test was terminated when the dynamic shear modulus of the asphalt test piece at the current loading cycle decreased by 50% compared to the initial dynamic shear modulus.

[0022] In this example, two asphalt test pieces were tested in parallel. According to the formula, the fatigue crack lengths of the two asphalt test pieces at the end of the time sweep test were both 0.637 mm. By analyzing the fracture images of the asphalt test pieces, the actual fatigue crack lengths of the two asphalt test pieces at the end of the time sweep test were 0.589 mm and 0.584 mm, respectively. Therefore, the predicted fatigue crack lengths of the asphalt test pieces were very close to the actual measured values.

[0023] Example 4: The example was substantially the same as Example 1, except that the asphalt test piece in this example was a long-term aged SBS modified asphalt, and the strain amplitude of the time sweep test was set to 15%. The test was terminated when the dynamic shear modulus of the asphalt test piece at the current loading cycle decreased by 80% compared to the initial dynamic shear modulus.

[0024] In this example, two asphalt test pieces were tested in parallel. According to the formula, the fatigue crack lengths of the two asphalt test pieces at the end of the time sweep test were both 1.327 mm. The fracture images of the asphalt test pieces in this example are shown in Figure 4 The method for calculating the actual fatigue crack length of the asphalt test piece according to the pixel size is shown in Figure 5As shown in the figure, analysis of the fracture images of the asphalt specimens reveals that the actual fatigue crack lengths of the two asphalt specimens at the end of the time scan test were 1.339 mm and 1.306 mm, respectively. Therefore, the predicted fatigue crack lengths of the asphalt specimens are very close to the measured values.

[0025] Example 5: The experiment was basically the same as in Example 4, except that the test was terminated when the dynamic shear modulus of the asphalt specimen in the current loading cycle decreased by 70% compared with its initial dynamic shear modulus.

[0026] In this embodiment, parallel tests were conducted on two asphalt specimens. Based on the predicted formula, the fatigue crack lengths of the two asphalt specimens at the end of the time-scan test were 1.040 mm and 1.039 mm, respectively. Analysis of the fracture images of the asphalt specimens showed that the actual fatigue crack lengths of the two asphalt specimens at the end of the time-scan test were 1.055 mm and 1.013 mm, respectively. Therefore, the predicted fatigue crack lengths of the asphalt specimens are very close to the measured values.

[0027] Example 6: The experiment was basically the same as in Example 4, except that the test was terminated when the dynamic shear modulus of the asphalt specimen in the current loading cycle decreased by 50% compared with its initial dynamic shear modulus.

[0028] In this embodiment, parallel tests were conducted on two asphalt specimens. According to the predicted formula, the length of the fatigue cracks in both asphalt specimens at the end of the time-scan test was 0.638 mm. Analysis of the fracture images of the asphalt specimens revealed that the actual lengths of the fatigue cracks in the two specimens at the end of the time-scan test were 0.616 mm and 0.564 mm, respectively. Therefore, the predicted fatigue crack lengths of the asphalt specimens are very close to the measured values.

[0029] The predicted and actual values ​​of fatigue crack length for 12 asphalt specimens in Examples 1-6 were summarized. A plot was created with the measured fatigue crack length on the x-axis and the predicted fatigue crack length on the y-axis to establish the relationship between the predicted and measured values. Figure 6 As shown. By Figure 6 It can be seen that there is a strong correlation between the predicted value and the measured value of fatigue crack length, with a determination coefficient of 0.9949. This proves that the method proposed in this invention can accurately predict the fatigue crack length of asphalt, thereby realizing the quantitative analysis of the fatigue cracking process of asphalt.

[0030] The above examples are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can be modified, or some technical features can be replaced by equivalent features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method of predicting asphalt fatigue crack length based on continuum damage mechanics, characterized by, The method comprises the following steps: S1, preparing an asphalt test piece after heating the asphalt to a flowing state; S2, selecting a test temperature and a loading frequency according to requirements; S3, performing a strain amplitude scanning test on the asphalt test piece at the test temperature and the loading frequency selected in step S2 by using a dynamic shear rheometer, collecting data of dynamic shear modulus and phase angle changing with strain amplitude, and determining a damage critical point of the asphalt test piece; S4, selecting a strain amplitude according to the damage critical point of the asphalt test piece determined in step S3, continuing to perform a time scanning test on the asphalt test piece at the test temperature and the loading frequency selected in step S2 by using the dynamic shear rheometer in a strain control mode, collecting data of dynamic shear modulus and phase angle changing with loading cycle, and determining an initial dynamic shear modulus of the asphalt test piece; S5, substituting the initial dynamic shear modulus determined in step S4 and the dynamic shear modulus of the asphalt test piece at a certain loading cycle into a prediction formula of asphalt fatigue crack length, so as to predict the fatigue crack length of the asphalt test piece at the loading cycle. The prediction formula is as follows: ； wherein, N is the number of loading cycles; c ( N ) is the fatigue crack length of the asphaltic specimen at the N th loading cycle; r 0 is the initial radius of the asphaltic specimen; G N is the dynamic shear modulus of the asphaltic specimen at the N th loading cycle; G 0 is the initial dynamic shear modulus of the asphaltic specimen.​ 2. The method of claim 1, wherein: In step S3, the damage critical point of the asphalt test piece is determined by drawing a curve of dynamic shear modulus changing with strain amplitude according to the data of dynamic shear modulus and phase angle changing with strain amplitude, taking the dynamic shear modulus of the asphalt test piece decreasing by 5% as a judgment basis, and determining the damage critical point of the asphalt test piece.

3. The method of claim 1, wherein: In step S4, after the time scanning test is completed, a curve of strain amplitude of the asphalt test piece changing with loading cycle is drawn, and the dynamic shear modulus corresponding to the loading cycle when the strain amplitude of the asphalt test piece reaches a set strain amplitude is selected as the initial dynamic shear modulus of the asphalt test piece.

4. The method of claim 1, wherein: In step S3, when the strain amplitude scanning test is performed and step S4 is performed, a parallel plate clamp with a diameter of 8 mm is used, and the distance between the upper and lower parallel plates is set to 2 mm.

5. The method of claim 1, wherein: The prediction formula in step S5 is derived based on a torque balance equation, a dissipated strain energy balance equation and a reversible strain energy balance equation.

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