Investigation of the Fatigue Life of Bottom-Up Cracking in Asphalt Concrete Pavements
Round 1
Reviewer 1 Report
Undoubtedly, the article contains data of practical value. However, the volume of scientific novelty in the article is clearly not significant: well-known methods and relations are used. An obvious disadvantage of the study can be considered the lack of studies of the fatigue durability of asphalt pavement during compression.
Author Response
Undoubtedly, the article contains data of practical value. However, the volume of scientific novelty in the article is clearly not significant: well-known methods and relations are used. An obvious disadvantage of the study can be considered the lack of studies of the fatigue durability of asphalt pavement during compression.
Reply: Thank you for your suggestion.
This paper aims to study the fatigue life of bottom-up cracks of asphalt pavements including fatigue cracking and crack propagation. Therefore, the maximum tensile stresses commonly developed at the bottom of the AC layer under repetitive loadings may be the main cause. However, the consideration of the reviewer is a good suggestion for further improving the research. Therefore, the authors will conduct this research in the following. Thank you again.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This study investigated the fatigue behavior of asphalt mixture with a bottom-up crack using experimental and numerical tests. It is an interesting topic for evaluating the fatigue life of asphalt pavement under different loads and temperatures. However, it need a major revision before the consideration for publication. Some comments are shown in follows.
(1) The title of this paper was inappropriate, since it could not summarize the whole research contents.
(2) In the section Abstract, please clarify the purpose and interest of this study.
(3) In the section Introduction, some details need to be improved:
The sentence “asphalt pavement … due to the obvious advantages of smooth surface …” is unclear. How do you define a smooth surface?
What are the causes of bottom-up crack? Do the bottom-up crack has a significant effect on the fatigue life of asphalt pavement?
The number of literatures is inadequate about the cracking study of asphalt mixtures. Some references can be included, such as:
Wei H, Li J, Wang F, et al. Numerical investigation on fracture evolution of asphalt mixture compared with acoustic emission[J]. International Journal of Pavement Engineering, 2022, 23(10): 3481-3491.
Praticò F G, Fedele R, Naumov V, et al. Detection and monitoring of bottom-up cracks in road pavement using a machine-learning approach[J]. Algorithms, 2020, 13(4): 81.
(4) Please add the section “Materials” including properties of raw materials, size gradations of three types of asphalt mixtures.
(5) In the section Experimental Study, why are both the compacted mold sizes and the asphalt mixture types inconsistent between the dynamic modulus test and the overlay tester (OT) test? In addition, at line 159, the phrase “Overlay Test (OT)” is wrong.
(6) In Figure 3 (c) and (d), please explain the reason for the abrupt change of curves at low temperature.
(7) The reviewer is confused that the section 4 seems to be an independent study. At Line 311, how were the tensile stresses at the bottom obtained? The relationship between fatigue cracking life and OT test results is not clear.
(8) The reference was missing at Line 347.
(9) What is the definitions of Fatigue Cracking Life and Fatigue Crack Life?
Author Response
Response to reviewer #2
This study investigated the fatigue behavior of asphalt mixture with a bottom-up crack using experimental and numerical tests. It is an interesting topic for evaluating the fatigue life of asphalt pavement under different loads and temperatures. However, it need a major revision before the consideration for publication. Some comments are shown in follows.
(1) The title of this paper was inappropriate, since it could not summarize the whole research contents.
Reply: Thank you.
The title of this paper has been revised as “Investigation of the fatigue life of bottom-up cracking in asphalt concrete pavements”.
(2) In the section Abstract, please clarify the purpose and interest of this study.
Reply: Thank you.
The Abstract has been improved in the revised manuscript as follows:
Abstract: Traditionally, fatigue cracking of asphalt pavement means fatigue failure, which is the basis for controlling the design thickness of asphalt pavement. In fact, the fatigue failure of asphalt pavement includes three stages: fatigue cracking, crack expansion and structural failure. Therefore, this paper aims to investigate the fatigue life of bottom-up cracking in asphalt concrete (AC) pavements considering the different stages of fatigue failure. The dynamic modulus of AC with different grading was experimental determined. The tensile stresses at the bottom of the AC layer was evaluated by embedding the tested dynamic modulus into the numerical simulation, which can be used to calculate the fatigue cracking life. Then, overlay tests (OTs) at different temperatures were conducted to obtain the fracture parameters and of asphalt mixture. The crack propagation life was calculated by Paris formula based on the fracture parameters and. Analysis results showed that the increase of AC thickness can effectively improve the fatigue crack life of pavement structure, and the proportion of crack propagation life to fatigue crack life at different temperatures varied significantly. Therefore, when analyzing and calculating the fatigue life of pavement structures, besides fatigue cracking life, the crack propagation life of after cracking at should also be considered, which is very important for accurately calculating the entire fatigue life of asphalt pavement structure.
Please see the lines 11 to 25 in the revised manuscript.
(3) In the section Introduction, some details need to be improved:
The sentence “asphalt pavement … due to the obvious advantages of smooth surface …” is unclear. How do you define a smooth surface?
Reply: Thank you for your suggestion.
The sentence “asphalt pavement … due to the obvious advantages of smooth surface …” has been rewritten as “Asphalt pavement is a paramount type of pavement and has been widely used around the world due to its excellent road performance, convenient rehabilitation measures, and comfortable driving conditions.”
A smooth surface is generally defined by IRI (International Roughness Index), which differs with different grade highways.
The section Introduction has been improved in the revised manuscript as follows:
Asphalt pavement is a paramount type of pavement and has been widely used around the world due to its excellent road performance, convenient rehabilitation measures, and comfortable driving conditions. With the rapid development of national economy and the further growth of modern road transportation demand, a considerable amount of asphalt pavement has been built. Therefore, some problems of early distresses for asphalt pavement are also obvious. Traditional thinking suggests that pavements will fail structurally in one of two ways, either deformation resulting from subgrade failure or bottom-up fatigue cracking. Distresses concentrated in asphalt concrete (AC) layer can lead to the failure of the pavement structure over time. The maximum tensile stresses are commonly developed at the bottom of the AC layer under repetitive loadings. As a result, cracks usually initiate at the bottom of the asphalt layer and start propagating to the surface of the pavement. This so-called bottom-up fatigue cracking is one of the main failure modes in asphalt pavements. Bottom-up crack may occur in concrete pavement with the increase of loads by traffic and environmental effect. Cracking in concrete pavements would produce serious damages in pavements since it induces water penetration in pavement structure and foundation. For state departments of transportation, the accurate prediction of flexible pavement service life in terms of potential fatigue cracking is crucial for pavement design, maintenance, and rehabilitation.
To this end, some researchers have conducted many studies to predict fatigue cracking. Li et al. [1] investigated fatigue cracking of expressway asphalt pavement, which pointed out that asphalt pavement was subjected to repeated action of driving load and temperature load. When the action times reached a certain number, fatigue cracking would occur. However, cracks are hard to spot until they reach the surface of the road. Therefore, it is very difficult to study the characteristics of fatigue cracks on actual pavement. With the development of computer technology, it is possible for researchers to study fatigue cracks by numerical analysis. Due to the singularity of the crack tip, the results calculated from the traditional strength theory are unreasonable. Therefore, fracture mechanics is introduced to study fractures. Ge et al. [2] obtained stress intensity factor (SIF) at the crack tip based on fracture mechanics, and used SIF to reflect the stress distribution at the crack tip. Uzan et al. [3] presented a mechanistic model for predicting performance of asphalt mixtures in terms of crack propagation rate, fatigue life assessment and permanent deformation characteristics. Ceylan et al. [4] used the neural networks (NN) approach to model the SIF as cracks grow upward through a hot-mix asphalt (HMA) overlay because of both load and thermal effects with and without reinforcing interlayers. Several cases under both thermal loading and traffic loading were considered and the NN models had significantly higher accuracy in predicting SIFs compared with the nonlinear regression approach. Based on seminal investigation of the integer transform, Hu et al. [5] proposed the modelling tensile strain response in asphalt pavements bottom-up and/or top-down fatigue crack initiation. The Texas A&M Transportation Institute developed a correlation between the number of cycles to failure and the fracture energy index using overlay tests (OTs) [6, 7]. Zhou and Scullion et al. [6] summarized how crack initiation is related to crack propagation and provided both the theory and validation for the usefulness of OT to assess fatigue cracking. Hiltunen and Roque [8] proposed the new mechanics-based thermal cracking performance model, and the calibrated model can be used to establish performance-based specification limits based on material properties or parameters determined from the new mixture test. At present, the fatigue crack growth formula proposed by Paris and Erdogan [9] based on experiments was the most widely used formula to study fatigue crack growth life, which was also known as the famous Paris formula. In 1970s, Majidzadeh et al. [10, 11] introduced the principle and method of fracture mechanics into the study of pavement structure cracking. Moghadas et al. [12] applied fracture mechanics to qualitatively analyze the mechanism of geotextiles for preventing crack propagation. Lytton [13] presented the fracture properties of asphaltic concrete under fatigue loading and illustrated the thermal contraction conditions and the way altered by the addition of geotextiles. Abo-Qudais and Shatnawi [14] predicted the number of cycles that cause fracture of hot-mix asphalt (HMA) based on the number of cycles, at which the slope of accumulated strain switched from decreasing to increasing mode, and evaluated the effect of aggregate gradation and temperature on fatigue behaviors of hot-mix asphalt. Doh et al. [15] developed a numerical prediction model for fatigue life by modifying crack growth rate of Paris law with horizontal deformation rate to compare relative performance of the material based on experimental test result. Wei et al. [16] proposed an accurate and efficient model using the discrete element method and the digital image processing technique to investigate the fracture evolution of asphalt mixture at the low temperature, which was well compared and verified by the acoustic emission activities. Additionally, the fatigue crack life of asphalt pavements has been also investigated by many researchers. Zhou et al. [17] used some index parameters as the main prediction variables of asphalt pavement fatigue cracking model, and obtained the prediction model of fatigue cracking life. Zheng et al. [18] proposed a method to predict the pavement fatigue crack initiation life and the fatigue life of a typical high modulus asphalt concrete (HMAC) overlay pavement which runs a risk of bottom-up cracking was predicted and validated. Obviously, concealed failures (e.g., bottom-up cracks) are, by definition, difficult to be identified and localized. To identify concealed cracks (particularly, bottom-up cracks) and monitor their growth over time, a supervised machine learning (ML)-based method for the identification and classification of the SHS of a differently cracked road pavement based on its vibro-acoustic signature was set up [19]. The stress intensity principal was used to determine the locations and lengths of cracks, and the hidden bottom-up cracks can be detected, which has significantly impacted the current pavement detection practice [20]. From the above literature analysis, researchers have carried out extensive studies on the crack initiation and propagation prediction of asphalt pavement. However, these studies have generally focused on the crack initiation or propagation to predict fatigue cracking. In fact, the fatigue failure of asphalt pavement includes three stages: fatigue cracking, crack expansion and structural failure. Therefore, the pavement structure design should fully consider the different stages of fatigue failure.
In view of the above reasons, this paper aims at obtaining the fatigue life of bottom-up cracks of asphalt pavements including fatigue cracking and crack propagation. OTs at different temperatures were conducted to obtain the fracture parameters and of asphalt mixture, and crack propagation life was further calculated by Paris formula. Additionally, the dynamic modulus of AC with different grading was also experimental determined, and related numerical simulation was performed to evaluate the tensile stress at the bottom of the AC layer, which can be used to calculate the fatigue cracking life. Therefore, the fatigue crack life of asphalt pavements can be predicted considering the different stages of fatigue failure, and some suggestions of pavement structure design can be provided.
Please see the lines 28 to 108 in the revised manuscript.
What are the causes of bottom-up crack? Do the bottom-up crack has a significant effect on the fatigue life of asphalt pavement?
Reply: Thank you.
Traditional thinking suggests that pavements will fail structurally in one of two ways, either deformation resulting from subgrade failure or bottom-up fatigue cracking. Distresses concentrated in asphalt concrete (AC) layer can lead to the failure of the pavement structure over time. The maximum tensile stresses are commonly developed at the bottom of the AC layer under repetitive loadings. As a result, cracks usually initiate at the bottom of the asphalt layer and start propagating to the surface of the pavement. This so-called bottom-up fatigue cracking is one of the main failure modes in asphalt pavements. Bottom-up crack may occur in concrete pavement with the increase of loads by traffic and environmental effect. Cracking in concrete pavements would produce serious damages in pavements since it induces water penetration in pavement structure and foundation. For state departments of transportation, the accurate prediction of flexible pavement service life in terms of potential fatigue cracking is crucial for pavement design, maintenance, and rehabilitation.
Please see the lines 32 to 43 in the revised manuscript.
The number of literatures is inadequate about the cracking study of asphalt mixtures. Some references can be included, such as:
Wei H, Li J, Wang F, et al. Numerical investigation on fracture evolution of asphalt mixture compared with acoustic emission[J]. International Journal of Pavement Engineering, 2022, 23(10): 3481-3491.
Praticò F G, Fedele R, Naumov V, et al. Detection and monitoring of bottom-up cracks in road pavement using a machine-learning approach[J]. Algorithms, 2020, 13(4): 81.
Reply: Thank you.
The section Introduction has been improved in the revised manuscript as follows:
Asphalt pavement is a paramount type of pavement and has been widely used around the world due to its excellent road performance, convenient rehabilitation measures, and comfortable driving conditions. With the rapid development of national economy and the further growth of modern road transportation demand, a considerable amount of asphalt pavement has been built. Therefore, some problems of early distresses for asphalt pavement are also obvious. Traditional thinking suggests that pavements will fail structurally in one of two ways, either deformation resulting from subgrade failure or bottom-up fatigue cracking. Distresses concentrated in asphalt concrete (AC) layer can lead to the failure of the pavement structure over time. The maximum tensile stresses are commonly developed at the bottom of the AC layer under repetitive loadings. As a result, cracks usually initiate at the bottom of the asphalt layer and start propagating to the surface of the pavement. This so-called bottom-up fatigue cracking is one of the main failure modes in asphalt pavements. Bottom-up crack may occur in concrete pavement with the increase of loads by traffic and environmental effect. Cracking in concrete pavements would produce serious damages in pavements since it induces water penetration in pavement structure and foundation. For state departments of transportation, the accurate prediction of flexible pavement service life in terms of potential fatigue cracking is crucial for pavement design, maintenance, and rehabilitation.
To this end, some researchers have conducted many studies to predict fatigue cracking. Li et al. [1] investigated fatigue cracking of expressway asphalt pavement, which pointed out that asphalt pavement was subjected to repeated action of driving load and temperature load. When the action times reached a certain number, fatigue cracking would occur. However, cracks are hard to spot until they reach the surface of the road. Therefore, it is very difficult to study the characteristics of fatigue cracks on actual pavement. With the development of computer technology, it is possible for researchers to study fatigue cracks by numerical analysis. Due to the singularity of the crack tip, the results calculated from the traditional strength theory are unreasonable. Therefore, fracture mechanics is introduced to study fractures. Ge et al. [2] obtained stress intensity factor (SIF) at the crack tip based on fracture mechanics, and used SIF to reflect the stress distribution at the crack tip. Uzan et al. [3] presented a mechanistic model for predicting performance of asphalt mixtures in terms of crack propagation rate, fatigue life assessment and permanent deformation characteristics. Ceylan et al. [4] used the neural networks (NN) approach to model the SIF as cracks grow upward through a hot-mix asphalt (HMA) overlay because of both load and thermal effects with and without reinforcing interlayers. Several cases under both thermal loading and traffic loading were considered and the NN models had significantly higher accuracy in predicting SIFs compared with the nonlinear regression approach. Based on seminal investigation of the integer transform, Hu et al. [5] proposed the modelling tensile strain response in asphalt pavements bottom-up and/or top-down fatigue crack initiation. The Texas A&M Transportation Institute developed a correlation between the number of cycles to failure and the fracture energy index using overlay tests (OTs) [6, 7]. Zhou and Scullion et al. [6] summarized how crack initiation is related to crack propagation and provided both the theory and validation for the usefulness of OT to assess fatigue cracking. Hiltunen and Roque [8] proposed the new mechanics-based thermal cracking performance model, and the calibrated model can be used to establish performance-based specification limits based on material properties or parameters determined from the new mixture test. At present, the fatigue crack growth formula proposed by Paris and Erdogan [9] based on experiments was the most widely used formula to study fatigue crack growth life, which was also known as the famous Paris formula. In 1970s, Majidzadeh et al. [10, 11] introduced the principle and method of fracture mechanics into the study of pavement structure cracking. Moghadas et al. [12] applied fracture mechanics to qualitatively analyze the mechanism of geotextiles for preventing crack propagation. Lytton [13] presented the fracture properties of asphaltic concrete under fatigue loading and illustrated the thermal contraction conditions and the way altered by the addition of geotextiles. Abo-Qudais and Shatnawi [14] predicted the number of cycles that cause fracture of hot-mix asphalt (HMA) based on the number of cycles, at which the slope of accumulated strain switched from decreasing to increasing mode, and evaluated the effect of aggregate gradation and temperature on fatigue behaviors of hot-mix asphalt. Doh et al. [15] developed a numerical prediction model for fatigue life by modifying crack growth rate of Paris law with horizontal deformation rate to compare relative performance of the material based on experimental test result. Wei et al. [16] proposed an accurate and efficient model using the discrete element method and the digital image processing technique to investigate the fracture evolution of asphalt mixture at the low temperature, which was well compared and verified by the acoustic emission activities. Additionally, the fatigue crack life of asphalt pavements has been also investigated by many researchers. Zhou et al. [17] used some index parameters as the main prediction variables of asphalt pavement fatigue cracking model, and obtained the prediction model of fatigue cracking life. Zheng et al. [18] proposed a method to predict the pavement fatigue crack initiation life and the fatigue life of a typical high modulus asphalt concrete (HMAC) overlay pavement which runs a risk of bottom-up cracking was predicted and validated. Obviously, concealed failures (e.g., bottom-up cracks) are, by definition, difficult to be identified and localized. To identify concealed cracks (particularly, bottom-up cracks) and monitor their growth over time, a supervised machine learning (ML)-based method for the identification and classification of the SHS of a differently cracked road pavement based on its vibro-acoustic signature was set up [19]. The stress intensity principal was used to determine the locations and lengths of cracks, and the hidden bottom-up cracks can be detected, which has significantly impacted the current pavement detection practice [20]. From the above literature analysis, researchers have carried out extensive studies on the crack initiation and propagation prediction of asphalt pavement. However, these studies have generally focused on the crack initiation or propagation to predict fatigue cracking. In fact, the fatigue failure of asphalt pavement includes three stages: fatigue cracking, crack expansion and structural failure. Therefore, the pavement structure design should fully consider the different stages of fatigue failure.
In view of the above reasons, this paper aims at obtaining the fatigue life of bottom-up cracks of asphalt pavements including fatigue cracking and crack propagation. OTs at different temperatures were conducted to obtain the fracture parameters and of asphalt mixture, and crack propagation life was further calculated by Paris formula. Additionally, the dynamic modulus of AC with different grading was also experimental determined, and related numerical simulation was performed to evaluate the tensile stress at the bottom of the AC layer, which can be used to calculate the fatigue cracking life. Therefore, the fatigue crack life of asphalt pavements can be predicted considering the different stages of fatigue failure, and some suggestions of pavement structure design can be provided.
Please see the lines 28 to 108 in the revised manuscript.
(4) Please add the section “Materials” including properties of raw materials, size gradations of three types of asphalt mixtures.
Reply: Thank you.
The section “Materials” has been added in the revised manuscript as follows:
Test Materials
In this paper, AH-70 common matrix asphalt was used in the laboratory mixture test, the coarse aggregate and fine aggregate are limestone, and the gradation was composite grading. The technical specifications of AH-70 are shown in Table 1. Three common asphalt mixtures (AC-13, AC-20 and AC-25) were adopted in the following experiments. The selection of AC at all levels is shown in Table 2, and the asphalt-stone ratios are 4.7%, 4.1% and 3.8%, respectively. Through testing, the basic performance indexes of asphalt and aggregate could meet the basic requirements of Technical Specifications for Construction of Highway Asphalt Pavement JTG F40-2004 [21].
Table 1. Test results of asphalt raw materials
|
Test items |
Measured data AH-70 |
Technical requirements AH-70 |
Test method |
|
Penetration (25 ℃, 100 g, 5 s, 0.1 mm) |
79.4 |
60～80 |
T0604 |
|
Softening point (℃) |
46.76 |
≥46 |
T0606 |
|
Ductility (10 ℃) (cm) |
147.5 |
≥20 |
T0605 |
|
Ductility (15 ℃) (cm) |
>200 |
≥100 |
|
|
60℃ Dynamic viscosity (Pa.s) |
297 |
≥180 |
T0620 |
|
Asphalt flash point (℃) |
284 |
≥46 |
T0611 |
|
Residual needle penetration ratio (25 ℃) |
82.1 |
≥61 |
T0604 |
|
Residual ductility (10 ℃) (cm) |
8.5 |
≥6 |
T0605 |
|
Residual ductility (15 ℃) (cm) |
33 |
≥15 |
T0605 |
Table 2. Asphalt mixture selection gradation
|
Mass percentage (%) through the square hole screen (mm) |
||||||||||||
|
Specifications |
26.5 |
19 |
16 |
13.2 |
9.5 |
4.75 |
2.36 |
1.18 |
0.6 |
0.3 |
0.15 |
0.075 |
|
AC-13 |
100 |
100 |
99.7 |
95.1 |
76.8 |
38.4 |
29.1 |
23.0 |
17.3 |
12.2 |
10.4 |
7.9 |
|
AC-20 |
100 |
99.1 |
91.1 |
73.3 |
54.9 |
30.3 |
23.6 |
18.7 |
14.2 |
10.0 |
8.6 |
6.6 |
|
AC-25 |
99.1 |
79.0 |
73.0 |
65.7 |
52.7 |
36.7 |
32.0 |
23.7 |
15.0 |
10.2 |
8.2 |
6.8 |
Please see the lines 112 to 127 in the revised manuscript.
(5) In the section Experimental Study, why are both the compacted mold sizes and the asphalt mixture types inconsistent between the dynamic modulus test and the overlay tester (OT) test? In addition, at line 159, the phrase “Overlay Test (OT)” is wrong.
Reply: Thank you.
Experimental studies of dynamic modulus test and OT are based on the Superpave test method, and the specimens are molded according to the target porosity. The difference in compacted mold sizes is due to the requirements of the test specification, however, this does not affect the subsequent comparative analysis.
At line 159, the phrase “Overlay Test (OT)” is wrong. It has been corrected in the revised manuscript.
(6) In Figure 3 (c) and (d), please explain the reason for the abrupt change of curves at low temperature.
Reply: Thank you for your suggestion.
The reason have been added in the revised manuscript as follows:
It can observe that there is an abrupt change of curves in Figure 3c and 3d at 0℃, which is not an sudden phenomenon. When the temperature was -10℃, the test load decreased rapidly to be stable with less number of cycles, and several data points were actually very discrete. When the temperature was 0℃, the test load decreased rapidly with the increase of the number of load cycles, but the number of load cycles was more than that at -10℃. There seemed to be an abrupt change at early stage of curves, which was the same variability as -10℃. Only a few data points at -10℃ did not look so obvious. However, the basic reason may be that the asphalt mixture is heterogeneous and obviously affected by low temperature. Data mutation easily occurs in the process of crack development, such as the fracture of stone.
Please see the lines 213 to 221 in the revised manuscript.
(7) The reviewer is confused that the section 4 seems to be an independent study. At Line 311, how were the tensile stresses at the bottom obtained? The relationship between fatigue cracking life and OT test results is not clear.
Reply: Thank you.
These contents have been added in the revised manuscript as follows:
In above Sections 2 and 3, we have obtained the tensile stresses at the bottom of the AC layer with different grading based on the dynamic modulus test and numerical simulation, as well as fracture parameters and based on OTs at different temperatures. Therefore, fatigue cracking life and crack propagation life of AC layer can be calculated based on some calculation models or theories in this section.
The tensile stresses at the bottom have been obtained in Figures 5 and 6 based on the dynamic modulus test and numerical simulation.
In this paper, the fatigue life of bottom-up cracks of asphalt pavements should include fatigue cracking and crack propagation according to different stages of fatigue failure.
In order to keep consistent with the design specifications in China, the fatigue model recommended Specifications for design of highway Asphalt Pavement [22] was adopted in this paper, as shown in Eq. (4).
(4)
where is tensile stress, and is fatigue cracking life.
OTs at different temperatures can be used to obtain the fracture parameters and of asphalt mixture, and the crack propagation life can be calculated based on Paris formula. Therefore, the relationship between fatigue cracking life and OT results can be elaborated.
Please see the lines 341 to 345 in the revised manuscript.
(8) The reference was missing at Line 347.
Reply: Thank you.
The reference has been added in the revised manuscript.
(9) What is the definitions of Fatigue Cracking Life and Fatigue Crack Life?
Reply: Thank you.
We can know that many studies have generally focused on the crack initiation or propagation to predict fatigue cracking. In fact, the fatigue failure of asphalt pavement includes three stages: fatigue cracking, crack expansion and structural failure. Therefore, the pavement structure design should fully consider the different stages of fatigue failure.
Therefore, fatigue cracking life refers to the life of asphalt mixture that will be damaged in the process of cracking.
Fatigue crack life refers to the life from crack initiation and propagation to final failure.
Author Response File: Author Response.pdf
Reviewer 3 Report
I have the following comment for the authors:
1_ Line 36 and elsewhere: you might replace “diseases” with “distresses”.
2_ Lines 37-38: The statement is partially true. Simple longitudinal cracks may be result of tensile strain development in the pavement surface (i.e., top-down cracks), and tensile strains at AC bottom that generate bottom-up cracks that as far as they propagate upwards, they appear at the surface as alligator (or crocodile cracks). Please revise.
3_ Lines 96-100: In parallel with the previous remark, the authors need to clarify which fatigue type they investigated (as is done in Line 440). The classical bottom-up fatigue or the top-down fatigue. Please also consult other studies, like https://doi.org/10.3390/infrastructures7050061.
4_ Lines 149-150: Which protocol did you follow for the dynamic modulus test? Please cite it. Also, why a sole frequency (that of 0.1Hz) is reported. Please elaborate.
5_ Lines 222-227: Please prefer a figure illustrating the investigate structures. Also, the other materials apart from AC were considered as linear elastic? Please comment.
6_ Tables 5 and 6: How was the maximum temperature set at 25oC? AC viscoelasticity is known to be more pronounced at even higher temperatures. Please comment.
7_ Lines 453-454: This is not scientifically correct. High AC thicknesses might make the pavement vulnerable to top-down cracking. Besides, simply raising the AC thickness without needed for structural reasons can sharply increase the costs of pavement construction. Please reconsider.
Overall, the content of the paper suits the journal’s aim, but the paper must be reconsidered after some necessary improvements.
Author Response
I have the following comment for the authors:
1_ Line 36 and elsewhere: you might replace “diseases” with “distresses”.
Reply: Thank you.
This mistakes have been corrected in the revised manuscript.
2_ Lines 37-38: The statement is partially true. Simple longitudinal cracks may be result of tensile strain development in the pavement surface (i.e., top-down cracks), and tensile strains at AC bottom that generate bottom-up cracks that as far as they propagate upwards, they appear at the surface as alligator (or crocodile cracks). Please revise.
Reply: Thank you.
This statement has been corrected in the Section Introduction in the revised manuscript as follows:
Traditional thinking suggests that pavements will fail structurally in one of two ways, either deformation resulting from subgrade failure or bottom-up fatigue cracking. Distresses concentrated in asphalt concrete (AC) layer can lead to the failure of the pavement structure over time. The maximum tensile stresses are commonly developed at the bottom of the AC layer under repetitive loadings. As a result, cracks usually initiate at the bottom of the asphalt layer and start propagating to the surface of the pavement. This so-called bottom-up fatigue cracking is one of the main failure modes in asphalt pavements. Bottom-up crack may occur in concrete pavement with the increase of loads by traffic and environmental effect. Cracking in concrete pavements would produce serious damages in pavements since it induces water penetration in pavement structure and foundation. For state departments of transportation, the accurate prediction of flexible pavement service life in terms of potential fatigue cracking is crucial for pavement design, maintenance, and rehabilitation.
Please see the lines 32 to 43 in the revised manuscript.
3_ Lines 96-100: In parallel with the previous remark, the authors need to clarify which fatigue type they investigated (as is done in Line 440). The classical bottom-up fatigue or the top-down fatigue. Please also consult other studies, like https://doi.org/10.3390/infrastructures7050061.
Reply: Thank you for your suggestions.
The section Introduction has been improved in the revised manuscript and this paper aims at obtaining the fatigue life of bottom-up cracks of asphalt pavements including fatigue cracking and crack propagation.
In addition, the content is further emphasized in the Section “Experiment Study ….” as follows:
In order to obtain the fatigue life of bottom-up cracks of asphalt pavements including fatigue cracking and crack propagation. OTs at different temperatures need to be conducted to obtain the fracture parameters and of asphalt mixture, and the dynamic modulus of AC with different grading can be used to evaluate the tensile stress at the bottom of the AC layer. Theses parameters will be utilized to determine the fatigue cracking and crack propagation.
Please see the lines 28 to 43, and lines 112 to 116 in the revised manuscript.
4_ Lines 149-150: Which protocol did you follow for the dynamic modulus test? Please cite it. Also, why a sole frequency (that of 0.1Hz) is reported. Please elaborate.
Reply: Thank you.
Three temperatures including - 10 ℃, 0 ℃ and 25 ℃ and loading frequency of 0.1 Hz are selected for this test. It is noting that as for 37 ℃ and 54 ℃ in the test specification, this paper mainly studies the ability of asphalt mixture to resist fatigue cracking at low temperature, thus the higher temperatures are not considered in the test. The dynamic modulus test follows ASTM D3497 and AASHTO TP62-03. The selection of 0.1 Hz mainly considers the standard frequency of the OT specification. Generally, the OT is loaded by the displacement control mode and the loading period is set as 10 s. In order to keep the consistent frequency of the two tests, the frequency in the dynamic modulus test is selected as 0.1 Hz.
Please see the lines 158 to 165 in the revised manuscript.
5_ Lines 222-227: Please prefer a figure illustrating the investigate structures. Also, the other materials apart from AC were considered as linear elastic? Please comment.
Reply: Thank you.
A figure has been added in the revised manuscript as follows:
Figure 5. Schematic diagram of OT model
The left side of the model limited the displacement in the X, Y and Z directions, while the right side limited the displacement in the Y and Z directions. Fixed constraints were used between the upper and lower layers. Therefore, the base layer is assumed to be non deformable. This OT model aims at studying the crack propagation of AC layer.
Please see the lines 275 to 279 in the revised manuscript.
6_ Tables 5 and 6: How was the maximum temperature set at 25oC? AC viscoelasticity is known to be more pronounced at even higher temperatures. Please comment.
Reply: Thank you.
Three temperatures including - 10 ℃, 0 ℃ and 25 ℃ and loading frequency of 0.1 Hz are selected for this test. It is noting that as for 37 ℃ and 54 ℃ in the test specification, this paper mainly studies the ability of asphalt mixture to resist fatigue cracking at low temperature, thus the higher temperatures are not considered in the test.
Please see the lines 158 to 165 in the revised manuscript.
7_ Lines 453-454: This is not scientifically correct. High AC thicknesses might make the pavement vulnerable to top-down cracking. Besides, simply raising the AC thickness without needed for structural reasons can sharply increase the costs of pavement construction. Please reconsider.
Reply: Thank you for your suggestion.
This conclusion has been corrected in the revised manuscript as follows:
The increase of asphalt surface thickness can effectively improve the fatigue crack life of pavement structure. Therefore, it is an ideal choice to increase the thickness of asphalt surface appropriately for improving the service life of pavement. Certainly, high AC thicknesses might make the pavement vulnerable to top-down cracking, and considering the cost, the reasonable thickness is worth further study.
Please see the lines 484 to 488 in the revised manuscript.
Overall, the content of the paper suits the journal’s aim, but the paper must be reconsidered after some necessary improvement
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The manuscript has been sufficiently improved to warrant publication in Applied Sciences now.
Reviewer 3 Report
The paper was refined.
It is out of the requested MDPI format.
