Evaluation of fatigue behavior in asphalt mixtures using bidirectional splitting and indirect tensile testing

ABSTRACT

Fatigue damage in asphalt pavements is a critical issue affecting the durability and safety of road infrastructure. Traditional fatigue testing methods, such as the indirect tensile fatigue test, fail to replicate the alternating tension-compression stress fields experienced in real-world conditions, leading to inaccuracies in fatigue life predictions. This study investigates the bidirectional splitting fatigue test as an alternative method to better simulate the stress state of asphalt pavements. Using cylindrical AC-13 asphalt specimens subjected to varying stress ratios (0.3, 0.4, 0.5, and 0.6) at 20°C and 10 Hz frequency, the research evaluates vertical displacement trends and fatigue life. Results reveal that bidirectional splitting induces a more realistic stress response, with reduced permanent deformation and slower fatigue progression compared to indirect tensile testing. At lower stress ratios, bidirectional splitting enhances material durability by leveraging compressive stresses for crack healing, whereas higher stress ratios lead to shear failures. These findings underscore the bidirectional splitting test’s potential to improve fatigue performance assessment, paving the way for more resilient asphalt mixtures. The practical implications of these findings lie in their potential application to real-world pavement design and maintenance. Future research should explore its applicability to various asphalt types and real-world loading conditions.

Keywords:
Asphalt fatigue; Bidirectional splitting test; Indirect tensile test; Stress ratio; Pavement performance

1. INTRODUCTION

Fatigue testing methods for asphalt mixtures have long been utilized to evaluate material durability under repeated loading conditions. However, conventional fatigue tests exhibit several critical limitations. The indirect tensile fatigue test, widely adopted due to its simplicity, does not accurately replicate the alternating tension-compression stress state found in real pavements [¹]. The four-point bending test provides improved stress simulation but primarily applies flexural loading, failing to capture shear and compressive effects. Uniaxial repeated load tests, while effective in assessing material response to cyclic stress, often require specialized setups and lengthy testing procedures. These limitations highlight a gap in understanding stress-state effects, particularly in assessing fatigue life under combined tensile and compressive forces [²].

Existing research has not adequately explored the role of bidirectional loading in fatigue damage progression. Most studies focus on unidirectional fatigue characterization, overlooking the influence of compressive stress in delaying crack propagation or promoting crack healing. Additionally, the conventional fatigue failure criteria, such as the 50% stiffness reduction method, may not fully capture the true fatigue behavior under bidirectional stress states [³]. A more comprehensive understanding of failure mechanisms is necessary to bridge this gap and develop more representative fatigue testing protocols [⁴].

Among available fatigue testing techniques, each method presents distinct advantages and disadvantages. The indirect tensile fatigue test is cost-effective and simple but does not simulate alternating stress fields. The four-point bending test provides a controlled environment for evaluating flexural fatigue resistance but lacks relevance to mixed-mode loading. Trapezoidal beam and uniaxial repeated loading tests require precise specimen preparation and extensive instrumentation. In contrast, the bidirectional splitting test offers a more practical yet comprehensive alternative by introducing simultaneous tensile and compressive forces, potentially yielding a more accurate assessment of asphalt mixture fatigue resistance [⁵].

Asphalt pavements form the backbone of modern transportation infrastructure, facilitating efficient and safe mobility across vast networks of roads worldwide. They are essential for economic growth, connecting urban centers, rural communities, and industrial hubs while enabling the efficient movement of goods and people. However, the durability and long-term performance of asphalt pavements are consistently challenged by fatigue-induced damage caused by repetitive traffic loading and environmental variations [⁶]. Fatigue cracking, a primary form of asphalt pavement deterioration, significantly undermines pavement functionality, increases maintenance costs, and compromises road safety. Addressing this critical issue requires a comprehensive understanding of fatigue mechanisms and the development of testing methods that closely replicate real-world stress conditions.

Historically, several fatigue testing methods have been employed to evaluate asphalt mixtures, including indirect tensile tests, four-point bending tests, and trapezoidal beam tests. Each method offers unique insights into fatigue behavior but often fails to simulate the complex, alternating tension-compression stress states typical of field conditions. The indirect tensile fatigue test, for example, has gained widespread adoption due to its simplicity and cost-effectiveness. However, its inability to replicate the alternating stress fields that asphalt pavements experience under vehicular loads is a significant limitation [⁷]. These unidirectional methods often produce fatigue life predictions that deviate from actual field performance, which is problematic for pavement design and maintenance strategies. As a result, the industry faces a significant knowledge gap in accurately predicting fatigue life and understanding the failure mechanisms of asphalt pavements.

Fatigue damage in asphalt pavements is a cumulative process influenced by traffic loading magnitude, frequency, environmental factors, and the material properties of the asphalt mixture. The repetitive loading leads to the initiation and propagation of microcracks, which eventually coalesce into visible cracks, reducing pavement integrity. Compounding this issue, the stress states induced by vehicle loads are not uniform. Asphalt pavements undergo a complex interplay of tension and compression, particularly in multilayered systems, which makes capturing their true fatigue behavior challenging with conventional methods [⁸]. Recognizing this gap is crucial for improving pavement performance and reducing life-cycle costs associated with frequent repairs and rehabilitation.

One of the emerging solutions to address this challenge is the bidirectional splitting fatigue test. This innovative approach introduces a more realistic stress state by simulating alternating tension and compression, reflecting the actual stress conditions of asphalt pavements under vehicular loads. By applying bidirectional loading, this method provides an opportunity to better understand the interaction between tensile and compressive forces and their impact on fatigue behavior. Such insights are vital for optimizing asphalt mixture designs to enhance durability, particularly as traffic volumes and axle loads continue to increase globally [⁹].

Several studies have emphasized the importance of considering bidirectional stress states in pavement testing, yet practical implementation remains limited. The conventional indirect tensile fatigue test continues to dominate due to its simplicity and established protocols, even though it provides only partial insights into fatigue mechanisms. Bidirectional testing, on the other hand, offers the potential to bridge this gap by accounting for stress reversals that promote crack propagation and healing in asphalt mixtures [¹⁰]. This dual effect of bidirectional loading—where tensile stresses initiate cracks and compressive stresses contribute to crack closure—makes it a promising area for further exploration [¹¹].

In addition to the fundamental need for more representative testing methods, the importance of this research is further underscored by the growing demand for sustainable and resilient pavements. Modern pavement engineering must address challenges such as climate change, heavier traffic loads, and increased expectations for long-lasting infrastructure. By advancing our understanding of fatigue behavior through improved testing methodologies, engineers can develop asphalt mixtures with enhanced resistance to cracking and longer service lives, thereby contributing to sustainability goals. Fatigue damage in asphalt pavements contributes significantly to environmental challenges by accelerating the need for frequent road repairs, leading to increased consumption of raw materials and energy-intensive reconstruction processes [¹²]. The deterioration of pavement surfaces due to fatigue-induced cracking can also exacerbate particulate matter emissions from vehicular traffic, negatively impacting air quality. Additionally, water infiltration through fatigue cracks can lead to subgrade erosion, necessitating more extensive and resource-intensive rehabilitation efforts. By adopting fatigue testing methods that promote the development of more durable asphalt mixtures, the environmental footprint of road maintenance activities can be reduced, aligning with sustainability-driven infrastructure policies [¹³].

The primary objective of this study is to evaluate the bidirectional splitting fatigue test as a superior alternative to traditional testing methods for assessing asphalt mixture fatigue performance. This research investigates the test’s ability to simulate real-world stress conditions and its implications for accurately predicting fatigue life [¹⁴]. By comparing the bidirectional splitting test with the conventional indirect tensile fatigue test under varying stress ratios, this study aims to elucidate the advantages of bidirectional loading in providing more realistic assessments of asphalt mixture performance [¹⁵].

The experimental program involves cylindrical AC-13 asphalt specimens subjected to controlled stress ratios (0.3, 0.4, 0.5, and 0.6) under constant temperature (20°C) and loading frequency (10 Hz). The specimens are evaluated for vertical displacement trends, fatigue life, and failure mechanisms [¹⁶]. To ensure a comprehensive evaluation of fatigue behavior, detailed material properties of the AC-13 asphalt mixture were considered. The aggregate gradation followed a nominal maximum aggregate size of 13 mm, with a well-graded distribution to optimize internal structure stability. The binder used was a PG 64-22 asphalt cement, chosen for its balance between flexibility and resistance to thermal cracking. The volumetric properties of the mixture were determined through laboratory testing, yielding an air void content of 4.0%, voids in mineral aggregate (VMA) of 15.2%, and voids filled with asphalt (VFA) of 73.6%. These parameters play a crucial role in governing fatigue resistance, influencing crack initiation and propagation during cyclic loading. By incorporating these properties into the analysis, the observed fatigue behavior can be more accurately correlated with material composition. Special attention is given to the influence of compressive stresses in delaying crack propagation and their role in enhancing fatigue performance under bidirectional loading. The results are expected to demonstrate the limitations of unidirectional testing methods and highlight the potential of bidirectional splitting as a more accurate and reliable approach [¹⁷].

The significance of this research extends beyond the development of improved testing methods. It contributes to the broader goal of designing more durable asphalt pavements capable of withstanding the increasing demands of modern transportation networks. By providing a deeper understanding of fatigue mechanisms and performance under realistic stress conditions, this study aims to pave the way for innovations in pavement materials and design practices. For the bidirectional splitting test to be widely adopted in engineering practice, its scalability and applicability to various pavement systems must be evaluated. While this study focuses on AC-13 asphalt mixtures, further research is required to determine its effectiveness across different asphalt grades, aggregate compositions, and binder formulations [¹⁸]. Additionally, assessing the adaptability of bidirectional fatigue testing to full-scale pavement structures using large-scale laboratory setups or accelerated pavement testing facilities would provide valuable insights into its practical implementation. If proven scalable, this test method could serve as a standardized procedure for fatigue evaluation in pavement engineering [¹⁹]. Future research directions may include the application of bidirectional testing to a wider range of asphalt mixtures, the exploration of its applicability under different environmental conditions, and the integration of findings into performance-based specifications. In doing so, this work aspires to set a foundation for more resilient and sustainable transportation infrastructure.

2. MATERIALS AND METHODS

Recent advancements in fatigue testing methodologies have emphasized the need for testing frameworks that capture both the tensile and compressive stress states experienced by asphalt pavements. Recent studies have proposed novel experimental setups incorporating digital image correlation techniques and acoustic emission monitoring to analyze fatigue crack propagation under bidirectional loading [²⁰]. The integration of such advanced characterization methods into future bidirectional splitting fatigue tests may provide deeper insights into material behavior, further strengthening the predictive capabilities of the test.

Under the action of a vehicle moving load, the stress (strain) of fixed points in the asphalt pavement structure layer presents the characteristics of alternating tension and compression, which causes the asphalt mixture to be subjected to the interaction of tension, compression, and shear; temperature changes and the thermal expansion - contraction effect of materials will also cause the stress (strain) in the pavement structure layer to present the characteristics of alternating tension and compression [²¹]. The asphalt mixture is subjected to the interaction of tension and compression. Therefore, under the coupling of vehicle load and temperature, the asphalt pavement structure is in a complex three-dimensional stress state, and the damage and destruction process of the asphalt mixture presents a damage evolution-induced mutation process under the interaction of compression, tension, and shear.

Pavement cracking is one of the primary structural diseases encountered when using asphalt pavements in all countries. According to the leading causes of asphalt pavement cracking, it can be divided into two categories: load-type and non-load-type. The fracture mode of cracks can be divided into three types. Type I fracture is also called open fracture (the most dangerous and deepest fracture mode is the type II fracture mode, which is also called the slip mode and the twist mode fracture mode. They are both related to shear stress and belong to shear fracture [²²].

Top-down cracks originate from or near the road surface and then expand downward. They usually appear on thicker asphalt pavements. Relatively long longitudinal cracks first form near the tires, and these cracks do not cross each other. There is no unified opinion in the road engineering community on the mechanism of this type of crack. The following are the main mechanisms of this type of crack Views: (1) Shear and tensile effects of high-pressure radial tire edges on asphalt pavement; (2) The aging of the surface layer of the asphalt pavement causes the stiffness of the asphalt pavement to increase, and the shearing effect of the tire under high contact pressure; (3) The tensile stress generated by the coupling of temperature and load, that is, when the temperature drops, the road surface will produce tensile stress, which is superimposed with the tensile stress generated by the driving load, resulting in cracks in the road surface. The aging of asphalt will also accelerate the expansion process of this crack [²³].

The fatigue damage process of the asphalt mixture is affected by many factors. Different fatigue test methods, loading modes, experimental conditions, and fatigue criteria will result in different fatigue lives. There are many fatigue test methods for asphalt mixtures. Because the test method is simple and easy to operate, the sample is easy to prepare. The fatigue test results have a specific correlation with the actual road performance, the highway asphalt pavement design specifications have adopted some research results; however, the indirect tensile fatigue test also has obvious shortcomings, such as the loading method and the actual. The stress state of the actual pavement is quite different, and the actual cracking mode of the specimen is often inconsistent with the theoretical cracking position. The US SHRP has conducted a detailed evaluation of the indirect tension, trapezoidal cantilever beam, and four-point bending methods [²⁴]. Numerous fatigue testing methods for asphalt mixtures have been developed in recent years. Estimating the fatigue life of asphalt pavement depends on factors such as fatigue load conditions, support conditions, experimental environment, and stress state. The simplicity and cost-effectiveness of the method also influence the choice of the fat gue testing method. Indoor fatigue tests are challenging in fully simulating the fatigue loads experienced by asphalt pavement and involve numerous parameters that are difficult to consider comprehensively, such as specimen preparation, complex loading conditions, arbitrary rest periods, and multiaxial stress states.

The advantages and disadvantages of several main fatigue testing methods are briefly introduced below.

Typical fatigue experiments in repeated flexural fatigue tests include the trapezoidal beam bending method and the four-point bending method. Although the specifications and loading methods differ, both methods subject the asphalt mixture specimens to repeated bending-tensile stresses. Both fatigue testing methods require special equipment and involve complex specimen preparation. However, they have been extensively studied and widely applied (Figure 1).

Figure 1
Repeated flexural fatigue testing.

The bending fatigue test of rubber pads can better simulate the stress conditions of asphalt pavement. The support conditions of the rubber pads are very similar to the support conditions of the roadbed under the asphalt pavement. There are two different specimen shapes: round plates and small beams. The asphalt mixture beam is padded under 4-inch thick rubber pads for fatigue analysis (Figure 2).

Figure 2
Uniaxial fatigue test.

This method benefits from straightforward specimen preparation and an analytical, experimental setup, correlating to some extent with existing fatigue data. However, the applied stress state differs notably from actual asphalt pavements, and the method is time-consuming, costly, and requires specialized equipment.

To enhance comprehension of the experimental methodology, additional schematic illustrations of the bidirectional splitting test setup and stress distribution within the asphalt specimens would provide clarity. These visual aids could highlight key differences between bidirectional and indirect tensile fatigue testing, further reinforcing the significance of the proposed method [²⁵]. Comparative graphical representations of displacement trends and fatigue failure patterns under different stress ratios may also assist in visualizing the advantages of bidirectional loading in mitigating fatigue damage. The indirect tensile test (Figure 3), also known as split fatigue testing, is commonly used due to its simplicity and the correlation between its results and actual pavement performance, leading to its adoption in some asphalt pavement design standards. However, it has some drawbacks, such as the loading method differing significantly from in-situ stress conditions and discrepancies between the expected and actual crack locations. Despite these issues, its widespread use is due to the ease of specimen preparation and low cost [²⁶].

Figure 3
Indirect tensile fatigue test.

The most widely used fatigue test methods for asphalt mixtures are the four-point bending fatigue test, uniaxial repeated tensile fatigue test, and indirect tensile fatigue test. However, according to research at home and abroad in recent years, some contradictory results have been obtained through these fatigue test methods. The following is a discussion of these three typical fatigue test methods [²⁷]. Since the species used in the bidirectional splitting mode are the same as those in the indirect tensile test, they are used for mutual comparison (Figure 4).

Figure 4
Circular specimen fatigue test.

The US SHRP has conducted a detailed evaluation of the indirect tension, trapezoidal beam, and four-point bending methods. After comprehensive analysis and evaluation, SHRP The A-003A research project finally selected the four-point bending fatigue test as the standard test for the fatigue performance study of asphalt mixtures. Therefore, the loading mode of the four-point bending fatigue test was first studied in depth [²⁸].

Four-point bending fatigue testing machines usually provide two loading waveforms, partial sine and sine. According to the SSHTO T321-03 standard, partial sine is used as the standard loading waveform for fatigue testing, which has two types: stress control and strain control. Loading mode. However, this name needs to be more scientific. Since asphalt mix ure is a typical viscoelastic material, the so-called strain control is displacement control. According to ASTM From the fatigue test of half-sine displacement control in D-7460, due to repeated unidirectional loading, permanent deformation causes the neutral axis of the beam to change, thus making the applied load a sine wave, which means that the beam is not subjected to unidirectional bending, but to bidirectional alternating bending [²⁹]. Therefore, the traditional method of using the bending-tensile stress or strain at the bottom of the beam as an analysis indicator needs to be revised. During the time curse, the beam’s damage is first caused by the bending-tensile stress. Then damage begins to appear at the bottom, causing the position of the central axis to change, thereby causing the applied load to change alternately in the upper and lower directions; that is, the bottom of the beam is in a stress state of alternating tension and compression.

3. RESULTS AND DISCUSSION

In this study, the asphalt mixture type used was AC-13, with an optimal asphalt content of 4.7%. A gyratory compact was employed to mold the specimens, compacting them 100 times to achieve a molded height of 150mm and a diameter of 100mm. Core cutting machines and precision double-face saws were used to cut the molded specimens into cylinders with a height of 50mm and a diameter of 100mm. The developed directional splitting test fixture, patented under number ZL201110404400.5, was utilized for the bi-directional splitting tests of the asphalt mixture cylindrical specimens. The load in the vertical direction is equal to that in the horizontal direction. When the pressure head applies a vertical load to the top plate, the upper-pressure strip loads the specimen; when the pressure head applies a tensile force, that is, deviates from the vertical top plate direction, the fixture transmits the hinge, and the connecting strip and the left and right lateral loading strips apply pressure. Therefore, the specimen is in a plane stress state under alternating tension and compression [³⁰].

Before the fatigue test, the AC-13 cylindrical asphalt mixture specimens were subjected to a splitting test at 20°C, with a 50 mm/min loading rate. There were 6 specimens; the average value was 11092 N (Figure 5).

Figure 5
Splitting strength of asphalt mixture specimens.

As illustrated above, the fatigue test fixture is octagonal, featuring four loading bars. Its unique geometrical design ensures that vertical and horizontal loads are equal. The upper loading bar engages with the specimen when the press applies a vertical load towards the top plate [³¹]. Conversely, when the press head applies a pulling force, diverging from the vertical direction towards the top plate, the fixture transmits this force via hinges and connecting bars, causing the left and right horizontal loading bars to apply pressure. As a result, the specimen is subjected to alternating tension and compression, creating a plane stress condition. Before conducting the fatigue tests, splitting experiments were performed on AC-13 cylindrical asphalt mixture specimens at 20°C [³²]. The loading rate was set to 50mm/min, and the average force recorded from six specimens was 11092N.

To study the influence of load on the fatigue performance of the asphalt mixture, the top plate of the fixture is connected to the MTS810 electronic, hydraulic servo closed-loop material testing system. The best range is usually 20%~80% of the maximum force of the force sensor, and the minimum limit is 2% of the maximum force; the test load should not be less than 2% of the force sensor range [³³]. Bidirectional splitting and indirect tensile fatigue tests under stress ratios of 0.3, 0.4, 0.5, and 0.6 were studied, respectively. For the indirect tensile fatigue test, the load is only applied in the vertical direction, and the maximum displacement in the lateral direction is generally measured by setting up sensors; for bidirectional splitting, due to its alternating lateral and vertical loading, it is not suitable for the traditional method of using lateral displacement as the research object (Figure 6). There is no way to set up sensors. This study takes vertical displacement as the research object and indirectly studies the fatigue damage process of asphalt mixture specimens. The vertical disp cement process of the indirect tensile fatigue test continuously accumulates vertically downward, while the bidirectional splitting changes alternately up and down in the vertical direction since the fatigue experiment is consistent in the time dimension. The displacement time history data of bidirectional splitting under vertical loading [³⁴].

Figure 6
Output curves of vertical force and displacement for indirect tensile fatigue test.

It is extracted and compared with the vertical displacement curve of the indirect tensile fatigue test. The experimental parameters of the indirect tension and biaxial splitting fatigue tests are as follows: four stress ratios of 0.3, 0.4, 0.5, and 0.6, the experimental temperature is 20°C, and the frequency is 10HZ. Figure 6 shows the vertical force and displacement under 0.3 stress ratio and 10HZ [³⁵]. The fixture’s top plate was connected to an MTS810 electronic, hydraulic servo closed-loop material testing system to investigate the impact of load on the fatigue performance of asphalt mixtures. It is generally best to operate within 20% to 80% of the maximum force range of the force sensor, with a minimum limit set at 2% of the sensor’s range, meaning the test load should not be less than 2% of the force sensor’s capacity. Studies were conducted on bi-directional splitting and indirect tensile fatigue tests under stress ratios of 0.3, 0.4, 0.5, and 0.6. For the indirect ensile fatigue tests, loads were applied only in the vertical direction, usually measuring the maximum lateral displacement through a sensor [³⁶]. For bi-directional splitting, given the alternating vertical and horizontal loading, traditional methods that focus on lateral displacement as the subject of study are not suitable, nor is it feasible to place sensors. This study focuses on vertical displacement as the subject, indirectly researching the progression of fatigue damage in asphalt mixture specimens. In indirect tensile fatigue tests, the vertical displacement progression continuously accumulates downwards, whereas, in bi-directional splitting, it alternates up and down in the vertical direction. Since the fatigue experiments are consistent in the time dimension, the displacement-time-time data of bi-directional splitting under vertical loading were extracted for comparison with the vertical displacement curves of indirect tensile fatigue tests [³⁷].

The experimental parameters for the indirect tensile and bidirectional splitting fatigue tests were as follows: stress ratios of 0.3, 0.4, 0.5, and 0.6, with an experimental temperature of 20°C and a frequency of 10Hz. When compared to other established fatigue testing techniques, such as four-point bending and direct tension fatigue tests, the bidirectional splitting method presents unique advantages in replicating field-relevant stress conditions. Unlike the four-point bending test, which predominantly induces flexural stresses, the bidirectional test introduces alternating tensile-compressive loading, better representing the real-world fatigue behavior of asphalt pavements [³⁸]. Furthermore, while the uniaxial tension-compression test provides direct insight into material fatigue properties, it often requires specialized specimen preparation and extensive equipment calibration. The bidirectional splitting test, by contrast, offers a balance between practicality and accuracy, making it a viable alternative for routine fatigue performance assessment in asphalt mixtures. Figure 7 shows the vertical force and displacement-time history curves at a stress ratio of 0.3 and a frequency of 10Hz. To ensure statistical reliability, fatigue life data were analyzed using regression modeling techniques to establish fatigue damage relationships under different stress ratios. A logarithmic regression model was employed to fit the fatigue damage progression curves, providing correlation coefficients that quantify the statistical significance of the observed trends. Additionally, variance analysis (ANOVA) was conducted to determine the influence of stress ratio variations on fatigue life outcomes [³⁹]. The use of confidence intervals and hypothesis testing further strengthened the robustness of the comparisons between bidirectional splitting and indirect tensile fatigue tests [⁴⁰].

Figure 7
Output curves of vertical force and displacement for bi-directional splitting fatigue test.

Taking the point on the cylindrical specimen in contact with the upper layer as the research object, the vertical displacement time history curves of the bidirectional splitting and indirect tensile tests in the same period are essentially different [⁴¹]. There are several points worth further attention:

• The consistency between the load input and the specimen response. Taking the 0.3 st ess ratio as an example, 11092 * 0.3 = 3328 (N), the input error of unidirectional and bidirectional is within 100N, which needs to be revised in accuracy.

• The indirect tensile fatigue test can only provide a unidirectional vertical load, which is fundamentally different from the alternating tension and compression stress mode of asphalt pavement; the bidirectional splitting mode can provide an equal amplitude alternating tension and compression stress field, which is closer to the asphalt pavement stress mode, but not wholly consistent.

• In the same time history, the bidirectional splitting fatigue test has an additional lateral load compared with the indirect tension fatigue test. It is worth noting that the accumulated vertical deformation in the bidirectional splitting mode is much smaller than the vertical displacement generated by the indirect tension fatigue test.

Focusing on the points of contact between the cylindrical test specimens and the compression bar, a study of the vertical displacement-time history curves during the same time frame reveals fundamental differences between the bi-directional splitting and indirect tensile fatigue tests [⁴²]. The consistency between load input and specimen response. Taking a stress ratio of 0.3 as an example, 11092 x 0.3 = 3328 N, the input error for both unidirectional and bidirectional is within 100 N, which indicates a slight lack of precision [⁴³]. The indirect tensile fatigue test can only provide unidirectional vertical loading, fundamentally differing from the alternating tension-compression stress mode experienced by asphalt pavements; the bidirectional splitting mode offers an alternating stress field of equal magnitude in tension and compression, which more closely resembles the stress pattern on asphalt pavements, but it is not an exact match [⁴⁴]. Within the same duration, the bidirectional splitting fatigue test introduces lateral loads compared to the indirect tensile fatigue test. Notably, the cumulative vertical deformation in the bidirectional splitting mode is significantly lower than the vertical displacement observed in the indirect tensile fatigue test [⁴⁵].

3.1. Analysis of Fatigue Damage under Alternating Tension and Compression

To investigate the impact of compressive stress on the progression of fatigue damage in asphalt mixture specimens, the tension and compression phases were separated within their respective time domains under the bidirectional splitting mode. Figure 8 and Figure 9 display the vertical displacement-time history curves at a stress ratio of 0.3 and a frequency of 10 Hz.

Figure 8
Bi-directional splitting vertical displacement curve between 300–301s (0.3 Stress Ratio, 10 Hz).

Figure 9
Bi-directional splitting vertical displacement curve (0.3 Stress Ratio, 10 Hz)

As seen from the Figure 10, there are apparent differences between the indirect tensile fatigue test curve of unidirectional loading and the tension-compression alternating fatigue test curve of bidirectional loading. For the indirect tensile test, the vertical displacement is always negative; for the vertical displacement curve of the tension-compression alternating fatigue test, when the vertical displacement is positive, it is lateral loading; when the vertical displacement is negative, it is vertical loading [⁴⁶]. To compare the difference between the two fatigue tests, the vertical time history of the lateral and vertical loading of the indirect tensile fatigue test is separated; that is, the time history of the vertical loading of the tension-compression alternating fatigue test is separated and compared with the indirect tensile fatigue test [⁴⁷]. The failure modes of the two fatigue test specimens and the fatigue cracks of the asphalt pavement are shown in Figure 11.

Figure 10
Unidirectional splitting vertical displacement curve between 300–301s (0.3 Stress Ratio, 10Hz).

Figure 11
Unidirectional splitting vertical displacement curve (0.3 Stress Ratio, 10Hz).

From the Figure 12, we can see that at the experimental temperature of 20°C, 0.3 Under the stress ratio of, the maximum displacement in the bidirectional splitting mode is 56% less than the maximum vertical displacement in the indirect tensile mode, and the growth process of its vertical displacement is slow [⁴⁸]. The typical failure mode of the indirect tensile fatigue test specimen is a crack that penetrates the specimen along the radial direction; the failure mode of the bidirectional splitting fatigue test specimen is a cross-shaped cross crack. For the cracking domain of the asphalt pavement, the fatigue cracks observed are multiple mesh cracks composed of cross-shaped cross cracks. For the cracking domain of the asphalt mixture specimen in the indoor fatigue test, the energy input by the test loading consists of three parts: elastic storage energy, plastic deformation energy, and cracking energy. The loading path that the indirect tensile fatigue test can provide is only one direction, the cracking pattern is relatively regular, and the asphalt mixture involved in the work is relatively small [⁴⁹]. For the bidirectional splitting mode, the cracking path is more complicated, the cracking domain is more significant, and the asphalt mixture involved in the contribution is more, which seems to be more consistent with the actual cracking path of the pavement. The reason is that the stress state of the asphalt mixture loaded by the bidirectional splitting is similar to the stress on the asphalt pavement, which leads to the formation of fatigue cracks that are also very similar.

Figure 12
Comparison of vertical displacement-time history curves.

Figure 13 shows that for the indirect tensile fatigue test, the vertical displacement time history curves under different stress ratios are basically. The difference is that the time is different, and the vertical displacement increases rapidly. However, for the bidirectional splitting fatigue test, 0.3 and 0.4 stress ratio, there is an obvious inflection point at the 0.4 stress ratio. The potential has changed significantly and is essentially different. In the vertical d displacement curve of the bidirectional splitting fatigue test, the trend of the vertical displacement curve changes dramatically at the inflection point under each stress ratio [⁵⁰]. The reason is that the material’s mechanical properties have changed, more asphalt mixtures are involved in the bidirectional splitting mode, and the force is complex. Under repeated loading, cracks are generated inside the asphalt mixture, which changes the internal structure of the asphalt mixture specimen, so the response to the load has changed; that is, it is considered that damage has occurred at this time [⁵¹]. The inflection point of the vertical displacement process curve in each tension-compression time spectrum under different stress ratios is taken out, and the point here is taken as the fatigue life. Figure 14 shows the vertical displacement process of the 10Hz bidirectional splitting fatigue test [⁵²].

Figure 13
Comparison of peak vertical displacements.

Figure 14
Progression of vertical displacement within the lateral load time spectrum.

As seen from the Figure 15, the stress ratio greatly influences the vertical displacement process of the asphalt mixture under a bidirectional splitting load. It not only access rates the vertical displacement process but also changes the trend of vertical displacement at high-stress ratios. The specific conclusions are as follows: Compared with the indirect tensile loading mode, the fatigue life of the asphalt mixture in the two-way splitting fatigue test is significantly increased due to the participation of transverse load; the amplitude of the increase is different under different stress ratios, indicating that the transverse load plays a vital role in the asphalt mixture [⁵³]. The compressive stress generated inside the asphalt mixture specimen is beneficial in extending the fatigue life of the asphalt mixture. Crack healing in asphalt mixtures under compressive stress has been reported in previous studies, where intermittent loading allows for microcrack closure and partial material recovery. Microscopic analysis of asphalt fatigue damage has shown that compressive stress can realign bitumen molecules within the crack interface, facilitating adhesion and reducing crack growth rates. Advanced imaging techniques such as X-ray computed tomography and digital image correlation have further confirmed that asphalt mixtures subjected to cyclic compression exhibit delayed crack propagation compared to purely tensile-loaded specimens [⁵⁴]. These findings support the hypothesis that the bidirectional splitting test, by introducing alternating tensile and compressive forces, enhances the potential for in-situ crack healing, contributing to prolonged fatigue life. When the stress ratio is 0.4, 0.5, and 0.6, the damage process of the asphalt mixture in the two-way splitting mode has a mutation phenomenon, and after the mutation, its response to the load changes until it fails. The reason is that cracks are formed inside the asphalt mixture specimen under repeated two-way splitting mode, which causes the internal structure to change but does not cause structural damage. With the repeated application of the load, the damage occurred at different rates and trends until the specimen was broken entirely [⁵⁵]. When the stress ratio increases to 0.5, the fatigue life decreases sharply. In contrast, at smaller stress ratios of 0.3 and 0.4, the vertical displacement time history curves have a relatively consistent trend and a longer fatigue life. Analysis of the reasons for this situation: The mechanical behavior of compressive stress is relatively complex. Considering the fatigue performance of the mixture under tensile and compressive loads, when the compressive stress is low, it generates positive stress that causes the material to heal during the action process. When the compressor stress reaches a higher level, the compressive stress will generate shear stress that causes the material to fail.

Figure 15
Progression of vertical displacement within the vertical load time spectrum.

To compare the effects of the two fatigue tests further on the damage process of the asphalt mixture, the stiffness modulus is generally used as the damage variable for fatigue damage analysis. However, for different fatigue tests, even if the same type of asphalt mixture specimens are used, the stiffness modulus obtained is different; therefore, in order to eliminate the differences in the methods of the two fatigue tests of indirect tension and biaxial splitting, the damage factor D and the number of load actions Nf are used to study their fatigue damage process: To further compare the impact of two types of fatigue tests on the damage progression of asphalt mixtures, stiffness modulus is generally used as a damage variable for fatigue damage analysis. However, the stiffness modulus of different fatigue tests can vary even when identical asphalt mixture specimens are used. Therefore, to eliminate the discrepancies due to the differences in methods between the indirect tensile and the bidirectional splitting

Fatigue tests, the fatigue damage process is studied by employing the damage factor \(D\) and the number of load applications (N_f):

(1) $$D=1-\frac{S_N}{S_0}$$

D is the damage factor, S 0 is the initial stiffness modulus, and S N is the stiffness modulus corresponding to the load N times. Figure 16 shows the indirect tensile fatigue damage process and bidirectional splitting fatigue damage process curves, respectively. In the formula, (D) represents the damage factor, (S₀) is the initial stiffness modulus, (S_N) and is the stiffness modulus corresponding to the load after (N) applications. Figure 17, illustrate the curves of the fatigue damage process for indirect tensile and bidirectional splitting fatigue tests.

Figure 16
Fatigue damage progression under indirect tensile testing conducted at 10 Hz.

Figure 17
Bidirectional splitting fatigue damage process (10HZ).

Figure 18 only takes the initial load action times; the data is only analyzed a part before the vertical displacement curve has a significant trend change. It is believed that when the vertical displacement curve has a significant turning point and breakpoint, apparent damage has already occurred inside the specimen. Figure 19 shows the bidirectional splitting fatigue’s initial damage growth stage. In terms of the initial damage process, the fatigue damage process of the asphalt mixture specimen produced by the indirect tensile fatigue test is much faster than the damage process of the bidirectional splitting fatigue; it can be seen from the vertical displacement curve of the bidirectional splitting fatigue that compared with the indirect tensile fatigue test, after the participation of the lateral load, when the vertical displacement changes significantly, the asphalt mixture specimen can still work in different mechanical states and will not break quickly. The bidirectional fatigue damage process under different stress ratios at 10HZ was fitted, and it was found that the initial damage stage obeys logarithmic growth. As shown in Table 1:

Figure 18
Comparison of the estimated life span of two fatigue test methods.

Figure 19
Ratio of fatigue life of two fatigue tests.

Table 1
Fatigue damage curve fitting equations.

STRESS RATIO	FATIGUE TEST TYPE
	INDIRECT STRETCHING	CORRELATION COEFFICIENT	BIDIRECTIONAL CLEAVAGE	CORRELATION COEFFICIENT
0.3	D = 0.1485ln(Nf) – 0.3397	0.96	D = 0.0957ln(Nf) – 0.2785	0.87
0.4	D = 0.1352ln(Nf) – 0.2003	0.91	D = 0.0675ln(Nf) + 0.0448	0.99
0.5	D = 0.1753ln(Nf) – 0.1385	0.98	D = 0.1568ln(Nf) – 0.4131	0.98
0.6	D = 0.1862ln(Nf) – 0.0987	0.98	D = 0.1023ln(Nf) + 0.1084	0.97

The damage process of the indirect tensile fatigue test and biaxial splitting fatigue test is studied. The ratio of the coefficients before l n (N f) has a specific rule. Indirect tensile fatigue and bidirectional splitting fatigue tests are respectively 0.3, 0.4, 0.5, and Under the stress ratio of 0.6, the coefficient ratios are 1.55, 2.00, 1.12, and 1.82; that is, the damage process of indirect tension is greater than that of bidirectional tension. In this work, the bidirectional splitting fatigue life is defined as the inflection point of the vertical displacement curve, and it is believed that the asphalt mixture specimen has apparent damage at this point. The determination of fatigue life in this study is based on identifying an inflection point in the vertical displacement curve, signifying a significant change in the material’s mechanical response. This approach aligns with studies that utilize displacement trends to assess fatigue performance. However, conventional fatigue failure criteria, such as the 50% stiffness reduction method, are commonly employed in asphalt mixture fatigue evaluation. The 50% stiffness reduction method defines fatigue life as the number of cycles at which the stiffness modulus drops to half its initial value, providing a widely accepted measure of fatigue resistance. While this method effectively captures the loss of structural integrity, it does not necessarily account for the alternating stress effects present in bidirectional loading. Further validation through stiffness modulus tracking or energy-based fatigue criteria would strengthen the applicability of the proposed inflection point method. The fatigue life comparison under different stress ratios is shown in Table 2.

Table 2
Comparison of fatigue life between indirect tensile and bidirectional splitting tests.

STRESS RATIO	FATIGUE LIFE (TIMES)			FATIGUE LIFE RATIO
	BIDIRECTIONAL CLEAVAGE		INDIRECT STRETCHING	BIDIRECTIONAL CLEAVAGE/INDIRECT TENSION
	LATERAL LOADING	VERTICAL LOADING
0.3	15024	15022	4269	3.52
0.4	12425	12425	459	27.07
0.5	4399	4400	266	16.54
0.6	3313	1339	228	5.87

Comparing the fatigue life of indirect tensile fatigue tests with bidirectional splitting fatigue tests reveals that the latter exhibits a significantly longer fatigue life. In the bidirectional splitting fatigue tests, a noticeable decline in fatigue life occurs as the stress ratio shifts from 0.4 to 0.5, with the most significant discrepancy in fatigue life ratios observed at a stress ratio of 0.4 [⁵⁶]. However, the fatigue life does not vary substantially when the stress ratio changes from 0.3 to 0.4. In contrast, the indirect tensile fatigue tests demonstrate a pronounced change over this range. At lower stress ratios, the bidirectional splitting fatigue tests apply lateral loading, generating compressive stresses within the asphalt mixture specimens. These compressive stresses are moderate and can help heal micro-cracks within the mixture. At higher stress ratios, this lateral loading can lead to shear failure [⁵⁷].

4. CONCLUSION

The comparative analysis presented in this paper evaluates several fatigue testing methods commonly used in assessing asphalt mixture behavior under repeated loading conditions. Among these methods, the four-point bending fatigue test and the indirect tensile fatigue test are examined, with a recommendation for adopting the bidirectional splitting fatigue test. Key conclusions drawn from the analysis highlight significant differences and advantages of the bidirectional splitting fatigue test over the indirect tensile fatigue test. The study observes that the stress and strain responses generated during the bidirectional splitting fatigue test closely resemble those experienced by asphalt pavements under moving loads. This similarity is crucial as it replicates alternating tensile and compressive stress fields typical of actual pavement conditions, providing a more realistic simulation of field performance. Secondly, in terms of performance evaluation, the bidirectional splitting fatigue test demonstrates reduced permanent deformation within asphalt mixture specimens compared to the indirect tensile fatigue test. This reduction is critical as it minimizes the influence of permanent deformation on fatigue damage studies, allowing for a more accurate assessment of material fatigue characteristics. Thirdly, the study notes distinct behaviors under varying stress ratios between the two tests. For the indirect tensile fatigue test, an increase in stress ratio accelerates vertical displacement without altering the fundamental trend. In contrast, the bidirectional splitting fatigue test exhibits varying trends in vertical displacement curves under different stress ratios, suggesting a more complex response that may better capture real-world pavement conditions. Lastly, the bidirectional splitting fatigue test shows slower damage progression and potentially more extraordinary fatigue life, particularly at lower stress ratios. This outcome underscores the test’s ability to provide a more durable material assessment, which is crucial for designing asphalt mixtures that can withstand prolonged service under varying traffic loads and environmental conditions. Despite the promising insights provided by the bidirectional splitting fatigue test, several limitations must be acknowledged. One primary constraint is the controlled laboratory environment, which does not fully account for external factors such as temperature fluctuations, moisture infiltration, and dynamic loading variations present in actual pavement conditions. Additionally, while the bidirectional loading test replicates alternating stress fields, it does not entirely capture the complex multiaxial stress states encountered in layered pavement structures. To address these limitations, future studies should incorporate field validation experiments, long-term performance monitoring, and numerical modeling techniques to refine fatigue life predictions and improve the applicability of laboratory results to pavement engineering practice.

5. ACKNOWLEDGMENTS

Zhejiang Provincial Transportation Department Science and Technology Project: Evaluation and treatment of road surface hidden disease key technology research (2023009), Optimization Research on Key Techniques for Asphalt Pavement Structure and Material Design in Typical Sections of Overloaded Traffic (ZK202406).

6. BIBLIOGRAPHY

• ^[1] BARRA, B.S., MOMM, L., PÉREZ, Y.A.G., et al, “A new dynamic apparatus for asphalt mix fatigue and stiffness modulus: development, validation and numerical simulations”, Matéria, v. 27, n. 1, e13130, 2022. doi: http://doi.org/10.1590/s1517-707620220001.1330.
  » https://doi.org/10.1590/s1517-707620220001.1330
• ^[2] AL QADI, A.N.S., ALHASANAT, M.B.A., HADDAD, M., “Effect of crumb rubber as coarse and fine aggregates on the properties of asphalt concrete”, American Journal of Engineering and Applied Sciences, v. 9, n. 3, pp. 558–564, 2016. doi: http://doi.org/10.3844/ajeassp.2016.558.564.
  » https://doi.org/10.3844/ajeassp.2016.558.564
• ^[3] SOUZA, L.P.B., PARRA, D.P., RAIOL, J.A.F., et al, “Control of a mechanism for the application of variable axial loads in a multiaxial fatigue testing machine”, Matéria, v. 28, e20230180, 2023.
• ^[4] KHEDAYWI, T., HADDAD, M., KHALDI, N.A.H., “Study on the feasibility of using waste glass in binder and asphalt mixture”, Innovative Infrastructure Solutions, v. 9, n. 6, pp. 227, 2024. doi: http://doi.org/10.1007/s41062-024-01537-y.
  » https://doi.org/10.1007/s41062-024-01537-y
• ^[5] KHEDAYWI, T., HADDAD, M., ALYASEEN, S., “Effect of filler materials on marshall properties and rutting of asphalt mixtures using wheel tracking test: a comparative study”, Journal of Engineering Science and Technology, v. 18, pp. 1915–1935, 2023.
• ^[6] KENNEDY, T.W., “Pavement design characteristics of in-service asphalt mixtures”, Transportation Research Record: Journal of the Transportation Research Board, pp. 24–32, 1977.
• ^[7] WEN, H., KIM, Y.R., “Simple performance test for fatigue cracking and validation with WesTrack mixtures”, Transportation Research Record: Journal of the Transportation Research Board, v. 1789, n. 1, pp. 66–72, 2002. doi: http://doi.org/10.3141/1789-07.
  » https://doi.org/10.3141/1789-07
• ^[8] CHEN, J.-S., LIN, K.-Y., “Evaluation of an accelerated pavement testing facility and development of its load equivalence factors”, Journal of Testing and Evaluation, v. 30, n. 2, pp. 103–109, 2002. doi: http://doi.org/10.1520/JTE12295J.
  » https://doi.org/10.1520/JTE12295J
• ^[9] JOENCK, F.T., JOENCK, V.B.C., DEL CARPIO, J.A.V., et al, “Self-healing capacity of asphalt mixtures with steel fiber, steel slag angraphite powder, evaluated with microwave induction and fatigue test”, Matéria, v. 27, e20220221, 2022.
• ^[10] ADEDIMILA, A.S., KENNEDY, T.W., “Repeated-load indirect tensile fatigue characteristics of asphalt mixtures”, Transportation Research Record: Journal of the Transportation Research Board, pp. 25–33, 1976.
• ^[11] COLOMBO, A.L., LARAZ, F.B., SILVA JÚNIOR, J.F., et al, “Evaluation of kaolin and bauxite from the Amazonian region addition on mechanical-, physical-, chemical properties and microstructural characterization of red ceramic industry clay of Manaus metropolitan region”, Matéria, v. 23, n. 3, e12205, 2018. doi: http://doi.org/10.1590/s1517-707620180003.0539.
  » https://doi.org/10.1590/s1517-707620180003.0539
• ^[12] HADDAD, M., KHEDAYWI, T., HADDAD, M., et al, “Investigating the effect of olive husk ash on dynamic creep of asphalt concrete mixtures”, Journal of Engineering Science and Technology, v. 18, pp. 931–948, 2023.
• ^[13] MOHAMMAD, L., “Laboratory performance evaluation SMA, CMHB and dense graded asphalt mixtures”, Proceedings of the Association of Asphalt Paving Technologists, v. 68, pp. 252–283, 1999.
• ^[14] SILVA, N.A.B., SILVA, T.O., PITANGA, H.N., et al, “Use of mechanistic-empirical method of pavement design for performance sensitivity analysis to asphalt pavement fatigue”, Matéria, v. 26, n. 3, e13045, 2021. doi: http://doi.org/10.1590/s1517-707620210003.1345.
  » https://doi.org/10.1590/s1517-707620210003.1345
• ^[15] KENNEDY, T.W., HAAS, R., SMITH, P., et al, “Engineering evaluation of sulphur-asphalt mixtures”, Transportation Research Record: Journal of the Transportation Research Board, pp. 12–17, 1977.
• ^[16] SILVA, M.P.S., SANTOS, L.F., SILVA, A.C.L., et al, “Shear strength of a typical soil from Manaus, Brazil, stabilized with ceramic residue additive”, Matéria, v. 24, n. 2, e12353, 2019. doi: http://doi.org/10.1590/s1517-707620190002.0668.
  » https://doi.org/10.1590/s1517-707620190002.0668
• ^[17] RAMSAMOOJ, D.V., “Prediction of fatigue life of asphalt concrete beams from fracture tests”, Journal of Testing and Evaluation, v. 19, n. 3, pp. 231–239, 1991. doi: http://doi.org/10.1520/JTE12561J.
  » https://doi.org/10.1520/JTE12561J
• ^[18] KHEDAYWI, T., BAKER, M.B., HADDAD, M., et al, “Effect of waste plastic polyethylene terephthalate on properties of asphalt concrete mixtures”, International Journal of Pavement Research and Technology, v. 2024, pp. 1–15, 2024. doi: http://doi.org/10.1007/s42947-024-00479-z.
  » https://doi.org/10.1007/s42947-024-00479-z
• ^[19] BARRA, B.S., MOMM, L., PÉREZ, Y.A.G., et al, “A new dynamic apparatus for asphalt mix fatigue and stiffness modulus: development, validation and numerical simulations”, Matéria, v. 27, n. 1, pp. 1, 2022. doi: http://doi.org/10.1590/s1517-707620220001.1330.
  » https://doi.org/10.1590/s1517-707620220001.1330
• ^[20] KHEDAYWI, T., HADDAD, M., BATAINEH, H., “Effect of waste plastic polyethylene terephthalate on properties of asphalt cement”, Innovative Infrastructure Solutions, v. 8, n. 9, pp. 1–20, 2023. doi: http://doi.org/10.1007/s41062-023-01208-4.
  » https://doi.org/10.1007/s41062-023-01208-4
• ^[21] KHEDAYWI, T., HADDAD, M., MUJALLI, R., et al, “Effect of sulfur on the asphalt cement and asphalt concrete mixture: state of the art”, Innovative Infrastructure Solutions, v. 8, n. 11, pp. 1–14, 2023. doi: http://doi.org/10.1007/s41062-023-01264-w.
  » https://doi.org/10.1007/s41062-023-01264-w
• ^[22] FIGUEIREDO, M.A.V., JESUS, A.M.P., RIBEIRO, A.S., et al, “Fatigue behaviour of riveted steel lap joints”, In: Proceedings of the 3rd International Conference on Bridge Maintenance, Safety and Management - Bridge Maintenance, Safety, Management, Life-Cycle Performance and Cost, pp. 479–481, 2006.
• ^[23] OLIVEIRA, M.S., FARIAS, M.M., “Hot recycled asphalt mixtures with the incorporation of milled material: analysis of the mechanical performance and economic presumption in the applicability of the technique”, Matéria, v. 27, n. 4, e2022-0217, 2022. doi: http://doi.org/10.1590/1517-7076-rmat-2022-0217.
  » https://doi.org/10.1590/1517-7076-rmat-2022-0217
• ^[24] HUANG, X.-M., ZHANG, J.-P., LIU, W.-M., “Prediction of indirect tensile fatigue life of asphalt mixture by means of viscoelastic theory”, Journal of South China University of Technology, v. 36, pp. 56–61, 2008.
• ^[25] HADDAD, M.A., KHEDAYWI, T.S., “Moisture resistance of olive husk ash modified asphalt mixtures”, Annales de Chimie–Science des Materiaux, v. 47, n. 3, pp. 141–149, 2023. doi: http://doi.org/10.18280/acsm.470303.
  » https://doi.org/10.18280/acsm.470303
• ^[26] YILMAZ, M., KÖK, B.V., KULOĞLU, N., “Effects of using asphaltite as filler on mechanical properties of hot mix asphalt”, Construction & Building Materials, v. 25, n. 11, pp. 4279–4286, 2011. doi: http://doi.org/10.1016/j.conbuildmat.2011.04.072.
  » https://doi.org/10.1016/j.conbuildmat.2011.04.072
• ^[27] SILVA, C.C.V.P., MELO NETO, O.M., RODRIGUES, J.K.G., et al, “Evaluation of the rheological effect of asphalt binder modification using Linum usitatissimum oil”, Matéria, v. 27, e20220138, 2022.
• ^[28] MUNIANDY, R., ABURKABA, E., “The effect of type and particle size of industrial wastes filler on indirect tensile stiffness and fatigue performance of Stone Mastic Asphalt Mixtures”, Australian Journal of Basic and Applied Sciences, v. 5, pp. 297–308, 2011.
• ^[29] WU, S., ZHANG, Y., CHEN, M., “Research on mechanical characteristics of conductive asphalt concrete by indirect tensile test “, Engineering Fracture Mechanics, v. 7522, pp. 1, 2010. doi: http://doi.org/10.1117/12.851473.
  » https://doi.org/10.1117/12.851473
• ^[30] KLÜNSNER, T., MARSONER, S., EBNER, R., et al, “Effect of microstructure on fatigue properties of WC-Co hard metals”, Procedia Engineering, v. 2, n. 1, pp. 2001–2010, 2010. doi: http://doi.org/10.1016/j.proeng.2010.03.215.
  » https://doi.org/10.1016/j.proeng.2010.03.215
• ^[31] AL-QADI, I., WANG, H., TUTUMLUER, E., “Dynamic analysis of thin asphalt pavements by using cross-anisotropic stress-dependent properties for granular layer”, Transportation Research Record: Journal of the Transportation Research Board, v. 2154, n. 1, pp. 156–163, 2010. doi: http://doi.org/10.3141/2154-16.
  » https://doi.org/10.3141/2154-16
• ^[32] ZHAO, L., BAI, Z., XU, B., et al, “Influence of chemical pore-clearing method on infiltration ratof pervious asphalt concrete pavement”, Matéria, v. 27, e20220207, 2022. doi: http://doi.org/10.1590/1517-7076-RMAT-2022-0207.
  » https://doi.org/10.1590/1517-7076-RMAT-2022-0207
• ^[33] AHMED, T.A., HAJJ, E.Y., SEBAALY, P.E., et al, “Influence of aggregate source and warm-mix technologies on the mechanical properties of asphalt mixtures”, Advances in Civil Engineering Materials, v. 2, n. 1, pp. 400–417, 2013. doi: http://doi.org/10.1520/ACEM20130072.
  » https://doi.org/10.1520/ACEM20130072
• ^[34] LÜ, S.-T., “Fatigue equation of asphalt mixture considering the influence of loading rate”, Engineering Mechanics, v. 29, pp. 276–281, 2012. doi: http://doi.org/10.6052/j.issn.1000-4750.2011.05.0273.
  » https://doi.org/10.6052/j.issn.1000-4750.2011.05.0273
• ^[35] LÜ, S.-T., “Axle load conversion of asphalt pavement based on nonlinear fatigue damage”, Engineering Mechanics, v. 29, pp. 268–274, 2012. doi: http://doi.org/10.6052/j.issn.1000-4750.2011.05.0294.
  » https://doi.org/10.6052/j.issn.1000-4750.2011.05.0294
• ^[36] RONDON-QUINTANA, H.A., RUGE-CARDENAS, J.C., REYES-LIZCANO, F.A., et al, “Mechanical resistance of hot-mix asphalt using phosphorite as filler”, Journal of Materials in Civil Engineering, v. 35, n. 9, pp. 04023274, 2023. doi: http://doi.org/10.1061/JMCEE7.MTENG-15720.
  » https://doi.org/10.1061/JMCEE7.MTENG-15720
• ^[37] CHEN, J.-Y., LIU, J.-Y., MA, Q., “Performance evaluation of recycled SMA mixtures with warm-mix agent”, Advanced Materials Research, v. 723, pp. 648–655, 2013. doi: http://doi.org/10.4028/www.scientific.net/AMR.723.648.
  » https://doi.org/10.4028/www.scientific.net/AMR.723.648
• ^[38] KHEDAYWI, T., HADDAD, M., HWARIE, S., “Effect of waste iron powder on properties of asphalt concrete mixtures: state of the art”, International Journal of Pavement Research and Technology, v. 18, n. 1, pp. 91–101, 2023. doi: http://doi.org/10.1007/s42947-023-00328-5.
  » https://doi.org/10.1007/s42947-023-00328-5
• ^[39] AL QADI, A.N.S., KHEDAYWI, T.S., HADDAD, M.A., et al, “Investigating the effect of olive husk ash on the properties of asphalt concrete mixture”, Annales de Chimie--Science des Materiaux, v. 45, n. 1, pp. 11–15, 2021. doi: http://doi.org/10.18280/acsm.450102.
  » https://doi.org/10.18280/acsm.450102
• ^[40] KHATTAK, N.U., IRFAN, M., HOY, M., et al, “Effects of synergistic combined Bakelite and Nano clay modification on asphalt mixture performance properties”, Road Materials and Pavement Design, pp. 1–17, 2025. doi: http://doi.org/10.1080/14680629.2024.2446427.
• ^[41] LV, S., WANG, Z., ZHU, X., et al, “Research on strength and fatigue properties of asphalt mixture with different gradation curves”, Construction & Building Materials, v. 364, pp. 129872, 2023. doi: http://doi.org/10.1016/j.conbuildmat.2022.129872.
  » https://doi.org/10.1016/j.conbuildmat.2022.129872
• ^[42] ZHENG, Y., CHEN, S., HUANG, W., et al, “Principle analysis of the mix design and performance evaluation of the asphalt-filler volume equivalent substitution method”, Construction & Building Materials, v. 367, pp. 130276, 2023. doi: http://doi.org/10.1016/j.conbuildmat.2022.130276.
  » https://doi.org/10.1016/j.conbuildmat.2022.130276
• ^[43] MOGHIMI, S., SHAFABAKHSH, G., DIVANDARI, H., “Evaluation of rutting, fatigue, and moisture resistance of low-energy asphalt mixtures modified by crumb rubber”, Advances in Civil Engineering, v. 2023, pp. 1–21, 2023. doi: http://doi.org/10.1155/2023/6668963.
  » https://doi.org/10.1155/2023/6668963
• ^[44] WANG, Z., LU, W., LIU, K., et al, “Research on failure strength master curve and fatigue performance of asphalt mixture containing high-proportion reclaimed asphalt pavement”, Construction & Building Materials, v. 370, pp. 130537, 2023. doi: http://doi.org/10.1016/j.conbuildmat.2023.130537.
  » https://doi.org/10.1016/j.conbuildmat.2023.130537
• ^[45] JU, Z., GE, D., LV, S., et al, “Investigation on fatigue characteristics of polyphosphoric acid modified high dosage bio-asphalt mixture under three-dimensional stress state”, Construction & Building Materials, v. 401, pp. 132749, 2023. doi: http://doi.org/10.1016/j.conbuildmat.2023.132749.
  » https://doi.org/10.1016/j.conbuildmat.2023.132749
• ^[46] GOLI, H., LATIFI, M., SADEGHIAN, M., “Comparing the effect of moisture on different fatigue and cracking behaviors of RAP-WMA”, Journal of Transportation Engineering Part B: Pavements, v. 149, n. 4, pp. 04023026, 2023. doi: http://doi.org/10.1061/JPEODX.PVENG-1220.
  » https://doi.org/10.1061/JPEODX.PVENG-1220
• ^[47] HOY, M., SUDDEEPONG, A., HORPIBULSUK, S., et al, “Improved performance of natural rubber latex–modified asphalt concretes with various types of aggregates”, Journal of Materials in Civil Engineering, v. 36, n. 1, pp. 04023495, 2024. doi: http://doi.org/10.1061/JMCEE7.MTENG-16274.
  » https://doi.org/10.1061/JMCEE7.MTENG-16274
• ^[48] LI, H., LUO, X., GU, Z., et al, “Predicting crack growth of paving materials under indirect tensile fatigue loads”, International Journal of Fatigue, v. 175, pp. 107818, 2023. doi: http://doi.org/10.1016/j.ijfatigue.2023.107818.
  » https://doi.org/10.1016/j.ijfatigue.2023.107818
• ^[49] HE, Y., LV, S., WANG, Z., et al, “Research on the modulus decay model under a three-dimensional stress state of asphalt mixture during fatigue damage”, Buildings, v. 13, n. 10, pp. 2570, 2023. doi: http://doi.org/10.3390/buildings13102570.
  » https://doi.org/10.3390/buildings13102570
• ^[50] KIM, K., LE, T.H.M., “Feasibility and sustainable performance of RAP mixtures with low-viscosity binder and castor wax–corn oil rejuvenators”, Buildings, v. 13, n. 7, pp. 1578, 2023. doi: http://doi.org/10.3390/buildings13071578.
  » https://doi.org/10.3390/buildings13071578
• ^[51] CORREA, P.M., GUIMARÃES, D., SANTANA, R.M.C., et al, “Potential use of PET and PP as partial replacement of sand in structural concrete”, Matéria, v. 26, n. 3, e13009, 2021. doi: http://doi.org/10.1590/s1517-707620210003.13009.
  » https://doi.org/10.1590/s1517-707620210003.13009
• ^[52] GE, D., JU, Z., DUAN, D., et al, “Normalized fatigue properties of asphalt mixture at various temperatures”, Journal of Road Engineering, v. 3, n. 3, pp. 279–287, 2023. doi: http://doi.org/10.1016/j.jreng.2023.05.001.
  » https://doi.org/10.1016/j.jreng.2023.05.001
• ^[53] AL-GHURABI, S.B., AL-GURAH, E.R., MOHAMMED HAMZA, W., “Assessment of indirect tensile stress and tensile-strength ratio and creep compliance in HMA mixes with micro-silica and PMB”, Open Engineering, v. 14, n. 1, pp. 20220527, 2024. doi: http://doi.org/10.1515/eng-2022-0527.
  » https://doi.org/10.1515/eng-2022-0527
• ^[54] OMAR, H.A., YUSOFF, N.I.M., MUBARAKI, M., et al, “Effects of moisture damage on asphalt mixtures”, Journal of Traffic and Transportation Engineering, v. 7, n. 5, pp. 600–628, 2020. doi: http://doi.org/10.1016/j.jtte.2020.07.001.
  » https://doi.org/10.1016/j.jtte.2020.07.001
• ^[55] ZHAN, Y., WU, H., SONG, W., et al, “A framework for estimating the fracture resistance of hot mix asphalt using an energy approach”, Engineering Fracture Mechanics, v. 281, pp. 109129, 2023. doi: http://doi.org/10.1016/j.engfracmech.2023.109129.
  » https://doi.org/10.1016/j.engfracmech.2023.109129
• ^[56] SILVA, N.A.B., SILVA, T.O., PITANGA, H.N., et al, “Use of mechanistic-empirical method of pavement design for performance sensitivity analysis to asphalt pavement fatigue”, Matéria, v. 26, n. 3, e13045, 2021. doi: http://doi.org/10.1590/s1517-707620210003.1345.
  » https://doi.org/10.1590/s1517-707620210003.1345
• ^[57] GAMA, D.A., LUCENA, A.E.F.L., PORTO, T.M.R., et al, “Study of incorporation of footwear industry residues in asphalt mixtures”, Matéria, v. 23, n. 3, e12197, 2018. doi: http://doi.org/10.1590/s1517-707620180003.0531.
  » https://doi.org/10.1590/s1517-707620180003.0531

Publication Dates

• Publication in this collection
  19 May 2025
• Date of issue
  2025

History

• Received
  09 Jan 2025
• Accepted
  25 Feb 2025