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Fatigue performance and self-repairing activity of asphalt binders are two properties that highly influence the fatigue cracking response of asphalt pavement. There are still numerous gaps in knowledge to fill linked with these two characteristics. For instance, current parameters fail to accommodate these two bitumen phenomena fully. This study aims to propose a new procedure to address this issue utilizing the linear amplitude sweep (LAS) test, LAS with rest period (RP) (LASH) test, and simplified viscoelastic continuum damage (S-VECD) model. This research work used four different types of asphalt binders: neat asphalt (NA), self-healing thermoplastic polyurethane (STPU)-modified bitumen (STPB), self-healing poly (dimethyl siloxane) crosslinked with urea bond (IPA1w)-modified bitumen (IPAB), and styrene–butadiene–styrene (SBS)-modified bitumen (SBSB). Before the testing process, all the materials were subjected to short-term and long-term aging. The new procedure showed a superior capacity to analyze and accommodate all bitumen fatigue performances and self-repairing activities compared to the current method. Another finding proved that asphalt binders with a higher self-restoration behavior failed to show a better fatigue performance. Moreover, the higher fatigue performance increments produced by STPU and IPA1w in NA concerning the control bitumen were 123.7% and 143.7%, respectively. Those values were obtained with 1.0% STPU and 0.5% IPA1w in NA. A breakthrough finding demonstrated that asphalt binder fatigue response is augmented when the RP was applied at a higher damage intensity (S) value. STPB and IPAB reached their highest increments of fatigue response, containing 1.0% of STPU and 0.5% of IPA1w, respectively. Those augmentations were 207.54% and 232.64%, respectively. [ABSTRACT FROM AUTHOR]

The comprehensive properties evaluation index of asphalt mixture has the characteristics of multilevel and multifactor. The weight of each road performance index is the key factor to assess the comprehensive properties of the asphalt mixture. However, how to determine the weight objectively is a very key problem in the performance evaluation model. In this study, the comparison matrix method was used to determine the performance weight objectively of rock asphalt modified bio-asphalt mixture (RABAM). First, the neat asphalt mixture (NAM), bio-asphalt mixture (BAM), rock asphalt modified asphalt mixture (RAM), and RABAM were prepared. Second, the high-temperature and low-temperature properties, water damage resistance, and fatigue characteristics of the different asphalt mixtures was analyzed. Finally, the comprehensive properties were evaluated under different climate zones in China. The results indicated that the rock asphalt improves the comprehensive performance of BAM. Applying the comparison matrix method to the field of road materials can effectively evaluate the applicability of road materials in different regions. [ABSTRACT FROM AUTHOR]

A full understanding of bitumen fatigue cracking behavior is extremely important as this phenomenon has a considerable influence on bituminous pavement performance. The current framework for assessing this asphalt binder property is inconsistent in ranking bitumen fatigue performance in terms of the failure definition and damage characteristic curve (DCC) analysis. This study used four different types of asphalt binders: neat asphalt (NA), self-healing thermoplastic polyurethane (STP)-modified bitumen, self-healing poly (dimethyl siloxane) crosslinked with urea bond (IPA1w)-modified bitumen, and styrene–butadiene–styrene (SBS)-modified bitumen (SBSB). All the bitumens were subjected to short-term and long-term aging, and they were also tested by utilizing the linear amplitude sweep (LAS) test and the simplified viscoelastic continuum damage (S-VECD) model. LAS and S-VECD procedures were used to apply the newly proposed and current frameworks in order to analyze bitumen performance. The current framework showed that the bitumens that used a higher number of loading cycles (N) to reach their failure points ( N f ) failed to exhibit greater fatigue performances in terms of DCC analysis. The developed framework (mainly based on the damage intensity [S] instead of N) was used to solve the inconsistency between the failure definition and DCC assessment in ranking bitumen performance. Additionally, the current framework (failure criterion) presented two R2 values below 0.1, but the developed framework (failure criterion) showed that all R2 values were greater than 0.9. The developed framework represents a turning point because, for the first time, this type of procedure is mainly being based on S instead of N. Although further tests are needed to confirm its efficiency, it eliminates the inconsistency between the failure definition and DCC assessment. [ABSTRACT FROM AUTHOR]

Fatigue damage can develop within asphalt pavement due to the continuous impact of driving loads and natural elements. Understanding the process of asphalt mixtures' fatigue damage is crucial for guiding the design, maintenance, and repair of asphalt pavement. This research aims to establish a model that characterizes the mixtures' modulus decay under a three-dimensional (3-D) stress state. Firstly, asphalt mixes were subjected to direct tensile (DT), indirect tensile (IDT), unconfined compressive (UC) strength and fatigue tests, and the resulting data were analyzed. Then, modulus decay models under DT, IDT, and UC conditions were established, and the modulus decay patterns under the three loading modes were compared and analyzed. Finally, using the fatigue stress strength ratio Δ (a fatigue resistance index for asphalt mixtures that takes into account the impacts of stress state and loading rate), a unified characterization model for asphalt mixes' modulus decay under a 3-D stress state was created. According to the study's findings, asphalt mixes' modulus decay during fatigue damage exhibits obvious nonlinear characteristics. While the asphalt mixes' modulus decay law with various loading modalities is similar under the same conditions, the decay rate may differ. Essentially, the speed of the modulus decay of a certain asphalt mixture primarily depends on the value of Δ during service. A larger Δ indicates a faster modulus decay. This study offers a theoretical foundation for the conversion from material fatigue damage to structural fatigue damage, which is vital for enhancing the asphalt pavements' construction quality and longevity. [ABSTRACT FROM AUTHOR]

Fatigue cracking is a common form of flexible pavement distress, which generally starts and spreads through bitumen. To address this issue, self-healing elastomer (SHE) modified bitumens were elaborated to assess whether these novel materials can overcome the neat asphalt (NA) fatigue performance and whether the current failure definition, failure criterion, and fatigue-restoration criteria can fit their performance. All bitumens were subjected to short-term and long-term aging. Linear amplitude sweep (LAS) test, LAS with rest period (LASH), and simplified viscoelastic-continuum-damage (S-VECD) model were utilized to appraise the behavior of the mentioned bitumens. The results showed that maximum stored pseudo-strain energy (PSE) and tau (τ) × N (number of loading cycles) failure definitions exhibited high efficiency to accommodate the fatigue life of NA and SHE-modified bitumens. Both failure criteria identified that SHE-modified bitumen (containing 1% of SHE) showed the highest increment of fatigue performance (67.1%) concerning NA. The failure criterion based on total released PSE, in terms of the area under the released PSE curve, was the only failure concept with high efficiency (R2 up to 0.999) to predict asphalt binder fatigue life. As well, the current framework to evaluate bitumen self-restoration failed to fully accommodate asphalt binder behavior, because bitumen with higher restoration could not exhibit greater fatigue performance. Consequently, a new procedure to assess this property including fatigue behavior was proposed, showing consistent results, and confirming that SHE-modified bitumen (containing 1% of SHE) exhibited the highest increment of fatigue performance (154.02%) after application of the rest period. Hence, the optimum SHE content in NA was 1%. Furthermore, it was found that a greater number of loading cycles to failure ( N f ) did not ensure better fatigue performance and stored PSE influenced the bitumen fatigue behavior. [ABSTRACT FROM AUTHOR]

In this paper, styrene butadiene rubber (SBR) was utilized to improve the low-temperature performance of Buton-rock asphalt (BRA)-modified asphalt. Firstly, the optimum content of SBR modifier agent was determined by basic mechanical property tests, including penetration, ductility, and soft point tests. The comprehensive road performance, including high- and low-temperature performance, moisture resistance, and antifatigue performance at a low-temperature condition, of SBR-BRA-modified asphalt mixtures was evaluated by comparison with a base asphalt mixture, SBR-modified asphalt mixture, BRA-modified asphalt, and styrene-butadiene-styrene (SBS)-modified asphalt mixture. The fatigue test under the experimental temperature of −10°C and loading frequencies of 0.01, 0.1, 1, 5, and 10 Hz were designed to evaluate the antifatigue capacity of SBR-BRA-modified asphalt mixture under the low-temperature region. The S-N fatigue equation with the stress ratio related to loading rates was proposed to characterize the fatigue property of asphalt mixtures and reveal the different effects of loading frequency and materials on the fatigue property of asphalt mixtures. The tests results demonstrated that the SBR-BRA-modified asphalt has an equal road performance to SBS-modified asphalt. Analyzed by the S-N fatigue equation with the stress ratio related to loading rates, the fatigue test results under different loading frequencies could be fitted to a fatigue curve, and the fatigue curves of different asphalt mixtures exist at an angle and intersect at point (1,1). [ABSTRACT FROM AUTHOR]

• The variation of strength with loading rate under various loading modes were revealed for cement-stabilized macadam. • The fatigue properties of cement stabilized macadam under different loading modes were uniformly characterized. • The new strength structure coefficient associated with the loading rate was proposed for cement-stabilized macadam. Cement-stabilized macadam is widely employed as a base-layer of pavement in China, because of its high strength and stiffness. However, fatigue cracking of the cement-stabilized macadam based pavement is prone to occur under multiple traffic loads, which affects the service life of the pavement. The main objective of this work is to reveal the fatigue characteristics of cement-stabilized macadam under various loading modes by developing a unified fatigue characteristics model. To this end, an unconfined compressive strength test, indirect tensile strength test, and four-point bending strength test were conducted for the cement-stabilized macadam samples under various loading rates. A power function was employed to the pattern of variation of strength with loading rates. The stress ratio of the fatigue test associated with the loading rate was obtained and defined as the rate-dependent stress ratio. Also, the fatigue tests under various loading modes were implemented based on the rate-dependent stress ratio and nominal stress ratio. The preliminary laboratory experimental results showed that it is challenging to compare fatigue performance under different loading modes based on nominal stress ratio. However, the problems of uncertainty and non-uniqueness of fatigue characteristics under various loading modes were resolved by employing the idea of rate-dependent stress ratio in the correlation analyses. Based on that, the new strength structure coefficient associated with the loading rate was proposed in this study. Therefore, the proposed research results provided the fundamental understanding of the fatigue resistance design of pavement with semi-rigid base-layer. [ABSTRACT FROM AUTHOR]

• Study fatigue based on modulus decay considering variance of compressive-tensile. • A synchronous test method of modulus was used to monitor modulus during fatigue test. • The modulus decay mode of tensile and compressive were established and compared. The cement stabilized macadam base experiences tensile and compressive stresses simultaneously in the actual pavement structures, resulting in the influence of stress states on fatigue performance. In this paper, the fatigue performance of cement stabilized macadam was analyzed based on modulus decay considering the difference between compressive and tensile modulus. A synchronous measurement method of tensile and compressive modulus, which based on convention four-point bending test, was utilized to measure modulus of cement stabilized macadam during a fatigue test. The four-point bending fatigue test was conducted upon four different stress levels of 0.25 MPa, 0.5 MPa, 1.0 MPa, and 1.5 MPa. The average of 10 closest modulus values nearby the first 1% of fatigue life was adopted to determine the initial modulus. The last 5 cycles before the failure of the specimen in the fatigue test was determined as the critical modulus value. It was observed from the tests results that the critical value of compressive fatigue modulus was 8 times higher than that of tensile fatigue modulus. The initial and critical values of both tensile and compression decreased with the increase of stress levels. Under different stress levels, the modulus decay mode of tensile and compressive modulus was similar, but the decay rates of tensile modulus were higher than that of compressive modulus. Based on the modulus decay mode, the concept of critical failure point was put forward to characterize the fatigue behavior of cement stabilized macadam. During the fatigue process, both tensile and compressive modulus decay presented three stages, i.e. preliminary stage, stable stage, and rapid attenuation stage. The stable stage of tensile modulus was shorter than that of compressive modulus, which means that the primary fatigue damage occurred in the tensile zone. [ABSTRACT FROM AUTHOR]

Highlights • The strength and fatigue tests of asphalt mixtures were implemented. • The evolution patterns of strength with loading rate were revealed. • The unified fatigue model of asphalt mixtures was established. • The behavior of thermal fatigue and strength failure was integrated. Abstract In order to reveal the thermal fatigue behavior of asphalt mixtures under low temperature conditions, the four-point bending beam tests of strength and fatigue were carried out. The asphalt mixtures are typical viscoelastic materials whose fatigue properties are significantly influenced by low loading frequency. Thus, the fatigue tests under low loading frequency were used to simulate the thermal fatigue of asphalt mixtures. Based on the nominal stress ratio (not considering the effect of loading rate on the strength value) and the real stress ratio (the strength value corresponding to the loading rate of fatigue test), the fatigue equations of asphalt mixtures under low temperature and low frequency conditions were established. The flexural strengths of the four-point bending beam tests at different loading rates at 0 °C, −10 °C and −20 °C were studied. The results show that the flexural strength of asphalt mixtures expresses a power function on the pattern of variation with the loading rates. The intersection of fatigue curve characterized by the nominal stress ratio and the abscissa axis is much larger than 1. The fatigue curve based on the nominal stress ratio cannot be extended to fatigue failure point (1,1). But the fatigue curve characterized by the real stress ratio can be extended to the strength failure point, whose fatigue life is 1. So, the behavior of strength failure and fatigue failure was integrated. The uniform characterization model of fatigue equations for asphalt mixture under low temperature and low loading frequency conditions was realized, which means that the fatigue equations and curves under different loading frequencies could be characterized by one equation and one curve. The results can provide a theoretical basis for predicting the thermal fatigue performance of asphalt mixtures under low temperature conditions more accurately. [ABSTRACT FROM AUTHOR]

In order to explore the moduli decay patterns of asphalt mixtures under different loading conditions, the nonlinear fatigue damage model was implemented in order to simulate the moduli decay patterns. Then, the direct tensile, indirect tensile, and uniaxial compression fatigue tests were employed under four kinds of stress levels with four parallel tests. The specimens of AC-13C Styrene-butadiene-styrene (SBS) modified mixtures were manufactured. Based on the test results, the decay patterns of the moduli during fatigue tests under different stress states were revealed, and the parameters of the damage model under different test conditions were obtained. By changing the values of the model parameters under a certain loading condition, fatigue curves were obtained. Then, the fatigue properties of asphalt mixtures under different stress states could be compared and analyzed directly. The result indicated that the evolution curves of fatigue damage for the direct tensile test, the indirect tensile test, and the uniaxial compression test all experienced three stages, which indicates that the fatigue damage characteristic of asphalt mixtures is non-linear. The decay patterns of the direct tensile moduli and the tensile moduli measured by the indirect tensile test are similar. The decay patterns of the uniaxial compression and the compression moduli measured by indirect tensile test are similar. The decay patterns of tensile and compressive moduli are obviously different. At the same cycle ratio state, the position of the decay curve for the compression moduli is higher than that of the tensile moduli. It indicates that the tensile failure is the main reason of the fatigue damage for asphalt mixture. The new analysis method of fatigue damage was proposed, which provides a possibility to compare the fatigue results that were obtained from different loading conditions and different specimen sizes. [ABSTRACT FROM AUTHOR]

The objective of this article is to establish a fatigue equation based on the true stress ratio for cement-treated aggregate base materials. The true stress ratio herein means the ratio of the stress and the true strength of the cement-treated aggregate base materials related to loading rates and curing times. The unconfined compressive strength tests and compressive resilience modulus tests were carried out under various loading rates and curing times of 3, 7, 14, 28, 60, 90 days, respectively. According to the test results, the relationship between the unconfined compressive strength (a mix design parameter in China) and the compressive resilience modulus (a structural design parameter and the construction quality control parameter in China) of the cement-treated aggregate base material with different curing times was established. However, it was found that the strengths varied with the loading rates, which is not reflected in the existing fatigue equations. Therefore, it is questionable to obtain the stress ratio of fatigue tests with a fixed strength value obtained from the standard strength test where the loading rate is fixed (in China, the fixed loading rate is 1 mm/min for cement-treated aggregate base materials). Thus, in this paper, the four-point bending strength (i.e., flexural strength) test was carried out at different loading rates to resolve such deficiencies. Based on the strength test results at different loading rates, the true stress ratio of the fatigue test corresponding to the fatigue loading rate can be calculated. Then the four-point bending fatigue test was conducted to establish an improved fatigue equation characterized by the true stress ratio. The results show that the patterns of variation for unconfined compressive strength increasing with the curing time were similar to that of the compressive resilience modulus. The fatigue equation curve based on the true stress ratio can be extended to the strength failure point of (1, 1), where both the true stress ratio and the fatigue life value are one. The internal relationship between the strength failure and the fatigue failure was unified. This article provides a theoretical method and basis for unifying the mix design parameters and the construction quality control parameters. [ABSTRACT FROM AUTHOR]

• The strength model under 3D stress state was proposed through conventional tests. • The characterization equation of fatigue characteristics under 3D stress state was established. • The fatigue strength model with equivalent stress as the index was developed. The cement-stabilized macadam (CSM) material is in a three-dimensional (3D) complex stress state in the pavement structure. It is difficult for the conventional test method to characterize the 3D fatigue strength characteristics of the CSM. In order to establish a 3D fatigue strength design criterion through simple strength methods, this work conducted the conventional unconfined compressive (UC), direct tensile (DT), and indirect tensile (IT) tests. The corresponding 3D strength model, including three parameters, was determined based on three strength testing methods. In addition, a normalized fatigue model including one parameter was obtained by three fatigue tests. Finally, the fatigue strength model under a 3D stress state was established by combining fatigue and the 3D strength model. The results indicate that the 3D strength model effectively characterized the CSM strength under any stress state, and the difference between the IT strengths predicted by the 3D strength model and obtained by the test is 18.43%. Moreover, the fatigue normalization model reflected the 3D fatigue failure of CSM in a complex stress state. The proposed fatigue strength of CSM based on the equivalent stress has clear physical meaning. This work provided a practical technology to obtain 3D fatigue strength resistance of CSM, which solved the technical problem of inaccurate measurement of pavement structure resistance. [ABSTRACT FROM AUTHOR]

• The strength properties of asphalt mixture with different gradation curves were evaluated. • A unified fatigue model was developed based on the fatigue stress strength ratio. • The gradation curve of asphalt mixture with the optimal strength and fatigue performance was determined. The gradation design has an essential influence on the mechanical properties of asphalt mixture. Strength and fatigue are two critical mechanical properties of asphalt pavement structure. The purpose of this paper is to reveal the strength and fatigue properties of asphalt mixture with four gradation curves within the range of AC-16, namely Types A, B, C, and D. Strength and fatigue tests were conducted under indirect tensile, direct tensile, and unconfined compressive loading modes. The strength of asphalt mixture with various gradation curves shows a power function relationship with the loading rate. The fatigue performance of asphalt mixture with different gradation curves was first analyzed based on the conventional S-N fatigue model. Then, the unified fatigue models under three different loading modes were established based on the fatigue stress strength ratio, which reduced the difference of S-N fatigue equation parameters. Furthermore, the unified fatigue equations achieved the unity of strength failure and primary fatigue failure. The analysis results indicate that the mixture with Type D gradation curve realizes the highest strength and most extended fatigue life. This research contributes to the gradation design of asphalt mixture. And the unified fatigue equation provides a reference for the durability design of pavement. [ABSTRACT FROM AUTHOR]

• A new fatigue model of asphalt mixture is established, which can normalize the fatigue characteristics under various temperatures and several loading frequencies. • Time-temperature equivalence of fatigue life is demonstrated and fatigue master curves was formed. • The time-temperature equivalence happens on fatigue and strength at the same time in the new model. This work presents a new method for evaluating the time-temperature equivalence and unified characterization of the fatigue performance for asphalt mixtures. For this purpose, direct tensile strength tests and direct tensile fatigue tests were carried out on asphalt mixtures at different temperatures and loading rates. A time-temperature-dependent stress ratio was established. By exploring the correlation between stress ratio and fatigue life, a new fatigue model considering the effect of temperature and loading time was built. The time-temperature equivalent of fatigue performance was confirmed by analysis of the fatigue dates under several temperatures and loading frequencies. The results showed that the direct tensile strength of the asphalt mixture changed non-linearly with the variation of the loading rate or temperature. The stress ratio was also related to temperature and loading rate. The time-temperature stress ratio was linearly related to fatigue life in a double logarithmic coordinate system, and a new S N fatigue curve was formed. The fatigue life under several temperatures and various loading frequencies can be described in one fatigue model and the time-temperature equivalent can be explored. The master curve of fatigue life or stress ratio was built. The time-temperature superposition principle was applicable for fatigue life estimation and stress ratio calculation. The fatigue life under different loading frequencies and various temperatures of the pavement in service can be completely estimated. The relative error between the test results and the calculated values is less than 30%. [ABSTRACT FROM AUTHOR]

• The strength variation of HMAC with loading rate under various loading patterns was revealed. • The fatigue properties of HMAC measured by diverse experiments were normalized. • The accuracy of fatigue resistances design parameters for high modulus asphalt pavements was improved. As a new material, high modulus asphalt concrete (HMAC) with good durability is widely used in the pavement engineering. One of the most critical performance indexes of HMAC is the fatigue cracking. However, in the experiment of evaluating the fatigue properties, different anti-fatigue effects are obtained only by adding different modifiers. In addition, using only one loading mode to determine the fatigue properties of HMAC neglects the fact that there is a difference among the fatigue test results in various loading modes, which artificially leads to the non-uniqueness and unscientific design of high modulus asphalt pavements for the fatigue resistance. Therefore, four internationally accepted mainstream strength tests at different loading rates, including direct tension, indirect tension, unconfined compression and four-point bending tests, were carried out to enhance the veracity of structural resistance design of high modulus asphalt pavements. It is revealed that the fitted curve for the variation of strength with loading rate is a power function with velocity dependence, and the models for direct tension, indirect tension, unconfined compression, and four-point bending strengths established as a function of loading rate are S D = 3.218v0.1425 , S T = 3.833v0.1768 , S C = 14.391v0.1130 and S F = 7.839v0.1489 respectively. Besides, it is shown that the conventional S-N fatigue equation does not take into account the velocity dependence of the strength of HMAC in the stress ratios determined by the tests, and the velocity-dependent stress ratios defined in this paper are determined by the strength model and therefore take into account the viscoelasticity of HMAC. In addition, it is found that extending the fatigue curve backwards, when the fatigue life of HMAC is also close to 1, the velocity-dependent stress ratio is 1. Meanwhile, the fatigue model N f = t v -5.318 was developed by unifying the characterization of HMAC and considering the effect of loading rate in various loading modes. It eliminated the difference of fatigue test results caused by the specimen sizes and loading modes, and effectively improved the completeness of structural design of high modulus asphalt pavements, which provided a theoretical basis for designing the high modulus asphalt pavements. [ABSTRACT FROM AUTHOR]

• The mechanical response between the field measured and the designed modulus was compared. • The optimization for modulus combinations of pavement structural was proposed. • The fatigue properties of material and structure were unified. The early damage of the semi-rigid base asphalt pavement is related to the pavement structure modulus's unreasonable matching. In this study, three typical pavement structures were selected to analyze the pavement structures' influence on the pavement service life. A three-dimensional finite element pavement structure model was established. The independent variables are subgrade modulus, base course modulus, and subbase modulus. The deflection, the bottom tensile stress, and maximum shear stress were chosen as the evaluation indexes. The effect of the modulus on the mechanical response of the pavement structure was analyzed. The optimal modulus combination of the pavement structure was determined through multi-factor range analysis. The mechanical response and fatigue life before and after the optimization pavement structure were compared. The results showed that the field measured modulus of Structure 1 and 2 was higher than the design modulus. Moreover, while the modulus of base course and subbase course was increased, the deflection gradually reduced. The base course's bottom tensile stress and the subbase were increased, and the maximum shear stress was basically unchanged. After the modulus combination optimized pavement structure, the mechanical response was significantly reduced. The fatigue life based on the deflection and bottom tensile stress, and the laboratory normalized fatigue equation were significantly increased. By the combination of fatigue performance of pavement materials and pavement structure, it was possible to provide an effective optimization method for the design of semi-rigid base asphalt pavement in this research work. [ABSTRACT FROM AUTHOR]

• The Ayyagari model was applied to semi-rigid layers materials. • The unified fatigue model was obtained based on yield criterion. • A new design index of structural resistance was proposed. As the primary high-grade pavement structure, asphalt pavement with semi-rigid layers has been extensively applied in China. Among the semi-rigid layers materials, cement-treated aggregates (CTA) are an essential pavement element, and its fatigue life significantly affects the durability of the asphalt pavement structure. Various fatigue tests have been adopted to evaluate the fatigue properties of CTA. However, the fatigue resistance of the CTA measured under various methods is different, which seriously affects the accuracy of the structural design of the semi-rigid layers. Hence, this work aims to establish a design criterion for CTA to characterize the structural resistance of semi-rigid layers. The uniaxial compression (UC), four-point bending (4 PB), and indirect tensile (IDT) strength and fatigue tests for CTA were carried out. According to the traditional S - N fatigue model, the curves of fatigue performance and stress ratio of CTA under various stress states are quite different. To intuitively compare the structural resistance of CTA under various test types, the mean stress and effective stress of CTA under different loading rates were obtained. The yield surface was then established based on the Ayyagari model, considering the multiaxial yield criterion of CTA. The effective stress ratio was defined, and its relationship with the fatigue life of CTA was established. Based on the Ayyagari model and the normalized equation, the fatigue resistance criterion of semi-rigid layers under the three-dimensional stress state was proposed. [ABSTRACT FROM AUTHOR]

• A connection between strength and fatigue was revealed. • The established new fatigue model eliminates the influence of test methods. • A quantitative analysis was made on the difference in fatigue properties. At present, many test methods and models have been used to evaluate the fatigue performance of pavement materials. However, different test methods and material types have a significant impact on the fatigue result evaluation. Thus, to evaluate the fatigue characteristics of different pavement materials under diverse test methods, the strength and fatigue performance of three pavement materials were characterized through direct tension, uniaxial compression, and indirect tensile tests at multiple loading rates and stress levels. In this paper, three pavement materials, such as SBS-modified asphalt mixture (SBS-MAM), crumb rubber asphalt mixtures (CRAM), and cement-stabilized macadam (CSM), were tested. On this basis, the strength yield surface models related to loading rates and the fatigue normalized unified model of three pavement materials under various stress states were established. Comparing the differences among the three pavement materials' fatigue performance, the results show that the fatigue results of the three pavement materials were completely different under dissimilar test methods. The conventional fatigue equation cannot evaluate the influence of specimen size and stress state on fatigue performance. However, the fatigue normalization model established in this paper can settle these problems. It is also clear that the fatigue performance of CSM is superior to those of the other two mixtures when the stress level is small. However, the fatigue life of CSM is significantly more sensitive to the stress level than those of the other two mixtures. Based on the establishment and comparative analysis of the normalized models of fatigue characteristics of different pavement materials, the scientific conversion of pavement material fatigue to structural fatigue is realized, which provides sights into the anti-fatigue design of pavement structures. [ABSTRACT FROM AUTHOR]

• A suitable yield criterion for rubberized asphalt mixtures was proposed. • A strength yield surface and unified fatigue equation were determined. • The impact of the test method on the results of the fatigue test was eliminated. Under the action of traffic load, the stress and failure state of pavement structure and materials are complex and diverse. Moreover, pavement materials are multi-phase, multi-component, and multi-scale mixtures. Their mechanical properties have significant differences in tension behavior, compression characteristics, and correlations with stress states. In view of the above problems, different testing approaches were carried out in this paper. A suitable yield criterion for rubberized asphalt mixtures was proposed. Then, the strength yield surface was determined under different loading rates. Based on the fatigue test results, the concept of fatigue stress ratio was further proposed. The relationship between the rubberized asphalt mixtures fatigue life and the fatigue stress ratio was established. The results showed that the yield criterion covers the impact of the loading rates and tensile-compression strength difference on the rubberized asphalt mixtures' mechanical behavior. The strength yield surface's shape is elliptical in the σ m - σ e stress space and expands outward as the loading rate increases. This paper unified the fatigue equations under different testing approaches. The established fatigue equations reflect the viscoelastic characteristics and strength characteristics of materials. The study effectively solves the difficult problem of fatigue equation selection in the structural design of asphalt rubber pavement. [ABSTRACT FROM AUTHOR]

The most common primary damage form of rubber asphalt pavements is fatigue cracking. At present, the indirect tension, direct tension, bending, and unconfined compression tests are the main considered fatigue parameters to design the structure of rubber asphalt pavement. However, the fatigue test results analyzed by various test methods have a quite significant divergence, which represents a lack of accuracy to access the durability of rubber asphalt mixture objectively. Thus, in the structural resistance design of rubber asphalt pavement, there exists a problem of artificial randomness of fatigue parameters. Hence, the primary objective of this study is to improve the procedure for determining the structural resistance of rubber asphalt pavement. To this end, the direct tensile, unconfined compressive, and indirect tensile strength tests of rubber asphalt mixture were performed under various loading rates to reveal the velocity-dependent of the strength of rubber asphalt mixture. The model of direct tensile strength, unconfined compressive strength, and indirect tensile strength increasing with loading rate are S D = 7.772 v 0.205, S C = 1.748 v 0.204, and S T = 1.077 v 0.207, respectively. The stress ratio related to both the traditional S–N fatigue equation and the loading rate was defined as the standard stress ratio and the velocity-dependent stress ratio, respectively. The fatigue test of rubber asphalt mixture was conducted. The results from those experiments were analyzed. A fatigue equation (N f = t v −5.129 R 2 = 0.853) related to the loading rate was established. The results indicated that the viscoelastic characteristics of rubber asphalt mixture are not taken into consideration in the traditional S–N fatigue equation, which contributed to the non-uniqueness and uncertainty of fatigue test results. The viscoelastic characteristics of rubber asphalt mixture are considered by the fatigue equation related to the velocity-dependent stress ratio. Thus, a new method (K v = N f 0.0958) considering the influence of the loading rate for calculating the strength structure coefficient of the rubber asphalt mixture was proposed. The effectiveness and completeness of the mechanical behavior of pavement structure characterized by material parameters were improved. Thus, the utilization rate of waste rubber for pavement construction can be significantly increased and the life cycle cost of asphalt pavement is reduced. • The velocity-dependent of rubber asphalt mixture strength was revealed under various loading modes. • A unified characterization model of fatigue performance was established under various loading modes. • A new method for calculating the strength structure coefficient was proposed. [ABSTRACT FROM AUTHOR]

Strength and fatigue life are essential parameters of pavement structure design. To accurately determine the pavement structure resistance of rubber asphalt mixture, the strength tests at various temperatures, loading rate, and fatigue tests at different stress levels were conducted in this research. Based on the proposed experiments, the change law of rubber asphalt mixture strength with different temperatures and loading rates was revealed. The phenomenological fatigue equation of rubber asphalt mixture was established. The genetic algorithm optimized backpropagation neural network (GA-BPNN) is highly reliable for optimizing production processes in civil engineering, and it has a remarkable application effect. A GA-BPNN strength and fatigue life prediction model was created in this study. The reliability of the prediction model was verified through experiments. The results showed that the rubber asphalt mixture strength decreases and increases with the increase of temperature and loading rate, respectively. The goodness of fit of the rubber asphalt mixture strength and fatigue life prediction model based on the GA-BPNN could reach 0.989 and 0.998, respectively. The indicators of the fatigue life prediction model are superior to the conventional phenomenological fatigue equation model. The GA-BPNN provides an effective method for predicting the rubber asphalt mixture strength and fatigue life, which significantly improves the accuracy of the resistance design of the rubber asphalt pavement structure. [ABSTRACT FROM AUTHOR]

• The variation patterns of fatigue parameters with aging degree were established. • Sensitivity analysis of fatigue parameters for aging asphalt mixture was carried out. • Statistical models of the relation between PV and fatigue life have been derived. The objective of this paper is to reveal the effects of aging on the fatigue performance of asphalt mixture based on variation patterns of fatigue parameters with aging degrees. Specimens with different aging degrees were prepared by modified SHRP's Long-Term-Oven Aging (LTOA) test method, in which five different aging durations, included 0, 1, 3, 5, 7 days, were adopted to substitute the fixed 5 days. The fatigue parameters, including stiffness modulus, fatigue life, phase angle, Plateau Value (PV), and cumulative dissipation energy of specimens with different aging degrees under different stress ratios were obtained by the tensile fatigue test. The relationship of fatigue parameters with aging degrees and stress ratios were established. It could be observed from the results that the aging degree and stress ratio had dramatic influences on the fatigue performance of asphalt mixture. Sensitivity analysis showed that aging had the most significant effect on the initial stiffness modulus of asphalt mixture, and should be used as a control index in fatigue design. Statistical models of the relation between (PV) and fatigue life (N f) established by the Rate of Dissipated Energy Change (RDEC) approach has an effective correlation. The Plateau Value model eliminated the effects of aging degrees and reflected the uniqueness of material parameters. Also, it could provide novel ideas for effective prediction of the fatigue life of asphalt mixtures with different aging degrees based on plateau value. [ABSTRACT FROM AUTHOR]

• The yield surface of cement-treated aggregates (CTA) was established. • Proposed a normalized characterization method of fatigue based on the yield criterion. • Fatigue behavior of CTA was characterized by the normalized characterization method. The objective of this paper is to propose a normalized characterization method based on the yield criterion to eliminate the impacts of different stress models on the fatigue behaviors characterization of cement-treated aggregates. Based on the theory of octahedral shear stress strength and yield surface mode, the yield surface of cement-treated aggregates was established with four-point bending, compression, and indirect tensile strength value under different loading rates. Then, the fatigue stress and corresponding ultimate strength could be characterized by the yield surface, uniformly and uniquely. In the yield surface space (I 1 , J 2 ), the fatigue stress growth route from initial stress to ultimate strength was identified as fatigue stress path. Based on the fatigue stress path, the fatigue stress ratios related to loading rate and stress model were calculated. With these stress ratios, the conventional S-N fatigue equation was modified, on the basis of which a normalized characterization method of fatigue behavior was proposed to characterize the fatigue behavior of cement-treated aggregates. Compared with the traditional characterized method, the normalized characterization method has considered the influence of loading rate and stress model on strength and fatigue test results. The test results demonstrated that different strength and fatigue test results were obtained under distinct stress model and loading rates. All strength values have been expressed indiscriminately in the yield surface. With the normalized characterization method, a unique fatigue curve was gained for cement-treated aggregates under different loading rates and stress models. Therefore, findings of this work realized the normalization characterization of fatigue behavior of cement-treated aggregates. [ABSTRACT FROM AUTHOR]

In order to describe the fatigue damage state of asphalt mixture more reasonably, direct tensile tests of the fatigue and the residual strength under stress levels of 1.00 MPa, 0.50 MPa and 0.25 MPa with five parallel tests were carried out. The trabecular specimens of AC-13C asphalt mixture (25 cm × 5 cm × 5 cm) were manufactured with Styrene-Butadiene-Styrene (SBS) modified asphalt, aggregate basalt and limestone mineral filler. The optimum asphalt-aggregate ratio was 5.2%. The dynamic modulus decay and the residual strength decay were termed as the damage variables to evaluate the fatigue damage process of asphalt mixtures, respectively. Based on the test results, the decay patterns of the dynamic modulus and the residual strength during fatigue tests under different stress states were revealed, and the model and the parameters of fatigue damage according to the corresponding decay patterns were obtained. Then, based on the assumption that the residual strength and dynamic modulus depend on the same damage state, the relationship between the two damage definitions was given, and the residual strength-dynamic modulus coupled model was established. The results showed that the residual strength-dynamic modulus coupled model could better describe the fatigue damage evolution law of asphalt mixture, and the parameter of this coupled model could be obtained by less residual strength tests. A modified formula for calculating the damage variables associated with residual strength and dynamic modulus was proposed based on the relationship between two kinds of damage variables. [ABSTRACT FROM AUTHOR]

• The strength and fatigue properties of PMBA mixture were investigated. • The Desai strength yield surface was studied for the PMBA mixture. • The normalized fatigue equation for the PMBA mixture was established. Polyphosphoric acid modified high dosage bio-asphalt (PMBA) could provide a new direction for saving asphalt resources. The fatigue performance of asphalt mixture is one of the critical factors that should pay more attention in achieving a life cycle cost-effective. This study aims to investigate the strength and fatigue performances of the PMBA mixture. The stress states of mixture tests include indirect tension, direct tension, and unconfined compressive, respectively. The S-N fatigue equations, Desai yield surface, and normalized fatigue equation were determined. At the same loading rate, the strength values of indirect tension and direct tension are close, while the strength of unconfined compressive is much larger than theirs. The S-N fatigue equations parameter obtained based on stress levels vary significantly under different stress states, with unconfined compressive being much more significant than indirect tension and direct tension. The Desai strength yield surface gradually expands outward with the increase of loading velocities. The diffusion rate decreases as the loading velocities increase. According to the Desai yield surface, the new fatigue stress path and stress ratio were defined. The normalized fatigue equation for PMBA mixture under various stress states is N f = Δ - 4.58 R 2 = 0.99. The normalized n value of PMBA asphalt mixtures is 4.58, 2.7% lower than that of SBS modified asphalt mixtures. This study is meaningful for applying high dosage bio-asphalt. The application of PMBA also provides new ideas for low carbon and environmental protection in road engineering. [ABSTRACT FROM AUTHOR]

• The stress ratio was redefined based on the strength failure envelope line under multi-field coupling conditions. • The unified model of fatigue performace under various stress states, temperatures, and loading frequencies were proposed. • The dispersion caused by different methods and test conditions can be eliminated by the unified fatigue model. For a scientific and reliable design of asphalt mixture subjected to fatigue damage, a comprehensive understanding and realistic prediction of asphalt mixture fatigue life under complex loading conditions with variable loading rates or temperature were a major concern. In this study, direct tensile test, uniaxial compression test, indirect tensile test, and four-point bending test were used to study the fatigue behavior of asphalt mixtures with a particular focus on the action of temperature and frequency. Strength and fatigue were investigated separately under varied loading rates at several temperatures. A new idea for determining the stress ratio based on the strength failure envelope line considering temperature and loading rate was proposed. The connection between strength and fatigue was established by the stress ratio. The test conditions for strength and fatigue tests were set to be the same leading to the fatigue data distributed regularly. Experimental data were analyzed and normalized by studying the evolution of the number of cycles with the stress ratio. A new analytical approach was introduced to simulate the fatigue performance. The fatigue performance under multi-field coupling conditions was uniformly characterized. The dispersion of fatigue equation caused by the test method and conditions is eliminated. Engineering application showed that the design deviation of the pavement fatigue resistance was reduced to less than 6%. [ABSTRACT FROM AUTHOR]

• Asphalt mixture containing high-proportion RAP was prepared by SMC regenerant. • The failure strength master curve of high-content RAP asphalt mixture was obtained. • The fatigue performance of high-proportion RAP asphalt mixture was studied. Reclaimed Asphalt Pavement (RAP) is a cleaner production widely used in road engineering. In order to investigate the failure strength and long-term performance of high-proportion RAP asphalt mixture, this research prepared two high-content RAP recycled asphalt mixtures (50% and 60% RAP-RAM) with the gradation of AC-20 based on Styreneic Methyl Copolymer (SMC) regenerant. Firstly, indirect tensile (IDT) strength tests were implemented on 50% and 60% RAP-RAM at four temperatures and six loading rates. Secondly, IDT fatigue tests at six stress levels were carried out. The relationships of strength and temperature, strength and loading rate were obtained based on strength test results. The master curve model of indirect tensile strength and loading rate of high-proportion RAP recycled asphalt mixture was established by linear and Sigmoidal functions. On the basis of the Sigmoidal strength master curve equation, the fatigue stress ratio was calculated. Finally, this paper established the fatigue equation of the high-content RAP recycled asphalt mixture based on the fatigue stress ratio. The analysis results show that 50% and 60% RAP-RAM based on SMC regenerant show favorable strength and fatigue properties. In addition, increasing the proportion of RAP improves the strength of the mix while reducing the loading rate sensitivity of strength. However, the fatigue performance of the mix reduces by increasing RAP content. The fatigue equation based on the fatigue stress ratio takes the factors of temperature and loading rate into account, reflecting the mix's fatigue performance more realistically. The strength and fatigue performance results verify the reliability of the high-content RAP recycled asphalt mixture based on SMC regenerant and provide a reference for the effective utilization of RAP which can generate environmental benefits of saving aggregate and asphalt and reducing energy consumption and carbon emissions. [ABSTRACT FROM AUTHOR]

• A damage model considering the interaction between fatigue and creep was established. • The model could reflect the effect of stress level on the damage evolution process. • The nonlinear characteristics of damage evolution could be well-reflected. To describe the interaction of fatigue-creep damage of an asphalt mixture under the action of semi-sine cyclic loading reasonably, a direct tension fatigue test was carried out under four different stress levels (0.5, 1, 1.5, and 2 MPa) based on the fact that semi-sine fatigue stress can be decomposed into creeping stress and simple fatigue stress. In addition, tension-compression fatigue and static creep tests were carried out under four stress levels: 0.25, 0.5, 0.75, 1 MPa. For each test, five parallel tests were carried out at the same stress level. The Chaboche fatigue damage model and Kachanov creep damage model were employed to evaluate the damage evolution of the mixture both in the fatigue and creep tests. According to the test results, the damage evolution trends were revealed under different test processes and stress levels, and the damage evolution models of three different test methods were obtained. Then, based on the principle of semi-sine fatigue stress decomposition, a fatigue-creep damage interaction model considering the interaction of fatigue and creep damage was established using normalized parameters (X = N / N f = t / t R) as the intermediate variable. The results indicated that the damage of asphalt mixture under the action of the semi-sine cyclic load was not a simple linear accumulation of fatigue damage and creep damage, but an overall result of the interaction of fatigue damage, creep damage, and fatigue-creep damage. The fatigue-creep damage interaction model provided a good fit with the experimental data and showed a high degree of consistency with the classical damage model. The model could be used to describe the damage evolution trend of asphalt mixture under the action of semi-sine cycle load and the interaction effect of fatigue damage and creep damage. [ABSTRACT FROM AUTHOR]