Dissipated Pseudo Strain Energy Research Articles

Energy-based characterization of the fatigue crack density evolution of asphalt binders through controlled-stress fatigue testing

Fatigue crack behavior of asphalt binder plays an important influence on the fatigue performance of asphalt pavements. To evaluate the fatigue crack density evolution within the steady growth stage of #70 unmodified asphalt binder and SBS modified asphalt binder, the crack initiation and propagation were characterized based on Griffith theory and modified Paris’ law, respectively. Aiming to calculate the horizontal length of crack initiation (a), the surface free energy of those two asphalt binders were calculated by contact angle measured with Wilhelmy plate test. Also, the stress sweep tests and time sweep tests were performed using Dynamic Shear Rheometer (DSR) to obtain the mechanical parameters of asphalt binders for calculation of fatigue crack density (ϕ) and dissipated pseudo strain energy (DPSE). They were fitted by modified Paris’ law, and coefficients n and A were determined. Results show that a for two asphalt binders increase with the increasing stress level and SBS modified asphalt binder shows a larger crack size in crack initiation, which means that SBS modified asphalt binder shows a better crack initiation resistance compared with unmodified asphalt binder. The ϕ and DPSE within the steady growth stage follow the linear relationship, indicating that the unit DPSE causes the equal amount of increase in ϕ. In addition, the A and n are independent on the stress levels. They are fundamental material properties and there is a linear relationship between the log(A) and n. SBS modified asphalt binder processes the better fatigue crack resistance because of the smaller value of n.

Modelling effects of aging on asphalt binder fatigue using complex modulus and the LAS test

The linear amplitude sweep (LAS) test is considered a useful tool for evaluating fatigue of asphalt binders. It has been confirmed that a good correlation exists between fatigue performance of binders and mixtures in a few studies. While the change in binder fatigue with load or strain level is well studied and modeled, the effects of oxidative aging remain difficult to explain or to model in a simple format. In this paper, the combined effects of strain and aging are investigated and a method for estimating binder fatigue behavior after different aging durations from limited measurements is introduced. LAS tests were conducted on eight binders at three different aging periods in the PAV. It is found that binder fatigue damage parameters C1 and C2 have a good linear relationship with aging level when using the dissipated pseudo-strain energy approach. The results also show that LAS parameters A and B at different aging duration maintain a linear relationship with the binder complex modulus (G*) measured at corresponding aging conditions. Therefore, a new fatigue life (Nf) model accounting for strain level and aging effect is proposed using a power function of the binder G*. To verify the model, its parameters are fitted using test data at first two aging conditions and used to extrapolate and predict the fatigue life at extended aging conditions. This study findings offer a simpler and reliable method to predicted values of fatigue life at new aging condition using both 35% damage level and maximum stress failure criteria that are recommended in AASHTO TP101-12 and AASHTO TP101-14, respectively. The new model will allow use of the LAS procedure to a wider range of aging and strain level conditions for which binders could be subjected to in the pavement.

Evaluation of rutting potential of flexible pavement structures using energy-based pseudo variables

Permanent deformation is a long-term irrecoverable depression accumulated in the wheel path when the flexible pavement is subjected to heavy loads at high temperature, which can be simulated using the vertically loaded wheel test (VLWT) in the laboratory. The objective of this study is to develop a new approach to analyze the vertically loaded wheel test results based on the elastic-viscoelastic correspondence principle. The energy-based pseudo variables are proposed to perform rutting evaluation of asphalt mixtures in the VLWT.Four types of styrene-butadienestyrene modified asphalt mixtures were prepared to conduct the undamaged compressive dynamic modulus test at different temperatures. Then the master curves of dynamic modulus for these mixtures were converted to get the relaxation modulus. The innovative VLWT for four types of two-layer structure with different asphalt mixture combinations were performed to investigate the rutting development. After that, a new mechanical-empirical rutting prediction model was introduced to predict the rutting development for each layer in the two-layer structure. The energy-based pseudo variables including pseudo strain, pseudo strain rate and dissipated pseudo strain energy (DPSE) were introduced to correlate with the rutting resistance.The results show that the developed mechanical-empirical rutting prediction model is proficient in capturing the rutting development of a two-layer structure of asphalt mixtures measured by a vertically loaded wheel tester. The rutting contributions of the top and bottom layers can be separated using this model. Compared with the total strain, the pseudo strain which removes the viscoelastic effect, is more accurate to evaluate the permanent deformation in a cyclic loading condition. The DPSE increases with the increase of loading cycles and rut depth. Two typical stages with an inflection point can be observed from the test results which indicate that the faster to reach the inflection point, the better rutting performance will be achieved.

Crack length based healing characterisation of bitumen at different levels of cracking damage

This study aims to characterise the healing properties of asphalt binders at different damage levels. The healing and the damage levels were quantified by crack length (CL) in binder samples generated by rotational shear fatigue loads in strain-controlled dynamic shear rheometer (DSR) tests. For comparison, the healing was also characterised by the commonly used material parameters including pseudo shear stiffness (S) and dissipated pseudo strain energy (DPSE). A normalized healing index was formulated using the above three parameters, respectively. A healing test of polymer-modified bitumen was designed based on DSR including a strain-controlled time sweep test plus a rest duration and followed by another strain-controlled time sweep test. The healing tests were performed at different rest start times (5min, 10min and 20min), rest durations (5s, 10s, 0.5min, 1min, 2min, 5min, 10min, 20min, and 40min), and amplitudes of the shear strain (5%, 7%, and 10%) at 20 °C and 10 Hz. Results show that the CL-based healing index is a fundamental and accurate parameter to evaluate the healing rate and healing potential of the bitumen. DPSE-based healing index is applicable only when the energy is mainly dissipated to generate cracks. Healing is underestimated when characterised using S or DPSE-based healing indices. Healing index increases due to the advance of rest duration or the decrease of the damage level, and the healing rate can be essentially modelled by Ramberg-Osgood model. Higher damage levels (introduced by higher load levels or longer loading time) can effectively decrease the binders’ healing potentials when the binders are at the relatively low damaged levels. The healing potential becomes low when the material is at severe damage state, thus will remain at that low levels even though the damage level increases.

A dissipated pseudo strain energy-based failure criterion for thermal cracking and its verification using thermal stress restrained specimen tests

Low-temperature cracking is one of the most prevalent types of distress in asphalt concrete pavements in regions where the air temperature undergoes a significant daily drop. This paper proposes a failure criterion that correlates the dissipated pseudo strain energy (DPSE) at the time of failure with the reduced strain rate. Uniaxial direct tension monotonic tests, axial compression dynamic modulus tests, and direct tension cyclic fatigue tests were performed using the Asphalt Mixture Performance Tester (AMPT) for a wide range of asphalt mixtures with different reclaimed asphalt pavement (RAP) contents, binder contents, virgin binder performance grades, and aging levels. The results show that the simplified viscoelastic continuum damage (S-VECD) model, which is characterized by the dynamic modulus and cyclic fatigue test results, can predict the stress-strain behavior of a given mixture subjected to monotonic tests at different temperatures and loading rates. This finding allows the prediction of DPSE in monotonic tension tests using the S-VECD model. The thermal stress restrained specimen test (TSRST) was then used to verify the DPSE-based failure criterion and the ability of the S-VECD model to predict thermal fracture behavior. The study results show that the predicted fracture temperatures match the measured ones for the study mixtures with reasonable accuracy. The study also used data from mixtures whose RAP contents, binder contents, virgin binder grades, and aging levels were systematically altered to verify the reasonableness of the proposed procedure to evaluate the differences in thermal fracture performance that are due to changes in these factors. The ability to predict the fracture stress and fracture temperature measured via the TSRST using the S-VECD model and the suggested DPSE failure criterion is of substantial practical and technical importance because it allows the prediction of both fatigue cracking and thermal cracking using a single set of tests, i.e., AMPT dynamic modulus and cyclic fatigue tests.

Quantification of Viscous and Fatigue Dissipation of Asphalt Concrete in Four-Point Bending Tests

Different methods are available to quantify the fatigue damage of the asphalt mixtures. Among these, methods based on the concept of dissipated energy are used predominantly. Characterizing fatigue damage using the concept of dissipated energy is complicated due to the presence of other modes of dissipation, for instance, viscous dissipation. Hence, most of the investigations attempt to separate the dissipation due to damage from the viscous dissipation. One of the widely used approaches to separate fatigue dissipation involves the use of a parameter called pseudostrain. The area under the stress-pseudostrain curve, called the dissipated pseudostrain energy, is used to characterize fatigue. In this study, the usefulness or otherwise of this approach to separate fatigue and viscous dissipation is explored. Toward this, experimental investigations were conducted using four-point bending for four types of asphalt mixtures at two different temperatures and four strain levels. It was observed that although the concept of pseudostrain to characterize the fatigue damage holds good in some specific cases, it cannot be adopted for all experimental data collected in this study. In view of this, a new strategy to separate the total dissipation into viscous and fatigue dissipation is proposed based on a constitutive assumption for the viscous dissipation of damaged asphalt concrete. This new method is then used to quantify fatigue damage in this study.

Fatigue performance predication model based on dissipated energy criteria using DSR under controlled-strain mode

Fatigue cracking is one of the primary modes of distress in flexible pavements that has an important economic impact. This paper describes the use of a dynamic shear rheometer (DSR) for fatigue performance testing of hot asphalt mixture under controlled-strain mode. 150 mm-diameter and 50 mm-height HMA finger samples used for the fatigue sequence procedure were developed and adopted to prepare the DSR samples. This paper reports the evaluation of fatigue resistance of asphalt mixture finger sample cores that were recovered from the field sections from Samawah–Nasiriyah City atrial road (97 km in the middle region of Iraq) using different continuum damage mechanics approach. The analysis has focused on comparing the dissipated pseudo strain energy (DPSE), energy ratio (ER) and energy stiffness ratio (ESR) in addition to the traditional approach under the controlled-strain mode. The results are used to develop guidelines for the design of fatigue-resistant mixtures in Iraq and to relate the mixture design to the structural design to optimize performance.

Comparative evaluation of fatigue resistance of warm fine aggregate asphalt mixtures

Fatigue cracking is one of the crucial distresses in asphalt pavements that affect its service life and rehabilitation process. The resistance of asphalt mixtures to fatigue failure in the laboratory experiments is influenced by several factors such as temperature, loading frequency, loading mode, sample type and geometry. This study focused on the evaluation of fatigue performance of different types of warm mix asphalt (WMA) mixture and comparing them with a hot asphalt mixture (control mixture). Warm fine aggregate mixtures (W-FAM) were fabricated using three different WMA additives: Advera, Sasobit, and Rediset which were short-term aged in the laboratory. Then, the W-FAM specimens were exposed to shear stress oscillation test by applying damaging stress level in the dynamic mechanical analyser (DMA) to examine the material fatigue resistance. The test results were analysed using the viscoelastic continuum damage (VECD) approach. The W-FAM exhibited lower dissipated pseudo-strain energy (DPSE) than the control mixture. However, there was no statistical significant difference between the W-FAM and control mix in terms of the number of cycles to failure resulted from the VECD analysis.

Evaluation of Fatigue Cracking in Asphalt Mixtures Based on Surface Energy

AbstractFatigue cracking in an asphalt mixture is a process whereby microcracks in the asphalt–aggregate interface propagate into extensive interconnected cracks under repeated loads. The fatigue performance of asphalt is influenced by the load as well as the intrinsic nature of the asphalt–aggregate system. This study used the surface energy concept of asphalt and aggregate systems to characterize the fatigue behavior of asphalt mixtures. The surface energy of asphalt and aggregate at different temperatures were measured using Wilhelmy plate method and contact angle meter, respectively. By using dissipated pseudostrain energy of nonlinear viscoelastic material and micromechanics cracking model, the effect of surface energy on fatigue life of the asphalt mixtures was analyzed. Laboratory test indicated that the surface energy of the asphalt generally decreased with an increase of temperature. Compared with AH70 grade asphalt, the surface energy of styrene-butadiene-styrene block copolymer (SBS)-modified a...

Anisotropic Characterization of Crack Growth in the Tertiary Flow of Asphalt Mixtures in Compression

Asphalt mixtures exhibit primary, secondary, and tertiary stages in sequence during a rutting deterioration. Many field asphalt pavements are still in service even when the asphalt layer is in the tertiary stage, and rehabilitation is not performed until a significant amount of rutting accompanied by numerous macrocracks is observed. The objective of this study was to provide a mechanistic method to model the anisotropic cracking of the asphalt mixtures in compression during the tertiary stage of rutting. Laboratory tests including nondestructive and destructive tests were performed to obtain the viscoelastic and viscofracture properties of the asphalt mixtures. Each of the measured axial and radial total strains in the destructive tests were decomposed into elastic, plastic, viscoelastic, viscoplastic, and viscofracture strains using the pseudostrain method in an extended elastic-viscoelastic correspondence principle. The viscofracture strains are caused by the crack growth, which is primarily signaled by the increase of phase angle in the tertiary flow. The viscofracture properties are characterized using the anisotropic damage densities (i.e., the ratio of the lost area caused by cracks to the original total area in orthogonal directions). Using the decomposed axial and radial viscofracture strains, the axial and radial damage densities were determined by using a dissipated pseudostrain energy balance principle and a geometric analysis of the cracks, respectively. Anisotropic pseudo J-integral Paris' laws in terms of damage densities were used to characterize the evolution of the cracks in compression. The material constants in the Paris' law are determined and found to be highly correlated. These tests, analysis, and modeling were performed on different asphalt mixtures with two binders, two air void contents, and three aging periods. Consistent results were obtained; for instance, a stiffer asphalt mixture is demonstrated to have a higher modulus, a lower phase angle, a greater flow number, and a larger n1 value (exponent of Paris' law). The calculation of the orientation of cracks demonstrates that the asphalt mixture with 4% air voids has a brittle fracture and a splitting crack mode, whereas the asphalt mixture with 7% air voids tends to have a ductile fracture and a diagonal sliding crack mode. Cracks of the asphalt mixtures in compression are inclined to propagate along the direction of the external compressive load.

Characterization of Fatigue Damage in Asphalt Mixtures Using Pseudostrain Energy

Fatigue cracking and permanent deformation develop simultaneously in asphalt mixtures under repeated destructive loading regardless of temperature. Because these two distinctively different damage mechanisms always occur together, it is not possible to obtain pure cracking damage or pure permanent deformation damage in any asphalt mixture by varying the temperature or loading level. This paper develops an energy-based method to separate fatigue cracking from permanent deformation in terms of energy consumption. Specifically, the dissipated pseudostrain energy (DPSE) expended on cracking is separated from that expended on permanent deformation. Controlled-strain repeated direct tension (RDT) tests are performed on asphalt mixture specimens to determine their nondestructive properties, critical nonlinear viscoelastic properties, and destructive properties. The total DPSE, which is the amount of energy dissipated for the fatigue damage, including both fatigue cracking and permanent deformation, is calculated based on the critical nonlinear viscoelastic properties in order to separate both linear and nonlinear viscoelastic effects from the strain energy that is available to cause damage. The energy distribution in an asphalt mixture under destructive loading is investigated at the microscopic level. Balance equations are established between the true stress/strain/energy of the intact material and the apparent stress/strain/energy of the bulk specimen. These balance equations are utilized to completely formulate the DPSE for cracking and the DPSE for permanent deformation, respectively. As a result, the DPSE for cracking is separated from the DPSE for permanent deformation. The formulations of the two types of DPSE and the RDT data will be used to calculate the amount of each type of DPSE. The DPSE for cracking will be used to predict the crack growth, average crack size, and number of cracks in the asphalt mixture under repeated destructive loading. The DPSE for permanent deformation will also be used to predict the growth of permanent deformation. This will be introduced in following papers. This paper is one of a series of companion papers that characterize nondestructive and destructive behaviors of an asphalt mixture under tensile loading.

Tension-Compression Fatigue Test Evaluation Using Fracture Mechanics and Field Data

ABSTRACT Fatigue cracking is one of the main distresses that affect asphalt pavements. In order to evaluate the cracking potential of several asphalt mixtures equivalent to the ones used in the sections of an accelerated loading pavement testing facility (PTF), uniaxial stress-controlled and strain-controlled direct tension-compression laboratory tests were performed. The laboratory-acquired data was analyzed using a crack growth equation with two separate techniques for estimating the dissipated pseudostrain energy. The results were compared to the observed PTF performance after subjecting the field sections to repeated load using a super-single truck tire accelerated loading device. The rankings of the mixtures based on their observed field performance and on the results of the crack growth equation were different, yielding parallel results for the strain-controlled laboratory test and opposite trends for the stress-controlled loading mode. The cause of the discrepancies could be explained by the onset and evolution of damage in each test protocol.

Tension-Compression Fatigue Test Evaluation Using Fracture Mechanics and Field Data

ABSTRACT Fatigue cracking is one of the main distresses that affect asphalt pavements. In order to evaluate the cracking potential of several asphalt mixtures equivalent to the ones used in the sections of an accelerated loading pavement testing facility (PTF), uniaxial stress-controlled and strain-controlled direct tension-compression laboratory tests were performed. The laboratory-acquired data was analyzed using a crack growth equation with two separate techniques for estimating the dissipated pseudostrain energy. The results were compared to the observed PTF performance after subjecting the field sections to repeated load using a super-single truck tire accelerated loading device. The rankings of the mixtures based on their observed field performance and on the results of the crack growth equation were different, yielding parallel results for the strain-controlled laboratory test and opposite trends for the stress-controlled loading mode. The cause of the discrepancies could be explained by the onset and evolution of damage in each test protocol.

Computation of pseudo strain energy and Paris law fracture coefficients from surface energy and uniaxial strain-controlled tension test data

Dissipated pseudo strain energy (DPSE) and Paris' law fracture coefficients constitute input parameters for fracture characterization of hot-mix asphalt concrete (HMAC) mixtures in continuum fracture-damage mechanics and energy based fatigue analysis approaches. In this paper, numerical analysis models for computing DPSE and Paris' law fracture coefficients from surface energy (SE) and uniaxial strain-controlled tension test data are presented. The applicability of the DPSE, Paris' law fracture coefficients, and the associated laboratory tests for comparatively quantifying HMAC mixture fracture properties including investigating the effects of aging is also presented. Analysis of the results indicated that the models utilized together with the computed parameters and the related laboratory tests provide a fundamental methodology of comparatively characterizing the fracture properties of HMAC mixtures. The numerical values obtained were within theoretical expectations. The results further showed that aging has a detrimental effect on the HMAC mixture fracture properties. However, more HMAC mixture characterization is recommended to further validate the general applicability of the models and the associated laboratory tests.

Characterization of Microdamage and Healing of Asphalt Concrete Mixtures

The pseudo-strain concept based on Schapery’s extended nonlinear elastic-viscoelastic correspondence principle is demonstrated by a considerable database to be able to characterize both microdamage and microdamage healing during the damage process. A change in pseudo stiffness can be used to quantify microdamage and healing during the fatigue test. Pseudo stiffness decreases consistently with increasing number of loading cycles, indicating that microdamage occurs during the fatigue test. The significant recovery of pseudo stiffness after rest periods demonstrates a healing effect due to rest periods. Dissipated pseudo-strain energy is a strong and consistent quantifier of damage and healing. High levels of cumulative dissipated pseudo-strain energy are consistent with high levels of fatigue damage, whereas low levels of cumulative pseudo-strain energy are associated with fatigue damage resistance. Pseudo stiffness is the chord slope of the stress-pseudo strain hysteresis loop. Since linear viscoelastic-based time effects are eliminated in this approach, pseudo stiffness and/or pseudo-strain energy are superior indicators of damage than either stiffness or total dissipated strain energy. The effects of rest periods on fatigue life extension due to healing of microcracks are significant. It has been demonstrated that longer rest periods result in more healing, and in turn in greater fatigue life.