*By Dr. John Noël, Ph.D.*

Not that long ago I was a graduate student in my twenties. Without much difficulty, I could find myself out at night until unreasonable hours and would then complain of tiredness as I dragged myself to the lab the next morning.

That said, some short relaxation with a cup of coffee would always help me bounce back. Since then, I graduated, found a job, got married, got older, lost hair and had my first child – a beautiful baby girl.

That is when I learned the true meaning of fatigue.

A few late nights here and there are manageable, but nightly 2 a.m. (and 3 a.m., and 4 a.m., etc.) wake-up calls, over time, built up quite the accumulation of tiredness. This was fatigue that a coffee break could no longer fix and I often felt as though I’d been run over by a truck.

Speaking of trucks, we are all aware that asphalt pavements also are fatigued over their service life, and fatigue resistance is an essential performance requirement for flexible pavements. In general terms, fatigue damage refers to the degradation of material properties under repeated loading.

Pavements experience stresses from each passing vehicle and are strained hundreds or thousands of times each day depending on the traffic volume. They also experience cyclical thermal stresses which can be further exacerbated by freeze-thaw cycles of water. While designing a road to withstand single loads could be straightforward; designing pavements to withstand repeated loads with stresses below the fracture strength is more challenging.

Pavement preparation and structure play a large role in controlling fatigue damage. Weak subgrade can result in larger strains in the pavement above and accelerate fatigue damage. Thick, full-depth pavements are less prone to fatigue damage as they experience smaller strains than thinner pavements under the same loading. Within a given pavement structure and under a certain loading, the fatigue tolerance will be determined by factors including mix design (volumetrics, aggregate properties, etc.) and by the properties of the asphalt binder.

Asphalt binder specifications to control fatigue have long been regarded as a difficult challenge. Many different test methods and specifications have been proposed or implemented to tackle fatigue damage. This article aims to give a brief overview of just a few of these fatigue parameters either in use today or proposed for future use.

**Phase angle**

Historically, ductility measurements were used as metrics for fatigue tolerance in North America and are still used in some parts of the world today. With the development of the Superpave™ binder specification system, |G*|sin(δ), where |G*| is the magnitude of the complex modulus and δ is the phase angle, was introduced as a fatigue cracking specification with a limit of 5000 kPa. However, there was little field validation conducted for this parameter, and the 5000 kPa limit was set on the basis of correlations to empirical data from the Zaca-Wigmore road trial. This parameter is easy to measure, however and can serve to limit binder stiffness. High stiffness can decrease the strain tolerance of the binder and in thin pavements that experience large strains, can in turn worsen fatigue performance. More recent studies have shown a rather poor correlation between |G*|sin(δ) and binder fatigue resistance.

Closer analysis of the |G*|sin(δ) parameter reveals that it is equivalent to the loss modulus, G’’, the viscous component of the complex modulus. It can then be observed that, in some cases, binders that are less prone to fatigue cracking might be more likely to fail the specification than binders more prone to fatigue cracking. If one considers two binders with equal values of |G*| but different phase angles, one will find that the binder with a higher phase angle will have a higher value of |G*|sin(δ), making it more likely to exceed the specification limit. Nonetheless, the higher phase angle is indicative of more fluid-like behavior, allowing the binder to better dissipate stresses and prevent the stress accumulation that can lead to cracking. An increase to the |G*|sin(δ) limit in the AASHTO M320 standard was made in 2021 in recognition of this challenge. Now, binders with 5001 < |G*|sin(δ) < 6000 kPa are accepted, provided that their phase angle is greater than 42°, proving they have the viscous behavior required at intermediate temperature to limit cracking.

While the change to the |G*|sin(δ) limit helps prevent high-quality, ductile binders from failing the specification, it does not preclude the use of low-phase angle binders that fall below the original 5000 kPa limit, even though these might be more prone to cracking. Recent research has indicated that a lower limit on the phase angle at constant modulus (which can be calculated from the current DSR-PAV test), could be a good specification for screening for binders prone to cracking on their own. A limit of a minimum of 42° has been suggested. Measured at constant modulus, the phase angle is independent of loading time and temperature (no need to select a specification temperature) and correlates well to binder composition (colloidal stability) and to Delta Tc.

**Delta Tc**

Delta Tc, and correspondingly the m-value from the bending beam rheometer test (AASHTO T 313), can be a good indicator of susceptibility to fatigue cracking, as well. Like the phase angle, the Delta Tc parameter can give an indication as to a binder’s capacity to relax applied stresses and resist cracking, though with poorer reproducibility than the phase angle. In essence, Delta Tc allows binders to be compared based on their capacity to relax stresses at a fixed stiffness (300 MPa). Specifications for Delta Tc are now present in several jurisdictions.

**Time sweep**

It has been noted in the literature that traditional DSR testing for fatigue (AASHTO T 315) faces the limitation of applying rather low strains compared to what is observed in real-life pavements, and runs for relatively few cycles, limiting the degree of fatigue that can be observed in the test. The time sweep test was developed during the NCHRP 9-10 research project as an alternate test to measure asphalt binder fatigue properties using the DSR while employing larger strains and many more loading cycles. In the time sweep test, a cyclical shear load of constant magnitude is applied to the binder. Over the course of the test, the complex modulus decreases linearly as the number of cycles increases (damage accumulation), before dropping radically at failure. The point of failure might be taken as the number of cycles at which the curve departs from linearity or the number of cycles at which the magnitude of the complex modulus has been reduced by a given percent. A criticism of the time sweep is that the test duration can be quite long, making it unsuitable for use as a specification.

**Linear amplitude sweep**

Building from the time sweep test is the linear amplitude sweep (LAS) test. The LAS test, like the time sweep, consists of repeated cyclic shear loads on the binder and is conducted using a DSR. Unlike the time sweep, the shear loading is not constant. In the LAS test, the shear strain amplitude is increased at a constant rate over the course of the test to accelerate failure. Data analysis for LAS test results can be more complex and usually relies on viscoelastic continuum damage models.

For the LAS test, there is some variation within the literature as to what the appropriate failure definition (what constitutes failure) and failure criterion (what value do we take away from the test) should be. Some failure definitions include the point at which: a certain percentage reduction in the complex modulus or loss modulus (AASHTO T 391) is obtained; the shear stress reaches a maximum; the plot of crack growth rate versus crack length reaches a minimum; and others. Some examined failure criteria include the number of cycles to failure, crack length at failure and percent reduction in |G*| or |G*|sinδ at failure.

DSR measurements of stress and strain are made with the assumption that the sample cross-sectional area is constant. However, during the LAS test, edge fracture, delamination, and instability flow can occur, changing the sample dimensions and leading to inaccuracies in the instrument readout. That is not to say that a good relative comparison of binder performance cannot be achieved, but it does make the correlation to other rheological properties difficult. With both the time sweep and LAS there is the added complexity in correctly interpreting a non-linear test and managing the resulting poorer reproducibility.

**Glover-Rowe parameter**

A more recently developed rheological parameter attained from DSR measurements for assessing binder propensity toward fatigue cracking is the Glover-Rowe parameter (GRP):

Based on the GRP measured at 0.005 rad/s and 15 °C, cracking onset is said to be expected at 180 kPa, with severe damage at 600 kPa and above. The GRP was initially developed as a proxy to traditional ductility tests and does correlate well to binder ductility, as well as to the Double- edge Notched Tension (DENT) test. Like the traditional |G*|sin(δ) parameter, the GRP is heavily influenced by the magnitude of the complex modulus. However, the GRP can have better quality differentiation than |G*|sin(δ) by better screening out binders with the low-phase angle at intermediate temperatures that could be prone to cracking, while more easily allowing higher-phase angle binders with more capacity to dissipate stress to pass.

NCHRP 9-59 now recommends measuring GRP at a higher frequency (10 rad/s) and at an intermediate temperature determined by the low-temperature grade alone and proposes a limit of 5000 kPa, similar to the existing fatigue specification in AASHTO M 320. This measurement can be made using the existing AASHTO T 315 protocol on PAV-aged material and has shown good correlation to binder fatigue strain capacity; however, further validation and examination of limits are likely needed. NCHRP 9-59 also suggests the R-value from the Christensen-Andersen model to be a good predictor of fatigue strain capacity. This value can be calculated from BBR stiffness and m-value but relies on an assumed constant value of the glassy modulus for all binders which might introduce inaccuracies. The R-value calculated in this manner correlates very well to Delta Tc which could be simpler to implement.

Are you feeling fatigued yet? We have touched on at least eight different tests to qualify the fatigue performance of asphalt binders. Others, such as the direct tension test and binder yield energy test, exist too.

This illustrates the breadth of approaches to tackle this challenge: from straightforward like the phase angle at constant modulus to more complex analysis like the LAS to empirical like ductility. While the range of potential fatigue specifications might feel overwhelming, they are proof that the asphalt industry is full of bright scientists and engineers working toward a shared goal: high-performing, fatigue-resistant asphalt pavements.

That is a fact that helps me sleep at night… until the next 2 a.m. wake-up call, of course.

*Noël is an Asphalt Technical Advisor for ExxonMobil and
is based in Ontario, Canada.*