Effect of Thermal Strain

 

Another potential reason for the difference between the beam fatigue tests and in-situ pavements is that daily and seasonal temperature changes cause changes to the asphalt materials that affect the fatigue properties. Cooling of an asphalt beam will cause the beam to contract, but in the pavement layer the material is restrained from contracting. In a linear elastic material this constraint would cause a semi-static tensile stress in the material.

 

For fatigue of metals several methods are used to add the effects of static and dynamic tensile stresses. The dynamic stress is normally sinusoidal, with an amplitude of σa, on which a static stress of σm is superimposed.

 

Goodman’s method of adding dynamic and static stresses states that failure is reached when:

                    

where:          σa is the amplitude of the dynamic stress,

                    σm is the static stress,

                    SN is the fatigue stress for N load applications, and

                    Su is the static strength.

 

If the fatigue equation for purely dynamic loading is used, the effect of the static stress may be considered by multiplying the amplitude of the dynamic stress by a factor f:

                    

For asphalt it appears that strain is more important than stress. For metals stress and strain are practically proportional, but for a viscoelastic material such as asphalt concrete that is not the case. The coefficient of thermal contraction (CTC) for asphalt depends on the temperature and range from 3 to 30 microstrain/°C for -20 to 55°C (Islam, 2015). Cooling an asphalt beam by 10˚C would cause it to contract by as much as 300 microstrain. To bring it back to the original length that strain must be imposed on the material. This will create a stress that relaxes over time, but the strain will remain.

 

When an asphalt pavement cools down it will contract in the vertical direction but not in the horizontal direction (at least not longitudinally). This will not create a measurable strain in the material, but on the level of the grain size it will. A strain will develop in the binder film when the grain contracts. The condition of the material will be the same as in a beam that is cooled and then strained to gain its original length. It makes sense, therefore, to consider a strain caused by temperature changes, although it would not be possible to measure such a strain in the material.

 

One possible way of including this strain would be to use the method given above, but with the static (temperature-induced) strain added to the dynamic (load-induced) strain. This would require a calculation of the static strain, and to do this the temperature at which the static strain is zero must be known. It is uncertain whether this temperature is constant during the year since it could be changing as a result of permanent deformation in the material, so it would be interesting to measure the contraction or expansion on cores or slabs cut from asphalt layers at different times and temperatures. The Goodman method would also require a maximum permissible static strain (or minimum temperature), which could possibly be related to the low temperature grade for PG grade materials.

 

An option for including temperature strains using the Goodman method has been added to CalME. This option is only activated for the thermal reflective cracking strains, i.e., the strain in the overlay caused by contraction of the underlying cracked layers. The temperature when thermal strain becomes zero () is set to 20°C. The temperature corresponding to maximum allowable temperature strain ()

where  is the thermal strain in the HMA layer caused by contraction of the underlying cracked layer,

and CTC is the coefficient of thermal contraction of the HMA layer

The following equation is used to calculate :

where  is the coefficient of reflective cracking strain transfer

           is the temperature of the underlying cracked layer, and

           is the coefficient of thermal contraction of the underlying cracked layer

 depends on whether it is an AC on AC overlay or an AC on PCC overlay.  is set to 1.20 for AC on AC overlays and 5.4 for AC on PCC overlays in CalME. The reason an old cracked AC layer transfers much less of its thermal strain to the AC overlay than an old cracked PCC layer is because of its lower stiffness (relative to the AC overlay) and its much higher creeping capability. The reason  is greater than 1.0 is because of the strain concentration caused by the existence of cracks or joints.

Note that the calculation of thermal reflective cracking strain still has a lot of open questions. The way it is handled in CalME will most likely be further refined and improved in the future.

Islam, R., Asce, S.M., Tarefder, R.A., and Asce, M. 2015. “Coefficients of Thermal Contraction and Expansion of Asphalt Concrete in the Laboratory.” Journal of Materials in Civil Engineering 27 (11): 04015020. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001277.