Dynamic testing – haversine vs sinusoidal loading

All dynamic four-point beam testing discussed in this study was carried out using a displacement controlled haversine loading wave. The haversine wave loading is the standard loading form prescribed in the AASHTO Standard T321 (formerly AASHTO TP8) based on work carried out for the Strategic Highway Research Program (SHRP). Haversine loading was adopted in this study because it was a requirement in the research project carried out by the Stellenbosch University for a United States client, a project which forms an integral part of this study.

There is general debate amongst researchers about the fact whether truly haversine loading can be applied to visco-elastic materials in a beam fatigue test. At the beginning of a displacement controlled beam fatigue test on hot-mix asphalt both the displacement and load signal are of a haversine shape. Pronk and Erkens (2001) however, stated that after only a few load cycles (within the first five on the material they tested), the load signal would change into a pure sinusoidal signal, while the displacement signal would retain its haversine shape.

They believe this to be the result of viscous deformation of the material or accumulation of residual strains occurring in the beam. As a result of this the shape of the beam (and the neutral axis) changes thereby from straight prior to loading to slightly bent during the running of the test. Consequently, the peak-to-peak strain of the sinusoidal displacement signal of the bent beam after a few load cycles would be equal to half the peak-to-peak strain of the specified haversine displacement signal of the straight beam at the beginning of the fatigue test.

Pronk and Erkens (2001) concluded that it is not possible to subject a beam of visco- elastic material to dynamic loading of a pure haversine shape. After only a few load repetitions a new equilibrium would be reached whereby the load signal has changed into a pure sinusoidal shape and whereby the peak-to-peak strain of the displacement signal has reduced to half the value of the specified strain amplitude.

They carried out a limited number of beam fatigue experiments, comparing specified sinusoidal loading with specified haversine loading of double the amplitude. In theory these two types of specified loading shapes should yield the same results. For the one mix tested (ACRE) this was experimentally found to be true. For another mix however (half-warm STAB), a better fatigue resistance was found when tested using a haversine loading signal. The experimental results of Pronk and Erkens were thus to a certain extent inconclusive and appear to be related to the type of material tested.

more prone to creep of the neutral axis occurring during fatigue testing than more pure elastic materials. The experimental testing of Pronk and Erkens (2001) was carried out at a temperature of 20ºC. At this temperature the response of hot-mix asphalt is more viscous than at lower temperatures. It would have been possible that they would have found larger differences between sinusoidal loading and haversine loading of twice the amplitude had the experimental testing been carried out at a lower temperature, i.e. with less viscous deformation of the beam.

The beam fatigue testing in this study was carried out a 5ºC, which would result in a less visco-elastic response of the material and a larger difference between sinusoidal loading and haversine loading of twice the amplitude. Over and above that, it is shown later on in this study that the viscous part of the stiffness (loss modulus) of the BSM mixes tested here is less than for hot-mix asphalt. This would result in a longer creep time of the neutral axis and even larger differences between sinusoidal loading and haversine loading of twice the amplitude compared to hot-mix asphalt.

The strain levels reported in this study are the specified strain amplitudes for a haversine loading signal. A limited evaluation of the load response during displacement controlled fatigue testing shows that creep of the neutral axis does occur in the BSM beam specimens. This evaluation consisted of analysing the maximum upward and downward force required to induce the haversine displacement for selected beam fatigue tests. If no viscous deformation of the neutral axis occurs and the load signal remains a haversine shape, the required downward force would be in excess of the required upward force. In case during the test the shape of the neutral axis does change from straight to slightly curved, and the loading signal changes to a pure sinusoidal signal, the downward force should be similar to the upward force.

There are indications that the load response of the BSM mixes tested in this study changes from haversine to sinusoidal during fatigue. Unlike HMA materials, where a change from haversine loading to sinusoidal loading takes place almost immediately, it takes longer for BSM materials to reach a new equilibrium. This is illustrated by Figure 74, in which it can be seen that after 10 load cycles the downward force is higher than the upward force and that the magnitudes of the downward and upward forces change relatively to each other. A new equilibrium is reached after approximately 100 load repetitions. The difference between the downward and upward force might have been larger during the first 10 load cycles, but unfortunately no data was sampled before the 10th load repetition. The equilibrium that is reached is typical of a sinusoidal load response. The constant difference between the upward and downward force is believed to be the results of the dead weight of the beam and that part of the testing rig that moves up and down with the beam during testing.

This behaviour was observed for all fatigue tests analysed, but the rate of change from a haversine load shape to a sinusoidal load shape differs per mix and per applied strain level. This is illustrated by Figure 75, which is the same mix as shown in Figure 74, save for the fact that 1% of cement was added to the mix. This mix has

reached after close to 10,000 load repetitions.

Unfortunately no experiments could be carried out whereby beams of the same mix would be subjected to both sinusoidal loading and haversine loading of twice the amplitude in order to establish a relation between the responses to these two different loading types. The fact that this relation would differ per mix and per strain level would require a comprehensive experiment.

It is therefore at this stage not possible to make any quantitative judgement on what the performance of the mixes, tested in this study with haversine loading specified, would be in case they would have been loaded with a specified sinusoidal load shape. It would however be incorrect to assume that the fatigue performance of the mixes tested with haversine loading specified would be equal to the performance with sinusoidal loading with half the strain amplitude. Due to the time required for the loading signal to change from haversine to sinusoidal (eg. see Figure 75), this would result in an underestimation of the actual fatigue life of the material.

It is however evident that a shift from haversine to sinusoidal loading is taking place when BSM beams are subjected to a four-point beam bending test (as shown in Figure 74 and Figure 75). Following this, it can be concluded that the actual applied strain reduces as the fatigue test progresses. Therefore, the fatigue lives as reported in this study are an overestimation of the actual fatigue performance of the material at the specified haversine strain levels. The fatigue lives as reported in this study should therefore be associated with a lower strain level that is somewhere between the initially applied haversine strain and the eventual sinusoidal strain at the end of the test, i.e. 50% of the initially applied haversine strain, The reduction from the specified haversine strain to the lower actual strain depends on the type of mix as well as the specified test strain level.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Load repetitions A b s o lu te v a lu e o f l o a d [k N

] max. upward force

max. downward force

Figure 74: Maximum forces during beam fatigue testing (Mix A-75C-0, 5ºC, 10 Hz, specified haversine displacement of 370 με)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Load repetitions A b s o lut e v a lue of load [ k N

] max. upward force

max. downward force

Figure 75: Maximum forces during beam fatigue testing (Mix A-75C-1, 5ºC, 10 Hz, specified haversine displacement of 400 με)

In order to prevent similar problems with future four-point beam testing of materials that exhibit visco-elastic behaviour it is recommended to only apply sinusoidal loading. Haversine type loading should not be considered for these types of materials.