Results and Discussion

Three samples of MA were tested as described in the Test Development section above and the average deflection found from the 3D digital image correlation soft­ware profile measurement was compared with the finite-element simulation and the

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analytic solution as shown in Figs. 9(a) and 9(b). The standard deviation in Fig. 9(d) was calculated from the image correlation measurement by taking different sections on two-dimensional (2D) vertical deflection contour plot shown in Fig. 9(c).

The blister growth estimated with the viscoelastic model produced different deflections depending on the pressure and temperature rate. The pressure and temperature histories from Fig. 7 resulted in vertical deflections shown in Fig. 10(a). The step-function temperature and pressure produced higher vertical deflection (1.7332 mm) compared to other types of temperature and pressure histories. The minimum vertical deflection was 1.0304 mm.

To assess only the effect of temperature increase in the MA, the temperature histories shown in Fig. 7(a) were applied while keeping the pressure (7.37 • 10~06MPa) in the blister constant for 12 h. The result in Fig. 10(b) indi­cates that temperature increasing rate has significant effect on the deflection of the plate. The entire deflection in the MA was almost completely caused by change in temperature. The deflections found from temperature variation were similar to those from simultaneous temperature and pressure variation as shown in Fig. 10(b). The maximum deflection was 1.7332mm for temperature and pressure step function and the minimum deflection of 1.0380 mm was pro­duced by the slowest temperature and pressure rate.

Moreover, the results shown in Fig. 11(a) is found when the temperature was constant throughout the thickness (25 °C) and a linearly varying load his­tory shown in Fig. 7(b) was applied. This result shows that the rate at which the pressure increases has no significant influence on the vertical deflection of the MA. The deflection found from pressure variation is clearly different to the deflection from simultaneous variation of temperature and pressure as shown in Fig. 11(b). The maximum vertical deflection obtained was 1.7332 mm and the minimum vertical deflection was 1.7148 mm.

In Fig. 12 the vertical deflection from pressure and temperature fluctuation in one week is presented. The highest deflection of 1.2877 mm was found for repeated simultaneously varied temperature and pressure. In case of fluctuating temperature and constant pressure (7.124 • 10~°6MPa corresponding to a tem­perature of 15 °C), a vertical deflection of 1.2228 mm was found. Pressure fluctu­ation had no significant influence, as shown previously, and results in the lowest deflection of 0.02521 mm. Moreover, Fig. 12 clearly shows that, repeated temperature and pressure cycles may well produce continuous blister growth. The blister growth tends to slow down when more cycles are applied. This corre­sponds to observations in practice as shown Fig. 6(a).

Conclusion

The time-dependent vertical deflection in MA blisters depends on three factors: material characterization of the model, temperature of the MA at the time of loading, and the rate at which the load is applied to the material. It was found that vertical deflection of MA is much more depending on the rate of the applied temperature than on the applied pressure. The 12-h simulation showed that, slower applied uniformly distributed pressure and temperature produces smaller vertical deflection.

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time (h)

rate of change in temperature (ДТ/дп

FIG. 10—(a) Vertical deflection at the center of the plate when both temperature (T, °C/day) and pressure (P, MPa/day) rate are involved (12 h), and (b) rate of change in temperature versus vertical deflections at the center of the plate.

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For constant pressure (p0 = 7.12 • 10~06 MPa) and fluctuating temperature, the temperature dependency of the material had a great influence on the vertical deflection of the blister. This indicates that constant gas pressure inside the blister can produce significant amount of blister growth with increasing temperature.

On the other hand, for constant temperature (T = 25 °C) and fluctuating pressure, as shown in Fig. 11(b), the blister growth is much less than in the pre­vious case. This is because of the fact that the MA has enough stiffness to resist pressure changes. In fact, deflection would even be less if the weight of the MA was incorporated in the simulation.

Finally, from simulation of the consecutive cycles of heating and cooling, it was noticed that the daily temperature variations have a significant influence on asphalt-pavement deflection. During the unloading process, i. e., when pressure and temperature decrease, the blister still grows at a slower rate. The simulation indicates that the blister can grow continuously under repeated loading condi­tions over subsequent days.