Temperature and Pressure Influence in Blister Growth

The thermal environmental conditions have significant impact on stability and long-term performance of a pavement during its life span. Daily temperature variations influence the deformation of asphalt pavement significantly. A linear viscoelastic 3D finite-element model is more realistic than a linear elastic model because it considers time-dependent behavior of the MA and temperature effects on material property. The 3D finite-element simulation will therefore be used to study blister growth (vertical deflection) of a MA pavement plate sub­jected to diurnal heating and cooling temperature fluctuation. During daytime of sunny days, heat energy transfer by interaction between pavement and its surroundings exists. This interaction consists of the radiation balance and exchange by convection which comprises solar radiation, thermal radiation heat flux and convection heat flux at the pavement surfaces or at the bottom of the bridge deck [20].

The 3D finite-element model in this study was developed based on the fol­lowing assumption. The bridge deck pavement lies directly on the bridge deck,

i. e., no PBM sheet is applied, the radius of the blister will remain constant, which prohibits horizontal blister growth, i. e., the adhesion between the MA and concrete (rigid substrate) has sufficient strength to prevent debonding. The pavement is idealized as thick plate. The MA is considered to be homogenous, isotropic and linear viscoelastic. The asphalt pavement’s temperature

TABLE 5—Prony series parameters at reference temperature 5 °C.

D0, MPa


Di, MPa

tri, s



5.68528967271 • 10_03



29.35788435 • 10_03



0.1712212104 • 10_03



29.592292201577 • 10_03


fluctuation is the same in the whole cross section of the pavement. The pressure build up inside the blister is only caused by gas pressure; vapor pressure and off-gassing pressures are not considered. The blister cavity is assumed to be closed; therefore, there is no exchange of gas between inside and outside of the blister. The analysis assumes constant Poisson’s ratio.

C3D20R Elements were used and one single layer was used to model the blister. Linear quasi-static analysis was used to model time-dependent material response, such as creep and recovery. ABAQUS allows controlling time incre­mentation automatically or directly by specifying the time. As long as the output results of the simulation are compared with closed form solution, the fixed-time incrementation of 0.8 s was applied in the analysis. The pressure load applied in this model was estimated from ideal gas law equation, Eq 18

P1V1 _ P2V2 T ~ T2

Where pj andp2 are initial pressure (0.1 MPa at 273.15 K) and the required pres­sure, respectively, Vj and V2 are initial volume and final volume of the blister, respectively, and Tj and T2 are initial temperature (273.15 K) and final tempera­ture, respectively.

It was assumed that the initial volume is equal to 268.083 mm3 (which corre­sponds to radius of 800 mm and blister height 1 • 10~04 mm) and the final volume is 4.02 • 1006 mm3 (for radius of 800 mm and blister height 1.5 mm). The pressures at 5 °C and 250C are calculated based on the input variables described in Eq 18.

The thick-plate modeling consisted of 80-mm-thick asphalt layer with a con­stant blister radius of 800 mm. Hence, the ratio of the width to height was 1/10, identical to that of the laboratory-produced blister.

To assess blister growth for 12 h (1/2 day) under uniformly applied pressure, an initial temperature of 15 °C was selected at start of the analysis and the tempera­ture of the MA was assumed to increase linearly up to 25 °C at different rates, as shown in Fig. 7(a). In addition, it was assumed that the temperature inside the blis­ter was rising simultaneously as in the asphalt layer. In this way, gas pressure in the blister corresponded directly to the temperature history as shown in Fig. 7(b).

Moreover, actual temperature measurements on and within the blister, as reported in Ref 21, are shown in Fig. 8(a). The temperature inside the blister was measured by putting a temperature probe in the MA, whereas the tempera­ture on the surface was measured by fixing the temperature probe using a trans­parent tape. Because the surface temperature was exposed to air convection it appeared that, the highest temperature was measured inside the blister. These temperature measurements were considered as basis to assess the significance of the daily temperature and pressure variations on the blister growth for one week, a history with repeated temperature and pressure cycles was investigated. For simplicity it was assumed that one cycle consisted of a linear increase within 12 h and a linear decrease within the following 12 h, as shown in Fig. 8(b). As indicated in the Data Reduction section above, the IDT test is con­ducted and a master curve for the temperature range between 5 °C to 25 °C is determined. Because the MA property is determined for the above specified

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step temperature

0.833 C/day

tmo (days)

FIG. 7—(a) Temperature history, and (b) pressure history for different rate (1/2 day).

FIG. 9—Comparison of MA plates with finite element method (FEM) simulation, first – order shear deformation (FSD) plate theory and measurement from image correlation; (a) vertical deflection profile, (b) max vertical defection as a function of time, (c) image correlation 2D plot of vertical deflection after 70s of measurement, and (d) vertical deflection with standard deviation.

temperature, the temperature in the finite-element simulation was assumed to vary moderately between 15 °C and 25 °C. The corresponding pressure history was defined using Eq 18, in a similar way varying from 7.12 • 10~06MPa to 7.37 • 10~°6MPa within one day. This frequency of temperature variation was chosen based on earlier experience [21] in a different case as shown in Fig. 8(b).