# Blistering Mechanism Analysis of Hydraulic Asphalt Concrete Facing
## 4 Model Test of the Blister
### Estimation of Steam Pressure  
The asphalt concrete facing with water in the impervious layer can be approximated as a closed vessel with water. The pressure in the vessel is composed of two parts, one part is the saturated vapor pressure (P\({}_{\mathrm{w}}\)), and the other is the pressure of air (P\({}_{\mathrm{a}}\)). According to the [PERSON]'s law of partial pressure [17], the total pressure P\({}_{\mathrm{t}}\) of the mixed gas in the vessel is equal to the sum of the partial pressures of the components:  
\[\mathrm{P_{t}}=\mathrm{P_{w}+P_{a}}. \tag{1}\]  
Under a closed vacuum condition, the gasification of water, and the liquefaction of vapor will gradually reach equilibrium. The pressure at the two-phase equilibrium is called the saturated vapor pressure; the saturated vapor pressure, P\({}_{\mathrm{w}}\), increases as the temperature, T, increases, and has no relation to the volume of the water. The saturated vapor pressure can be described by the following Antoine equation [18; 19]:  
\[\mathrm{logP_{w}}=\mathrm{A}-\frac{\mathrm{B}}{\mathrm{T}+\mathrm{C}} \tag{2}\]  
where P\({}_{\mathrm{w}}\) is saturated vapor pressure, mmHg; T is Kelvin temperature, K; and A, B, C--are constants. There are small differences in the values of A, B, and C in different papers; for example, in paper [20], for water of 0-60 \({}^{\circ}\)C, A = 8.1332, B = 1762.39, and C = 235.66. It is assumed that the relationship between the air pressure P\({}_{\mathrm{a}}\) and the temperature T can be approximated by the following ideal gas state equation:  
\[\frac{\mathrm{P_{a}}}{\mathrm{T}}=\frac{\mathrm{nR}}{\mathrm{V}} \tag{3}\]  
where P\({}_{\mathrm{a}}\) is the pressure of the gas, Pa; V is the volume of the gas, ml; n is the amount of substance of the gas, mol; R is the universal gas constant, 8.314 J\(\cdot\)mol\({}^{-1}\cdot\)K\({}^{-1}\); and T is Kelvin temperature, K. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Station** & \multirow{2}{*}{**Elevation/m**} & **Diameter of** & \multirow{2}{*}{**Depth of**} & \multicolumn{2}{c}{**Drainage Layer**} & **Void Content of** \\ \cline{4-7}  & & & & **Blister/cm** & & **Void** & **Permeability** & **Impermeable** \\  & **Number** & & & & **Content \%** & **Coefficient cm/s** & **Layer \%** \\ \hline
1 & 1 + 713 & 809.0 & 30 & 2.7–5.8 & 20.4 & 0.114 & 2.85 \\
2 & 1 + 627 & 810.0 & 40 & 7.4–9.1 & 17.2 & 0.206 & 2.90 \\
3 & 2 + 356 & 809.0 & 30 & 6.1–8.9 & 17.3 & 0.085 & 2.47 \\
4 & 2 + 349 & 806.5 & 40 & 5.2–7.3 & 20.2 & 0.137 & 2.89 \\
5 & 2 + 390.5 & 809.0 & 40 & 5.3–7.6 & 16.0 & 0.267 & 2.68 \\
6 & 2 + 741 & 809.0 & 20 & 7.3–8.5 & 18.3 & 0.098 & 2.75 \\
7 & 2 + 769 & 809.0 & 40 & 2.2–3.3 & 19.4 & 0.103 & 2.67 \\
8 & 0 + 56 & 806.5 & 40 & 2.6–9.3 & 20.1 & 0.115 & 2.95 \\
9 & 0 + 127 & 808.0 & 30 & 3.1–4.5 & 20.5 & 0.201 & 2.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test results of additional samples. The above analysis shows that the pressure value in the asphalt facing is related to the initial temperature. During actual construction, when the vibrating roller compaction water enters the impervious layer, the initial rolling temperature of the impervious layer can reach about 140 \({}^{\circ}\)C. However, the layer has not been compacted and closed, and the entering water is also in a state of intense phase change, with water vapor continuously leaking. The final temperature of the vibrating roller is also about 90 \({}^{\circ}\)C. The asphalt concrete has different permeability coefficients for water and water vapor, and the water vapor has a large permeability coefficient. Since water vapor may leak for a long time, it was assumed here that the initial temperature was related to the annual average temperature of the asphalt facing, and it is not necessary to consider the influence of temperature changes for many years. Determining the initial temperature of the water vapor pressure in the blister during the operation period is a complicated issue which needs further study.