A falling-pressure method for measuring air permeability of asphalt in laboratory
Introduction
Air permeability is one of the most important parameters in all gas flow simulations (e.g. Shan et al., 1992; Shan, 1995). The common method for determining the air permeability of unsaturated rock, soil or other materials is to measure the steady-state air flux through the soil sample (e.g. Stonestrom and Rubin, 1989; Springer et al., 1998). Although the data analysis of this method is simple, the experiment apparatus is complex and expensive in order to maintain and measure the steady-state air flux. Massmann and Johnson (2001) proposed a very simple method to estimate air permeability in laboratory. The main drawback of their method is that the air is treated as an incompressible fluid. This assumption can only be used when the variation range of the air pressure in the experiment is sufficiently small. This paper introduces a falling-pressure method to measure air permeability in laboratory. The air is treated as compressible fluid. An analytical solution describing the air pressure versus time relationship is derived. Test data of 15 samples are analyzed both analytically and numerically to examine the applicability of the falling-pressure method.
Section snippets
Description of the test
The apparatus comprises a 20 cm diameter cylinder in which the column-shaped sample is fixed and sealed around the perimeter with a silicone sealant. The lower surface of the sample and the cylinder form an air chamber. The upper surface of the sample is open to the atmosphere. A simple foot pump is used to pressurize the air chamber through an air inlet. Then the valve of the air inlet is closed so that the air in the air chamber can only leak out through the porous sample. A water manometer
Mathematical model
If the gravitational component of the driving force is negligible in comparison to the force of the applied pressure gradient, the one-dimensional isothermal air flow through the sample can be ideally described by the extended Darcy's law for gases (Muskat, 1946, pp. 76–78; Stonestrom and Rubin, 1989)Here q is the volumetric flux [L T−1], k is the slip-enhanced air permeability [L2], μ is the dynamic viscosity of the gas [M L−1 T−1], PSmpl(z,t) is the air-phase pressure [M L−1 T−2
Application examples
In this section, the method introduced in Section 3.2 will be used to analyze the test data of 15 asphalt samples. These samples were collected from two different locations C402 and C409 at the runway of the Hong Kong International Airport (GCG LTD, 2001). The diameter of each samples is 18.8 cm, so the cross-section area The thickness of each sample is The atmosphere pressure is taken to be and the initial pressure in the air chamber is
Numerical verification
Although the condition δ≪1, which justifies the approximate analytical solution , , has been verified at the end of Section 4, the verification is not straightforward and the estimation is posterior. Furthermore, the condition δ≪1 only gives the description to the error between the exact solution of the models , , , , and the approximate analytical solution (18). The quantitative error between the analytically estimated and true values of the air permeability of the sample is unknown. Due to
Conclusions
A simple analytical solution is presented to estimate air permeability using the test data obtained by a falling-pressure method in laboratory. Compared with the common method that has to measure the steady-state air flux through the soil sample, the falling-pressure method has the advantages such as simplicity and economy. It does not need to measure the air flux leaking through the sample. What is needed to record is the air pressure change with time in the air chamber. This can be easily
Acknowledgements
This research was supported by Committee on Research and Conference Grants (CRCG) at the University of Hong Kong, the Hong Kong Research Grants Council (RGC) of the Hong Kong Special Administration Region, China, and the National Science Foundation of China (No. 40372111). The authors are very grateful to Dr C. Shan and another anonymous reviewer for their valuable comments.
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