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PDP User’s Guide Appendix G:Converting Permittivity to Density
G-1
Converting Permittivity to Density
The relationship between permittivity and density is a function of many variables,
namely, the properties of the binder and the properties of the aggregate. As a
result, the permittivity to density conversion must address these factors.
Site specific conversion of permittivity, K, to density
𝜌
can expressed in many ways.
The various forms are density, site-specific density, normalized density, and air-
void content, the latter being expressed as a fractional volume (or ratio) of the total
volume.
We have determined that the simplest way to express the relationship is a
quadratic equation. Any of the above listed density forms, X, can be expressed in
the basic form:
𝑋 = 𝐴 + 𝐵 ∗ 𝐾 + 𝐶 ∗ 𝐾
2
At many sites, the most common parameter
X is density,
𝜌
; as a result we have
chosen always to use the A , B and C values that represent density (other form
coefficients can be readily determined from these values).
The common practice is to use the PDP to measure the permittivity K at a number
of locations and obtain the density from cores or indirectly from nuclear density
gauge measurements. The end result is a set of tabulated data such as below.
Permittivity K Density,
𝝆
K1
𝜌1
K2
𝜌2
K3
𝜌3
K4
𝜌4
K5
𝜌6
K6
𝜌6
The observed data are used to do a regression analysis to obtain A, B, and C. A, B,
C have the same units (g/cm
3
, Mg/m
3
, lb/ft
3
) as the density measurement; K is a
dimensionless parameter.
The PDP Toolkit PC software provides a ready means to compute A, B, and C. The
site- specific values of A, B, and C can be used to recompute density for data
already collected and can also be entered into the PDP system to convert
observations into site-specific density while collecting data in real-time.
Note that an additional important parameter that needs to be obtained for site-
specific density analysis is the
maximum density for the asphalt mix. The
maximum density must be known to convert density into normalized density,