In most saturated soils, advection and diffusion/dispersion do not transport contaminants as fast as might be expected from a consideration only of these processes. Often, there is a movement of contaminant from the liquid phase to the solid phase due
to various physio-chemical processes (see Section 6.3.2). Together, these processes act to retard the contaminant flux. Where the soil solids are, in effect, clean with respect to the contaminant prior to the contaminant’s arrival, this retardation may be expressed using a very simple equation:
fR = 1 + Pdkd
where fR is the retardation factor (no units), kd (almost invariably expressed in units of l/kg = mL/g) is the partition factor which is discussed in the next paragraph and pd is the dry density of the soil (for which units of Mg/m3 will allow Eq. 6.14 to be used directly if kd is expressed in units of l/kg).
The rate of contaminant flux is slowed by a factor of 1/R from that which would be expected assuming only advection, diffusion and dispersion have an effect. This approach allows the effects of physio-chemical processes to be simply modelled by adapting the advection-dispersion Eq. 6.9 as follows:
Dl d2C Dt d2C vx dC _ dC
fR dx2 + fR dx2 fR dx dt
The partition factor, kd, is a very simple means of describing the concentration of a contaminant in the solid phase to the concentration of a contaminant in the fluid phase at equilibrium conditions. At low concentrations such as those normally experienced in the highway environment (except, perhaps, after certain spillages from vehicle accidents), a linear “isotherm” (relationship between the two concentrations) may not be too inaccurate and is a commonly used characterisation having the benefit of simplicity. Therefore, in such situations, a constant value of kd is used.
Values of kd are highly dependent on soil type, fluid and contaminant species. Values vary by several orders of magnitude for apparently small changes in some of these factors. Even with specific laboratory testing, the natural variability of ground conditions, mineral composition, particle size, etc. from place to place in a soil profile means that prediction of the retardation effect is very imprecise. Accordingly it is common to use published values and to compute the most and the least likely retardations that are credible. Values of kd are available from many sources, notably from the US EPA (EPA, 1999).
It is possible for enhancement, the inverse of retardation, to occur, for example when a spillage changes the fluid chemistry causing leaching of contaminants previously bound into the soil or aggregate. When enhancement takes place, the contaminant flux is higher than would otherwise be anticipated. This can be modelled by a value of fR of less than 1.0, although Eq. 6.15 will not be directly applicable as it assumes that the soil is initially clean as far as the contaminant of interest is concerned.
