In the construction of barriers, the variability in the hydraulic gradient is important as it affects the contaminant transportation. This transportation is attempting to be stopped by a soil-bentonite cutoff wall which draws water from the ground within the closure and produces an inward hydraulic gradient. This causes the inward flux to oppose the outward flux of the contaminant. In this case, five soil-bentonite walls were examined to see the results of an average hydraulic gradient being used as compared to a point-to-point gradient.
Variability in Hydraulic Conductivity:
There are three main sources that change the variability of the hydraulic gradient. The first source is the variability of the mixture of the soil-bentonite backfill. This happens due to natural causes but the effects are minimized if a more homogeneous soil from off-site is used instead of soil from the excavation of the trench. Different amounts of bentonite in the soil can alter the properties of the soil; a higher concentration of bentonite reduces the average permeability. The variation of hydraulic conductivity can be measured at different stages in the construction process of the cutoff wall to estimate this type of variability.
The second source of variability is due to defects when excavating trenches or when applying the soil as a backfill. Settlement of the coarse-grained particles through the support slurries can occur from these processes.
The final source is any change occuring after construction of the soil-bentonite cutoff wall has been completed. These effects are difficult to predict since there are many factors involved. For example, the cutoff wall may react with different compounds in the soil and a continuous cycle of freeze-thaw or wetting-drying may cause the hydraulic gradient to vary. Also, as stress changes with the depth of the soil, more pressure is applied to the walls and affects the hydraulic gradient.
The results from five cases of cutoff walls show a log-normal distribution to be a better model than a normal distribution for the hydraulic conductivity of the soil.
Analysis of Contaminant Transport:
The cutoff wall is separated into small fractions with respect to the negative logarithm of hydraulic conductivity (k). These fractions are then normalized so that they equal are equal to one. The ‘k’ value is varied while the width, effective diffusion, and porosity of the cutoff wall are kept constant. The concentration of contaminants is initially kept at zero inside the cutoff wall; the concentration outside the wall is zero while the concentration inside the wall is constant at a value of c0. In actuality, the water flow and contaminant transport have complex behaviours, however in these cases the flow model is one-dimensional.
Peclet Number is of high important to the contribution towards area-weighted normalized flux which will determine what area of the cutoff wall is contaminated transport. Depending on the value of the Peclet number i.e. whether it’s negative or positive will indicate if the hydraulic gradient is inward or outward for a circumferential cutoff wall. “Peclet number is negative for a circumferential cutoff with an inward hydraulic gradient.” As for Fig. 2 which will illustrate the steady-state flux through cutoff wall with the Peclet number less than zero. Analyzing the graph portrays that when PAVG = 0 the contaminated transport is fully controlled by diffusion & hence JSS/JD* = 1. As PAVG increases in the negative direction JSS/JD* decreases as a result of inward advection counteracts outward diffusion. Increasing the variability in the hydraulic conductivity for a given PAVG increases JSS/JD* because the decrease in flux caused by inward advection in sub areas where hydraulic conductivity (k) is greater than PAVG is small as compared to the increase in flux caused by diffusion in sub areas with k less than PAVG. So variability of k is a function of PAVG as compared to JSS/JD* on whether PAVG is increasing or decreasing.
Positive Peclet Number:
“The Peclet number is positive for a circumferential cutoff wall with an outward hydraulic gradient.” Once again if PAVG = 0 then the contaminant transport alone is controlled by diffusion and hence JSS/JD* = 1. Where PAVG is large the advective flux dominates diffusive flux and both are in the same direction so that JSS/JD* approaches PAVG values. The affect or influence on the variability of the hydraulic conductivity is significantly less than for positive Peclet number as compared to negative Peclet values. Regardless of the hydraulic conductivity distribution about the average, the increase in flux is nearly balanced by decreases in flux. This balance occurs when k flux versus Peclet number relationship is nearly linear.
The area contaminant flux through the wall may be largely affected by the variability of the hydraulic conductivity when applied from point to point through a cutoff wall. The variability is mostly affected when the hydraulic conductivity & the concentration hydraulic act in the opposite directions. This phenomenon is best described when the Peclet number is negative where the circumferential cutoff wall has an inward hydraulic gradient. If this is the case, increasing the hydraulic conductivity will affect the flux escaping the wall as compared to the flux evaluated using only the average hydraulic conductivity, which means that calculating the contaminant flux maybe incorrect if variability, is not taken into account.