ESTIMATION OF AVERAGE TRU ACTIVITY IN SOIL SUBSURFACE INTERVALS
DIFFERENT FROM THOSE SAMPLED
DOE/ERSP TECH NOTE NO. 19.0
. DATED: 4 August 1979
AUTHOR: M. G. Barnes, DRI
In order to determine whether an island meets Condition D*, information is needed about the TRU
activity in any 5 em subsurface soil depth increment. However, subsurface sampling normally
ineludes the intervals 0 to 5 em, 5 to 10 em, ete., to some predetermined maximum depth. Thus, if
it is not immediately clear from the sampling data whether or not condition D is satisfied, estimates
must be made of activity in other intervals. This note describes a method of making such estimates,
and gives an example of its use for data from islands Belle and Daisy. The method can be applied to
any set of data for which the assumptions mentioned below hold.
On an island where fallout is the main source of contamination, with natural weathering the primary
process affecting redistribution of contamination in the soil, it is reasonable to accept an
exponential decline in contamination with depth. That is, the TRU activity at depth x, denoted TRU
{x), is described by the equation:
TRU(x)
= ke7cx
where k is the surface activity and c is a constant. This assumption is commonin the radiological
literature, including, for example, NVO-140.
Given k and ¢c, the average activity over any 5 em depth interval, say x1 to x; + 5, is:
i #4 79
5
x1
ke
-¢x
dx
=
kL
5¢
( “CXy-e (x1 + 5.)
e
-e
a,
5.
oi
= 5
}
ke
-ex
_ k
dx = Bee (1
_
10
| ke “* dx = x (ee
5
a, = :
e
Se
).
png
Ordinarily, however, all that is available is the sampling data, which is already in the form of
averages Over 5 cm intervals. In this case, if the assumption of exponential decline in activity with
depth is correct, k and e can be estimated from the data. For example, if the 0 to 5 and 5 to 10 em
intervals were sampled, with activity measured as ay and ag respectively, then we have:
ele)
Then
4
and
10¢ _
4 - ee
_.3
e@=- 5 In
“Sery
5e) = ese
1-e°
(2)
ay ;
ays
c
hence k = ————
~5e\.
(1 -e
)
*Condition D requires that the TRU activity in any 5 em depth interval below the surface not
exceed 160 pCi/g when averaged over 1/16 ha. B-19-1
lat coe
i) . eve