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Table 3. Synthesis of the UCL values and the S
w
dimension for different probability values
Figure 16. Risk in function of the probability of
exceeding the CSC value 10µg/l
Probability of exceeding %
UCL (µg/l)
S
w
(m)
20
18.74
1517
30
21.68
1375
40
25.29
1269
50
29.74
1138
60
35.44
1027
70
42.22
882
80
50.45
746
90
59.42
582
é
ì
í
ü
ý
ù
the risk the formulations obtained previously for
the two parameters S
w
and Source Representa-
tive Concentration, it is possible to analyze the
variability of the risk throughout the variability
of these parameters.
The distribution of the concentration C(x) along
the longitudinal direction of flow x in contaminated
groundwater can be expressed by the Domenico
solution (APAT, 2008)). In the hypothesis of an
aquifer of limited thickness in which the vertical
dispersion can be neglected, with a source of con-
tamination characterized by a width
S
é
ù
ï
ï
ï
î
ï
ï
ï
la
ïï
ï
ï
þ
ï
ï
ï
æ
è
ö
ø
x
4
R
ê
ê
ê
ê
S
ú
ú
ú
ú
÷
÷
÷
÷
÷
-+
ç
ç
ç
ç
ê
ê
ê
ú
ú
ú
RC
=
exp
1
1
1
xi
×
erf
w
* *
EM
T
R
2
a
v
4 a
x
ë
û
x
e
ë
û
y
(29)
Being:
E
M
= daily effective exposure;
T = pollutant toxicity;
α
x
= longitudinal dispersivity [L];
α
y
= transversal dispersivity [L];
v
e
= groundwater effective velocity [L·T
-1
];
λ
1
= 1st order decay coefficient for the con-
taminant in dissolved phase [T
-1
];
R
i
= delay coefficient in groundwater
In the case study, assuming the values of the
exposure parameters recommended by APAT
Manual (2008) and considering, according to the
legislation, the point of compliance distant 500 m,
expressing the risk in function of the probability
of exceeding the Threshold Concentration of
Contamination, the function reported in Figure
16 can be obtained.
The obtained risk function appears monotoni-
cally increasing and permits to carry out evalua-
tions in relation to the different operable choices,
using also the other available information.
For example, in case in which elements of
³ 8 a
, assuming the value of the error function equal to
1, the Domenico equation assumes a simplified
form. For the industrial area in study, fixed a de-
fined area source of contamination in groundwater
with corresponding representative concentration,
assuming groundwater ingestion as only modality
of exposure, by means of inserting the Domenico
simplified expression in the risk formulation it
is possible to obtain the “Risk Function” whose
expression can be analyzed in relation to the deci-
sions chosen for the assumption of the probability
of exceeding the CSC value.
x
w
y
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