poster - International Conference of Agricultural Engineering

widely used for various fields such as physics, engineering, biology, medical and food
sciences. But, as a mentioned above, the RSM has limitations of efficiency and errors in the
sensitivity of the reliability index. In this study, MLS-RSM was performed for modelling of
contaminants transport.
A limit state function was approximated by response surface function (RSF), given by:
~
G(
x)
a
0
n
a x
n
i i
i1 i1
a
ii
x
2
i
(4)
~
where G ( x ) is the approximated RSF, n is the number of random variables, and a
0
, a i
, aii
are unknown coefficients. The approximated RSF can be defined in terms of basis functions
p (x) and coefficient vector a (x)
:
~
T
G(
x)
p(
x)
a(
x)
(5)
The vector of unknown coefficients, a (x)
, is determined by minimizing the error between the
observations and approximations by the limit state function:
n
i1
2
T
p(
x ) a(
x)
G(
x )
E ( x)
w(
x xi
)
i
i
(6)
where n is the number of experimental points, w( x xi
) is a weight function depending on
the distance between x and the observation points x
i
, given by:
2 3 4
x xi
1
6r
8r
3r
for r 1
w(
x xi ) w(
r )
(7)
d
mi 0
for r 1
The coefficient vector a (x)
can be estimated by:
T
1 T
a(
x)
( P W ( x)
P)
P W ( x)
G
(8)
The most probable failure point (MPFP) is determined using by first order reliability method
(FORM) and the MPFP was used as additional input point until the difference between MFPF
and next MPFP is acceptably small (or converge).
3. 1-D Transport of chemical contaminants though groundwater
The transport of contaminants model cosidering dispersion, advection and retardation is
given by (Van Genuchten & Alves, 1982):