Environmental Engineering Reference
In-Depth Information
Fig. 16.3
Effect of the vertical regularity of the masonry construction and wall failure: (
a
)
Categories of structural vulnerability; (
b
) Crack pattern of masonry panels due to “out of plan”
flood effect
Where:I
v
(i,j) = 1 if the i-
th
parameter, i = 1..N (N = 14 governing parameters), is
such that the structure has to be classified into the j-
th
category, j = 1..M (M = 4:
categories « A », « B », « C » and « D »).
-
A vulnerability function is associated with each damage category, which
expresses the residual risk of failure, (Fig.
16.4
):
…
…
()
…
…
2
2
()
−
()
PhPh
Ph Ph
hh
hh
−
−
vi
vi
0
P
=
P ij
,
and
+
max
=
1
(16.5)
(
)
−
()
v
v
vi
max
vi
0
max
0
Where:P
v
(i,j) = structural failure due to the i-
th
parameter (i = 1 up to N) when
the structure is classified into the j-
th
category (j = 1 up to M); h = water level
values taken by the random variable H (water height); h
max
= maximal or upper
limiting value of H; h
0
= the reference value; P
vi
(h) = value of the probability
P
v
(i,j) which represents the single damage contribution of the governing i-
th
parameter, in the structural j-
th
category, for the water depth h (Figs.
16.3
and
16.4
).
-
Global vulnerability derived from the combined influence of individual and
supposed independent governing parameters is expressed as:
N
(
)
∏
(16.6)
P
=− −
1
1
P
where
PPI
=
:
f
vi
vi
v
v
i
=
1
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