Geology Reference
In-Depth Information
Table 9. Optimum results starting from different initial design parameters as per Table 8
Preliminary
design
Over
design 1
Over
design 2
Under
design 1
Under
design 2
Design parameter
x
d
(1) =
X
( 3
=
h
b
[
cm
]
57.0
58.4
56.5
53.6
58.0
x
d
(2) =
X
( 5
=
h
c
[
cm
]
40.3
41.1
40.3
45.6
40.4
x
d
(3) =
X
( 6
=
ρ
0.00617
0.00586
0.00813
0.00711
0.00644
span
x
d
(4) =
X
( 7
=
ρ
0.01028
0.01122
0.01300
0.01303
0.01051
end
x
d
(5) =
X
( 8
=
ρ
0.02130
0.01672
0.01553
0.01152
0.01814
col
Initial cost
C
0
(
x
d,
) [$]
2601
2569
2559
2546
2568
Repair cost
C
d
(
x
d
) [$]
1020
1008
1004
999
1007
Total cost [$]
3621
3577
3563
3545
3575
λ = capacity factor, fraction of
D
defining the
limit displacement;
a
G
= peak ground acceleration;
ω
S
= soil frequency in the Kanai-Tajimi Power
Spectral Density function;
T
= duration of the strong motion part of the ac-
celerogram record;
M
= applied mass;
D
R
= soil relative density;
r
= nominal variable representing the different
ground motion records.
The resulting model, developed for the similar
problem of a metal fastener in wood (Foschi, 2000)
depends solely on mechanical properties of the
pile and the soil, and produces the hysteretic loop
for any input excitation, automatically developing
the pinching and degradation characteristics. The
p
(
w
) relationship used here was taken from Yan
and Byrne (1992),
E
w
if
w
≤
α
2
D
max
( )
=
p w
0 5
.
D
w
d
2
E
α
if
w
>
α
D
max
The pile is considered as an elasto-plastic
beam on a nonlinear foundation. The pressure on
the soil,
p
(
w
), is a function of the displacement w
which varies along the length
L
.
The structural analysis for the pile-cap dis-
placement Δ can be done by considering the
dynamic equilibrium of the mass
M
as a single
degree of freedom system. Using a beam finite
element model of the pile, the restoring hysteretic
force
F
(Δ) can be calculated by integration of
the reactions
p
(
w
), after the deflected shape
w
is
determined. The nonlinear, compression-only, soil
reactions
p
(
w
) take into account the development
of gaps between the pile and the surrounding soil.
(50)
in which
α
= 0.5 (
D
R
)
-0.8
and
D
R
is the soil relative
density. The modulus
E
max
depends on the specific
weight of the soil and the depth of the soil layer
and it is detailed by Yan and Byrne (1992). In this
work only the relative density was considered to
be a random variable.
The calculation of Δ can be integrated directly
into the reliability calculation using the perfor-
mance function in Eq.(49) or into the optimization
for the mass
M
which can be sustained to match a
prescribed reliability level. As a modeling alter-
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