Geology Reference
In-Depth Information
51 was found to give satisfactory results. Figure
3 depicts the influence of
N
f
on the convergence
of the objective function for constraints scenarios
1 and 4 (see Table 3).
the total energy and PGA, the worst input is nar-
row band (highly resonant) and the structure
deformation is conservative (see Figure 4 and
Table 4). Furthermore, most of the power of the
Fourier amplitude is concentrated at a frequency
close to the natural frequency of the elastic struc-
ture. This amplitude gets shifted towards a
higher frequency when the strain hardening ratio
increases. The Fourier amplitudes at other frequen-
cies are low and uniformly distributed. This result
is substantially different from that for the elastic
structure where all power of the acceleration
amplitude is concentrated around
ω
0
with no
amplitude at other frequencies (Abbas & Manohar,
2002). Additional constraints on the Fourier am-
plitude spectra (see Table 3) force the Fourier
amplitude of the worst acceleration to get distrib-
uted across other frequencies. The critical accel-
eration possesses a dominant frequency that is
close to the average dominant frequency observed
in past records (see Figure 5). The realism of the
earthquake input is also evident from the maximum
damage index it produces. For instance, the dam-
4.1.3 Numerical Results and
Discussions
The numerical results obtained are presented in
Figures 4, 5, 6, 7, 8 and 9 and Table 4. Figure 4
shows results for constraint scenario 1 and similar
results for case 4 are shown in Figure 5. Each of
these figures shows the Fourier amplitude spec-
trum of the worst ground acceleration, the inelastic
deformation, the hysteretic force and the energy
dissipated by the structure. Figure 6 shows the
time history of the ground acceleration. Based
on extensive analysis of the numerical results,
the major observations are summarized below.
The frequency content and Fourier amplitude
of the worst earthquake are strongly dependent
on the constraints imposed (see Table 3). If avail-
able information on earthquake data is limited to
Table 2. Information on past recorded ground motion records for a firm soil site
Earthquake date
Magnitude
Epic. Dist.
(km)
Comp-
onent
PGA
(m/s
2
)
PGV
(m/s)
PGD
(m)
Energy*
(m/s
1.5
)
Site
Mamoth lakes
05.25.1980
Loma prieta
10.18.1989
Morgan hill
04.24.1984
San Fernando
02.09.1971
Parkfield
12.20.1994
Caolinga
05.02.1983
Northridge
01.17.1994
Cape Mendocino
04.25.1992
Westmorland
04.26.1981
Imperial valley
10.15.1979
6.2
1.5
W
S
W
S
S60E
S30W
N69W
N21E
W
S
W
N
S74E
S16W
W
S
E
S
S45W
N45W
4.02
3.92
3.91
4.63
3.06
1.53
3.09
2.66
2.88
3.80
2.83
2.20
3.81
3.43
3.25
2.89
4.35
3.54
2.68
1.98
0.21
0.23
0.31
0.36
0.40
0.30
0.17
0.28
0.44
0.10
0.26
0.26
0.60
0.34
0.45
0.24
0.33
0.44
0.22
0.19
0.05
0.05
0.07
0.11
0.07
0.02
0.04
0.10
0.01
0.01
0.10
0.10
0.12
0.09
0.15
0.08
0.11
0.15
0.10
0.15
3.73
4.01
3.82
2.61
2.33
1.64
2.07
2.47
1.33
1.74
2.67
2.14
4.17
3.50
2.44
2.31
3.26
3.25
2.30
2.14
Convict Greek
7.0
9.7
Capitola
6.1
4.5
Halls valley
6.6
27.6
Castaic old ridge
5.0
9.1
Parkfield fault
6.5
30.1
Cantua creek
6.7
5.9
Canoga park
7.0
5.4
Petrolia general
5.0
6.6
Westmorland fire
6.4
17.4
Calexico fire
∞
∫
2
]
/
1 2
*
E
=
[
v t dt
g
( )
(Arias, 1970).
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