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A SIMPLE ESTIMATION METHOD OF THE PROBABILITY DISTRIBUTION OF RESIDUAL DEFORMATION OF QUAY WALLS CONSIDERING VARIATION OF EARTHQUAKE GROUND MOTION
16th World Conference on Earthquake Engineering
January 11th
Toshiyuki HiraiNEWJEC Inc.
Takashi Nagao Research Center for Urban Safety and Security, Kobe Univ.
Contents
1. Introduction
2. Study method
3. Study results
4. Conclusions
Introduction
An example of the Damage of gravity type quay walls at Kobe port by the 1995 South Hyogo Prefecture Earthquake
Sea Land
2.74m
Structural members of the quay wall was not damaged but the quay wall was not available
Land
Sea
Introduction
In the earthquake resistant design for gravity type quay walls, the residual deformation is the target of the performance verification.
In Japan, earthquake ground motions for earthquake resistant design are evaluated by the probabilistic seismic hazard analysis.
Probabilistic performance verification method is desirable.
And, source effects, path effects and site effects are uncertain about earthquake ground motions.
Introduction
The residual deformation of a quay wall cannot be evaluated analytically because of nonlinearity of foundation soil layers.
It is difficult to use Monte Calro simulation method because finite element earthquake response analysis must be used considering effects of liquefactions of soil layers. The analysis need much computational load.
We try to propose a simple estimation method that can evaluate the probability distribution of the residual deformation of quay walls by performing earthquake response analysis only few times.
Study method
Earthquake ground motion can be evaluated by source, path, site effects.
Source effects
Path effects
Fault
Site effects(amplification factor and phase characteristics)
Seismic bedrock
Engineering bedrockSubsurface
-3
-2
-1
0
1
2
3
0 50 100 150
acceleration(m/s2)
time(s)0.1
1.0
10.0
100.0
0.1 1.0 10.0
Ampl
ification factor
Frequency(Hz)
Study method
013,013,
012,012,013012 )(
MYGiMYGi
MYGiMYGiMYGMYG RO
ROfGfG
Known site amplification factor
Observed record
epicenter distance
Variation of site amplitude factors
Base input motion
replaced
Study method
The finite element model of a quay wall
Seawater Reclaimed sand 10m
9m
Replaced sand Clay
Reinforced concrete caisson
Gravel
Rubble foundation
Liquefiable
Study results
An example of the earthquake response analysis.
Residual horizontal deformation : -0.048mResidual vertical deformation: -0.022mResidual angle of inclination : 0.12°
Liquefaction
0
2
4
6
8
10
12
14
16
18
0.011 0.131 0.251 0.371 0.491
Frequency
Residual deformation(m)
Frequency
Logarithmic normal
distribution
Study results
Frequency distribution regarding as logarithmic normal distribution
Histogram of the residual deformations
0.800.820.840.860.880.900.920.940.960.981.00
0.0 0.2 0.4
Cumulative probability
Residual deformation(m)
Relative cumulative
frequencyNormal distribution
Logarithmic normal
distribution
0.0
0.5
1.0
0.0 0.2 0.4
Cum
ulat
ive
prob
abili
ty
Residual deformation(m)
Relative cumulativefrequency
Normal distribution
Logarithmic normaldistribution
Study results
Cumulative probability of residual deformation
Upper tail is important.
Logarithmic normal distribution gives larger deformation than normal distribution.
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.3
Cumulative probability
Residual deformation(m)
Relative cumulative
frequencyNormal distribution
Logarithmic normal
distributionSimple estimation
Study resultsSimple estimation by conducting analysis several times
0.1
1.0
10.0
100.0
0.1 1.0 10.0
Am
plifi
catio
n fa
ctor
Frequency(Hz)
Very large estimation
Large or small at every frequency
Large at certain freq. and small at another
To try to estimate cumulative probability by simple method
0.1
1.0
10.0
100.0
0.1 1.0 10.0
Amplification factor
Frequency(Hz)
Study resultsTo consider the sum of the amplification factor as index
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 500 1000 1500 2000 2500
Residual deformation(m)
Sum of site amplification factors
with range from 0.5Hz to 5.0Hz
Study results
Mean site effects
Mean + standard deviation site effects
Mean - standard deviation site effects
The correlation is high
The relationship between the residual deformation and the index
y = 0.071x' + 0.11
0
0.1
0.2
0.3
-2 -1 0 1 2Residual deformation(m)
x'
Study results
136
136'amp
ampampx
Mean site effects
Mean + standard deviation site effects
Mean - standard deviation site effects
The regression equation by a least squares approximation
Study results
0.0
0.5
1.0
0.0 0.2 0.4
Cum
ulat
ive
prob
abili
ty
Residual deformation(m)
Relative cumulative frequency
Logarithmic normal distribution
Logarithmic normal distribution(3-point approximation)
0.800.820.840.860.880.900.920.940.960.981.00
0.0 0.2 0.4 0.6
Cumulative probability
Residual deformation(m)
Relative cumulative
frequency
Logarithmic normal
distribution
Logarithmic normal
distribution (3-
point approximation)
ConclusionsWe tried to estimate the cumulative probability of the logarithmic normal distribution by conducting earthquake response analysis only several times.
We showed that the distribution of the residual deformations can be estimated by 3 earthquake response analyses, when we considered the sum of the site amplification factor as the index of magnitude of site amplification factor.
ConclusionsAs a future problem, it is necessary to verify the applicability of the proposed method to other sites.
In this study, only the variation in earthquake ground motions is considered in the response analysis, but it is necessary to consider the variation in both earthquake ground motion and soil property.