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.