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Damping Ratio Estimation of an Existing 8-story Building Considering Soil-Structure Interaction

Using Strong Motion Observation Data

by

Koichi Morita1

ABSTRACT

In this study, damping ratio of an exiting 8-story

SRC building using the strong observation data

is identified. Strong motion observation is

continually carried out since just after the

completion of the building. Damping ratio are

identified with the effect of interaction and

without the effect. The effect of the dynamicinteraction of the building to damping ratio will

be discussed.

KEYWORDS: Amplitude Dependence,

Damping Ratio,

Health Monitoring,

Identification Method

1. INTRODUCTION

Damping ratio is one of the important indexes to

predict the response of the building. Dampingratio value used for structural design does not

always agree with the measured value, though

those of natural frequency and participation

function agree with the measured value.

Although the consideration of the structure

classification is done, the first damping ratio has

been set at 2% and 3%, etc. regardless of the

condition of the building. This setting seems to

base on experience and practice in the past, and

the reason which is clearly physical is not shown.

It is very difficult to evaluate the damping ratio

by the theoretical method, so, in the present state,

the tendency of damping ratio should be grasped

by the observations and measurements.

The database of building damping ratio is made

on various experiments and observations results

carried out in the past, and the statistical

examination of damping ratio has been made.

[1] This data is analyzed from many points such

as characteristics of buildings, and the

influential factor to damping ratio is analyzed.

The correlation is being found on some factors,

but clear tendency cannot be found out because

of large dispersion. From these results, large

dispersion is included in damping ratio. It seems

to become a situation in which structural

designers must use the practice value.

Many kinds of experimental method and

evaluation technique for estimating damping

ratio has been proposed. It has also been

indicated that the identified results of dampingratio change by the setting of conditions such as

technique itself and band pass filter, curve fitting

and so on. In case of damping database, such

difference from technique cause large dispersion.

The authors carried out microtremor observation

in same observation method and evaluation

method to exclude the dispersion from method.

Though the correlation between the aging

number and damping ratio is shown as strong,

clear tendency cannot be shown because of large

dispersion of damping.

In the other research, very much observation iscarried out on one building continually, and

damping ratio tendency are grasped. On one

building, tendency such as amplitude

dependence and aging of damping are examined.

Tendency of the natural frequency is very clear,

but damping ratio is included large dispersion.

As the characteristics of the damping ratio, the

amplitude dependence is mentioned. Many

examples of the experimental studies which

noticed the amplitude dependence of damping

are observed. On the amplitude dependence,

damping ratio will increase as amplitude

increases, or there is some leveling off in this

increase. It has also been indicated that the

effect of the non-structural members is large.

Authors collected the data on amplitude

dependence of damping ratio on many buildings.

Damping ratio increases to some drift angle,

after that leveling-off can be found out.

As a factor of the damping ratio of the building,

1 Senior Researcher , Building Research Institute,

Tsukuba-shi, Ibaraki-ken 305-0802, Japan

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the underground dissipation by the dynamic

soil-structure interaction is mentioned. It is

necessary to measure vertical motion of the

input layer at more than 2 points in order toremove the effect of the rocking. The case for

such measurement is few, and the evaluation

example of damping ratio considering

soil-structure interaction effect is very little.

In this study, damping ratio of an exiting 8-story

SRC building using the strong observation data

is identified. Strong motion observation is

continually carried out since just after the

completion of the building. Damping ratio are

identified with the effect of interaction and

without the effect. The effect of the dynamic

interaction of the building to damping ratio willbe discussed.

2. OUTLINE OF TARGET BUILDING AND

INSTALLED SENSORS

2.1 Building Characteristics

The target building is Urban Disaster Prevention

Research Center in National Institute for Land

and Infrastructure Management (NILIM) that

was completed in March 1998. Outline of

building characteristics are shown in Table1.

2.2 Installed Sensors

The sensors are installed with 11 locations (33

channels) in the building. The sensor

configuration is shown in Fig. 2 and 3.

(Kashima 2004) In addition to these

accelerometers, maximum response memory

sensors of story displacements are installed. In

this study, only accelerometers installed at

ground(A01), basement, 1st , 2nd, 5th and 8th

story are used for system identification.

3. THREE TYPES OF DAMPING RATIO

3.1 Three Types of Damping Ratio Identified in

This Study

Using the data of strong motion seismometer

shown in Figure 1, damping ratio is identified.

In this study, three types of damping ratio

considering the interaction effect are identified

as following;

1) the SRB type damping ratio hSRB including

basement horizontal motion and the rotation

motion. (input motion is ground motion.)

2) the RB type damping ratio hRB including the

rotation motion. (input motion is basement

floor motion.)3) the B type damping ratio hB including only

the building motion. (input motion is

basement floor motion plus rocking motion.)

B

3.2 Types of Damping Ratio by Experimental

Methods

The types of damping ratio are different by the

experimental methods. The types of the damping

ratio by experimental methods are shown in

Tables 2.

In the past experiments, most damping ratio are

estimated in SRB or RB type, and the B typedamping ratio is very rare. The example just

after the completion of the building is frequent

in the time of the observation.

3.3 Type of Damping Ratio in Response

Analysis

In the response analysis, the damping ratio of B

type is indicated in the case of first damping

ratio 2%. From this fact, the damping ratio

generally used by the analysis indicates the B

type. By facing, the damping ratio by the

experimental observation can be called beingSRB type or RB type.

4. OUTLINE OF SYSTEM IDENTIFICATION

In this monitoring system, accelerometer data of

basement, 1st, 2nd, 5th and 8th story are used.

Parameter identification based on the ARX

model is applied for input-output data of

vibration measurements. The ARX model

structure is the simple linear difference equation

)1(...)(

)(...)1()(

1

1

+++=

+++

nbnktubnktub

natyatyaty

nb

na, (1)

which relates the current output y(t) to a finite

number of past outputs y(t-k) and inputs u(t-k).

The structure is thus entirely defined by the

three integers na, nb, and nk. na is equal to the

number of poles and nb-1 is the number of zeros,

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while nk is the pure time-delay (the dead-time)

in the system. From this model structure, the

coefficients aj and bj are estimated.

If A and B are expressed as,

=

+=

an

j

j

jqaqA1

1)( , (2)

=

+=

b

k

n

j

nj

jqbqB1

1)( , (3)

jz p is the root of A(z)=0 and is the

residue of a partial fraction expansion ofB(z)/A(z).

jz r

Natural frequency and damping ratio

are expressed as the following.

jf

jh

t

ppf

jzjz

j

+=

2

)(arg)(log 22

, (4)

tf

ph

j

jz

j

=

2

log, (5)

When model numbers change as na=70 to 80

(even numbers), nb=na+1, and nk=0, we select

the numbers in which Akaike's Information

Criteria (AIC) [2] is estimated as small.

5. IDENTIFICATION RESULTS

5.1 Tendency of Damping Ratio in All Data

430 strong motion records from June 1996 to

December 2006 are used for identification. For

all strong motion records (all duration time),

three types damping ratio are identified, and the

relationship between the aging number is shown

in Figure 2 to 4. In all these figures, there are

some dispersions in damping ratio. The SRB

and RB type damping ratio decrease in about

initial 3 years. The tendency changed to the

increase afterwards can be seen. The B type

damping ratio in Figure 4 has also large

dispersion, but tends to increase as the aging

year increases. In Figure 5, ratio between two

damping ratios in which SRB or RB damping is

divided by B type is shown. According to this

figure, ratio between two damping tends to

decrease as the aging.

5.2 Secular Change of Damping Ratio

In 5.1, since the result of various amplitude

levels is included, the dispersion increases.

Then, the result of extracting only the data over

30cm/s2 at the maximum response acceleration

is shown in Figure 6, in order to reduce the

effect by the amplitude level. The SRB and

RB type damping ratio similarly decrease in

initial 3 years, and tendency is changed to the

increase afterwards. Just after completion, the

ratio between two damping takes the value ofabout 2 to 4, as shown in Figure 7. The ratio

between two damping tends to decrease to some

aging, after some point the ratio approaches to 1.

The result of extracting only the data of about

5cm/s2 (4.5 5.5) at the largest response

acceleration is shown in Figure 8, in order to

reduce the effect of the amplitude level. The

SRB and RB type damping ratios decrease in

initial 3 years, and tendency is changed to the

increase afterwards. The B type damping ratio

tends to increase as aging. The ratio between

two damping is shown in Figure 9. Just after thecompletion of building, the value of ratio is

about 2 to 6. The tendency in the decrease is

traced with the aging, and the ratio tends to

approach 1 when it becomes to some extent

aging number. Similar tendency can be observed

in other response levels.

5.3 On Amplitude Dependence of Damping

Ratio

From 5.1 and 5.2, damping ratio and those ratios

change according to the aging number. In

order to reduce these effects, the data in which

aging number is from 4.5 to 5.5 years are

extracted and tendency is shown in Figure 10.

SRB and RB damping ratios tend to increase, as

acceleration increases. The B type damping ratio

tends to decrease with the acceleration level.

The ratio of two damping tends to increase with

the increase of the level of the response

acceleration shown in Figure 11.

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6. CONCLUSIONS

Using the strong motion record data of an

existing building, damping ratios areidentified. . As a result of evaluating the three

types of damping ratio (SRB,RB,B type)

considering the dynamic soil-structure

interaction effect, conclusions of this study are

shown in the below:

1) Most becomes SRB or RB type for the

damping ratio based on experiment and

observation reported in past research. On the

other hand, the damping ratio in the design stage

indicates the B type.

2) SRB and RB type damping tend to decrease

in initial about 3 years, and are changed to theincrease afterwards. .

3) The B type damping ratio tends to increase by

the aging.

4) In initial time, the ratio in which SRB or RB

type damping is divided by B type takes the

value of about 2 from 4. It tends to approach 1

constant value with the aging.

5) As the acceleration level is higher, SRB and

RB type damping ratio tend to be larger. Asthe acceleration level is higher, B type damping

ratio tends to be smaller.

6) As the acceleration level is higher, the ratio in

which SRB or RB type damping is divided by B

type takes larger value.

7. REFERENCES

1. N. Satake, K. Suda, T. Arakawa, A. Sasaki, Y.

Tamura Damping Evaluation using

Full-Scale Data of Buildings in Japan

Journal of Structural Engineering, Vol. 129,No. 4,, pp. 470-477, 2003.4

2. Akaike, H., 1973. Information theory and an

extension of the maximum likelihood

principle, 2nd Inter. Symp. On Information

Theory (Petrov, B.N. and Csaki, F. eds. ),

Akademiai Kiado, Budapest 267-281

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Figure 1. Exterior of Target Building

Table 1. Outline of Building Characteristics.

Structure type steel encased reinforced concrete

Number of story 8-story

Height 30.9m

Total building area 5050m2

Foundation type mat foundation

Sandy ClClayey S

Loam

North

20 m

A01

Figure 2. Vertical Sensor Configuration

7.5m 7.5 m 6.0 m

9.0m

9.0m

8.0m

1 2 3 4

A

B

C

D

B1F

7.5m 7.5 m 6.0 m

9.0m

9.0m

8.0m

1 2 3 4

A

B

C

D

8F

ELV

BFN

BFS

BFE

8FN

8FS

8FE

Figure 3. Sensor Configuration at Basement Floor and 8th Floor

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Table 2. Type of Damping Ratio by Experimental Method.Experimental method Estimation method Type

Free vibration test logarithmic decrement etc. SRB

Forced vibration test Resonance curve SRB

Microtremor observation, Wind observation Random decrement SRB

Microtremor observation & Strong motion observation(only horizontal) Transfer function etc. RB

Microtremor observation & Strong motion observation(including up-down

components

Transfer function etc. B

Table 3. Type of Damping Ratio in Response Analysis.

analytical method Type

time history response analysis B

response spectrum method B

0 1 2 3 4 5 6 7 8

0

2

4

6

8

9

1stdampingratio(SRB)[%]

structural age[year]

Figure 4. Secular Change of Damping Ratio (SRB)

0 1 2 3 4 5 6 7 8 90

2

4

6

8

1stdampingratio(RB)[%]

structural age[year]

Figure 5. Secular Change of Damping Ratio (RB)

0 1 2 3 4 5 6 7 8 90

2

4

6

1stdampingratio(B)[%]

structural age[year]

Figure 6. Secular Change of Damping Ratio (B)

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0 1 2 3 4 5 6 7 8 90

1

2

3

4

5

6damp(SRB)/damp(B)damp(RB)/damp(B)

ratiobetweentwodampings

structural age[year]

Figure 7. Secular Change of Ratio between Two Damping

0 1 2 3 4 5 6 7 8 90

1

2

3

4

5damp(SRB)damp(RB)damp(B)

1stdampingratio[%]

structural age[year]

Figure 8. Secular Change of Damping Ratio (Peak response is more than 30cm/s2)

0 1 2 3 4 5 6 7 8 90

1

2

3

4

damp(SRB)/damp(B)damp(RB)/damp(B)

ratiobetweentwodampings

structural age[year]

Figure 9. Secular Change of Ratio between two damping (Peak response is more than 30cm/s2)

0 1 2 3 4 5 6 7 8 90

1

2

3

4

5

6 damp(SRB)damp(RB)damp(B)

1stdampingratio[%]

structural age[year]

Figure 10. Secular Change of Damping Ratio (Peak response is about 5cm/s2)

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0 1 2 3 4 5 6 7 8 90

1

2

3

4

5

6damp(SRB)/damp(B)damp(RB)/damp(B)

ratiobetween

twodampings

structural age[year]

Figure 11. Secular Change of Ratio between Two Damping (Peak response is about 5cm/s2)

1 10 1000

1

2

3

4

5SRBRBB

1stdampingratio[%]

max. acc. at 8F [cm/s2]

Figure 12. Amplitude Dependence of Damping Ratio (Aging number is about 5 years)

1 10 1000.0

0.5

1.0

1.5

2.0

2.5SRB/BRB/B

ratiobetweentwodamping

s

max. acc. at 8F [cm/s2]

Figure 13. Amplitude Dependence of Ratio between Two Damping (Aging number is about 5 years)