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 dynamic
interaction 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. Damping
ratio 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 damping
ratio 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 is
carried 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
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 to
remove 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 will
be 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.
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 type
damping 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 being
SRB 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
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
y (t ) + a1 y (t − 1) + ... + a na y (t − na )
= b1u (t − nk ) + ... + bnb u (t − nk − nb + 1)
, (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,
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,
na
A(q ) = 1 + ∑ a j q − j ,
(2)
j =1
nb
B(q ) = ∑ b j q − j +1−nk ,
(3)
j =1
z
p j is the root of A(z)=0 and
z
r j is the
residue of a partial fraction expansion of
B(z)/A(z).
Natural frequency f j and damping ratio
h j are expressed as the following.
fj =
(log z p j ) 2 + (arg z p j ) 2
hj =
2πΔt
− log z p j
2πf j Δt
,
,
(4)
(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.
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 of
about 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 the
completion 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. 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
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.
6. CONCLUSIONS
Using the strong motion record data of an
existing building, damping ratios are
identified. . 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 the
increase 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. As
the 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
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
North
20 m
A01
Figure 2.
Loam
Sandy Cla
Clayey S
Sandy Cl
Vertical Sensor Configuration
D
D
BFN
9.0 m
9.0 m
8FN
C
C
8.0 m
8.0 m
ELV
BFE
B
8FE
9.0 m
9.0 m
B
BFS
8FS
A
A
B1F
7.5 m
1
Figure 3.
7.5 m
2
7.5 m
6.0 m
3
4
8F
1
7.5 m
2
6.0 m
3
4
Sensor Configuration at Basement Floor and 8th Floor
Table 2.
Type of Damping Ratio by Experimental Method.
Experimental method
Free vibration test
Forced vibration test
Microtremor observation, Wind observation
Microtremor observation & Strong motion observation(only horizontal)
Microtremor observation & Strong motion observation(including up-down
components）
Table 3.
Estimation method
logarithmic decrement etc.
Resonance curve
Random decrement
Transfer function etc.
Transfer function etc.
Type of Damping Ratio in Response Analysis.
analytical method
Type
time history response analysis
B
response spectrum method
B
1st damping ratio(SRB)[%]
8
6
4
2
0
0
1
2
3
4
5
Figure 4.
7
8
9
Secular Change of Damping Ratio (SRB)
g [y
8
1st damping ratio(RB)[%]
6
structural age[year]
8
]
6
4
2
0
0
1
2
3
4
5
Figure 5.
7
8
9
Secular Change of Damping Ratio (RB)
g y
8
1st damping ratio(B)[%]
6
structural age[year]
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
structural age[year]
Figure 6.
Secular Change of Damping Ratio (B)
Type
SRB
SRB
SRB
RB
B
ratio between two dampings
6
damp(SRB)/damp(B)
damp(RB)/damp(B)
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
structural age[year]
Figure 7.
Secular Change of Ratio between Two Damping
5
damp(SRB)
damp(RB)
damp(B)
1st damping ratio[%]
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
structural age[year]
Figure 8.
Secular Change of Damping Ratio (Peak response is more than 30cm/s2)
ratio between two dampings
4
damp(SRB)/damp(B)
damp(RB)/damp(B)
3
2
1
0
0
1
2
3
4
5
6
7
8
9
structural age[year]
Figure 9.
Secular Change of Ratio between two damping (Peak response is more than 30cm/s2)
6
damp(SRB)
damp(RB)
damp(B)
1st damping ratio[%]
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
structural age[year]
Figure 10. Secular Change of Damping Ratio (Peak response is about 5cm/s2)
ratio between two dampings
6
damp(SRB)/damp(B)
damp(RB)/damp(B)
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
structural age[year]
Figure 11. Secular Change of Ratio between Two Damping (Peak response is about 5cm/s2)
5
SRB
RB
B
1st damping ratio[%]
4
3
2
1
0
1
10
100
max. acc. at 8F [cm/s2]
Figure 12. Amplitude Dependence of Damping Ratio (Aging number is about 5 years)
ratio between two dampings
2.5
SRB/B
RB/B
2.0
1.5
1.0
0.5
0.0
1
10
100
max. acc. at 8F [cm/s2]
Figure 13. Amplitude Dependence of Ratio between Two Damping (Aging number is about 5 years)