STRUCTURE OBSERVATION &IDENTIFICATIONCONSIDERING SOIL-STRUCTURE INTERACTION
OF STORY STIFFNESS AND DAMPING RATIO OF
8-STORY STEEL ENCASED REINFORCE CONCRETESTRUCTURE BY MICROTREMORSupervisor: Koichi MORITA ∗∗REN Jun ∗MEE08164

ABSTRACTThe author attempts to consider the effect of soil-structure interaction by identifying the dynamic
parameters of an existing building. Target building is an 8-story steel encased reinforced concretebuilding which was constructed in 1998. In the study, an eight degree of freedom analytical model isutilized to analyze the data from microtremor measurement. Then, nonparametric and parametrictechniques are employed to determine natural frequency, damping ratio and story stiffness of thestructure. For these two cases, one is without considering the effect of soil-structure interaction; theother is with considering the effect of soil-structure interaction. Comparing the results of these twocases, the effect of soil-structure interaction can be confirmed. Nonparametric methods include thewell known transfer function and Random Decrement method. The parametric method employedherein is the off-line system identification method ARX (Auto-Regression with eXtra input).
Keywords: Soil-Structure Interaction, Damping Ratio, Story Stiffness.

1. INTRODUCTION
System identification (SI) deals with the problem of building mathematical models of dynamic
systems based on observed system data (Ljung 1999). SI not only plays the role of calibrating
structural building models which could not otherwise be validated through experimentation but also
implicitly aids the design of high performance and high reliability structures. Existing experimental
modal analysis techniques usually require excitation and response data with a high signal-to-noise(s/n) ratio and all sources of excitation be measured and uncorrelated (Moore et al. 2007). The
combination of utilizing application specific SI methods and random ambient vibration excitation tocapture highly sensitive damping ratio formulates the basis for this study. The complexity of structureand soil-structure interaction is usually troublesome to obtain accurate results for their dynamical
behavior. Previous studies have shown that story stiffness of the structures are commonly obtained
based without considering the effect of rocking of structure. In this context, the estimation of dynamic
characteristics of 8-story steel encased reinforce concrete structure is conducted with excluded
soil-structure interaction. Fundamentally, the simple method to acquire dynamic properties of a target
structure is microtremor observation. Based on considering the effect of rocking motion obtained fromthis observation, the damping ratio and story stiffness are more accurately determined by getting rid ofsoil-structure interaction.

∗

Earthquake Administration of Shaanxi Province, China.
Department of Structural Engineering, Building Research Institute, Japan.

∗∗1In order to identify the physical characteristics of a structural system, microtremor
measurement has been widely used for decades. Microtremor measurement is very useful method to
obtain dynamic characteristics of structural systems including the predominant natural frequencies andstructural amplification factors. Based on theoretical concept, microtremor measurements with good
sensor accelerometers provide the response of structural systems in terms of low frequency seismic
signals. However, in the urban area where artificial noises or signals may be superimposed atmeasured microtremor generating unexpected amplification ratios. Moreover, microtremor
measurements’ amplification ratios usually provide only first or second natural frequency of structural
systems. The reason is that at higher frequencies, ambient noises and signals are generally combinedwith microtremor signals that cause the unidentifiable amplification ratios.

2. TARGET BUILDING
The target building is Urban Disaster Prevention Research Center (UDPRC) in National Institute forLand and Infrastructure Management (NILIM) that was completed in March 1998. The eight story
structure is of steel encased reinforced concrete type. The height and building area are 30.9 m and5050 m2, respectively. The foundation is of mat type.
In this study, a portable ambient vibration monitoring system was established. The placementof the twelve available seismometers for observation was planned and reviewed. Evaluation of thesoil-structure interaction required capturing the behavior between the building and external excitation.
Ten horizontally oriented accelerometers were placed on the floors and pavement area adjacent thebuilding, and two vertically oriented accelerometers were placed in the basement, as shown on thecolor-coded elevation and plan drawings of Figure 1. (Blue color-coded is horizontal sensor and redcolor-coded is vertical sensor). The
regular floor plan allowed forconsistentandconvenientseismometer placement in thebuilding. The advantage of having
multiple sensors is the ability toadequately capture natural modeshapes of the structure. The verticalorientation of the basement level
seismometers is chosen to capture any
rocking behavior, an insightfuldescriptor of the surrounding soil
Figure 1. Instrumentation Placement
stiffness. With sensors temporarily in-situ,(i) Elevation, (ii) Plan
15-minute ambient vibration observation
were performed at a sampling frequency of 100 Hz on EW and NS direction respectively. An
analytical model is now developed and analyzed to deduce the expected behavior of the dynamic
building/soil system.

3. DATA ANALYSIS AND RESULTS
3.1. Analytical Model and Estimate of Rocking Motion
To conceptually understand the relationship between input ground motion and structure, the eight
degree of freedom rocking building shown in Figure 2 was analyzed. The model includes theassumptions of rigid vertical and rocking motion. Where abase is horizontal oriented accelerometer
input in basement, and Mi, ki are concentrated story mass and story stiffness of the building
respectively.

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In general, the vibration of thebuilding consists of rocking, sway andrelative displacement. Rocking motion
represents
thedifferent
verticaldisplacement of the building. Sway motion
is a relative displacement between groundand the building. Relative displacement
represents the lateral deformation of eachstory with respect to the other. In the study,
the author considers the soil-structureinteraction which results in rocking motionof the building.
The author tries to exclude theeffect of rocking motion and identify thereal story stiffness of the building from therecord of microtremor observation; therefore,
this model was employed to analysis the data to
exclude the effect of rocking action of thebuilding. The model was shown on Figure 3.

Figure 2. The vibration types considered forthe building

Ri=a3+[(a2-a1)/length]*height(1)

where 1ch, 2ch, 3ch are three channel records of
two vertical oriented accelerometers signal andone horizontal oriental accelerometers signal inbasement in Figure 3(i). In the Fig 11(ii), a1, a2
are records of accelerometers 1 and 2 (verticaloriented); a3 and ai are records of accelerometers
on basement and i-th story (horizontal oriented);
Ri is rocking effect on the i-th story. Eq.(1)captures the rocking motion for each story.

(i)
(ii)
Figure 3. Model of rocking action(i) Rocking action of building;(ii) Calculated model for rocking effect3.2. Transfer function and Random Decrement method
Table 1. TF Modal Estimates on EW & NS
direction
EW direction
NS directionMode
fn [Hz] ζ [%] fn [Hz] ζ [%]1.76
3.2115 1.4289 1.7179
1st model
5.02
2.2925 4.1911 2.1389
2nd model

From the Transfer functions, the first andsecond natural frequencies of UDPRC are easy
to find out. These frequencies as target
frequencies are then used for determining thedamping ratio. By Random Decrement
Technique, these damping ratio for UDPRC
are determined approximately in the Table 1.

3.3 Parameters Identification by using ARX Method
In this monitoring system, accelerometer data of 1-8F story are used as outputs and accelerometer ofbasement as input, so system identification will be based on eight concentrated lumped mass model.
Parameter identification based on the ARX (Auto Regressive eXtra input) model is applied for
input-output data of vibration measurements. The ARX model structure is the simple linear difference
equation:y (t ) + a1 y (t − 1) + K + ana y (t − na ) = b1u (t − nk ) + K + bnb u (t − nk − nb + 1)
(2)
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 poles3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,naA(q ) = 1 + ∑ a j q − jj =1
nb

B(q) = 1 + ∑ b j q(3)− j +1− nk

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, damping ratio h j and participation function βu j are expressed as the following.

fj =(log z p j ) 2 + (arg z p j )2

hj =

2πΔt
− log z p j
2π f j Δt⎡⎤
2 z rj 1 − h 2j⎢⎥
βuj = ℜ⎢ T (2π f j h j − isign[ℑ[ z p j ]]2π f j (1 − 2h 2j )) ⎥
⎣
⎦

(4)
(5)

(6)

The measured stiffness matrix [K] is estimated from the mass-normalized measured mode shapes [Φ]( [Φ]T[M][ Φ]=[I][Λ ]; [Φ] is determined from the participation function βuj ) and frequencies [Λ] as[ K ] ≅ ([Φ ][Λ ]−1 [Φ ]T ) −1

(7)

In this system identification, stiffness matrix will be obtained by Eq. (7) if eight modal
properties are identified because of the assumption of eight lumped mass model. In the target building,
it is difficult to identify above second modal property. Therefore, the stiffness matrix is obtained using
Moore and Penrose inverse matrix (Penrose 1955) which is one of the generalized inverse matrix.
Story stiffness will be estimated by multiplying [K] by a displacement vector, in which each relative
story displacement is 1 from the right.
In the study, the properties of UDPRC were determined by using ARX method and theresults including/excluding rocking motion were shown on Table 2, 3, 4 and 5 on EW and NS
direction .
Table 2. The identified result including rocking motion on EW direction
1F
2F
3F
4F
5F
6F
Floor
7F
8F
1st natural frequency [Hz]1.7411
1st Damping ratio[ %]3.73640.0215 0.1235 0.2235 0.4668 0.5896 0.8073 0.9632 0.9221
1st modal shape
Story stiffness [ 108N/m] 4.3766 4.331 4.0737 3.6282 2.781 1.8716 0.9176 0.2195
Table 3 The identified result excluding rocking motion on EW direction
Floor
1F
2F
3F
4F
5F
6F
7F
8F
1st natural frequency [Hz]1.7145
1st Damping ratio[ %]3.68590.0491 0.0738 0.1835 0.3275 0.3462 0.4443 0.4468 0.3424
1st modal shape
Story stiffness [ 108N/m] 5.2882 5.0564 4.7174 3.9256 2.6931 1.642 0.6722 0.1266

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Table 4. The identified result including rocking motion on NS direction
Floor
1F
2F
3F
4F
5F
6F
7F
8F
1st natural frequency [Hz]1.4357
1st Damping ratio[ %]2.8216
0.0764 0.1557 0.145 0.214 0.3161 0.4093 0.4527 0.4942
1st modal shape
Story stiffness [ 108N/m] 3.3101 3.0905 2.6661 2.2991 1.807 1.1885 0.5793 0.1578
Table 5. The identified result excluding rocking motion on NS direction
Floor
1F
2F
3F
4F
5F
6F
7F
8F
1st natural frequency [Hz]1.4042
1st Damping ratio[ %]3.27470.0486 0.0422 0.1792 0.2039 0.2927 0.3682 0.3556 0.2877
1st modal shape
Story stiffness [ 108N/m] 3.4509 3.2648 3.1073 2.4824 1.8565 1.1167 0.4517 0.0904
3.4. Comparing Two Results of Each Story Stiffness between two cases
In this section, it is desirable to compare thestory stiffness with including rocking
motion and excluding rocking motion onthese two directions. The combination ofmodal shape is used. For 1st modes, themodalshapesareobtainedfrommicrotremor observation by ARX method(Figure 4).
Figure 5 shows the two results ofthe story stiffness with including andexcluding rocking motion by ARX method
on EW and NS direction. An interesting
phenomenon was observed that the story
stiffness below the fifth floor, identified by
excluding the rocking motion, increased all,but these above it decreased all. Meanwhile,

NS-Modal shape

9

9

8

8

7

7

6

6

5

5

Story

Story

EW-Modal shape

4

4

3

3

2

2

With rocking

1With rocking

1

Without rocking

Without rocking

0

0

0

0.5

1

1.5

0

0.2

0.4

0.6

(i)
(ii)
Figure 4. 1st Modal shape of UDPRC(i) 1st Modal shape of EW direction (ii) 1st
Modal shape of NS direction
Story stiffness-NS

Story stiffness-EW
9

Story stiffness-NS
9With rocking motion

With rocking motion

Without rocking motion

8

With rocking motion

Without rocking motion

8

Without rocking motion

7

6

6

6

6

5

5

5

5

3
2
1
0
0

1

2

3

4

Story stiffness[108N/m]

5

6

4

Story

7

Story

7

4

4

4

3

3

3

2

2

2

1

1

1

0

0

0

1

2

3

4

0.1

1
Story stiffness[108N/m]

Story stiffness[108N/m]

(i)
(ii)
Figure 5. The comparing of identified story
stiffness on two directions(i) Story stiffness on EW direction; (ii) Story
stiffness on NS direction;

Without rocking motion

8

7

Story

Story

9

With rocking motion

8

Story stiffness-EW
9

10

0
0.01

0.1

1

Story stiffness[108N/m]

(i)
(ii)
Figure 6. The effect of rocking motion to story
stiffness on two directions(i) Story stiffness on EW direction; (ii) Story
stiffness on NS direction;

5

10

same tendency existed in EW and NS direction. In these figures, blue lines are including the rocking
motion and pink lines are excluding the rocking motion.
For the further observing, these results of the story stiffness, identified in different cases,
presented in logarithmic scale at X-axis (Figure 6). The bigger decreasing of the story stiffness withremoving the rocking motion were found out on top floor, almost two times reduction on both
direction.

4. CONCLUSIONSIn this study, damping ratio and story stiffness were estimated, and the effect of rocking motion was
evaluated for UDPRC. In an effort to evaluate the soil characteristics of the surrounding soil,
nonparametric and parametric techniques were employed to capture natural frequency and damping
ratio for the first and second translational modes. Furthermore, the effect to story stiffness was focusedon rocking motion of the building. Lastly, the rocking behavior of the UDPRC was identified. Basedon previously identified results, the magnitudes of rocking motion were shown, utilizing basement tofloor by using ARX method.
Results from this study can be summarized as follows:
1. The first and second natural frequencies are found to be about 1.76 Hz and 4.89 Hz on EW
direction and 1.43 Hz and 4.19 Hz on NS direction, respectively. However, the third andforth natural frequencies are not able to be identified from microtremor observation.
2. From analyses results in earlier section, there is a strong belief that the effect ofsoil-structure interaction of UDPRC is obvious. If we have to reduce life cycle costs of abuilding from construction to maintenance, it is very necessary to obtain more precise
structural properties of a building. Therefore, utilizing system identification withconsidering rocking motion from the basement to floors will produce more accurate modalparameter and stiffness estimates. The conclusions of this research would be strengthened
with supplemental identification utilizing additional time and frequency domain methods. In
this manner, the effect of soil-structure interaction to SI results from ambient vibration
records will be better understood as well as the extent of strengths and weaknesses of
equivalent stories stiffness.

AKNOWLEDGEMENT
I would like to express my sincere gratitude to my adviser Dr. Saito, T. for his continuous support,
valuable suggestion and guidance during my study.
REFERENCES
Akira Mita, Structural Dynamics for Health Monitoring, Keio University (Japan), Sankeisha co., Ltd.
Douglas E. Adams, Purdue University (USA), John Wiley & Sons, Ltd.
Koyama, S., 2007, IISEE lecture note, Building Research Institute, Tsukuba, Japan.
Ljung, L. 1999, PTR Prentice Hall, Upper Saddle River, N.J..
Moore SM, et al 2007, Mechanical Systems and Signal Processing.
Morita, K., 2007, IISEE lecture note, Building Research Institute, Tsukuba, Japan.
Morita, K., 2006, SPIE 11th Annual International Symposium on NDE for Health Monitoring and
Diagnostics, San Diego, USA.
Penrose, R., 1955, A Generalized Inverse for Matrices Proc. Cambridge Phil. Soc. 51, 406-413.
Schmitt, S., Jr., 2007, the East Asia and Pacific Summer Institutes Program Report.

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