Assessment of soil-structure interaction on a 51-story building from the spectral ratio of earthquake recordings

The soil-structure interaction (SSI) can significantly alter the characteristics of recorded motions in buildings. The ratio of Fourier amplitude spectrum of the top-story accelerations to that of the foundation accelerations permits the identification of the natural frequency of the fixed-base building. In this study, records of the Chi-Chi earthquake and the 1226 Hengchun earthquake doublet from the structural array in a 51-story highrise building are used to obtain the dynamic characteristics of the buildings by the transfer function (TF) method. As a result, the acceleration amplification of seismic excitation on the 47 storey of buildings is 4.24, in the horizontal component, from the Chi-Chi earthquake data greater than those of the 1226 Hengchun earthquake doublet with a value of 2.82 and 2.06, respectively. In addition, from the spectral ratio of the accelerations (47 floor/basement), together with the Fourier Amplitude Spectrum (FAS) of the 47 floor and basement accelerations, it is noted that the peaks of the 47 floor FAS and the spectral ratio appear to coincide with each other from the records of 1226 Hengchun earthquake doublet, suggesting that there is no significant SSI effects in both the longitudinal and transverse directions.


Introduction
Taiwan is located in the Circum-Pacific seismic belt. The Philippine Sea plate and the Eurasian plate collide with each other around Taiwan. Therefore, it is not surprising that large earthquakes have repeatedly hit the Taiwan [1]. Safeguarding life and property from destructive effects of earthquakes is a major concern of the people there. Since the most widespread damaging effects of earthquakes are caused by strong ground shaking, effective reduction of life and property losses from strong earthquakes requires conscientious application of earthquake resistant building codes and implementation of appropriate retrofit measures. Ideally, implementation of these mitigation measures should be based on instrumental recordings of strong earthquakes, for such data are crucial for improving earthquake resistant design of buildings [2]. The inclusion of SSI phenomena in the seismic analysis and design of structures has been addressed in seismic code provisions, including the FEMA450 document [3].
The effects of SSI on the seismic response of structures had been seriously taken into account since the 1971 SanFernando earthquake and the beginning of nuclear plant construction in the earthquake-prone California. In the 1980s and 1990s, many studies investigated the effects of SSI on special structures [4]. Two schemes of SSI are widely recognized for structures founded on or in soils: inertial and kinematic interaction. Inertial interaction results from inertia forces produced by seismic accelerations of the structure. Inertia forces increase the base shear and overturning moments acting on the foundation, resulting in relative displacements between the free field and foundation [3]. Kinematic interaction, on the other hand, occurs due to the inability of the relatively rigid foundation to conform to the ground motion, causing deviation of the foundation motion from the free-field motion. This is particularly accentuated by incoherent ground motion, wave inclination, and foundation embedment effects [5]. A detailed discussion on SSI effects and analysis techniques is presented by [6].
In general, SSI can decrease the base shear, lateral forces, and overturning moments experienced by a structure during earthquakes. However, it increases lateral displacements and secondary forces associated with P-delta effects [7]. Therefore, SSI effects should be considered during the design process [3]. Aviles and Perez-Rocha [8] investigated site effects and SSI during the Mexico earthquake of 1985. They found that interaction effects were larger for tall and slender structures than for short and squat structures of the same period, and these effects decreased as the foundation depth increased. Crouse and Ramirez [9] identified SSI effects and nonlinear site response as the main reasons for the differences observed in three sets of earthquake records for two buildings in the Jensen filtration plant during the Northridge main shock and aftershock motions.
Full-scale monitoring can provide valuable data for realistic evaluation of the dynamic behaviors of tall buildings under earthquake excitations. Analyses of records obtained in buildings during strong earthquakes and ambient vibrations from building have shown the natural frequencies and damping ratio may vary with increasing amplitude of shaking [10][11][12][13][14][15][16][17]. At present reliable field measurements of earthquake effects on tall buildings are still limited [3]. Fortunately, the Central Weather Bureau (CWB) of Taiwan has installed 60 digital strong-motion array systems in buildings and other structures for engineering and scientific purposes since 1992, as part of its Taiwan Strong Motion Instrumentation Program (TSMIP) [18]. It is remarkable that these digital strong-motion arrays have capabilities to record building responses not only due to strong motions but also weak ambient vibrations, owing to a flexible gain selection of the amplifier-filter unit at 1, 10, or 100 [2].
In this study, seismic data recorded in the structural array of a 51-story highrise building in Kaohsiung City are analyzed with several vibration parameters, including its transfer functions and natural frequencies. In addition, the spectral ratio of the accelerations (47 th floor / basement), together with the Fourier Amplitude Spectrum (FAS) of the 47 th floor and basement accelerations excited by the M7.6 Chi-Chi earthquake and the 1226 Hengchun earthquake doublet, are used to assess the SSI effects in both the longitudinal and transverse directions.

Seismic data
The KBA0 Building is located in Kaohsiung. The building has 51 stories with a total height of 222.1 m at the roof, as shown in Figure 1. A typical floor plan of the KBA0 Building has a rectangular shape, with a length of 42.5m in the NS (i.e. x-x or longitudinal) direction and a width of 34.5m in the EW (i.e. y-y or transverse) direction. A total of 26 accelerometers are placed at the basement, 1 st , 15 th , 30 th and 47 th floor. These floors are at height of -19.5m, 0.0m, 57.6m, 119.2m, and 191.7m relative to the ground surface, respectively ( Figure 1).
A major earthquake of M w magnitude 7.6 took place in central Taiwan at 17:47:16 UT of 20 September 1999. The epicenter was located near the town of Chi-Chi, after which the event was named. This was the largest inland earthquake to strike Taiwan in the twentieth century. The CWB located its epicenter at 120.82 oˤ E and 23.85 o N, with a focal depth of 8 km [1]. In addition, on 26 December 2006, two closely linked earthquakes, both ML 7.0, occurred only 8 minutes apart at 12:26:21 and 12:34:15 UT, respectively, in southwestern offshore of Taiwan near Pingtung. The epicenters of three earthquakes and location of the KBA0 building array station, as shown in Figure 2 and given in Table 1, were selected for this study. Records of the Chi-Chi earthquake and the 1226 Hengchun earthquake doublet from the structural array in the KBA0 Building are shown in Figures 3,  4, and 5, respectively. The accelerograms of channel number 1, 4, 7, 10, 13, 15, 17, 19, 21 and 24 are plotted for the accelerometers installed in the NS component and channel number 2, 5, 8, 11, 14, 16, 18, 20, 22 and 25 are those in the EW component as well as channel number 3, 6, 9, 12, 23 and 26 are those in the UD component. The largest peak acceleration of 101 cm/sec 2 was recorded in Channel 21, located at the 47 th floor of the KBA0 Building as shown in Figure 3. Table 1. The earthquake parameters used in this study.
Remark: The moment magnitude (M w ) adopted from the Harvard CMT.   Figure 2. Location of the KBA0 building array station and the three epicenters of earthquakes used in this study.

Parameters of vibration of the KBA0 building
The measured acceleration data are used to obtain the dynamic characteristics of the buildings. Different sets of modal parameters can be determined from the recorded time histories by several system identification methods, either in frequency domain or time domain. Most commonly used methods are based in frequency domain [19]. In order to identify the natural frequencies of the KBA0 Building, the transfer function (TF) method are used. Details of the TF method can be found in [20][21][22], respectively.

Identification of soil-structure interaction in the KBA0 building
The soil-structure interaction (SSI) can significantly alter the characteristics of recorded motions in buildings. The dominant frequency of a building subject to SSI will be smaller than that of a fixedbase building. The ratio of Fourier amplitude spectrum of the top-story accelerations to that of the foundation accelerations permits the identification of the natural frequency of the fixed-base building [13,23].

Naturaltural frequencies of vibration of the KBA0 building
In the present study, only the first five modes of the building response are considered since higher modes are of little significance in overall building responses [24]. In the following the recorded data in the KBA0 Building from three earthquakes are used to identify the natural frequencies of the 1 st , 2 nd , 3 rd , 4 th , and 5 th modes of vibration in the longitudinal and transverse directions.  The natural frequencies of the first five translational modes in each direction evaluated by using the TF method from the observed acceleration data are summarized in Table 2 Taking the KBA0 Building as a steel structure with eccentrically braced frame, the corresponding fundamental mode period according to the building code can be calculated as follows [25]: Where h n is the height of building from the ground. The calculated natural frequencies for the first five modes are 0.248, 0.745, 1.242, 1.738, and 2.235 Hz, respectively. It is found that these frequencies conducted from the code formula are closer to those identified from actual data.
In addition, the building array with 26-channel accelerograms recorded from the three earthquakes has been analyzed to study the acceleration amplification of seismic excitation on the 47 story of KBA0 building. The results as shown in Figure 7 show the amplification factor is 4.24, in the horizontal component, from the Chi-Chi earthquake data greater than those of the 1226 Hengchun earthquake doublet with a value of 2.82 and 2.06, respectively.

Identification of soil-structure interaction in the KBA0 building
It has been demonstrated that the fundamental frequency of the building may vary with the intensity of excitation force. The change in frequency may be attributed to one or more of the following causes: 1. Change in building effective stiffness, which could be due to the cracking of RC sections on the tension side and/or the disengagement of stiffness-contributing nonstructural elements; 2. Change of foundation stiffness due to softening in the soil at larger strains and the resulting effect of soilstructure interaction; and 3. Structural damage [14][15]17]. In order to understand the characteristics of response spectra between the three earthquakes and torsional predominant frequency, the Fourier amplitude spectrum of the basement, in Figure 8 are shown the chi-chi earthquake, Hengchun M7.0 earthquake, and Hengchun M6.9 earthquake, respectively. In addition, the Fourier amplitude spectra of the three earthquakes in the 47 th floor are plot in the Figure 9. The top, middle and bottom panels in Figure 9 are shown the longitudinal, lateral, and vertical direction, respectively. From the Figures 8 and 9, we can find the following results: (1) it shows that amplitude spectrum decrease with increasing frequency, especially for that of the chi-chi earthquake. It probably due to that the difference of vary for frequency content decay with distance. (2) The high story (47F) has high Fourier spectrum while the frequency is lower than 0.8 Hz among the three earthquakes, especially for the horizontal component and chi-chi earthquake. (3) The torsional predominant frequency is 0.960 Hz after comparing the recording from the different site in the transverse direction of same floor.  In order to determine if the frequency reduction in the earthquake was caused by soil-structure interaction, we calculated spectral ratio for the three earthquakes. The spectral ratio of the accelerations (47 th floor/ basement), together with the Fourier Amplitude Spectrum (FAS) of the 47 th floor and basement accelerations are shown in Figures 10 and 11 for the Hengchun M7.0 earthquake in the longitudinal and transverse directions, respectively. It is noted that the peaks of the 47 th floor FAS and the spectral ratio appear to coincide with each other from the records of 1226 Hengchun earthquake doublet, suggesting that there is no significant SSI effects in both the longitudinal and transverse directions.

Conclusion
The present study investigates the dynamic characteristics of a 51-story high-rise building by the transfer function (TF) method as well as assesses the SSI effects. Based on above results and discussion, we can draw the following conclusions: 1. Based on the observed transfer functions from the records of the Chi-Chi earthquake, the natural frequencies of the 1 st , 2 nd , 3 rd 4 th , and 5 th longitudinal modes of the KBA0 Building are found to be 0.238, 0.697, 1.284, 1.834 and 2.207 Hz, respectively. Likewise, the corresponding results for the transverse component are 0.220, 0.715, 1.290, 1.797, and 2.293 Hz, respectively. It is found that these frequencies conducted from the code formula are closer to those identified from actual data. 2. From the building array with 26-channel accelerograms recorded from the three earthquakes, the acceleration amplification of seismic excitation on the 47 storey of KBA0 building is 4.24, in the horizontal component, from the Chi-Chi earthquake data greater than those of the 1226 Hengchun earthquake doublet with a value of 2.82 and 2.06, respectively. 3. From the spectral ratio of the accelerations (47F/ basement), along with the FAS of the 47-story and basement accelerations for the 1226 Hengchun earthquake doublet Chi-Chi earthquake, it is noted that the peaks of the 47 th floor FAS and the spectral ratio seem to coincide with each other, suggesting that there is no significant SSI effects in both the longitudinal and transverse directions.