Damping Ratio Estimation of an Existing -story Building Considering Soil-Structure Interaction Using Strong Motion Observation Data by Koichi Morita ABSTRACT In this study, damping ratio of an exiting -story SRC building using the strong observation data is identified. Strong motion observation is continually carried out since ust 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. 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 % and %, 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. [] This data is analyed from many points such as characteristics of buildings, and the influential factor to damping ratio is analyed. 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, Senior Researcher, Building Research Institute, Tsukuba-shi, Ibaraki-ken -, 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 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 -story SRC building using the strong observation data is identified. Strong motion observation is continually carried out since ust 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.. OUTLINE OF TARGET BUILDING AND INSTALLED SENSORS. 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 99. Outline of building characteristics are shown in Table.. Installed Sensors The sensors are installed with locations ( channels) in the building. The sensor configuration is shown in Fig. and. (Kashima ) In addition to these accelerometers, maximum response memory sensors of story displacements are installed. In this study, only accelerometers installed at ground(a), basement, st, nd, th and th story are used for system identification.. THREE TYPES OF DAMPING RATIO. Three Types of Damping Ratio Identified in This Study Using the data of strong motion seismometer shown in Figure, damping ratio is identified. In this study, three types of damping ratio considering the interaction effect are identified as following; ) the SRB type damping ratio h SRB including basement horiontal motion and the rotation motion. (input motion is ground motion.) ) the RB type damping ratio h RB including the rotation motion. (input motion is basement floor motion.) ) the B type damping ratio h B including only the building motion. (input motion is basement floor motion plus rocking motion.). 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. 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 ust after the completion of the building is frequent in the time of the observation.. 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 %. 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.. OUTLINE OF SYSTEM IDENTIFICATION In this monitoring system, accelerometer data of basement, st, nd, th and th 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 y( t) + a y( t ) +... + ana y( t na), () = b u( t nk) +... + b u( t nk nb + ) nb 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- is the number of eros,
while nk is the pure time-delay (the dead-time) in the system. From this model structure, the coefficients a and b are estimated. If A and B are expressed as, n a A( q) = + a q, () = n B q + = b b q nk ( ), () = p is the root of A()= and r is the residue of a partial fraction expansion of B()/A(). Natural frequency f and damping ratio are expressed as the following. h f = h (log p πδt log p = πf Δt ) + (arg p ), (), () When model numbers change as na=7 to (even numbers), nb=na+, and nk=, we select the numbers in which Akaike's Information Criteria (AIC) [] is estimated as small.. IDENTIFICATION RESULTS. Tendency of Damping Ratio in All Data strong motion records from June 99 to December 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 to. In all these figures, there are some dispersions in damping ratio. The SRB and RB type damping ratio decrease in about initial years. The tendency changed to the increase afterwards can be seen. The B type damping ratio in Figure has also large dispersion, but tends to increase as the aging year increases. In Figure, 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.. Secular Change of Damping Ratio In., since the result of various amplitude levels is included, the dispersion increases. Then, the result of extracting only the data over cm/s at the maximum response acceleration is shown in Figure, in order to reduce the effect by the amplitude level. The SRB and RB type damping ratio similarly decrease in initial years, and tendency is changed to the increase afterwards. Just after completion, the ratio between two damping takes the value of about to, as shown in Figure 7. The ratio between two damping tends to decrease to some aging, after some point the ratio approaches to. The result of extracting only the data of about cm/s (. ~.) at the largest response acceleration is shown in Figure, in order to reduce the effect of the amplitude level. The SRB and RB type damping ratios decrease in initial 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 to. The tendency in the decrease is traced with the aging, and the ratio tends to approach when it becomes to some extent aging number. Similar tendency can be observed in other response levels.. On Amplitude Dependence of Damping Ratio From. and., 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. to. years are extracted and tendency is shown in Figure. 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.
. 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: ) 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. ) SRB and RB type damping tend to decrease in initial about years, and are changed to the increase afterwards.. ) The B type damping ratio tends to increase by the aging. ) In initial time, the ratio in which SRB or RB type damping is divided by B type takes the value of about from. It tends to approach constant value with the aging. ) 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. ) 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. 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. 9, No.,, pp. 7-77,.. Akaike, H., 97. Information theory and an extension of the maximum likelihood principle, nd Inter. Symp. On Information Theory (Petrov, B.N. and Csaki, F. eds. ), Akademiai Kiado, Budapest 7-
Figure. Exterior of Target Building Table. Outline of Building Characteristics. Structure type steel encased reinforced concrete Number of story -story Height.9m Total building area m Foundation type mat foundation North m A Loam Sandy Cla Clayey S Sandy Cl Figure. Vertical Sensor Configuration D BFN D FN 9. m. m 9. m C B BFE 9. m. m 9. m C B ELV FE BFS FS A A 7. m 7. m. m BF 7. m 7. m. m F Figure. Sensor Configuration at Basement Floor and th Floor
Table. 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 horiontal) Transfer function etc. RB Microtremor observation & Strong motion observation(including up-down components) Transfer function etc. B Table. Type of Damping Ratio in Response Analysis. analytical method Type time history response analysis B response spectrum method B st damping ratio(srb)[%] 7 9 Figure. Secular Change of Damping Ratio (SRB) g[y ] st damping ratio(rb)[%] 7 9 Figure. Secular Change of Damping Ratio (RB) g y st damping ratio(b)[%] 7 9 Figure. Secular Change of Damping Ratio (B)
ratio between two dampings damp(srb)/damp(b) damp(rb)/damp(b) 7 9 Figure 7. Secular Change of Ratio between Two Damping damp(srb) damp(rb) damp(b) st damping ratio[%] 7 9 Figure. Secular Change of Damping Ratio (Peak response is more than cm/s) ratio between two dampings damp(srb)/damp(b) damp(rb)/damp(b) 7 9 Figure 9. Secular Change of Ratio between two damping (Peak response is more than cm/s) damp(srb) damp(rb) damp(b) st damping ratio[%] 7 9 Figure. Secular Change of Damping Ratio (Peak response is about cm/s)
ratio between two dampings damp(srb)/damp(b) damp(rb)/damp(b) 7 9 Figure. Secular Change of Ratio between Two Damping (Peak response is about cm/s) SRB RB B st damping ratio[%] max. acc. at F [cm/s ] Figure. Amplitude Dependence of Damping Ratio (Aging number is about years) ratio between two dampings..... SRB/B RB/B. max. acc. at F [cm/s ] Figure. Amplitude Dependence of Ratio between Two Damping (Aging number is about years)