DEVELOPMENT OF THE RESIDUAL SEISMIC CAPACITY EVALUATION SYSTEM WITH CAPACITY SPECTRUM METHOD

Transcription

1 1NCEE Tenth US National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 21 Anchorage, Alaska DEVELOPMENT OF THE RESIDUAL SEISMIC CAPACITY EVALUATION SYSTEM WITH CAPACITY SPECTRUM METHOD Koichi Kusunoki 1, Akira Tasai 2, Masaomi Teshigawara and Daiki Hinata ABSTRACT Once a big earthquake occurs, many buildings are severely damaged, and consequently it gives rise to many homeless The damage level could increase due to an aftershock in some buildings Thus enormous harm to the inhabitants in such buildings could occur On the contrary, some people could get caught up in fear and would escape from even the buildings that have enough residual seismic capacity from the engineering point of view Hence, the number of homeless can increase drastically In order to reduce further damage due to an aftershock and to reduce the number of homeless, a quick inspection on the damaged buildings must be carried out Authors have been developing the real-time residual seismic capacity evaluation system, which needs only few relatively inexpensive accelerometers The system calculates the capacity and demand curves from a measured acceleration of the basement and of each point of a structure, and further estimate the residual seismic capacity of a structure by comparing these curves Response displacements are derived from measured accelerations by double integral with the wavelet transform method The validity of the proposed method to derive the capacity curve from measured accelerations is confirmed with the actual response of an existing building during the 211 Tohoku Earthquake, shaking table test with full-scale -story R/C structure and 1/ scale 1-story R/C structure 1 Associate Professor, Dept of Architecture, Yokohama National University, Yokohama, Japan, Professor, Dept of Architecture, Yokohama National University, Yokohama, Japan, Professor, Dept of Architecture, Nagoya University, Nagoya, Japan, Graduate Student, Dept of Architecture, Graduate School of Yokohama National University, Yokohama, Japan, Koichi KUSUNOKI, Akira Tasai, Masaomi Teshigawara, and Daiki Hinata Development of residual seismic capacity evaluation system with capacity spectrum method Proceedings of the 1 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 21

2 1NCEE Tenth US National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 21 Anchorage, Alaska Development of the Residual Seismic Capacity Evaluation System with Capacity Spectrum Method Koichi Kusunoki 1, Akira Tasai 2, Masaomi Teshigawara, and Daiki Hinata ABSTRACT In order to reduce the enormous harm to the inhabitants during an aftershocks in the damaged buildings due to a main shock, and to reduce the number of refugees from the buildings that have enough residual seismic capacity, quick inspection needs to be conducted soon after a main shock In this paper, a new quick inspection system with inexpensive accelerometers is proposed, which is based on the capacity spectrum method To draw the capacity curve from the measurements, displacement must be derived from the measured acceleration by double integral The wavelet transform method is applied for reducing the effect of the error contained in the measured acceleration and to take the first mode The validity is confirmed with the real response of the instrumented building during the 211 Tohoku Earthquake and two shaking table tests Introduction Once a big earthquake occurs, many buildings are severely damaged, and consequently it gives rise to many homeless The damage level could increase due to an aftershock in some buildings Thus enormous harm to the inhabitants in such buildings could occur On the contrary, some people could get caught up in fear and would escape from even the buildings that have enough residual seismic capacity from the engineering point of view Hence, the number of homeless can increase drastically In order to reduce further damage due to an aftershock and to reduce the number of homeless, a quick inspection on the damaged buildings must be carried out soon after a main shock However, under the present situation, the buildings have to be investigated one by one by engineers or researchers [1] For example, 5,68 engineers and 19 days were needed to investigate 6, buildings on a damaged area at the Kobe earthquake [2] Nineteen days were too long and yet the number of investigated buildings was not enough Moreover, many buildings were judged as Caution level, which needs detailed investigation by engineers Caution judgement is a gray zone and it could not take away anxieties from inhabitants Furthermore, the current quick investigation system presents a dilemma since buildings should 1 Associate Professor, Dept of Architecture, Yokohama National University, Yokohama, Japan, Professor, Dept of Architecture, Yokohama National University, Yokohama, Japan, Professor, Dept of Architecture, Nagoya University, Nagoya, Japan, Graduate Student, Dept of Architecture, Graduate School of Yokohama National University, Yokohama, Japan, Koichi KUSUNOKI, Akira Tasai, Masaomi Teshigawara, and Daiki Hinata Development of residual seismic capacity evaluation system with capacity spectrum method Proceedings of the 1 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 21

3 be investigated by visual observation of engineers Thus, this judgement varies according to the engineers experiences After 211 Tohoku Earthquake, it was also found that visual investigation takes too long time for high-rise buildings Furthermore, most of them were designed so that building forms weak beam strong column mechanism, which makes visual investigation difficult, since beams are usually covered by finishing such as ceiling system In order to solve the problems mentioned above, authors have been developing the real-time residual seismic capacity evaluation system, which needs only few relatively inexpensive accelerometers The system calculates the capacity and demand curves from a measured acceleration of the basement and of each point of a structure with inexpensive accelerometers, and further estimate the residual seismic capacity of a structure by comparing these curves To draw the capacity curve, the absolute response acceleration and relative response displacement at each point are needed Response displacements are derived from measured accelerations by double integral It is well-known that the error components contained in the measured acceleration grows much by double integral Therefore, the Wavelet Transform Method (WTM), which is a powerful time-frequency analysis method, is applied The WTM is a method that decomposes a signal in temporal domain with holding the best relationship between the time increment and frequency increment for the decomposition The error component that has relatively long period can be decomposed and eliminated by using the WTM Capacity Curve Decomposition with the Wavelet Transform Method Outline of the Wavelet Transform Method The WTM is a time-frequency analysis method to show the similarity between a signal and a mother wavelet [][] The signal of N data points,, is decomposed into a signal that has only certain frequency band,, and remaining,, by Eq 1 = + (1) The decomposed signals and have N/2 data points By repeating the decomposition procedure, the original signal is decomposed as Eq 2 = (2) The number of decomposition, n, is calculated as Eq = () The eventual remaining f n is a single value The decomposed components g i are orthogonal to each other The WTM is a time-frequency analysis method using a mother wavelet as window The width of the window in temporal domain 2Δ and frequency domain 2Δ has the uncertainty relation as stated by Eq

4 2 2 2 () The time increment for, Δ,, is calculated as Eq 5 with the time increment Δ of an original signal, Δ, =Δ 2 (5) Thus, the Nyquist frequency of, Δ,, is calculated by Eq 6 from Eq Δ, = (6) The WTM is one of the most efficient time-frequency analysis methods, since it theoretically satisfies the minimum uncertainty relation Mode Decomposition by Using the WTM The measured input acceleration at the basement, x and measured absolute response acceleration at each floor,, can be decomposed to each rank,, as Eq 7 and 8 x =, +, +, + +, +, (7) X =, +, +, + +, +, (8) The 1 st mode component of the measured acceleration can be derived by taking the decomposed components,, of which Nyquist frequencies are close to the predominant frequency of the building Fig1 shows an example of the transfer function and Nyquist frequency for each rank (Δ = 5 ) 1 Rank 7 Rank 8 Rank 6 298Hz Rank 5 12 Transfar Function Frequency (Hz) Figure 1 Transfer function and Nyquist frequencies

5 According to Fig 1 and capacity curve of each rank, 1 st mode components can be calculated from rank 6 to rank 9, then the ground acceleration for the 1 st mode, x, and the absolute response acceleration at i-th floor, X, can be calculated as Eq 9 and 1 x =, +, +, +, (9) X = +, +, +,, (1) The relative acceleration at i-th floor to the basement is calculated as Eq 11 from Eq 9 and 1 x = X x (11) The relative displacement at i-th floor to the basement,, is derived from the relative acceleration by double integral as Eq 12 [5][6] = x (12) Capacity Curve for the First Mode The measured response of a multi-degree-of-freedom system is simplified down to singledegree-of-freedom system to draw the capacity curve The capacity curve is the relationship between the representative restoring force (or representative acceleration in the unit of m/s 2 ), Δ + x, and representative displacement (in the unit of m), Δ Where Δ is the representative relative acceleration Δ + x and Δ are calculated as Eq 1 and 1, respectively [5][6][7][8] + = (1) = Where: : Mass for i-th story, N: Number of stories, and : Inertia force at i-th floor According to the modal analysis, is calculated as Eq 15 with the participation vector for the 1 st mode, β u P = + (1) (15) Therefore, the representative force, Δ + x, is derived as Eq 16 from Eq 1 and 15 + = + = + (16)

6 Monitoring an Existing Instrumented Building during 211 Tohoku Earthquake The proposed health monitoring system is installed into the building for the department of architecture of Yokohama National University in the beginning of the year of 28 The building has 8 stories and 1 underground floor The total height of the building is 8m and its structural type is steel reinforced concrete structure The building was designed before 1981, when the Japanese building code was revised to confirm the ultimate strength of buildings It was found that the building did not have enough ultimate strength, and then the building was retrofitted The retrofitting construction had been conducted from July 28 to May 29, and the sensors were removed at that time The key plan and elevation in the EW direction are shown in Fig 2 EW direction is the longitudinal direction and NS direction is transverse direction ºº ºº ºº ºº ºº ºº ºº (a) Key plan (b) Elevation in the EW direction (w/ Observed crack) Figure 2 Key plan and elevation of the instrumented building The health monitoring system worked well during the 211 Tohoku Earthquake The maximum measured acceleration was 915 m/s 2 on the basement and 1 m/s 2 on the roof The predominant component of the acceleration lasted about 18 sec The measured capacity curve in the EW direction are shown in Fig Since the natural period in the EW direction before the earthquake was about 1sec, the equivalent period of 8 is longer than the period before the earthquake Fig shows the slopes for the periods of 1sec and 8sec, too It is clearly found that the stiffness degrading started at the representative acceleration of about 1m/s 2 The stiffness degraded down to 7% according to the change of the period from 1sec to 8sec Fig 2 (b) shows observed cracks after the 211 Tohoku Earthquake Several minor cracks are observed at the bottom of the continuous walls, which probably cause the stiffness deterioration

7 Representative Force (m/s 2 ) T=1sec T=8sec Represenative Disp (m) Figure Measured capacity curve of the instrumented building during the 211 Tohoku Earthquake From Fig, it can be said that the frequency change can be observed more accurately from the capacity curve than from the transfer function, since the slope of the capacity curve is square of the predominant angular frequency, ω The transfer function sometimes does not show any predominant frequency if a large nonlinearity occurs during an earthquake Moreover, while the capacity curve shows that the building has not yielded yet, it is unclear whether the damage is serious only from the frequency change One-Span-One-Bay 1-story Specimen [9] Shaking Table Test Results The specimen had 1-soty and four columns as shown in Fig The dimension of the column was 1 1mm with main bars of -D16 and hoop of D6@5 The weight of the specimen was 251 ton The EW component of the earthquake recorded at the Hachinohe station during the 1968 Tokachi Oki Earthquake was applied for the input motion The input motion was scaled so that PGA was 5 m/s 2 The duration of the input motion was 85 sec At 85 seconds, the specimen fell down to safety frame Time increment of data acquisition system was 5sec Rank 1 (5Hz) to rank 8 (9625Hz) were applied for the analysis Fig 5 shows the capacity curve derived from only accelerometers (solid line) and from accelerometers and transducers to measure relative response displacement to the basement Since the structure has only one story, the accuracy of the double integral with the WTM can be discussed with Fig 5 It can be seen that the capacity curves coincide with each other up to the point where the tangent stiffness degraded drastically However, the maximum displacement in

8 the positive direction measured by transducer is much larger than the displacement calculated by double integral This is because the structure collapsed and landed on the safety frame at 85 seconds Therefore the time history terminated at 85 seconds and the permanent residual displacement became large The permanent residual displacement was classified as extremely long period component and eliminated by the WTM, and the response tend to come back to the origin at the end 8 8 R/C Weight Figure Plan and elevation of the structure (one-story structure) [9] 6 W/ Accceleromete Only W/ Transducers Representative Force (m/s 2 ) Represenative Disp (m) Figure 5 Capacity curves of the one-story structure (solid line: calculated with accelerometers only (without transducers), dotted line: calculated with both accelerometers and transducers) Real Scale -Story Specimen The specimen had -soty and four columns at each story as shown in Fig 6 The dimensions and bar arrangements of the column and beams are listed in Table 1 The weight of the specimen was

9 728kN (1F), 77kN (2F), and 95kN (F), respectively Predominant periods were sec for the 1 st mode, 1sec for the 2 nd mode and 5sec for the rd mode [9]The EW component of the earthquake recorded at the Hachinohe station during the 1968 Tokachi Oki Earthquake was applied for the input motion The input motion was scaled so that PGA was 6 m/s 2 Yield hinges were formed at all ends of beams and bottom of the columns in the first story Time increment of data acquisition system was 5sec Rank 6 (15625Hz) to rank 9 (1951Hz) were taken as the 1 st mode component Input Direction Shaking table Figure 6 Dimensions of the structure (three-story structure) [1] Table 1 Details of members (real-scale -story specimen) Member Dimension (mm) Main bar Hoop Column D22 D1@2mm Beam (Roof) 25 5 Top 2-D22 Bottom 2-D16 D1@2mm Beam (1 st and 2 nd Top 2-D22+1-D19 5 floor) Bottom 2-D22 D1@2 Fig 7 shows the capacity curve derived from only accelerometers (solid line) and from accelerometers and transducers to measure relative response displacement to the basement Since the structure has three stories, the first mode was taken with the WTM The slope of the first mode period of sec is also superimposed on the figure The initial stiffness of the capacity curve agreed very well with the first mode period, which indicates that the WTM choosed the first mode successfully It can be also seen that the capacity curves coincide with each other, since the permanent residual displacement was relatively small

10 6 W/ Accceleromete Only W/ Transducers sec Representative Force (m/s 2 ) Represenative Disp (m) Figure 7 Capacity curves of the three-story structure (solid line: calculated with accelerometers only (without transducers), dotted line: calculated with both accelerometers and transducers) Conclusions A capacity curve decomposition method using the Wavelet transform method was proposed to clear off the higher mode effects from a capacity curve and to eliminate the effect of error contained in the measured accelerations The validity of the method was confirmed with the monitoring data of the existing building in Yokohama National University during the 211 Tohoku Earthquake, and shaking table test results Results from the studies are summarized as follows; A capacity curve decomposition method using the Wavelet transform method was proposed The actual damage of the existing building during the 211 Tohoku Earthquake was successfully evaluated From the shaking table tests with one-span-one-bay -story full-scale structure and onespan-one-bay single-story structure, it can be said that the proposed method is valid not only for elastic response range, but also for non-linear response range The first mode response can be taken from the measured response of a multi-degree-offreedom system with the Wavelet transform method Residual displacement can be eliminated by the Wavelet transform method, since the permanent residual displacement is considered an extremely long period component and eliminated with error component during the Wavelet transform Even if the permanent residual displacement is large, the capacity curve can be derived accurately up to the stiffness degrading point

11 Acknowledgments Authors acknowledge Prof Keiji Kitajima and Prof Kenji Kabayama for providing the shaking table test data, and Graduate Students Yuuki Hattori for their great contributions to analyze records The installation and maintenance of the measurement system has been supported by Mr Masayuki Araki, Mr Takamori Ito and other staffs of A Labo Co Ltd The research was partially supported by the Grant-in-Aid for Scientific Research (C) References 1 Japan Building Research Promotion Association (BRPA)Guidelines for Performance Evaluation of Reinforced Cconcrete Buildings, Gihodo (in Japanese), 27 2 Building Center of Japan (BCJ) Report on The Reconnaissance Committee on The Building Damages due to the Hanshin-Awaji Great Earthquake Disaster, Summerization - (in Japanese), 1996 Susumu SAKAKIBARA SUURI KAGAKU Wavelet Beginners Guide, Tokyo Denki University Publishing (in Japanese), 1995 Paul S Addison The Illustrated Wavelet Transform Handbook, Institute of Physics publishing, 22 5 Koichi KUSUNOKI, Ahmed Elgamal, Masaomi TESHIGAWARA and Joel P Conte Evaluation of Structural Condition using Wavelet Transforms, 1 th world conference on earthquake engineering, CD-Rom, 28 6 Koichi KUSUNOKI, Akira TASAI, and Masaomi TESHIGAWARA Development of Building Monitoring System to Evaluate Residual Seismic Capacity after an Earthquake, 15 th world conference on earthquake engineering, CD-Rom, Koichi KUSUNOKI and Masaomi Teshigawara A New Acceleration Integration Method to Develop A Real- Time Residual Seismic Capacity Evaluation System, Journal of Structural And Construction Engineering, No569, (in Japanese), 2 8 Koichi KUSUNOKI and Masaomi TESHIGAWARA Development of Real-Time Residual Seismic Capacity Evaluation System Integral Method and Shaking Table Test With Plain Steel Frame-, 1 th world conference on earthquake engineering, CD-Rom, 2 9 I Kogoma, T Hayashida, and C Minowa Experimental Studies on the Collapse of RC Columns during Strong Earthquake Motion, 1 th world conference on earthquake engineering, pp 1-17, Keiji Kitajima, Koichi Kusunoki, et Al Shaking Table Test of Full-Scale Reinforced Concrete Three-Story Frame Structure Part 1 to Part, Summaries of technical papers of annual meeting, Architectural Institute of Japan, pp 77-71, 1995