Recent Advances to Obtain Real - time Displacements for Engineering Applications

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1 Recent Advances to Obtain Real - time Displacements for Engineering Applications Mehmet Çelebi USGS (MS977), 345 Middlefield Rd., Menlo Park, Ca. 945 Abstract This paper presents recent developments and approaches (using GPS technology and real-time double-integration) to obtain displacements and, in turn, drift ratios, in real-time or near real-time to meet the needs of the engineering and user community in seismic monitoring and assessing the functionality and damage condition of structures. Drift ratios computed in near real-time allow technical assessment of the damage condition of a building. Relevant parameters, such as the type of connections and story structural characteristics (including geometry) are used in computing drifts corresponding to several pre-selected threshold stages of damage. Thus, drift ratios determined from real-time monitoring can be compared to pre-computed threshold drift ratios. The approaches described herein can be used for performance evaluation of structures and can be considered as building health-monitoring applications. Introduction Seismic monitoring of structural systems constitutes an integral part of hazard reduction strategies in seismically active regions of the world. In addition to the United States, extensive programs for seismic monitoring of structures have been established in Japan, Taiwan, Mexico and Chile. Other active programs exist in Italy, Turkey and Greece. Nuclear facilities usually have rather unique aims and strategies in seismic instrumentation. However, at least the second approach that is described in this study can be easily adopted for nuclear facilities as well. In general, and until recently, accelerometers have been used to capture the time-variant level of shaking at strategically selected orientations and locations within a structure. Recordings of the acceleration response of structures have served the scientific and engineering community well and have been useful in assessing design/analysis procedures, improving code provisions, and in correlating the system response with damage. Unfortunately, there are only a few records from damaged instrumented structures to facilitate studies of the initiation and progression of damage during strong shaking (e.g. Imperial County Services Building during the 979 Imperial Valley earthquake, [Rojahn and Mork, 98]). In the future, instrumentation programs should consider this deficiency. Jennings (997) summarizes this view as follows: As more records become available and understood, it seems inevitable that the process of earthquake resistant design will be increasingly, and quite appropriately, based more and more upon records and measured properties of materials, and less and less upon empiricism and qualitative assessments of earthquake performance. This process is well along now in the design of special structures.

2 An instrumented structure should provide enough information to (a) reconstruct the response of the structure in sufficient detail to compare with the response predicted by mathematical models and those observed in laboratories, the goal being to improve the models, (b) make it possible to explain the reasons for any damage to the structure, and (c) to facilitate decisions to retrofit/strengthen the structural systems when warranted. In addition, a structural array should include, if physically possible, an associated free-field tri-axial accelerograph so that the interaction between soil and structure can be quantified. Recent trends in the development of performance-based earthquake-resistant design methods and related needs of the engineering community, as well as advances in computation, communication and data transmission capabilities, have prompted development of new approaches for structural monitoring applications. In particular, (a) verification of performance-based design methods and (b) needs of owners to rapidly and informedly assess the damage condition and therefore the functionality of a building following an event require measurement of displacement rather than, or in addition to, accelerations as is commonly done. However, it has to be acknowledged that the development of the new monitoring tools is being driven not only by the stated needs of engineers but also by the advent of the data acquisition systems with specific software that can record, digitize and process accelerations and, integrate to displacements and transmit both accelerations and displacements in real-time or near real-time. Displacement Measurement Needs and Arrays Two important factors are driving the recent push for developing technologies for measuring displacements in real-time or near real-time: (a) the evolution of performance-based design methods and procedures which rely on displacement as the main parameter and (b) the needs of local and state officials and prudent property owners to establish procedures to assess the functionality of buildings and other important structures, such as lifelines, following a significant seismic event. As a result, structural engineers increasingly want the measurement of displacements during strong shaking events in order to assess drift ratios that in turn are related to performance of the structure. A challenge to meeting these objectives is the fact that dynamically measuring relative displacements between floors of a building directly is very difficult and, except for tests conducted in a laboratory (e.g., using displacement transducers), has yet to be readily and feasibly achieved for a variety of real-life structures. However, recent technological developments have already made it possible to successfully develop and implement two approaches to dynamically measure and/or compute real-time displacements from which drift ratios or average drift ratios can be computed. Both approaches can be used for performance evaluation of structures and can be considered as building health-monitoring applications. Drift ratios can be related to damage as shown schematically in Figure. Once drift ratios are computed in near real-time, technical assessment of the damage condition of a building can be made. Relevant parameters, such as the type of connections and story structural characteristics (including geometry e.g. story height) are used in computing drifts corresponding to several pre-selected threshold stages of damage. Thus, recorded (or observed) drift ratios are compared with those precomputed threshold drift ratios to technically assess the damage condition of a building. Use of GPS for direct measurements of displacements

3 For long-period structures such as tall buildings and long-span bridges, dynamic displacement measurements are now possible using differential Global Positioning Systems (GPS) (Çelebi and Sanli, ). However, GPS technology is limited to sampling rates of - Hz and, for buildings, measurement of displacement is possible only at the roof. Currently, the accuracy of GPS measurements is ± cm horizontal and ± cm vertical. A schematic and photos of an application in the use of GPS to directly measure displacements is shown in Figure. In this particular case, two GPS units are used in order to capture both the translational and torsional response of the 34-story building in San Francisco, Ca. Furthermore, at the same locations as the GPS antennas, tri-axial accelerometers are deployed to compare the displacements measured by GPS with those obtained by doubleintegration of the accelerometer records. Real-time acceleration and displacement data streaming into the PC based monitoring system is shown also in Figure. In absence of strong shaking data from the deployed system, ambient data obtained are analyzed to infer the validity of the recorded vibration signals even though both the signal amplitude and signal to noise ratio are low (Figure 3). The GPS displacement data is within the margin of error specified by the manufacturer (< cm. horizontal). Figure. Hypothetical displacement time-history as related to FEMA- 74. In Figure 4, cross-spectra () of pairs of parallel records (north-south component of north deployment [N_N] vs. north-south component of south deployment [S_N], and east-west component of north deployment [N_E] vs east-west component of south deployment [S_E]) from accelerometers are calculated. The same is repeated for the differential displacement records from GPS units. The clearly indicate a dominant frequency of.4-.5 Hz from both acceleration and displacement data. This frequency is within the band of expected frequency for a 34-story building. The lower amplitude peak in frequency (near ~. Hz) seen in the cross-spectra of displacement records is due to noise, which is probably microseisms. It is expected that during larger amplitude motions with higher signalto-noise ratios, such low frequency amplitudes due to noise will not be noticeable. In the acceleration data, a second frequency at.3 Hz is apparent. The.4-.5 Hz is the fundamental translational frequency (in both directions). This is confirmed by the fact that at this frequency, the cross spectra of parallel acceleration records have a coherency of approximately unity (~ ) and they are in-phase ( o ). On the other hand, the of parallel acceleration records at.3 Hz also show coherency of approximately unity but they are out of phase (8 o ). Therefore, this frequency corresponds to a torsional mode. 3

4 Figure. Special instrumentation using GPS and accelerometers (San Francisco, CA.): (Left)- Schematic of the overall system, (Center)- GPS and Radio modem antenna and the recorders connected to PC, (Right)- streaming of acceleration and displacement data in realtime (Çelebi and Sanli, ). x -3 N_N x -3 N_E x N_N x -3 - N_E GPS_N_N ACC_N_Y (ACC_N_N) - - x -3 S_N 5 x S_E -3 5 ACC_N_X (ACC_N_E) x -3 S_N x -3 S_E N 45 o NORTH GPS_N_E DISPL[CM] DISPL[CM] N_N COMPONENT S_N COMPONENT ACC_S_Y (ACC_S_N) SOUTH GPS_S_N DISPL[CM] DISPL[CM ] ACC_S_X (ACC_S_E) GPS_S_E N_E COMPONENT S_E COMPONENT Figure 3. With locations defined in the central schematic, (Top) remotely-triggered and recorded ( and 6 second windows) accelerations at N (North) and S (South) locations. (Bottom) remotely triggered and recorded displacements from GPS at N (North) and S (South) locations. 4

5 For the fundamental frequency at.4 Hz, the displacement data exhibits a o phase angle; however, the coherencies are lower (~.6-.7). The fact that the fundamental frequency (.4 Hz) can be identified from the GPS displacement data, amplitudes of which are within the manufacturer specified error range, and that it can be confirmed by the acceleration data, is an indication of promise of better results when larger displacements can be recorded during strong shaking caused by earthquakes or strong winds. Since the deployment of the pioneering GPS units in San Francisco, CA, multiple other such arrays have been developed. An important array for monitoring the wind response of tall buildings in Chicago, IL has been developed by Kijewski-Correa and Kareem (4). x 5 CROSS-SPECTRUM 3.5 ACCELERATION [FROM ACCELEROMETER] N_N vs S_N.3.5 x 4 CROSS-SPECTRUM ACCELERATION [FROM ACCELEROMETER].3 N_E vs S_E CROSS-SPECTRUM.4 DISPL. [FROM GPS] N_N vs S_N.5 CROSS-SPECTRUM DISPL. [FROM GPS] N_E vs S_E.5 ACC:N_N vs S_N ACC:N_E vs S_E PHASE ANG.(DEG) PHASE ANG.(DEG) DISPL:N_N vs S_N DISPL:N_E vs S_E PHASE ANG.(DEG) PHASE ANG.(DEG) Figure 4. Cross-spectra () and associated coherency and phase angle plots of horizontal, and parallel accelerations and displacements. [Note: In the coherency-phase angle plots, solid lines are coherency and dashed lines are phase-angle]. Displacement via real-time double integration As mentioned previously, GPS applications are currently limited to sampling at Hz, and for building monitoring, these displacements measurements are possible only on at the roof. This limits the application to long period structures rather than wide variety of structural systems. Therefore, the alternative strategy is to compute displacements from recorded acceleration responses in real-time or near real-time. A new approach in obtaining displacements in real-time is depicted in Figure 5 which also shows the distribution of accelerometers in the building array designed to provide data from several pairs of neighboring floors to facilitate drift computations. The system has a server that (a) digitizes continuous analog acceleration data, (b) pre-processes the sps digitized data with low-pass filters (herein called as the preliminarily filtered uncorrected data), (c) decimates the data to sps and streams it locally, (d) monitors and applies server triggering threshold criteria and locally records 5

6 (with a pre-event memory) when prescribed thresholds are exceeded, and (e) broadcasts the data continuously to remote users by high-speed internet. Figure 5. General schematic of data acquisition and transmittal for seismic monitoring of the building. The broadcast streamed real-time acceleration data are acquired remotely using Client Software configured to compute velocity, displacement and a selected number of drift ratios. Figure 6 shows two PC screen snapshots of the client software display configured for channels of streaming acceleration or velocity or displacement or drift ratio time series. Each paired set of acceleration response streams is displayed with a different color. The amplitude spectrum for one of the selected channels is periodically recomputed and clearly displays several identifiable frequencies. In the lower left, time series of drift ratios are shown for 6 locations, with each color corresponding to the same pair of acceleration data from the window above. Drift ratios are computed using real-time, filtered and double integrated acceleration data. Specific filter options are built into the client software for processing of the acceleration data. To compute drift ratios, story heights are entered manually (Figure 6). This figure also shows the computed pairs of displacements that are used to compute the drift ratios. Corresponding to each drift ratio, there are 4 stages of colored indicators. When only the green color indicator is activated, it indicates that the computed drift ratio is below the first of three specific thresholds. The thresholds of drift ratios for selected pairs of data must also be manually entered in the boxes. As drift ratios exceed the designated three thresholds, additional indicators are activated with a different color (Figure 6). The drift ratios are calculated using data from any pair of accelerometer channels oriented in the same direction. The threshold drift ratios for alarming and recording are computed and decided by structural engineers using structural information and are compatible with the performance-based theme, as illustrated in Figure (Figure C-3 of FEMA-74 [ATC 997]) and summarized in Table for this particular building. Figure 6 hypothetically shows that the first level of threshold is exceeded, and the client software is recording data as indicated by the illuminated red button. 6

7 Table. Summary of Threshold Stages and Corresponding Drift Ratios Threshold Stage 3 Adopted Drift Ratio.%.8%.4 -.% Figure 6. (Left) Screen snapshot of client software display showing acceleration streams and computed amplitude and response spectra. (Right) Screen snapshot of client software display showing -channel (six pairs with each pair a different color) displacement and corresponding six-drift ratio (each corresponding to the same color displacement) streams. Also shown to the upper right are alarm systems corresponding to thresholds that must be manually input. The first threshold for the first drift ratio is hypothetically exceeded to indicate the starting of the recording and change in the color of the alarm from green to yellow. Sample Ambient Data and Analyses Sample data recorded on February 3 via the client software are shown in Figure 7. The data are from the two parallel roof channels (CH and CH) and their difference as well as the roof orthogonal channel (CH3). The intent of the differential accelerations of parallel channels (CH- CH) is to illustrate the strong presence of torsion. The recorded peak accelerations are about.-. gals (~.-. cm/s/s). The computed amplitude spectra clearly indicate a peak frequency for the fundamental translational mode (in both directions) at ~.4 Hz (~.5 second period) for all channels and at ~.6 Hz (~.67 s) for the torsional motion. Furthermore, the signal to noise ratio is high enough to identify the second translational mode at ~.HZ (~.83 s). Similarly, the second torsional mode is at ~.8 Hz (.56 s). The identified translational frequency is typical of a framed building that is 4 stories high. The identified modes and frequencies are further supported with the cross-spectrum, coherency, and phase angle plots in Figures 8 and 9. The cross spectrum, coherency, and phase angle plots of the motions recorded by CH and CH (the two parallel accelerometers at the roof level) are shown in Figure 4. The cross spectrum actually exhibits all of the significant frequencies identified in Figure 3 with very high coherency (~). At.4 and. Hz, the phase angles between the parallel motions are both degrees, which indicate that they are in phase and therefore belong to translational modes. At.6 Hz and.8 Hz, the phase angles are ~8 degrees which indicate that they are out of phase and belong to torsional modes. The strong torsional response is further illustrated through Figure 5 that exhibits cross spectrum, coherency, and phase angle plots of the differences of motions recorded by parallel channels (CH-CH) at the roof and (CH-CH9) at the 8 th floor. Again, at ~ 7

8 .6 Hz, these torsional motions exhibit significant cross-spectral amplitude with very high coherency (~) and degree phase angle. Therefore,.6 Hz belongs to the first torsional mode. At the level of low amplitude acceleration response recorded and exhibited in this set of sample data, the signal-to-noise ratio is quite high and is satisfactory to indicate several modal frequencies. It is expected that the coherency of motions between such pairs of channels will further improve when the signal-to-noise ratio is even higher during strong-shaking events. Further detailed analyses of strong shaking data will be carried out when such data become available in the future. ACCELERATION (CM/S/S) AMBIENT : CH CH CH-CH CH3 AMPLITUDE(CM/S) AMBIENT : CH(SOLID) CH(DASHED) CH-CH CH Figure 7. Twenty seconds of ambient acceleration response data obtained at the roof from parallel channels (CH & CH), their difference (CH-CH), and from CH3, orthogonal to CH and CH (left) and corresponding amplitude spectra (right). Sample Low-amplitude Earthquake Response Data and Analyses During the December, 3 San Simeon, Ca. earthquake (Mw=6.4), at an epicentral distance of 58 km., a complete set of low-amplitude earthquake response data was recorded in the building. The largest peak acceleration was approximately % of g. Synchronized bandpass-filtered accelerations and corresponding double-integrated displacements are exhibited in Figure 9 for one side of the building. Figure further exhibits computed displacements -4 s into the record and reveals the propagation of waves from the ground floor to the roof. The travel time is extracted as about.5 seconds. Since the height of the building is known (6.5 ft [8m]), travel velocity is computed as 6 m/s. One of the possible approaches in detection of possible damage to structures by keeping track of significant changes in the travel time since such travel of waves will be delayed if there are cracks in the structural system (Safak, 999). 8

9 AMBIENT: AMBIENT: CH & CH CH-CH & CH-CH PHASE (DEG.) - PHASE(DEG.) Figure 8. [Left] Cross spectrum, coherency, and phase angle plots of ambient acceleration response data obtained from parallel channels (CH and CH) at the roof and [Right] Cross spectrum, coherency, and phase angle plots of ambient acceleration response data obtained from differences of parallel channels, CH-CH at the roof and CH-CH9 at the 8 th floor. In Figure, the two parallel and orthogonal motions recorded at the roof are used to identify the first mode translational and torsional frequencies as.38 Hz and.6hz respectively. Figures and 3 similarly exhibit the cross-spectrum () and coherency and phase angles at these frequencies. ACCELERATIONS PARALLEL TO FIRST STREET DISPLACEMENTS: PARALLEL TO FIRST STREET 4 CH3 (ROOF) 8 CH3 (ROOF) ACCELERATION (CM/S/S) CH9 (3RD. ) CH8 (8TH. ) CH7 (7TH. ) CH6 (4TH. ) CH5 (TH. ) CH4 (7TH. ) CH3 (6TH. ) CH (EL. 5FT.) CH (GR. ) DISPLACEMENT (CM) CH9 (3RD.) CH8 (8TH.) CH7 (7TH.) CH6 (4TH.) CH5 (TH.) CH4 (7TH.) CH3 (6TH.) CH (EL. 5 ) FT. CH (GR.) Figure9. Bandpass-filtered accelerations (left) and double-integrated displacements (right) at each instrumented floor (from ground floor to the roof) on one side of the building [San Simeon earthquake, December, 3]. 9

10 DISPLACEMENTS: PARALLEL TO FIRST STREET 8 CH3 (ROOF) DISPLACEMENT (CM) CH9 (3RD.) CH8 (8TH.) CH7 (7TH.) CH6 (4TH.) CH5 (TH.) CH4 (7TH.) CH3 (6TH.) CH (EL. 5 ) FT. CH (GR.) Figure. A twenty second window plotted from -4seconds into the record of computed displacements. Travel time of propagating vibrational waves from the ground floor to the roof of the 8 m tall building is approximately.5 second. EQ: DEC., 3 EQ: DEC., CH CH (SOLID) CH (DASHED).8 ACCELERATION (CM/S/S) 4 3 CH CH - CH CH3 AMPLITUDE (CM/S).5.5 CH - CH.5.5 CH Figure. Acceleration response data [San Simeon, Ca. earthquake of December, 3) obtained at the roof from parallel channels (CH & CH), their difference (CH-CH), and from CH3, orthogonal to CH and CH (left) and corresponding amplitude spectra (right).

11 EQ: DEC., CH & CH PHASE ANG.(DEG.) Figure. Cross spectrum, coherency, and phase angle plots of ambient acceleration response data obtained from parallel channels (CH and CH) at the roof. 6 EQ: DEC., 3 4 CH - CH & CH - CH PHASE (DEG.) Figure 3. Cross spectrum, coherency, and phase angle plots of ambient acceleration response data obtained from differences of parallel channels, CH- H at the roof and CH- CH9 at the 8 th floor.

12 Conclusions Capitalizing on advances in global positioning systems, computational and data transmission technology, it is now possible to configure and implement a seismic monitoring system for a specific building with the objective of rapidly obtaining and evaluating response data during a strong shaking event in order to help make informed decisions regarding the health and occupancy of that specific building. Using GPS technology and/or real-time double-integration and related data acquisition systems, displacements and, in turn, drift ratios, in real-time or near real-time are obtained. Drift ratios are related to damage condition of the structural system by using relevant parameters of the type of connections and story structural characteristics including its geometry. Thus, once observed drift ratios are computed in near real-time, technical assessment of the damage condition of a building can be made by comparing the observed with pre-computed threshold stages of drift ratios corresponding to pre-selected damage levels. Both GPS and double integration applications can be used for performance evaluation of structures and can be considered as building health-monitoring applications. Benefits in using such real-time systems in either direct measurement of displacements using GPS or real-time computation of displacements by double-integration of accelerations during very strong shaking caused by earthquakes or other extreme events are yet to be recorded and proven. However, analyses of data recorded during smaller events or low-amplitude shaking are promising. References Applied Technology Council (ATC), 997. NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings, prepared for the Building Seismic Safety Council, published by the Federal Emergency Management Agency, FEMA 74, Washington, D.C. Celebi, M., Sanli, A., Sinclair, M., Gallant, S., and Radulescu, D., 4, Real-Time Seismic Monitoring Needs of a Building Owner and the solution A Cooperative Effort, Journal of EERI, Earthquake Spectra, v.9, Issue, pp.-3. Çelebi, M., and Sanli, A.,, GPS in Pioneering Dynamic Monitoring of Long-Period Structures, Earthquake Spectra, Journal of EERI,. Volume 8, No., pages 47 6, February. Jennings, P.C., 997, Use if strong-motion data in earthquake resistant design, in Proc.SMIP97 Seminar on Utilization of Strong-motion Data, California strong Motion Instrumentation Program, Div. of Mines and Geology, California Dept. of Conservation, Sacramento, Ca.,-8. Kijewski-Correa, T. and Kareem, A., (4, The Height of Precision: New Perspectives in Structural Monitoring, Proceedings of Earth & Space: 9 th Aerospace Division International Conference on Engineering, Construction and Operations Challenging Environments, 7- March, Houston, Tx. Rojahn, C., and Mork, P.N., 98, An analysis of strong-motion data from a severely damaged structure, the Imperial County Services Building, El Centro, California: U.S. Geological Survey Open-File Report Safak, E. (999). Wave-propagation formulation of seismic response of multistory buildings, ASCE, Journal of Structural Engineering, vol. 5, no. 4, April 999, pp