Experimental Verification of Damage Monitoring and Evaluation Method for Building Structures based on Measurement of Relative Story Displacements

Experimental Verification of Damage Monitoring and Evaluation Method for Building Structures based on Measurement of Relative Story Displacements T. Hatada, R. Katamura & H. Hagiwara Kajima Technical Research Institute, Kajima Corporation, Japan M. Takahashi Kobori Research Complex, Japan Y. Nitta Department of Architecture, Ashikaga Institute of Technology, Japan A. Nishitani Department of Architecture, Waseda University, Japan SUMMARY: This study presents the experimental verification of a damage monitoring and evaluation method for building structures based on the measurement of Relative Story Displacements (RSDs). The damage evaluation method is formulated to detect the damaged locations of structural elements and evaluate their damage degree based on the displacement loading analysis by the time histories of measured RSDs. Furthermore in the evaluation process, the analytical technique is introduced to compensate for the measurement errors associated with the properties of sensors. The monitoring accuracies are analyzed through the shaking table test of a full-scale 4-sotry steel-moment resisting framing building carried out at E-defense in Japan. The results indicate the effectiveness of the proposed damage evaluation method in its applications to the Structural Health Monitoring (SHM) system. Keywords: Monitoring, Relative story displacement, Damage evaluation, Displacement loading, E-defense 1. INTRODUCTION To securely mitigate the resulting disasters against earthquakes, Takahashi et al. (23) reported the needs of appropriate strategies based on the information about building damages. Among them, the Structural Health Monitoring (SHM) system can provide viable means both for buildings and their users (Nitta et al. 23). The SHM system is applied for the diagnosis on structural deteriorations during the building lifespan, or the diagnosis on structural damages right after earthquake shocks. The latter one is especially useful for the early recovery of building functions after earthquakes. In utilizing the SHM system to evaluate the structural damages of buildings for earthquakes, the Relative Story Displacement (RSD) can give the direct and clear index. RSD is an important index specifically in the structural design process of buildings, and we can detect detailed structural damages by utilizing the RSDs during earthquakes. To measure the RSDs directly, we have developed a simple RSD measurement system with high accuracy based on two noncontact-type sensors utilizing a Position Sensitive Detector (PSD) and a PhotoTransistor (PTr) array, and verified the basic properties through the shaking table tests (Matsuya et al. 211, Kanekawa et al. 21) and verified the practical effectiveness through the forced vibration test on an actual building (Hatada et al. 21). In the application of the SHM system, as an indispensable component with the measurement system, we have to set up an appropriate damage evaluation method for building structures. In the past reports, we can survey two-type methods to evaluate the macro-damage or the micro-damage of building structures. Among the methods to evaluate the macro-damage of building structures, the typical method is to evaluate the changes of story stiffness through the identification scheme (Morita et al. 27, Ono et al. 211). As another approach, Kusunoki et al. (23) introduced the damage index to express the residual seismic capacity of buildings. On the other hand, among the methods to evaluate the micro-damage of building structures, i.e. the damage of structural elements, Inoue et al. (29) reported the two-stage

identification scheme, and Tanaka et al. (27) evaluated the structural damage through the dynamic analysis. To evaluate the micro-damage of building structures right after earthquakes, we have developed a damage evaluation method based on the displacement loading analysis by measured RSDs, and verified its applicability through numerical simulations on a model building subjected to a large earthquake (Hatada et al. 211). This paper presents the experimental verification of a damage monitoring and evaluation method for building structures based on the measurement of RSDs. First, we formulate a damage evaluation method to detect the damaged locations of structural elements and evaluate their damage degree based on the displacement loading analysis by the time histories of measured RSDs. Next in the evaluation process, we introduce the analytical technique to compensate for the measurement errors associated with the properties of sensors. Finally, we analyze the monitoring accuracies through the shaking table test of a full-scale 4-sotry steel-moment resisting framing building carried out at E-defense in Japan (Yamada et al. 28 and 29, Suita et al 28 and 29), and clarify the effectiveness of the proposed damage evaluation method in its applications to the SHM system. 2. RSD MEASUREMENT SYSTEM In this study, we introduce a noncontact-type optical sensor for the RSD measurement system. The sensor is composed of a light source and a sensing unit. Figure 1 illustrates the conceptual schematic of the RSD measurement system. The light source and the sensing unit are located on the upper and the lower floors of the objective story. The sensor directly measures the relative displacement in the lateral direction between them, i.e. RSD, by detecting the light spot emitted from the light source on the sensing unit. By appropriately setting up the design parameters, the sensor can measure wide-ranged displacements induced by various intensities of earthquakes, and we can construct the applicable and compact measurement system for buildings (Matsuya et al. 211, Kanekawa et al. 21, Hatada et al. 21). Upper floor (structural member) Measurement direction Light source Light Sensing unit Measurement distance Lower floor (structural member) The arrangement of light source and sensing unit can be reversible. Figure 1. Conceptual schematic of RSD measurement system 3. FORMULATION OF DAMAGE EVALUATION METHOD 3.1. Displacement Loading Analysis In the SHM system for earthquakes based on the direct measurement of RSDs, we formulate a damage evaluation method to detect the damaged locations of structural elements and evaluate their damage

degree. The proposed damage evaluation method is based on the displacement loading analysis by the time histories of measured RSDs. First, the building is modeled as a three-dimensional (3D) frame model composed of structural elements, e.g. columns, beams and joint panels, considering the appropriate elasto-plastic characteristics on the stiffness of each structural element. For this analytical model, consider the dynamic equilibrium of this n- degree-of-freedom system with m-known displacement subset subjected to an external excitation. The equation of motion at time instant t can be written in the following form as: k k 11 21 k k 12 22 x x 1 2 ( t) f = ( t) f 1 2 ( t) ( t) (3.1) where x 1 (t) is an m-known displacement vector; x 2 (t) is an (n-m)-unknown displacement vector; f 1 (t) and f 2 (t) are the resisting force vectors composed of inertia, damping and excitation forces, corresponding to x 1 (t) and x 2 (t), respectively; and k 11, k 12, k 21 and k 22 are the stiffness subset matrices composed of the structural element properties. Here, let us set each floor displacement of the building given by the measured RSDs to known displacement vector x 1 (t). Under the rigid floor assumption, x 1 (t) can be represented as two horizontal and a torsional directions. Assuming that the effect of f 2 (t) corresponding to x 2 (t) is negligible since its effect is generally small comparing to that of f 1 (t) corresponding to x 1 (t), x 2 (t) and f 1 (t) can be solved as: x f 1 2 ( 22 21 1 t t) = k k x ( ) (3.2) 1 t) = [ k k k k ] x ( ) (3.3) 1( 11 12 22 21 1 t Thus, we can clarify the relationship of resisting forces and displacements of the system, and evaluate the damages of each structural element by expanding Eqn. 3.1 to each structural element stiffness matrix. In the evaluation process, right after the earthquake duration, we perform the displacement loading analysis for the building model by the time histories of measured RSDs, and evaluate the hysteretic transitions of the stiffness of each structural element. As a result, we can directly detect the damaged locations of structural elements, and evaluate their damage degree. In the proposed method, we estimate the behaviors and damages of each structural element by directly tracing the building responses during earthquakes, and can evaluate the structural damage only by the stiffness-relating information on the structural elements without any information on the mass or damping properties of the building. As an additional feature, the analysis is not affected by the stiffness of nonstructural members like partition walls in the building, since the effect of the mass, damping and the stiffness of nonstructural members is included in the measured RSDs, the building responses for earthquake inputs, in the evaluation process. Based on these features, the proposed damage evaluation method is analytically robust against the uncertainties intrinsically accompanying the modeling of the building. 3.2. Correction of Measurement Error induced by Local Rotation In the RSD measurement system by noncontact-type optical sensors, it is possible for the displacement component by the local rotation at the locations of the light source or the sensing unit to affect the measurement accuracy as shown in Figure 2 (Hatada et al. 21). To compensate for the measurement errors associated with this effect, we introduce the following analytical technique in the evaluation process: δ (i) Assume (1), the estimated RSD time history, to be δ ' including the effect of local rotation, the measured RSD time history. (ii) Perform the displacement loading analysis for the building model by δ (1).

Forcing direction Deformation shape of structural member Light source Light Sensing unit Figure 2. Schematic of the local rotation effect δ by removing the measurement error from δ ', being, the local rotation angle time history computed in the displacement loading δ is expressed as: (iii) Evaluate the updated estimation (2) estimated by θ (1) analysis. Here, (2) δ ( 2) δ ' hθ (1) = (3.4) where h is a measurement distance. (iv) Repeat the steps (ii) and (iii) by applying the updated estimations toward the convergence over the whole time history. 3.3. Damage Evaluation Flow Relative story displacement Displacement component by local deflection As the complete formulation of algorithm, being composed of the displacement loading analysis and the measurement error correction scheme, the damage evaluation flow is shown in Figure 3. Following this flow, we can accurately evaluate the structural damage of the building right after earthquake shocks. Structural model 3D frame model Composed of structural elements No need for mass, damping and nonstructural members RSD measurement Direct measurement of RSD Effect of local rotation Displacement loading analysis Figure 3. Damage evaluation flow Trace of building responses during eq. Computation of local rotation angle Evaluation of structural element damage Measurement error correction Removal of measurement error Convergence Judgment over whole time history Damage evaluation results Animation of displacement and damage Maximum of displacement and damage

4. VERIFICATION THROUGH E-DEFENSE SHAKING TABLE TEST OF FULL-SCALE 4-STORY STEEL BUILDING 4.1 Objective Experiment and Analysis Conditions To assess the basic features and verify the applicability of the proposed damage evaluation method, we analyze the monitoring accuracies through the shaking table test of a full-scale building carried out at E-defense in Japan. Here, to verify the evaluation accuracies of the proposed method detecting the structural element damage, we use the experimental results three-dimensionally excited by NS, EW and UD components of 6%-scaled JR Takatori records of 1995 Hyogoken-Nanbu earthquake. The test specimen is a 4-story steel-moment-resisting framing structure of 14.375m height, weighing about 255kN. Figure 4 shows the floor plan and the structural framing elevation. The RSD sensors are assumed to be installed at the center of A1-B1 and A1-A2 spanned beam on each floor. RFL RSD sensor (Upper unit) B A 6 RSD sensor 5 5 1 1 2 3 14375 3875 35 35 35 175 175 175 15 4FL 3FL 2FL 1FL Y (a) Floor plan X 1 5 5 1 2 3 For the analysis in the damage evaluation process, the building is modeled as a 3D frame model composed of columns, beams and joint panels under the rigid floor assumption. To evaluate the structural damage, we give the appropriate elasto-plastic characteristics on the stiffness of each structural element, being determined by its yield moment. In this analysis, to verify the validity of the damage evaluation method itself, each yield moment is based on the measured yield strength of each steel member. 4.2. Analysis Results (b) Structural framing elevation (A-frame in the Y-direction) Figure 4. Floor plan and structural framing elevation of the test specimen The RSD time histories measured by RSD sensors are prepared by taking into account the effect of local rotations to the accurately-measured RSDs in the experiment. In the evaluation process composed of the displacement loading analysis and the measurement error correction scheme, we evaluate the structural damage only by the stiffness-relating information of the building analytical model and the measured RSD time histories including the effect of local rotations.

First, let us examine the validity of the measurement error correction scheme. Figure 5 shows the RSD time stories of the 1 st story in the Y-direction, comparing the exact, measured and error-corrected values, where the corrected time history is the result through five iterations. We observe the measurement error associated with the effect of local rations; on the other hand, the error-corrected time history agrees very well with the exact value and we recognize no errors on the time histories, indicating that we can remove the measurement error accurately through the measurement error correction scheme. 8 Exact Measured Corrected 4 (cm) -4-8 15 17 19 21 23 25 Time (s) Figure 5. RSD time histories of the 1st story in the Y-direction Next, let us investigate the damage evaluation results by the error-corrected RSD time histories. Figures 6, 7 and 8 show the hysteretic curves of a beam, a column and a joint panel, respectively, comparing the exact and estimated damages. From these results, we can accurately estimate the shape of hysteretic curves, representing the damage degree of each structural element, through the proposed evaluation method although we give simple bi-linear elasto-plastic characteristics on the stiffness of each structural element in the analytical model. 5 5 Bending moment (kn m) 25-25 Bending moment (kn m) 25-25 -5-5 -.1 -.5..5.1 -.1 -.5..5.1 Rotation angle (rad) Rotation angle (rad) (a) Test result (Exact damage) (b) Proposed evaluation (Estimated damage) Figure 6. Hysteretic curve of beam (A1-end, A1-A2 span on the 2nd floor) 4 4 Beding moment (kn m) 2-2 Bending moment (kn m) 2-2 -4 -.24 -.12..12.24 Rotation angle (rad) -4 -.24 -.12..12.24 Rotation angle (rad) (a) Test result (Exact damage) (b) Proposed evaluation (Estimated damage) Figure 7. Hysteretic curve of column (A1 column bottom of the 1st story in the Y-direction)

6 6 Bending moment (kn m) 3-3 Beding moment (kn m) 3-3 -6 -.1 -.5..5.1 Shear strain angle (rad) -6 -.1 -.5..5.1 Shear strain angle (rad) (a) Test result (Exact damage) (b) Proposed evaluation (Estimated damage) Figure 8. Hysteretic curve of joint panel (A2 column of the 3rd floor in the Y-direction) 5. CONCLUSIONS In this study, we have presented the experimental verification of a damage monitoring and evaluation method for building structures based on the measurement of RSDs. The damage evaluation method is formulated to detect the damaged locations of structural elements and evaluate their damage degree based on the displacement loading analysis by the time histories of measured RSDs. In the proposed method, we have estimated the behaviors and damages of each structural element by directly tracing the building responses during earthquakes. Furthermore in the evaluation process, we have introduced the analytical technique to compensate for the measurement errors associated with the properties of sensors. To assess the basic features and verify the applicability of the proposed damage evaluation method, we have analyzed the monitoring accuracies through the shaking table test of a full-scale 4-sotry steel-moment resisting framing building carried out at E-defense in Japan. The results indicate the effectiveness of the proposed damage evaluation method in its applications to the SHM system. ACKNOWLEDGMENTS This research was supported by Grant-in-Aid for Scientific Research (B) of the Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT), No. 2136271 with Dr. Akira Nishitani as Principal Investigator. This support is gratefully acknowledged. The advice on the development of the sensors of Dr. Iwao Ohdomari, Dr. Shuichi Shoji, Dr. Takashi Tanii, Dr. Iwao Matsuya and Mr. Kiyoshi Kanekawa at Waseda University are greatly appreciated. The cooperation on the numerical analysis of Dr. Satoru Miura, Mr. Masatoshi Ishida and Dr. Yasutsugu Suzuki at Kajima Corporation are also greatly appreciated. REFERENCES Takahashi, M., Nasu, T. and Kobori, T. (23). Proposal for Real-time Disaster Mitigation System with Structural Control Systems. Proceedings of the Structural Health Monitoring and Intelligent Infrastructure. 2, 953-961. Nitta, Y. and Nishitani, A. (23). Structural Health Monitoring of Story Stiffness based on Identification of Subsystem representing Specific Story of a Building. Journal of Structural and Construction Engineering, Transactions of AIJ. 573, 75-79.* Matsuya, I., Tomishi, R., Sato, M., Kanekawa, K., Nitta, Y., Takahashi, M., Miura, S., Suzuki, Y., Hatada, T., Katamura, R., Tanii, T., Shoji. S., Nishitani, A. and Ohdomari, I. (211). Development of Lateral Displacement Sensor for Real-time Detection of Structural Damage. IEEJ Transactions on Electrical and Electronic Engineering. 6, 266-272. Kanekawa, K., Matsuya, I., Sato, M., Tomishi, R., Takahashi, M., Miura, S., Suzuki, Y., Hatada, T., Katamura, R., Nitta, Y., Tanii, T., Shoji, S., Nishitani, A. and Ohdomari, I. (21). An Experimental Study on Relative Displacement Sensing using Phototransistor Array for Building Structures. IEEJ Transactions on Electrical and Electronic Engineering. 5, 251-255.

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