finite element modeling of reinforced concrete ... - PublicationsList.org
FINITE ELEMENT MODELING OF REINFORCED CONCRETE BUILDING UNDERGOING MAJOR RENOVATION AND MODEL VALIDATION USING AMBINET VIBRATION MEASUREMENT J.P. Ghimire1), Y. Matsumoto, N. Areemit and H. Yamaguchi Department of Civil and Environmental Engineering, Saitama University 255 shimo-Ohkubo, Sakura-ku, Saitama 338-8570, Japan 1) E-mail: [email protected] ABSTRACT The building of Civil and Environmental Engineering Department of Saitama University was renovated and major structural changes were made. Different finite element models of this four-storey reinforced concrete building, supported on prestressed concrete pile foundation, were developed so as to identify the dynamic characteristics at different stages of the renovation. Significant changes in the dynamic characteristics were observed from the results of ambient vibration measurements conducted before and after each major renovation stage as well as from the results of analytical models, developed to represent the different renovation stages. Soil-structure interaction was observed from the measurement in which first vibration mode obtained was a rigid body mode, where the mass of whole building was lumped as a single mass, and stiffness was contributed by the piles and surrounding soil. This soil-structure interaction was incorporated in the analytical model by considering one additional storey in the model. Modal properties obtained from the models developed showed reasonable agreement with experimental results. KEY WORDS: Finite element modeling; building renovation; soil-structure interaction; model validation; ambient vibration INTRODUCTION The dynamic behavior is one of the most important design considerations for civil engineering structures especially for multistory buildings. Because of the seismic hazard, there is an increasing interest to evaluate that new and existing buildings can safely withstand the forces induced by earthquakes. This requires a better understanding of building’s dynamic behavior as well as accurate mathematical models to properly represent this behavior. The dynamic characteristics of structure such as natural frequencies, mode shapes and damping ratio contain useful information about its state (Peeters et al., 2001). Ambient vibration testing is generally preferred to non-destructive forced vibration measurement techniques for obtaining the dynamic characteristics of the building: a structure can be adequately excited by wind, micro tremors, traffic, and human activities and the resulting response can readily be measured so that expensive devices to excite the structure are not needed. Consequently, the overall cost of the measurements conducted on a large structure could be reduced. The objective of this study was to identify the changes in dynamic characteristics of the Civil and Environmental Engineering Department Building of Saitama University due to the changes made in the structural system of the building during the renovation. In this study, three dimensional finite element models of the building were developed to represent the building at different stages to identify the dynamic characteristics, i.e., natural frequencies and mode shapes analytically. Ambient vibration measurements were also made and the measured data were used to validate the analytical models. DESCRIPTION OF THE BUILDING The building under consideration was a 4-storey reinforced concrete frame building. The lateral force resisting structural system consisted of concrete shear walls and moment frames in the transverse (North-South) as well as in the longitudinal (East-West) direction, as shown in Fig.1. The superstructure of building was supported on 23meter long prestressed concrete piles having diameter of 0.40m each. The total numbers of piles used in the foundation before renovation was 86. The building was of 31.2 m × 13.2 m in plan and 14.4 m high with 3.6 m storey height. The water tank was on top of the building and was placed on concrete floor constructed to cover the staircase. Before renovation, there were three frames in the longitudinal (East-West) direction and five frames in the transverse (North-South) direction as shown in Fig 1(a). Later building was renovated by removing
4.2 m
the shear wall in the longitudinal (East-West) direction middle frame and two more reinforced concrete frames were added in the longitudinal (EastWest) direction as 20mm thick wall column 2.0 m 4 @ 7.8 m=31.2 m shown in Fig. 1(b). column The new frames were added 2.4 m throughout the height of the building, and were made monolithic with old frames of Roving Sensors Reference Sensor 4 @ 7.8 m=31.2 m the building, with Sensor placed at the ground concrete slab and (b) After renovation (a) Before renovation shear walls as shown in Fig. 1(b). The Fig. 1 Plan of building before and after renovation showing the location of sensors during the measurement additional 29 prestressed concrete piles of diameter of 0.4 m each were used for the foundation of new frames. UP
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13.2 m
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AMBIENT VIBRATION MEASUREMENT The ambient responses of the building were measured with a 5-channel data acquisition system using unidirectional Servo accelerometers (Model VSE-15T, Tokyo Sokushin Co.). A laptop computer was used for data acquisition and data storage. For each measurement, the data were recorded for a period of 140 seconds at the rate of 500 samples per second. Measurement was carried out at each floor separately because the number of accelerometers was limited (i.e, five). In order to measure the translational modes in both directions and torsional modes of the building, three sensors were used on each floor in the longitudinal (East-West) and transverse (North-South) direction separately. One reference sensor was placed on the third floor near the east column of the building. Another reference sensor was placed on the ground to measure the vibration of ground nearby. The directions of reference sensor and ground sensor were changed to both directions according to the direction of the roving sensors. The location of sensors is shown in Fig. 1(a). The measurement was carried out at all five floors including roof and ground floor, two-times in each direction. Table 1. Different stages of the building during renovation Stages Stage-1 Stage-2 Stage-3 Stage-4 Stage-5 Stage-6 Stage-7
Condition of the building Initial condition of the building Damage occurred by removing some shear walls Piles were installed for new frames up to ground New frames were constructed up to second floor New frames were constructed up to third floor New frames were constructed up to fourth floor New frames were constructed up to roof
Stage-1
Stage-5
Stage-2
Stage-3
Stage-6
Stage-4
Stage-7
Fig. 2 Different renovation stages of the building
Floors
Floors
Floors
The measurements were taken for different renovation 5 5 5 stages, which are shown in 4 4 4 Table 1 and Fig. 2. The 3 3 3 building was not in use during the whole 2 2 2 measurement period for all 1 1 1 stages: because of 0.00 1.00 2.00 0.00 1.00 2.00 -2.00 0.00 2.00 construction activities at Normalized amplitude Normalized amplitude daytime, measurement was Normalized amplitude made either at night or early (a) (b) ( c) in the morning. Fig. 3. Mode shapes of the building from the experiment for stage-1: (a) First translational mode The Eigenvalue in transverse(North-South) direction, f=4.41 Hz, (b) First translational mode in longitudinal(East-West) Realization Algorithm direction,f=6.30 Hz and (c) Second translational mode in longitudinal(East-West) direction,f=15.35 Hz
(ERA) technique was used to identify the modal parameters, i.e., natural frequencies, mode shapes and modal damping ratios from the measurement data of the building vibration. It was observed from the measurement that the building had significant displacement at the base in first fundamental vibration mode of both directions. It shows that the building vibrates as a rigid body in which the whole building acts as a single mass and; stiffness is contributed by the piles used in the foundation and surrounding soil. All the vibration modes, other than those rigid body modes, obtained from the measurement at stage-1, for example, are shown in Fig. 3. The first translational mode in the transverse (North-South) direction had natural frequency of 4.41 Hz, the first translational mode in the longitudinal (East-West) direction was with natural frequency of 6.30 Hz and the second translatonal mode in the longitudinal (East-West) direction had natural frequency of 15.35 Hz. Fig.3 shows that there was small base displacement in all modes of vibration obtained. FINITE ELEMENT MODELING OF THE BUILDING The building was modeled to represent the rigid body behavior by considering the whole building as a single mass, and the stiffness, which was contributed by the pile foundation and surrounding soil, was calculated by taking the active length of pile. The active length used to calculate the stiffness of piles was taken as 9 times diameter of pile used (Gazetas, 1991). The results of rigid body mode obtained from this model agreed with the results obtained from the experimental analysis, although the data are not presented in this paper. In order to identify the vibration modes, other than the rigid body modes of the building analytically, three dimensional finite element models of the building were developed by using commercially available finite element software, DIANA Release 7.2. In the models developed, the columns and beams were modeled as 3-D beam elements (L13BE), concrete shear walls and horizontal concrete floors were modeled as flat shell elements (Q24SF). The staircase cover at the top of the building in which the water tank was placed, was also included in the models. Brownjohn et al. (2000) concluded that openings in shear walls have significant effect to torsional response of building. All the openings made for doors and windows in shear walls of the building were considered in the model. Non-structural members, like partitions etc., were not included in the models. Properties of materials used for superstructure and piles were taken from the information available in the design and construction drawings of the building. Modeling of building in initial condition Finite element model of the building for stage-1 was developed first, by considering the building foundation as fixed. However, the fixed base model developed gave higher natural frequencies than those obtained from the experiment. These lower natural frequencies may be attributed to the soil-structure interaction as observed in the rigid body modes as well as in the higher modes which have small displacement at the base of building as shown in Fig.3. In order to incorporate this soil-structure interaction, one additional storey was added in the model. The stiffness of the additional storey was calculated by calculating the lateral spring constants of the piles in both directions considering the effect of soil, the size and number of piles used in the foundation. The height of the additional storey was equal to the active length of pile calculated as above. Modal analysis was carried out for the developed model with the additional storey for stage-1. The first few of obtained natural frequencies and mode shapes are shown in Fig 4, in which the first (c) (a) (b) translational mode in the transverse Fig. 4. Mode shapes of the building from finite element model for stage-1: (North-South) direction was with natural (a) First translational mode in transverse (North-South) direction, f=5.23 Hz; frequency of 5.23 Hz, the first translational (b) First translational mode in longitudinal(East-West) direction, f=5.93 Hz and mode in the longitudinal (East-West) (c) First translational mode in longitudinal(East-West) direction,f=13.58 Hz direction had natural frequency of 5.93 Hz and the second translational mode in the longitudinal (East-West) direction was with natural frequency of 13.58 Hz. These three modes correspond to the modes shown in Fig. 3, which were obtained from the experiment. The natural frequencies for those modes obtained from the finite element model showed reasonable agreement with experimental results. Modeling of building at different renovation stages After having the reasonable agreement between the results calculated from the analytical model and experimental results for the initial condition (stage-1) of the building, finite element models were developed for
Natural frequencies(Hz)
Natural frequencies(Hz)
all other stages, i.e., from stage-2 to stage-7. The developed finite element models were analyzed to identify the dynamic characteristics, i.e., natural frequencies and mode shapes of buildings. Analyzing the measured data also identified modal parameters for all those stages. Fig. 5 shows the comparison of natural frequencies for the first and second translational modes in the longitudinal (East-West) direction and the first translational mode in the transverse (North-South) direction obtained from the experiment and the finite element model for all stages of the renovation. The first torsional mode and second translational mode in the transverse (North-South) direction, which were not obtained from the experimental results, are also shown in Fig 5. The results obtained from the analytical model showed reasonable agreement with the experimental results for all stages. From Fig. 5(a), it can be seen from the experimental and analytical results that, the natural frequencies of the building for the translational First mode(E) 18 14 Second mode(E) modes in the First mode(A) 16 First torsion mode(A) 12 longitudinal(EastSecond mode(A) 14 First mode(E) West) direction 10 12 First mode(A) reduced Second mode(A) 8 10 significantly at 8 6 stage-2 in which the 6 4 shear walls in the 4 2 longitudinal (East2 0 West) direction 0 Stage-1 Stage-2 Stage-3 Stage-4 Stage-5 Stage-6 Stage-7 Stage-1 Stage-2 Stage-3 Stage-4 Stage-5 Stage-6 Stage-7 were removed. The Different renovation stages Different renovation stages natural frequency reduction for first (a) (b) translational mode Fig. 5 Natural frequencies of the building obtained from the experiment and finite element model in in the longitudinal (a) longitudinal(East-West) direction and (b) transverse(North-South) direction (E: Experimental; A: Analytical) (East-West) direction from stage-1 to stage-2 was found 50% in the analytical results and 30% in the experimental results, and reduction in second translational mode natural frequency in the longitudinal (East-West)direction, from stage-1 to stage-2, was 33% in both experimental and analytical results. This reduction in natural frequencies may be attributed to the reduction in stiffness of the building in the longitudinal (East-West) direction after removing shear walls. When the renovation started adding new frames to the building as shown in Fig.2, the natural frequencies of the building in the longitudinal direction increased as shown in Fig.5 (a). CONCLUSIONS Dynamic characteristics of the building, i.e.,natural frequencies and mode shapes were identified by finite element modeling. Results obtained from finite element models were in reasonable agreement with those obtained from ambient vibration measurements. Changes in the dynamic characteristics of the building due to changes made in the structural system of the building during the renovation were observed from both finite element model as well as experimental results. Effect of shear wall, removed during the renovation, on the dynamic characteristics of the building was found significant in the longitudinal (East-West) direction of the building. Soil-structure interaction observed in the building from the experimental results can be incorporated in analytical model of the building by considering one additional storey. REFERENCES Brownjohn, J.M.W., Pan T.C. and Deng X.Y. Correlating dynamic characteristics from field measurements and numerical analysis of a high-rise building, Earthquake Engineering and Structural Dynamics, 29, 2000,pp.523543 Gazetas,G., Foundation Vibrations, Foundation Engineering Handbook By Hsai-Yang Fang, Van Nostran Reinhold, second edition, January 1991. Peeters, B., Maeck J. and Roeck, G.D. Vibration-based damage detection in civil engineering: excitation sources and temperature effects, Smart Materials and Structures, 10,2001,pp.518-527.
4.2 m
the shear wall in the longitudinal (East-West) direction middle frame and two more reinforced concrete frames were added in the longitudinal (EastWest) direction as 20mm thick wall column 2.0 m 4 @ 7.8 m=31.2 m shown in Fig. 1(b). column The new frames were added 2.4 m throughout the height of the building, and were made monolithic with old frames of Roving Sensors Reference Sensor 4 @ 7.8 m=31.2 m the building, with Sensor placed at the ground concrete slab and (b) After renovation (a) Before renovation shear walls as shown in Fig. 1(b). The Fig. 1 Plan of building before and after renovation showing the location of sensors during the measurement additional 29 prestressed concrete piles of diameter of 0.4 m each were used for the foundation of new frames. UP
UP
UP
13.2 m
UP
AMBIENT VIBRATION MEASUREMENT The ambient responses of the building were measured with a 5-channel data acquisition system using unidirectional Servo accelerometers (Model VSE-15T, Tokyo Sokushin Co.). A laptop computer was used for data acquisition and data storage. For each measurement, the data were recorded for a period of 140 seconds at the rate of 500 samples per second. Measurement was carried out at each floor separately because the number of accelerometers was limited (i.e, five). In order to measure the translational modes in both directions and torsional modes of the building, three sensors were used on each floor in the longitudinal (East-West) and transverse (North-South) direction separately. One reference sensor was placed on the third floor near the east column of the building. Another reference sensor was placed on the ground to measure the vibration of ground nearby. The directions of reference sensor and ground sensor were changed to both directions according to the direction of the roving sensors. The location of sensors is shown in Fig. 1(a). The measurement was carried out at all five floors including roof and ground floor, two-times in each direction. Table 1. Different stages of the building during renovation Stages Stage-1 Stage-2 Stage-3 Stage-4 Stage-5 Stage-6 Stage-7
Condition of the building Initial condition of the building Damage occurred by removing some shear walls Piles were installed for new frames up to ground New frames were constructed up to second floor New frames were constructed up to third floor New frames were constructed up to fourth floor New frames were constructed up to roof
Stage-1
Stage-5
Stage-2
Stage-3
Stage-6
Stage-4
Stage-7
Fig. 2 Different renovation stages of the building
Floors
Floors
Floors
The measurements were taken for different renovation 5 5 5 stages, which are shown in 4 4 4 Table 1 and Fig. 2. The 3 3 3 building was not in use during the whole 2 2 2 measurement period for all 1 1 1 stages: because of 0.00 1.00 2.00 0.00 1.00 2.00 -2.00 0.00 2.00 construction activities at Normalized amplitude Normalized amplitude daytime, measurement was Normalized amplitude made either at night or early (a) (b) ( c) in the morning. Fig. 3. Mode shapes of the building from the experiment for stage-1: (a) First translational mode The Eigenvalue in transverse(North-South) direction, f=4.41 Hz, (b) First translational mode in longitudinal(East-West) Realization Algorithm direction,f=6.30 Hz and (c) Second translational mode in longitudinal(East-West) direction,f=15.35 Hz
(ERA) technique was used to identify the modal parameters, i.e., natural frequencies, mode shapes and modal damping ratios from the measurement data of the building vibration. It was observed from the measurement that the building had significant displacement at the base in first fundamental vibration mode of both directions. It shows that the building vibrates as a rigid body in which the whole building acts as a single mass and; stiffness is contributed by the piles used in the foundation and surrounding soil. All the vibration modes, other than those rigid body modes, obtained from the measurement at stage-1, for example, are shown in Fig. 3. The first translational mode in the transverse (North-South) direction had natural frequency of 4.41 Hz, the first translational mode in the longitudinal (East-West) direction was with natural frequency of 6.30 Hz and the second translatonal mode in the longitudinal (East-West) direction had natural frequency of 15.35 Hz. Fig.3 shows that there was small base displacement in all modes of vibration obtained. FINITE ELEMENT MODELING OF THE BUILDING The building was modeled to represent the rigid body behavior by considering the whole building as a single mass, and the stiffness, which was contributed by the pile foundation and surrounding soil, was calculated by taking the active length of pile. The active length used to calculate the stiffness of piles was taken as 9 times diameter of pile used (Gazetas, 1991). The results of rigid body mode obtained from this model agreed with the results obtained from the experimental analysis, although the data are not presented in this paper. In order to identify the vibration modes, other than the rigid body modes of the building analytically, three dimensional finite element models of the building were developed by using commercially available finite element software, DIANA Release 7.2. In the models developed, the columns and beams were modeled as 3-D beam elements (L13BE), concrete shear walls and horizontal concrete floors were modeled as flat shell elements (Q24SF). The staircase cover at the top of the building in which the water tank was placed, was also included in the models. Brownjohn et al. (2000) concluded that openings in shear walls have significant effect to torsional response of building. All the openings made for doors and windows in shear walls of the building were considered in the model. Non-structural members, like partitions etc., were not included in the models. Properties of materials used for superstructure and piles were taken from the information available in the design and construction drawings of the building. Modeling of building in initial condition Finite element model of the building for stage-1 was developed first, by considering the building foundation as fixed. However, the fixed base model developed gave higher natural frequencies than those obtained from the experiment. These lower natural frequencies may be attributed to the soil-structure interaction as observed in the rigid body modes as well as in the higher modes which have small displacement at the base of building as shown in Fig.3. In order to incorporate this soil-structure interaction, one additional storey was added in the model. The stiffness of the additional storey was calculated by calculating the lateral spring constants of the piles in both directions considering the effect of soil, the size and number of piles used in the foundation. The height of the additional storey was equal to the active length of pile calculated as above. Modal analysis was carried out for the developed model with the additional storey for stage-1. The first few of obtained natural frequencies and mode shapes are shown in Fig 4, in which the first (c) (a) (b) translational mode in the transverse Fig. 4. Mode shapes of the building from finite element model for stage-1: (North-South) direction was with natural (a) First translational mode in transverse (North-South) direction, f=5.23 Hz; frequency of 5.23 Hz, the first translational (b) First translational mode in longitudinal(East-West) direction, f=5.93 Hz and mode in the longitudinal (East-West) (c) First translational mode in longitudinal(East-West) direction,f=13.58 Hz direction had natural frequency of 5.93 Hz and the second translational mode in the longitudinal (East-West) direction was with natural frequency of 13.58 Hz. These three modes correspond to the modes shown in Fig. 3, which were obtained from the experiment. The natural frequencies for those modes obtained from the finite element model showed reasonable agreement with experimental results. Modeling of building at different renovation stages After having the reasonable agreement between the results calculated from the analytical model and experimental results for the initial condition (stage-1) of the building, finite element models were developed for
Natural frequencies(Hz)
Natural frequencies(Hz)
all other stages, i.e., from stage-2 to stage-7. The developed finite element models were analyzed to identify the dynamic characteristics, i.e., natural frequencies and mode shapes of buildings. Analyzing the measured data also identified modal parameters for all those stages. Fig. 5 shows the comparison of natural frequencies for the first and second translational modes in the longitudinal (East-West) direction and the first translational mode in the transverse (North-South) direction obtained from the experiment and the finite element model for all stages of the renovation. The first torsional mode and second translational mode in the transverse (North-South) direction, which were not obtained from the experimental results, are also shown in Fig 5. The results obtained from the analytical model showed reasonable agreement with the experimental results for all stages. From Fig. 5(a), it can be seen from the experimental and analytical results that, the natural frequencies of the building for the translational First mode(E) 18 14 Second mode(E) modes in the First mode(A) 16 First torsion mode(A) 12 longitudinal(EastSecond mode(A) 14 First mode(E) West) direction 10 12 First mode(A) reduced Second mode(A) 8 10 significantly at 8 6 stage-2 in which the 6 4 shear walls in the 4 2 longitudinal (East2 0 West) direction 0 Stage-1 Stage-2 Stage-3 Stage-4 Stage-5 Stage-6 Stage-7 Stage-1 Stage-2 Stage-3 Stage-4 Stage-5 Stage-6 Stage-7 were removed. The Different renovation stages Different renovation stages natural frequency reduction for first (a) (b) translational mode Fig. 5 Natural frequencies of the building obtained from the experiment and finite element model in in the longitudinal (a) longitudinal(East-West) direction and (b) transverse(North-South) direction (E: Experimental; A: Analytical) (East-West) direction from stage-1 to stage-2 was found 50% in the analytical results and 30% in the experimental results, and reduction in second translational mode natural frequency in the longitudinal (East-West)direction, from stage-1 to stage-2, was 33% in both experimental and analytical results. This reduction in natural frequencies may be attributed to the reduction in stiffness of the building in the longitudinal (East-West) direction after removing shear walls. When the renovation started adding new frames to the building as shown in Fig.2, the natural frequencies of the building in the longitudinal direction increased as shown in Fig.5 (a). CONCLUSIONS Dynamic characteristics of the building, i.e.,natural frequencies and mode shapes were identified by finite element modeling. Results obtained from finite element models were in reasonable agreement with those obtained from ambient vibration measurements. Changes in the dynamic characteristics of the building due to changes made in the structural system of the building during the renovation were observed from both finite element model as well as experimental results. Effect of shear wall, removed during the renovation, on the dynamic characteristics of the building was found significant in the longitudinal (East-West) direction of the building. Soil-structure interaction observed in the building from the experimental results can be incorporated in analytical model of the building by considering one additional storey. REFERENCES Brownjohn, J.M.W., Pan T.C. and Deng X.Y. Correlating dynamic characteristics from field measurements and numerical analysis of a high-rise building, Earthquake Engineering and Structural Dynamics, 29, 2000,pp.523543 Gazetas,G., Foundation Vibrations, Foundation Engineering Handbook By Hsai-Yang Fang, Van Nostran Reinhold, second edition, January 1991. Peeters, B., Maeck J. and Roeck, G.D. Vibration-based damage detection in civil engineering: excitation sources and temperature effects, Smart Materials and Structures, 10,2001,pp.518-527.
