Modeling the dynamic behavior of dam-reservoir-foundation systems considering generalized damping. Development of a 3DFEM state formulation

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1 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 Porto, Portugal, June - July 4 A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.) ISSN: -9; ISBN: Modeling the dynamic behavior of dam-reservoir-foundation systems considering generalized damping. Development of a DFEM state formulation Oliveira S., Silvestre A. Espada M., Câmara R. Concrete Dams Department, Laboratório Nacional de Engenharia Civil, Av. do Brasil, 7-66 Lisboa, Portugal soliveira@lnec.pt, asilvestre@lnec.pt, mespada@lnec.pt, romano@lnec.pt ABSTRACT: The safety control of large structures under dynamic loads, involving observation data and numerical modeling, is now one of the challenges being faced by structural engineering. Structures as large concrete dams involving water-structure dynamic interaction may present non-stationary vibration modes, which cannot be simulated by simple models based on the hypothesis of classical damping of Rayleigh type (proportional to the global mass and/or stiffness matrices). In order to take into account the existence of non-stationary vibration modes, a D finite-element model was developed in MATLAB for modeling the dynamic behavior of dam-reservoir-foundation systems, using a state formulation that enables the consideration of the generalized damping hypothesis (non-proportional to mass and stiffness global matrices). This model also allows to separate the dam vibration modes from the reservoir vibration modes, through the computation of the kinetic energy of each mode related with the dam body. In this paper is presented the case of Cabril dam, the highest Portuguese arch dam (6 years old; m high; horizontal cracking near the crest). The data from a long-term dynamic monitoring system that was installed in this dam by LNEC in 8, is analyzed using modal identification techniques and a comparison with the numerical model results is performed in order to study the evolution of natural frequencies, modal damping, and mode shapes. Finally the developed DFE state space model is used to estimate the time response of Cabril dam to a seismic accelerogram with a peak ground acceleration of about.g. KEY WORDS: Long-term dam dynamic monitoring; modal identification; deterioration; seismic monitoring. INTRODUCTION The complexity of the dam-reservoir-foundation geometry, the presence of different types of discontinuities, the waterstructure-foundation interaction ( [], []) the influence of thermal and water level variations, the development of deterioration and damage processes over time and the occurrence of exceptional events such as major floods or earthquakes ([], [4]), makes the structural safety control of large dams an activity that requires a continuous updating, both in terms of equipment for measuring, transmission, and storage of the data, and in terms of computer applications to support the automation process of collecting, processing, analysis and management of all information required to the safety control. Regarding the safety control of large dams, the continuous monitoring vibration systems have been referenced as being systems of great interest to the measurement of the dam dynamic response under both ambient excitation and seismic actions. As such, with these systems it s possible to: i) Measure the dam dynamic response under ambient excitation with the purpose of obtaining experimental values of natural frequencies (for different reservoir water levels) and of the corresponding mode shapes (using few, accurately placed sensors; between and sensors might be enough) as well as modal damping; ii) Measure the dam dynamic response under seismic actions in order to obtain experimental values about the amplitude of the seismic vibrations at various points of the dam foundation and about the amplitude of the dam body vibrations (for several earthquakes and for different reservoir water levels); All the agents involved in the design, construction, management and safety control of large dams have come to recognize the interest and the potential to dam safety control of the aforementioned dynamic monitoring systems (Figure ) This recognition is closely related to the technological advancements on the equipments for measuring vibrations (sensors, cables, digitalizes, computers, ) and on the software for data processing. However, and despite the relatively low cost, the investment in such dam vibration monitoring systems has not yet generalized. One of the main reasons for the delay in this investment is connected to the fact that the companies that provide the equipments for vibration measurement, aren t presenting full solutions that include all the software needed for automatic analysis of the gathered data and for automatically sending synthesized results (to the technicians in charge of the dam safety control). In this paper, the main guidelines for the innovation effort that still needs to be done will be presented. The goal is contributing to the installation of these monitoring vibration systems in the vast majority of large dams, especially those located on seismic regions. On this innovation effort, it stands out the need of developing software for: i) Automatic modal analysis adapted to the case of damreservoir-foundation systems (complex modes are currently identified); 699

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 ii) Automatic analysis of the measured seismic response; iii) The automatic comparison between experimental modal

seismic actions taking into account the measured experimental results.

The main objective of these tests is the health and seismic monitoring, but they have also been used in order to obtain experimental information to calibrate and update existing numerical models.

Based on recent experience of Cabril dam dynamic analysis it was concluded that the consideration of finite water elements in the reservoir and joint FE (finite elements) to simulate the

SPECTRAL ANALYSIS Wave Wave Wave 9 Wave 8 Wave 7 Wave 6 Wave Wave 4 Wave Wave Wave Mean value a(t) t Figure.Integrated use of dynamic monitoring data, modal identification methodologies and FE models.

2 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 ii) Automatic analysis of the measured seismic response; iii) The automatic comparison between experimental modal analysis results and Finite Element Models of Dam-ReservoirFoundation systems (state formulations should be used in order to simulate generalized damping); iv) Modeling the dynamic dam behavior under seismic actions taking into account the measured experimental results. In what concerns the dynamic behavior of concrete dams it should be mentioned that it has been observed using forced and ambient vibration. The main objective of these tests is the health and seismic monitoring, but they have also been used in order to obtain experimental information to calibrate and update existing numerical models. Figure. ModalId. interface. Based on recent experience of Cabril dam dynamic analysis it was concluded that the consideration of finite water elements in the reservoir and joint FE (finite elements) to simulate the water-structure interface is an adequate solution for the numerical analysis of the seismic behavior of damreservoir-foundation systems. SPECTRAL ANALYSIS Wave Wave Wave 9 Wave 8 Wave 7 Wave 6 Wave Wave 4 Wave Wave Wave Mean value a(t) t Figure.Integrated use of dynamic monitoring data, modal identification methodologies and FE models. The Automatic Data Acquisition System (ADAS) installed in Cabril dam, for vibration continuous monitoring (Figure ), allows dynamic data storage in the form of binary files with a sample rate of Hz, that are automatic analyzed using modal identification techniques (based on frequency domain decomposition methods). The results are presented graphically and recorded in.dxf file format for easy visualization. The time evolution of the identified modal parameters (natural frequencies, mode shapes and modal damping) can be compared with numerical results from finite element models []and/or discrete element models []. 7 DYNAMIC BEHAVIOUR OF DAM-RESERVOIR-FOUNDATION SYSTEMS. MODELING AND MONITORING The interest of ADAS for continuous monitoring of dam dynamic behavior depends not only on the hardware but also depends greatly on the potentialities of the software used for the automatic data analysis. So it is fundamental to develop software for data analysis automation that allows generating and/or updating, every hour, synthetic information under graphical form to be used by the engineers and other technicians of the staff in charge of the dam safety control. With that graphical information it should be easy to analyze the temporal evolution of the main parameters and variables that characterize the dam dynamic response: modal parameters, water level, maximum accelerations, acceleration spectra, etc. This software should include computational modules that allow the detection of special events (earthquakes, civil works nearby the dam site, hydraulic discharges, etc.) and the detection of abnormal structural changes throughout the comparison of the dynamic monitored response (analyzed by modal identification) and the dam response predicted by numerical modeling and by means of statistical models for effects separation ( []) In the numerical modeling, it should be considered the damreservoir interaction and the hypothesis of generalized damping (not proportional to the mass and stiffness global matrices). So, it was developed a DFE program, using MATLAB, named Dynamic State Space Analysis (DySSA.) based on a state space formulation (Figure ).

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 Figure. DySSA. interface. In DySSA.

Physically, these complex values correspond to the existence of non-stationary modes.

atan(im(φjn)/re(φjn)) [6]. From the modal decomposition of the state matrix, the main complex vibration modes are identified.

structure. CABRIL DAM Structural description Cabril dam (Zêzere river, Portugal) is a sixty year-old double curvature arch dam (see Figure 4), that is the highest Portuguese dam ( m). Figure 4. Cabril Dam.

3 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 Figure. DySSA. interface. In DySSA. it was adopted distinct damping coefficients between the reservoir, dam and the foundation. The eigenvalues λn of the state matrix and the eigenvectors φjn are complex values. Physically, these complex values correspond to the existence of non-stationary modes. Through this values we can extract the four most important modal parameters: i) natural frequency ωn= λn ; ii) modal damping, ξn=-re(λn)/ωn; iii) amplitude φjn ; and iv) phase angle atan(im(φjn)/re(φjn)) [6]. From the modal decomposition of the state matrix, the main complex vibration modes are identified. The modes associated to the reservoir are separated from the ones associated to the dam [7] using the concept of kinetic energy of each vibration mode using the DOF (degrees of freedom) of the solid structure. CABRIL DAM Structural description Cabril dam (Zêzere river, Portugal) is a sixty year-old double curvature arch dam (see Figure 4), that is the highest Portuguese dam ( m). Figure 4. Cabril Dam. In this dam significant horizontal cracking occurred near the crest (Figure ) since the first filling of the reservoir, and a concrete swelling process was recently detected; the water level presents important variations along the year. Figure. Cabril dam cracking distribution at downstream face. Evolution from 97 to 98 [7].. Dynamic Monitoring of Cabril dam In what concerns the monitoring system, although it is quite complete, it should be noticed that only the dynamic monitoring component is automated, since 8, with the financial support of the Foundation of Science and Technology (FCT-PNRC National Plan for Scientific Reequipment) and EDP. This system is composed by triaxial, accelerometers and sixteen uniaxial accelerometers (radial direction) as it can be seen in Figure 6, allowing for continuous measurement of accelerations with a sample rate of Hz. Figure 6. Main components of the continuous dynamic monitoring system [8]. The Figure 7 shows the spectrum corresponding to the measured accelerogram on 6 November, between h and h, with the water level at 64. m (power groups off). These spectrums were computed for each hour (over acceleration records of 6s, originally with a sample rate of 7

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 Hz; the analysis was performed after decimate to Hz (taking average values on decimation intervals), by averaging

-. Hz, it can be clearly identified two peaks at the frequencies:. and.4hz, both associated to the intake tower dynamic behavior[9]. At the frequency range of. -.

Frequency.6Hz.. Time(s).7 Frequency.7Hz Frequency 4.6Hz.. Time(s).7 Point Point 4 Point Point 6.. Time(s).7 Point 7 4 6 78 9 Figure 9. Mode shapes automatically identified. 4 6 64. m.

4 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 Hz; the analysis was performed after decimate to Hz (taking average values on decimation intervals), by averaging using time windows of s and Tukey windows superposed at /. From these spectrum we can see that high amplitude vibrations occur near the center of the crest gallery (point ). At the frequency range of.-. Hz, it can be clearly identified two peaks at the frequencies:. and.4hz, both associated to the intake tower dynamic behavior[9]. At the frequency range of. -. Hz, it can be clearly identified two important peaks at the frequencies.6 and.7hz. In this case, due to the vibration conditions imposed, it was identified that both peeks are anti-symmetric modes. Frequency.6Hz.. Time(s).7 Frequency.7Hz Frequency 4.6Hz.. Time(s).7 Point Point 4 Point Point 6.. Time(s).7 Point Figure 9. Mode shapes automatically identified m. As was said before, it was developed a program in MATLAB of finite elements, named DySSA., to study the dynamic analysis of the tridimensional system ReservoirDam-Foundation using the state of space formulation. The finite element mesh, as it is represented in the Figure, is composed by 78 isoparametric elements of points (94 for representation of the dam and foundation and 84 for the reservoir), and 76 joint elements (46 to simulate the interface dam-reservoir and to simulate the horizontal cracking on the dam s body). Point: - Amplitude ((ms ) /Hz).9e-8 Numerical modeling of Cabril Dam. Comparison with experimental results.e-8.4e-8 7.e-9 4 Frequency(Hz) Figure 7. Spectrum of the accelerations at point. For automatic peaks identification it was used a singular value decomposition (SVD) of the SPD (Spectral power density) matrix computed after the application of the random decrement (RD) technique to filter the acceleration time histories measured at the 6 points (Figure 8). Figure. Cabril dam. Finite element mesh of the system dam-reservoir-foundation. Amplitude.7 In the interface between water-concrete it was admitted a normal stiffness equal to the Kv of the water and a shear modulus null. In this model it was considered one Young s modulus for the concrete at.gpa, a Poisson's ratio of. and one specific weight of 4KN/m (Figure )... Frequency(Hz) 4 Figure 8. Spectrum of the st singular value of SPD matrix. In Figure 9. Mode shapes automatically identified.figure 9 the mode shapes automatically identified are presented using a time representation for five the central points at the crest gallery. 7

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 m w= Water K v =,7 GPa G = ton/m cα w, cβ w Interface Water-concrete m =, c cα c, cβ c ton/m Concrete E =,GPa b νb =,

5 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 m w= Water K v =,7 GPa G = ton/m cα w, cβ w Interface Water-concrete m =, c cα c, cβ c ton/m Concrete E =,GPa b νb =, K Crack K= τ,7 GPa (joint elem.) Contraction joints ccrack t Ambient and operational excitation Crack N=,7 GPa Crack cα f, cβ f Foundation E f = ~ E c ν f = ~ ν c m f= =x( ~ cα c, cβ c ) x x a ~ S Seismic accelerogram x T t Figure. Dam-Reservoir-Foundation system. In what concerns the damping coefficients used in the Rayleigh hypothesis, it was considered c α =. and c β =7.x - for the water, c α =.; c β =x -4 for the foundation and c α =.; c β =x - for the dam body. For the interface elements used to simulate the cracking it was used c β =x -. In Figure are represented the Rayleigh curves for each material (water, concrete and rock foundation). ξ (%) 4 Dam Foundation Reservoir 4 Frequency (Hz) Figure. Rayleigh curves for c α and c β values used in FE model (different values are used for dam, foundation and reservoir) [7]. Figure. Spectra and main mode shapes of Cabril dam computed with DySSA. (water level at 6 m) [7]. In Figure 4 it can be seen the evolution of the frequencies from to 7/Nov/. The modal frequencies obtained from DySSA. fit well the frequencies of the main spectral peaks obtained from the acceleration measurements. The modal frequencies for different water levels computed with DySSA. are represented by colored lines passing through the bands of points representing the frequencies of the peaks experimentally identified for different water levels. It is also interesting to see that in the frequency range.7- Hz there are two distinct point green bands, which show a good agreement with the results obtained from DySSA.. Since the intake tower is not considered in the FE model the peaks corresponding to the main vibration modes of the tower could not be detected with the numerical model [6] In Figure are presented the spectra of the computed displacements at five central points located in the upper zone of the dam and the three first modal configurations (corresponding to the three first peaks). As it can be seen these peaks are in the range.hz - Hz, as expected. The first mode is anti-symmetric at the frequency of.64hz while the second and third modes are symmetric at frequencies of.8 and.84hz. 7

6 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 Frequency(Hz) 4 Peak Frequencies Automatically Identified //-7// Legend Symmetric Anti-symmetric Influence lines (DySSA) Amplitude (m/s ) Accelerogram (downstream->upstream) Time(s) Figure. Accelerogram (downstream-> upstream). Figure 6 shows the radial displacement response over time at the top of the central cantilever. The maximum peak displacement is.976 mm to upstream and.788 mm in the opposite direction (downstream). 9 6 Displacement (downstream->upstream) Water level(m) Figure 4. Peak frequencies automatically identified between and 7Nov. Comparison with the results of DySSA.. 4 SEISMIC RESPONSE SIMULATION The measured dam dynamic response under ambient/operational excitation was used to evaluate the main modal characteristics which were used to calibrate a FE model. This model, considering full reservoir, was then used to perform a seismic computation considering a seismic accelerogram (Figure ), measured in Alcobaça (Portugal) in 999. The amplitude of this accelerogram was adjusted for a maximum peak acceleration of m/s (.g) which agrees with the amplitude of the OBE (Operating Basis earthquake) prescribed for the dam location. It was performed a time domain analysis considering a state space formulation in modal coordinates (complex values) []. The accelerogram was applied in the downstream upstream direction and in vertical direction affected by a factor of /. Amplitude (mm) Time (s) Figure 6. Seismic displacement response at the top of the central cantilever. Figure 7 shows the acceleration response at the same point. The maximum peak acceleration occurs at 4.4s in the upstream direction with an amplitude of. m/s (.g), meaning that the amplification ratio is about. (for Pacoima dam a value of about. was computed for half full reservoir []). Amplitude (m/s ) Acceleration (downstream->upstream) Time: 4.4 s a:. m/s Time (s) Figure 7. Seismic acceleration response at the top center of the dam. 74

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 Figure 8 presents the deformation of the dam for the upstream maximum displacement. It occurs at 6.

The tensions are the red lines with a maximum of about.6 MPa. The compressions (blue) presents the maximum value of about.7 MPa (center near the crest).

Figure 8. Maximum deformation of the dam (upstream direction). Figure 9. Principal stresses in the dam body (upstream maximum displacement).

CONCLUSION For the vibration monitoring system installed at Cabril dam, the equipments and the software were described.

It was used a D FE model of the system dam-reservoirfoundation taking into account the water-structure interaction using a state formulation.

7 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 Figure 8 presents the deformation of the dam for the upstream maximum displacement. It occurs at 6.s (as can be seen in Figure 6) with a maximum amplitude of about mm in the top central cantilever. For the same instant the principal stresses are shown in Figure 9. The tensions are the red lines with a maximum of about.6 MPa. The compressions (blue) presents the maximum value of about.7 MPa (center near the crest). At this instant the principal stresses are shown Figure. The maximum compressions are of about.6 MPa and maximum tensions of about. MPa. Figure. Principal stresses in the dam body (downstream maximum displacement). Figure 8. Maximum deformation of the dam (upstream direction). Figure 9. Principal stresses in the dam body (upstream maximum displacement). Figure presents the deformation of the dam for the downstream maximum displacement. Figure. Maximum deformation of the dam (downstream direction). CONCLUSION For the vibration monitoring system installed at Cabril dam, the equipments and the software were described. Modal identification software as well as the Finite Element software for D dynamic computations were developed using MATLAB (the graphical interface was written using GUIDE). It was used a D FE model of the system dam-reservoirfoundation taking into account the water-structure interaction using a state formulation. This model was adjusted using data from modal identification and afterwards, it was used to simulate the seismic behavior of the dam (the reservoir was discretized with water FE using a displacement formulation as well as the dam body and the foundation; the water-structure interface was simulated using joint FE as well as the horizontal cracking below the crest). From the safety control point of view, the developed software has the advantage of allowing the integrated use of modal identification techniques and FE models in an automatic manner. In Cabril dam the installed system hardware (accelerometers, digitizers, data concentrators and computer) and software for acquisition (CabrilAquis), management and analysis (ModalId.) allows the automatic detection of small variations on peak frequencies, and the identification of the natural frequencies, modal damping coefficients and mode shapes. The presented Cabril dam results showed that the use of Automatic Data Acquisition Systems (in this case the ModalId.) for Continuous Dynamic Monitoring of Large Arch Dams allows to gather very relevant information to the characterization of the dynamic behavior of dam-reservoirfoundation systems. Namely, with this kind of systems it is possible to identify with great accuracy the time variation of the spectral peak frequencies corresponding to the main vibration modes of the dam-reservoir-foundation system as well as the mode shapes. The presented results, regarding a 4 day period ( to 7 Nov), show that the aforementioned spectral peaks have 7

8 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 4 relative amplitudes which can vary significantly with the excitation conditions and water level. REFERENCES [] S. Oliveira and P. Mendes, "Development of a Cabril Dam Finite Element Model For Dynamic Analysis Using Ambient Vibration Test Results," III ECCSM, Lisbon (LNEC), 6. [] J. Lemos, S. Oliveira and P. Mendes, "Analysis of the Dynamic Behaviour of Cabril Dam Considering the Influence of Contraction Joints," in 7th European Conference on Structural Dynamics, Univ. de Southampton, 8. [] H. Chen, "On the obstacles and way to assess the seismic catastrophe for high arch dams. Science in China Series E: Technological Sciences," in Vol., Supp. I: -9., 7. [4] M. Wieland, "Features of seismic hazard in large dams projects and strong motion monitoring of large dams," 9. [] S. Oliveira, M. Espada and R. Câmara, Long term dynamic monitoring of arch dams. The case of Cabril dam, Portugal, Lisboa: WCEE,. [6] S. Oliveira, A. Silvestre, M. Espada, Câmara and R., "Monitoring and Modeling of Dynamic Behavior of Concrete Dams. Dam-reservoirfoundation interaction," Porto,. [7] A. Silvestre, "Modeling of the Dynamic Behavior of Dam-Foundation- Albufeira Systems. State spaces formulation with generalized damping," Thesis (in Portuguese) ISEL, Lisbon,. [8] S. Oliveira, P. Mendes, A. Garret, O. Costa and J. Reis, Long-term dynamic monitoring systems for the safety control of large concrete dams.the case of Cabril dam, Portugal: 6th International conference on dam engineering,. [9] M. Espada, P. Mendes and S. Oliveira, "Observation and analysis of the dinamic behaivor of Cabril dam intake tower.," vol. 9, no. Mecânica Experiemental,. [] R. Câmara, "A method for coupled arch dam-foundation-reservoir seismic behaivour analysis," Earthquake engineering & structural dynamics, vol. 9 Number 4, pp ,. 76

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