5.1 Dam characteristics and installed SSHM system
Cabril dam, the highest dam in Portugal (Fig. 6), has been in operation since 1954. Located on the Zêzere river, it is a 132 m high double curvature arch dam, with a 290 m long crest, at the elevation 297 m. The central section maximum thickness is of about 20 m at the dam base, and the minimumthickness is 4.5 m, about 10 m below the crest (see central section in Fig.6). Regarding the foundation, Cabril dam was constructed on a good quality granite rock mass. The reservoir water level usually ranges from a minimum at el. 265 m to the maximum storage level at el. 295 m. Concerning the appurtenant works there is a reinforced concrete intake tower upstream of the dam, which is connected to the crest of central cantilever through a concrete walkway, with a joint in the dam-tower contact.
In what concerns the dam’s structural health, it is worth mentioning that horizontal cracking was observed at upper part of the downstream face, around el. 280 m to 290 m, during the first filling of the reservoir. Also, a concrete swelling process was detected in the late 1990s.
The continuous dynamic monitoring system of the Cabril dam was conceived and implemented as part of a research project(Oliveira, 2002), financed by the FCT and supported by EDP, carried out in collaboration with the Department of Concrete Dams and the Scientific Instrumentation Center of LNEC.The development of this system(Mendes, 2010) involved the design of the monitoring scheme, the assembling and installation of all equipment (optical fiber networks, data concentrators, accelerometers, etc.), and finally the development of software for automatic data processing, management, and analysis. The goal of this SSHM system was to continuously monitor the dam’s dynamic behavior over time in normal operating conditions and to measure the dam response during seismic events.
Therefore, the monitoring scheme (Fig. 7) was outlined to record accelerations at the upper part of the dam structure and near the dam-rock interface, using 16 uniaxial (EpiSensor ES-U2) and 3 triaxial (EpiSensor ES‑T) force balance accelerometers from Kinemetrics, Inc. (https://kinemetrics.com/). The uniaxial sensors measure accelerations in the radial direction: 9 are located in the upper gallery, at el. 294 m, below the crest, and 7 are positioned in the second gallery, at el. 274 m, below the cracked zone. As for the triaxial sensors, one is installed in the upper gallery, in the central section, while the other two are located inside the dam base gallery, in both banks, around el. 274 m. Aiming to achieve a high dynamic range(Mendes, 2010), to enable the accurate measurement of low amplitude vibrations, due to ambient/operational sources or lower intensity earthquakes, and high amplitude vibrations, cause by strong earthquakes, full-scale recording ranges of ± 0.25g and of ± 1g were prescribed for uniaxial and triaxial sensors, respectively. In what concerns data acquisition and transmission, all 25 channels are connected to a modular system, composed by an optical fiber network and four data acquisition units that gather all recorded data, which is then sent to the central computer server installed in the office at the dam’s power plant. Basically, 25 acceleration time histories are recorded, in 24 bit and at a sampling rate of 1000 Hz, collected, and stored in the central server, every hour. The system was not active during some periods over the first decade of monitoring, due to either malfunctions or damages in sensors and/or data acquisition units. However, the several visits for maintenance and repairs, the system has been fully operational since June 2008.
In order to ensure a proper operation of the system and to provide useful information on Cabril dam’s behavior, the SSHM system was complemented with the installation of specific software, namely for collecting and processing measured data, automatic data management and analysis, including the module for detection of vibrations induced by seismic events (DamSeismicVibID), and for automatic modal identification of dams (DamModalID).5
5.2 Numerical Model of Cabril dam
The linear and non-linear dynamic behavior of Cabril dam is simulated using the program DamDySSA and the 3DFE model of the dam-reservoir-foundation system presented in Fig. 8. The dam concrete and the foundation rock are isotropic materials, considering Young’s modulus E = 25 GPa and Poisson’s ratio v = 0.2, assuming a factor of 1.3 applied to E for dynamic calculations. The water in the reservoir is a compressible fluid with a pressure wave propagation velocity of cw = 1440 m/s (mean temperature of around 15º C). The existing cracking band is simulated as a single horizontal crack, incorporated by introducing duplicate notes and joint elements at el. 285 m. However, the current model does not include the intake tower.
For linear dynamic analysis, the concrete has linear behavior (no damage) and a version of the model without any joints is used. As for non-linear seismic analysis, the non-linear behavior of concrete up to failure is simulated using a strain-softening constitutive damage model, considering tensile strength ft = 3 MPa and compressive strength ft = - 30 MPa; moreover, all vertical contraction joints and the surface along the dam-foundation interface are incorporated into the model, considering appropriate normal and shear stiffness values and stress-displacement laws to simulate opening/closing and sliding movements.
5.3 Modal Analysis. Evolution of natural frequencies over time
This section presents results on the dynamic behavior of Cabril dam in normal operating conditions, under ambient/operational vibrations, for the monitoring period between December 2008 and December 2020. The natural frequencies and modal configurations identified using DamModalID are presented and compared with numerical results obtained with DamDySSA. The aim is, on the one hand, to evaluate the influence of reservoir level variations on the dynamic behavior of the dam-reservoir-foundation system, and, on the other hand, to show how this study can be of value for vibration-based damage detection.
Fig. 9 shows the evolution of the identified natural frequencies for the first five vibration modes of Cabril dam, for the whole monitoring period (2008-2020), with a reservoir level variation from el 261.5 m, 31.5 m below the crest, to el. 295 m, 2 m below the top, representing a maximum 33.5 m variation. Based on these results it is possible to see that the dynamic properties of the dam-reservoir-foundation system and thus the dynamic behavior the dam are clearly affected by the water level in the reservoir, given that the frequency values follow the water level variations over time: the higher the water level, the higher the global mass of the system, the lower the frequency values. This effect is more noticeable for the modes with higher natural frequencies. As for thermal variations, the air temperature amplitude of only around ± 8º over the year, and thus its influence in the dynamic response of the dam is not considered here.
Furthermore, the modal identification results show the frequencies associated with the operation of the energy production groups, with rotation frequency of 3.57 Hz, as well as the detection of modes that are most likely associated with the vibrations of the intake tower – for lower water levels, the tower leans against the dam, inducing a certain dam-tower dynamic interaction(Mendes & Oliveira, 2009) while for higher water levels the joint opens and tower and dam are separated.
The frequencies and modal configurations, estimated from the accelerations measured on June 16, 2018 (17h-18h), and on May 4, 2019 (4h-5h), are also presented. The first and fifth modes are antisymmetric, while the second and third modes are symmetric. Also, it is worth noting that the configuration of the fourth mode is clearly influenced by the horizontal cracking in the dam, resulting in the oscillation of the upper part of the dam.
Fig. 10 presents the comparison between the identified (circles) and computed (lines) natural frequencies over time, as well as the numerical frequency values and mode shapes calculated for reservoir levels at el. 285 m and 293.5 m. Overall, this comparative analysis shows that there is a good agreement between experimental and numerical natural frequencies for the first five vibration modes, especially for higher water levels (given that the dam-tower interaction is not as significant). Regarding modal configurations, the shapes of modes 1 (antisymmetric), 2 (symmetric), and 3 (symmetric) are well reproduced by the model, while for modes 4 and 5 the mode shapes are swapped.
The results achieved in this application study allowed to show the usefulness of the SSHM installed in Cabril dam and the potential of the 3DFE program DamDySSA for simulating the dynamic response of the dam-reservoir-foundation system. Nevertheless, additional studies are proposed in the future to better understand the phenomena associated with the intake tower and with the horizontal cracking.
In order to show how the combined use of information extracted from continuous vibrations monitoring and of numerical results can be applied for vibration-based damage detection and hence to evaluate structural integrity of dams, an additional comparison is provided next (Fig. 11). The identified natural frequency values of the first mode (in red) are compared with the computed frequencies (in blue), using a) a linear reference model, without concrete damage, and b) a test model that simulates the scenario of evolutive damage during the period under analysis (2008-2020), considering a gradual damage variation between 0 and 5% over the whole dam body. Based on these results, it can be noted that the identified frequency values based on recent data are similar to the values in the early monitoring period. Furthermore, the differences between the identified frequencies and the values computed with the reference model without damage are the same (for similar water levels) over the whole monitoring period. Additionally, the frequency curves computed for a scenario of evolutive damage start to diverge from the identified frequencies. Therefore, it is possible to conclude that Cabril dam’s structural integrity and thus its dynamic behavior has not been affected by the existing deterioration phenomena.
5.4 Measured seismic response
In this section theanalysis of the dynamic response of Cabril dam during a seismic event is presented. The seismic acceleration time histories recorded with the SSHM systemare compared with the numerical accelerations computed with DamDySSA4.0, in order to investigate how to simulate the measured dam response, namely, in order to investigate theaccelerations amplification from the dam-rock surface to the crest center point, and the required damping ratios to be used in the numerical model.
The seismic response of Cabril is analyzed for an earthquake of magnitude 4.6 that occurred on September 4, 2018, with epicenter in the Peniche abyssal region (off the coast of Portugal), at 205 km from the dam. The seismic waves hit the dam from the west-northwest, approximately in the cross-valley direction. On that day, the water level was at 281.2 m, 15.8 m below the crest. This earthquake originated low amplitude vibrations in Cabril dam, from 1 mg to 4 mg. As expected, the greater accelerations were recorded at the central upper part of the structure. The peak ground acceleration at the dam-rock interface (1.31 mg) was recorded with the triaxial sensor at the right bank, while the maximum acceleration in the dam body (3.62 mg) was measured at the top of central section, both in the upstream downstream direction – the amplification factor for accelerations (from the RB foundation to the crest center) was of around 2.8.
The FE seismic simulations were conducted using the previously shown numerical model, considering linear behavior, the reservoir level at el. 281 m, and using the accelerations recorded at the right bank as the uniform seismic input. Fig. 12 shows the comparison between measured and computed accelerations at the upper gallery, in the central section of the dam, in the cross-valley, upstream-downstream, and vertical directions: these results show that there is a good fit with the computed accelerations in the upstream-downstream direction, while in the cross-valley and vertical directions the response is clearly overestimated. To achieve this results it was necessary to use a damping ratio of about 10% around the frequency band 2-3 Hz (first vibration modes), which is an unusually high value for an arch dam(Chopra & Wang, 2012; Proulx & Darbre, 2008; Robbe et al., 2017).
The provided results showed not only the reliability of Cabril dam’s SSHM system to measure vibrations during seismic events, even those of lower amplitude induced by earthquakes with epicenters at a great distance from the dam site, but also the interest of seismic records measured on site to help in the validation and calibration of numerical models used for dam seismic behavior simulation. However, this comparative study also raised important questions on the numerical modelling of the linear seismic response of Cabril dam, namely in what concerns the need to use such a high damping value in order to reproduce the measured response. In the case of this dam, this difficulty may in fact be related to the use of an inadequate seismic input. In fact, it was used as input a seismic accelerogram measured in dam body near the RB upper dam-foundation interface. At the Cabril dam, an accelerometer has not yet been installed on the foundation, in the central section of the dam's base. In this context, in order to improve the characterization of the seismic action and allow a better understanding of the seismic behavior of the dam, it is planned to install a new triaxial accelerometer in the Cabril dam, on the foundation near the base of the dam, at the bottom of the valley.
5.5 Non-linear seismic response. Safety assessment based on Endurance Time Analysis
This section presents the most important results from a study on the non-linear seismic behavior of Cabril dam under intensifying seismic accelerations (Fig.13). , in order to evaluate the dam’s performance based on an Endurance Time Analysis(Estekanchi et al., 2004).Therefore, the tensile and compressive damage distributions are analyzed at increasing levels of excitation to assess seismic safety (Fig.14).
The numerical simulations were carried out using DamDySSA and the non-linear version of the model presented above, considering damage in concrete and joint movements. The seismic response was calculated for the dynamic load combination involving the dam’s self-weight (SW), the hydrostatic pressure for full reservoir (HP297), and an intensifying seismic load (SeismicL) applied in the upstream-downstream direction. For seismic input, an ETA acceleration time history provided in (Salamon et al., 2021), with increasing peak accelerations (ap) from 0 to 1.5g (at 15 s), was used (Fig. 13).
In what concerns the safety assessment, an empirical evaluation of the dam’s seismic performance was considered. In this study, the seismic safety was verified at the end of each second of the numerical simulation, based on the damage distributions at both upstream and downstream faces, and along the thickness, until an endurance limit was reached. The criterion adopted here respects to the damage extension, particularly along the thickness of the dam’s cantilevers: the occurrence of considerable areas of the dam in which tensile damage propagates across the whole thickness is considered inacceptable.
For the case of Cabril dam, the referred endurance limit was of 6 s (ap = 0.6 g), since that at this excitation level significant tensile damage stars to cover an extensive area of the downstream face(Fig. 14), which start to propagate along the thickness of some of the shorter, lateral cantilevers. there is an increase of tensile damage at the upstream face and that concrete failure starts to propagate from upstream to downstream in some areas of the upper part of the dam, even in the central cantilevers. However, it is worth emphasizing that compressive damages only appear after 10 s(ap = 1 g)., when the first concrete failure under compression occurs at the top of the central cantilevers, and increase progressively as shown in Fig.14, until 14 s (ap = 1.4 g).
In synthesis, the results of the non-linear seismic response of Cabril dam obtained with the Endurance Time Analysis allowed to conclude that Cabril dam presents a very good performance for high excitation levels, corresponding to peak ground accelerations that could perfectly be prescribed for seismic safety verification studies.The Cabril dam is capable of withstanding seismic accelerations 2.5 times greater than those defined for the Maximum Design Earthquake (MDE: ap = 0.2g) without severe tension damage and 7 times greater than that defined for the MDE without severe compressive damage (no collapse).