Dynamic Characteristics of a 17 th Century Church in Quito, Ecuador

Dynamic Characteristics of a 17 th Century Church in Quito, Ecuador Martin Turek (1) (1) Graduate Student Department of Civil Engineering University of British Columbia 2324 Main Mall, Vancouver, BC, Canada V6T 2E7 meturek@civil.ubc.ca Carlos E. Ventura (2) (2) Professor Department of Civil Engineering University of British Columbia 2324 Main Mall, Vancouver, BC, Canada V6T 2E7 ventura@civil.ubc.ca Patricio Placencia (3) (3) Professor Escuela Politécnica Nacional Quito-Ecuador P.O. Box 01-17-693 pplacencia@mail.com ABSTRACT This paper presents the results of a study on the ambient vibration analysis of a historical monument in Ecuador, South America. La Iglesia de la Compañía de Jesus [the Church of the Jesuit Order] was constructed over a period of 80 years, from the mid 16 th to the early 17 th century and is located in the capital city of Quito. Ecuador is located in a region of high seismic activity. To protect this historical monument from potential seismic damage, it was structurally retrofitted in the late 1990s. Vibration tests were performed on the church in 1998 and 1999, just prior to and immediately after the retrofit. In 2001, the church is still undergoing additional repair, and a more comprehensive series of ambient vibration tests was recently conducted by researchers of the University of British Columbia, Canada, and the Escuela Politécnica Nacional del Ecuador. Ambient vibration measurements were taken on selected locations on the overall structure, as well as local measurements on the major dome and other secondary elements. The church cross section was idealized as a portal frame. The modes of vibration in three orthogonal directions were obtained. The main dome and the cantilevered spire at the front of the church were instrumented and modelled separately. These experimental results are compared to a study that was conducted previously to examine the effect of a retrofit on a historic monument and to help confirm the appropriateness of the computer model representing the retrofitted structure. INTRODUCTION The city of Quito is located in the northern part of Ecuador, and is approximately 100 km from an active subduction fault. The region is subjected to a high level of seismic activity and many of the significant seismic events that have occurred affected Quito. La Iglasia de la Compañía (Figure 1) was built in the late 16 th century, and throughout its history has been subject to many of these events. There is much evidence of the damage caused by these events, and this evidence displays the performance of the structure, and reveals its weak points. The church was built using many of the common characteristics of the period, and even in churches built today. It was constructed using stone, brick masonry and adobe. The main walls and structure are built using a brick masonry support system with a stone façade. The arched roof and dome structures are made using an adobe-concrete material. All of the materials used in the original construction were intended to resist compressive forces only. For this reason, most of the damage inflicted on the structure during seismic loadings occurs in regions that have high tensile stresses. The church has been repaired many times throughout its history, and has undergone changes in terms of structure as well as additions and upgrades. The behaviour of the structure is also affected by the addition and modification of adjacent structures, which have appeared over time. In 1987 the church experienced a significant earthquake, which measured 6.9 on the Richter scale. The source was approximately 90 km away from the city. The ground motions were very small at the site, with peak accelerations of only 0.06 g. Even though there was a high attenuation of the motion, there was significant damage to the church. All of the cracking was featured in areas of high tensile stress. The external walls, the barrel arch, and the main dome were all damaged during the earthquake. The church has been partially repaired over the years after the earthquake, and in 1998, the structure was completely repaired by injection of grout material into the cracks. This was done to prepare the structure for an upcoming retrofit project, to begin in 1999. After the repair, the fundamental period of the structure was obtained from ambient vibration measurements, performed by a group of French engineers [1]. The church displayed a fundamental period in the transverse direction between 0.28 and 0.36 s. There were no mode shapes associated with these values due to the simplified nature of the testing. The retrofit project was begun in 1999, and shortly after it began the church was instrumented again. This time the period had shifted to being between 0.25 and 0.30 s. This increase in lateral stiffness of the structure is expected due to the upgrades. In 2001, researchers from the University of British Columbia were given the opportunity to perform a more detailed analysis of the structure, this time attempting to obtain mode shapes. DESCRIPTION OF THE STRUCTURAL SYSTEM One of the main features of the church is that the main longitudinal and lateral sections converge on a point to form the shape of a crucifix. This arrangement provides the structure with some ability to resist lateral loadings. This system requires adequate stiffness of the exterior walls because much of the lateral resistance will be developed by the torsional behaviour of the structure. 1259

This potential lateral system taken into consideration, it is important to note that these churches were designed to resist vertical loads only. As mentioned previously, all of the materials used in the construction of the church can only resist compressive forces. As a result, the effectiveness of any lateral resistance is dependent on the ability of the system to distribute loads in compression while minimizing the tensile forces. All of the major clear-roof sections throughout the church are covered by barrel-arches made of adobe. These do not perform well under lateral loads and will crack under small deformations. The church is rectangular in plan with dimensions of 22 x 70 m. The exterior walls are made of brick masonry, 600 mm thick. The front façade of the church is 18 m high to the top of the spire. The interior of the main section of the church features a long corridor with a barrel-arch ceiling extending along its length. On either side of this main corridor are two smaller arched corridors. This leads to a central section, which is capped by a large dome. This dome is a composite structure that has adobe-concrete arches meeting at a central cylindrical structure. In between the converging arches is a series of tiles. ambient vibration techniques. The ambient vibration system used for this experiment is based on concepts from the Hybrid Bridge Evaluation System [2]. The system uses a network of force balance accelerometers which capture relative measurements of the ambient level vibration that are present in the structure. The recorded data was acquired through a signal conditioner and A/D converter system (Kinemetrics VSS 3000), collected on a notebook computer using the DasyLab [3] software. All of the data was then processed using MathCAD [4] signal analysis programs. This allows for a quality assessment of the data, filter for the frequency range of interest, address any aliasing issues and decimate the data to the desired sampling rate. The processed data was then analysed through the ARTeMIS [5] extractor software program. This program offers frequency-domain and time-domain methods to determine the natural frequencies and corresponding mode shapes of the test subject. A spatial representation of the sensor locations throughout the structure is input to the program to infer the mode shapes. The frequency-domain technique is the Frequency Domain Decomposition method (FDD). This generates plots of the singular values of the spectral density matrix. These are used to isolate the natural frequencies of the structure. The time-domain technique is the Stochastic Subspace Iteration method (SSI). It consists of fitting a parametric model to the time series collected by the sensors. Using a specific representation of the transfer function the modal characteristics can be found. Figure 1. La Iglesia de la Compañía de Jesus VIBRATION TESTING To determine the modal characteristics of the church such as its natural frequencies and corresponding mode shapes, ambient vibration measurements were taken. Unlike forced vibration testing, the forces applied to a structure are unknown. The accelerations are measured for a long period of time to ensure that the modes of interest are sufficiently excited. This type of testing offers the unique opportunity to assess the characteristics of a more complex structure, such as the church presented here. The mode shapes are difficult to infer intuitively, and the behaviour is difficult to predict. With a minimum amount of labour and budget, the natural frequencies and mode shapes can be identified using Figure 2. ARTeMIS model of the church TEST DESCRIPTION The vibration measurements were performed on May 3, 2001. The opportunity arose to do a very limited test of the structure, with the desire to possibly capture some of its modal behaviour. The testing was limited due to time and labour constraints. At the time of testing the structure was undergoing a retrofit so it was impossible to place instruments in all of the desired locations. Six setups were needed, grouped into three components. The first component, which involved the first three setups, focused on the main portion of the church. This section begins at the front of the church and stretches back to the main dome section. The fourth test setup performs a brief examination of 1260

the main dome, the fifth setup examines the secondary dome and the sixth setup examines the small spire at the front of the church. For all of the test setups the same reference channel was used. It was located at the top of the barrel arch, at the west end of the main section. Setup 1-3 The first three setups were measured in three individual lines along the main section. Setup 1 measured motions primarily in the transverse direction along the outside wall on the north side of the church. Halfway along the main section, a tri-axial sensor was used which measured all three orthogonal directions. Setup 2 measured similar motions at the bottom edge of the barrel arch on the north side. Likewise it measured transverse only, except at the midpoint which measured all three orthogonal directions. Setup 3 again measured similar motions, along the top ridge of the barrel arch. The third setup added an additional measurement at the reference sensor location which confirms the data at that point. Figure 3 shows a plan view of the main section of the church illustrating the sensor locations for the first three tests. Figure 4. ARTeMIS Dome Model; Elevation and Plan Views Figure 5. Dome Instrumentation Setup; Plan View Figure 3. Main Section Setups Plan View Setup 4 The fourth setup examined in more detail the main dome structure. The intent was to determine the primary mode in the vertical direction, as well as any possible transverse modes. It may also be possible to observe a torsional mode about the central vertical axis of the dome. The same reference sensor was used from Setup 1-3, which allows the data to be combined with the first three setups in a global analysis. Five sensors were placed in total on the dome structure. Four were set tangentially at the opposite sides of the dome. One tri-axial sensor was placed near the top of the dome. Since this dome has a small tower at the top, it was not possible to place a sensor at the very top. Therefore it was recorded at the base of this small tower, on the south side. Figure 4 shows an elevation view and a plan view of the geometry used in the ARTeMIS model. Figure 5 shows a plan view of the instrument setup locations for the dome test. Figure 6 shows a picture looking east towards the main dome structure. Setup 5 The fifth setup measured a few points near the secondary dome, which is located west of the main dome structure. This allowed further identification of the transverse Figure 6. Main Dome Structure and torsional modes of the church. There were no points measured at the top of this secondary dome, so it was not possible to get vertical modes. An additional measurement was taken at the base of the spire at the front of the church. Setup 6 Setup number six tested a point at the top of the spire at the front of the church. The other channels (except for the reference) were disconnected for this setup. NATURAL FREQUENCIES AND MODE SHAPES The purpose of the ambient vibration tests performed was to identify the natural frequencies and mode shapes of the church. This type of testing is useful in circumstances where a complex structure is involved, and a clear expectation of the behaviour prior to testing is not available. 1261

The testing that was performed on the church determined the frequencies of several of the modes, as well as some of the fundamental mode shapes. Since the instrumentation was limited, it is not possible to clearly capture the higher modes of the church. This is the case on both the overall analysis and the dome analysis. In an ideal case, it is desirable to do a very high-resolution measurement of the church so that clear shapes of all the important modes are determined. This data is then used to update the finite element model, so that the physical properties used in the model are more closely related to the actual structure. In this case it was not intended to update the finite element model. Instead, the existing finite element model that was previously updated will be used to examine the modal behaviour of the structure and to interpret the partial results of the ambient vibration test. This is valid if the fundamental modes are similar, and the higher frequencies are comparable as well. instrumentation. These represent the most significant frequencies captured below 10 Hz. VIBRATION ANALYSIS RESULTS The results of the ambient vibration analysis displayed several mode shapes in every direction, as well as some localized mode shapes on various parts of the structure. The data was analysed using three separate models. The first model contained the main section of the church only (Figure 3), and this was done to examine the transverse behaviour of the main cross-section of the church, and also to examine the behaviour of the barrel-arch section. The second model was of the main dome only (Figure 4), and this was done to isolate the results from the rest of the structure, and considering that the dome would vibrate at a higher frequency, to more closely examine the frequency range of interest. The third model was of the overall structure (Figure 2), and this contained the main section, the main dome, as well as some extra measurements located west of the main dome. The first model displayed several partial mode shapes based on six distinct peaks on the power spectrum obtained (Figure 8). A fundamental transverse mode appeared at 3.25 Hz (Figure 7) in a damped set of peaks on the spectrum. There is a cluster of 4 modes that appears around 5 Hz. These modes are not well defined graphically in the ARTeMIS model due to the lack of instrumentation. The first two peaks of the cluster occurred at 4.6 and 4.9 Hz, and both have a similar vertical/transverse motion of the barrel-arch. It is difficult to distinguish between these two possible modes. The next peak occurs at 5.1 Hz and displays a predominant transverse motion in the barrel-arch. The fourth peak of the cluster occurs at 5.3 Hz, and displays predominant motion in the transverse direction of the main structure. The barrelarch does not move very much in this possible mode. In order to distinguish between these modes and make an attempt at identifying the individual modes it will be necessary to compare them with the finite element model. These modes could represent a vertical mode of the barrelarch, a transverse mode of the barrel-arch, and also a torsional mode of the entire structure. An apparent higher order transverse mode appears at 8 Hz. Again it is difficult to specify the exact nature of the mode due to the lack of Figure 7. Fundamental Transverse Mode 3.25 Hz Figure 8. Singular Values of the Power Spectral Density Matrix of the Main Section Model The overall model was used to confirm the transverse and vertical mode shapes, and illustrated the transverse modes of the church with the additional measurements taken. It displayed all of the modes that were seen in the main section model. The dome was analysed using a separate model and it displayed the most interesting behaviour. The dome displayed motion in the vertical, transverse and torsional directions at the same frequency, 20 Hz (Figure 9). The frequency obtained is reasonable considering the high stiffness of the dome. The power spectrum obtained for the dome model is shown in Figure 10. It is difficult to determine if the three motions are coupled modes, very closely spaced modes, or not actually those three specific modes. One or more of these motions may not be a true mode. Based on the orientation of the instrumentation shown in Figure 5, it is believed that the torsional motion is exaggerated due to the direction of measurement and is not a mode. This leaves the transverse and vertical motions, one of which may also not be a mode shape. This can be more readily determined by comparison with the finite element model. The software used also determines a very strong mode at 40 Hz that displays the same shape. This is believed to be the second mode, but 1262

cannot be conclusively identified due to the low resolution of the accelerometer network. To confirm the potential behaviour of the dome, the results are again compared to the SAP analytical model. measurements were taken, the latter values will be the values used for comparison. The SAP 2000 model that is available of the church provides a great deal of information. There are two separate models, one is a complex 2-D frame, which illustrates the transverse motion of the main section as well as the vertical motion of the barrel-arch. The second model is of the entire structure, and gives an illustration of all modes, as well as the main dome structure. Table 1. Full Model Results Figure 9. Dome Modal Behaviour at 20 Hz Test Mode Description Frequency [Hz] 1998 1 1 st Trans 2.8 to 3.6 1999 1 1 st Trans 3.3 to 4.0 Frame SAP 1 1 st Trans 2.48 Model 2 1 st Vert (B/A) 4.68 3 2 nd Vert (B/A) 9.71 4 3rd Vert (Wall) 13.1 2001 1 1 st Trans 3.25 2 1 st Vert (B/A) 4.6 to 4.9 3 2 nd Trans 5.1 to 5.3 4 2 nd Vert (B/A) 8.0 The main section test shows a fundamental frequency at 3.25 Hz. The SAP model displays a fundamental mode at 2.5 Hz, and the experimental values display a range between 3.3 and 4.0 Hz. Based on these results it is apparent that the first transverse mode is between 3.2 and 3.5 Hz, and the SAP model is slightly flexible. Figure 10. Singular Values of the Power Spectral Density Matrix of the Dome Models COMPARISON WITH THE PRIOR RESULTS There are three sets of results available to compare the current ambient vibration test with. The first set is of experimental measurements from a test performed in 1998 after the church was repaired but before the retrofit project was initiated. The second set of experimental measurements were taken in 1999 after the church retrofit project was initiated. The third set of results are analytical, and these are obtained using a finite element model created with SAP 2000. This model was created and then updated using the results of the two experimental tests. This model offers the opportunity to explore higher modes, and present an idea of how the mode shapes might look, where on the two experimental tests did not provide any mode shapes. Since the testing was only partial coverage of the structure, this model is useful for identifying modes. All of these results are summarized in tables 1 and 2. The 1998 and 1999 test results provided a range of frequencies for the fundamental mode. The first test reported a fundamental transverse frequency between 2.8 and 3.6 Hz. One year later after the retrofit was initiated, a similar test reported values of 3.3 to 4.0 Hz. Since it is assumed that this change is due to the stiffening of the structure and that there should be no loss of stiffness since those The cluster of frequencies that is displayed in the experimental results is not reflected in the SAP model. This indicates that the two peaks at 4.6 Hz and 4.9 HZ are likely the same mode, although which peak is the real frequency is difficult to determine. These peaks could be split due to damping effects, or due to the resolution of data available. Since these frequencies represent a vertical motion, these could represent the second mode of the structure. 5.1 Hz and 5.3 Hz show a similar transverse motion and this could represent the second transverse mode of the structure. The SAP model shows the second vertical mode of the barrelarch, second transverse mode of the exterior walls at 9.71 Hz. These could represent the same motion, but it is not clear from the experimental results if this is true. If both sets of peaks in the cluster are split because of damping effects, it could be a lack of damping in the SAP model that causes the frequency of this mode to be high. It is more likely that the mode at 5.2 Hz does not exist in the SAP model, and that the modes at 8.0 Hz and 9.71 Hz are representing the same mode. The experimental mode at 8.0 Hz has motions which could be the second transverse, and some vertical components as well. The dome provides the most interesting data for comparison. The original concept of the instrumentation layout was to determine the fundamental vertical mode and possibly the fundamental transverse mode. Upon studying the SAP model of the dome independently from the rest of the structure, the modes of the dome were found to be in this order: transverse, longitudinal, vertical, second transverse/vertical, third transverse/vertical. The numerical 1263

values of these modes are presented in Table 2. Since the experimental results displayed all three primary motions at the same frequency, it is difficult to determine which order the modes should appear. It was stated previously that it is likely the torsional component is an exaggeration of the rotation measured by the orientation of the instrumentation. If the fundamental torsional mode is higher as shown in the SAP model, this fact could be confirmed. The remaining two motions, transverse and vertical both are shown in the SAP model between 13 and 24 Hz. If the two translational modes are not considered to be part of the experimental mode, then the mode for comparison in SAP is either 18.5, 21.55 or 24.39 Hz. The first of these three is a pure vertical mode with the walls of the dome base buckling outwards in the mode shape. The second mode resembles the second transverse mode, with the top of the dome (the compression ring) rocking about its midpoint, and the two opposite walls of the base moving in the same direction. The third mode is a coupled vertical/transverse mode with the compression ring twisting about a diagonal axis. When the experimental mode is compared to these three modes, it most resembles the second at 21.55 Hz. A first observation of the experimental mode identifies it as a vertical mode. But if it is to be considered that the vertical measurement was only taken on one side of the compression ring, it is apparent that it is impossible to know what is happening on the other side. The vertical component in Figure 9 does not consider this fact. It displays both sides of the compression ring moving with the same amplitude and direction. Therefore, since there is a high transverse component, and a slight vertical component, it seems possible to be a transverse mode. At 21.55 Hz in the SAP model the compression ring is moving transversely and vertically. The visual of the experimental mode has one more property that should be considered. The transverse motion is at a 45 degree angle to the longitudinal axis of measurement. This is similar to the motion of the mode at 24.39 Hz. The conclusion of these comparisons is that the experimental mode obtained is a transverse mode, likely relating to the SAP mode at 21.55 Hz, but possibly to the next mode at 24.39 Hz. This would require more data to be determined conclusively. Table 2. Dome Model Results Test Mode Description Frequency [Hz] SAP 1 1 st Transverse 13.83 2 1 st Longitudinal 16.18 3 1 st Vertical 18.48 4 2 nd Trans/Vert 21.55 5 3 rd Trans/Vert 24.39 6 1 st Torsion 26.60 2001 1 1 st Vert/Trans/Tor 19.80 2 2 nd Vert/Trans/Tor 40.00 CONCLUSIONS The ambient vibration tests performed were sufficient to capture the fundamental modes of the various components of the church. It proved to be a very useful method in confirming some of the complex mode shapes which were predicted in the finite element model. The fundamental transverse mode of the church was at 3.25 Hz. The first vertical mode of the barrel-arch was between 4.6 and 4.9 Hz. A second mode in the transverse direction is between 5.1 and 5.3 Hz. The second vertical mode of the barrel-arch is at 8.0 Hz. The dome tests captured two modes, one at 19.8 Hz and a second at 40.0 Hz. This first mode is a transverse mode of the dome, either the second or third (transverse) mode. This was inconclusive due to the lack of instrumentation. The second mode at 40.0 Hz may be a torsional mode, but was also inconclusive. While ambient vibration tests are valuable to determine some of the mode shapes, in order to properly calibrate the finite element model a more detailed array of setups are required. ACKNOWLEDGMENTS The authors would like to acknowledge Professor Eduardo Márquez, who provided valuable assistance during the tests. His enthusiasm and support for this project contributed to its success. Professor Enrique Garcia Alvear was also a valuable contributor to this project. REFERENCES [1] Placencia, P., Reforzamiento structural de la Iglesia de la Compañía, Escuela Politécnica Nacional, 2000 [2] Felber, A.J., Development of a Hybrid Bridge Evaluation System, PhD Thesis, 1993 [3] DasyLAB Software V 5.10, Copyright Datalog GmbH 1992-1998 [4] MathCAD User s Guide, Copyright 1986-1999 Mathsoft, Inc. [5] ARTeMIS User s Guide, Copyright Structural Vibration Solutions ApS, 2001 The second experimental mode at 40 Hz does not directly relate to any modes in the SAP model. It could possibly be a torsional mode, although this cannot be determined conclusively from the tests. 1264