Sezer Atamturktur¹,  Aleksandar Pavic²,  Paul Reynolds³

¹ Graduate Research Assistant, Department of Architectural Engineering, The Pennsylvania State University, University Park, PA 16802 USA
² Professor of Vibration Engineering, Department of Civil & Structural Engineering, University of Sheffield, UK
³ Senior Lecturer, Department of Civil & Structural Engineering, University of Sheffield, UK

Citation

Atamturktur, S., Pavic, A., Reynolds, P., (2008), “Sensitivity of Modal Parameters of Historic Monuments to Geometric Distortion,” Proceedings of 26th International Modal Analysis Conference, Orlando, Florida, USA.

Abstract

A unique opportunity to investigate the sensitivity of modal parameters of complex vaulted masonry systems to geometric distortions due to abrupt changes in boundary conditions is found in Beverley Minster, UK. Over the last eight centuries, the accumulated support settlements of the buttresses have pulled the main nave walls outwards, causing severe Sabouret cracks along the edges of masonry vaults. At certain locations, the separation of the walls from the nave vaults has reached 150 mm, while bays closer to the main crossing tower remain integral with the walls. Due to large deformations, the crown of the damaged vaults sags approximately 200 mm relative to the undamaged vaults. The sag of the crown and inverse curvature of the damaged vaults are visually observable. To compare different states of the vaulted system, representative sections of both undamaged and damaged vaults were subjected to modal analyses by measurable hammer impact excitation. The deviations of the natural frequencies and mode shapes between the two cases are quantified. The discrepancies of the modal parameters are found to be as low as the measurement errors, and thus insufficient to yield conclusions on the state of damage to the vaults. However, magnitudes of frequency response functions are significantly greater for the damaged vaults.

Introduction

The structural maintenance of historic masonry monuments should be a worldwide concern. Each historic monument is unique due to variations in construction techniques, materials and workmanship. Distinct structural styles and irregularities of construction further complicate the structural assessment of these buildings. As the collapse of masonry systems can occur suddenly and without warning, the consequences can be catastrophic [1, 2, 3]. Thus, the development of reliable assessment tools, to predict the performance of masonry monuments, is an area of research that carries significant value.

For the assessment of civil engineering systems, the use of in situ vibration measurements has become an actively pursued research topic. In civil engineering, vibration data can be used for several purposes. One common purpose of vibration data is in the updating of uncertain features and parameters of finite element (FE) models. Model updating is done by correlating the modal data obtained from in situ tests with FE model predictions and then making systematic adjustments to improve the quality of the model. The reason for improving the predictive ability of the numeric models is to predict the performance of the structural system under loading conditions that are impractical to test. Another purpose of the vibration data is in detecting damage in civil structures from changes in their vibration characteristics. Previous research efforts in these two fields have mainly focused on bridges [4, 5, 6, and 7].

Recently, the research on vibration testing of historic masonry systems has started to increase. The first masonry systems studied were bridges, specifically masonry arch bridges. Armstrong et al. [8], used modal tests on a masonry bridge for active condition assessment. In [9], a half scale, 2-story brick masonry building was tested on a shaking table and the first nine modal parameters were identified. Full scale dynamic tests were completed by [10] in a two story building. In this study, the excitation forces were induced by shakers and the obtained modal parameters were used in the prediction of the physical parameters of the FE model.  The authors of [11] identified the dynamic characteristics of a recently rehabilitated historic masonry church by exploiting ambient vibration excitation. The transducers, in this study, were evenly distributed along the longitudinal axis of the church, and thus the global behavior of the church was captured. Extracted dynamic characteristics of the church were then compared to the data from the dynamic tests conducted before the rehabilitation. A similar methodology was applied to the dome of a monastery church by. In [12], the findings of modal testing on the complex vaults of historic masonry systems were presented. This study focused on vertical vibrations solely with the intention to illustrate a manual FE model updating exercise with the feedback from in situ modal test. Similar methodology was successfully applied to tile masonry domes [13]. Gentile and Saisi [14] recently published the results of ambient vibration tests on a historic masonry bell tower. In this study, the identified modal parameters were then used to update the uncertain variables of FE model. In [15], alternative ambient excitation sources, such as organ, orchestra, peal-bells and carillon bells, are exploited, and found to yield consistent results.

The success of these research programs in the identification of modal parameters of historic monuments raises the question of whether the emerging topics of structural health monitoring and damage detection are applicable to masonry monuments. To answer this question, the sensitivity of the modal parameters to the typical damage types seen in masonry systems (damage caused by cracks, support settlement, separation of walls, etc.) need to be clearly identified. Such an investigation is only possible if the undamaged and damaged states of the same structure can be tested separately. However, it is not conscionable to damage historic structures solely for research purposes.

An opportunity to access two virtually identical vaults, representing the damaged and undamaged states of a structure, was available in Beverley Minster, UK. The support settlement of the buttresses pulled the nave walls outward, detaching walls from the masonry vaults. This detachment led to a loss of curvature in the nave vaults, particularly toward the west end of the main nave [Figure 1]. As the movement of walls was not uniform, the Minster has ten nearly identical vaults with different damage states.

Although the techniques of damage assessment are clearly intended for practical applications, previous experimental validation has been done on scaled experimental specimens (undamaged vs. damaged) [16, 17]. These idealized laboratory specimens lack the influence of real life conditions, such as the ambient vibration loading, the unknown accumulated damages in the system, the irregularities inherent in the medieval constructions, etc. The value of this study stems from test structures and testing conditions. The study draws a realistic picture about the sensitivity of modal parameters when acquired from full-scale historic masonry monuments.

The theory and procedures involved in structural health monitoring and damage assessment are completely different than the theory and procedures pursued in this study. However, the findings presented herein reveal interesting conclusions about the dependency of modal parameters on structural damage, and can be useful in the future applications of structural health monitoring.

Structure Under Study: Beverly Minster

The test structure, Beverley Minster, is considered to be among the finest examples of the English Gothic style by many historians [Figure 2] [18]. This paper focuses on the main nave of the Minster. The nave is covered with even level quadripartite rib vaults, which are supported vertically by arches and piers; horizontally, by flying buttresses [Figure 3]. Buttresses transfer horizontal thrust to aisle vaults on each side. The church is predominantly built with limestone of different hardness, though brickwork is used to form the vaults [18].

According to historical documents, the movement of its nave walls has been a concern since the nave was built in the early 13th century [19]. The nave walls leaned steadily over the centuries and ties were added (in the 18th century) at roof level to prevent the increasing separation of the walls. The movement must have continued, because a century later a similar repair was made [Figure 4]. Ties were fixed to each nave wall and may have slowed the movement of the walls. These ties, however, did not eliminate movement within the structure.

Assessment reports, completed by the Price & Meyers Consulting Engineers in 2004, document the magnitude and patterns of movement of the walls [19]. According to their survey, maximum separation between the south and north is 135 mm and located close to the west side of the nave [Figure 5]. The displacement of the south wall is noted to be more severe compared to the north wall. The east end and west seem to be restrained by the transept tower and walls of transepts, thus remain relatively stationary [Figure 1].

Test Vaults

Although the ten nave vaults are nominally identical, slight differences between each vault are present due to imperfections of medieval construction and the variations in workmanship and in masonry assembly. However, the displacement of the walls, the sag of the crown and the geometric distortion of vaults is visually perceivable. As such, in this study, the difference caused by construction of the vaults will be considered as insignificant, and the changes observed in modal testing measurements collected from the damaged and undamaged vaults will be solely attributed to the existing structural damage.

The second vault from the west end of the Minster is where the walls deflected the most, while the second vault from the transept tower is where the structure’s movement was insignificant. These two vaults, representing the most damaged and least damaged states of the complex vaulting system, are selected as the test prototypes and henceforth will be referred to as ‘damaged’ and ‘undamaged’ vaults [Figure 1]. The geometric survey completed by research teams revealed the reduction in curvature and severity of geometric distortion of each damaged vault. Figure 6 presents a schematic comparison of the geometric state of the two vaults of interest.

During the original medieval construction, the brick webbing of the vaults and the limestone nave walls were not flush [Figure 7]. All vaults are inherently detached from the nave walls. Therefore, the difference between the two structural states, damaged and undamaged, is not due to structural connectivity. Instead, the term damage refers to the distortion of the vault geometry.

Modal Testing

The objective of the present experimental program is to investigate whether the modal parameters of masonry vaults are sensitive to damage levels that are visually perceivable. For this, deviations between the modal parameters of the two initially identical masonry vaults will be quantified by modal testing.

Although the theory and practice of modal testing developed significantly in the last few decades, modal testing of historic masonry structures is still in its infancy. Thus, a brief overview of the experimental program as applied to Beverley Minster is necessary and will be provided in the sections below. A comprehensive discussion on particulars and practicalities of in situ vibration testing on complex vaulted masonry structures can be found in [20].

Exploiting the predictive abilities of FE models during the development of the experimental program is an advisable practice. The preliminary modal predictions of the initial FE model of the Minster are used in deciding the distribution of the measurement points as well as in deciding the excitation locations. Although the details of the FE model are out of our scope and will not be discussed any further, Figure 8 is provided to give a general idea to the reader about the level of detail included in the modeling phase.

Experimental Program

The excitation source was the first critical decision. In earlier studies, both ambient and forced excitation techniques have been successfully performed on historic masonry monuments [20, 21]. Studies exploiting ambient vibration eliminate the need for an excitation device and are advantageous during the execution of the test. However, it has been proven that controlled excitation techniques can yield better quality measurements as evidenced by higher coherence, clean FRF measurements and clear mode shapes [4, 17]. In this study, practical difficulties in the execution of forced excitation were tolerable, and forced excitation is preferred over natural excitation sources.

Next, the controlled excitation devices were selected. Among the exciters that applied to civil structures, impact hammers and shakers are the most common. When testing historic monuments, difficulty in transportation, positioning, and alignment of the shaker device at the top of the vaults is prohibitive. Transient hammer impact excitation provides a practical and convenient alternative.

As such, modal testing was conducted by mounting vibration transducers in a predefined test grid and inducing low amplitude controlled vibrations using an instrumented sledge hammer. The test variables that factor into the overall quality of the experimental program are briefly discussed in the following sections.

Test grid

The density of the test grid was determined by considering the time constraints, the number of available accelerometers and number of channels in the signal analyzer. A total of 47 measurement points were distributed on the three adjacent vaults; 39 were spaced along the ribs of the vault of interest, while 8 of them were mounted on the two adjacent vaults [Figure 9].

Transducers

The transducers used in this study were Q-Flex QA 750 model force balance  accelerometers, manufactured by Honeywell Inc, with a nominal sensitivity of 1.5 mA/g, which when dropped over a 5 kΩ resistor results in a voltage sensitivity of 6.5 V/g. They maintain a frequency range of 0-300 Hz and an amplitude range of ±30 g. These accelerometers were mounted on brick masonry vaults such that their axis was vertical. The adjustable screws of the mounting cases enabled precise alignment [Figure 10].

Instrumented Impulse Hammer

The mass of the hammer and stiffness of its tip are influential factors in hammer selection. Initially, a model 5802A instrumented impulse hammer (3 lb head), manufactured by Dytran Inc, was used to excite the structure. It was observed that the energy input generated by this hammer was not capable of producing the necessary vibration amplitudes. Poor signal to noise ratio was evidenced by low amplitudes in coherence functions and reduced clarity in FRF functions. A larger hammer, 5803A model sledge hammer (12 lb head), manufactured by Dytran Inc, was deemed to be a more suitable choice. To broaden the impact duration and induce low frequency vibration, the softest hammer tip was preferred.

The hammer operator excited the structure consistently in the vertical direction [Figure 11]. To reduce the degrading effects of ambient noise, 5 impact data sets were measured and averaged for each excitation location.

Because the geometry of vaulted structures is inherently complex, the mode shapes tend to be very complicated. Based on earlier experiences gained from testing on these structures, four critical excitation locations were deemed necessary [Figure 9].

Data Acquisition

Force input and acceleration response time histories from each impact were transferred into the frequency domain and averaged to obtain the coherence and frequency response functions. Data acquisition was carried out using a 24 channel 24 bit Data Physics Mobilyzer II spectrum analyzer. The upper frequency limit was 100 Hz and the data capture time was 16 seconds. This data configuration yielded a 0.0625 Hz frequency resolution and 0.005 second time resolution. As the response diminished within the data capture time frame, a rectangular window function was used for both impact and response signals.

Modal Extraction

Standard experimental modal analysis applications assume that the test specimen exhibits linearity and reciprocity. As part of the quality assurance procedure, suggested in [22] linearity and reciprocity checks were completed to confirm this fundamental assumption. Due to low amplitude excitation forces, the measurements exhibited linearly elastic behavior.

Modal extraction is a systematic process of matching the analytical representation of modal parameters to the experimentally obtained FRF measurements, also known as curve-fitting. The modal extraction was carried out using the ME'scopeVES Version 4.0 software, developed by Vibrant Technology Inc.

To achieve a good analytical reduction of experimental measurements, the frequency bandwidth and the number of expected modes should be defined properly. Modal indicator functions and modal peak functions, built in the software package, were exploited to determine the number of modes to be extracted. Approximately 20 modes of significant amplitude were observed between 0 Hz to 20 Hz. As the natural frequencies increase the mode shapes became complex, and the identification of correspondence between the damaged and undamaged vaults became quite difficult. As such, the data for the correlation of the two states of the vaults was limited to the first 10 modes. The identification of the first ten modes was completed using a multiple reference global curve-fitting algorithm, which incorporates FRF measurement data from multiple excitation locations.

The use of an exponential window introduces an artificial damping to the measurements. Because masonry systems have relatively high damping in their response, artificial damping can result in overwhelming of lower amplitude modes by adjacent modes of higher magnitude [23]. Thus, during data acquisition, the exponential window was avoided. However, during modal extraction stage, it is a good practice to apply a low order exponential window to clean the degrading effects of extraneous excitation. In this study, the modal extraction was repeated with and without the application of exponential window.

Results and Discussion

Once the modal parameters for damaged and undamaged states were identified from the FRF measurements, the differences between the natural frequencies and mode shapes were quantified [Table 1]. The correlation between the two sets of mode shapes was done using the modal assurance criterion (MAC). A MAC value of 1.0 represents a perfect correlation between two identical modes, while 0.0 indicates two orthogonal modes. Because of the complexities introduced due to the experimentation, MAC values of 80% or higher are deemed to be satisfactory for correlation purposes.

As seen in Table 1, the differences in natural frequencies are not sufficient to indicate a difference between the structural systems of test vaults. In fact, the variations of natural frequencies of the two states can be attributed to the measurement errors–perhaps caused by the introduction of the dynamics of the hammer operator to the system.

Table 1: The correlation of the modal parameters of damaged and undamaged vaults of Beverley Minster, UK.

In general, a good correlation between natural frequencies is achieved [Figure 12].  The first three mode shapes correlate well in their MAC value [Figure 13], while higher order modes show less correspondence. Three of the first ten mode shapes (modes 4, 5 and 7) are visually and numerically (in terms of their MAC values) unrelated. Although these uncorrelated mode shapes can be considered as an indication of the differences between two structural conditions, this qualitative difference does not support a positive inference of a difference between the response of the two vaults.

Another important observation is that although FRFs acquired from the undamaged and damaged vaults compare fairly well for the first 10 modes, as the natural frequencies increase this correlation is reduced [Figure 14]. It is certain that higher order modal parameters are more sensitive features to the different structural states.  However, as mentioned earlier, due to the inherently complex geometry of the vaulted structures, the higher order modes are often clustered and mode shapes become further complicated--making mode shape pairing and correlation almost impossible.

While the lower order modal parameters are observed to be insensitive to the damage present in Beverley Minster, the pairing of the FRF measurements revealed an interesting characteristic: the FRFs obtained from undamaged vaults have significantly lower amplitudes than the FRFs obtained from damaged vaults [Figure 15]. This trend is observed to be consistent for all measurement data sets.

Conclusions

The nave walls supporting the vaults of Beverley Minster have been steadily moving for 8 centuries. Because of this movement, the originally identical 10 masonry vaults have undergone a non-uniform damage pattern. The objective of the study was to assess the sensitivity of the modal parameters of a historic masonry vault to severe geometric distortions, which typically cause reduction in structural strength of a masonry system.

Modal testing with hammer impact was performed on both damaged and undamaged vaults and the modal frequencies and mode shapes of these two systems were estimated.  Due to the inherent complexity of the spatial configuration of these vaults, the comparison of modal parameters was limited to the first ten modes.  The mode shape pairing was done by solely focusing on the natural frequencies.

Although one would expect the damaged vault to have lower natural frequencies than the undamaged one, among the first ten modes, no significant variation between the natural frequencies of undamaged and damaged vaults was observed.  However, three of the paired mode couples were noted to have completely independent mode shapes.  The differences in modal parameters may serve as correlation feature during future studies.

The amplitudes of the FRFs, however, were observed to yield an immediate comparison of the states of the two vaults.  The amplitudes of the FRFs collected from the damaged vault were significantly higher than the FRFs obtained from the undamaged vault.  In other words, as one would expect, the hammer tap caused the damaged vault deflect more than the undamaged vault.

Although the damage induced in the vaults because of the movement of the nave vaults was visually observable, the modal parameters did not yield a significant sensitivity to portray this difference.  The direct comparison and correlation of the FRF graphs seem to be a more sensitive and more convenient method for the future studies on the health monitoring or damage assessment of historic masonry vaults.

Acknowledgments

The first author gratefully acknowledges the support of the World University Network for the fellowship funding that enabled her to visit University of Sheffield. Authors are thankful to Minster personnel, Steve Everett and Steve Riall, for their support and welcoming attitude during site visits. Thanks to Price and Meyers for sharing their drawings and reports. Special thanks to Chris Middleton, Stefanie Terentiuk and Eunice Lawton for their help during the field test and to Prasenjit Mohanty and Donald Nyawako for their help during the preparation phase of the test. Sally Gimbert has completed the geometric survey. And finally, thanks to Prof. Thomas E. Boothby, for initiating and supporting this research program.

References

1. M. Bruneau, M. Lamontagne, (1993), “Damage from 20th Century Earthquakes in Eastern Canada and Seismic Vulnerability of Unreinforced Masonry Buildings,” Canadian Journal of Civil Engineering, vol. 21, no. 4, pp. 643-662.
2. Binda L., Saisi A., (2002), “State of the Art of Research on Historic Structures in Italy State of the Art of Research on Historic Structures in Italy,” Proceedings of 11th Advanced Research Initiation Assisting and Developing Networks in Europe (ARIADNE ) workshop, May 20-26, 2002.
3. Lagomarsino, S., Podestà, S., (2004), “Damage and Vulnerability Assessment of Churches after the 2002 Molise, Italy, Earthquake,” Earthquake Spectra, vol. 20, no. S1, pp. 271- 283.
4. Salawu, O. S., Williams, C., (1995), “Review of full-scale dynamic testing of bridge structures,” Engineering Structures, vol. 17, no. 2, pp. 113- 121.
5. Brownjohn, J. M. W., Dumanoglu, A. A., Severn R., T., (1992), “Ambient vibration survey of the Faith Sultan Mehmet (Second Bosporus) suspension bridge,” Earthquake Engineering and Structural Dynamics, vol. 21 pp. 907- 24.
6. Pavic, A., Armitage, T., Reynolds, P. and Wright, J. (2002), “Methodology for Modal Testing of the Millennium Bridge, London,” Proceedings of the Institution of Civil Engineers: Structures and Buildings, vol. 152, no. 2, pp. 111-122.
7. Xia, P., Q., Brownjohn, M., W., (2004), “Bridge Condition Assessment Using Systematically Validated Finite-Element Model,” Journal of Bridge Engineering, vol. 9, no. 5, pp. 418- 423.
8. Armstrong, D. M., Sibbald, A., Fairfield, C. A., Forde, M. C., (1995), “Modal Analysis for Masonry Arch Bridge Spandrel Wall Separation Identification,” NDT&E International, vol. 28, no. 6, pp. 377-386.
9. Zembart, Z., Kowalski, M., (2000), “Dynamic Identification of a Brick Masonry Building,” Archives of Civil Engineering, vol. 46, no. 1, pp. 106- 136.
10. Sortis, A. D., Antonacci, E., Vestroni, F., (2004), “Dynamic Identification of a Masonry Building Using Forced Vibration Tests,” Engineering Structures, vol. 27, pp. 155- 165.
11. Turek, M., Ventura, C., E., Placencia, P., (2002), “Dynamic Characteristics of a 17th Century Church in Quito,” Proceedings of the International Society of Optical Engineering, vol. 4753, no. 2, pp. 1259- 1264.
12. Erdogmus, E., (2004), “Structural Appraisal of the Florentine Gothic Construction System,” PhD Thesis, The Pennsylvania State University. 
13. Atamturktur, S., (2006), “Structural Assessment of Guastavino Domes,” M.S. Thesis, The Pennsylvania State University.
14. Gentile, C., Saisi, A., (2007), “Ambient vibration testing of historic masonry towers for structural identification and damage assessment”, Construction and Building Materials, vol. 21, no. 6, pp. 1311- 1321.
15. Atamturktur, S., Fanning, P., Boothby, T., (2007), “Traditional & Operational Modal Testing of Monumental Masonry Structures,” Proceedings of International Operational Modal Analysis Conference, Copenhagen, Denmark.
16. Xia, P. Q., Brownjohn, M. W., (2004), “Bridge Structural Condition Assessment Using Systematically Validated Finite-Element Model,” Journal of Bridge Engineering, vol. 9, no. 5, pp. 418- 423.
17. Zonta, D., Elgamal, A., Fraser, M., Priestley, M. J., (2007), “Analysis of Change in Dynamic Properties of a Frame-Resistant Test Building,” Engineering Structures, doi:10.1016/j.engr.struct.2007.02.022.
18. Horrox, R., (2000), Beverley Minster: An Illustrated History, University Press, Cambridge.
19. Price & Meyers Consulting Engineers, Beverley Minster: Report on Recent Movement in the Nave Vaults, July 2004, ref: 1273.
20. Atamturktur, S., Hanagan L., Boothby, T., (2007), “Extension of Large Scale Modal Analysis Techniques to Historic Masonry Vaults,” Proceedings of 25th International Modal Analysis Conference, Orlando, Florida.
21. Atamturktur, S., Fanning, P., Boothby, T., (2007), “Traditional & Operational Modal Testing of Monumental Masonry Structures,” International Operational Modal Analysis Conference, Copenhagen, Denmark.
22. Reynolds, P., Pavic, A., (2000), “Quality Assurance Procedures for the Modal Testing of Building Floor Structures,” Experimental Techniques, Vol. 24, No. 4, pp.36- 41.
23. Avitabile, P., (2001), “Experimental Modal Analysis,” Sound and Vibration, January, 2001.