Vibration characteristics of the Bayon temple main tower ... · 3 Micro-tremor measurements 3.1 Equipments and acquisition parameters We used portable battery-operated three-component

Vibration characteristics of the Bayon temple main tower, Angkor, Cambodia

T. Maeda1, Y. Sugiura2 & T. Hirai3 1Department of Architecture, Waseda University, Japan 2Nihon Sekkei, Inc. Japan 3School of Science and Engineering, Waseda University, Japan

Abstract

Bayon temple, Angkor, built in the late 12th century to the early 13th century, is a masonry temple made of sandstone which has deteriorated possibly due to rain, plants, settlements, and so on. Strong winds blowing more than 20m/sec were observed in the rainy season, which may cause vibration of the structure either directly or via ground motion, we may add wind induced vibration to the list of deterioration causes. Proceeding to a study on the response of the masonry structure to the strong wind, we carried out a micro tremor measurement to evaluate the vibration characteristics of the main tower and surrounding sub-towers in the temple. We identified translational and torsion modes of towers with their predominant frequencies, damping factors, and base-fixed frequencies. We examined all of the sub-towers to find statistically the effects of height and corridor connectivity on their vibration characteristics. Then, we attempted to construct an FEM model for the main tower by simulating the base-fixed natural frequencies of the horizontal translational modes. The model with an elastic modulus practically used for sandstone shows much higher frequencies, which let us decrease the modulus to less than 1/10. We also find that this reduced stiffness model shows about a half the observed vertical translational frequency so as to suggest a lack of consistency with continuum modelling of basically discontinuous masonry structure. Keywords: Bayon temple, micro-tremo observation, vibration characteristics, FEM modelling, simulation of elastic modulus.

1 Introduction

Bayon temple, Angkor, built in late 12th century to early 13th century, is a masonry temple made of sandstone being deteriorated possibly due to rain,

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Structural Studies, Repairs and Maintenance of Heritage Architecture IX 255

plants, settlements, and so on. Strong wind blowing more than 20m/sec was observed in the rainy season, which may cause vibration of the structure either directly or via ground motion, we may add wind induced vibration in the list of deterioration causes. Proceeding to a study on the response of the masonry structure to the strong wind, we carried out micro tremor measurement to evaluate vibration characteristics, e.g. predominant frequencies, damping factors, mode shapes, of the main tower and surrounding sub-towers in the temple in 2003 and 2004.

The main tower consists of a central tower of about 30m high and attached eight central sub-towers. The central tower has fundamental frequency of 2.8Hz and damping factor around 2%. Each attached central sub-tower has principal axes of motion in radial and tangential directions to the central tower with different predominated frequencies around 8Hz (Sugiura et al. [1]). We also measured micro-tremor at all of the twenty-two sub-towers located around the main tower. With these data, we can conclude that corridor connectivity affect stiffness of the towers by adding stiffness in corridor direction, but the effects of height on vibration characteristics are obscure and can be masked by corridor effects.

We attempted to construct FEM model for the main tower and one of sub-towers by simulating base-fixed natural frequencies in horizontal translation inferred from transfer functions. The model with elastic modulus practically used for sandstone shows much higher frequencies, which let us reduce the modulus to less than 1/10. We also find that this reduced stiffness model shows about a half as observed vertical translational frequency to suggest lack of consistency with continuum modelling of basically discontinuous masonry structure.

2 Structure of the temple Bayon temple shown in fig. 1 consists of main tower and sub towers constructed by sandstone dry-masonry (Dumarcay [2]). They are built on artificial soil with different ground levels up to the depth of about 10 m at the deepest around the center of the temple occupied by the main tower. The main tower consists of central tower and surrounding eight central sub-towers; the central tower of about 30m high and central sub-towers about 20m high have a base structure in common up to gallery level at about 15 m from the basement as shown in fig. 2. The twenty-two sub-towers with smiling God face relieves, varying their heights ranging from 12.1 m to 15.4 m, are connected by corridors with each other to form a kind of labyrinth in the temple.

3 Micro-tremor measurements 3.1 Equipments and acquisition parameters We used portable battery-operated three-component seismograph GPL-6A3P made by Akashi, which contains over-damped velocity meters and data logger. Acceleration is acquired from the differentiated over-damped pendulum motion with frequency range of 0.1Hz to 100Hz and sensitivity of 1 mV/gal. Thirty seconds of sensor outputs were low-pass filtered at 30Hz and amplified by 1000 times, then discretized by 20 bit AD converter with 100 Hz sampling.


256 Structural Studies, Repairs and Maintenance of Heritage Architecture IX

Figure 1: Layout of towers in the Bayon temple [2].

Figure 2: Structure and sensor arrangements of the main tower [2].



3.2 Sensor arrangements

Due to limited number of seismographs, we provided several sensor arrangements even for the same structure according to the measuring objectives. In order to understand overall vibration characteristics of the main tower, which is a complex structure made up of nine towers having base structure in common, we provided sensor arrangements for mode shapes and for long-term measurement of the central tower, as well as an arrangement for four of eight central sub-towers off the NS and EW axes with an origin at the central tower. Twenty-two sub-towers were simply measured at the top and the bottom for statistic study, but mode shape measurement was carried out for one of these sub-towers.

Fig. 2 shows the sensor arrangement for mode shapes applied to the central tower with three external sensors at the top, two of one-component sensor in radial direction and one in circumferential direction in the middle, one seismograph at the gallery, one at the top of the central sub-tower, and two at the basement. For long term measurement, we used sensors at the top and one seismograph at the basement with additional wind velocity meter at the top of the central sub-tower. Fig. 3 shows sensor arrangement for sub-tower mode shape with three sensors at the top, two sensors in the middle, and four seismographs at the basement.

Figure 3: Sensor arrangement for mode shape of the central sub-tower.

3.3 Data processing

In order to capture vibration characteristics, we basically resorted to ensemble average of stationary signal for auto power spectrum and cross power spectrum. We have used Hv evaluation for transfer function obtained by eigenvalue



problem defined in eqn (1) with input auto power spectrum xxS , output auto power spectrum yyS , and cross power spectra xyS and yxS , which is optimal for noise contained input and output data with the smallest eigenvalue of ε .

−

=

−

11

vv

yyyx

xyxx HHSSSS

ε (1)

Figure 4: Auto power spectra of the main tower.

Random decrement method proposed by Ibrahim [3], which is a superposition of time history samples starting with local maximum or minimum, was used to evaluate logarithmic damping factor of synthesized pseudo free vibration time history.

4 Vibration characteristics of the towers

4.1 The main tower

Fig. 4 shows auto power spectra obtained at the main tower. Those spectra show peaks at 2.8 Hz for the central tower, gallery, and the central sub-towers in common, implying associated fundamental mode. Fig. 5 shows band-pass filtered micro tremor time histories and distribution of amplitudes to show that the central tower oscillates in the first mode at 2.8 Hz and in the second mode at 5.1 Hz. Fig. 6 shows random decrement pseudo free vibration time history, from which we evaluate damping ratio of the first mode is about 2 %. Transfer function shown in fig. 7 reveals the base-fixed fundamental frequency of the central tower is a little more than 3 Hz.

In order to find principal axes of central sub-towers, we have done principal value analyses in horizontal plane to find the principal axes of each central sub-tower lie in radial and tangential direction of the central tower as shown in fig. 8. We have examined micro tremor data in these two directions to find predominant frequency ranges from 6 Hz to 9 Hz and damping ratio from 1 % to 4 %, for the first mode of central sub-towers. Table 1 and table 2 summarize vibration characteristics of the main tower.



Table 1: Vibration characteristics of the central tower.

NS EW 1st mode 2nd mode 1st mode 2nd mode Predominant frequency [Hz] 2.8 5.0 2.8 5.1 Damping factor [%] 2.1 - 2.3 - Base-fixed frequency [Hz] 3.1 5.1 3.0 5.3

Table 2: Vibration characteristics of the central sub-towers.

Radial component Tangential component Tower location NE SE NW NE SE NW Predominant frequency [Hz]

6.8 9.0 6.8 7.9 9.7 7.8

Damping factor [%] 3.1 3.4 1.1 2.1 3.1 1.3

Figure 5: Amplitude distribution and band-pass filtered time traces.

Figure 6: Pseudo free vibration waveform by RD method, the central tower.



Figure 7: Transfer functions of the central tower.

Figure 8: Principal axes of the central sub-towers.

4.2 Surrounding sub-towers

We have studied twenty-two sub-towers; three of which are without a corridor, four with two corridors at north and south sides, eight with east and west sides, and seven at a corner with two corridors. In fig. 9a, it is shown that 2nd predominant frequency of horizontal motion is twice as large as 1st frequency regardless of horizontal direction. In fig. 9b, comparison of 1st and 2nd predominant frequencies in NS and EW components with corridor type classification shows that the direction with two corridors have higher predominant frequencies compared to the other direction.

Considering stiffness added by corridors, we have compared predominant frequencies in vertical motion with lower horizontal frequencies in two directions, excluding sub-towers located at corners. In fig. 10a, we have good correlation between horizontal and vertical predominant frequencies with vertical frequencies over 15 to 20 Hz .In fig. 10b, height and horizontal frequencies are compared to show weak inverse tendency, but poor correlation.

5 FEM modelling

In order to study whether three-dimensional continuum model is applicable to masonry structure, we have constructed FEM model for the central tower and



one of the sub-towers without a corridor to deduce equivalent elastic modulus simulating base-fixed frequencies in horizontal translation. Poisson’s ratio of 0.28 and density of 2500kg/m3 are assumed according to JSA [4]. FEM model is constructed referring to figures and photos provided by [2]. We have used 1583 parallelepiped solid elements for the central tower and 2806 elements for the sub-tower.

(a) 1st and 2nd frequencies (b) Corridor direction dependence

Figure 9: Relation between horizontal frequencies.

(a) Horizontal and vertical frequencies (b) Horizontal frequencies and heights

Figure 10: Relation between horizontal frequencies and vertical frequencies or tower heights.

FEM models for the central tower is shown in fig. 11, and 1st horizontal modes are compared in fig. 12 with frequencies shown in table 3, where Young’s modulus is reduced to 1,200 N/mm2 from 17,000 N/mm2 of practically used value for sandstone, which is about 1/14. Horizontal components are well simulated with this Young’s modulus; however, the vertical component is underestimated as about a half of observed frequency. For the sub-tower, similar results are obtained with lesser Young’s modulus of 950 N/mm2, about 1/18 of



practical value with 30 % underestimated vertical frequency as shown in fig. 12 and table 3.

Figure 11: FEM models (left: main tower, right: sub-tower).

Figure 12: 1st horizontal mode shapes obtained by FEM (left: main tower, right: sub-tower).

Table 3: Comparison of observed and analyzed base-fixed frequencies [Hz].

Central tower Sub-tower Observation Analysis Observation Analysis 1st Horizontal 3.1 3.2 4.0, 4.1 4.0 2nd Horizontal

5.2 5.4 8.6, 8.7 9.1

1st Vertical 18.2 9.5 19.2 13.3

6 Conclusions

We have measured micro-tremor in the Bayon temple of Angkor remains to study vibration characteristics of sandstone masonry structure prior to evaluate the effects of wind induced vibration on deterioration of the structure. We have



identified major vibration modes, predominant frequencies, damping factors, and base-fixed frequencies for the central tower, as well as principal axes of the central sub-towers. We have depicted corridor effects on predominant frequencies of sub-towers by analyzing whole sub-tower data statistically.

With those free vibration characteristics at hand, we have constructed three-dimensional FEM model for the central tower and the sub-tower with solid elements to show equivalent elastic modulus for horizontal frequencies should be less than 1/10 of that used for sandstone in practice. Moreover, the models calibrated for horizontal motion underestimate base-fixed frequencies for vertical component by 30 % to 50 %. The models are based on figures and photos available and are not regarded as very precise; however, the tendency of underestimating equivalent elastic modulus for vertical component should be tackled to better understand continuum substitute for real discontinuous medium.

We acknowledge to JSA for their support on micro-tremor observation and to Mr. Kurauchi, Ms Fukumoto, Mr. Nagashima, and Mr. Matsuura for taking part in measurement and analysis.

References

[1] Sugiura, Y., Fukumoto, Y. & Maeda, T., Vibration Characteristics of Main Tower at Bayon Temple, 21st International congress of theoretical and applied mechanics, Warsaw, Poland, 2004.

[2] Dumarcay, J., Le Bayon, PEFEO, 1976. [3] Ibrahim, S. R., Random decrement technique for modal identification of

structures, AIAA/ASEM 18th Structures, Structural Dynamics and Material Conference, San Diego, CA. 1977.

[4] JSA (Japanese Government Team for Safeguarding Angkor), Annual Report on the Technical Survey of Angkor Monument 2001.



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Vibration characteristics of the Bayon temple main tower ... · 3 Micro-tremor measurements 3.1 Equipments and acquisition parameters We used portable battery-operated three-component