# Comparing Direct Observation of Torsion with Array-Derived Rotation in Civil Engineering Structures

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data

^{−8}rad/s–0.5 rad/s in the frequency range 0.01–50 Hz) and its flat transfer function between 0 (i.e., DC) and a few kHz mean that this sensor can be used as a single point of measurement for rotation. However, its position near OGH6 in one corner of the building was determined to guarantee sufficiently accurate rotation measurement above the noise, without a priori information on the amplitudes expected. In this study, only rotation around the vertical axis ${\dot{\theta}}_{z}$ (i.e., the building torsion response, ${\dot{\theta}}_{HJZ}$ according to the FDSN norm) is considered.

## 3. Data Processing

## 4. Results and Discussion

#### 4.1. Variation of Translation and Rotation Frequencies

#### 4.2. Comparison of Rotation Values

^{−7}rad/s, which is the experimental sensitivity of the BlueSeis-3A sensor (compared with the theoretical sensitivity of 2.5 × 10

^{−8}rad/s). Consolidating the experimental infrastructure could have reduced experimental sensitivity.

#### 4.3. Acceleration versus Rotation and Phase Velocity

^{−7}rad/s) over the midnight period. At ground level, the ${\dot{\theta}}_{12}$ values fall below the detection threshold of the BlueSeis-3A, since this instrument does not enable rotation measurement at the bottom of the structure in this case (with the exception of the window covering the storm, to be compared with the accelerations produced by earthquakes in the free-field). The variations between acceleration and rotation and between top and bottom are relatively consistent. The average ratios are provided in Table 2.

^{2}. A linear fit to the data of the form y = ax + b is applied, at the top and bottom of the structure, giving the following relationships:

^{2}and 3 m/s

^{2}, respectively. The fit coefficients a are 1.301 [47] and 1.454 [48]. The motion at the bottom of the structure show a $\dot{\theta}$/$\ddot{u}$ ratio three times greater under ambient vibrations than under moderate earthquake conditions [47]. This ratio increases to 10 at the top, confirming the dynamic effect of rotation and the significant contribution of rotation to the overall structural response, at least under ambient vibrations. A misfit at the bottom of the structure is also observed for the two periods with the strongest accelerations (at the time of the storm), due to interaction between the soil and the structure. The data available is not sufficient to distinguish the effect of accident torsion due to rotational ground motion and due to dynamic effects. Most previous studies focused on the effects of rotational ground motion on the torsional response with favourable characteristics (e.g., Ω < 2/3 and Fy > 2 Hz in [9]; Ω < 1 and Fy > 3 Hz in [12]; Ω < 1 and Fy > 1 Hz in [49]). The overall observation is that the rotational ground motion effect is much greater in symmetrical buildings, like the GCH building. Shakib and Tohidi [49] also showed the significant effect of site conditions and soil-structure interaction.

#### 4.4. Phase Velocity Derived from the Rotation Measurement

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Rutenberg, A. Nonlinear response asymmetric building structures and seismic codes: A state of the art review. In Nonlinear Seismic Analysis and Design of Reinforced Concrete Buildings; Fajfar, P., Krawinkler, H., Eds.; Elsevier Applied Science Eds: London, UK; New York, NY, USA, 1992; pp. 328–356. [Google Scholar]
- Anagnostopoulos, S.A.; Kyrkos, M.T.; Stathopoulos, K.G. Earthquake induced torsion in buildings: Critical review and state of the art. Earthq. Struct.
**2015**, 8, 305–377. [Google Scholar] [CrossRef] [Green Version] - Kan, C.L.; Chopra, A.K. Elastic earthquake analysis of torsionally coupled multistorey buildings. Earthq. Eng. Struct. Dyn.
**1977**, 5, 395–412. [Google Scholar] [CrossRef] - Chandler, A.M.; Duan, X.N. Inelastic torsional behaviour of asymmetric buildings under severe earthquake shaking. Struct Eng. Rev.
**1990**, 2, 141–159. [Google Scholar] - Kan, C.L.; Chopra, A.K. Torsional Coupling and Earthquake Response of Simple Elastic and Inelastic Systems. J. Struct. Div.
**1981**, 107, 1569–1588. [Google Scholar] - Chandler, A.M.; Hutchinson, G.L. Torsional coupling effects in the earthquake response of asymmetric buildings. Eng. Struct.
**1986**, 8, 222–236. [Google Scholar] [CrossRef] - Newmark, N.M. Torsion in symmetrical buildings. In Proceedings of the 4th World Conference on Earthquake Engineering, Santiago, Chile, 13–18 January 1969; pp. 19–32. [Google Scholar]
- Bolt, B.A.; Tsai, Y.B.; Yeh, K.; Hsu, M.K. Earthquake strong motions recorded by a large near-source array of digital seismographs. Earthq. Eng. Struct. Dyn.
**1982**, 10, 561–573. [Google Scholar] [CrossRef] - De la Llera, J.C.; Chopra, A.K. Accidental torsion in buildings due to base rotational excitation. Earthq. Eng. Struct. Dyn.
**1994**, 23, 1003–1021. [Google Scholar] [CrossRef] - Hart, G.C.; Lew, M.; DiJulio, R.M. Torsional response of high–rise buildings. J. Struct. Division
**1975**, 101, 397–416. [Google Scholar] - Chandler, A.M. Building damage in Mexico City earthquake. Nature
**1986**, 320, 497–501. [Google Scholar] [CrossRef] - Ghayamghamian, M.R.; Nouri, G.R.; Igel, H.; Tobita, T. The Effect of Torsional Ground Motion on Structural Response: Code Recommendation for Accidental Eccentricity. Bull. Seismol. Soc. Am.
**2009**, 99, 1261–1270. [Google Scholar] [CrossRef] - Şafak, E. Response of a 42–storey steel–frame building to the MS=7.1 Loma Prieta earthquake. Eng. Struct.
**1993**, 15, 403–421. [Google Scholar] [CrossRef] - Li, Y.; Mau, S.T. Learning from Recorded Earthquake Motion of Buildings. J. Struct. Eng.
**1997**, 123, 62–69. [Google Scholar] [CrossRef] - Todorovska, M.I.; Trifunac, M.D. Earthquake damage detection in the Imperial County Services Building III: Analysis of wave travel times via impulse response functions. Soil Dyn. Earthq. Eng.
**2008**, 28, 387–404. [Google Scholar] [CrossRef] - Lemnitzer, A.; Massone, L.M.; Skolnik, D.A.; Martin, J.C.D.L.L.; Wallace, J.W. Aftershock response of RC buildings in Santiago, Chile, succeeding the magnitude 8.8 Maule earthquake. Eng. Struct.
**2014**, 76, 324–338. [Google Scholar] [CrossRef] - Çelebi, M. Recorded Earthquake Responses from the Integrated Seismic Monitoring Network of the Atwood Building, Anchorage, Alaska. Earthq. Spectra
**2006**, 22, 847–864. [Google Scholar] [CrossRef] - Michel, C.; Guéguen, P.; El Arem, S.; Mazars, J.; Kotronis, P. Full-scale dynamic response of an RC building under weak seismic motions using earthquake recordings, ambient vibrations and modelling. Earthq. Eng. Struct. Dyn.
**2010**, 39, 419–441. [Google Scholar] [CrossRef] [Green Version] - Oliveira, C.S.; Bolt, B.A. Rotational components of surface strong ground motion. Earthq. Eng. Struct. Dyn.
**1989**, 18, 517–526. [Google Scholar] [CrossRef] - Cochard, A.; Igel, H.; Schuberth, B.; Suryanto, W.; Velikoseltsev, A.; Schreiber, U.; Wassermann, J.; Scherbaum, F.; Vollmer, D. Rotational Motions in Seismology: Theory, Observation, Simulation. In Earthquake Source Asymmetry, Structural Media and Rotation Effects; Springer: Berlin/Heidelberg, Germany, 2006; pp. 391–411. [Google Scholar]
- Castellani, A. Array-derived rotational seismic motions: Revisited. Bull. Earthq. Eng.
**2016**, 15, 813–825. [Google Scholar] [CrossRef] - Trifunac, M.D. Differential earthquake motion of building foundations. J. Struct. Eng.
**1997**, 4, 414–422. [Google Scholar] [CrossRef] - Guéguen, P.; Bard, P.-Y. Soil-structure and soil-structure-soil interaction: Experimental evidence at the Volvi test site. J. Earthq. Eng.
**2005**, 9, 657–693. [Google Scholar] [CrossRef] - Çelebi, M.; Okawa, I.; Kashima, T.; Koyama, S.; Iiba, M. Response of a tall building far from the epicenter of the 11 March 2011 M 9.0 Great East Japan earthquake and aftershocks. Struct. Des. Tall Spec. Build.
**2014**, 23, 427–441. [Google Scholar] [CrossRef] [Green Version] - Rahmani, M.; Todorovska, M.I. 1D System identification of a 54-story steel frame building by seismic interferometry. Earthq. Eng. Struct. Dyn.
**2014**, 43, 627–640. [Google Scholar] [CrossRef] - Lin, C.-J.; Huang, W.-G.; Huang, H.-P.; Huang, B.S.; Ku, C.-S.; Liu, C.-C. Investigation of array-derived rotation in TAIPEI 101. J. Seismol.
**2012**, 16, 721–731. [Google Scholar] [CrossRef] - Hou, S.; Zeng, C.; Zhang, H.; Ou, J. Monitoring interstory drift in buildings under seismic loading using MEMS inclinometers. Constr. Build. Mater.
**2018**, 185, 453–467. [Google Scholar] [CrossRef] - Hester, D.; Brownjohn, J.; Huseynov, F.; Obrien, E.; Gonzalez, A.; Casero, M. Identifying damage in a bridge by analysing rotation response to a moving load. Struct. Infrastruct. Eng.
**2020**, 16, 1050–1065. [Google Scholar] [CrossRef] - Bas, S.; Apaydın, N.M.; Ilki, A.; Catbas, F.N. Structural health monitoring system of the long-span bridges in Turkey. Struct. Infrastruct. Eng.
**2018**, 14, 425–444. [Google Scholar] [CrossRef] - Huseynov, F.; Kim, C.; Obrien, E.J.; Brownjohn, J.M.W.; Hester, D.; Chang, K.C. Bridge damage detection using rotation measurements—Experimental validation. Mech. Syst. Signal Process.
**2020**, 135, 106380. [Google Scholar] [CrossRef] - Sousa, H.; Cavadas, F.; Henriques, A.; Bento, J.; Figueiras, J. Bridge deflection evaluation using strain and rotation measurements. Smart Struct. Syst.
**2013**, 11, 365–386. [Google Scholar] [CrossRef] - Lee, V.W.; Trifunac, M.D. Empirical Scaling of Rotational Spectra of Strong Earthquake Ground Motion. Bull. Seismol. Soc. Am.
**2009**, 99, 1378–1390. [Google Scholar] [CrossRef] - Bernauer, F.; Wassermann, J.; Igel, H. Rotational sensors—a comparison of different sensor types. J. Seismol.
**2012**, 16, 595–602. [Google Scholar] [CrossRef] - Igel, H.; Cochard, A.; Wassermann, J.; Flaws, A.; Schreiber, U.; Velikoseltsev, A.; Dinh, N.P. Broad-band observations of earthquake-induced rotational ground motions. Geophys. J. Int.
**2007**, 168, 182–196. [Google Scholar] [CrossRef] [Green Version] - Lee, W.H.K.; Huang, B.-S.; Langston, C.A.; Lin, C.-J.; Liu, C.-C.; Shin, T.-C.; Teng, T.-L.; Wu, C.-F. Review: Progress in Rotational Ground-Motion Observations from Explosions and Local Earthquakes in Taiwan. Bull. Seismol. Soc. Am.
**2009**, 99, 958–967. [Google Scholar] [CrossRef] [Green Version] - Guéguen, P.; Cornou, C.; Garambois, S.; Banton, J. On the Limitation of the H/V Spectral Ratio Using Seismic Noise as an Exploration Tool: Application to the Grenoble Valley (France), a Small Apex Ratio Basin. Pure Appl. Geophys.
**2007**, 164, 115–134. [Google Scholar] [CrossRef] - Cornou, C.; Bard, P.Y.; Dietrich, M. Contribution of dense array analysis to the identification and quantification of basin–edge–induced waves, Part II: Application to Grenoble basin (French Alps). Bull. Seismol. Soc. Am.
**2003**, 93, 2624–2648. [Google Scholar] [CrossRef] - Guéguen, P.; Langlais, M.; Garambois, S.; Voisin, C.; Douste-Bacqué, I. How sensitive are site effects and building response to extreme cold temperature? The case of the Grenoble’s (France) City Hall building. Bull. Earthq. Eng.
**2017**, 15, 889–906. [Google Scholar] [CrossRef] - Péquegnat, C.; Guéguen, P.; Hatzfeld, D.; Langlais, M. The French Accelerometric Network (RAP) and National Data Centre (RAP-NDC). Seismol. Res. Lett.
**2008**, 79, 79–89. [Google Scholar] [CrossRef] - Michel, C. Vulnérabilité Sismique de l’échelle du Bâtiment à Celle de la Ville—Apport des Techniques Expérimentales In Situ—Application à Grenoble. Ph.D. Thesis, Université Joseph–Fourier, Grenoble, France, 2007. [Google Scholar]
- Cao, Y.; Mavroeidis, G.P.; Ashoory, M. Comparison of observed and synthetic near–fault dynamic ground strains and rotations from the 2004 M w 6.0 Parkfield, California, earthquake. Bull. Seismol. Soc. Am.
**2018**, 108, 1240–1256. [Google Scholar] [CrossRef] - Spudich, P.; Fletcher, J.B. Observation and Prediction of Dynamic Ground Strains, Tilts, and Torsions Caused by the Mw 6.0 2004 Parkfield, California, Earthquake and Aftershocks, Derived from UPSAR Array Observations. Bull. Seismol. Soc. Am.
**2008**, 98, 1898–1914. [Google Scholar] [CrossRef] - Guéguen, P.; Johnson, P.; Roux, P. Nonlinear dynamics induced in a structure by seismic and environmental loading. J. Acoust. Soc. Am.
**2016**, 140, 582–590. [Google Scholar] [CrossRef] - Clinton, J.F.; Bradford, S.C.; Heaton, T.H.; Favela, J. The observed wander of the natural frequencies in a structure. Bull. Seismol. Soc. Am.
**2006**, 96, 237–257. [Google Scholar] [CrossRef] [Green Version] - Astorga, A.; Guéguen, P.; Kashima, T. Nonlinear Elasticity Observed in Buildings during a Long Sequence of Earthquakes. Bull. Seismol. Soc. Am.
**2018**, 108, 1185–1198. [Google Scholar] [CrossRef] - Cole, H. On–Line Failure Detection and Damping Measurement of Aerospace Structures by Random Decrement Signatures; Technical Report NASA CR–2205; NASA: Washington, DC, USA, 1973.
- Takeo, M. Rotational Motions Observed during an Earthquake Swarm in April 1998 Offshore Ito, Japan. Bull. Seismol. Soc. Am.
**2009**, 99, 1457–1467. [Google Scholar] [CrossRef] - Liu, C.-C.; Huang, B.-S.; Lee, W.H.K.; Lin, C.-J. Observing Rotational and Translational Ground Motions at the HGSD Station in Taiwan from 2007 to 2008. Bull. Seismol. Soc. Am.
**2009**, 99, 1228–1236. [Google Scholar] [CrossRef] - Shakib, H.; Tohidi, R.Z. Evaluation of accidental eccentricity in buildings due to rotational component of earthquake. J. Earthq. Eng.
**2002**, 6, 431–445. [Google Scholar] [CrossRef] - Snieder, R.; Şafak, E. Extracting the building response using seismic interferometry: Theory and application to the Millikan Library in Pasadena, California. Bull. Seismol. Soc. Am.
**2006**, 96, 586–598. [Google Scholar] [CrossRef] [Green Version] - Mehta, K.; Snieder, R.; Graizer, V. Extraction of near-surface properties for a lossy layered medium using the propagator matrix. Geophys. J. Int.
**2007**, 169, 271–280. [Google Scholar] [CrossRef] [Green Version] - Nakata, N.; Snieder, R. Estimating near-surface shear wave velocities in Japan by applying seismic interferometry to KiK-net data. J. Geophys. Res. Solid Earth
**2012**, 117. [Google Scholar] [CrossRef] [Green Version] - Chandra, J.; Guéguen, P.; Steidl, J.H.; Bonilla, L.F. In situ assessment of the G–γ curve for characterizing the nonlinear response of soil: Application to the Garner Valley downhole array and the wildlife liquefaction array. Bull. Seismol. Soc. Am.
**2015**, 105, 993–1010. [Google Scholar] [CrossRef] - Chandra, J.; Guéguen, P.; Bonilla, L.F. PGA-PGV/Vs considered as a stress–strain proxy for predicting nonlinear soil response. Soil Dyn. Earthq. Eng.
**2016**, 85, 146–160. [Google Scholar] [CrossRef] - Nakata, N.; Tanaka, W.; Oda, Y. Damage Detection of a Building Caused by the 2011 Tohoku-Oki Earthquake with Seismic Interferometry. Bull. Seismol. Soc. Am.
**2015**, 105, 2411–2419. [Google Scholar] [CrossRef] [Green Version] - Ebrahimian, M.; Rahmani, M.; Todorovska, M.I. Nonparametric estimation of wave dispersion in high-rise buildings by seismic interferometry. Earthq. Eng. Struct. Dyn.
**2014**, 43, 2361–2375. [Google Scholar] [CrossRef] - Guéguen, P.; Mercerat, E.D.; Alarcon, F. Parametric Study on the Interpretation of Wave Velocity Obtained by Seismic Interferometry in Beam-Like Buildings. Bull. Seismol. Soc. Am.
**2019**, 109, 1829–1842. [Google Scholar] [CrossRef] - Michel, C.; Guéguen, P. Interpretation of the velocity measured in buildings by seismic interferometry based on Timoshenko beam theory under weak and moderate motion. Soil Dyn. Earthq. Eng.
**2018**, 104, 131–142. [Google Scholar] [CrossRef] - Ferreira, A.M.G.; Igel, H. Rotational Motions of Seismic Surface Waves in a Laterally Heterogeneous Earth. Bull. Seismol. Soc. Am.
**2009**, 99, 1429–1436. [Google Scholar] [CrossRef] - Pandey, A.K.; Biswas, M. Damage Detection in Structures Using Changes in Flexibility. J. Sound Vib.
**1994**, 169, 3–17. [Google Scholar] [CrossRef] - Roux, P.; Guéguen, P.; Baillet, L.; Hamze, A. Structural-change localization and monitoring through a perturbation-based inverse problem. J. Acoust. Soc. Am.
**2014**, 136, 2586–2597. [Google Scholar] [CrossRef]

**Figure 2.**Description and representation of the instrumentation deployed in GCH and identification of the translation and rotation components.

**Figure 3.**Schematic view of the rotations calculated by the array (

**a**) in the case of shear deformation and (

**b**) in rigid body conditions.

**Figure 4.**Example of 10 min recordings in translation and in rotation, (

**a**) under ambient vibrations, (

**b**) at the time of the local storm. Note the amplitude difference on the y axes.

**Figure 5.**Averaged Fourier spectra of the 10 min windows. (

**a**) acceleration in translation at station OGH6; (

**b**) rotation rate obtained by rotation sensor HJZ and derived from the array using OGH4 and OGH5 stations (Equation (1)).

**Figure 6.**Time variation of weather conditions (temperature and wind velocity) and resonance frequencies in translation in directions x and y (station OGH6), and in rotation obtained by the rotation sensor HJZ.

**Figure 7.**Comparison of the rotation rates calculated by the array-derived method at the top (

**a**); with the rotation sensor HJZ (

**b**) and at the bottom of the structure (

**c**).

**Figure 8.**Amplitude variation of the RMS values of translation and array-derived rotations during the experiment, at the top and at the bottom of the structure. The dashed horizontal line corresponds to the sensitivity limit of the rotation sensor, estimated experimentally.

**Figure 9.**Comparison between translation and array-derived rotation at the bottom (

**a**) and at the top (

**b**) of the structure.

**Figure 10.**Interferograms obtained by seismic interferometry by deconvolution (SIbyD) between the horizontal components of sensors OGH6 and OGH3 in directions x and y, and with the array-derived rotation rates at the top ${\dot{\theta}}_{45}$ and at the bottom ${\dot{\theta}}_{12}$ of the structure.

**Figure 11.**(

**a**) Phase velocity variations calculated from the ratio between acceleration and array-derived rotation rate at the bottom of the structure; (

**b**) Comparison of velocities calculated by SIbyD and derived from the ratios between acceleration and rotation at the top of the building.

**Table 1.**Characteristics of the variations of the weather parameters and modal parameters (Δ corresponds to the variations during the local storm).

Parameters | μ | σ | σ/μ | Δ | |
---|---|---|---|---|---|

Temperature °C | 18 | 4 | 24% | −30% | |

Wind speed m/s | 1.6 | 2 | 116 | 78% | |

Frequency Hz | y-dir | 1.212 | 0.003 | 0.3% | −1.1% |

x-dir | 1.155 | 0.004 | 0.3% | −1.3% | |

z-dir (${\dot{\theta}}_{HJZ}$) | 1.442 | 0.003 | 0.2% | −0.9% |

**Table 2.**Average ratios of root mean square (RMS) values between translation acceleration and torsion rate at the top and at the bottom of the structure.

RMS Ratio | Mean | Std | COV (%) |
---|---|---|---|

$\ddot{u}$ Top/Bot | 18.3 | 6.3 | 34 |

${\dot{\theta}}_{45}$/${\dot{\theta}}_{12}$ | 40.6 | 26.4 | 65 |

$u$ Top/${\dot{\theta}}_{45}$ | 315.3 | 261.1 | 83 |

$u$ Bot/${\dot{\theta}}_{12}$ | 404.5 | 38.4 | 9 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guéguen, P.; Guattari, F.; Aubert, C.; Laudat, T.
Comparing Direct Observation of Torsion with Array-Derived Rotation in Civil Engineering Structures. *Sensors* **2021**, *21*, 142.
https://doi.org/10.3390/s21010142

**AMA Style**

Guéguen P, Guattari F, Aubert C, Laudat T.
Comparing Direct Observation of Torsion with Array-Derived Rotation in Civil Engineering Structures. *Sensors*. 2021; 21(1):142.
https://doi.org/10.3390/s21010142

**Chicago/Turabian Style**

Guéguen, Philippe, Frédéric Guattari, Coralie Aubert, and Theo Laudat.
2021. "Comparing Direct Observation of Torsion with Array-Derived Rotation in Civil Engineering Structures" *Sensors* 21, no. 1: 142.
https://doi.org/10.3390/s21010142