Using DEM to Investigate Boundary Conditions for Rocking URM Facades Subjected to Earthquake Motion
Publication: Journal of Structural Engineering
Volume 147, Issue 11
Abstract
Façade overturning is a frequently observed collapse mechanism occurring in unreinforced masonry (URM) buildings during high-intensity, earthquake-induced shaking. Following complete separation from a building, the rocking motion of a URM façade and the associated impact against the return walls are the factors that continue to contribute to the façade out-of-plane capacity. Seismic vulnerability studies of URM façades have historically neglected the interaction between building earthquake response and the rocking response of the façade, whereas in the study reported herein this interaction was analyzed using the discrete element modeling (DEM) approach, resulting in a façade out-of-plane capacity reduction. The increment in the dynamic rocking capacity caused by the frictional connection between the URM façade and the building was also analyzed and is reported.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This project was partially supported by QuakeCoRE, a New Zealand Tertiary Education Commission-funded Centre. This is QuakeCoRE publication number 634. The authors also gratefully acknowledge the software 3DEC provided by Itasca consulting group under the Itasca Educational Partnership program. Use was made in this paper of a solid geometry generation tool developed by Dr. Daniele Malomo (MDRG-Matthew DeJong Research Group, University of California, Berkeley), who is gratefully acknowledged.
References
Abeling, S., and J. M. Ingham. 2020. “Volume loss fatality model for as-built and retrofitted clay brick unreinforced masonry buildings damaged in the 2010/11 Canterbury earthquakes.” Structures 24 (Apr): 940–954. https://doi.org/10.1016/j.istruc.2020.02.014.
AlShawa, O., D. Liberatore, and L. Sorrentino. 2019. “Dynamic one-sided out-of-plane behavior of unreinforced-masonry wall restrained by elasto-plastic tie-rods.” Int. J. Archit. Heritage 13 (3): 340–357. https://doi.org/10.1080/15583058.2018.1563226.
Aslam, M., W. G. Godden, and D. T. Scalise. 1975. “Sliding response of rigid bodies to earthquake motions.” In A report of an analytical and experimental study of the sliding response of rigid blocks under simultaneous horizontal and vertical earthquake accelerations. Berkeley, CA: Univ. of California.
Bao, Y., and D. Konstantinidis. 2020. “Dynamics of a sliding-rocking block considering impact with an adjacent wall.” Earthquake Eng. Struct. Dyn. 49 (5): 498–523. https://doi.org/10.1002/eqe.3250.
Bathe, K. J., and E. L. Wilson. 1976. Numerical methods in finite element analysis. New York: Prentice-Hall.
Benito, B., et al. 2007. “An overview of the damaging and low magnitude Mw 4.8 La Paca earthquake on 29 January 2005: Context, seismotectonics, and seismic risk implications for southeast Spain.” Bull. Seismol. Soc. Am. 97 (3): 671–690. https://doi.org/10.1785/0120050150.
Bruneau, M. 1994. “State-of-the-art report on seismic performance of unreinforced masonry buildings.” J. Struct. Eng. 120 (1): 230–251. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:1(230).
Casapulla, C., L. Giresini, L. U. Argiento, and A. Maione. 2019a. “Nonlinear static and dynamic analysis of rocking masonry corners using rigid macro-block modeling.” Int. J. Struct. Stab. Dyn. 19 (11): 1950137. https://doi.org/10.1142/S0219455419501372.
Casapulla, C., L. Giresini, and P. B. Lourenço. 2017. “Rocking and kinematic approaches for rigid block analysis of masonry walls: State of the art and recent developments.” Buildings 7 (3): 69. https://doi.org/10.3390/buildings7030069.
Casapulla, C., and A. Maione. 2017. “Free damped vibrations of rocking rigid blocks as uniformly accelerated motions.” Int. J. Struct. Stab. Dyn. 17 (6): 1750058. https://doi.org/10.1142/S0219455417500584.
Casapulla, C., A. Maione, and L. U. Argiento. 2019b. “Performance-based seismic analysis of rocking masonry façades using non-linear kinematics with frictional resistances: A case study.” Int. J. Archit. Heritage 2019 (Oct): 1–15. https://doi.org/10.1080/15583058.2019.1674944.
Cattari, S., D. Camilletti, G. Magenes, C. F. Manzini, P. Morandi, E. Spacone, F. Cannizzaro, B. Calderoni, G. Camata, C. Marano, G. Occhipinti, and A. E. S. Cordasco. 2018. “A comparative study on a 2-story benchmark case study through nonlinear seismic analysis.” In Proc., 16th European Conf. on Earthquake Engineering. Thessaloniki, Greece: European Conference on Earthquake Engineering.
Cattari, S., and G. Magenes. 2021. “Benchmarking the software packages to model and assess the seismic response of URM existing buildings through nonlinear analyses.” Bull. Earthquake Eng. https://doi.org/10.1007/s10518-021-01078-0.
Degli Abbati, S., S. Cattari, and S. Lagomarsino. 2018. “Theoretically-based and practice-oriented formulations for the floor spectra evaluation.” Earthquakes Struct. 15 (5): 565–581. https://doi.org/10.12989/eas.2018.15.5.565.
DeJong, M. J. 2009. “Seismic assessment strategies for masonry structures.” Ph.D. dissertation, Dept. of Architecture, Massachusetts Institute of Technology.
Derakhshan, H., D. Y. Dizhur, M. C. Griffith, and J. M. Ingham. 2014. “Seismic assessment of out-of-plane loaded unreinforced masonry walls in multi-storey buildings.” Bull. N. Z. Soc. Earthquake Eng. 47 (2): 119–138. https://doi.org/10.5459/bnzsee.47.2.119-138.
Dimitri, R., L. De Lorenzis, and G. Zavarise. 2011. “Numerical study on the dynamic behavior of masonry columns and arches on buttresses with the discrete element method.” Eng. Struct. 33 (12): 3172–3188. https://doi.org/10.1016/j.engstruct.2011.08.018.
Dizhur, D., N. Ismail, C. Knox, R. Lumantarna, and J. M. Ingham. 2010. “Performance of unreinforced and retrofitted masonry buildings during the 2010 Darfield earthquake.” Bull. N. Z. Soc. Earthquake Eng. 43 (4): 321–339. https://doi.org/10.5459/bnzsee.43.4.321-339.
ElGawady, M. A., Q. Ma, J. W. Butterworth, and J. Ingham. 2011. “Effects of interface material on the performance of free rocking blocks.” Earthquake Eng. Struct. Dyn. 40 (4): 375–392. https://doi.org/10.1002/eqe.1025.
European Committee for Standardization. 2004. “Design of structures for earthquake resistance.” In Part 1: General rules, seismic actions and rules for buildings. Brussels, Belgium: CEN.
Galvez, F., S. Segatta, M. Giaretton, K. Q. Walsh, I. Giongo, and D. Dizhur. 2018. “FE and DE modelling of out-of-plane two-way bending behaviour of unreinforced masonry walls.” In Proc., 16th European Conf. on Earthquake Engineering. Thessaloniki, Greece: European Conference on Earthquake Engineering.
Giaretton, M., D. Dizhur, and J. M. Ingham. 2016. “Dynamic testing of as-built clay brick unreinforced masonry parapets.” Eng. Struct. 127 (Nov): 676–685. https://doi.org/10.1016/j.engstruct.2016.09.016.
Giresini, L. 2017. “Design strategy for the rocking stability of horizontally restrained masonry walls.” In Proc., 6th Int. Conf. on Computational Methods in Structural Dynamics and Earthquake Engineering, 2963–2979. Athens, Greece: National Technical Univ. of Athens.
Giresini, L., C. Casapulla, R. Denysiuk, J. Matos, and M. Sassu. 2018. “Fragility curves for free and restrained rocking masonry façades in one-sided motion.” Eng. Struct. 164 (Jun): 195–213. https://doi.org/10.1016/j.engstruct.2018.03.003.
Giresini, L., M. Fragiacomo, and P. B. Lourenço. 2015. “Comparison between rocking analysis and kinematic analysis for the dynamic out-of-plane behavior of masonry walls.” Earthquake Eng. Struct. Dyn. 44 (13): 2359–2376. https://doi.org/10.1002/eqe.2592.
Giresini, L., and M. Sassu. 2016. “Horizontally restrained rocking blocks: Evaluation of the role of boundary conditions with static and dynamic approaches.” Bull. Earthquake Eng. 15 (1): 385–410. https://doi.org/10.1007/s10518-016-9967-7.
Giresini, L., F. Solarino, O. Paganelli, D. Oliveira, and M. Froli. 2019. “ONE-SIDED rocking analysis of corner mechanisms in masonry structures: Influence of geometry, energy dissipation, boundary conditions.” Soil Dyn. Earthquake Eng. 123 (Aug): 357–370. https://doi.org/10.1016/j.soildyn.2019.05.012.
Gubana, A., and M. Melotto. 2019. “Discrete-element analysis of floor influence on seismic response of masonry structures.” Proc. Inst.Civ. Eng. Struct. Build. 174 (6): 1–30. https://doi.org/10.1680/jstbu.19.00099.
Hess, R. L. 2007. “Impacts of a M7.8 southern San Andreas earthquake on unreinforced masonry (URM) buildings.” In The ShakeOut scenario, suplemental study—Unreinforced masonry (URM) buildings. Sacramento, CA: California Geological Survey.
Housner, G. W. 1963. “The behavior of inverted pendulum structures during earthquakes.” Bull. Seismol. Soc. Am. 53 (2): 403–417. https://doi.org/10.1785/BSSA0530020403.
Ishiyama, Y. 1982. “Motions of rigid bodies and criteria for overturning by earthquake excitations.” Earthquake Eng. Struct. Dyn. 10 (1): 635–650. https://doi.org/10.1002/eqe.4290100502.
Itasca. 2013. 3DEC (3-Dimensional distinct element code). Minneapolis, MN: Itasca.
Jing, L., and O. Stephansson. 2007. “Explicit discrete element method for block systems—The distinct element method.” In Fundamentals of discrete element methods for rock engineering, 235–316. Amsterdam, Netherlands: Elsevier.
Kalliontzis, D., S. Sritharan, and A. Schultz. 2016. “Improved coefficient of restitution estimation for free rocking members.” J. Struct. Eng. 142 (12): 06016002. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001598.
Lagomarsino, S. 1998. “A new methodology for the post-earthquake investigation of ancient churches.” In Proc., 11th European Conf. on Earthquake Engineering. Rotterdam, Netherlands: A.A. Balkema.
Lagomarsino, S. 2015. “Seismic assessment of rocking masonry structures.” Bull. Earthquake Eng. 13 (1): 97–128. https://doi.org/10.1007/s10518-014-9609-x.
Lemos, J. V., and A. Campos Costa. 2017. “Simulation of shake table tests on out-of-plane masonry buildings. Part (V): Discrete element approach.” Int. J. Archit. Heritage 11 (1): 117–124. https://doi.org/10.1080/15583058.2016.1237587.
Lipo, B., and G. de Felice. 2016. “Smooth-rocking oscillator under natural accelerograms.” In Proc., ECCOMAS Congress 2016—VII European Congress on Computational Methods in Applied Sciences and Engineering. Island, Greece: European Congress on Computational Methods.
Lipscombe, P. R., and S. Pellegrino. 1993. “Free rocking of prismatic blocks.” J. Eng. Mech. 119 (7): 1387–1410. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:7(1387).
Lorig, L. J., and R. D. Hart. 1993. “Block dynamics modeling in support of seismic design.” In Dynamic analysis and design considerations for high-level nuclear waste repositories, 228–242. New York: ASCE.
MathWorks. 2008. MATLAB User´s manual. Natick, MA: MathWorks.
Menon, A., and G. Magenes. 2011. “Definition of seismic input for out-of-plane response of masonry walls: I. Parametric study.” J. Earthquake Eng. 15 (2): 165–194. https://doi.org/10.1080/13632460903456981.
Meriggi, P., G. de Felice, S. De Santis, F. Gobbin, A. Mordanova, and B. Pantò. 2019. “Distinct element modelling of masonry walls under out-of-plane seismic loading.” Int. J. Archit. Heritage 13 (7): 1110–1123. https://doi.org/10.1080/15583058.2019.1615152.
Mordanova, A., G. de Felice, and A. Genoese. 2017. “Assessment of the stability condition of the Claudio aqueduct.” In Proc., 3rd Int. Conf. on Protection of Historical Constructions. Lisbon, Portugal: Protection of Historical Constructions.
Olcese, S. 2018. “Use of discrete element modeling for the seismic assessment of a benchmark case study masonry structure.” Master’s thesis, Dipartimento di Ingegneria Civile, Chimica e Ambientale, Università degli Studi di Genova.
Papantonopoulos, C., I. N. Psycharis, D. Y. Papastamatiou, J. V. Lemos, and H. P. Mouzakis. 2002. “Numerical prediction of the earthquake response of classical columns using the distinct element method.” Earthquake Eng. Struct. Dyn. 31 (9): 1699–1717. https://doi.org/10.1002/eqe.185.
Priestley, M. J. N. 1985. “Seismic behaviour of unreinforced masonry walls.” Bull. N. Z. Nat. Soc. Earthquake Eng. 18 (2): 191–205. https://doi.org/10.5459/bnzsee.18.2.191-205.
Psycharis, I. N., and P. C. Jennings. 1983. “Rocking of slender rigid bodies allowed to uplift.” Earthquake Eng. Struct. Dyn. 11 (Sep): 57–76. https://doi.org/10.1002/eqe.4290110106.
Psycharis, I. N., J. V. Lemos, D. Y. Papastamatiou, C. Zambas, and C. Papantonopoulos. 2003. “Numerical study of the seismic behaviour of a part of the Parthenon Pronaos.” Earthquake Eng. Struct. Dyn. 32 (13): 2063–2084. https://doi.org/10.1002/eqe.315.
Pulatsu, B., F. Gencer, and E. Erdogmus. 2020. “Study of the effect of construction techniques on the seismic capacity of ancient dry-joint masonry towers through DEM.” Eur. J. Environ. Civ. Eng. 2020 (Sep): 1–18. https://doi.org/10.1080/19648189.2020.1824823.
Robert McNeel and Associates. 2014. Rhinoceros. Seattle: Robert McNeel and Associates.
Shawa, O. A., G. de Felice, A. Mauro, and L. Sorrentino. 2012. “Out-of-plane seismic behaviour of rocking masonry walls.” J. Earthquake Eng. Struct. Dyn. 5 (2): 253–271. https://doi.org/10.1002/eqe.1168.
Sigurdsson, G. Ö., R. Rupakhety, and S. Ólafsson. 2019. A study of rigid blocks rocking against rigid walls, 323–334. Cham, Switzerland: Springer.
Sorrentino, L., O. AlShawa, and L. D. Decanini. 2011. “The relevance of energy damping in unreinforced masonry rocking mechanisms. Experimental and analytic investigations.” Bull. Earthquake Eng. 9 (5): 1617–1642. https://doi.org/10.1007/s10518-011-9291-1.
Sorrentino, L., S. Kunnath, G. Monti, and G. Scalora. 2008. “Seismically induced one-sided rocking response of unreinforced masonry façades.” Eng. Struct. 30 (8): 2140–2153. https://doi.org/10.1016/j.engstruct.2007.02.021.
Standards Australia. 2007. Structural design actions, part 4: Earthquake actions in Australia. AS1170.4. Sydney, Australia: Standards Australia.
Standards New Zealand. 2004. Structural design actions, part 5: Earthquake actions—New Zealand. NZS 1170.5:2004. Wellington, New Zealand: Standards New Zealand.
Ther, T., and L. P. Kollár. 2016. “Refinement of Housner’s model on rocking blocks.” Bull. Earthquake Eng. 15 (5): 2305–2319. https://doi.org/10.1007/s10518-016-0048-8.
Tomassetti, U., F. Graziotti, L. Sorrentino, and A. Penna. 2019. “Modelling rocking response via equivalent viscous damping.” Earthquake. Eng. Struct. Dyn. 2020 (Sep): 1–18. https://doi.org/10.1002/eqe.3182.
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Dec 1, 2020
Accepted: Jul 9, 2021
Published online: Sep 2, 2021
Published in print: Nov 1, 2021
Discussion open until: Feb 2, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- F. Galvez, D. Dizhur, J. M. Ingham, Adjacent interacting masonry structures: shake table test blind prediction discrete element method simulation, Bulletin of Earthquake Engineering, 10.1007/s10518-023-01640-y, (2023).
- Michele Angiolilli, Andrea Brunelli, Serena Cattari, Fragility curves of masonry buildings in aggregate accounting for local mechanisms and site effects, Bulletin of Earthquake Engineering, 10.1007/s10518-023-01635-9, (2023).
- Elyse Hamp, Rachel Gerber, Bora Pulatsu, Mario Quintero, Jeffrey Erochko, Nonlinear Seismic Assessment of a Historic Rubble Masonry Building via Simplified and Advanced Computational Approaches, Buildings, 10.3390/buildings12081130, 12, 8, (1130), (2022).
- Marco Francesco Funari, Bora Pulatsu, Simon Szabó, Paulo B. Lourenço, A solution for the frictional resistance in macro-block limit analysis of non-periodic masonry, Structures, 10.1016/j.istruc.2022.06.072, 43, (847-859), (2022).
- Sanjeev Prajapati, Giacomo Destro Bisol, Omar AlShawa, Luigi Sorrentino, Non‐linear dynamic model of a two‐bodies vertical spanning wall elastically restrained at the top, Earthquake Engineering & Structural Dynamics, 10.1002/eqe.3692, 51, 11, (2627-2647), (2022).
- Francisco Galvez, Luigi Sorrentino, Dmytro Dizhur, Jason M. Ingham, Seismic rocking simulation of unreinforced masonry parapets and façades using the discrete element method, Earthquake Engineering & Structural Dynamics, 10.1002/eqe.3641, 51, 8, (1840-1856), (2022).