Trilinear Model for the Out-of-Plane Seismic Assessment of Vertically Spanning Unreinforced Masonry Walls
Publication: Journal of Structural Engineering
Volume 145, Issue 12
Abstract
Out-of-plane failure of masonry walls is often responsible for the partial collapse of unreinforced masonry structures. Modeling the out-of-plane response of these walls is therefore key in the assessment of existing buildings. The paper presents a new trilinear model describing the force-displacement response of vertically spanning unreinforced masonry walls subjected to out-of-plane loading. Different factors that affect the response of the walls are captured by the model: the support conditions, the level of applied axial load, the slenderness ratio, and the deformability of the wall. The model is validated against experimental results from shake table tests. The force and displacement parameters of the model are described by analytical expressions that are derived from a mechanical model previously developed for unreinforced masonry. They offer an alternative to existing trilinear models in which corner displacements are mainly defined by empirical relationships.
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Acknowledgments
The work presented in this paper was founded by the Swiss Federal Office of the Environment and the Construction Department of the Canton Basel-Stadt. Additionally, the authors would like to thank Prof. Michael Griffith (University of Adelaide), Prof. Andrea Penna (University of Pavia), and Dr. Francesco Graziotti (University of Pavia) for furnishing the data set used for validation of the present research.
References
Al Shawa, O., G. Felice, A. Mauro, and L. Sorrentino. 2012. “Out-of-plane seismic behaviour of rocking masonry walls.” Earthquake Eng. Struct. Dyn. 41 (5): 949–968. https://doi.org/10.1002/eqe.1168.
Brencich, A., C. Corradi, and L. Gambarotta. 2008. “Eccentrically loaded brickwork: Theoretical and experimental results.” Eng. Struct. 30 (12): 3629–3643. https://doi.org/10.1016/j.engstruct.2008.05.010.
Cavaleri, L., M. Fossetti, and M. Papia. 2009. “Modeling of out-of-plane behavior of masonry walls.” J. Struct. Eng. 135 (12): 1522–1532. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:12(1522).
Chapman, J. C., and J. Slatford. 1957. “The elastic buckling of brittle columns.” Proc. Inst. Civ. Eng. 6 (1): 107–125. https://doi.org/10.1680/iicep.1957.12395.
D’Ayala, D., and E. Speranza. 2003. “Definition of collapse mechanisms and seismic vulnerability of historic masonry buildings.” Earthquake Spectra 19 (3): 479–509. https://doi.org/10.1193/1.1599896.
Dazio, A. 2009. “The effect of the boundary conditions on the out-of-plane behaviour of unreinforced masonry walls.” In Proc., 14th World Conf. on Earthquake Engineering. Beijing: International Association for Earthquake Engineering.
Degli Abbati, S., and S. Lagomarsino. 2017. “Out-of-plane static and dynamic response of masonry panels.” Eng. Struct. 150 (Nov): 803–820. https://doi.org/10.1016/j.engstruct.2017.07.070.
Derakhshan, H., D. Dizhur, M. C. Griffith, and J. M. Ingham. 2014. “In situ out-of-plane testing of as-built and retrofitted unreinforced masonry walls.” J. Struct. Eng. 140 (6): 04014022. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000960.
Derakhshan, H., M. C. Griffith, and J. M. Ingham. 2013a. “Airbag testing of multi-leaf unreinforced masonry walls subjected to one-way bending.” Eng. Struct. 57 (Dec): 512–522. https://doi.org/10.1016/j.engstruct.2013.10.006.
Derakhshan, H., M. C. Griffith, and J. M. Ingham. 2013b. “Out-of-plane behavior of one-way spanning unreinforced masonry walls.” J. Eng. Mech. 139 (4): 409–417. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000347.
Derakhshan, H., M. C. Griffith, and J. M. Ingham. 2016. “Out-of-plane seismic response of vertically spanning URM walls connected to flexible diaphragms.” Earthquake Eng. Struct. Dyn. 45 (4): 563–580. https://doi.org/10.1002/eqe.2671.
Derakhshan, H., Y. Nakamura, J. M. Ingham, and M. C. Griffith. 2017. “Simulation of shake table tests on out-of-plane masonry buildings. Part I: Displacement-based approach using simple failure mechanisms.” Int. J. Architect. Heritage 11 (1): 72–78. https://doi.org/10.1080/15583058.2016.1237590.
Doherty, K. 2000. “An investigation of the weak links in the seismic load path of unreinforced masonry building.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Adelaide.
Doherty, K., M. C. Griffith, N. T. K. Lam, and J. Wilson. 2002. “Displacement-based seismic analysis for out-of-plane bending of unreinforced masonry walls.” Earthquake Eng. Struct. Dyn. 31 (4): 833–850. https://doi.org/10.1002/eqe.126.
Ferreira, T. M., A. A. Costa, A. Arede, A. Gomes, and A. Costa. 2015. “Experimental characterization of the out-of-plane performance of regular stone masonry walls, including test setups and axial load influence.” Bull. Earthquake Eng. 13 (9): 2667–2692. https://doi.org/10.1007/s10518-015-9742-1.
Giaretton, M., D. Dizhur, F. da Porto, and J. M. Ingham. 2016a. “Construction details and observed earthquake performance of unreinforced clay brick masonry cavity-walls.” Structures 6 (May): 159–169. https://doi.org/10.1016/j.istruc.2016.04.004.
Giaretton, M., D. Dizhur, and J. M. Ingham. 2016b. “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.
Godio, M., and K. Beyer. 2017. “Analytical model for the out-of-plane response of vertically spanning unreinforced masonry walls.” Earthquake Eng. Struct. Dyn. 46 (15): 2757–2776. https://doi.org/10.1002/eqe.2929.
Godio, M., and K. Beyer. 2019. “Evaluation of force-based and displacement-based out-of-plane seismic assessment methods for unreinforced masonry walls through refined model simulations.” Earthquake Eng. Struct. Dyn. 48 (4): 454–475. https://doi.org/10.1002/eqe.3144.
Graziotti, F., U. Tomassetti, A. Penna, and G. Magenes. 2016. “Out-of-plane shaking table tests on URM cavity walls.” Eng. Struct. 125 (Oct): 455–470. https://doi.org/10.1016/j.engstruct.2016.07.011.
Griffith, M. C., N. T. K. Lam, J. L. Wilson, and K. Doherty. 2004. “Experimental investigation of unreinforced brick masonry walls in flexure.” J. Struct. Eng. 130 (3): 423–432. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:3(423).
Griffith, M. C., G. Magenes, G. Melis, and L. Picchi. 2003. “Evaluation of out-of-plane stability of unreinforced masonry walls subjected to seismic excitation.” J. Earthquake Eng. 7 (1): 141–169. https://doi.org/10.1080/13632460309350476.
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.
Lam, N. T. K., J. L. Wilson, and G. L. Hutchinson. 1995. “The seismic resistance of unreinforced masonry cantilever walls in low seismicity areas.” Bull. N. Z. Nat. Soc. Earthquake Eng. 28 (3): 179–195.
Landi, L., R. Gabellieri, and P. P. Diotallevi. 2015. “A model for the out-of-plane dynamic analysis of unreinforced masonry walls in buildings with flexible diaphragms.” Soil Dyn. Earthquake Eng. 79 (Dec): 211–222. https://doi.org/10.1016/j.soildyn.2015.09.013.
Lu, M., A. E. Schultz, and H. K. Stolarski. 2004. “Analysis of the influence of tensile strength on the stability of eccentrically compressed slender unreinforced masonry walls under lateral loads.” J. Struct. Eng. 130 (6): 921–933. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:6(921).
Meisl, C. S., K. J. Elwood, and C. E. Ventura. 2007. “Shake table tests on the out-of-plane response of unreinforced masonry walls.” Can. J. Civ. Eng. 34 (11): 1381–1392. https://doi.org/10.1139/L07-059.
Melis, G. 2002. “Displacement-based seismic analysis for out of plane bending of unreinforced masonry walls.” M.S. dissertation, Rose School, Univ. of Pavia.
Morandi, P., G. Magenes, and M. C. Griffith. 2008. “Second order effects in out-of-plane strength of unreinforced masonry walls subjected to bending and compression.” Aust. J. Struct. Eng. 8 (2): 133–144. https://doi.org/10.1080/13287982.2008.11464993.
NTC (Norme Tecniche per le Costruzioni). 2008. Decreto Ministeriale 14/1/2008. Nuove norme tecniche per le costruzioni. Ministry of Infrastructures and Transportations. [In Italian.]. Rome: Gazzetta Ufficiale della Repubblica Italiana.
NZSEE (New Zealand Society for Earthquake Engineering). 2014. Assessment and improvement of the structural performance of buildings in earthquakes. Recommendations of a NZSEE Study Group on Earthquake Risk Buildings. Wellington, New Zealand: NZSEE.
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. 1985. “Seismic behaviour of unreinforced masonry walls.” Bull. N. Z. Nat. Soc. Earthquake Eng. 18 (2): 191–205.
Psycharis, I. N., D. Y. Papastamatiou, and A. P. Alexandris. 2000. “Parametric investigation of the stability of classic al columns under harmonic and earthquake excitations.” Earthquake Eng. Struct. Dyn. 29 (8): 1093–1109. https://doi.org/10.1002/1096-9845(200008)29:8%3C1093::AID-EQE953%3E3.0.CO;2-S.
Sorrentino, L. 2003. Dinamica di muri sollecitati fuori del piano come sistemi di corpi rigidi. La Sapienza, Italy: Univ. of Rome.
Sorrentino, L., D. D’Ayala, G. de Felice, M. C. Griffith, S. Lagomarsino, and G. Magenes. 2016. “Review of out-of-plane seismic assessment techniques applied to existing masonry buildings.” Int. J. Architect. Heritage 11 (1): 1–20. https://doi.org/10.1080/15583058.2016.1237586.
Sorrentino, L., R. Masiani, and M. C. Griffith. 2008. “The vertical spanning strip wall as a coupled rocking rigid body assembly.” Struct. Eng. Mech. 29 (4): 433–453. https://doi.org/10.12989/sem.2008.29.4.433.
Tomassetti, U., F. Graziotti, A. Penna, and G. Magenes. 2018. “Modelling one-way out-of-plane response of single-leaf and cavity walls.” Eng. Struct. 167 (Feb): 241–255. https://doi.org/10.1016/j.engstruct.2018.04.007.
Tondelli, M., K. Beyer, and M. DeJong. 2016. “Influence of boundary conditions on the out-of-plane response of brick masonry walls in buildings with RC slabs.” Earthquake Eng. Struct. Dyn. 45 (8): 1337–1356. https://doi.org/10.1002/eqe.2710.
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Published In
Journal of Structural Engineering
Volume 145 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Nov 2, 2017
Accepted: Apr 5, 2019
Published online: Oct 1, 2019
Published in print: Dec 1, 2019
Discussion open until: Mar 1, 2020
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