Abstract
A framework for evaluating the risk of the out-of-plane mechanism of masonry façades subjected to earthquake excitations is presented. The effect of seismic events on masonry façades is investigated and results are presented in terms of fragility curves and seismic risk for several masonry supporting restrictions. The restrictions considered are (1) masonry façade unrestricted to rock on a firm base, (2) masonry façade restricted to rock in one direction, and (3) restrained rocking masonry façade in one-sided motion. Because the available empirical information is insufficient to obtain fragility functions for masonry façades, the study is based on numerical analysis and recent studies on seismic risk. The conceptual framework is illustrated with information from masonry façades characteristic of Mexican religious structures and within the seismic hazard areas of Mexico. Since the frequency characteristics of ground motions strongly depend on the distance from the epicenter to the site, which is of cardinal importance to the vulnerability of these structures, the impact of this distance for hard-soil sites is thoroughly investigated. The probability of failure for the three types of masonry façades was calculated. It was found that the probability of failure decreases with an increased width-to-height relation; conversely, the probability of failure (reported in terms of the reliability index) increases with increased block size dimensions. Results in this study show that restraining conditions of the façades inconsequentially affect the probability of failure. Although the reliability of freestanding masonry façades are marginally greater, this finding holds true regardless of whether or not one considers far-field ground motions. The results in this study can be useful for evaluation and reinforcement tasks of masonry façades located in areas of high seismic hazard.
Similar content being viewed by others
References
Abrahamson NA, Silva WJ (1997) Empirical response spectral attenuation relations for shallow crustal earthquakes. Seismol Res Lett 68(1):94–127
AlShawa O, Liberatore D, Sorrentino L (2019) Dynamic one-sided out-of-plane behavior of unreinforced-masonry wall restrained by elasto-plastic tie-rods. Int J Architsssssss Heritage 13(3):340–357
Arroyo D, García D, Ordaz M, Mora MA, Singh SK (2010) Strong ground-motion relations for Mexican interplate earthquakes. J Seismolog 14(4):769–785
ASCE/SEI 7–10 (2010) Minimum design loads for buildings and other structures (ASCE/ SEI 7–10)
Bachmann JA, Strand M, Vassiliou MF, Broccardo M, Stojadinović B (2018) Is rocking motion predictable? Earthq Eng Struct Dyn 47(2):535–552
Baker JW (2015) Efficient analytical fragility function fitting using dynamic structural analysis. Earthq Spectra 31(1):579–599
BSSC (2004) NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, 2003 Edition. Part 1 - Provisions, Part 2 Commentary. Technical Report FEMA 450, Building Seismic Safety Council for the Federal Emergency Management Agency, Washington, D.C
Butcher JC (2016) Numerical methods for ordinary differential equations. Wiley, Hoboken
Candia G, Macedo J, Jaimes MA, Magna-Verdugo C (2019) A new state-of-the-art platform for probabilistic and deterministic seismic hazard assessment. Seismol Res Lett Seismol Res Lett 90(6):2262–2275
Casapulla C, Giresini L, Lourenço PB (2017) Rocking and kinematic approaches for rigid block analysis of masonry walls: state of the art and recent developments. Buildings 7(3):69
Ceran HB, Erberik MA (2013) Effect of out-of-plane behavior on seismic fragility of masonry buildings in Turkey. Bull Earthq Eng 11(5):1775–1795
Chavez M, Peña F, Reyes R (2017) Out of plane behavior of a typical Colonial temple scale 1:8. In: 6th Structural Engineers World Congress, Cancún México
Chavez M, Peña F, García N, Durán D (2020). Damages patterns in historical temples of Puebla, Morelos and Oaxaca after september 2017 Mexico earthquakes. In: 12th International Conference on Structural Analysis of Historical Constructions (SAHC 2020)
Colonna S, Imperatore S, Ferracuti B (2019). Fragility curves of masonry churches façades. In: Papadrakakis M, Fragiadakis M (eds) COMPDYN 2019 7th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, pp. 778–731
Cornell CA (1969) A probability-based structural code. J Proc 66(12):974–985
Cornell CA (1968) Engineering seismic risk analysis. Bull Seismol Soc Am 58(5):1583–1606
D’Ayala D, Shi Y (2011) Modeling masonry historic buildings by multi-body dynamics. Int J Archit Heritage 5(4–5):483–512
Dimitrakopoulos EG, Paraskeva TS (2015) Dimensionless fragility curves for rocking response to near-fault excitations. Earthq Eng Struct Dyn 44(12):2015–2033
Dizhur D, Ingham J, Moon L, Griffith M, Schultz A, Senaldi I, Magenes G, Dickie J, Lissel S, Centeno J, Ventura C, Leite J, Lourenco P (2011) Performance of masonry buildings and churches in the 22 February 2011 christchurch earthquake. Bull N Z Soc Earthq Eng 44(4):279–296
Ericksen GE, Fernández-Concha J, Salgado E (1954) The Cusco, Peru, earthquake of May 21, 1950. Bull Seismol Soc Am 44(2A):97–112
Esteva L (1967) Criterios para la construcción de espectros para diseño sísmico. In: 3er Simposio Panamericano de Estructuras, Caracas, Venezuela (in Spanish)
García D (2006) Estimación de parámetros del movimiento fuerte del suelo para terremotos interplaca e intraslab en México central. PhD Thesis, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Madrid (in Spanish)
García D, Singh SK, Herráiz M, Pacheco JF, Ordaz M (2004) Inslab earthquakes of central Mexico: Q, source spectra, and stress drop. Bull Seismol Soc Am 94(3):789–802
García D, Singh SK, Herráiz M, Ordaz M, Pacheco JF (2005) Inslab earthquakes of central Mexico: peak ground-motion parameters and response spectra. Bull Seismol Soc Am 95(6):2272–2282
Gelagoti F, Kourkoulis R, Anastasopoulos I, Gazetas G (2012) Rocking isolation of low-rise frame structures founded on isolated footings. Earthq Eng Struct Dyn 41(7):1177–1197
Giresini L, Sassu M (2017) Horizontally restrained rocking blocks: evaluation of the role of boundary conditions with static and dynamic approaches. Bull Earthq Eng 15(1):385–410
Giresini L, Fragiacomo M, Lourenço PB (2015) Comparison between rocking analysis and kinematic analysis for the dynamic out-of-plane behavior of masonry walls. Earthq Eng Struct Dyn 44(13):2359–2376
Giresini L, Fragiacomo M, Sassu M (2016) Rocking analysis of masonry walls interacting with roofs. Eng Struct 116:107–120
Giresini L, Casapulla C, Denysiuk R, Matos J, Sassu M (2018) Fragility curves for free and restrained rocking masonry façades in one-sided motion. Eng Struct 164:195–213
Housner GW (1963) The behavior of inverted pendulum structures during earthquakes. Bull Seismol Soc Am 53(2):403–417
Ingham J, Griffith M (2010) Performance of unreinforced masonry buildings during the 2010 Darfield (Christchurch, NZ) earthquake. Aust J Struct Eng 11(3):207–224
Jaimes MA, Lermo J, García-Soto AD (2016) Ground-motion prediction model froml local earthquakes of the Mexico Basin at the hill zone of Mexico City. Bull Seismol Soc Am 106(6):2532–2544
Jaimes MA, Reinoso E (2006) Comparación del comportamiento de edificios en el valle de México ante sismos de subducción y de falla normal. Revista de Ingeniería Sísmica 75:1–22 (in Spanish)
Jaimes MA, Reinoso E, Ordaz M (2006) Comparison of methods to predict response spectra at instrumented sites given the magnitude and distance of an earthquake. J Earthq Eng 10(6):887–902
Jaimes MA, Ramirez-Gaytán A, Reinoso E (2015) Ground-motion prediction model from intermediate-depth intraslab earthquakes at the hill and lake-bed zones of Mexico City. J Earthq Eng 19(8):1260–1278
Kafle B, Lam NT, Gad EF, Wilson J (2011) Displacement controlled rocking behaviour of rigid objects. Earthq Eng Struct Dyn 40(15):1653–1669
Kiureghian AD, Neuenhofer A (1992) Response spectrum method for multi-support seismic excitations. Earthq Eng Struct Dyn 21(8):713–740
Lagomarsino S, Podesta S (2004) Damage and vulnerability assessment of churches after the 2002 Molise, Italy, earthquake. Earthq Spectra 20(s1):s271–s283
Lermo J, Chávez-García FJ (1993) Site effect evaluation using spectral ratios with only one station. Bull Seismol Soc Am 83(5):1574–1594
Makris N (2014b) The role of the rotational inertia on the seismic resistance of free-standing rocking columns and articulated frames. Bull Seismol Soc Am 104(5):2226–2239
Makris N (2014a) A half-century of rocking isolation. Earthquakes and Structures 7(6):1187–1221
Makris N, Kampas G (2016) Size versus slenderness: two competing parameters in the seismic stability of free-standing rocking columns. Bull Seismol Soc Am 106(1):104–122
Makris N, Roussos Y (2000) Rocking response of rigid blocks under near-source ground motions. Geotechnique 50(3):243–262
Makris N, Roussos Y, Zhang J (1999). Rocking response of rigid blocks under near-source motions. In: Proceedings 13th ASCE Engineering Mechanics Division Conference, June, pp. 13–16
Mavroulis S, Grampas A, Alexoudi V, Taflampas I, Carydis P, Lekkas E (2019) Using earthquake-induced damage on historical constructions for the detection of the basic seismological parameters of historical earthquakes. In: Aguilar R, Torrealva D, Moreira S, Pando MA, Ramos LF (eds) Structural analysis of historical constructions. Springer, Cham, pp 2368–2376
McGuire RK (2008) Probabilistic seismic hazard analysis: early history. Earthq Eng Struct Dyn 37(3):329–338
Meli R, Sánchez-Ramírez R (2007) Criteria and experiences on structural rehabilitation of stone masonry buildings in Mexico City. Int J Archit Heritage 1(1):3–28
NTCS (2017) Normas técnicas complementarias para diseño por sismo. Reglamento de Construcciones para el Distrito Federal, Gaceta Oficial del Departamento del Distrito Federal (in Spanish)
Ordaz M, Singh KS (1992) Source spectra and spectral attenuation of seismic waves from Mexican earthquakes, and evidence of amplification in the hill zone of Mexico City. Bull Seismol Soc Am 82(1):24–43
Ordaz M, Reyes C (1999) Earthquake hazard in Mexico City: observations versus computations. Bull Seismol Soc Am 89(5):1379–1383
Pacheco JF, Singh SK (1995) Estimation of ground motions in the valley of Mexico from normal-faulting, intermediate-depth earthquakes in the subducted cocos plate. Earthq Spectra 11(2):233–247
Peña F, Chavez MM (2016) Seismic behaviour of Mexican Colonial churches. Int J Archit Heritage 10(2–3):332–345
Peña F, Lourenço PB, Lemos JV (2006). Modeling the dynamic behaviour of masonry walls as rigid blocks. In: Mota SCA et al. (eds) III European Conference on Computational Mechanics Solids. Lisbon, Portugal, June
Peña F, Prieto F, Lourenço PB, Campos-Costa A, Lemos JV (2007) On the dynamics of rocking motion of single rigid-block structures. Earthq Eng Struct Dyn 36(15):2383–2399
Peña F, Lourenço PB, Campos-Costa A (2008) Experimental dynamic behavior of free-standing multi-block structures under seismic loadings. J Earthq Eng 12(6):953–979
Pich P (1994). Nonlinear rigid block dynamics. California Institute of Technology (unpublished). https://authors.library.caltech.edu/26396/
Preciado A, Orduña A (2014) A correlation between damage and intensity on old masonry churches in Colima, Mexico by the 2003 M7.5 earthquake. Case Stud Struct Eng 2:1–8
Preciado A, Santos JC, Silva C, Ramirez-Gaytan A, Falcon JM (2020) Seismic damage and retrofitting identification in unreinforced masonry churches and bell towers by September 19, 2017 (Mw = 7.1) Puebla-Morelos earthquake. Eng Fail Anal 118:104924
Rosenblueth E, Esteva L (1972) Reliability basis for some Mexican codes. Spec Publ 31:1–42
Schwartz DP, Coppersmith KJ (1984) Fault behavior and characteristic earthquakes: examples from the Wasatch and San Andreas fault zones. J Geophys Res Solid Earth 89(B7):5681–5698
Seed HB, Romo MP, Sun J, Jaime A, Lysmer J (1987) Relationships between soil conditions and earthquake ground motions in Mexico City in the earthquake of September 19, 1985. Rpt No UCB/EERC 87:15
Singh SK, Rodriguez M, Esteva L (1983) Statistics of small earthquakes and frequency of occurrence of large earthquakes along the Mexican subduction zone. Bull Seismol Soc Am 73(6A):1779–1796
Sorrentino L, Liberatore L, Decanini LD, Liberatore D (2014) The performance of churches in the 2012 Emilia earthquakes. Bull Earthq Eng 12(5):2299–2331
Tarque N (2008) Seismic risk assessment of adobe dwellings. Istituto Universitario di Studi Superiori di Pavia, Universitá degli Studi di Pavia
Vamvatsikos D, Cornell CA (2002) Incremental dynamic analysis. Earthq Eng Struct Dynam 31(3):491–514
Voyagaki E, Psycharis IN, Mylonakis G (2013) Rocking response and overturning criteria for free standing rigid blocks to single—lobe pulses. Soil Dyn Earthq Eng 46:85–95
Vrouwenvelder AC (2002) Developments towards full probabilistic design codes. Struct Saf 24(2–4):417–432
Watson-Lamprey J, Abrahamson N (2006) Selection of ground motion time series and limits on scaling. Soil Dyn Earthq Eng 26(5):477–482
Wesnousky SG (1994) The Gutenberg-Richter or characteristic earthquake distribution, which is it? Bull Seismol Soc Am 84(6):1940–1959
Yim SC, Lin H (1992) Probabilistic analysis of a chaotic dynamical system. In: Kim JH, Stringer J (eds) Applied chaos. Wiley, New York, pp 219–241
Yim SC, Lin H (1991) Nonlinear impact and chaotic response of slender rocking objects. J Eng Mech 117(9):2079–2100
Acknowledgements
This research was financially supported by the Project IA100519-PAPIIT-UNAM “Propuesta de una metodología para la evaluación del riesgo de deslizamiento sísmico en equipos eléctricos debido a sismo”. Additional support was partially sponsored by Instituto de Ingeniería at UNAM through the Research Fund R974. The authors thank the anonymous reviewers for their comments and suggestions that help to improve this study. They also thank Brian Pirttima for his time and generous help with final edits to this article.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Rights and permissions
About this article
Cite this article
Jaimes, M.A., Chávez, M.M., Peña, F. et al. Out-of-plane mechanism in the seismic risk of masonry façades. Bull Earthquake Eng 19, 1509–1535 (2021). https://doi.org/10.1007/s10518-020-01029-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10518-020-01029-1