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Dynamic stiffness of monumental flexible masonry foundations

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Abstract

In this paper we propose reduction factors accounting for the decrease of stiffness of monumental masonry foundations due to aging, weathering, or other deteriorating effects. The proposed reduced stiffness values can be readily used in finite element structural analysis software in the framework of performance-based assessment, representing linear elastic springs at the foundation level. These springs account for foundation-soil system flexibility and soil-foundation interaction (SFI) at low-frequency vibrations. Accordingly, we propose a procedure to reduce monumental masonry foundation-wall stiffness from the rigid-footing assumption, with respect to the relative stiffness between the foundation and the soil. The proposed procedure is applied to the historical structure Arsenal De Milly in the Medieval City of Rhodes, where period elongation and ductility increase are highlighted, because of SFI and foundation flexibility.

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References

  • ABAQUS (2012) Theory and analysis user’s manual-version 6.12. Dassault Systemes, SIMULIA Inc, USA

  • Bielak J (1975) Dynamic behavior of structures with embedded foundations. Earthq Eng Struct Dyn 3:259–274

    Article  Google Scholar 

  • Bowles J (2001) Foundation analysis and design. McGraw-Hill, New York

    Google Scholar 

  • Cattari S, Karatzetzou A, Degli Abbati S, Gkoktsi K, Pitilakis D, Negulescu C (2013) Performance-based assessment of the Arsenal de Milly of the medieval city of Rhodes. In: Papadrakakis M, Papadopoulos V, Plevris V (eds) Proceedings of 4th ECCOMAS thematic conference on computational methods in structural dynamics and earthquake engineering, Kos Island, Greece

  • Cattari S, Lagomarsino S, Karatzetzou A, Pitilakis D (2014) Vulnerability assessment of Hassan Bey’s Mansion in Rhodes. Bull Earthq Eng (this issue)

  • CEN (European Committee for Standardization) (2004) Eurocode 8: design of structures for earthquake resistance, part 1: general rules, seismic actions and rules for buildings. EN 1998-1:2004. Brussels, Belgium

  • CEN (European Committee for Standardization) (2005) Eurocode 8: design of structures for earthquake resistance, part 3: assessment and retrofitting of buildings. EN 1998-3:2005. Brussels, Belgium

  • Chen SS, Hou G Jr (2009) Modal analysis of circular flexible foundations under vertical vibration. Soil Dyn Earthq Eng 29(5):898–908

    Article  Google Scholar 

  • Chen WF, Saleeb AF (1994) Constitutive equations for engineering materials. Elasticity and modelling, vol I. Elsevier, New York

  • Chongbin Z, Valliappan S (1993) A dynamic infinite element for three-dimensional infinite-domain wave problems. Int Journal for Numer Methods Eng 36(15):2567–2580

    Article  Google Scholar 

  • Chopra AK (2011) Dynamics of structures: theory and applications to earthquake engineering, 4th edn. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Drucker DC, Prager W (1952) Soil mechanics and plastic analysis for limit design. Q Appl Math 10(2):157–165

    Google Scholar 

  • Foundation for the financial administration and realization of archaeological projects (FFARAP), Ministry of Cultures, Greece. (http://www.tdpeae.gr/)

  • Gazetas G (1983) Analysis of machine foundation vibrations: state of the art. Soil Dyn Earthq Eng 2(1):2–42

    Google Scholar 

  • Gazetas G (1991) Formulas and charts for impedances of surface and embedded foundations. J Geotech Eng 117(9):1363–1381

    Article  Google Scholar 

  • Gucunski N, Peek R (1993a) Parametric study of vertical oscillations of circular flexible foundations on layered media. Earthq Eng Struct Dyn 22(8):685–694

    Article  Google Scholar 

  • Gucunski N, Peek R (1993b) Vertical vibrations of flexible foundations on layered media. Soil Dyn Earthq Eng 12(3):183–192

    Article  Google Scholar 

  • Iguchi M, Luco JE (1981) Dynamic response of flexible rectangular foundations on an elastic half-space. Earthq Eng Struct Dyn 9:239–249

    Article  Google Scholar 

  • Kallioudakis E, Pitilakis K, Karatzetzou A, Pitilakis D (2011) Intermediate report on the application of the proposed methodology to the case studies selected Task 7.3. Deliverable D28, PERPETUATE project. FP7—Theme ENV.2009.3.2.1.1—ENVIRONMENT, Grant agreement No: 244229. (www.perpetuate.eu)

  • Karabalis DL (2004) Non-singular time domain bem with applications to 3d inertial soil-structure interaction. Soil Dyn Earthq Eng 24(3):281–293

    Article  Google Scholar 

  • Kržan M, Bosiljkov V, Gostič S, Zupančič P (2012) Influence of ageing and deterioration of masonry on load bearing capacity of historical building. In: 15th world conference of earthquake engineering, Lisbon, Portugal, 24–28 Sep 2012

  • Kržan M, Gostič S, Bosiljkov V (2014) Application of different in-situ testing techniques and vulnerability assessment of Kolizej Palace in Ljubljana. Bull Earthq Eng (this special issue)

  • Lagomarsino S, Modaressi H, Pitilakis K, Bosjlikov V, Calderini C, D’Ayala D, Benouar D, Cattari S (2010) PERPETUATE Project: the proposal of a performance-based approach to earthquake protection of cultural heritage. Adv Mater Res 133–134:1119–1124. doi:10.4028/www.scientific.net/AMR.133-134.1119

  • Lagomarsino S, Penna A, Galasco A, Cattari S (2013) Tremuri program: an equivalent frame model for the nonlinear seismic analysis of masonry buildings. Eng Struct 56:1787–1799

    Article  Google Scholar 

  • Liou GS, Huang PH (1994) Effect of flexibility on impedance functions for circular foundation. J Eng Mech 120(7):1429–1446

    Article  Google Scholar 

  • Lysmer J, Kuhlemeyer RL (1969) Finite dynamic model for infinite media. J Eng Mech Div 95(EM4):859–877

    Google Scholar 

  • McKenna F, Fenves GL, Jeremic B (2007) MH. Scott, Open system for earthquake engineering simulation. http://opensees.berkeley.edu

  • Meek JW, Veletsos AS (1973) Simple models for foundations in lateral and rocking motion. In: Proceedings of the 5th world conference earthquake engineering. Rome, Italy pp 2610–2613

  • Mylonakis G, Nikolaou S, Gazetas G (2006) Footings under seismic loading: analysis and design issues with emphasis on bridge foundations. Soil Dyn Earthq Eng 26(9):824–853

    Article  Google Scholar 

  • Negulescu C, Manakou M, Francois B, Seyedi D, Pitilakis D, Karatzetzou A, Pitilakis K (2014) Ambient vibration measurements on monuments in the Medieval City of Rhodes. Bull Earthq Eng (this special issue)

  • NTC (2008) Decreto Ministeriale 14/1/2008. Norme tecniche per le costruzioni. Ministry of Infrastructures and Transportations. G.U. S.O. n.30 on 4/2/2008 (in Italian)

  • Pais A, Kausel E (1988) Approximate formulas for dynamic stiffness of rigid foundations. Soil Dyn Earthq Eng 7(4):213–227

    Article  Google Scholar 

  • Papayanni I, Stefanidou M, Konopisi S, Anastasiou E, Pachta V (2004) Stability issues of the Fortification of the Medieval City of Rhodes. Technical report (in Greek). Civil Engineering Department, Aristotle University of Thessaloniki, Laboratory of Building Materials

  • Pitilakis D, Clouteau D (2010) Equivalent linear substructure approximation of soil-foundation-structure interaction: model presentation and validation. Bull Earthq Eng 8(2):257–282

    Article  Google Scholar 

  • Pitilakis D, Moderessi-Farahmand-Razavi A, Clouteau D (2013) Equivalent-linear dynamic impedance functions of surface foundations. J Geotech Geoenviron Eng 139(7):1130–1139

    Article  Google Scholar 

  • Pitilakis D, Karatzetzou A (2012) Performance-based design of soil—foundation—structure systems. In: Proceedings of the 15th world conference on earthquake engineering, Lisbon, Portugal

  • Pitilakis K, Galazoula J, Sextos A (2002) Stability issues of the foundation of the fortification of the Medieval City of Rhodes—Arsenal De Milly: pathology, static and earthquake resistance study of rehabilitation and restoration. Technical report (in Greek), Civil Engineering Department, Aristotle University of Thessaloniki

  • Pitilakis K, Pitilakis D, Karatzetzou A, Tsinidis G (2011) Report on the SFI effects for ground shaking. Deliverable D14, PERPETUATE project. FP7—Theme ENV.2009.3.2.1.1—ENVIRONMENT, Grant agreement No: 244229 (www.perpetuate.eu)

  • Veletsos AS, Meek J (1974) Dynamic behaviour of building-foundation systems. Earthq Eng Struct Dyn 3(January):121–138

  • Yerli H, Kacin S, Kocak S (2003) A parallel finite-infinite element model for two-dimensional soil-structure interaction problems. Soil Dyn Earthq Eng 23(4):249–253

    Article  Google Scholar 

Download references

Acknowledgments

This work has been funded by the PERPETUATE (Performance-based approach to earthquake protection of cultural heritage in European and Mediterranean countries) project of the EC-Research Framework Programme FP7. The authors are grateful to the “Foundation for the Financial Administration and Realization of Archaeological Projects” of Ministry of Cultures of Greece, and more specifically to Dr. Georgios Ntellas and Emmanuil Kallioudakis for supporting and providing all data for the monuments of the Medieval City of Rhodes in Greece. We thank Grigoris Tsinidis of Aristotle University Thessaloniki, for helping us in the numerical modeling of soil-foundation interaction, and Kyriaki Gkoktsi for her help in the numerical modeling of Arsenal De Milly.

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Pitilakis, D., Karatzetzou, A. Dynamic stiffness of monumental flexible masonry foundations. Bull Earthquake Eng 13, 67–82 (2015). https://doi.org/10.1007/s10518-014-9611-3

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