Technical Papers
Aug 10, 2021

Scaling Laws for Rigid-Body Response of Masonry Structures under Blast Loads

Publication: Journal of Engineering Mechanics
Volume 147, Issue 10

Abstract

The response of masonry structures to explosions cannot be exclusively investigated relying only on numerical and analytical tools. Experimental tests are of paramount importance for improving current understanding and validating existing models. However, experiments involving blast scenarios are, at present, partial and limited in number compared to tests under different dynamic conditions, such as earthquakes. The reason for lies in the fact that full-scale blast experiments present many difficulties, mainly due to the nature of loading action. In constrast, experiments on a reduced scale offer greater flexibility. Nevertheless, appropriate scaling laws for the response of masonry structures under blast excitations are needed before such tests are performed. We propose here new scaling laws for the dynamic, rigid-body response, and structural failure modes (e.g., overturning) of masonry structures under blast loads. This work grows out of previous studies, where closed-form solutions for the rocking response of slender blocks due to explosions were derived and validated against numerical and experimental tests. The proposed scaling laws are validated here with detailed numerical simulations accounting for combined rocking, uplifting, and sliding mechanisms of monolithic structures. Then the application to blocky masonry structures is studied. Multidrum stone columns are considered as examples for the application of scaling laws. In particular, we show that, despite the presence of complex behaviors, such as wobbling and impacts, similarity is assured.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

The authors would like to acknowledge Professor Paolo Vannucci (LMV, UMR 8100, Université de Versailles et Saint-Quentin) for various discussions relating to dynamics and blast loading of structures.

References

ABAQUS. 2018. Abaqus analysis user’s guide: Report no. Abaqus 6.14 documentation. Providence, RI: Dassault Systems Simulia Corporation.
Abou-Zeid, B. M., W. W. El-Dakhakhni, A. G. Razaqpur, and S. Foo. 2011. “Response of arching unreinforced concrete masonry walls to blast loading.” J. Struct. Eng. 137 (10): 1205–1214. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000344.
Baker, W. E., P. S. Westine, and F. T. Dodge. 1991. “Simulating rigid body motion.” In Vol. 12 of Similarity methods in engineering dynamics. Fundamental studies in engineering, 73–95. Amsterdam, Netherlands: Elsevier.
Bertrand, J. 1878. “Sur l’homogénéité dans les formules de physique.” Cah. Recherche Acad. Sci. 86 (15): 916–920.
Çakti, E., Ö. Saygili, J. V. Lemos, and C. S. Oliveira. 2016. “Discrete element modeling of a scaled masonry structure and its validation.” Eng. Struct. 126 (Nov): 224–236. https://doi.org/10.1016/j.engstruct.2016.07.044.
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.
Cranz, C. 1925. Lehrbuch der ballistik, 27. Berlin: Springer.
Dimitrakopoulos, E. G., and M. J. DeJong. 2012. “Revisiting the rocking block: Closed-form solutions and similarity laws.” Proc. R. Soc. London, Ser. A 468 (2144): 2294–2318. https://doi.org/10.1098/rspa.2012.0026.
Draganić, H., D. Varevac, and S. Lukić. 2018. “An overview of methods for blast load testing and devices for pressure measurement.” Adv. Civ. Eng. 2018: 3780482. https://doi.org/10.1155/2018/3780482.
Drosos, V., and I. Anastasopoulos. 2014. “Shaking table testing of multidrum columns and portals.” Earthquake Eng. Struct. Dyn. 43 (11): 1703–1723. https://doi.org/10.1002/eqe.2418.
Forgács, T., V. Sarhosis, and K. Bagi. 2017. “Minimum thickness of semi-circular skewed masonry arches.” Eng. Struct. 140 (Jun): 317–336. https://doi.org/10.1016/j.engstruct.2017.02.036.
Forgács, T., V. Sarhosis, and K. Bagi. 2018. “Influence of construction method on the load bearing capacity of skew masonry arches.” Eng. Struct. 168 (Aug): 612–627. https://doi.org/10.1016/j.engstruct.2018.05.005.
Fragiadakis, M., I. Stefanou, and I. N. Psycharis. 2016. “Vulnerability assessment of damaged classical multidrum columns.” In Computational modeling of masonry structures using the discrete element method, 235–253. Hershey, PA: IGI Global.
Friedlander, F. G. 1946. “The diffraction of sound pulses. Part I: Diffraction by a semi-infinite plate.” Proc. R. Soc. London, Ser. A 186 (1006): 322–344. https://doi.org/10.1098/rspa.1946.0046.
Gabrielsen, B., C. Wilton, and K. Kaplan. 1975. Response of arching walls and debris from interior walls caused by blast loading. San Mateo, CA: URS Reasearch Company.
Gilbert, M., B. Hobbs, and T. Molyneaux. 2002. “The performance of unreinforced masonry walls subjected to low-velocity impacts: Experiments.” Int. J. Impact Eng. 27 (3): 231–251. https://doi.org/10.1016/S0734-743X(01)00049-5.
Godio, M., I. Stefanou, and K. Sab. 2018. “Effects of the dilatancy of joints and of the size of the building blocks on the mechanical behavior of masonry structures.” Meccanica 53 (7): 1629–1643. https://doi.org/10.1007/s11012-017-0688-z.
Hopkinson, B. 1915. British ordinance board minutes 13565, 11. Kew, UK: National Archives.
Housner, G. W. 1963. “The behavior of inverted pendulum structures during earthquakes.” Bull. Seismol. Soc. Am. 53 (2): 403–417.
Kassotakis, N., V. Sarhosis, B. Riveiro, B. Conde, A. M. D’Altri, J. Mills, G. Milani, S. de Miranda, and G. Castellazzi. 2020. “Three-dimensional discrete element modelling of rubble masonry structures from dense point clouds.” Autom. Constr. 119 (Nov): 103365. https://doi.org/10.1016/j.autcon.2020.103365.
Keys, R. A., and S. K. Clubley. 2017. “Experimental analysis of debris distribution of masonry panels subjected to long duration blast loading.” Eng. Struct. 130 (Jan): 229–241. https://doi.org/10.1016/j.engstruct.2016.10.054.
Kingery, C. N., and G. Bulmash. 1984. Air blast parameters from TNT spherical air burst and hemispherical burst. Vicksburg, MS: US Army Ballistic Research Laboratory.
Konstantinidis, D., and N. Makris. 2005. “Seismic response analysis of multidrum classical columns.” Earthquake Eng. Struct. Dyn. 34 (10): 1243–1270. https://doi.org/10.1002/eqe.478.
Krauthammer, T., and A. Altenberg. 2000. “Negative phase blast effects on glass panels.” Int. J. Impact Eng. 24 (1): 1–17. https://doi.org/10.1016/S0734-743X(99)00043-3.
Li, Z., L. Chen, Q. Fang, H. Hao, Y. Zhang, H. Xiang, W. Chen, S. Yang, and Q. Bao. 2017. “Experimental and numerical study of unreinforced clay brick masonry walls subjected to vented gas explosions.” Int. J. Impact Eng. 104 (Jun): 107–126. https://doi.org/10.1016/j.ijimpeng.2017.02.002.
Makris, N., and C. J. Black. 2004. “Dimensional analysis of rigid-plastic and elastoplastic structures under pulse-type excitations.” J. Eng. Mech. 130 (9): 1006–1018. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:9(1006).
Makris, N., and M. F. Vassiliou. 2012. “Sizing the slenderness of free-standing rocking columns to withstand earthquake shaking.” Arch. Appl. Mech. 82 (10): 1497–1511. https://doi.org/10.1007/s00419-012-0681-x.
Makris, N., and M. F. Vassiliou. 2013. “Planar rocking response and stability analysis of an array of free-standing columns capped with a freely supported rigid beam.” Earthquake Eng. Struct. Dyn. 42 (3): 431–449. https://doi.org/10.1002/eqe.2222.
Masi, F. 2020. “Fast-dynamic response and failure modes of masonry structures of non-standard geometry subjected to blast loads.” Ph.D. thesis, Dept. of Engineering, École Centrale de Nantes.
Masi, F., I. Stefanou, V. Maffi-Berthier, and P. Vannucci. 2020a. “A discrete element method based-approach for arched masonry structures under blast loads.” Eng. Struct. 216: 110721. https://doi.org/10.1016/j.engstruct.2020.110721.
Masi, F., I. Stefanou, P. Vannucci, and V. Maffi-Berthier. 2019a. “A discrete element method approach for the preservation of the architectural heritage against explosions.” In Proc., 12th HSTAM Int. Congress on Mechanics. Athens, Greece: Hellenic Society for Theoretical and Applied Mechanics.
Masi, F., I. Stefanou, P. Vannucci, and V. Maffi-Berthier. 2019b. “Rocking response of inverted pendulum structures under blast loading.” Int. J. Mech. Sci. 157–158 (Jul): 833–848. https://doi.org/10.1016/j.ijmecsci.2019.05.024.
Masi, F., I. Stefanou, P. Vannucci, and V. Maffi-Berthier. 2020b. “Resistance of museum artefacts against blast loading.” J. Cult. Heritage 44 (Jul): 163–173. https://doi.org/10.1016/j.culher.2020.01.015.
Michaloudis, G., and N. Gebbeken. 2019. “Modeling masonry walls under far-field and contact detonations.” Int. J. Impact Eng. 123 (Jan): 84–97. https://doi.org/10.1016/j.ijimpeng.2018.09.019.
Neils, J. 2005. The Parthenon: From antiquity to the present. Cambridge, UK: Cambridge University Press.
Peña, F., F. Prieto, P. B. Lourenço, A. Campos Costa, and J. V. Lemos. 2007. “On the dynamics of rocking motion of single rigidblock structures.” Earthquake Eng. Struct. Dyn. 36 (15): 2383–2399. https://doi.org/10.1002/eqe.739.
Psycharis, I., D. Y. Papastamatiou, and A. P. Alexandris. 2000. “Parametric investigation of the stability of classical 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.
Rigby, S. E., A. Tyas, T. Bennett, S. D. Clarke, and S. D. Fay. 2014. “The negative phase of the blast load.” Int. J. Prot. Struct. 5 (1): 1–19. https://doi.org/10.1260/2041-4196.5.1.1.
Sarhosis, V., P. Asteris, T. Wang, W. Hu, and Y. Han. 2016. “On the stability of colonnade structural systems under static and dynamic loading conditions.” Bull. Earthquake Eng. 14 (4): 1131–1152. https://doi.org/10.1007/s10518-016-9881-z.
Stefanou, I., M. Fragiadakis, and I. N. Psycharis. 2015. “Seismic reliability assessment of classical columns subjected to near source ground motions.” In Seismic assessment, behavior and retrofit of heritage buildings and monuments, 61–82. New York: Springer.
Stefanou, I., I. Psycharis, and I.-O. Georgopoulos. 2011a. “Dynamic response of reinforced masonry columns in classical monuments.” Constr. Build. Mater. 25 (12): 4325–4337. https://doi.org/10.1016/j.conbuildmat.2010.12.042.
Stefanou, I., I. Vardoulakis, and A. Mavraganis. 2011b. “Dynamic motion of a conical frustum over a rough horizontal plane.” Int. J. Non Linear Mech. 46 (1): 114–124. https://doi.org/10.1016/j.ijnonlinmec.2010.07.008.
Stockdale, G. L., V. Sarhosis, and G. Milani. 2020. “Seismic capacity and multi-mechanism analysis for dry-stack masonry arches subjected to hinge control.” Bull. Earthquake Eng. 18 (2): 673–724. https://doi.org/10.1007/s10518-019-00583-7.
USACE. 2008. Structures to resist the effects of accidental explosions. UFC 3-340-02. Washington, DC: USACE.
Vannucci, P., F. Masi, and I. Stefanou. 2017a. A comparative study on the effects of blast actions on a monumental structure. Paris: Université de Versailles Saint-Quentin-en-yvelines, École Nationale des Ponts et Chaussées.
Vannucci, P., F. Masi, I. Stefanou, and V. Maffi-Berthier. 2019. Structural integrity of Notre Dame Cathedral after the fire of April 15th, 2019. Paris: Université de Versailles Saint-Quentin-en-yvelines, École Nationale des Ponts et Chaussées, Ingérop.
Vannucci, P., I. Stefanou, and F. Masi. 2017b. Report of the project “Cathédralesdurables’’. Paris: Centre National de la Recherche Scientifique.
Varma, R. K., C. P. S. Tomar, S. Parkash, and V. S. Sethi. 1997. “Damage to brick masonry panel walls under high explosive detonations.” Press. Vessels Pip. Div. 351: 207–216.
Vassiliou, M. F. 2018. “Seismic response of a wobbling 3d frame.” Earthquake Eng. Struct. Dyn. 47 (5): 1212–1228. https://doi.org/10.1002/eqe.3013.
Voyagaki, E., I. N. Psycharis, and G. Mylonakis. 2013. “Rocking response and overturning criteria for free standing rigid blocks to single–lobe pulses.” Soil Dyn. Earthquake Eng. 46 (Mar): 85–95. https://doi.org/10.1016/j.soildyn.2012.11.010.
Wang, W., D. Zhang, F. Lu, S.-C. Wang, and F. Tang. 2012. “Experimental study on scaling the explosion resistance of a one-way square reinforced concrete slab under a close-in blast loading.” Int. J. Impact Eng. 49 (Nov): 158–164. https://doi.org/10.1016/j.ijimpeng.2012.03.010.
Zhang, J., and N. Makris. 2001. “Rocking response of free-standing blocks under cycloidal pulses.” J. Eng. Mech. 127 (5): 473–483. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:5(473).

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 147Issue 10October 2021

History

Received: Nov 20, 2020
Accepted: May 11, 2021
Published online: Aug 10, 2021
Published in print: Oct 1, 2021
Discussion open until: Jan 10, 2022

Permissions

Request permissions for this article.

ASCE Technical Topics:

Authors

Affiliations

Institut de Recherche en Génie Civil et Mécanique, Unité Mixte de Recherche 6183, Centre National de la Recherche Scientifique, Ecole Centrale de Nantes, Université de Nantes, 1 rue de la Nöe, Nantes F-44300, France (corresponding author). ORCID: https://orcid.org/0000-0001-8899-6700. Email: [email protected]
Ioannis Stefanou [email protected]
Professor, Institut de Recherche en Génie Civil et Mécanique, Unité Mixte de Recherche 6183, Centre National de la Recherche Scientifique, Ecole Centrale de Nantes, Université de Nantes, 1 rue de la Nöe, Nantes F-44300, France. Email: [email protected]
Victor Maffi-Berthier [email protected]
Engineer, Ingérop Conseil et Ingénierie, 18 rue des Deux Gares, Rueil-Malmaison F-92500, France. Email: [email protected]

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

  • Recent Advances on the Mechanics of Masonry Structures, Journal of Engineering Mechanics, 10.1061/(ASCE)EM.1943-7889.0002112, 148, 6, (2022).
  • Intensity measures, fragility analysis and dimensionality reduction of rocking under far‐field ground motions, Earthquake Engineering & Structural Dynamics, 10.1002/eqe.3740, 51, 15, (3639-3657), (2022).
  • Finite element modeling of free‐standing cylindrical columns under seismic excitation, Earthquake Engineering & Structural Dynamics, 10.1002/eqe.3651, 51, 9, (2016-2035), (2022).
  • A Comprehensive Analysis Structure for the Design of Masonry Arches, The Open Civil Engineering Journal, 10.2174/1874149502115010381, 15, 1, (381-397), (2021).

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share