Abstract

This paper focuses on the simulation of irregular stone masonry by the lattice discrete particle model (LDPM), which simulates the fracture and failure behavior of quasi-brittle heterogeneous materials by modeling the interaction among coarse material heterogeneities. LDPM is formulated at the length scale of the masonry stones whose interaction is described through constitutive equations featuring softening in tension and strain hardening in compression. The numerical results relevant to diagonal compression tests show that the intrinsic stochastic character of LDPM can quantify the variation of the mechanical properties of irregular masonry resulting from random stone size and stone-size distribution. Furthermore, the paper presents an analysis of the size effect on irregular stone masonry structures. This was obtained by simulating the shear behavior of geometrically similar samples of different sizes. The simulations demonstrate that increasing structural size leads to a significant reduction of both structural strength and structural ductility. The magnitude of the predicted size effect suggests that, contrary to typical experimental results on reduced size samples, real irregular masonry structures must be considered as perfectly brittle.

Get full access to this article

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

Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

Acknowledgments

The work of the first and third authors was sponsored by the University of L’Aquila.

References

Alnaggar, M., G. Di Luzio, and G. Cusatis. 2017. “Modeling time-dependent behavior of concrete affected by alkali silica reaction in variable environmental conditions.” Materials (Basel) 10 (5): 471. https://doi.org/10.3390/ma10050471.
Alnaggar, M., D. Pelessone, and G. Cusatis. 2019. “Lattice discrete particle modeling of reinforced concrete flexural behavior.” J. Struct. Eng. 145 (1): 04018231. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002230.
Aloisio, A., E. Antonacci, M. Fragiacomo, and R. Alaggio. 2020a. “The recorded seismic response of the Santa Maria di Collemaggio basilica to low-intensity earthquakes.” Int. J. Archit. Heritage 15 (1): 1–13. https://doi.org/10.1080/15583058.2020.1836531.
Aloisio, A., I. Capanna, R. Cirella, R. Alaggio, F. Di Fabio, and M. Fragiacomo. 2020b. “Identification and model update of the dynamic properties of the San Silvestro belfry in L’Aquila and estimation of bell’s dynamic actions.” Appl. Sci. 10 (12): 4289. https://doi.org/10.3390/app10124289.
Aloisio, A., M. Fragiacomo, and G. D’Alò. 2019. “The 18th-century baraccato of L’Aquila.” Int. J. Archit. Heritage 14 (6): 1–15. https://doi.org/10.1080/15583058.2019.1570390.
Angiolilli, M., and A. Gregori. 2020. “Triplet test on rubble stone masonry: Numerical assessment of the shear mechanical parameters.” Buildings 10 (3): 49. https://doi.org/10.3390/buildings10030049.
Angiolilli, M., A. Gregori, and D. Martini. 2019. “Mechanical characterization of the cyclic behavior of historic masonry panels reinforced by frcm system subject to diagonal compression tests.” [In Italian.] In Proc., ANIDIS XVIII, Ascoli Piceno, 116–126. Pisa, Italy: Pisa University Press.
Angiolilli, M., A. Gregori, M. Pathirage, and G. Cusatis. 2020. “Fiber reinforced cementitious matrix (FRCM) for strengthening historical stone masonry structures: Experiments and computations.” Eng. Struct. 224 (Dec): 111102. https://doi.org/10.1016/j.engstruct.2020.111102.
Armesto, J., J. Roca-Pardiñas, H. Lorenzo, and P. Arias. 2010. “Modelling masonry arches shape using terrestrial laser scanning data and nonparametric methods.” Eng. Struct. 32 (2): 607–615. https://doi.org/10.1016/j.engstruct.2009.11.007.
ASTM. 2002. Standard test method for diagonal tension (shear) in masonry assemblages. ASTM E519-02. West Conshohocken, PA: ASTM.
Bažant, Z. P. 2002a. “Concrete fracture models: Testing and practice.” Eng. Fract. Mech. 69 (2): 165–205. https://doi.org/10.1016/S0013-7944(01)00084-4.
Bažant, Z. P. 2002b. Scaling of structural strength. Boca Raton, FL: CRC Press.
Bažant, Z. P., and P. A. Pfeiffer. 1987. “Determination of fracture energy from size effect and brittleness number.” ACI Mater. J. 84 (6): 463–480.
Bažant, Z. P., and J. Planas. 1997. Vol. 16 of Fracture and size effect in concrete and other quasibrittle materials. Boca Raton, FL: CRC Press.
Bocca, P., A. Carpinteri, and S. Valente. 1989. “Fracture mechanics of brick masonry: Size effects and snap-back analysis.” Mater. Struct. 22 (5): 364–373. https://doi.org/10.1007/BF02472507.
Bolhassani, M., A. A. Hamid, A. C. Lau, and F. Moon. 2015. “Simplified micro modeling of partially grouted masonry assemblages.” Constr. Build. Mater. 83 (May): 159–173. https://doi.org/10.1016/j.conbuildmat.2015.03.021.
Brandonisio, G., G. Lucibello, E. Mele, and A. De Luca. 2013. “Damage and performance evaluation of masonry churches in the 2009 L’Aquila earthquake.” Eng. Fail. Anal. 34 (Dec): 693–714. https://doi.org/10.1016/j.engfailanal.2013.01.021.
Brignola, A., S. Frumento, S. Lagomarsino, and S. Podesta. 2008. “Identification of shear parameters of masonry panels through the in-situ diagonal compression test.” Int. J. Archit. Heritage 3 (1): 52–73. https://doi.org/10.1080/15583050802138634.
Calderini, C., S. Cattari, and S. Lagomarsino. 2010. “The use of the diagonal compression test to identify the shear mechanical parameters of masonry.” Constr. Build. Mater. 24 (5): 677–685. https://doi.org/10.1016/j.conbuildmat.2009.11.001.
Carol, I., and Z. P. Bazant. 1997. “Damage and plasticity in microplane theory.” Int. J. Solids Struct. 34 (29): 3807–3835. https://doi.org/10.1016/S0020-7683(96)00238-7.
Ceccato, C., M. Salviato, C. Pellegrino, and G. Cusatis. 2017. “Simulation of concrete failure and fiber reinforced polymer fracture in confined columns with different cross sectional shape.” Int. J. Solids Struct. 108 (Mar): 216–229. https://doi.org/10.1016/j.ijsolstr.2016.12.017.
Ceccato, C., J. Teng, and G. Cusatis. 2020. “Numerical prediction of the ultimate condition of circular concrete columns confined with a fiber reinforced polymer jacket.” Compos. Struct. 241 (Jun): 112103. https://doi.org/10.1016/j.compstruct.2020.112103.
CEN (European Committee for Standardization). 2005. Eurocode 6: Design of masonry structures. Part 1-1: General rules for reinforced and unreinforced masonry structures. EC6. Brussels, Belgium: CEN.
Cervera, M., J. Oliver, and R. Faria. 1995. “Seismic evaluation of concrete dams via continuum damage models.” Earthquake Eng. Struct. Dyn. 24 (9): 1225–1245. https://doi.org/10.1002/eqe.4290240905.
Circolare, N. 2019. Istruzioni per l’applicazione dell’aggiornamento delle norme tecniche per le costruzioni di cui al dm 17 gennaio 2018. [In Italian.] Rome: Ministero delle Infrastrutture e dei trasporti.
Corradi, M., A. Borri, G. Castori, and R. Sisti. 2014. “Shear strengthening of wall panels through jacketing with cement mortar reinforced by GFRP grids.” Composites, Part B 64 (Aug): 33–42. https://doi.org/10.1016/j.compositesb.2014.03.022.
Corradi, M., A. Borri, and A. Vignoli. 2003. “Experimental study on the determination of strength of masonry walls.” Constr. Build. Mater. 17 (5): 325–337. https://doi.org/10.1016/S0950-0618(03)00007-2.
Costa, A. A., A. Arêde, A. Costa, J. Guedes, and B. Silva. 2012. “Experimental testing, numerical modelling and seismic strengthening of traditional stone masonry: Comprehensive study of a real azorian pier.” Bull. Earthquake Eng. 10 (1): 135–159. https://doi.org/10.1007/s10518-010-9209-3.
Cusatis, G., Z. P. Bažant, and L. Cedolin. 2003a. “Confinement-shear lattice model for concrete damage in tension and compression. I: Theory.” J. Eng. Mech. 129 (12): 1439–1448. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:12(1449).
Cusatis, G., Z. P. Bažant, and L. Cedolin. 2003b. “Confinement-shear lattice model for concrete damage in tension and compression. II: Computation and validation.” J. Eng. Mech. 129 (12): 1449–1458. https://doi.org/10.1061/%28ASCE%290733-9399%282003%29129%3A12%281449%29.
Cusatis, G., A. Mencarelli, D. Pelessone, and J. Baylot. 2011a. “Lattice discrete particle model (LDPM) for failure behavior of concrete. II: Calibration and validation.” Cem. Concr. Compos. 33 (9): 891–905. https://doi.org/10.1016/j.cemconcomp.2011.02.010.
Cusatis, G., D. Pelessone, and A. Mencarelli. 2011b. “Lattice discrete particle model (LDPM) for failure behavior of concrete. I: Theory.” Cem. Concr. Compos. 33 (9): 881–890. https://doi.org/10.1016/j.cemconcomp.2011.02.011.
Cusatis, G., and X. Zhou. 2014. “High-order microplane theory for quasi-brittle materials with multiple characteristic lengths.” J. Eng. Mech. 140 (7): 04014046. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000747.
D’Ayala, D. F., and S. Paganoni. 2011. “Assessment and analysis of damage in L’Aquila historic city centre after 6th April 2009.” Bull. Earthquake Eng. 9 (1): 81–104. https://doi.org/10.1007/s10518-010-9224-4.
Di Nino, S., and D. Zulli. 2020. “Homogenization of ancient masonry buildings: A case study.” Appl. Sci. 10 (19): 6687. https://doi.org/10.3390/app10196687.
Formisano, A. 2017. “Theoretical and numerical seismic analysis of masonry building aggregates: Case studies in San Pio delle Camere (L’aquila, Italy).” J. Earthquake Eng. 21 (2): 227–245. https://doi.org/10.1080/13632469.2016.1172376.
Frocht, M. M. 1931. “Recent advances in photoelasticity and an investigation of the stress distribution in square blocks subjected to diagonal compression.” Trans. ASME 53: 135–153. https://doi.org/10.1016/B978-0-08-012998-3.50009-4.
Gambarotta, L., and S. Lagomarsino. 1997. “Damage models for the seismic response of brick masonry shear walls. Part II: The continuum model and its applications.” Earthquake Eng. Struct. Dyn. 26 (4): 441–462. https://doi.org/10.1002/(SICI)1096-9845(199704)26:4%3C441::AID-EQE651%3E3.0.CO;2-0.
Giamundo, V., V. Sarhosis, G. Lignola, Y. Sheng, and G. Manfredi. 2014. “Evaluation of different computational modelling strategies for the analysis of low strength masonry structures.” Eng. Struct. 73 (Aug): 160–169. https://doi.org/10.1016/j.engstruct.2014.05.007.
Han, L., M. Pathirage, A.-T. Akono, and G. Cusatis. 2021. “Lattice discrete particle modeling of size effect in slab scratch tests.” J. Appl. Mech. 88 (2): 021009. https://doi.org/10.1115/1.4048989.
Hillerborg, A., M. Modéer, and P.-E. Petersson. 1976. “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cem. Concr. Res. 6 (6): 773–781. https://doi.org/10.1016/0008-8846(76)90007-7.
Jin, C., N. Buratti, M. Stacchini, M. Savoia, and G. Cusatis. 2016. “Lattice discrete particle modeling of fiber reinforced concrete: Experiments and simulations.” Eur. J. Mech. A. Solids 57 (May): 85–107. https://doi.org/10.1016/j.euromechsol.2015.12.002.
Karnopp, D. 1985. “Computer simulation of stick-slip friction in mechanical dynamic systems.” J. Dyn. Syst. Meas. Control 107 (1): 100–103. https://doi.org/10.1115/1.3140698.
Kouris, L. A. S., D. A. Bournas, O. T. Akintayo, A. A. Konstantinidis, and E. C. Aifantis. 2020. “A gradient elastic homogenisation model for brick masonry.” Eng. Struct. 208 (Apr): 110311. https://doi.org/10.1016/j.engstruct.2020.110311.
Lale, E., R. Rezakhani, M. Alnaggar, and G. Cusatis. 2018. “Homogenization coarse graining (HCG) of the lattice discrete particle model (LDPM) for the analysis of reinforced concrete structures.” Eng. Fract. Mech. 197 (Jun): 259–277. https://doi.org/10.1016/j.engfracmech.2018.04.043.
Lemos, J. V. 2007. “Discrete element modeling of masonry structures.” Int. J. Archit. Heritage 1 (2): 190–213. https://doi.org/10.1080/15583050601176868.
Lourenço, P. 1998. “Simulations of size effect in masonry structures.” In Vol. 3 of Proc., Fracture Mechanics of Concrete Structures, FRAMCOS-3, 2001–2010. Freiburg, Germany: Aedificatio Publishers.
Lourenço, P., and J. Barros. 2000. “Size effect on masonry subjected to out-of-plane loading.” In Vol. 2 of Proc., 12th Int. Brick/Block Masonry Conf., 1085–1098. Madrid, Spain: Citeseer.
Lourenço, P. B. 1996. A user/programmer guide for the micro-modeling of masonry structures. Delft, Netherlands: Delft Univ. of Technology.
Lourenço, P. B., and J. G. Rots. 1997. “Multisurface interface model for analysis of masonry structures.” J. Eng. Mech. 123 (7): 660–668. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:7(660).
Lourenço, P. B., J. G. Rots, and J. Blaauwendraad. 1998. “Continuum model for masonry: Parameter estimation and validation.” J. Struct. Eng. 124 (6): 642–652. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:6(642).
Lourenço, P. J. B. B. 1997. “Computational strategies for masonry structures.” Ph.D. thesis, Dept. of Civil Engineering, Delft Univ. of Technology.
Magenes, G., A. Penna, A. Galasco, and M. Rota. 2010. “Experimental characterisation of stone masonry mechanical properties.” In Proc., 8th Int. Masonry Conf. Stoke-on-Trent, UK: International Masonry Society.
Mercuri, M., M. Pathirage, A. Gregori, and G. Cusatis. 2020. “Computational modeling of the out-of-plane behavior of unreinforced irregular masonry.” Eng. Struct. 223 (Nov): 111181. https://doi.org/10.1016/j.engstruct.2020.111181.
Milosevic, J., A. S. Gago, M. Lopes, and R. Bento. 2013. “Experimental assessment of shear strength parameters on rubble stone masonry specimens.” Constr. Build. Mater. 47 (Oct): 1372–1380. https://doi.org/10.1016/j.conbuildmat.2013.06.036.
Nguyen, H., M. Pathirage, M. Rezaei, M. Issa, G. Cusatis, and Z. P. Bažant. 2020a. “New perspective of fracture mechanics inspired by gap test with crack-parallel compression.” Proc. Natl. Acad. Sci. 117 (25): 14015–14020. https://doi.org/10.1073/pnas.2005646117.
Nguyen, H. T., M. Pathirage, G. Cusatis, and Z. P. Bažant. 2020b. “Gap test of crack-parallel stress effect on quasibrittle fracture and its consequences.” J Appl. Mech. 87 (7): 071012. https://doi.org/10.1115/1.4047215.
NTC (Norme Tecniche per le Costruzioni). 2018. Norme tecniche per le costruzioni in zone sismiche. [In Italian.]. Rome: NTC.
Pathirage, M., D. Bentz, G. Di Luzio, E. Masoero, and G. Cusatis. 2019a. “The ONIX model: A parameter-free multiscale framework for the prediction of self-desiccation in concrete.” Cem. Concr. Compos. 103 (Oct): 36–48. https://doi.org/10.1016/j.cemconcomp.2019.04.011.
Pathirage, M., F. Bousikhane, M. D’Ambrosia, M. Alnaggar, and G. Cusatis. 2019b. “Effect of alkali silica reaction on the mechanical properties of aging mortar bars: Experiments and numerical modeling.” Int. J. Damage Mech. 28 (2): 291–322. https://doi.org/10.1177/1056789517750213.
Pelessone, D. 2009. Mars: Modeling and analysis of the response of structures user’s manual. San Diego: ES3 Prime Logistics Group.
Pulatsu, B., E. M. Bretas, and P. B. Lourenco. 2016. “Discrete element modeling of masonry structures: Validation and application.” Earthquake Struct. 11 (4): 563–582. https://doi.org/10.12989/eas.2016.11.4.563.
Rezakhani, R., and G. Cusatis. 2016. “Asymptotic expansion homogenization of discrete fine-scale models with rotational degrees of freedom for the simulation of quasi-brittle materials.” J. Mech. Phys. Solids 88 (Mar): 320–345. https://doi.org/10.1016/j.jmps.2016.01.001.
RILEM. 1994. “Lum b6 diagonal tensile strength tests of small wall specimens, 1991.” In RILEM recommendations for the testing and use of constructions materials, 488–489. London: E & FN Spon.
Roca, P., M. Cervera, and G. Gariup. 2010. “Structural analysis of masonry historical constructions. classical and advanced approaches.” Arch. Comput. Methods Eng. 17 (3): 299–325. https://doi.org/10.1007/s11831-010-9046-1.
Schauffert, E. A., and G. Cusatis. 2011. “Lattice discrete particle model for fiber-reinforced concrete. I: Theory.” J. Eng. Mech. 138 (7): 826–833. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000387.
Si, H. 2015. “TetGen, a Delaunay-based quality tetrahedral mesh generator.” ACM Trans. Math. Software 41 (2): 1–36. https://doi.org/10.1145/2629697.
Silva, B., J. M. Guedes, A. Arêde, and A. Costa. 2012. “Calibration and application of a continuum damage model on the simulation of stone masonry structures: Gondar church as a case study.” Bull. Earthquake Eng. 10 (1): 211–234. https://doi.org/10.1007/s10518-010-9216-4.
Smith, J., and G. Cusatis. 2017. “Numerical analysis of projectile penetration and perforation of plain and fiber reinforced concrete slabs.” Int. J. Numer. Anal. Methods Geomech. 41 (3): 315–337. https://doi.org/10.1002/nag.2555.
Tóth, A. R., Z. Orbán, and K. Bagi. 2009. “Discrete element analysis of a stone masonry arch.” Mech. Res. Commun. 36 (4): 469–480. https://doi.org/10.1016/j.mechrescom.2009.01.001.
Walsh, P. 1976. “Crack initiation in plain concrete.” Mag. Concr. Res. 28 (94): 37–41. https://doi.org/10.1680/macr.1976.28.94.37.
Weibull, W. 1939. “A statistical theory of strength of materials.” IVB-Handl. 151: 1–45.
Yokel, F. Y., and S. G. Fattal. 1976. “Failure hypothesis for masonry shear walls.” J. Struct. Div. 102 (3): 515–532. https://doi.org/10.1061/JSDEAG.0004294.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 147Issue 9September 2021

History

Received: May 20, 2020
Accepted: Apr 7, 2021
Published online: Jun 23, 2021
Published in print: Sep 1, 2021
Discussion open until: Nov 23, 2021

Permissions

Request permissions for this article.

Authors

Affiliations

Postdoctoral Researcher, Dept. of Civil, Construction and Environmental Engineering, Univ. of L’Aquila, L’Aquila 67100, Italy. ORCID: https://orcid.org/0000-0002-7584-9485. Email: [email protected]
Postdoctoral Researcher, Dept. of Civil and Environmental Engineering, McCormick School of Engineering and Applied Science Northwestern Univ., Evanston, IL 60208. ORCID: https://orcid.org/0000-0002-6014-0158. Email: [email protected]
Amedeo Gregori, Ph.D. [email protected]
Professor, Dept. of Civil, Construction and Environmental Engineering, Univ. of L’Aquila, L’Aquila 67100, Italy. Email: [email protected]
Professor, Dept. of Civil and Environmental Engineering, McCormick School of Engineering and Applied Science Northwestern Univ., Evanston, IL 60208 (corresponding author). ORCID: https://orcid.org/0000-0001-7436-3910. 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

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