Advanced Modeling of a Historical Masonry Umbrella Vault: Settlement Analysis and Crack Tracking via Adaptive NURBS Kinematic Analysis
Publication: Journal of Engineering Mechanics
Volume 147, Issue 11
Abstract
In this work, the study of a complex masonry umbrella vault located within Masegra Castle (Museum of Sondrio territory, Northern Italy) is presented. Built during the renewal of the castle in the 16th century, the umbrella vault of Masegra Castle is characterized by a total of eight sails, with four half-cross vaults added at the corners, supported by four walls, and resulting in a quadrangular horizontal plan. The observed crack pattern seems to derive from vertical settlement phenomena involving at least one of the supporting walls. A multidisciplinary approach based on innovative technologies for the geometric reconstruction, detailed analysis of the construction, the historical evolution, and its state of conservation, has been followed. Starting from dense laser scanner point clouds and photogrammetric surveys, historical building information modeling (HBIM) models have been created and allowed the generation of an accurate geometrical representation of the umbrella vault through nonuniform rational basis-splines (NURBS) surfaces. Starting from the NURBS-based model, an adaptive kinematic procedure is used to determine the failure behavior under settlements. A discretization through triangular NURBS elements, in which the real geometry remains unvaried, is adopted. Each element is idealized as a rigid block and jumps of displacement are allowed at the boundaries only. By applying the principle of virtual works, a discontinuous displacement field deriving from an imposed settlement is obtained. As a consequence of the reduced number of elements adopted, a metaheuristic mesh adaptation procedure is finally applied to find the correct disposition of fracture lines. Different settlement typologies are adopted in the analyses to reproduce the crack pattern observed on the umbrella vault. Finally, an inverse analysis is conducted to estimate the shape of the occurred settlements starting from the observed crack pattern.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Barazzetti, L., F. Banfi, R. Brumana, G. Gusmeroli, M. Previtali, and G. Schiantarelli. 2015a. “Cloud-to-BIM-to-FEM: Structural simulation with accurate historic BIM from laser scans.” Simul. Modell. Pract. Theory 57 (Sep): 71–87. https://doi.org/10.1016/j.simpat.2015.06.004.
Barazzetti, L., F. Banfi, R. Brumana, and M. Previtali. 2015b. “Creation of parametric BIM objects from point clouds using nurbs.” Photogramm. Rec. 30 (152): 339–362. https://doi.org/10.1111/phor.12122.
Barazzetti, L., R. Brumana, S. Della Torre, G. Gusmeroli, and G. Schiantarelli. 2018 “Point clouds turned into finite elements: The umbrella vault of Castel Masegra.” In Vol. 364 of Proc., IOP Conf. Series: Materials Science and Engineering, 012087. Florence, Italy: Univ. of Florence. https://doi.org/10.1088/1757-899X/364/1/012087.
Bergström, P. 2006. ‘IGES toolbox’, MATLAB central, file exchange, user community. Natick, MA: Mathworks.
Bianconi, F., G. P. Salachoris, F. Clementi, and S. Lenci. 2020. “A genetic algorithm procedure for the automatic updating of fem based on ambient vibration tests.” Sensors 20 (11): 3315. https://doi.org/10.3390/s20113315.
Block, P., and J. Ochsendorf. 2007. “Thrust network analysis: A new methodology for three-dimensional equilibrium.” J.-Int. Assoc. Shell Spatial Struct. 48 (3): 167–173.
Bonetti, L., and S. Perlini. 2013. Masegra. Storia del castello di Sondrio. Sondrio, Italy: Città di Sondrio–Museo Valtellinese di Storia e Arte.
Castellazzi, G., A. M. D’Altri, S. de Miranda, and F. Ubertini. 2017. “An innovative numerical modeling strategy for the structural analysis of historical monumental buildings.” Eng. Struct. 132 (Feb): 229–248. https://doi.org/10.1016/j.engstruct.2016.11.032.
Cazzani, A., M. Malagù, and E. Turco. 2016. “Isogeometric analysis: A powerful numerical tool for the elastic analysis of historical masonry arches.” Contin. Mech. Thermodyn. 28 (1–2): 139–156. https://doi.org/10.1007/s00161-014-0409-y.
Chieffo, N., F. Clementi, A. Formisano, and S. Lenci. 2019. “Comparative fragility methods for seismic assessment of masonry buildings located in Muccia (Italy).” J. Build. Eng. 25 (Sep): 100813. https://doi.org/10.1016/j.jobe.2019.100813.
Chieffo, N., and A. Formisano. 2019. “Geo-hazard-based approach for the estimation of seismic vulnerability and damage scenarios of the old city of senerchia (Avellino, Italy).” Geosciences 9 (2): 59. https://doi.org/10.3390/geosciences9020059.
Chiozzi, A., G. Milani, and A. Tralli. 2017a. “Fast kinematic limit analysis of FRP-reinforced masonry vaults. Part I: A general genetic algorithm NURBS-based formulation.” J. Eng. Mech. 143 (9): 04017071. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001267.
Chiozzi, A., G. Milani, and A. Tralli. 2017b. “A genetic algorithm NURBS-based new approach for fast kinematic limit analysis of masonry vaults.” Comput. Struct. 182 (Apr): 187–204. https://doi.org/10.1016/j.compstruc.2016.11.003.
Como, M. 2013a. “Settlement response of masonry constructions.” In Geotechnical engineering for the preservation of monuments and historic sites, 265–272. London: Taylor & Francis.
Como, M. 2013b. Statics of historic masonry constructions. Berlin: Springer.
Conti, F., V. Hybsch, and A. Vicenti. 1991. I castelli della Lombardia. Novara, Italy: Istituto Geografico De Agostini.
Creazza, G., R. Matteazzi, A. Saetta, and R. Vitaliani. 2002. “Analyses of masonry vaults: A macro approach based on three-dimensional damage model.” J. Struct. Eng. 128 (5): 646–654. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:5(646).
D’Alfonso, A. 2013. “Sondrio, Castel Masegra. Sito protostorico e strutture medievali.” In Notiziario della Soprintendenza per i Beni Archeologici della Lombardia, 277–279. Rome: Ministero dei Beni e delle attività Culturali e del Turismo.
Della Misericordia, M. 2006. Divenire comunità. Comuni rurali, poteri locali, identità sociali e territoriali in Valtellina e nella montagna lombarda nel tardo Medioevo. Milano, Italy: Unicopli.
Della Torre, S. 1988. “La funzione, il tipo, la fabbrica: Il Sant’Anna nella storia dell’architettura ospedaliera.” In La storia, gli spazi, le funzioni. Il recupero dell’ex-ospedale di S.Anna in Como, Como 1988, edited by S. Della Torre, L. Martinelli, and M. Dubini, 9–59. Como, Italy: New Press.
Dell’Oca Fiordi, A. 1994. “Sondrio. Mura urbiche ed abitazioni medievali.” In Notiziario della Soprintendenza per i Beni Archeologici della Lombardia, 161. Rome: Ministero dei Beni e delle attività Culturali e del Turismo.
De Vanna, L. 2015. “Scheda 3. Sondrio, castel Masegra, abitato protostorico.” In La Valtellina nei secoli. Studi e ricerche archeologiche. Volume II: Ricerche e materiali archeologici, 303–311. Mantova, Italy: SAP Società Archeologica.
Ferrante, A., F. Clementi, and G. Milani. 2020. “Advanced numerical analyses by the Non-Smooth Contact Dynamics method of an ancient masonry bell tower.” Math. Methods Appl. Sci. 43 (13): 7706–7725. https://doi.org/10.1002/mma.6113.
Formisano, A., N. Chieffo, and M. Mosoarca. 2017. “Seismic vulnerability and damage speedy estimation of an urban sector within the municipality of San Potito Sannitico (Caserta, Italy).” Open Civ. Eng. J. 11 (1): 1106–1121. https://doi.org/10.2174/1874149501711011106.
Formisano, A., G. Di Lorenzo, L. Krstevska, and R. Landolfo. 2020. “Fem model calibration of experimental environmental vibration tests on two churches hit by l’aquila earthquake.” Int. J. Archit. Heritage 15 (1): 113–131. https://doi.org/10.1080/15583058.2020.1719233.
Formisano, A., and A. Massimilla. 2018. “A novel procedure for simplified nonlinear numerical modeling of structural units in masonry aggregates.” Int. J. Archit. Heritage 12 (7–8): 1162–1170. https://doi.org/10.1080/15583058.2018.1503365.
Gaetani, A., N. Bianchini, and P. B. Lourenço. 2021. “‘Simplified micro-modelling of masonry cross vaults: Stereotomy and interface issues’, Internationl Journal of Masonry.” Res. Innovation 6 (1): 97–125. https://doi.org/10.1504/IJMRI.2021.112076.
Gavazzi, S. B. 2002. “Il castello Masegra.” In Residenze nobiliari di Valtellina e Valchiavenna. Le dimore delle famiglie Salis e Sertoli, 143–153. Milano, Italy: Silvana Editoriale.
Gavazzi, S. B., and A. Corbellini. 2004. Il Castello Masegra di Sondrio: Approfondimento documentario. Sondrio, Italy: Comune di Sondrio.
Giordano, E., F. Clementi, A. Nespeca, and S. Lenci. 2019. “Damage assessment by numerical modeling of sant’agostino’s sanctuary in offida during the central Italy 2016–2017 Seismic Sequence.” Front. Built Environ. 4 (Jan): 87. https://doi.org/10.3389/fbuil.2018.00087.
Grillanda, N. 2019. iges2matlab, MATLAB central, file exchange. Natick, MA: Mathworks.
Grillanda, N., A. Chiozzi, F. Bondi, A. Tralli, F. Manconi, F. Stochino, and A. Cazzani. 2021a. “Numerical insights on the structural assessment of historical masonry stellar vaults: The case of Santa Maria del Monte in Cagliari.” Contin. Mech. Thermodyn. 33 (1): 1–24. https://doi.org/10.1007/s00161-019-00752-8.
Grillanda, N., A. Chiozzi, G. Milani, and A. Tralli. 2019. “Collapse behavior of masonry domes under seismic loads: An adaptive NURBS kinematic limit analysis approach.” Eng. Struct. 200 (Dec): 109517. https://doi.org/10.1016/j.engstruct.2019.109517.
Grillanda, N., A. Chiozzi, G. Milani, and A. Tralli. 2020a. “Efficient meta-heuristic mesh adaptation strategies for NURBS–based upper–bound limit analysis of general curved three-dimensional masonry structures.” Comput. Struct. 236 (Aug): 106271. https://doi.org/10.1016/j.compstruc.2020.106271.
Grillanda, N., A. Chiozzi, G. Milani, and A. Tralli. 2021b. “Tilting plane tests for the ultimate shear capacity evaluation of perforated dry joint masonry panels. Part II: Numerical analyses.” Eng. Struct. 228 (Feb): 111460. https://doi.org/10.1016/j.engstruct.2020.111460.
Grillanda, N., G. Milani, S. Ghosh, B. Halani, and M. Varma. 2021c. “SHM of a severely cracked masonry arch bridge in India: Experimental campaign and adaptive NURBS limit analysis numerical investigation.” Constr. Build. Mater. 280 (Apr): 122490. https://doi.org/10.1016/j.conbuildmat.2021.122490.
Grillanda, N., M. Valente, and G. Milani. 2020b. “ANUB-aggregates: A fully automatic NURBS-based software for advanced local failure analyses of historical masonry aggregates.” Bull. Earthquake Eng. 18 (8): 3935–3961. https://doi.org/10.1007/s10518-020-00848-6.
Gusmeroli, G., and G. Schiantarelli. 2014. “From laser clouds to BIM and finite element analysis: The case study of castel masegra.” Master thesis, Dept. of Civil Engineering for Risk Mitigation, Politecnico di Milano.
Haupt, R. L., and S. E. Haupt. 1998. Practical genetic algorithms. New York: Wiley.
Heyman, J. 1966. “The stone skeleton.” Int. J. Solids Struct. 2 (2): 249–279. https://doi.org/10.1016/0020-7683(66)90018-7.
Heyman, J. 1969. “The safety of masonry arches.” Int. J. Mech. Sci. 11 (4): 363–385.
Huerta Fernández, S. 2001. “Mechanics of masonry vaults: The equilibrium approach.” In Historical constructions. Possibilities of numerical and experimental techniques, edited by P. B. Lourenço and P. Roca. Guimaraes, Portugal: Universidade do Minho.
Iannuzzo, A., M. Angelillo, E. De Chiara, F. De Guglielmo, F. De Serio, F. Ribera, and A. Gesualdo. 2018. “Modelling the cracks produced by settlements in masonry structures.” Meccanica 53 (7): 1857–1873. https://doi.org/10.1007/s11012-017-0721-2.
Kennicott, P. R. 1996. Initial graphics exchange specification. North Charleston, SC: US Product Data Association.
Mariotti, V. 1994. “Sondrio. Mura urbiche ed abitazioni medievali. Lo scavo.” In Notiziario della Soprintendenza per i Beni Archeologici della Lombardia, 161–162. Rome: Ministero dei Beni e delle attività Culturali e del Turismo.
Marmo, F., and L. Rosati. 2017. “Reformulation and extension of the thrust network analysis.” Comput. Struct. 182 (Apr): 104–118. https://doi.org/10.1016/j.compstruc.2016.11.016.
Milani, E., G. Milani, and A. Tralli. 2008. “Limit analysis of masonry vaults by means of curved shell finite elements and homogenization.” Int. J. Solids Struct. 45 (20): 5258–5288. https://doi.org/10.1016/j.ijsolstr.2008.05.019.
Milani, G., and F. Clementi. 2019. “Advanced seismic assessment of four masonry bell towers in Italy after operational modal analysis (OMA) identification.” Int. J. Archit. Heritage 15 (1): 157–186. https://doi.org/10.1080/15583058.2019.1697768.
Milani, G., E. Milani, and A. Tralli. 2009. “Upper bound limit analysis model for FRP: Reinforced masonry curved structures. Part II: Structural analyses.” Comput. Struct. 87 (23–24): 1534–1558. https://doi.org/10.1016/j.compstruc.2009.07.010.
Milani, G., M. Rossi, C. Calderini, and S. Lagomarsino. 2016. “Tilting plane tests on a small-scale masonry cross vault: Experimental results and numerical simulations through a heterogeneous approach.” Eng. Struct. 123 (Sep): 300–312. https://doi.org/10.1016/j.engstruct.2016.05.017.
Milani, G., M. Simoni, and A. Tralli. 2014. “Advanced numerical models for the analysis of masonry cross vaults: A case-study in Italy.” Eng. Struct. 76 (Oct): 339–358. https://doi.org/10.1016/j.engstruct.2014.07.018.
Pavlovic, M., E. Reccia, and A. Cecchi. 2016. “A procedure to investigate the collapse behavior of masonry domes: Some meaningful cases.” Int. J. Archit. Heritage 10 (1): 67–83. https://doi.org/10.1080/15583058.2014.951797.
Piegl, L., and W. Tiller. 1995. The NURBS book. Berlin: Springer.
Rao, R. 2015. “I castelli della Valtellina nei secoli centrali del Medioevo (X-XII): Habitat fortificato, paesaggi e dinamiche di popolamento.” In La Valtellina nei secoli. Studi e ricerche archeologiche. Volume I: Saggi, 195–212. Mantova, Italy: SAP Società Archeologica.
Scacco, J., G. Milani, and P. B. Lourenço. 2020. “Automatic mesh generator for the non-linear homogenized analysis of double curvature masonry structures.” Adv. Eng. Software 150 (Dec): 102919. https://doi.org/10.1016/j.advengsoft.2020.102919.
Standoli, G., E. Giordano, G. Milani, and F. Clementi. 2020. “Model updating of historical belfries based on oma identification techniques.” Int. J. Archit. Heritage 15 (1): 132–156. https://doi.org/10.1080/15583058.2020.1723735.
Tiberti, S., N. Grillanda, V. Mallardo, and G. Milani. 2020. “A genetic algorithm adaptive homogeneous approach for evaluating settlement-induced cracks in masonry walls.” Eng. Struct. 221 (Oct): 111073. https://doi.org/10.1016/j.engstruct.2020.111073.
Tralli, A., C. Alessandri, and G. Milani. 2014. “Computational methods for masonry vaults: A review of recent results.” Open Civ. Eng. J. 8 (1): 272–287. https://doi.org/10.2174/1874149501408010272.
Tralli, A., A. Chiozzi, N. Grillanda, and G. Milani. 2020. “Masonry structures in the presence of foundation settlements and unilateral contact problems.” Int. J. Solids Struct. 191–192 (May): 187–201. https://doi.org/10.1016/j.ijsolstr.2019.12.005.
Valente, M., G. Milani, E. Grande, and A. Formisano. 2019. “Historical masonry building aggregates: Advanced numerical insight for an effective seismic assessment on two row housing compounds.” Eng. Struct. 190 (Jul): 360–379. https://doi.org/10.1016/j.engstruct.2019.04.025.
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Published In
Journal of Engineering Mechanics
Volume 147 • Issue 11 • November 2021
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© 2021 American Society of Civil Engineers.
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Received: Jan 14, 2021
Accepted: May 11, 2021
Published online: Aug 30, 2021
Published in print: Nov 1, 2021
Discussion open until: Jan 30, 2022
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