Commenced in January 2007
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Edition: International
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Young’s Modulus Variability: Influence on Masonry Vault Behavior

Authors: A. Zanaz, S. Yotte, F. Fouchal, A. Chateauneuf

Abstract:

This paper presents a methodology for probabilistic assessment of bearing capacity and prediction of failure mechanism of masonry vaults at the ultimate state with consideration of the natural variability of Young’s modulus of stones. First, the computation model is explained. The failure mode corresponds to the four-hinge mechanism. Based on this consideration, the study of a vault composed of 16 segments is presented. The Young’s modulus of the segments is considered as random variable defined by a mean value and a coefficient of variation. A relationship linking the vault bearing capacity to the voussoirs modulus variation is proposed. The most probable failure mechanisms, in addition to that observed in the deterministic case, are identified for each variability level as well as their probability of occurrence. The results show that the mechanism observed in the deterministic case has decreasing probability of occurrence in terms of variability, while the number of other mechanisms and their probability of occurrence increases with the coefficient of variation of Young’s modulus. This means that if a significant change in the Young’s modulus of the segments is proven, taking it into account in computations becomes mandatory, both for determining the vault bearing capacity and for predicting its failure mechanism.

Keywords: Probability, Masonry, variability, Mechanism, vault

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1108394

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References:


[1] P. de Buhan and G. de Felice, “A homogenization approach to the ultimate strength of brick masonry,” J. Mech. Phys. Solids, vol. 45, no. 7, pp. 1085–1104, Jul. 1997.
[2] P. Pegon and A. Anthoine, “Numerical strategies for solving continuum damage problems with softening: Application to the homogenization of Masonry,” Comput. Struct., vol. 64, no. 1–4, pp. 623–642, Jul. 1997.
[3] R. Luciano and E. Sacco, Homogenization technique and damage model for old masonry material,” Int. J. Solids Struct., vol. 34, no. 24, pp. 3191–3208, Aug. 1997.
[4] A. Zucchini and P. B. Lourenço, “A micro-mechanical model for the homogenisation of masonry,” Int. J. Solids Struct., vol. 39, no. 12, pp. 3233–3255, Jun. 2002.
[5] M. Mistler, A. Anthoine, and C. Butenweg, “In-plane and out-of-plane homogenisation of masonry,” Comput. Struct., vol. 85, no. 17–18, pp. 1321–1330, Sep. 2007.
[6] A. Zucchini and P. B. Lourenço, “A micro-mechanical homogenisation model for masonry: Application to shear walls,” Int. J. Solids Struct., vol. 46, no. 3–4, pp. 871–886, Feb. 2009.
[7] F. Cluni and V. Gusella, “Homogenization of non-periodic masonry structures,” Int. J. Solids Struct., vol. 41, no. 7, pp. 1911–1923, Apr. 2004.
[8] Gusella and Cluni, “Random field and homogenization for masonry with nonperiodic microstructure,” J. Mech. Mater. Struct., vol. 1, no. 2, p. 357e386, 2006.
[9] C. Huet, “Application of variational concepts to size effects in elastic heterogeneous bodies,” J. Mech. Phys. Solids, vol. 38, no. 6, pp. 813– 841, 1990.
[10] L. Binda, G. Baronio, C. Tiraboschi, and C. Tedeschi, “Experimental research for the choice of adequate materials for the reconstruction of the Cathedral of Noto,” Constr. Build. Mater., vol. 17, no. 8, pp. 629– 639, Dec. 2003.
[11] PIPPARD A. J. S., “A study of the Voussoir arch,” His Majesty’s stationery Office, National Building Studies, Research Paper n°11, 52p., 1951.
[12] Christchurch, “MEXE. Military Engineering experimental Establishment.” « Military load classification of civil bridges by reconnaissance and correlation methods», 1963.
[13] Kooharian, “Limit Analysis of Voussoir (Segmental) and Concrete Arches,” Journal of the American Concrete Institute 317-328, V. 24, N° 4, Dec. 1952, Proceedings V. 49., 1953.
[14] G. A. Drosopoulos, G. E. Stavroulakis, and C. V. Massalas, “Limit analysis of a single span masonry bridge with unilateral frictional contact interfaces,” Eng. Struct., vol. 28, no. 13, pp. 1864–1873, Nov. 2006.
[15] A. Cavicchi and L. Gambarotta, “Lower bound limit analysis of masonry bridges including arch–fill interaction,” Eng. Struct., vol. 29, no. 11, pp. 3002–3014, Nov. 2007.
[16] E. Milani, G. Milani, and A. Tralli, “Limit analysis of masonry vaults by means of curved shell finite elements and homogenization,” Int. J. Solids Struct., vol. 45, no. 20, pp. 5258–5288, Oct. 2008.
[17] TRAUTWINE, J. C., Civil engineer’s pocket-book. New York Wiley publisher, 1871, 770 p., 1871.
[18] Harvey, “Rule of thumb method for the assessment of arches.” Rapport UIC, draft, 2007, pp. 22, 2007.
[19] ORBAN, Z., “Improving assessment, optimisation of maintenance and development of database for masonry arch bridges.” International Union of Railways, UIC infrastructure Department, 13 p., 2008, 2008.
[20] Harvey WEJ, “Application of the mechanism analysis to masonry arches,” Struct Eng 1988, vol. 66, no. 5, pp. 77–84, 1988.
[21] Buhan P., Mangiavacchi R., Nova R., Pellegrini G., and Salencon J., “Yield design of reinforced earth walls by a homogenization method,” J Geotech., vol. 39, no. 2, pp. 189–201, 1989.
[22] B. T. Rosson, K. Søyland, and T. E. Boothby, “Inelastic behavior of sand-lime mortar joint masonry arches,” Eng. Struct., vol. 20, no. 1–2, pp. 14–24, Jan. 1998.
[23] P. J. Fanning and T. E. Boothby, “Three-dimensional modelling and full-scale testing of stone arch bridges,” Comput. Struct., vol. 79, no. 29–30, pp. 2645–2662, Nov. 2001.
[24] E. Reccia, G. Milani, A. Cecchi, and A. Tralli, “Full 3D homogenization approach to investigate the behavior of masonry arch bridges: The Venice trans-lagoon railway bridge,” Constr. Build. Mater., vol. 66, pp. 567–586, Sep. 2014.
[25] A. R. Tóth, Z. Orbán, and K. Bagi, “Discrete element analysis of a stone masonry arch,” Mech. Res. Commun., vol. 36, no. 4, pp. 469–480, Jun. 2009.
[26] G. Milani and P. B. Lourenço, “3D non-linear behavior of masonry arch bridges,” Comput. Struct., vol. 110–111, pp. 133–150, Nov. 2012.
[27] K.-H. Ng and C. A. Fairfield, “Monte Carlo simulation for arch bridge assessment,” Constr. Build. Mater., vol. 16, no. 5, pp. 271–280, Jul. 2002.
[28] J. R. Casas, “Reliability-based assessment of masonry arch bridges,” Constr. Build. Mater., vol. 25, no. 4, pp. 1621–1631, Apr. 2011.