Young’s Modulus Variability: Influence on Masonry Vault Behavior
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.
[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.
[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.
@article{"International Journal of Architectural, Civil and Construction Sciences:70730", author = "A. Zanaz and S. Yotte and F. Fouchal and A. Chateauneuf", title = "Young’s Modulus Variability: Influence on Masonry Vault Behavior", 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 = "Masonry, mechanism, probability, variability, vault.", volume = "9", number = "9", pages = "1176-7", }
