Spatial Correlation of Material Properties and Structural Strength of Masonry in Horizontal Bending
Publication: Journal of Structural Engineering
Volume 142, Issue 11
Abstract
Spatial variability of material properties might significantly affect the structural performance and reliability of unreinforced masonry (URM) walls. The paper develops a computational method to predict the strength for URM walls subject to one-way horizontal bending considering unit-to-unit spatial variability of the material properties of mortar joints and bricks. In this context, the term unit is being used to describe the location in the wall associated with a single brick and the adjacent mortar joints. In this way, the material properties are assumed to be uniform along the length, height, and thickness of individual bricks but may vary from brick to brick within the wall. Tensile strength, shear bond strength, and associated fracture energies of the mortar joints and tensile strength and fracture energy of the bricks are the main parameters considered herein. The authors examine how correlation and spatial variability in unit strengths (mortar joints and bricks) affect the variability of ultimate strength and damage progression of clay brick URM walls in one-way horizontal bending. Stochastic analysis in the form of Monte Carlo simulations used a three-dimensional (3D) nonlinear finite-element analysis. The results were validated from a database of available experimental results on masonry four-course beams. It was found that good agreement of peak load exists between the stochastic simulation and the experimental results for the four-course beam subject to horizontal bending.
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Acknowledgments
The authors gratefully acknowledge the financial support of the Australian Research Council and Think Brick Australia for Linkage Project LP0669538 as well as test data results from Paulo B. Lourenco.
References
AS (Australian Standard). (2001). “Concrete structures.” AS 3600, Sydney, Australia.
AS (Australian Standard). (2011). “Masonry structures.” AS 3700, Sydney, Australia.
AS/NZS (Australian/New Zealand Standard). (2003). “Masonry units, segmental pavers and flags—Methods of test—Method 15: Determining lateral modulus of rupture.” AS/NZS 4456.15, Sydney, Australia.
Baker, L. R. (1981). “The flexural action of masonry structures under lateral load.” Ph.D. thesis, Deakin Univ., Australia.
Baker, L. R., and Franken, G. L. (1976). “Variability aspects of the flexural strength of brickwork.” Proc., 4th Int. Brick Masonry Conf., Brussels, Belgium.
Bazant, Z. P., and Pfeiffer, P. A. (1987). “Determination of fracture energy from size effect and brittleness number.” ACI Mater. J., 84, 463–480.
Bazant, Z. P., and Prat, P. C. (1988). “Measurement of mode III fracture energy of concrete.” Nucl. Eng. Des., 106(1), 1–8.
Chan, C., Hover, K. C., and Folliard, K. J. (2005). “Spatial variations in material properties of segmental retaining wall (SRW) units. Part I: Observed variations.” J. ASTM Int., 2(2), 63–79.
CEN (European Committee for Standardization). (2002). “Methods of test for masonry. Determination of initial shear strength.”, Brussels, Belgium.
de Witte, F. C., and Kikstra, W. P. (2007). “Diana finite element analysis user’s manual. Release 9.2. Material library.” TNO DIANA, Delft, Netherlands.
Ellingwood, B. R., Galambos, T. V., Macgregor, J. G., and Cornell, C. A. (1980). “Development of probability based load criterion for American National Standard A58.” U.S. Government Printing Office, Washington, DC.
Haach, V. G., Vasconcelos, G., and Lourenco, P. B. (2011). “Numerical analysis of concrete block masonry beams under three point bending.” Eng. Struct., 33(12), 3226–3237.
Heffler, L. M. (2009). “Variability of unit flexural bond strength and its effect on strength in clay brick unreinforced masonry walls subject to vertical bending.” M.S. thesis, Univ. of Newcastle, Callaghan, Australia.
Heffler, L. M., Stewart, M. G., Masia, M. J., and Corrêa, M. R. S. (2008). “Statistical analysis and spatial correlation of flexural bond strength for masonry walls.” Masonry Int.: J. Int. Masonry Soc., 21, 59–70.
Lawrence, S. J. (1983). “Behaviour of brick masonry walls under lateral loading.” Ph.D. thesis, Univ. of New South Wales, New South Wales, Australia.
Lawrence, S. J. (1985). “Random variations in brickwork properties.” Proc., 7th Int. Brick Masonry Conf., Melbourne, Australia, 537–547.
Lawrence, S. J. (1991). “Stochastic analysis of masonry structures.” Comput. Meth. Struct. Masonry, 104–113.
Lawrence, S. J. (1995). “The behaviour of masonry in horizontal flexure.” Proc., 7th Canadian Masonry Symp., Hamilton, ON, Canada, 525–536.
Lawrence, S. J., and Cao, H. T. (1988). “Cracking of non-loadbearing masonry walls under lateral forces.” Proc., 8th Int. Brick Masonry Conf., Dublin, Ireland, 1184–1194.
Lawrence, S. J., and Lu, J. P. (1991a). “An elastic analysis of laterally loaded masonry walls with openings.” Proc., Int. Symp. on Computer Methods in Structual Masonry, Swansea, U.K., 39–48.
Lawrence, S. J., and Lu, J. P. (1991b). “Cracking of brickwork walls with lateral loading.” Proc., Asia-Pacific Masonry Conf., Singapore.
Li, J., Masia, M. J., Stewart, M. G., and Lawrence, S. J. (2014a). “Spatial variability and stochastic strength prediction of unreinforced masonry walls in vertical bending.” Eng. Struct., 59, 787–797.
Li, J., Stewart, M. G., Masia, M. J., and Lawrence, S. J. (2014b). “Spatial variability and stochastic strength prediction of unreinforced masonry walls in horizontal bending.” 9th Int. Masonry Conf., Portugal.
Lourenco, P. (1996b). “A user/programmer guide for the micro-modeling of masonry structures.”, Delft Univ. of Technology, Faculty of Civil Engineering, Delft, Netherlands.
Lourenco, P. B. (1996a). “Computational strategies for masonry structures.” Ph.D. thesis, Delft Univ. of Technology, Delft, Netherlands.
Lourenco, P. B., Almeida, J. C., and Barros, J. A. (2005). “Experimental investigation of bricks under uniaxial tensile testing.” Masonry Int., 18(1), 11–20.
Masia, M. J., Han, Y., Player, C. J., Corrêa, M. R. S., and Page, A. W. (2007). “Torsion shear test for mortar joints in masonry: Preliminary experimental results.” Proc., 10th North American Masonry Conf., St Louis, MO.
Masia, M. J., Simundic, G., and Page, A. W. (2012). “Assessment of The AS3700 relationship between shear bond strength and flexural tensile bond strength in unreinforced masonry.” Proc., 15th IBMAC, Florianopolis, Brazil.
Petersen, R. B. (2009). “In-plane shear behaviour of unreinforced masonry panels strengthened with fibre reinforced polymer strips.” Ph.D. thesis, Univ. of Newcastle, Australia.
Petersen, R. B., Ismail, N., Masia, M. J., and Ingham, J. M. (2012). “Finite element modelling of unreinforced masonry shear wallettes strengthened using twisted steel bars.” Constr. Build. Mater., 33, 14–24.
Stewart, M. G. (2004). “Spatial variability of pitting corrosion and its influence on structural fragility and reliability of RC beams in flexure.” Struct. Saf., 26(4), 453–470.
Stewart, M. G., and Lawrence, S. J. (2002). “Structural reliability of masonry walls in flexure.” Masonry Int., 15(2), 48–52.
Vaculik, J., and Griffith, M. C. (2010). “Probabilistic approach for calculating the ultimate strength of unreinforced masonry in horizontal bending.” Proc., 8th Int. Masonry Conf., Dresden, 1765–1774.
Van der Pluijm, R. (1997). “Non-linear behaviour of masonry under tension.” Heron, 42(1), 25–54.
Van der Pluijm, R. (1999). “Out of plane bending of masonry: Behaviour and strength.” Ph.D. thesis, Univ. of Technology, Eindhoven, Netherlands.
Vanmarcke, E., Shinozuka, M., Nakagiri, S., Schuëller, G. I., and Grigoriu, M. (1986). “Random fields and stochastic finite elements.” Struct. Saf., 3(3–4), 143–166.
Vasconcelos, G., Lourenco, P. B., Alves, C. A. S., and Pamplona, J. (2007). “Experimental characterization of the tensile behaviour of granites.” Int. J. Rock Mech. Min. Sci., 45(2), 268–277.
Willis, C. R., Griffith, M. C., and Lawrence, S. J. (2004). “Horizontal bending of unreinforced clay brick masonry.” Masonry Int., 17(3), 109–121.
Information & Authors
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Published In
Journal of Structural Engineering
Volume 142 • Issue 11 • November 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Nov 18, 2014
Accepted: Dec 9, 2015
Published online: Jun 21, 2016
Published in print: Nov 1, 2016
Discussion open until: Nov 21, 2016
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