Assessment of Masonry Compressive Strength in Existing Structures Using a Bayesian Method
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 1
Abstract
In comparison to contemporary masonry structures, the material properties of existing masonry often show very high variability. Furthermore, the limited number of material tests in the assessment of existing structures introduces statistical uncertainties, which have to be adequately considered. The safety formats for the design of new masonry structures may therefore be inappropriate. To fill this gap, a method for determining characteristic values and partial safety factors for the compressive strength of existing masonry is developed. First, testing data regarding unit and mortar strength from the solid clay brick masonry of 72 existing buildings is evaluated in order to model prior distributions for the typical variance of unit and mortar strength. Second, the model for estimating masonry compressive strength based on unit and mortar strength according to Eurocode 6 is analyzed, and the corresponding model uncertainty is quantified. Finally, the proposed method is presented. The influence of prior information is demonstrated, and diagrams are provided, which enable a practice-oriented way of determining characteristic values and partial safety factors for a specific building.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The authors thank Jonny Henkel of AK Bauwerksdiagnostik in 16356 Ahrensfelde, Germany, for providing data regarding material tests on existing masonry as well as for interesting discussions on the topic. Financial support from the Zukunft Bau program of the German Federal Institute for Research on Building, Urban Affairs and Spatial Development is gratefully acknowledged.
References
Boffill, Y., H. Blanco, I. Lombillo, and L. Villegas. 2019. “Assessment of historic brickwork under compression and comparison with available equations.” Constr. Build. Mater. 207 (May): 258–272. https://doi.org/10.1016/j.conbuildmat.2019.02.083.
Brehm, E. 2011. “Reliability of unreinforced masonry bracing walls—Probabilistic approach and optimized target values.” Doctoral dissertation, Dept. of Civil and Environmental Engineering, Technische Universität Darmstadt.
Caspeele, R., and L. Taerwe. 2012. “Bayesian assessment of the characteristic concrete compressive strength using combined vague–informative priors.” Constr. Build. Mater. 28 (1): 342–350. https://doi.org/10.1016/j.conbuildmat.2011.08.065.
CEN (European Committee for Standardization). 1998. Methods of test for masonry—Part 1: Determination of compressive strength. EN 1052-1. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2002. Eurocode—Basis of structural design. EN 1990. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2011. Methods of test for masonry units—Part 1: Determination of compressive strength. EN 772-1. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2012. Design of masonry structures—Part 1-1: General rules for reinforced and unreinforced masonry structures. EN 1996-1-1. Eurocode 6. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2019. Methods of test for mortar for masonry—Part 11: Determination of flexural and compressive strength of hardened mortar. EN 1015-11. Brussels, Belgium: CEN.
DIN (Deutsches Institut für Normung). 2019. Nationaler Anhang—National festgelegte Parameter—Eurocode 6: Bemessung und Konstruktion von Mauerwerksbauten—Teil 1-1: Allgemeine Regeln für bewehrtes und unbewehrtes Mauerwerk. DIN EN 1996-1-1/NA. Berlin: DIN.
Egermann, R. 1992. “Zur nachträglichen Bestimmung der mechanischen Eigenschaften von Mauerziegeln.” In Erhalten historisch bedeutsamer Bauwerke: Baugefüge, Konstruktionen, Werkstoffe: Jahrbuch Sonderforschungsbereich 315, 159–182. Berlin: Ernst & Sohn.
Ferretti, D. 2020. “Dimensional analysis and calibration of a power model for compressive strength of solid-clay-brick masonry.” Eng. Struct. 205 (Feb): 110064. https://doi.org/10.1016/j.engstruct.2019.110064.
fib (Fédération internationale du betón). 2016. Partial factor methods for existing concrete structures: Recommendation: Bulletin 80. Lausanne, Switzerland: fib.
Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2013. Bayesian data analysis. 3rd ed. Hoboken, NJ: CRC Press.
Henkel, J. 2016. “Evaluation of the quality of historic brickwork.” Mauerwerk Eur. J. Masonry 20 (5): 391–406. https://doi.org/10.1002/dama.201620711.
Hilsdorf, H. K. 1969. “Investigation into the failure mechanism of brick masonry loaded in axial compression.” In Designing, engineering and constructing with masonry products, edited by F. B. Johnson, 34–41. Houston: Gulf Publishing Company.
JCSS (Joint Committee on Structural Safety). 2002. “Probabilistic model code—Part 3: Material properties.” Accessed July 1, 2020. https://www.jcss-lc.org/jcss-probabilistic-model-code/.
Kirtschig, K., and J. Meyer. 1987. Auswertung von Mauerwerksversuchen zur Festlegung von zulässigen Spannungen und charakteristischen Mauerwerksfestigkeiten—Heft 54. Hannover, Germany: Institut für Baustoffkunde und Materialprüfung der Universität Hannover.
Lumantarna, R., D. T. Biggs, and J. M. Ingham. 2014. “Uniaxial compressive strength and stiffness of field-extracted and laboratory-constructed masonry prisms.” J. Mater. Civ. Eng. 26 (4): 567–575. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000731.
Mann, W. 1983. “Druckfestigkeit von Mauerwerk: Eine statistische Auswertung von Versuchsergebnissen in geschlossener Darstellung mit Hilfe von Potenzfunktionen.” In Mauerwerk-Kalender, edited by P. Funk, 687–699. Berlin: Ernst & Sohn.
Melchers, R. E., and A. T. Beck. 2018. Structural reliability analysis and prediction. Hoboken, NJ: Wiley.
Müller, D., V. Förster, and C.-A. Graubner. 2017. “Influence of material spatial variability on required safety factors for masonry walls in compression.” Mauerwerk Eur. J. Masonry 21 (4): 209–222. https://doi.org/10.1002/dama.201700004.
Müller, D., and C.-A. Graubner. 2018. “Uncertainties in the assessment of existing masonry structures.” In Proc., IALCCE 2018, edited by R. Caspeele, L. Taerwe, and D. Frangopol, 369–376, London: CRC Press.
Rackwitz, R. 1983. “Predictive distribution of strength under control.” Matér. Constr. 16 (94): 259–267. https://doi.org/10.1007/BF02473691.
Raiffa, H., and R. Schlaifer. 1961. Applied statistical decision theory. New York: Wiley.
Schubert, P. 2010. “Eigenschaftswerte von Mauerwerk, Mauersteinen, Mauermörtel und Putzen.” In Mauerwerk-Kalender 2010, edited by W. Jäger. Berlin: Ernst & Sohn.
Schueremans, L. 2001. “Probabilistic evaluation of structural unreinforced masonry.” Doctoral dissertation, Faculty of Applied Science, KU Leuven.
Sýkora, M., D. Diamantidis, M. Holický, J. Marková, and Á. Rózsás. 2018. “Assessment of compressive strength of historic masonry using non-destructive and destructive techniques.” Constr. Build. Mater. 193 (Dec): 196–210. https://doi.org/10.1016/j.conbuildmat.2018.10.180.
Tschötschel, M. 1990. “Zuverlässigkeitstheoretisches Konzept zur Bemessung von Mauerwerkskonstruktionen.” Doctoral dissertation, Technische Hochschule Leipzig.
Val, D. V., and M. G. Stewart. 2002. “Safety factors for assessment of existing structures.” J. Struct. Eng. 128 (2): 258–265. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:2(258).
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© 2020 American Society of Civil Engineers.
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Received: Jul 3, 2020
Accepted: Oct 6, 2020
Published online: Dec 16, 2020
Published in print: Mar 1, 2021
Discussion open until: May 16, 2021
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