Probabilistic Behavior and Variance-Based Sensitivity Analysis of Reinforced Concrete Masonry Walls Considering Slenderness Effect
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 8, Issue 4
Abstract
Inherent uncertainties associated with masonry structures result in large scatter in experimentally or analytically predicted behavior. Rigorous investigation of uncertainties in the structural behavior of masonry structures is of paramount importance to lay down the basis for reliable structural design. In this study, the probabilistic behavior of reinforced masonry walls under out-of-plane (OOP) loading was investigated. Uncertainties in material and geometric properties were incorporated in finite-element (FE) models for probabilistic structural analysis. The individual and combined effect of different uncertain input parameters on the overall probabilistic behavior was evaluated. Furthermore, the relative importance of uncertain variables to the load and deformation capacities was assessed using variance-based sensitivity analysis. The model uncertainty in FE-predicted load capacity was quantified to characterize the model error. The results indicate that model uncertainty contributes to the variance in lateral load capacity more than all the other uncertainties in material and geometric properties.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request, including the validated macro FE model for reinforced concrete masonry walls, code, and data for the probabilistic analysis and sensitivity analysis.
Acknowledgments
The authors would like to acknowledge the financial support provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada through the Collaborative Research and Development (CRD) Grant (CRDPJ 528050-18).
References
Abbiati, G., S. Marelli, N. Tsokanas, B. Sudret, and B. Stojadinović. 2021. “A global sensitivity analysis framework for hybrid simulation.” Mech. Syst. Sig. Process. 146 (Jan): 106997. https://doi.org/10.1016/j.ymssp.2020.106997.
AbdelRahman, B., and K. Galal. 2022. “Sensitivity of the seismic response of reinforced concrete masonry walls with boundary elements to design parameters.” Eng. Struct. 255 (Feb): 113953. https://doi.org/10.1016/j.engstruct.2022.113953.
Abdulla, K. F., L. S. Cunningham, and M. Gillie. 2017. “Simulating masonry wall behavior using a simplified micro-model approach.” Eng. Struct. 151 (Nov): 349–365. https://doi.org/10.1016/j.engstruct.2017.08.021.
ACI-SEASC Task Committee on Slender Walls. 1982. Test report on slender walls. Los Angeles, CA: ACI Task Committee.
Barbato, M., Q. Gu, and J. P. Conte. 2010. “Probabilistic push-over analysis of structural and soil-structure systems.” J. Struct. Eng. 136 (11): 1330–1341. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000231.
Barbato, M., A. Zona, and J. P. Conte. 2014. “Probabilistic nonlinear response analysis of steel-concrete composite beams.” J. Struct. Eng. 140 (1): 4013034. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000803.
Bilotta, M., and Y. Cruz. 2021. “Evaluation of second-order effects in slender reinforced masonry walls.” In Proc., 14th Canadian Masonry Symp. Mississauga, ON, Canada: Canada Masonry Design Center.
Bui, T. T., A. Limam, V. Sarhosis, and M. Hjiaj. 2017. “Discrete element modelling of the in-plane and out-of-plane behavior of dry-joint masonry wall constructions.” Eng. Struct. 136 (Apr): 277–294. https://doi.org/10.1016/j.engstruct.2017.01.020.
Buonopane, S. G. 2008. “Strength and reliability of steel frames with random properties.” J. Struct. Eng. 134 (2): 337–344. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:2(337).
Chen, W. F., and T. Atsuta. 1973. “Strength of eccentrically loaded walls.” Int. J. Solids Struct. 9 (10): 1283–1300. https://doi.org/10.1016/0020-7683(73)90115-7.
Chisari, C., L. Macorini, C. Amadio, and B. A. Izzuddin. 2018. “Identification of mesoscale model parameters for brick-masonry.” Int. J. Solids Struct. 146 (Aug): 224–240. https://doi.org/10.1016/j.ijsolstr.2018.04.003.
CSA (Canadian Standards Association). 2014. Design of masonry structures. CSA S304. Toronto: CSA.
D’Altri, A. M., S. de Miranda, G. Castellazzi, and V. Sarhosis. 2018. “A 3D detailed micro-model for the in-plane and out-of-plane numerical analysis of masonry panels.” Comput. Struct. 206 (Aug): 18–30. https://doi.org/10.1016/j.compstruc.2018.06.007.
D’Altri, A. M., V. Sarhosis, G. Milani, J. Rots, S. Cattari, S. Lagomarsino, E. Sacco, A. Tralli, C. Castellazzi, and S. de Miranda. 2019. “A review of numerical models for masonry structures.” In Numerical modeling of masonry and historical structures, 3–53. Cambridge, UK: Woodhead Publishing.
Drysdale, R. G., and A. A. Hamid. 2005. Masonry structures behavior and design. Mississauga, ON, Canada: Canada Masonry Design Centre.
Ellingwood, B., and A. Tallin. 1985. “Limit states criteria for masonry construction.” J. Struct. Eng. 111 (1): 108–122. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:1(108).
Ganduscio, S., and F. Romano. 1997. “FEM and analytical solutions for buckling of nonlinear masonry members.” J. Struct. Eng. 123 (1): 104–111. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:1(104).
Grubišić, M., J. Ivošević, and A. Grubišić. 2019. “Reliability analysis of reinforced concrete frame by finite element method with implicit limit state functions.” Buildings 9 (5): 119. https://doi.org/10.3390/buildings9050119.
Haach, V. G., G. Vasconcelos, and P. B. Lourenço. 2011. “Parametrical study of masonry walls subjected to in-plane loading through numerical modeling.” Eng. Struct. 33 (4): 1377–1389. https://doi.org/10.1016/j.engstruct.2011.01.015.
Hariri-Ardebili, M. A., G. Mahdavi, A. Abdollahi, and A. Amini. 2021. “An RF-PCE hybrid surrogate model for sensitivity analysis of dams.” Water 13 (3): 302. https://doi.org/10.3390/w13030302.
Hatzinikolas, M., J. Longworth, and J. Warwaruk. 1978. Concrete masonry walls. Edmonton, AB, Canada: Univ. of Alberta.
Holický, M., J. V. Retief, and M. Sýkora. 2016. “Assessment of model uncertainties for structural resistance.” Probab. Eng. Mech. 45 (Jul): 188–197. https://doi.org/10.1016/j.probengmech.2015.09.008.
Iannacone, L., M. Andreini, P. Gardoni, and M. Sassu. 2021. “Probabilistic models and fragility estimates for unreinforced masonry walls subject to in-plane horizontal forces.” J. Struct. Eng. 147 (6): 1–13. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003006.
Jiang, Z., W. Chen, Y. Fu, and R. Yang. 2013. “Reliability-based design optimization with model bias and data uncertainty.” SAE Int. J. Mater. Manuf. 6 (3): 502–516. https://doi.org/10.4271/2013-01-1384.
Li, J., M. J. Masia, M. G. Stewart, and S. J. Lawrence. 2014. “Spatial variability and stochastic strength prediction of unreinforced masonry walls in vertical bending.” Eng. Struct. 59 (Feb): 787–797. https://doi.org/10.1016/j.engstruct.2013.11.031.
Li, J., M. G. Stewart, M. J. Masia, and S. J. Lawrence. 2016. “Spatial correlation of material properties and structural strength of masonry in horizontal bending.” J. Struct. Eng. 142 (11): 4016112. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001488.
Liu, Y., and J. L. Dawe. 2003. “Analytical modeling of masonry load-bearing walls.” Can. J. Civ. Eng. 30 (5): 795–806. https://doi.org/10.1139/l03-036.
Mckenna, F., M. H. Scott, and G. L. Fenves. 2010. “Nonlinear finite-element analysis software architecture using object composition.” J. Comput. Civ. Eng. 24 (1): 95–107. https://doi.org/10.1061/ASCECP.1943-5487.0000002.
Melander, J. M., and L. R. Lauersdorf. 1993. Masonry: Design and construction, problems and repair. West Conshohocken, PA: ASTM.
Minga, E., L. Macorini, B. A. Izzuddin, and I. Calió. 2019. “Macromodeling.” Chap. 8 in Numerical modeling of masonry and historical structures, edited by B. Ghiassi and G. Milani, 263–294. Cambridge, UK: Woodhead Publishing. https://doi.org/10.1016/B978-0-08-102439-3.00008-7.
Mirza, S. A. 1998. “Monte Carlo simulation of dispersions in composite steel-concrete column strength interaction.” Eng. Struct. 20 (1): 97–104. https://doi.org/10.1016/S0141-0296(97)00049-7.
Mohsin, E. 2005. “Support stiffness effect on tall load bearing masonry walls.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Alberta.
Moosavi, H. 2017. “Structural reliability of non-slender loadbearing concrete masonry members under concentric and eccentric loads.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Alberta.
Moosavi, H., and Y. Korany. 2014. “Assessment of the structural reliability of loadbearing concrete masonry designed to the Canadian standard S304.1.” Can. J. Civ. Eng. 41 (12): 1046–1053. https://doi.org/10.1139/cjce-2013-0498.
Mukherjee, D., B. N. Rao, and A. Meher Prasad. 2011. “Global sensitivity analysis of unreinforced masonry structure using high dimensional model representation.” Eng. Struct. 33 (4): 1316–1325. https://doi.org/10.1016/j.engstruct.2011.01.008.
Pettit, C. 2020. “Effect of rotational base stiffness on the behavior of loadbearing masonry walls.” M.Sc. thesis, Dept. of Civil and Environmental Engineering, Univ. of Alberta.
Priestley, M. J. N., and D. M. Elder. 1983. “Stress–strain curves for unconfined and confined concrete masonry.” ACI J. 80 (3): 192–201.
Sarhosis, V., and J. V. Lemos. 2018. “A detailed micro-modelling approach for the structural analysis of masonry assemblages.” Comput. Struct. 206 (Aug): 66–81. https://doi.org/10.1016/j.compstruc.2018.06.003.
Sobol, I. M. 2001. “Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates.” Math. Comput. Simul. 55 (1–3): 271–280. https://doi.org/10.1016/s0378-4754(00)00270-6.
Su, L., H. Wan, Y. Y. Li, and X. Ling. 2018. “Soil-pile-quay wall system with liquefaction-induced lateral spreading: Experimental investigation, numerical simulation, and global sensitivity analysis.” J. Geotech. Geoenviron. Eng. 144 (11): 04018087. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001977.
Sudret, B. 2008. “Global sensitivity analysis using polynomial chaos expansions.” Reliab. Eng. Syst. Saf. 93 (7): 964–979. https://doi.org/10.1016/j.ress.2007.04.002.
Suwalski, P. D. 1986. “Capacity of eccentrically loaded slender concrete block walls.” M.Sc. thesis, Dept. of Civil Engineering, McMaster Univ.
van der Pluijm, R. 1999. Out-of-plane bending of masonry: Behavior and strength. Eindhoven, Netherlands: Technische Universiteit Eindhoven. https://doi.org/10.6100/IR528212.
Wang, R., A. E. Elwi, and M. A. Hatzinikolas. 1997. “Numerical study of tall masonry cavity walls subjected to eccentric loads.” J. Struct. Eng. 123 (10): 1287–1294. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:10(1287).
Yokel, F. Y., R. G. Mathey, and R. D. Dikkers. 1970. Compressive strength of slender concrete masonry walls. Building science series 33. Washington, DC: US National Bureau of Standards.
Zeng, B., Y. Li, and C. C. Noguez. 2021. “Modeling and parameter importance investigation for simulating in-plane and out-of-plane behaviors of un-reinforced masonry walls.” Eng. Struct. 248 (2021): 113233. https://doi.org/10.1016/j.engstruct.2021.113233.
Zhai, X., and M. G. Stewart. 2010. “Structural reliability analysis of reinforced grouted concrete block masonry walls in compression.” Eng. Struct. 32 (1): 106–114. https://doi.org/10.1016/j.engstruct.2009.08.020.
Zhu, F., Q. Zhou, F. Wang, and X. Yang. 2017. “Spatial variability and sensitivity analysis on the compressive strength of hollow concrete block masonry wallettes.” Constr. Build. Mater. 140 (Jun): 129–138. https://doi.org/10.1016/j.conbuildmat.2017.02.099.
Information & Authors
Information
Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 8 • Issue 4 • December 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Nov 1, 2021
Accepted: Jul 12, 2022
Published online: Sep 14, 2022
Published in print: Dec 1, 2022
Discussion open until: Feb 14, 2023
ASCE Technical Topics:
- Analysis (by type)
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Errors (statistics)
- Finite element method
- Foundation design
- Foundations
- Geotechnical engineering
- Load bearing capacity
- Material mechanics
- Material properties
- Materials engineering
- Mathematics
- Methodology (by type)
- Motion (dynamics)
- Numerical methods
- Probability
- Sensitivity analysis
- Solid mechanics
- Statistics
- Structural behavior
- Structural engineering
- Uncertainty principles
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Ziead Metwally, Yong Li, Bowen Zeng, Finite element-based reliability analysis of reinforced concrete masonry walls under eccentric axial loading considering slenderness effects, Engineering Structures, 10.1016/j.engstruct.2024.117597, 304, (117597), (2024).