Unreinforced concrete masonry under compression: Brazilian statistics, reliability analysis and code calibration

Santiago, Wagner Carvalho; Souza, Tiago de Macedo; Akisue, Rafael Akira

doi:10.1590/S1983-41952024000500013

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Revista IBRACON de Estruturas e Materiais

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 17 (5) • 2024 • https://doi.org/10.1590/S1983-41952024000500013 copy

Unreinforced concrete masonry under compression: Brazilian statistics, reliability analysis and code calibration

Alvenarias de concreto não-armadas sob compressão: estatísticas brasileiras, análises de confiabilidade e calibração de norma

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Although the new Brazilian code is considered an advancement, it still lacks a reliability-based calibration of partial safety factors. Therefore, this paper presents a comprehensive set of reliability analyses oriented to structural masonry members under compression in Brazil. This study was based on structural reliability theory, which allowed a safety assessment through the reliability index (β). Walls with hollow concrete blocks of three classes (A, B and C) and two modular sizes (M-15 and M-20), two ratios between the prism strength and the block compressive strength ( $η$ = 0.5 and 0.6), and three ratios between effective height and effective width (λ = 14, 19 and 24) were evaluated. Considering that each one of the 36 elements is described by five ratios between live and dead loads and the five ratios between wind and dead loads, 900 configurations were analyzed. Reliability procedures, the structural configurations and the calibration methodology were implemented and solved in the StRAnD – Structural Reliability Analysis and Design software. Results showed that the reliability indexes are greater for unreinforced masonry walls under compression with modular size M-20 than modular size M-15. It can be noted that the block compressive strength not only represents the greatest impact on the masonry’s safety level, but is also the most relevant random variable. Based on the reliability-based calibration of the Brazilian code, it is recommended that unreinforced masonry presents different partial safety factors ( $ɣ_{m}$ ) than reinforced masonry. This work represents a stepping stone in evaluating the safety of Brazilian masonry structures, indicating a possible path in terms of achieving a more uniform reliability in masonry design.

Keywords:
reliability; safety; structures; masonry; concrete blocks

Random Variable			Distribution	Mean	COV	References
f_b	A	M-15	Normal	1.358.f_bk	0.239	Santiago and Beck [¹⁷17 W. C. Santiago and A. T. Beck, "Study of Brazilian structural concrete block conformity," Rev. IBRACON Estrut. Mater., vol. 11, no. 4, pp. 652–672, 2018, http://doi.org/10.1590/s1983-41952018000400002. http://doi.org/10.1590/s1983-41952018000... ] and Almeida et al. [¹⁸18 V. B. Almeida et al., “Estudo da conformidade dos blocos estruturais de concreto da Classe C produzidos no Brasil,” in Proc. 62º Braz. Concr. Congr., Florianópolis, 2021.]
	A	M-20	Normal	1.364.f_bk	0.197
	B	M-15	Normal	1.592.f_bk	0.279
	B	M-20	Normal	1.328.f_bk	0.248
	C	M-15	Normal	1.566.f_bk	0.294
	C	M-20	Normal	1.419.f_bk	0.221
t	A	M-15	Normal	1.003.t_n	0.005	Santiago and Beck [¹⁷17 W. C. Santiago and A. T. Beck, "Study of Brazilian structural concrete block conformity," Rev. IBRACON Estrut. Mater., vol. 11, no. 4, pp. 652–672, 2018, http://doi.org/10.1590/s1983-41952018000400002. http://doi.org/10.1590/s1983-41952018000... ] and Almeida et al. [¹⁸18 V. B. Almeida et al., “Estudo da conformidade dos blocos estruturais de concreto da Classe C produzidos no Brasil,” in Proc. 62º Braz. Concr. Congr., Florianópolis, 2021.]
	A	M-20	Normal	1.002.t_n	0.003
	B	M-15	Normal	1.003.t_n	0.025
	B	M-20	Normal	1.002.t_n	0.010
	C	M-15	Normal	1.005.t_n	0.021
	C	M-20	Normal	1.001.t_n	0.003
θ_R			Normal	1.940	0.137	This work

Random Variable	Distribution	Mean	COV	References
f_b	Normal	1.41.f_bk	0.17	Kezemi et al. [¹¹11 M. Kazemi et al., “Reliability analysis of masonry members under compression,” in Proc. Struct. Congr., Las Vegas, 2011.]
f_b	Normal	1.46.f_bk	0.205	Moosavi and Korany [¹²12 H. Moosavi and Y. Korany, "Assessment of the structural reliability of loadbearing concrete masonry designed to the Canadian Standard S304.1," Can. J. Civ. Eng., vol. 41, no. 12, pp. 1046–1053, 2014, http://doi.org/10.1139/cjce-2013-0498. http://doi.org/10.1139/cjce-2013-0498... ]
t	Normal	t_n	0.02	Stewart and Lawrence [²⁵25 M. G. Stewart and S. J. Lawrence, Reliability-based Code Calibration of Structural Masonry in Compression Designed to Australian Standards. Australia: University of Newcastle, 2008.]
t	Normal	t_n	0.01	Moosavi and Korany [¹²12 H. Moosavi and Y. Korany, "Assessment of the structural reliability of loadbearing concrete masonry designed to the Canadian Standard S304.1," Can. J. Civ. Eng., vol. 41, no. 12, pp. 1046–1053, 2014, http://doi.org/10.1139/cjce-2013-0498. http://doi.org/10.1139/cjce-2013-0498... ]
θ_R	Lognormal	2.18	0.20	Stewart and Lawrence [⁹9 M. G. Stewart and S. J. Lawrence, "Model error, structural reliability and partial safety factors for structural masonry in compression," Mason. Int., vol. 20, no. 3, pp. 107–116, 2007.]

Random Variable	Distribution	Mean	COV	References
D	Normal	1.06.D_n	0.12	Santiago [²⁷27 W. C. Santiago, “Calibração baseada em confiabilidade dos coeficientes parciais de segurança das principais normas brasileiras de projeto estrutural,” Ph.D. dissertation, Esc. Eng. São Carlos, Univ. São Paulo. São Carlos, 2019.]
L_apt	Gamma	0.21.L_n	0.76	Costa et al. [²⁸28 L. G. L. Costa, W. C. Santiago, and A. T. Beck, "Probabilistic models for live loads in buildings: critical review, comparison to Brazilian design standards and calibration of partial safety factors," Rev. IBRACON Estrut. Mater., vol. 16, no. 2, pp. 2–22, 2023, http://doi.org/10.1590/s1983-41952023000200004. http://doi.org/10.1590/s1983-41952023000... ]
L₅₀	Gumbel	0.92.L_n	0.25	Costa et al. [²⁸28 L. G. L. Costa, W. C. Santiago, and A. T. Beck, "Probabilistic models for live loads in buildings: critical review, comparison to Brazilian design standards and calibration of partial safety factors," Rev. IBRACON Estrut. Mater., vol. 16, no. 2, pp. 2–22, 2023, http://doi.org/10.1590/s1983-41952023000200004. http://doi.org/10.1590/s1983-41952023000... ]
W₁	Gumbel	0.33.W_n	0.47	Beck and Souza [²⁹29 A. T. Beck and A. C. Souza Jr., "A first attempt towards reliability-based calibration of Brazilian structural design codes," J. Braz. Soc. Mech. Sci. Eng., vol. 32, no. 2, pp. 119–127, 2010, http://doi.org/10.1590/S1678-58782010000200004. http://doi.org/10.1590/S1678-58782010000... ]
W₅₀	Gumbel	0.90.W_n	0.34	Beck and Souza [²⁹29 A. T. Beck and A. C. Souza Jr., "A first attempt towards reliability-based calibration of Brazilian structural design codes," J. Braz. Soc. Mech. Sci. Eng., vol. 32, no. 2, pp. 119–127, 2010, http://doi.org/10.1590/S1678-58782010000200004. http://doi.org/10.1590/S1678-58782010000... ]
θ_L	Lognormal	1.00	0.05	JCSS [³⁰30 Joint Committee on Structural Safety. “Probabilistic Model Code.” 2001. [Online]. Available: https://www.jcss-lc.org/jcss-probabilistic-model-code/ https://www.jcss-lc.org/jcss-probabilist... ]

L_n/D_n or W_n/D_n	Weight (%)
0.0	36
0.5	36
1.0	20
1.5	6
2.0	2
3.0	0
5.0	0

Parameter	Value
Population number (Np)	60.0
Inertia weight (Wi)	0.9
Cognitive learning factor (C1)	2.0
Social learning factor (C2)	2.0
Maximum velocity (Vmax)	1.0

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E-mail: arlene@ibracon.org.br

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[1] Corresponding author: Wagner Carvalho Santiago. E-mail: wagner.santiago@univasf.edu.br