Estimate models of compression strength of prisms from structural masonry components

Leite, Maria de Lourdes Pereira; Liberati, Elyson Andrew Pozo; Parsekian, Guilherme Aris

doi:10.1590/S1983-41952024000600001

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 17 (6) • 2024 • https://doi.org/10.1590/S1983-41952024000600001 copy

Estimate models of compression strength of prisms from structural masonry components

Modelos de estimativas de resistência à compressão de prismas a partir de componentes da alvenaria estrutural

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This work proposes models to estimate the resistance of hollow and grouted concrete blocks prisms based on the compressive strength of their components. A database composed of 27,426 tests results on hollow and grouted prisms, mortar, grout and concrete blocks was assessed, grouped into 875 samples. Different statistical analysis models were proposed, and the best model was selected for each predetermined block resistance range. The blocks strength r ranges are Range 1 (up to 8 MPa), Range 2 (from 8 to 18 MPa) and Range 3 (above of 18 MPa). An adjustment factor of 95% confidence was calculated for each model. When comparing the results of the models with the results estimated by the design codes, it was observed that, in general, the estimates of the models of hollow and grouted prisms were similar to those of prism resistance of ABNT NBR 16868-1 (2020), except for the Range 3 resistance, in which the code is more conservative, and the proposed model with the intrinsic adjustment factor estimated values lower than those proposed by the norm. Regarding the international standards, AS-3700 (2017), TMS 602 (2021) and CSA S304 (2014) presented more conservative estimates, while Eurocode 6 (2020) adapted better to the results of the proposed models. Models considered as safe are proposed, based on the hundreds of analyzed samples, allowing estimating the hollow and grouted prism strength from their components strengths for concrete blocks structural masonry.

Keywords:
structural masonry; structural concrete block; compressive strength; prisms

Characteristic compressive strength (MPa)					f_pk/f_bk	f_pk/f_bk*
f_bk	f_a	f_gk	f_pk	f_pk*	f_pk/f_bk	f_pk/f_bk*
3	4	15	2.4	4.8	0.8	2.0
4	4	15	3.2	6.4	0.8	2.0
6	6	15	4.5	7.9	0.75	1.75
8	6	20	6	10.5	0.75	1.75
10	8	20	7.0	12.3	0.7	1.75
12	8	25	8.4	13.4	0.7	1.6
14	12	25	9.8	15.7	0.7	1.6
16	12	30	10.4	16.6	0.65	1.6
18	14	30	11.7	18.7	0.65	1.6
20	14	35	12.0	19.2	0.6	1.6
22	18	35	12.1	19.4	0.55	1.6
24	18	40	13.2	21.1	0.55	1.6

Concrete block compressive strength - net area (MPa) ¹ 1 For units with less than 102 mm nominal height, use 85% of the listed values.	Concrete masonry compression strength - net area ASTM C90 (MPa)
	Mortar type M or S	Mortar type N
12.07	-	13.79
13.79	13.79	18.27
15.51	17.93	23.44
17.24	22.41	28.96
18.96	26.89	-
20.96	31.03	-

Masonry unit	Type of joint	Mortar class	f’_uc (MPa)								k_m
Masonry unit	Type of joint	Mortar class	5	10	15	20	25	30	40	≥ 50	k_m
Concrete	Total1	M3	3.10	4.4	5.4	6.3	7.0	7.7	8.8	9.9	1.4
Concrete	Lateral2	M3	3.60	5.1	6.2	7.2	8.0	8.8	10.1	11.3	1.6

Concrete block compressive strength – net area (MPa)	Mortar type S		Mortar type N
Concrete block compressive strength – net area (MPa)	Hollow prism unit strength (MPa)	Grouted prism unit strength (MPa)	Hollow prism unit strength (MPa)	Grouted prism unit strength (MPa)
≥ 30	17.5	13.5	12.0	9.0
20	13.0	10.0	10.0	7.5
15	10.0	7.5	8.0	6.0
10	6.5	5.0	6.0	4.5

Masonry unit		General purpose mortar	Thin layer mortar	Lightweight mortar
Masonry unit		General purpose mortar	Thin layer mortar	600 ≤ ρd ≤ 800 (kg/m²)	800 ≤ ρd ≤ 1300 (kg/m²)
Aggregate concrete	Group 1	0.55	0.8	0.45	0.45
	Group 2	0.45	0.65	0.45	0.45
	Group 3	0.40	0.50	-	-
	Group 4	0.35	-	-	-

Total		875
Filters	Variation greater than 20% - Block	10
	Variation greater than 20% - Hollow prism	10
	Variation greater than 20% - Grouted prism	2
	Grout (f_g < 15 MPa)	105
	Mortar (f_a < 4 MPa; f_a < 0.7f_b; f_a > 1.5f_b)	303
Total after filtering (there are data points that have been excluded in more than one filter)		559

Compression strength Range	Total
1 (≤ 8 MPa)	65
2 (> 8 MPa and < 18 MPa)	325
3 (≥ 18 MPa)	169

Compression strength Range	Compression strength (MPa)
Compression strength Range	Concrete block	Mortar	Grout
1	5.35 – 7.97	4.02 – 9.68	15.58 – 38.73
2	8.02 – 17.89	4.88 – 25.32	15.02 – 43.93
3	18.08 – 34.36	11.51 – 35.40	22.78 – 50.78

Compression strength range	Equation	R²	AIC	BIC
1	f_pk = 0.662 f_bk + 0.081 f_a (8)	0.973	176.36	182.88
	f_pk = 3.931 + 0.141f_bk + 0.052 f_a (9)	0.737	155.55	164.25
	f_pk = 3.227f_bk^0.179 x (0.75f_a)^0.087 (10)	0.802	155.32	164.02
2	f_pk = 0.548f_bk + 0.167f_a (11)	0.979	1158.91	1170.26
	f_pk = 0.157 + 0.535f_bk + 0.167f_a (12)	0.713	1160.73	1175.86
	f_pk = 0.828f_bk^0.629 x (0.75f_a)^0.283 (13)	0.902	1162.07	1177.21
3	f_pk = 0.530f_bk + 0.161f_a (14)	0.971	665.94	675.79
	f_pk = 3.512 + 0.389f_bk + 0.152f_a (15)	0.737	656.27	675.33
	f_pk = 1.439f_bk^0.521 x (0.75f_a)^0.271 (16)	0.732	654.57	667.08

Compression strength range	Equation	R²	AIC	BIC
1	f_pk =* 2.33f_b_k - 0.811f_a + 0.140f_gk (17)	0.960	105.90	110.08
	f_pk =* 7.566 + 1.417f_bk - 0,775f_a + 0.079f_gk (18)	0.222	105.94	111.16
	f_pk =* 0.182 f_b^1.574 x (0.75f_a)^-0.367 (19)	0.382	106.09	110.27
2	f_pk =* 0.631f_bk + 0.155f_a + 0.235f_g,k (20)	0.980	1001.12	1014.56
	f_pk =* 0.842 + 0.584f_bk + 0.161f_a + 0.223f_gk (21)	0.651	1002.23	1019.04
	f_pk =* 2.261f_b^0.587 x (0.75f_a)^0.209 (22)	0.250	1043.16	1056.60
3	f_pk =* 0.537f_bk + 0.08f_a + 0.280f_gk (23)	0.989	823.532	836.027
	f_pk =* 7.676 + 0.351f_bk + 0.087f_a + 0.192f_gk (24)	0.406	808.803	824.422
	f_pk = 4.545 x f_b^0.408 x (0.75 x f_a)^0.152* (25)	0.792	824.018	836.513

f_bk (MPa)	f_a (MPa)	Range	f_pk (MPa)
f_bk (MPa)	f_a (MPa)	Range	Model¹ 1 Linear Model - Equations 8, 11, and 14; 2Model: fpk (net area)= 13.17 ln(fb,k(net area)) - 20.13.	Fitting factor	NBR 16868 [¹1 Brazilian Association of Technical Standards, ABNT NBR 16868-1 – Structural Masonry – Part 1: Project, 2020. ]	AS 3700 [¹⁰10 Standards Association of Australia, AS 3700: Masonry Structures, 2017.]	Eurocode 6 [¹¹11 Eurocode 6, EN 1996-1-1: Design of Concrete Structures - Part 1-1: General Rules for Reinforced and Unreinforced Masonry, Including Lateral Loading, 2020.]	Fortes et al. [¹³13 E. S. Fortes, G. A. Parsekian, and F. S. Fonseca, “Relationship between the compressive strength of concrete masonry and the compressive strength of concrete masonry units,” J. Mater. Civ. Eng., vol. 27, pp. 1–12, 2014, http://dx.doi.org/10.1061/(ASCE)MT.1943-5533.0001204. http://dx.doi.org/10.1061/(ASCE)MT.1943-... ]2
3.00	4.00	1	2.31	1.69	2.40	1.88	2.10	-
4.00	4.00	1	2.97	2.17	3.20	2.17	2.57	-
6.00	6.00	1	4.46	3.26	4.50	2.66	3.86	-
8.00	6.00	2	5.39	3.99	6.00	3.07	4.72	-
10.00	8.00	2	6.82	5.05	7.00	3.43	6.01	-
12.00	8.00	2	7.92	5.86	8.40	3.76	6.83	10.86
14.00	12.00	2	9.69	7.17	9.80	4.06	8.59	11.88
16.00	12.00	2	10.78	7.98	10.40	4.34	9.44	12.76
18.00	14.00	3	11.80	9.92	11.70	4.60	10.73	13.53
20.00	14.00	3	12.87	10.81	12.00	4.85	11.55	14.23
22.00	18.00	3	14.57	12.24	12.10	5.09	13.32	14.85
24.00	18.00	3	15.63	13.13	13.20	5.31	14.15	15.43

TMS 602 [⁹9 The Masonry Society, TMS 402/602: Building Code Requirements for Masonry Structures. Longmont, CO, U.S., The Masonry Society, 2021. ]		CSA S304 [¹²12 Canadian Standards Association, CSA S304: Design of Masonry Structures. Mississauga, ON, Canada, Canadian Standards Association, 2014.]
f_b (MPa)¹ 1 Mortar type M e S; 2Mortar type S.	f_p (MPa)	f_b (MPa)2	f_p (MPa)	f_p* (MPa)
6.89	6.89	5.00	3.25	4.40
8.95	7.75	7.50	5.00	6.59
11.20	8.62	7.50	5.00	8.79
13.44	9.48	15.00	8.75	11.87
15.51	10.48	-	-	-

f_bk (MPa)	f_a (MPa)	f_gk (MPa)	Range	f_p_k* (MPa)
f_bk (MPa)	f_a (MPa)	f_gk (MPa)	Range	Model¹ 1 Linear Model - Equations 17, 20, and 23; 2Model: fp*k = 8.942 ln(fb,k(net area)) – 10.27.	Fitting factor	NBR 16868 [¹1 Brazilian Association of Technical Standards, ABNT NBR 16868-1 – Structural Masonry – Part 1: Project, 2020. ]	AS 3700 [¹⁰10 Standards Association of Australia, AS 3700: Masonry Structures, 2017.]	Eurocode 6 [¹¹11 Eurocode 6, EN 1996-1-1: Design of Concrete Structures - Part 1-1: General Rules for Reinforced and Unreinforced Masonry, Including Lateral Loading, 2020.]	Fortes et al. [¹³13 E. S. Fortes, G. A. Parsekian, and F. S. Fonseca, “Relationship between the compressive strength of concrete masonry and the compressive strength of concrete masonry units,” J. Mater. Civ. Eng., vol. 27, pp. 1–12, 2014, http://dx.doi.org/10.1061/(ASCE)MT.1943-5533.0001204. http://dx.doi.org/10.1061/(ASCE)MT.1943-... ]2
3.00	4.00	15.00	1	4.77	2.75	4.80	3.12	4.17	-
4.00	4.00	15.00	1	7.10	4.09	6.40	3.62	5.11	-
6.00	6.00	15.00	1	9.61	5.53	7.90	4.62	7.66	-
8.00	6.00	20.00	2	10.98	8.60	10.50	6.07	9.37	-
10.00	8.00	20.00	2	12.66	9.91	12.30	7.07	11.94	-
12.00	8.00	25.00	2	15.10	11.82	13.40	8.58	13.56	18.15
14.00	12.00	25.00	2	17.18	13.46	15.70	9.58	15.76	19.53
16.00	12.00	30.00	2	19.62	15.37	16.60	11.16	17.91	20.72
18.00	14.00	30.00	3	19.55	16.68	18.70	12.16	18.75	21.77
20.00	14.00	35.00	3	22.02	18.79	19.20	13.82	20.89	22.72
22.00	18.00	35.00	3	23.52	20.07	19.40	14.82	22.53	23.57
24.00	18.00	40.00	3	25.99	22.18	21.10	16.59	24.73	24.35

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[1] Corresponding author: Elyson Andrew Pozo Liberati. E-mail: eapliberati@uem.br

Ratio between masonry unit height and mortar joint thickness	0.0	3.3	7.6	9.0	11.9	16.2	19.0
k_h	0.00	0.78	1.00	1.05	1.14	1.24	1.30