Evaluation of concrete resistances: an alternative to the criteria of Brazilian standard NBR 12655 based on a Bayesian approach

Interlandi, Claudia; Stucchi, Fernando Rebouças; Martha, Luiz Fernando Campos Ramos; Santos, Sergio Hampshire de Carvalho

doi:10.1590/S1983-41952020000400011

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 13 (4) • 2020 • https://doi.org/10.1590/S1983-41952020000400011 copy

Evaluation of concrete resistances: an alternative to the criteria of Brazilian standard NBR 12655 based on a Bayesian approach

Avaliação das resistências do concreto: uma alternativa aos critérios da norma brasileira NBR 12655 baseada em uma abordagem Bayesiana

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Frequently the required concrete resistance is not attained in Brazilian constructions. Partially to circumvent this problem, a new revision of Brazilian Standard ABNT NBR 12655 was issued in 2015. This revision maintains the insufficiently stringent criteria for evaluation of the concrete compression strength in existent and under construction structures of the revision of 1996. This evaluation can be based on very few test specimens, even in the result of a single test. It is shown herein that these criteria are clearly unsafe. Alternative criteria are proposed, based in a Bayesian approach. The proposed criteria are checked against some hundred tests done on actual structures of different characteristics, bridges and buildings.

Keywords:
concrete resistance; Brazilian standard; Bayesian approach

Identification (the more demanding in each case)	Main solicitations in the structural elements
Identification (the more demanding in each case)	Compression or compression and flexure	Pure flexure b
Concrete volume	50 m³	100 m³
Number of floors	1	1
Time of pouring	Three days of pouring c

Preparation condition	Number of specimens (n)
Preparation condition	2	3	4	5	6	7	8	10	12	14	$\geq$ 16
A	0.82	0.86	0.89	0.91	0.92	0.94	0.95	0.97	0.99	1.00	1.02
B or C	0.75	0.80	0.84	0.87	0.89	0.91	0.93	0.96	0.98	1.00	1.02

RMCP	SÉRIE	Data Conc.	Tipo	Local Aplicação	Itens Concretados	Vol (m³)	*f_ck*	Data Rompimento	Idade (dias)
RMCP	SÉRIE	Data Conc.	Tipo	Local Aplicação	Itens Concretados	Vol (m³)	*f_ck*	Data Rompimento	Idade (dias)	CP1		CP2		CP3
*Kgf*	*f_ck*	*Kgf*	*f_ck*	*Kgf*	*f_ck*
008	035	08/06/16	Convencional	Rio Guaraí	Apoio 02	8,0	35,0	06/07/16	28	0,00	36,00	0,00	36,40	0,00	0,00
008	036	08/06/16	Convencional	Rio Guaraí	Apoio 03	8,0	35,0	06/07/16	28	0,00	32,40	0,00	32,70	0,00	0,00
008	038	08/06/16	Convencional	Rio Guaraí	Apoio 04	8,0	35,0	06/07/16	28	0,00	34,30	0,00	34,90	0,00	0,00
008	040	08/06/16	Convencional	Rio Guaraí	Apoio 05	8,0	35,0	06/07/16	28	0,00	35,40	0,00	36,20	0,00	0,00
008	041	08/06/16	Convencional	Rio Guaraí	Apoio 06	8,0	35,0	06/07/16	28	0,00	36,20	0,00	36,50	0,00	0,00
008	042	08/06/16	Convencional	Rio Guaraí	Apoio 07	3,0	35,0	06/07/16	28	0,00	34,50	0,00	34,70	0,00	0,00
010	045	20/06/16	Convencional	Rio Guaraí	Apoio 05	8,0	35,0	18/07/16	28	0,00	44,10	0,00	44,90	0,00	45,20
010	046	20/06/16	Convencional	Rio Guaraí	Apoio 05	8,0	35,0	18/07/16	28	0,00	41,30	0,00	41,60	0,00	42,60
010	047	20/06/16	Convencional	Rio Guaraí	Apoio 05	8,0	35,0	18/07/16	28	0,00	41,20	0,00	42,70	0,00	44,00
010	048	20/06/16	Convencional	Rio Guaraí	Apoio 05	8,0	35,0	18/07/16	28	0,00	41,60	0,00	41,80	0,00	42,40
010	049	20/06/16	Convencional	Rio Guaraí	Apoio 05	8,0	35,0	18/07/16	28	0,00	47,10	0,00	47,40	0,00	47,70
010	050	20/06/16	Convencional	Rio Guaraí	Apoio 05	8,0	35,0	18/07/16	28	0,00	41,20	0,00	41,90	0,00	43,30
013	061	24/06/16	Convencional	Rio Guaraí	Apoio 03	8,0	35,0	22/07/16	28	36,04	45,08	36,95	46,22	35,96	44,98
013	062	24/06/16	Convencional	Rio Guaraí	Apoio 03	8,0	35,0	22/07/16	28	33,41	41,79	32,96	41,23	35,03	43,82
013	063	24/06/16	Convencional	Rio Guaraí	Apoio 03	8,0	35,0	22/07/16	28	35,93	44,94	34,82	43,56	36,13	45,19
013	064	24/06/16	Convencional	Rio Guaraí	Apoio 03	8,0	35,0	22/07/16	28	33,90	42,41	34,20	42,78	32,97	41,24
013	065	24/06/16	Convencional	Rio Guaraí	Apoio 03	8,0	35,0	22/07/16	28	34,96	43,73	37,59	47,02	37,14	46,46
013	066	24/06/16	Convencional	Rio Guaraí	Apoio 03 C	8,0	35,0	22/07/16	28	33,26	41,60	35,33	44,19	38,08	47,63
016	074	30/06/16	Convencional	Rio Guaraí	Apoio 04	8,0	35,0	28/07/16	28	38,18	47,76	39,25	49,10	38,86	48,61
016	075	30/06/16	Convencional	Rio Guaraí	Apoio 04	8,0	35,0	28/07/16	28	34,13	42,69	37,45	46,85	33,66	42,11
016	076	30/06/16	Convencional	Rio Guaraí	Apoio 04	8,0	35,0	28/07/16	28	33,95	42,47	33,55	41,97	35,20	44,03
016	077	30/06/16	Convencional	Rio Guaraí	Apoio 04	8,0	35,0	28/07/16	28	37,07	46,37	35,71	44,67	34,59	43,27
016	078	30/06/16	Convencional	Rio Guaraí	Apoio 04	8,0	35,0	28/07/16	28	35,22	44,06	34,11	42,67	34,58	43,26
016	079	30/06/16	Convencional	Rio Guaraí	Apoio 04	3,0	35,0	28/07/16	28	35,43	44,32	35,17	43,99	36,36	45,48

Concrete lot	Column	Results of tests (MPa)						f_ck
Concrete lot	Column	Results of tests (MPa)						Equations 2 and 3	Equation 4
8	2	36.4	32.7	34.9	36.2	36.5	34.7	32.50	32.82
10	5	44.9	42.6	44.0	42.4	47.7	43.3	41.70	40.91
13	3	46.2	43.8	45.2	42.8	47.0	47.6	41.41	42.35
16	4	49.1	46.9	44.0	46.4	44.1	45.5	42.61	42.81

Test	NBR 12655	Bayesian approach	f_ck =0.93 f_cm	Deviation
35	36.4	33.2	33.7	1.5%
36	32.7	30.8	30.3	1.6%
38	34.9	32.2	32.2	-
40	36.2	32.9	33.3	1.2%
41	36.5	33.3	33.8	1.5%
42	34.7	32.3	32.2	-

Concrete lot	$f_{c k}$ (MPa) Equation 2	$f_{c k}$ (MPa) Equation 3	$f_{c k}$ (MPa) Estimated	$f_{c k}$ Design	ACCEPTED?	$f_{c k}$ Normal	$f_{c k}$ T-Student
1	29.7	28.8	29.7	30	NO	29.60	30
2	28.4	27.2	28.4	30	NO	27.58	30
3	38.6	38.6	38.6	40	NO	39.40	40
4	39.9	38.9	39.9	40	NO	40.56	40
5	44.3	41.0	44.3	35	YES	44.19	35
6	41.1	40.2	41.1	40	YES	40.52	40
7	29.6	30.5	30.5	35	NO	32.45	35
8	40.6	41.3	41.3	40	YES	41.54	40
9	32.3	34.4	34.4	35	NO	35.32	35
10	34.1	32.8	34.1	30	YES	33.80	30
11	28.9	25.8	28.9	30	NO	29.14	30
12	28.1	28.6	28.6	30	NO	29.52	30
13	34.6	34.1	34.6	30	YES	34.47	30
14	39.6	38.6	39.6	45	NO	42.01	45
15	43.9	41.5	43.9	45	NO	42.56	45
16	36.3	37.6	37.6	40	NO	39.13	40
17	41.7	40.2	41.7	40	YES	42.22	40
18	41.2	39.2	41.2	45	NO	39.94	45
19	48.0	47.2	48.0	45	YES	48.18	45
20	42.6	44.7	44.7	45	NO	44.29	45
21	42.9	40.9	42.9	45	NO	43.54	45
22	48.8	46.9	48.8	45	YES	49.49	45
23	32.4	29.9	32.4	35	NO	31.32	35
24	44.3	44.9	44.9	45	NO	44.78	45
25	40.2	38.2	40.2	40	YES	39.25	40

Lot	n_e	f_ck (MPa)	n
Lot	n_e	f_ck (MPa)	1	2	3	4	5	6	7	8	9	10	11	12	13
1	9	30	30.8	30.9	30.4	30.0	30.3	30.8	32.8	31.1	31.3
2	12	30	37.5	37.0	31.4	34.5	31.3	31.5	31.2	34.2	35.0	32.5	28.4	27.5
3	10	40	42.2	45.1	39.8	49.4	44.0	44.1	42.8	44.0	47.8	47.7
4	8	40	43.9	41.2	40.9	43.0	43.4	43.4	45.2	42.2
5	6	35	44.7	45.0	45.6	45.9	46.4	44.6
6	11	40	41.7	44.8	43.4	44.8	46.6	44.1	43.5	41.0	42.3	41.7	42.3
7	6	35	38.5	37.6	27.6	34.0	33.2	40.0
8	12	40	47.4	49.6	44.1	50.8	47.1	52.3	50.8	46.5	43.5	48.6	41.7	43.4
9	8	35	41.2	42.9	43.0	36.4	37.5	36.2	41.1	41.8
10	8	30	36.5	36.8	39.3	34.5	35.4	40.8	41.1	38.1
11	12	30	36.0	34.0	38.9	35.4	34.8	39.2	36.7	36.1	37.3	26.1	31.3	40.3
12	9	30	35.5	38.1	34.8	34.7	33.5	29.8	29.8	50.4	44.7	51.0	47.7
13	11	30	35.4	39.2	42.3	37.5	37.7	34.8	40.1	40.1	38.0	37.3	36.6
14	9	45	51.8	50.2	52.8	54.7	51.2	40.2	44.5	49.5	49.0
15	7	45	47.1	44.5	44.2	49.5	48.4	44.8	51.4
16	9	40	48.8	52.8	58.0	39.2	49.0	47.5	50.0	53.9	41.0
17	11	40	52.8	47.9	45.8	54.6	41.0	48.8	48.6	50.4	44.7	51.0	47.7
18	7	45	52.8	41.7	46.2	47.9	46.6	43.2	43.7
19	13	45	50.4	53.4	52.5	52.6	50.4	52.0	47.4	52.3	48.9	51.4	50.0	54.2	50.8
20	10	45	56.8	57.0	46.2	54.8	47.8	51.1	52.0	53.1	46.1	47.3
21	7	45	45.5	46.2	43.5	45.1	45.4	44.9	44.3
22	12	45	57.1	60.8	52.8	59.5	55.9	47.4	54.7	55.8	54.8	57.0	59.5	51.9
23	6	35	34.1	32.5	39.0	38.9	34.2	39.2
24	11	45	46.6	51.1	48.8	46.9	49.5	45.8	48.9	46.9	55.0	51.1	51.1
25	7	40	42.2	40.6	43.7	41.8	48.3	47.2	47.9

Lot	n_i	f_ck (Design)	f_ck (Total)	$n_{0} = 3$	$n_{0} = 10$	$n_{0} = 20$	$n_{0} = 50$	0.93*f_cm	% $(n_{0} = 10)$
1	1	30.0	30.8	20.2	28.1	29.1	29.6	28.4	1.11
	2	30.0	30.9	20.3	28.2	29.1	29.6	28.5	0.91
	3	30.0	30.4	19.8	27.9	29.0	29.6	28.1	0.67
	4	30.0	30.0	19.4	27.7	28.9	29.6	27.8	0.39
	5	30.0	30.3	19.7	27.9	29.0	29.6	28.0	0.50
	6	30.0	30.8	20.3	28.2	29.1	29.6	28.5	0.91
	7	30.0	32.8	22.5	29.1	29.6	29.8	30.0	3.23
	8	30.0	31.1	20.7	28.3	29.2	29.7	28.7	1.54
	9	30.0	31.3	21.0	28.5	29.3	29.7	29.0	1.65

Lot	n_i	f_ck (Design)	f_ck (Total)	$n_{0} = 3$	$n_{0} = 10$	$n_{0} = 20$	$n_{0} = 50$	0.93*f_cm	% $(n_{0} = 10)$
24	1	45.0	46.6	31.2	42.6	43.8	44.5	43.2	1.4
	2	45.0	51.1	37.3	44.9	45.0	45.0	47.4	5.53
	3	45.0	48.8	33.8	43.7	44.4	44.8	45.1	3.11
	4	45.0	46.9	31.3	42.6	43.9	44.6	43.3	1.62
	5	45.0	49.5	35.2	44.2	44.7	44.9	46.0	4.05
	6	45.0	45.8	30.1	42.1	43.6	44.4	42.4	0.73
	7	45.0	48.9	33.8	43.7	44.4	44.8	45.0	3.00
	8	45.0	46.9	31.0	42.5	43.8	44.5	43.1	1.42
	9	45.0	55.0	42.9	46.1	45.6	45.2	51.1	10.75
	10	45.0	51.1	37.2	44.8	45.0	45.0	47.3	5.56
	11	45.0	51.1	37.2	44.8	45.0	45.0	47.3	5.56

Lot	n_i	f_ck(Design)	f_ck (Total)	$n_{0} = 3$	$n_{0} = 10$	$n_{0} = 20$	$n_{0} = 50$	0.93*f_cm	% $(n_{0} = 10)$
4	1	40.0	43.9	30.7	39.1	39.6	39.9	40.50	3.58
	2	40.0	41.2	27.3	37.7	38.9	39.5	38.08	1.02
	3	40.0	40.9	26.6	37.3	38.7	39.5	37.57	0.73
	4	40.0	43.0	29.4	38.6	39.4	39.8	39.62	2.64
	5	40.0	43.4	29.7	38.7	39.4	39.8	39.80	2.85
	6	40.0	43.4	29.8	38.7	39.4	39.8	39.9	3.09
	7	40.0	45.2	32.6	39.7	39.9	40.0	41.76	5.18
	8	40.0	42.2	28.4	38.1	39.1	39.7	38.87	2.03

Lot	n_i	f_ck(Design)	f_ck (Total)	$n_{0} = 3$	$n_{0} = 10$	$n_{0} = 20$	$n_{0} = 50$	0.93*f_cm	% $(n_{0} = 10)$
9	1	35.0	41.2	30.4	35.3	35.2	35.1	37.8	6.96
	2	35.0	42.9	33.3	35.9	35.4	35.2	39.7	10.62
	3	35.0	43.0	33.4	35.9	35.4	35.2	39.8	10.75
	4	35.0	36.4	24.4	33.2	34.1	34.7	33.7	1.54
	5	35.0	37.5	25.8	33.8	34.4	34.8	34.7	2.63
	6	35.0	36.2	23.8	32.9	34.0	34.6	33.3	1.06
	7	35.0	41.1	30.7	35.4	35.2	35.1	38.0	7.32
	8	35.0	41.8	31.6	35.6	35.3	35.1	38.6	8.28

Lot	n_i	f_ck (Design)	f_ck (Total)	$n_{0} = 3$	$n_{0} = 10$	$n_{0} = 20$	$n_{0} = 50$	0.93*f_cm	% $(n_{0} = 10)$
20	1	45	56.8	45.2	46.4	45.7	45.2	52.6	13.34
	2	45	57.0	45.6	46.4	45.7	45.3	52.9	14.05
	3	45	46.2	30.3	42.2	43.6	44.5	42.6	0.93
	4	45	54.8	42.3	46.0	45.5	45.2	50.7	10.18
	5	45	47.8	32.6	43.2	44.2	44.7	44.2	2.26
	6	45	51.1	37.2	44.9	45.0	45.0	47.3	5.43
	7	45	52.0	38.4	45.2	45.1	45.1	48.1	6.48
	8	45	53.1	39.9	45.6	45.3	45.1	49.1	7.68
	9	45	46.1	30.5	42.3	43.7	44.5	42.7	1.02
	10	45	47.3	32.0	42.9	44.0	44.6	43.8	2.00

Site of concrete production	Standard deviation
	MPa
	Level 1	Level 2	Level 3	Level 4
Concrete batcher	Sn $<$ 3.0	3.0 $<$ Sn $<$ 4.0	4.0 $<$ Sn $<$ 5.0	Sn $>$ 5.0

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E-mail: arlene@ibracon.org.br

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[1] Corresponding author: Claudia Interlandi. E-mail: interlandiclaudia11@gmail.com