Numerical and parametric study of the yield stress limits of reinforcement bars in clay block masonry structures

Izquierdo, Orieta Soto; Corrêa, Márcio Roberto Silva; Izquierdo, Indara Soto; Araújo, Iván Gómez

doi:10.1590/S1983-41952021000600011

Orieta Soto Izquierdo

Universidade Federal do Tocantins – UFT, Curso de Engenharia Civil, Palmas, TO, Brasil

http://orcid.org/0000-0003-4978-1816

Márcio Roberto Silva Corrêa

Universidade de São Paulo – USP, Departamento de Estruturas, São Carlos, SP, Brasil

http://orcid.org/0000-0003-3224-5945

Indara Soto Izquierdo

Universidade Federal do Tocantins – UFT, Curso de Engenharia Civil, Palmas, TO, Brasil

http://orcid.org/0000-0001-6411-331X

Iván Gómez Araújo

Universidade Federal da Integração Latino-Americana – UNILA, Departamento de Engenharia Civil e de Infraestrutura, Foz do Iguaçu, PR, Brasil

http://orcid.org/0000-0001-7088-8322

Corresponding author: Orieta Soto Izquierdo. E-mail: orietasi@uft.edu.br

Conflict of interest: Nothing to declare.

Author contributions: OS: conceptualization, supervision, writing, data curation, formal analysis, methodology; MRS: funding acquisition, supervision, formal analysis, methodology, writing; II: data curation, methodology, writing; IG: formal analysis, writing.

Editors: Edgar Bacarji, Guilherme Aris Parsekian.

Figures (18)
Tables (10)

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Figure 1
Push-out specimens: (a) Nominal dimensions [in mm], (b) test rig and (c) experimental test (Adapted from Izquierdo et al. [¹¹11 O. S. Izquierdo, M. R. S. Corrêa, and I. I. Soto, "Study of the block/grout interface in concrete and clay block masonry structures," IBRACON Struct. Mater. J., vol. 10, no. 4, pp. 924–936, Aug 2017, http://dx.doi.org/10.1590/s1983-41952017000400009.
http://dx.doi.org/10.1590/s1983-41952017... ]).

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Figure 2
Pull-out specimens: (a) Nominal dimensions [in mm], (b) test rig and (c) experimental test (Adapted from Izquierdo et al. [¹¹11 O. S. Izquierdo, M. R. S. Corrêa, and I. I. Soto, "Study of the block/grout interface in concrete and clay block masonry structures," IBRACON Struct. Mater. J., vol. 10, no. 4, pp. 924–936, Aug 2017, http://dx.doi.org/10.1590/s1983-41952017000400009.
http://dx.doi.org/10.1590/s1983-41952017... ]).

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Figure 3
Results of the pull-out of clay block specimens with yield load and maximum load of the reinforcements [¹¹11 O. S. Izquierdo, M. R. S. Corrêa, and I. I. Soto, "Study of the block/grout interface in concrete and clay block masonry structures," IBRACON Struct. Mater. J., vol. 10, no. 4, pp. 924–936, Aug 2017, http://dx.doi.org/10.1590/s1983-41952017000400009.
http://dx.doi.org/10.1590/s1983-41952017... ].

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Figure 4
(a) HX24L solid element of the units and grout and (b) TP18L solid element of the steel reinforcement used in the numerical modeling [¹³13 TNO DIANA, DIANA Finite Element Analysis – User's Manual Release 9.6. Delft, Netherland, 2015. Accessed: June 7, 2020. [Online]. Available: http://tnodiana.com
http://tnodiana.com... ].

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Figure 5
Q24IF interface element [¹³13 TNO DIANA, DIANA Finite Element Analysis – User's Manual Release 9.6. Delft, Netherland, 2015. Accessed: June 7, 2020. [Online]. Available: http://tnodiana.com
http://tnodiana.com... ].

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Figure 6
Vertical displacements of the (a) push-out and (b) pull-out specimens.

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Figure 7
Mechanical behavior of the units used in numerical modeling: (a) tension, (b) compression, and (c) shear [¹³13 TNO DIANA, DIANA Finite Element Analysis – User's Manual Release 9.6. Delft, Netherland, 2015. Accessed: June 7, 2020. [Online]. Available: http://tnodiana.com
http://tnodiana.com... ].

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Figure 8
Constitutive model for masonry interfaces [²²22 P. B. Lourenço and J. G. Rots, "Multisurface interface model for analysis of masonry structures," J. Eng. Mech., vol. 123, no. 7, pp. 660–668, Jul 1997, http://dx.doi.org/10.1061/(ASCE)0733-9399(1997)123:7(660).
http://dx.doi.org/10.1061/(ASCE)0733-939... ] adapted from Haach [¹⁶16 V. G. Haach, “Development of a design method for reinforced masonry subjected to in-plane loading based on experimental and numerical analysis,” Ph.D. dissertation, Univ. Minho, Guimaraes, Portugal, 2009. [Online]. Available: www.civil.uminho.pt/masonry].

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Figure 9
Validation of numerical results of the ClG14 series of push-out tests: (a) force vs displacement diagrams and (b) mean maximum load.

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Figure 10
Validation of numerical results of the ClG30 series of push-out tests: (a) force vs displacement diagrams and (b) mean maximum load.

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Figure 11
Displacement of the grout according to the ClG14 series (a) numerical model and (b) bottom face of the physical model.

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Figure 12
Validation of numerical results of the ClG14S12 series of pull-out tests: (a) force vs displacement diagrams and (b) mean maximum load.

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Figure 15
Validation of numerical results of the ClG30S16 series of pull-out tests: (a) force vs displacement diagrams and (b) mean maximum load.

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Figure 13
Validation of numerical results of the ClG14S16 series of pull-out tests: (a) force vs displacement diagrams and (b) mean maximum load.

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Figure 14
Validation of numerical results of the ClG30S12 series of pull-out tests: (a) force vs displacement diagrams and (b) mean maximum load.

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Figure 16
Displacement of the grout according to (a) the numerical model and (b) physical model of the ClG14S12 series.

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Figure 17
Pull-out tests with rebar diameters of Ø10 mm (a) parametric results (load vs displacement diagrams) and (b) maximum load.

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Figure 18
Pull-out tests with rebar diameters of Ø20 mm (a) parametric results (load vs displacement diagrams) and (b) maximum load.

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Table 1
Results of the steel reinforcements Ø 12.5mm and Ø 16 mm used in clay blocks.

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Table 2
Results of the push-out tests [¹¹11 O. S. Izquierdo, M. R. S. Corrêa, and I. I. Soto, "Study of the block/grout interface in concrete and clay block masonry structures," IBRACON Struct. Mater. J., vol. 10, no. 4, pp. 924–936, Aug 2017, http://dx.doi.org/10.1590/s1983-41952017000400009.
http://dx.doi.org/10.1590/s1983-41952017... ].

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Table 3
Results of the pull-out of clay block specimens [¹¹11 O. S. Izquierdo, M. R. S. Corrêa, and I. I. Soto, "Study of the block/grout interface in concrete and clay block masonry structures," IBRACON Struct. Mater. J., vol. 10, no. 4, pp. 924–936, Aug 2017, http://dx.doi.org/10.1590/s1983-41952017000400009.
http://dx.doi.org/10.1590/s1983-41952017... ].

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Table 4
Load limited by bond and ultimate load of the pull-out tests of clay blocks [¹¹11 O. S. Izquierdo, M. R. S. Corrêa, and I. I. Soto, "Study of the block/grout interface in concrete and clay block masonry structures," IBRACON Struct. Mater. J., vol. 10, no. 4, pp. 924–936, Aug 2017, http://dx.doi.org/10.1590/s1983-41952017000400009.
http://dx.doi.org/10.1590/s1983-41952017... ].

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Table 5
Number and size elements of the push-out mesh.

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Table 6
Number and size elements of the pull-out mesh.

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Table 7
Mechanical properties of the Total Strain Crack Model (masonry units and grout).

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Table 8
Mechanical properties of the Composite Interface Model (block/grout interface and the bed joints masonry).

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Table 9
Mechanical properties used for the Von Mises model (reinforcement).

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Table 10
Ultimate stress of the pull-out tests of clay blocks with respect to the yield stress of the steel rebar for different diameters.

Diameter rebar (mm)	Area of reinforcement cross section (mm²)		Mean Ultimate Load (kN)	Mean Yield Load (kN)	Mean Ultimate Stress (MPa)	Mean Yield Stress (MPa)
12.5	125		93.32	65.55	760.43	534.15
		S.D	1.30	1.94	10.58	15.77
		C.V (%)	1.39	2.95	1.39	2.95
16	200		159.86	117.32	795.05	583.52
		S.D	1.91	3.28	9.52	16.30
		C.V (%)	1.20	2.79	1.20	2.79

Series	Mean Ultimate Load (kN)	S.D	C.V (%)	Bond Strength (MPa)	S.D	C.V (%)
ClG14	11.64	1.32	11.31	0.16	0.02	8.87
ClG30	14.02	1.24	8.87	0.19	0.02	8.87

Series	Mean Ultimate Load (kN)	S.D	C.V (%)	Mean Ultimate Stress (MPa)	S.D	C.V (%)
ClG14S12	48.47	1.14	2.36	394.95	9.31	2.36
ClG30S12	59.26	7.42	10.51	482.91	50.75	10.51
ClG14S16	48.96	1.76	3.60	243.49	8.76	3.60
ClG30S16	60.11	5.11	8.50	298.94	25.40	8.50

Push-out specimens		Pull-out specimens
Ultimate Load x 4 (kN)		Ultimate Load (kN)
G14	G30	ClG14S12	ClG14S16	ClG30S12	ClG30S16
46.56	56.12	48.49	48.96	59.26	60.10

	Clay block	Grout	Block/grout interface
Elements number	1260	462	180
Size of elements (mm)	10x10x40	10x10x40	40x10
Subtotal	1722		180
Total	1902

	Clay block	Grout	Reinforcement	Block/grout interface	Grout/reinforcement interface	Bed joints masonry
Elements number	5040	1848	500	720	180	252
Size of elements (mm)	10x10x40	10x10x40	10x10x200	40x10	10x200	10x10
Subtotal	7388			1152
Total	8540

Parameters	Symbol/Units	Clay block	Grout G14	Grout G30
Elastic modulus (exp)	E (MPa)	9876.43	20521.17	29719.67
Poisson (exp)	υ	0.20	0.20	0.20
Tensile strength (exp)	f_t (MPa)	1.08	1.43	2.35
Fracture energy for Mode I (cal)	G_fI (MPa·mm)	0.06	0.03	0.06
Compressive strength (exp)	f_c (MPa)	30.92	14.18	31.43
Fracture energy under compression (cal)	G_c (MPa·mm)	5.51	3.19	5.57
Shear retention (cal)	β	0.5	0.5	0.5

Parameters	Symbol/Units	Block/grout interface	Block/grout interface	Bed joints masonry
Normal stiffness (exp)	k_n (MPa/mm)	1.00	1.00	11.71
Tangential stiffness (exp)	k_t (MPa/mm)	1.76	1.19	11.71
Cohesion (exp)	fv₀ (MPa)	0.16	0.19	0.20
Friction coefficient (exp)	tan φ₀	0.70	0.70	0.250
Dilatancy coefficient (exp)	tan Ψ	1.00 × 10⁻⁴	1.00 × 10⁻⁴	1.723
Residual friction coefficient (exp)	tan φ_r	0.39	0.39	0.29
Confining normal stress (exp)	σ_u (MPa)	−1.18	−1.18	−1.37
Exponential degradation coefficient (cal)	δ	1.85	1.85	0
Tensile strength (exp)	f_t (MPa)	0.23	0.23	0.29
Fracture energy for Mode I (exp)	G_fI (MPa·mm)	0.02	0.02	0.02
Fracture energy for Mode II (exp)	G_fII (MPa·mm)	0.19	0.24	0.22
Cap critical compressive strength (exp)	f_c (MPa)	3.15	3.15	3.05
Shear traction control factor (cal)	C_s	4.00	4.00	4.00
Compressive fracture energy (cal)	G_fc (MPa·mm)	1.18	1.18	5.00

Parameters	Symbol/Units	Ø 12.5 mm	Ø 16 mm
Elastic modulus (exp)	E (MPa)	198513.12	200844.39
Poisson (cal)	υ	0.30	0.30
Yield stress (exp)	f_y (MPa)	556.24	588.60

Rebar Diameters (mm)	Ultimate Stress
Rebar Diameters (mm)	G14	G30
Ø 8	100% f_yk	100% f_yk
Ø 10	100% f_yk	100% f_yk
Ø 12.5	74% f_yk	90% f_yk
Ø 16	42% f_yk	51% f_yk
Ø 20	27% f_yk	33% f_yk

[1] Corresponding author: Orieta Soto Izquierdo. E-mail: orietasi@uft.edu.br

Brasil

Brasil

Numerical and parametric study of the yield stress limits of reinforcement bars in clay block masonry structures

Estudo numérico e paramétrico sobre o limite da tensão de escoamento da armadura na alvenaria estrutural de blocos cerâmicos

abstract: