Evaluation of rheological models for concrete submitted to alkali-aggregate reaction based on numerical analysis of damping - free expansion

Cavalcanti, Marlon de Barros; Torres, Sandro Marden; Lima Filho, Marçal Rosas Florentino; Santos, Alexsandro José Virgínio dos

doi:10.1590/S1983-41952021000200005

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 14 (2) • 2021 • https://doi.org/10.1590/S1983-41952021000200005 copy

Evaluation of rheological models for concrete submitted to alkali-aggregate reaction based on numerical analysis of damping - free expansion

Avaliação de modelos reológicos para concreto submetido a reação álcali-agregado baseada em análise numérica de amortecimento - expansão livre

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The Alkali-Aggregate Reaction (AAR) phenomenon in concrete structures is perceived via expansion and cracking, swelling of gel like material, causing damage and disruption in structural elements. Despite extensive standardization, AAR cases are still persistently occurring worldwide. The literature on susceptibility of concrete to AAR reported examples of false negative and positive results. Hence, long-term prediction is a problem still posing great challenge to engineers. The severity of AAR on the structural integrity can be mostly elucidated by the assessment of the historic of elastic properties. There is consensus that AAR causes decrease in the load capacity concrete, reflected by reduction of elasticity modulus due damage progresses. Non-destructive techniques are often used as first approach, as they can provide relatively fast assessment in situ as well as in large structural elements. Its data interpretation carries certain degree of complexity due intrinsic characteristic of many of these methods. This is the case of Ultrasonic Pulse Velocity (UPV), which have been considered to present several limitations for such purpose. This paper deals the potential use of the Longitudinal Resonance Frequency (LRF) method as tool to evaluate the elastic historic of AAR prone elements. The LRF possesses higher energy than UPV. Also, using modulation of frequency in input signal combined the test geometry, the LRF allow application to larger samples as well as to extract complementary information alongside the dynamic elastic modulus. This way, the LRF was applied to study concrete beams tested under controlled conditions for about 1.5 year. The independent variables to the tests are: time, frequency, aggregate type, cement content, alkali content and water to cement ratio. The dependent variables are: damping, loss factor and elasticity modulus. The analysis associate damage with vibration damping, confirming reduction of elasticity through damage with experimental validation and prediction of AAR under rheological model.

Keywords:
alkali-aggregate reaction; rheological model; damping

Concrete beam	Description
I1 (C420-I-L)	Dimensions 10 x 10 x 114 cm; cement content 420 kg/m³ of concrete; coarse aggregate innocuous; free expansion
I2 (C500-I-L)	Dimensions 10 x 10 x 114 cm; cement content 500 kg/m³ of concrete; coarse aggregate innocuous; free expansion
R1 (C420-R-L)	Dimensions 10 x 10 x 114 cm; cement content 420 kg/m³ of concrete; coarse aggregate reactive; free expansion
R2 (C500-R-L)	Dimensions 10 x 10 x 114 cm; cement content 500 kg/m³ of concrete; coarse aggregate reactive; free expansion

Author	Mix	Reactive Aggregate	Cem.	w/c	E	T	h	Na₂O_eq
Author	Mix	Reactive Aggregate	kg/m³	w/c	GPa	ºC	%	%
Barreto [³3 A. M. Barreto, “Técnicas não destrutivas para detecção da reação álcali-agregado em prismas de concreto,” Ph.D. dissertation, Univ. Fed. Paraíba, João Pessoa, 2019.]	C420-R-L	Quartz, biotite, Albite and microline (coarse)	420	0.45	25.90	36 - 40	> 95	1.47
	C500-R-L	Quartz, biotite, Albite and microline (coarse)	500	0.45	29.58	36 - 40	> 95	1.47
Larive [¹⁰10 COPEM, “Relatório de Modelagem e Recalibração das Estruturas da Usina de PA-IV, CH01-C-0031-R6, 2001.], [¹¹11 R. Esposito, “The deteriorating impact of alkali-silica reaction on concrete – expansion and mechanical properties”, Ph.D. dissertation, Univ. Parma, Parma, Italy, 2016.]	-	Tournaisis limestone (thin and coarse)	410	0.44	-	38	97	1.25
ISE [¹⁰10 COPEM, “Relatório de Modelagem e Recalibração das Estruturas da Usina de PA-IV, CH01-C-0031-R6, 2001.]	1^*
PA-IV [¹⁰10 COPEM, “Relatório de Modelagem e Recalibração das Estruturas da Usina de PA-IV, CH01-C-0031-R6, 2001.]	-	Biotite-gneiss, rosy granite and amphibolite (coarse)	357	0.53	25.00	38	100	0.92
Esposito [¹¹11 R. Esposito, “The deteriorating impact of alkali-silica reaction on concrete – expansion and mechanical properties”, Ph.D. dissertation, Univ. Parma, Parma, Italy, 2016.]	RR1	Quartzite, quartz, limestone, volcanic rock fragments (fine and coarse)	380	0.46	42.70	38	96	1.17
	RR2	Coarse-grained quartz, quartzite, gneiss, metariolite (fine and coarse)	380	0.45	30.46	38	96	1.17
Giaccio et al. [¹²12 G. Giaccio, R. Zerbino, J. M. Ponce, and O. R. Batic, "Mechanical behavior of concretes damaged by alkali-silica reaction," Cement Concr. Res., vol. 38, pp. 993–1004, 2008.]	R2	Opal and chalcedony (thin)	420	0.42	32.00	38	2^*	1.25
	R4	Feldspars (orthoclase and plagioclase), quartz, mica, epidote, zircon and dark minerals (coarse)	420	0.42	38.10	38	2^*	1.25
Swamy [¹³13 R. N. Swamy, "Assessment and rehabilitation of aar-affected structures," Cement Concr. Compos., vol. 19, pp. 427–440, 1997.]	4.5% opal	Beltane Opal (thin)	520	0.44	-	20	96	1.00
Sanchez et al. [¹⁴14 L. F. M. Sanchez, B. Fournier, M. Jolin, D. Mitchell, and J. Bastien, "Overall assessment of Alkali-Aggregate Reaction (AAR) in concretes presenting different strengths and incorporating a wide range of reactive aggregate types and natures," Cement Concr. Res., vol. 93, pp. 17–31, 2017.]	Wt + HP 35	Polymeric sand, quartz and feldspar (fine)	370	0.47	-	38	100	1.25
Ahmed et al. [¹⁵15 T. Ahmed, E. Burley, S. Rigden, and A. Abu-Tair, "The effect of alkali reactivity on the mechanical properties of concrete," Constr. Build. Mater., vol. 17, pp. 123–144, 2003.]	B	Fused Silica (fine)	400	0.50	21.13	38	3^*	1.75

Model	Creep Function
Maxwell	$\frac{1}{E} (1 + \frac{E}{C} t)$
Kevin-Voigt	$\frac{1}{E} (1 - e^{- \frac{E}{C} t})$
Zener (Figure 10 - 3a)	$\frac{1}{E_{1}} + \frac{1}{E_{2}} - \frac{e^{- \frac{E_{2}}{C} t}}{E_{2}}$
antiZener (Figure 10 - 4b)	$(\frac{1}{C_{1} + C_{2}}) t + \frac{C_{2}}{E (C_{1} + C_{2})} (1 - \frac{C_{1}}{C_{1} + C_{2}}) (1 - e^{- \frac{E (C_{1} + C_{2})}{C_{1} C_{2}} t})$
Burgers (Figure 10 - 5a)	$\frac{1}{E_{1}} + \frac{1}{E_{2}} - \frac{e^{- \frac{E_{2}}{C_{2}} t}}{E_{2}} + \frac{t}{C_{1}}$

Model	Complex Modulus
Histerese	$E (1 + i η)$
Maxwell	$\frac{i ω E C}{E + i ω C}$
Kelvin-Voigt	$E + i ω C$
Zener (Figure 10 - 3a)	$\frac{E_{1} (E_{2} + i ω C)}{E_{1} + E_{2} + i ω C}$
antiZener (Figure 10 - 4b)	$\frac{{E i ω C}_{2}}{{i ω C}_{2} + E} + {i ω C}_{1}$
Burgers^* * AUTHOR (Figure 10 - 5a)	${(\frac{1}{E_{1}} + \frac{1}{{i ω C}_{1}} + \frac{1}{E_{2} + {i ω C}_{2}})}^{- 1}$

Model	$α$	$β$
Histerese	$η$
Maxwell	$\frac{E}{C}$	-
Kelvin-Voigt	-	$\frac{C}{E}$
Zener (Figure 10 - 3a)	$\frac{E_{2} + \frac{E_{2}^{2}}{E_{1}}}{C}$	$\frac{C}{E_{1}}$
antiZener^* * Semblat [22] (Figure 10 - 4b)	$\frac{E (C_{1} + C_{2})}{C_{2}^{2}}$	$\frac{C_{1}}{E}$
Burgers (Figure 10 - 5a)	By analogy: E₁ = E_maxwell; E₂ = E_2(zener); C₁ = C_2(antizener); C₂ = C_kelvinvoigt

Time (days)	Expansion (%)	Amplitude	$ω_{r e s}$ (Hz)	$η$	C (Pa . s)	E (GPa)
1	0	0.000285455	1,829.9	0.01118	580.78264	10.84121
14	0.008	0.000257711	2,871	0.01141	930.25535	26.68638
29	0.02	0.000230823	2,828.4	0.01302	1,046.09	25.90031
379	0.094	7.01E-05	1,781.7	0.01467	742.27642	10.27766
514	0.104	5.48E-05	1,350.9	0.02087	800.86654	5.90843

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E-mail: arlene@ibracon.org.br

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[1] Corresponding author: Marlon de Barros Cavalcanti. E-mail: marlonbc@chesf.gov.br, marlonbcavalcanti@gmail.com