Computational modeling for predicting corrosion initiation in reinforced concrete structures

This article presents a model for penetration of chloride by diffusion in reinforced concrete structures based on the solution of the Fick's 2nd Law, using the finite element method (FEM) in two-dimensional domain. This model predicts the time, in a given situation, so that a certain limit of chlorides for depassivation of reinforcement is reached, characterizing the end of service life. Several approaches for the chloride surface concentration and for the diffusion coefficient are used, parameter which must be corrected due to the effects of temperature, solar radiation, exposure time, and relative humidity. Moreover, a parametric analysis is carried out in order to study the factors involved and their impact on the ingress of chlorides by diffusion, contributing to a better understanding of the phenomenon. In addition, the developed model is applied to the cities of Vitória (ES) and Florianópolis (SC) to analyze the service life for different concrete covers, making a comparison with the Brazilian standard.

Keywords:
chlorides; corrosion; diffusion; finite element method; service life.

Authorship

W. K. DOMINICINI

Universidade Federal do Espírito Santo, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Civil, Vitória, ES, Brasil. wagner.kd@gmail.com calmonbarcelona@gmail.comUniversidade Federal do Espírito SantoBrazilVitória, ES, BrazilUniversidade Federal do Espírito Santo, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Civil, Vitória, ES, Brasil. wagner.kd@gmail.com calmonbarcelona@gmail.com

J. L. CALMON

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (17)
Tables (15)

Type of soil	ρ
Recent snow	80-90%
No recent snow	60-70%
Cropping areas:	-
Without vegetation	10-15%
Dry grass	28-32%
Prairie and forests	15-30%
Sandy area	15-25%
Cement, concrete	55%
Light sand	25-40%
Water:	-
Summer	5%
Winter	18%

Authors	Equation	Description
-	$C_{S} = c t e$	Constant during all the structure's service life
Uji et al. (1990)	$C_{S} = S \sqrt{t}$	Increases with exposure time.
Collins e Grace (1997)	$C_{S} = C_{s, u l t} . \frac{t}{t + T_{C S}}$	After initial increase in the first few years, becomes constant
Ann et al. (2009)	$C_{S} = C_{0} + k \sqrt{t}$	Shows initial accumulation and increases with exposure time
Song et al. (2008)	$C_{S} = C_{0} + α \ln t$	Shows initial accumulation and increases with exposure time

Control variables		Value
Geometry	Dimensions	8 cm x 8 cm
Geometry	Concrete cover	3 cm
Mesh	Type of elements	Linear triangular
	Size of elements	0.002
	Number of nodes	2141
	Number of elements	4088
Time parameters	Final time (T)	50 years
Time parameters	Time step (Δ_t)	5 days

Control variables		Value
Boundary conditions	Initial concentration (C₀)	0 %
Boundary conditions	Chloride surface concentration (C_s)	2 % cement weight
Diffusion coefficient	Reference diffusion coefficient (D_c,ref)	1x10 - 12 m²/s
	Reference temperature (T_ref)	23 ºC
	Activation Energy (U)	41.8 kJ/mol
	Humidity parameter h_c	0.75

Climatic parameters		Florianópolis (SC)	João Pessoa (PB)	Vancouver (BC)
Temperature	Maximum (ºC)	24.6	27.2	18
	Minimum (ºC)	16.5	24.2	3.6
	Day of maximum annual	45	45	210
Relative humidity	Maximum (%)	84	87	81.2
	Minimum (%)	80	73	61.4
	Day of maximum annual	195	195	15

JAN		FEB		MAR		APR
João Pessoa	Florianópolis	João Pessoa	Florianópolis	João Pessoa	Florianópolis	João Pessoa	Florianópolis
22	18	20	16	20	14	18	12
MAY		JUN		JUL		AUG
João Pessoa	Florianópolis	João Pessoa	Florianópolis	João Pessoa	Florianópolis	João Pessoa	Florianópolis
16	10	14	8	14	8	18	10
SEPT		OCT		NOV		DEC
João Pessoa	Florianópolis	João Pessoa	Florianópolis	João Pessoa	Florianópolis	João Pessoa	Florianópolis
20	12	22	16	20	18	20	18
Parameters for calculating increase in temperature
City			João Pessoa			Florianópolis
Latitude			27.5º			7.0º
Surface slope			90º			90º
Surface azimuth			30º			30º
Reflection coefficient of surroundings			0.5			0.5
Absorption factor			60%			60%
heat transfer coefficient			25 Kcal/m²h ºC			25 Kcal/m²h ºC

Case	Chloride concentration [% of cement weight]
Case	5 years	10 years	20 years	50 years
Constant Dc	0.3432	0.8725	1.3710	1.7635
Florianópolis	0.1582	0.5523	1.0612	1.5166
João Pessoa	0.2203	0.6770	1.1933	1.6237
Vancouver	0.0000	0.0000	0.0283	0.2332

Model	Equation	Parameters
-	$C_{S} = cte$	Cs = 5.1541
Uji et al. (1990)	$C_{S} = S \sqrt{t}$	S = 2.51e-05
Collins and Grace (1997)	$C_{S} = C_{s, ult} . \frac{t}{t + T_{CS}}$	Cs,ult = 0.8651 ; Tcs = 533.5267
Ann et al. (2009)	$C_{S} = C_{0} + k \sqrt{t}$	C0 = 3.3593 ; k = 0.3488
Song et al. (2008)	$C_{S} = C_{0} + α \ln t$	C0 = 3.0431; α = 0.6856

Approach	Chloride concentration [% of cement weight]
Approach	5 years	10 years	20 years	50 years
Constant Cs	0,8845	2,2484	3,5331	4,5446
Uji et al. (1990)	0,1761	0,7829	2,0521	4,8225
Collins and Grace (1997)	0,4270	1,6747	3,2969	4,7543
Ann et al. (2009)	0,6431	1,7610	3,0757	4,7780
Song et al. (2008)	0,5220	1,6745	3,1381	4,7933

Daily global solar radiation on a monthly average received by a horizontal surface for each month of the year [MJ/m².day]
JAN	FEB	MAR	APR
18	18	18	14
MAY	JUN	JUL	AUG
14	12	12	14
SEPT	OCT	NOV	DEC
14	16	16	16
Parameters for calculating increase in temperature
Latitude		20,3 º
Surface slope		90 º
Surface azimuth		30 º
Reflection coefficient of surroundings		0,5
Absorption factor		60 %
heat transfer coefficient		25 Kcal/m²hºC

Case	Chloride concentration [% of cement weight]
Case	5 years	10 years	20 years	50 years
Constant Dc	0.3432	0.8725	1.3710	1.7635
Ordinary Portland cement; m=0.264	0,0370	0,1367	0,3033	0,4674
Ground Granulated Blast-furnace slag; m=0.621	0	0	0	0
Fly Ash; m=0.699	0	0	0	0