PSI - Issue 84

3

Paolo Andrea Miglietta et al. / Procedia Structural Integrity 84 (2026) 1111–1118 P.A. Maglietta et al. / Structural Integrity Procedia 00 (2026) 000–000

1113

( )

( ) t k k k R C W t e c        − 1 ,0 s t ACC

2

x t

=

(1)

where x(t) = carbonation penetration, k c , k e and k t = experimentally calibrated parameters, C s = carbon dioxide concentration in kg/m 3 , RACC,0 -1 = inverse effective carbonation resistance of concrete, W(t) = weather function depending on the number of rainfall days per year and t = time in years. The onset of steel corrosion occurs once the reinforcement surface is reached by carbonation. The corrosion triggering time, t i , is attained as x(t) in Equation (1) gets equal to concrete cover. The corrosion process results in a reduction of the cross-sectional area of steel reinforcement. The accurate estimation of the corrosion rate, v corr , is challenging due to the large number of influencing factors, including RH, environmental temperature T, concrete quality and cover thickness. (Sung et al., 2010) proposed two models for estimating the corrosion rate for uncracked and cracked concrete, as shown in Equations (2).

3 1.36 1.83 2

45

100    − RH

   

2.5  =

v

v

(2)

0.04

T

1.02

−

v

e

c

t



=





c c ,

c u ,

, c u

where v c,u and v c,c = corrosion rates in μm /year for the uncracked and cracked stages respectively, T = average annual temperature in °C, RH = relative humidity, c = concrete cover thickness in mm and t = time (years). Corrosion reaction products generally fill a volume approximately 6 times that of the original steel. Such products induce radial pressure on the surrounding concrete, leading to cracking and/or cover spalling. El Maaddawy and Soudki proposed an analytical formulation to relate the corrosion-induced pressure, P corr , with the steel mass loss percentage M loss , as shown in Equation (3) (El Maaddawy and Soudki, 2007). In such formulation, concrete is modelled as a thick-walled cylinder with a wall thickness equal to the concrete cover subjected to internal radial pressure.

0    2

(  + +  +  ef loss M E ) (  

E

ef

P

=

) ( −

(3)

) (

) 0

corr

90.1 1

2

1

2

0 

+ +  +



In Equation (3), M loss = percentage mass loss, E ef = concrete elastic modulus in MPa reduced due to the creep effect, Φ = nominal rebar diameter in mm, ν = concrete Poisson ratio, δ 0 = thickness of the porous layer around the reinforcement in mm and ψ = geometrical parameter. The concrete cover cracking occurs when the circumferential stress approaches the concrete tensile strength, f ct . The effect of reinforcement corrosion on the tensile behavior of rebars is generally considered in simplified approaches by reducing the steel mechanical properties, as shown by Equation (4). ( ) 0 y,corr 1 f y loss y f k M  = −  ( ) 0 t,corr 1 f t loss t f k M  = −  0 u,corr u k M u loss e    = −  (4) where f y,corr , f t,corr and ε u,corr = corroded yield strength, tensile strength and ultimate strain respectively, M loss = percentage steel mass loss, f y0 , f t0 and ε u = mechanical properties of the pristine steel and k y , k t and k u = experimental parameters defined according to experimental tests carried out on corroded rebars. The model proposed by (Imperatore et al., 2017) was employed herein, with k y =0.0143, k t =0.0125 and k u =0.0547. As reinforcement corrosion also results in a reduction of the concrete- steel bond strength τ bu , a reduction factor, R, was considered for τ bu , as a function of M loss , according to the simplified model proposed by (Wang, 2023). Concrete cracking due to reinforcement corrosion may be considered by reducing the compressive strength as a function of the corrosion penetration. The model proposed by (Coronelli and Gambarova, 2004) was adopted in this study, as shown in Equation (5).