Calibrating a Physics-Based Corrosion Model with Field-Based Bridge Condition Data

Acknowledgments

Notation

A₀

original rebar area (mm²);

A₁

area parameter 1 depending on D₀, P(t), θ₁, and b in the pitting corrosion model (mm²);

A₂

area parameter 2 depending on D₀, P(t), θ₂, and b in the pitting corrosion model (mm²);

A(t)

rebar area at time t (mm²);

b

width of the pit area (mm);

C

thickness of the concrete cover (mm);

C_crit

critical chloride content (kg/m³);

C_Cl(x, t)

chloride concentration at spatial coordinate x and time t (kg/m³);

C_s

chloride content on the concrete exterior surface (kg/m³);

D₀

original rebar diameter (mm);

D_CI

effective chloride diffusion coefficient of concrete (mm²/s);

E_c

elastic modulus of concrete (MPa);

erf(·)

error function (—);

f₀

yield strength of noncorroded reinforcement (MPa);

f(t)

effective yield strength of corroded rebar at time t (MPa);

f_ct

tensile strength of concrete (MPa);

i_corr

current density;

K

=ratio of λ(t)_afcrack to λ(t)_bfcrack (—);

m_loss

percent of rebar mass loss (or area loss per unit length) due to corrosion (—);

P(t)

pit depth (mm);

P_corr

internal pressure caused by rust expansion (MPa);

Q_corr

percent weight loss (or area loss) of rebar (—);

R

pitting factor (—);

r₀

radius of the thick-wall cylinder (concrete cover) (mm);

r

distance from the center of the thick-wall model to the interface between the rust and concrete (mm);

r_i

radius of rebar (mm);

W(t)

crack width of concrete cover at time t as predicted by the corrosion model (mm);

W_LB(t)

lower bound of crack width derived from deterioration curves at time t (mm);

W_UB(t)

upper bound of crack width derived from deterioration curves at time t (mm);

W_cri

critical crack width, which is the cover crack width beyond which the corrosion rate is assumed to become constant (mm);

$\overline{W}(t)$

average crack width derived from deterioration curves at time t (mm);

ΔA(t)

cross-sectional area loss of reinforcement at time t (mm²);

δ₀

thickness of the porous zone (mm);

λ(t)_corr

corrosion rate, amount of metallic material loss in thickness over a unit time (mm/year);

λ(t)_afcrack

corrosion rate at critical crack width (mm/year);

λ(t)_bfcrack

corrosion rate before cracking (mm/year);

ν

Poisson’s ratio of concrete (—);

θ₁

angle parameter 1 depending on D₀, P(t), and b in the pitting corrosion model (—);

θ₂

angle parameter 2 depending on D₀, P(t), and b in the pitting corrosion model (—); and

σ

circumferential stress caused by rust expansion (MPa).

References