MODELING THE TIME TO CRACKING
Corrosion cracking model
Due to the complexity of the problem, the corrosion
cracking model is restricted to the stresses resulting from the expansion of corrosion products. Other effects causing bridge deck cracking, such as dynamic loading and freezing
and thawing, are not being considered at this time; however,
they may influence the processes of corrosion damage.
It is assumed that uniform corrosion products are formed
around the steel surface to simplify the analysis, although
corrosion takes place in concrete as pitting corrosion; therefore
it’s nonuniform. However, as pitting corrosion progresses it
appears as uniform corrosion and the uniform corrosion
assumption is reasonable. The uniform corrosion products
result in a uniform expansive stress applied to the
surrounding concrete. Figure 5 presents a schematic diagram
of the basic model for the corrosion cracking processes.
Three stages are considered in the proposed model and are
briefly explained as follows:
1. Free expansion—As the passive film is broken by chloride
ions, the metallic Fe at the anode is oxidized to form
ferrous ions that can react with hydroxyl ions to produce
ferrous hydroxide and then can be further converted to
hydrated ferric oxide. In the present model, it has been
assumed that there exists a porous zone around the
steel/concrete interface caused by the transition from cement
paste to steel, entrapped/entrained air voids, and corrosion
products diffusing into the capillary voids in the cement
paste. The volume of this porous zone is directly related to
the surface area of reinforcement, water-cement ratio (w/c),
degree of hydration, and degree of consolidation. As the
corrosion takes place on the surface of the steel, the porous
zone will gradually fill with the corrosion products. When
the total amount of corrosion products WT is less than the
amount of corrosion products required to fill the porous zone
around the steel/concrete interface WP. The formation of
corrosion products at this stage will not create any stress on
the surrounding concrete.
2. Stress initiation—As the total amount of corrosion
products WT exceeds the amount of corrosion products
needed to fill the porous zone around the steel/concrete
interface WP, the formation of corrosion products starts to create
expansive pressure on the surrounding concrete, and this
pressure increases with an increase in corrosion products.
3. Cracking—When the total amount of corrosion products
WT reaches the critical amount of corrosion products
Wcrit (the limiting amount of the corrosion products needed
to induce cracking of the cover concrete), the internal stress
from the volume increase of rust products will exceed the
tensile strength of concrete and crack the cover concrete. It
is obvious that Wcrit is mainly dependent on quality of
concrete and cover depth. The value of Wcrit may be relatively
high in high-strength concrete with a thick cover
depth, while it is small in low-strength concrete with a thin
cover depth. It needs to be pointed out that the quantity of
critical rust products is a function of the amount of the void
structure around the bar. For high-strength concrete, the
voids structure around the bar may be small and, thus, the
amount of critical products needed to crack the cover
concrete may be smaller than currently believed.
MODELING THE TIME TO CRACKING
Corrosion cracking model
Due to the complexity of the problem, the corrosion
cracking model is restricted to the stresses resulting from the expansion of corrosion products. Other effects causing bridge deck cracking, such as dynamic loading and freezing
and thawing, are not being considered at this time; however,
they may influence the processes of corrosion damage.
It is assumed that uniform corrosion products are formed
around the steel surface to simplify the analysis, although
corrosion takes place in concrete as pitting corrosion; therefore
it’s nonuniform. However, as pitting corrosion progresses it
appears as uniform corrosion and the uniform corrosion
assumption is reasonable. The uniform corrosion products
result in a uniform expansive stress applied to the
surrounding concrete. Figure 5 presents a schematic diagram
of the basic model for the corrosion cracking processes.
Three stages are considered in the proposed model and are
briefly explained as follows:
1. Free expansion—As the passive film is broken by chloride
ions, the metallic Fe at the anode is oxidized to form
ferrous ions that can react with hydroxyl ions to produce
ferrous hydroxide and then can be further converted to
hydrated ferric oxide. In the present model, it has been
assumed that there exists a porous zone around the
steel/concrete interface caused by the transition from cement
paste to steel, entrapped/entrained air voids, and corrosion
products diffusing into the capillary voids in the cement
paste. The volume of this porous zone is directly related to
the surface area of reinforcement, water-cement ratio (w/c),
degree of hydration, and degree of consolidation. As the
corrosion takes place on the surface of the steel, the porous
zone will gradually fill with the corrosion products. When
the total amount of corrosion products WT is less than the
amount of corrosion products required to fill the porous zone
around the steel/concrete interface WP. The formation of
corrosion products at this stage will not create any stress on
the surrounding concrete.
2. Stress initiation—As the total amount of corrosion
products WT exceeds the amount of corrosion products
needed to fill the porous zone around the steel/concrete
interface WP, the formation of corrosion products starts to create
expansive pressure on the surrounding concrete, and this
pressure increases with an increase in corrosion products.
3. Cracking—When the total amount of corrosion products
WT reaches the critical amount of corrosion products
Wcrit (the limiting amount of the corrosion products needed
to induce cracking of the cover concrete), the internal stress
from the volume increase of rust products will exceed the
tensile strength of concrete and crack the cover concrete. It
is obvious that Wcrit is mainly dependent on quality of
concrete and cover depth. The value of Wcrit may be relatively
high in high-strength concrete with a thick cover
depth, while it is small in low-strength concrete with a thin
cover depth. It needs to be pointed out that the quantity of
critical rust products is a function of the amount of the void
structure around the bar. For high-strength concrete, the
voids structure around the bar may be small and, thus, the
amount of critical products needed to crack the cover
concrete may be smaller than currently believed.
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