### 3.1 Reinforcement Corrosion and Crack Development

Figure 4 shows the relationship between maximum corrosion weight loss percentages and average corrosion weight loss percentages. Maximum corrosion weight loss percentage was measured every 2.5 cm in highly corroded area and average corrosion weight loss percentage was measured for entire length. The slope of regression line for all specimens is 2.14. The slope of regression line for the entire corrosion series (“A” specimens) is 1.87. These ratio values were decreased with an increase of the length of the corroded area.

Figures 5, 6, and 7 show the corrosion weight loss percentages with respect to the corrosion areas throughout the ‘A’ and ‘H’ specimens, respectively, including the crack development of the concrete in terms of the corrosion percentage. The cracks that occurred due to the stress transfer from the rebar to the concrete also are presented in Figs. 5 and 6.

Corrosion cracks in the parallel direction of rebar did not occur when the corrosion weight loss percentage was less than 2.04 %. In addition, corrosion cracks occurred mostly at the surface of the concrete that was in contact with the copper plate or at the side face of the concrete on the specimen.

For the ‘A’ corrosion case, longitudinal cracks developed throughout the entire length of the specimen. Transverse cracks were often occurred with an increase in the corrosion weight loss percentage.

For the ‘H’ local corrosion case, the corrosion crack width was smaller than for the ‘A’ corrosion case at the same amount of corrosion weight loss percentage.

In the case of ‘C’ corrosion and ‘S’ local corrosion, there are more longitudinal corrosion cracks than transverse corrosion cracks. This outcome may be the result of the longitudinal expansion of the local area with a high intensity of corrosion; those areas are very limited and have a shallow concrete cover.

Figure 8 shows the average corrosion weight loss percentages versus maximum corrosion cracks. The corrosion cracks have been developed on one surface, which was intended in this study.

Figure 9 shows the relationship between the average corrosion weight loss percentage of the rebar over the entire length of the specimen and the number of cracks obtained from the tensile test results.

For the control specimen without any corrosion, three tensile cracks developed, and the number of tensile cracks tended to decrease with an increase in the corrosion weight loss percentage of the rebar. The reason for this outcome is that the corrosion of the rebar resulted in reducing the distribution capacity of the cracks, whereas the length of 80 cm is relatively short such that previously developed transverse corrosion cracks mainly affected the formation of tensile cracks.

### 3.2 Tension Stiffening Effects of Concrete

Figure 10 shows the tensile stress versus average strain values for the specimens with different levels of corrosion and no corrosion and includes the relationship between the average stress of the concrete and the average strain. The average stress of the concrete was calculated based on the tension stiffening effect of the concrete.

In the ‘A’ (all) corrosion case, the initial stiffness for specimens A-5 and A-6 with transverse cracks decreased until tensile cracks formed, and the initial peak indicates when the cracking point of the concrete was no longer observed. Moreover, the remaining stress of the concrete at the strain of 0.002 decreased as the corrosion level increased, but the difference is insignificant. In short, when the corrosion level was high, the number of cracks due to stress increased, and the amount of slip that occurred around the transverse cracks increased. Therefore, less displacement in the tensile stress was observed at the time new cracks appeared. However, slip between the rebar and concrete that was caused by longitudinal cracks followed by tensile cracks led to higher average strain values under the same level of stress with an increase in the corrosion level of the rebar.

In the ‘H’ (half) corrosion case, the tension stiffening effect rapidly decreased due to the increase in steel corrosion when corrosion cracks occurred in concrete specimen H-5.

In the ‘C’ (center) local corrosion and ‘S’ (side) local corrosion cases, the decrease in the tension stiffening influences is associated with the steel corrosion, as seen in the relationship between the stress versus average strain values and the concrete stress versus average strain values. However, the stress contribution in the ‘C’ and “S” corrosion cases was higher than in the ‘H’ and ‘A’ corrosion cases.

The deformation of the rebar increased at the cracking point when transverse cracks occurred in the reinforced concrete that was subjected to tensile stress. In addition, deformation increased with the corrosion of the rebar. This outcome was a result of the loss of bond strength due to the steel corrosion and the loss of the cross-section of the reinforcement as well. After the cracks formed, the concrete was hardly affected by the corrosion of the reinforcement, whereas the tension stiffening effects of the concrete with considerable local corrosion apparently decreased.

### 3.3 Bond Strength and Slip

Slip occurs due to the reduced bond strength between the concrete and the rebar that is induced by developing cracks in the concrete along with expansion that is due to the accumulation of corroded products.

For the finite element analysis in this study, plate bond elements were adopted to model the reinforced concrete with corroded rebar. These bond elements can be presented with bond stress and shear stiffness. The bond strength and slip with respect to the corrosion level must be formulated to determine the bond element of the reinforced concrete with corrosion. Therefore, the force equilibrium condition of the bond force between the rebar and concrete and the tensile force at the concrete crack were used to determine the bond stress. Once a crack due to tensile force develops in the concrete surrounding the rebar, the stress distribution in the concrete and steel is different for various locations, as seen in Fig. 11. The bond stress is the difference between the concrete and rebar in terms of tensile deformation such that the bond stress can be written as Eq. (1):

$$ A_{c} \sigma_{ct} = \pi d_{b} \mathop \smallint \limits_{0}^{{l_{t} }} \tau_{x} dx $$

(1)

where *A*
_{
c
} is the cross-section of the concrete, *d*
_{
b
} is the diameter of the reinforcement, *σ*
_{
ct
} is the tensile strength of the concrete (at the crack), *τ*
_{
x
} is the bond stress within the transfer length, and *l*
_{
t
} is the transfer length of the bond stress.

The force equilibrium is used with linear approximation, as seen in Fig. 11. The bond strength can be calculated using Eqs. (2) and (3).

$$ A_{c} \sigma_{ct} = \frac{1}{2}\pi d_{b} l_{t} \tau_{max} $$

(2)

$$ \tau_{{max} } = \frac{{2(N + 1)A_{c} \sigma_{ct} }}{\pi rL} $$

(3)

where *N* is the number of tensile cracks in the specimen.

Figure 12 shows the relationship between the bond stress and corrosion weight loss of the reinforcement as obtained from the tests. In addition, the bond strength derived from the corrosion weight loss and bond stress can be formulated using Eq. (4).

$$ \tau_{c,max} = \tau_{s,max} \left( {1.306e^{ - 0.0948\Delta w} } \right) $$

(4)

where *τ*
_{
c,max
} is the shear stress of the reinforcement with corrosion (N/mm^{2}), *τ*
_{
s,max
} is the bond stress of the reinforcement without corrosion (N/mm^{2}), and *ΔW* is the average corrosion weight loss of the reinforcement (%), (*ΔW* ≥ 2.04 %).

The slip between the rebar and the concrete under tensile stress can be calculated approximately using the widths of the cracks that develop in the concrete (Soltani et al. 2013). The surface deformation of the concrete was ignored in this study. The slip between the rebar and the concrete in the reinforced concrete member is half the maximum crack width according to CEB-FIP Model Code 1990, (1991). Therefore, Eq. (5) can be rewritten as Eq. (6).

$$ W_{max} = s_{r} \left( {\varepsilon_{sm} - \varepsilon_{cm} } \right)(l_{t} \le S_{r} \le 2l_{t} ) $$

(5)

$$ s\left( x \right) = l_{t} \left( {\varepsilon_{s} - \varepsilon_{c} } \right) = \frac{1}{2}S_{r} \left( {\varepsilon_{s} - \varepsilon_{c} } \right) = \frac{W}{2} $$

(6)

where *W* is the crack width and *S*(*x*) is the average maximum slip between the reinforcement and the concrete in a reinforced concrete member subjected to tension loading (displacement at a load of 30 kN in this study).

Figure 13 shows the relationship between amounts of slip computed using Eq. (6) and the corrosion weight loss percentage of the rebar. As the corrosion level increases, the slip and relative displacement also increase.