# Assessment of Mechanical Properties of Corroded Prestressing Strands
## 2 Investigation of Corrosion in External Tendons
### Corrosion Inspection  
The corrosion on the strands along the length had very irregular pits, which made it difficult to determine the worst part of the corroded wire by visual inspection. To quantify the corrosion of the specimen, the ASTM G46-94 [8] corrosion measurement method was used, as introduced in a previous study [15]. This method uses a pit-depth gauge (Mitutoyo Corporation, Kanagawa, Japan) to measure the depth of the pit, as shown in Figure 2; however, this method is unable to evaluate the section loss. Therefore, as in the previous research, a section-loss evaluation method using the pit depth was suggested.  
Figure 3 illustrates five cases of corroded strands located near the anchorage and their cut sections. The samples had different levels of corrosion, and the corrosion pits were easily observed when the corrosion is severe. The five samples were divided into corroded and non-corroded parts. Because a high number of strands exist in a tendon bundle, one portion is exposed to the air and another portion is in contact with neighboring strands. This results in the corrosion being concentrated on several strands. These samples were not the specimens used in the tensile test, because the cut section pictures could not be taken before the tensile test.  
Figure 2: Measuring pit depth of corroded wire.  
Figure 4 shows an idealized model for the evaluation of each wire's actual section loss pattern and the section loss suggested by previous research [15]. Equations (1)-(3) were used for the evaluation of the section loss for each pattern, using only the measured pit depth of the corroded strands. This approach does result in errors between the actual and measured corrosion values, but it is the most feasible method for an onsite inspector to evaluate the corrosion, and therefore it was used in this research. The remaining corrosion residue on the extracted specimen was removed by a corrosion removal solution. Next, along the strand's length, the depth of the corrosion was measured every 20 mm using a pit-depth gauge, as shown in Figure 5. Excluding the core wire, which could not be evaluated for section loss, the degree of corrosion of each strand was evaluated as the summation of each section loss of the remaining six wires, as given in Equations (1)-(3). The highlighted part in Figure 5 is the section that was determined to be the most corroded (the highest section loss) by comparing the summations of the section losses.  
\[A_{sl,1}=2r^{2}\bigg{[}\arccos\bigg{(}1-\frac{d_{p}}{2r}\bigg{)}-\frac{1}{2} \sin\bigg{\{}2\arccos\bigg{(}1-\frac{d_{p}}{2r}\bigg{)}\bigg{\}}\bigg{]} \tag{1}\]  
\[A_{sl,2}=r^{2}\bigg{[}2\bigg{\{}\arccos\bigg{(}-\frac{d_{p}}{2r}\bigg{)}\bigg{\}}- \pi sin\bigg{\{}2\arccos\bigg{(}-\frac{d_{p}}{2r}\bigg{)}\bigg{\}}\bigg{]} \tag{2}\]  
\[A_{sl,3}=r^{2}\bigg{[}\arccos\bigg{(}1-\frac{d_{p}}{r}\bigg{)}-\frac{1}{2}sin \bigg{\{}2\arccos\bigg{(}1-\frac{d_{p}}{r}\bigg{)}\bigg{\}}\bigg{]} \tag{3}\]  
where \(A_{sl,1-3}\) are the losses of sectional areas according to the type of pit configuration, \(r\) is the radius of the wire, and \(d_{p}\) is the pit depth (from 0 to 2\(r\)) measured by a depth gauge at the deepest location.  
Figure 3: Corrosion of a strand near the anchor in Bridge B.