Flexural Capacity Prediction of Corroded PC Beams Incorporating Bond Degradation

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Bond strength degradation of corroded strands

Corrosion-induced cracking reduces the protective effect of cover on strand, and degrades the interlock, friction and bond properties between strand and concrete, which degrades the bond strength of strand. For PC structures, especially pre-tensioned concrete structures, the effective bond strength is a key factor to ensure the strand and concrete working together.
Many researches have been undertaken to investigate the bond behavior of corroded steels in RC structures, which can be concluded as: experimental research, theoretical analysis and numerical simulation [48]. Some scholars experimentally explored the bond-slip behavior of corroded steels with stirrup constraints [49-51]. Almusallam et al. [52] studied the bond strength and failure modes of corroded reinforced concrete beams with the pull-out tests. The effects of relevant parameters (concrete cover thickness, steel diameter, concrete strength, type of stirrups and crack widths) on bond performance of corroded steels have been discussed [53, 54]. Al-Hammoud et al. [55] compared the difference of bonding properties of corroded reinforced concrete beams under static and dynamic loads. Choi et al. [56] discussed the difference of the bond properties of concrete structures under natural corrosion and accelerated corrosion, and pointed out that the accelerated corrosion method may underestimate the effect of corrosion on the bond degradation. Additionally, some scholars had also discussed the bond degradation behavior of corroded reinforced concrete with common aggregates and recycled aggregates [57].
Some analytical models have also been proposed to predict the bond performance of corroded reinforced concrete beams. Wang et al. [58] pointed out that the bond strength between corroded steel and concrete was affected by many factors, such as the corrosion degree, bar type, the adjacent bar spacing and the number of stirrups. Among these factors, the corrosion degree is most significant to affect the bond strength. Coccia et al. [59] considered the relationship between corrosion depth of steel and the radial displacement of concrete, and proposed a model to predict the bond strength of corroded steel based on the thick-walled theory. Chen et al. [48] proposed a model to predict the bond strength of corroded RC beams, incorporating the softening behavior of cracked concrete.
Some scholars have employed the finite element software to numerically simulate the bond behavior of corroded RC beams. Lee et al. [60] used the bond plane unit and bond interface unit to numerically model the bonding properties of corroded RC beams. Berto et al. [61] simulated the bond properties of corroded RC beams with two numerical methods, i.e. the friction type method and damage type method. Lundgren et al. [62] discussed the influences of corrosion on the bonding properties of ribbed and plain bars, respectively. Grass et al. [63] used the Lattice approaches to simulate the bond properties of corroded RC beams, which can reasonably model the influence of filling extent of corrosion products in cracks.
The degradation law of bond performance after steel corrosion has been clarified. Abosrra et al. [64] indicated that the bond performance of steel would increase at the early stage of corrosion. As corrosion further increases, the bond performance of steel will gradually decrease. Kearsley et al. [65] pointed out that corrosion would lead to an increase in the bond strength when the corrosion loss of steel is less than 2%, and the bond strength decreases when the corrosion loss is greater than 2%. However, some other scholars indicated that a 2% diameter loss of steel would cause an 80% bond degradation. Chung et al. [66] pointed out that the critical corrosion loss of steel bond degradation was 3%. Wu et al. [67] showed that the failure mode of the corroded concrete members would change from the fracture failure of steel to the concrete crushing with corrosion increases. Bhargava et al. [68] reviewed the existing literatures on bond-slip of corroded steels, and proposed an empirical formula to predict the bond degradation of corroded RC beams.

Flexural capacity of corroded PC beams

Strand corrosion in concrete is one of the main factors for the degradation of structural performance. Corrosion can lead to the section area reduction of strand, the deterioration of mechanical properties of materials, concrete cracking and bond degradation. These factors will weaken the bearing capacity of concrete structures. Additionally, corroded PC beams often exhibit the brittle failure without warnings under high stress state, which is more danger than RC members. It is significant to investigate the flexural capacity of corroded PC beams for ensuring its safety operation.
Many experimental studies have been carried out to study the bending performance degradation of corroded RC beams. The failure mode of specimens changes from the bending failure to the shear failure with corrosion increases [78-80]. Relative to the studies on the flexural capacity of corroded RC beams, the researches on the flexural capacity of corroded PC beams is relatively rare. Some experimental studies investigate the effect of corrosion on cracking, stiffness, ultimate strength, ductility and failure mode of PC members [81]. It is found that corrosion can reduce the number of bending cracks and increase the crack spacing, and decrease the ultimate load of beams [76]. The bearing capacity decreased by 67% when the corrosion loss reached 20% [82].
Corrosion can reduce the section area of strand, deteriorate the material property, induce concrete cracking and degrade bond strength, which can further decrease the bearing capacity of PC beams. The bending capacity prediction model should reasonably consider the combined effects of these factors. Additionally, the aforementioned models fail to consider the effect of load cracks on the bending capacity of PC beams. The load cracks may change the bond strength in the longitudinal direction, which will affect the bending capacity. Neglecting the effect of flexural cracks may overestimate the flexural capacity of corroded PC beams. How to reasonably consider the aforementioned factors on the flexural capacity of corroded PC beams still needs to be studied further.

Crack width and corrosion loss measurement

Micro cracks form, firstly, in the cross-section when tangential stress exceeds the concrete tensile strength. With increasing corrosion loss, the internal cracks could propagate to the concrete surface. The outer cracks on the concrete surface usually extend and join together to be a continuous crack along the specimen, which is named a longitudinal crack in the present study. After the accelerated corrosion test, the longitudinal cracks were observed on the concrete surface. The longitudinal cracks have different widths in various regions due to the uncertainty of corrosion and material properties. A portable microscope with the resolution of 0.01 mm was used to measure crack widths.
To investigate the crack patterns in the radial direction and the filling of corrosion products in cracks, four 15 mm-thick cross-sectional slices were cut out from each beam after the accelerated corrosion. The location of the four slices is shown in Fig. 2.1 and labeled as A, B, C, and D, respectively. For example, the four slices of S6 are named as S6A, S6B, S6C, and S6D, respectively. The total number of slices was 48. The cracking angle was used to describe the crack distribution in the radial direction. Since the filling of corrosion products in cracks varied at different positions, the average rust-filling depth was used to reflect the filling of corrosion products in cracks.
The cracking angle was measured using a contour gauge. In the present testing, the maximum crack was selected to calculate the cracking angle. The measurement program was as follows: first, the contour shapes of cracks in the radial direction were painted to graph paper; next, the sketch maps of cracks were scanned into the computer. The cracking angle was defined as the angle of two sides of the crack; finally, the cracking angles were calculated by the aided drafting program. More details on the contour gauge can be seen in Higgins and Farrow [101]. The rust-filling depth was also measured using similar methods.
Strand corrosion exhibited variability in various regions. Local area loss and average mass loss were commonly used to evaluate the corrosion degree of strand. Some experimental studies showed that the average mass loss correlated well with the corrosion-induced crack widths for slightly corroded reinforcement [102]. In the present experimental testing, slight corrosion loss was found to induce cover cracking due to the large diameter of strand. Therefore, the average mass loss of the strand in 10 mm lengths was also employed to evaluate the corrosion degree.
The mass loss was measured after the accelerated corrosion, and the program was as follows. First, concrete cover was removed by the destructive method. Next, the strand was taken out and the concrete on its surface was removed by slightly knocking. Following this, the corroded strand was cleaned by 12% hydrochloric acid solution and then neutralized with alkali [103]. The strand was kept in the dry environment (relative humidity less than 25%). Finally, the average mass loss of the strand in 10 mm length was measured.

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Corrosion morphology, cracking propagation, and corrosion loss

Strand used in the present study includes the core wire and six outer wires. Fig. 2.3 shows the corrosion morphology of the strand. The strand showed pitting and crevice corrosion. Some small corrosion pits were observed on the strand surface. These corrosion pits exhibited oval or circle and their depths were small. Additionally, the gaps existed between the core wire and outer wires and could provide a path for the flow of aggressive liquid, resulting in crevice corrosion.
The movement of corrosive liquid along the crevices can lead to the range extension of corrosion along the strand, which will accelerate the corrosion rate of the strand. Corrosion loss in the strand can be higher than in steel reinforcement due to crevice effects, resulting in a larger corroding area per unit length. The corrosion rate of the steel increases with the increase of current density. The uniform corrosion occurred with a low current density. For a high current density, pitting corrosion occurred extensively on the steel surface [104]. In the present test, the current density was designed as the constant value. More studies on various current densities are needed in the future.

Crack width and corrosion loss

With corrosion propagation, the first visible crack was found through the portable microscope. The crack then widened and extended along the corroded strand. Some corrosion products were found to flow out from the longitudinal cracks. Fig. 2.4 shows corrosion products on the concrete surface from 10 mm to 110 mm for S6, S11, and S9, respectively. The average crack widths of S6, S11, and S9 are 0.13, 0.48, and 0.83 mm, respectively. Scarce corrosion products were found to flow out from the narrow longitudinal cracks. With cracking propagation, more corrosion products appeared on the concrete surface. The filling of corrosion products propagates with the widening crack.

Composition of corrosion products

The compositions of corrosion products depends on the alkalinity degree, the oxygen supply, and the moisture content [107]. Corrosion products also exhibit various colors at different regions in the present study. Three colors of corrosion products were observed: black, brownish-red, and puce. Fig. 2.11 shows the black rust at the strand-concrete interface. The cover prevents the oxygen to reach the strand-concrete interface. For the reaction with some oxygen, the main compositions of corrosion products are ferrous oxide (FeO) and ferroferric oxide (Fe3O4) [33, 95]. The colors of FeO and Fe3O4 are black. FeO is unstable and can easily become Fe3O4 in air. Therefore, Fe3O4 is considered as the primarily composition of black rust.

Table of contents :

Chapter 1. Introduction
1.1 Backgrounds and significances
1.2 Literatures review
1.2.1 Corrosion morphology of strands
1.2.2 Corrosion-induced concrete cracking
1.2.3 Bond strength degradation of corroded strands
1.2.4 Corrosion-induced prestress loss
1.2.5 Flexural capacity of corroded PC beams
1.3 Discussions of existing researches
1.4 Layout of the dissertation
1.5 Summary
Chapter 2. Concrete Cracking Prediction Including the Filling Proportion of Strand Corrosion Products
2.1 Introduction
2. 2 Experimental program
2.2.1 Specimen details
2.2.2 Accelerated corrosion of the strand
2.2.3 Crack width and corrosion loss measurement
2.3 Experimental results and discussions
2.3.1 Corrosion morphology, cracking propagation, and corrosion loss
2.3.2 Filling of corrosion products in cracks
2.4 Prediction model of crack propagation
2.4.1 Corrosion products at the micro-crack formation
2.4.2 Crack width on the concrete surface
2.4.3 Validation of the prediction model
2.5. Conclusions
Chapter 3 Crack Width Prediction under Combined Prestress and Strand Corrosion . 
3.1 Introduction
3.2 Experimental program
3.2.1 Details of specimens
3.2.2 Accelerated corrosion and corrosion product measurement
3.2.3 Measurement of crack width and corrosion loss
3.3 Experimental results and discussions
3.3.1 Expansion ratio of strand corrosion products
3.3.2 Crack propagation under various prestress
3.4 Prediction of corrosion-induced cracking in PC beams
3.4.1 Model for corrosion-induced cracking
3.4.2 Model validation
3.5 Conclusions
Chapter 4 Prestress Loss Prediction in Pre-tensioned Concrete Structures with Corrosive Cracking
4.1 Introduction
4.2 Model for prestress loss in corroded PT structures
4.2.1 Concrete cracking induced by strand corrosion
4.2.2 Bond degradation due to strand corrosion
4.2.3 Corrosion-induced prestress loss
4.3 Evaluation of effective prestress in corroded PT beams
4.3.1 Specimen details
4.3.2 Accelerated corrosion and corrosion loss measurement
4.3.3 Effective prestress evaluation under various stress levels
4.3.4 Validation on prestress loss model
4.4 Conclusions
Chapter 5 Flexural Capacity Prediction of Corroded PC Beams Incorporating Bond Degradation
5.1 Introduction
5.2 Concept of flexural capacity model
5.3 Bond strength of corroded strand considering flexural cracks
5.3.1 Corrosion-induced cracking and bond degradation
5.3.2 Equivalent bond strength considering flexural cracks
5.4 Calculation procedure of flexural capacity
5.5 Model validation
5.6 Conclusions
Chapter 6 Conclusions and Perspectives
6.1 Conclusions
6.2 Perspectives


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