Open AccessArticle

The Effect of the Corrosion Degree of Prestressed Steel Reinforcements on the Strain of Concrete Box Girders: An Experimental Fatigue Study

Zhao-Yuan Zhang

¹,

Ping Wei

¹,

Peng Cao

and

Hai-Bin Huang

^3,*

CCCC Third Highway Engineering Co., Ltd., Beijing 100020, China

College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China

School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin 300401, China

Author to whom correspondence should be addressed.

Buildings 2025, 15(5), 655; https://doi.org/10.3390/buildings15050655

Submission received: 20 December 2024 / Revised: 15 January 2025 / Accepted: 17 January 2025 / Published: 20 February 2025

(This article belongs to the Topic 3D Computer Vision and Smart Building and City, 2nd Volume)

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Figure 1
Arrangement of prestressed reinforcement in the test beam (cm). (a) Half elevation of vertical arrangement of longitudinal prestressed reinforcement in the test girder. (b) Distribution of prestressed reinforcement in the section of the pivot point. (c) Distribution of prestressed reinforcement in mid-span section. "> Figure 2
Arrangement of ordinary reinforcement in the test beam (cm). (a) Half elevation of ordinary reinforcement in test beam. (b) Distribution of ordinary reinforcement in the pivot section. (c) Distribution of ordinary reinforcement in mid-span section. "> Figure 3
Structural drawing of corrosion tank. "> Figure 4
CAD schematic diagram of the loading experiment (cm). "> Figure 5
Test beam load–deflection curve at mid-span. "> Figure 6
Schematic diagram of test beam S1’s elevation cracks. "> Figure 7
Fracture surface of corroded prestressed strand wire in this test. "> Figure 8
All fracture surfaces and fracture modes of the strand wires at the breakage location. "> Figure 9
Crack distribution in the final stage of fatigue loading of test beams. (a) F-0. (b) F-4. (c) F-8. "> Figure 10
Strain changes in ordinary steel reinforcements under fatigue loading. (a) F-0: load–ordinary reinforcement strain curve. (b) F-0: variation in strain with number of fatigue loadings in ordinary steel reinforcement. (c) F-4: load–ordinary reinforcement strain curve. (d) F-4: variation in strain with number of fatigue loadings in ordinary steel reinforcement. (e) F-8: load–ordinary reinforcement strain curve. (f) F-8: variation in strain with number of fatigue loadings in ordinary steel reinforcement. "> Figure 10 Cont.
Strain changes in ordinary steel reinforcements under fatigue loading. (a) F-0: load–ordinary reinforcement strain curve. (b) F-0: variation in strain with number of fatigue loadings in ordinary steel reinforcement. (c) F-4: load–ordinary reinforcement strain curve. (d) F-4: variation in strain with number of fatigue loadings in ordinary steel reinforcement. (e) F-8: load–ordinary reinforcement strain curve. (f) F-8: variation in strain with number of fatigue loadings in ordinary steel reinforcement. "> Figure 11
Strain variation in prestressed reinforcements under fatigue loading. (a) F-0: load–prestressed reinforcement strain curve. (b) F-0: relationship between strain and number of fatigue loadings of prestressed reinforcement. (c) F-4: load–prestressed reinforcement strain curve. (d) F-4: relationship between strain and number of fatigue loadings of prestressed reinforcement. (e) F-8: load–prestressed reinforcement strain curve. (f) F-8: relationship between strain and number of fatigue loadings of prestressed reinforcement. "> Figure 12
The ratio between the strain amplitude of prestressed reinforcements and ordinary reinforcements under fatigue loading. "> Figure 13
Concrete strain changes in the compression zone of test beams during fatigue loading. (a) F-0: relationship between load and concrete strain in the compression zone. (b) F-4: relationship between load and concrete strain in the compression zone. (c) F-8: relationship between load and concrete strain in the compression zone. "> Figure 14
Relationship between cumulative residual strain of concrete in the compression zone and the amount of fatigue loading. "> Figure 15
Comparison between calculated and test data curves of cumulative residual strain of concrete in compression zone. ">

Versions Notes

Abstract

In order to investigate the relationship between the strain of prestressed concrete girders under fatigue loading and the corrosion degree of prestressed steel reinforcements, four 12.4-m-long large-size post-tensioned prestressed concrete box girders were designed and fabricated in this study, and prestressed steel reinforcements were corroded at different degrees by the Electric Accelerated Corrosion Method. The same equal-amplitude loads were used during fatigue loading. The relationship between the strain of different materials (strains of the plain reinforcements and prestressed steel reinforcements, as well as concrete strains in compression zones) and the corrosion degree was investigated. Then, the calculation method for the cumulative residual strain of concrete in the compression zone of the test beam was obtained. The test results show the following: the strains of the test beams under different corrosion degrees all show a three-stage development law; the ratio of the strain amplitude of the prestressed steel reinforcement to that of the regular steel reinforcement during fatigue loading basically stays in the range of 0.65–0.75, and the ratio rises with the corrosion degree of the prestressed steel reinforcement; the increase in strain of the compressed concrete is due to the accumulation of the residual strain of the concrete, and the increase in material strain is almost directly proportional to the growth of corrosion degree under the same fatigue load; the calculated values of the accumulated residual strain of the concrete agree well with the test values and satisfy the accuracy requirements of engineering.

Keywords:

prestressed concrete box girders; corrosion of the prestressed steel reinforcement; fatigue experiment; performance under fatigue loading; strain analysis

1. Introduction

Prestressed concrete structures are now being used more and more widely due to their advantages. During their service life, they will be subjected to repetitive loads, such as vehicle and wind loads, and at the same time will be subjected to the corrosion effects of the environment [1]. High-cycle tensile fatigue tests on corroded steel reinforcements have shown that fatigue behavior is more sensitive to corrosion than static tensile behavior [2], the performance of prestressed concrete girders is degraded under the combined effect of fatigue and corrosion, and that grids are highly susceptible to brittle damage after fatigue corrosion. Naito et al. [3] carried out a series of forensic analyses on beams decommissioned from a bridge. Their research shows that, in prestressed concrete girders, prestressed strands are highly susceptible to corrosion damage in harsh environments. Li et al. [4] investigated the damage forms of corroded strands and analyzed the mechanism of loss of the prestressing force. Their study shows that both the mass loss of the corroded part and the corroded length have a significant effect on the prestress loss. The corrosion of prestressed strands usually has a greater impact on structures than the corrosion of ordinary steel bars for several reasons: (1) high-strength-grade steel is more sensitive to corrosive effects; (2) prestressed strands are in a high stress state and are subject to a greater degree of stress corrosion, which can accelerate corrosion efficiency [5]; (3) the cross-sectional area of prestressed strands is relatively small compared to that of ordinary steel reinforcements, and if a thin layer of corrosion or even a pitting corrosion is produced by corrosion, the relative area of the prestressed strand will be greatly reduced, in addition to the prestressed strand itself being subject to high stress, which will cause a large stress concentration phenomena. At the present time, the existing research work mainly focuses on the corrosion mechanism of corroded prestressed strands, tensile property degradation, and the mechanical property degradation of corroded strands in prestressed concrete structures under static loading [4,6,7,8,9,10,11,12].

Relevant studies show that during the fatigue process of concrete, the internal microstructure, microcracks, and other microscopic variables will produce great changes, which cause the fatigue damage to keep increasing and cause the gradual deterioration of macroscopic mechanical properties [13]. Among these, the residual deformation of concrete can reflect the irreversible development of concrete, which can be used as a macroscopic physical measure of concrete material damage to describe the degree of damage.

For the calculation of residual strain in the concrete compression zone, Wu et al. [14] of Tsinghua University conducted a large number of concrete fatigue tests and proposed a fatigue residual strain accumulation model considering the fatigue stress ratio and the number of cycles of concrete. Feng [15] conducted equal-amplitude fatigue tests on prestressed concrete beams with nine sets of different stress ratios, considering the upper limit of the fatigue stress in concrete, and obtained a formula for calculating the cumulative residual strain in concrete. Holmén [16] considers the effect of the upper and lower limits of fatigue stresses in concrete to derive an equation for calculating the cumulative residual strain in concrete. Jia et al. [17] study the relationship between the strain and corrosion levels of prestressed concrete beams under fatigue loading. The results of the study showed that the corrosion of the steel reinforcement led to an increase in the strain of the concrete under the same load, and the residual strain of the concrete increased with the increase in the cyclic cycle, showing a clear three-phase characteristic.

This study focuses on investigating the fatigue behavior of partially prestressed concrete girders and the corrosive effects of prestressed strands, and four 12.4 m long partially prestressed concrete box girders were fabricated for this. One of the test beams, S-0, was used as a stationary load to determine the relevant static load performance, as well as to determine the reasonableness of the cross-section dimensions and reinforcement design, to provide a reference basis for fatigue loading to compare with the fatigue test. In addition, different degrees of corrosion were enforced via the method of applying an electric current to the prestressed strands of the two test beams (F-4, F-8). Then, fatigue loads were applied to three girders with different corrosion rates of prestressed strands (including an uncorroded test girder, F-0) in order to investigate the effect of the corrosion of the prestressed strands on the strain of the partially prestressed concrete girders, and to give a method for calculating the cumulative residual strain of concrete in the compression zone of the test girders. The results of this study provide a reference for investigating the effect of corrosion degree on the properties of prestressed concrete.

2. Program of Experiments

2.1. Design of Experimental Beams

In this study, with reference to the ‘Specifications for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts (JTG 3362-2018)’, four post-tensioned bonded prestressed concrete box girders were designed and fabricated with a beam width of 1.2 m, height of 0.8 m, calculated span of 12.0 m, and prefabricated length of 12.4 m, weighing 18.6 t. They were configured with four bundles of bending prestressed reinforcements (each prestressed reinforcement bundle contained 6 strand sets, each consisting of 7 strands of

φ^{s} 15.2

). In order to diffuse the stress of the tension anchorage, prevent the concentration of concrete stress, and reduce the stress per unit area of concrete, the test beam section was set as a variable section, and the web and bottom plates were thickened at the end of the beam. The arrangements of the prestressed reinforcements and ordinary reinforcements in the test beams are shown in Figure 1 and Figure 2, respectively.

The test beams are constructed with C50 concrete, and there are two kinds of ordinary steel reinforcement in the test beams: 12 mm and 16 mm in diameter. The longitudinal reinforcement (①) type is HRB400, being 16 mm in diameter, and the rest of them are structural reinforcements. The structural reinforcement type is HRB335, being 12 mm in diameter, and the prestressed reinforcement adopts 1 × 7 strands of 1860-grade steel strands.

2.2. Corrosion Tests on the Prestressed Reinforcement

In this test, only the prestressed reinforcements within 1.5 m of the pure bending section in the span of the test beams were corroded. In this experiment, only the prestressed tendons within the 1.5 m pure bending section in the mid-span of the corrosion test beams were corroded. The corrosion of the steel strands was accelerated using a direct current (DC) corrosion method, with the main steps as follows: A corrosion tank was prepared (as shown in Figure 3) with sponges soaked in 5% NACL solution. The stainless-steel pipe in the tank served as the cathode, the prestressed reinforcement in the test beam acted as the anode, and 5% NACL solution served as the medium. DC power was then applied to initiate the corrosion. During the corrosion process, it was essential to periodically calibrate the DC regulated power supply to ensure consistent current flow for both test beams. The designed corrosion rates for the prestressed reinforcements were 4% and 8%, respectively, which, according to Faraday’s law [18], required charging durations of 757.5 h and 1515 h. After the specimens failed during testing, the actual measured corrosion rates were 3.23% and 6.86%.

2.3. Experimental Loading Program

Since this study primarily investigates the flexural fatigue performance of prestressed concrete box girders under normal section conditions, a two-point symmetric loading method was adopted to create a pure bending section. Considering the limitations of laboratory loading conditions and the safety of personnel, a 1.5 m pure bending section was established in the mid-span. The total length of the test beam was 12.4 m, with an effective span of 12.0 m. Given that the test beam weighed 18.6 t, a sliding hinge support system was simulated by placing two polytetrafluoroethylene (PTFE) plates under the hinge support of the test beam, with lubricating oil applied between the plates to minimize friction. The loading setup is illustrated in Figure 4. All loading procedures strictly adhered to the “Standards for Test Methods of Concrete Structures (GB/T 50152-2012)”, and the fatigue test methodology was developed with reference to the “Fatigue Test Methods for Simply Supported Prestressed Concrete Beams (TB/T 2326-1992)”.

A static load test was conducted on a test beam (S-0) with uncorroded prestressed reinforcements, utilizing a 200-t jack for incremental loading. For the fatigue test, a dynamic electro-hydraulic servo actuator was used to apply constant amplitude loading. Based on the ultimate bearing capacity

P_{u}

under the static load of the uncorroded beam F-0, beams F-0, F-4, and F-8, with actual prestressed reinforcement corrosion rates of 0%, 3.23%, and 6.86%, respectively, were subjected to the same fatigue stress range. The fatigue load upper limits were set to 0.4

P_{u}

of the ultimate static capacity, while the lower limits were set to 0.05

P_{u}

[19,20,21]. Prior to applying the fatigue load, a 12-level incremental loading process up to the fatigue load upper limit was conducted, followed by unloading. Fatigue loading commenced immediately after the static loading. Concrete strain gauges were arranged along one side of the mid-span cross-section from top to bottom, while strain gauges for the ordinary reinforcements and prestressed reinforcements were placed at both loading points and at the mid-span. At each load increment, concrete strain, rebar strain, and crack width were recorded. Fatigue testing was paused after cumulative cycles of 0, 1000, 10,000, 20,000, 50,000, 100,000, 300,000, 500,000, 800,000, 1 million, 1.5 million, and 2 million, during which a cyclic static load test was performed to measure relevant data. If no fatigue failure occurred after 2 million cycles, fatigue loading was terminated.

3. Determination of Parameters for Fatigue Tests

Taking into account various factors, the fatigue test adopted sine wave loading with a loading frequency of 1.5 Hz. To accurately determine the fatigue stress level of the test beam during fatigue testing, a static load failure test was conducted on test beam S-0. The ultimate load-bearing capacity of the beam was measured to be 1764 kN. The load-deflection curve for beam S-0 is shown in Figure 5. During static loading, initial cracks appeared on the inner side of the pure bending segment near the loading point, predominantly in a vertical orientation. Subsequently, vertical cracks appeared in the web of the bending–shear segment. As the static load increased, the number of inclined cracks in the web increased progressively. The failure mechanism of the test beam initiated with the yielding of the ordinary tensile reinforcement, followed by a sudden crushing of concrete on the compression side near the loading point in the mid-span region. This failure mode, characterized as a typical bending failure, indicates that the beam’s reinforcement is appropriately designed, classifying it as a moderately reinforced beam. The failure pattern is illustrated in Figure 6.

4. Results and Discussion of Fatigue Tests

The purpose of conducting fatigue testing on specimen F-0 was to investigate the fatigue performance of the test beam under normal service conditions (with a target fatigue life of ≥2 million cycles). The results indicated that F-0 achieved the target fatigue life of 2 million cycles. Fatigue tests on specimens F-4 and F-8 were conducted to study the fatigue performance of partially prestressed concrete beams following corrosion of the prestressed steel strands. Specimen F-8 exhibited fatigue failure at 860,182 cycles, whereas specimens F-0 and F-4 did not experience fatigue failure after 2 million cycles of fatigue loading. The results of the fatigue tests are presented in Table 1.

During the fatigue testing of specimen F-8, an audible sound indicative of rebar fracture was clearly heard in the laboratory when the load cycle count reached 860,182. Upon dismantling the fractured specimen and extracting the reinforcement, it was observed that no fatigue fractures had occurred in the ordinary reinforcement bars of specimen F-8. However, significant fatigue fractures were evident in the prestressed steel strands, with no signs of necking deformation. The fractured surfaces of the corroded prestressed steel wires from this test are shown in Figure 7. Since the prestressed steel strand comprises multiple wires, unlike conventional tensile reinforcements, the strand does not experience uniform stress distribution during loading. Therefore, one wire tends to fracture first, marking the initiation of fatigue failure. A schematic representation of the fractured region of the steel strand is provided in Figure 8. Consequently, even after the fracture of some strands, the test beam was able to continue supporting a certain level of load [22].

At approximately 10,000 cycles of fatigue loading, the majority of cracks on the test beams had fully developed, with the number of cracks remaining essentially constant. However, both the height and width of these cracks gradually increased, a trend that became particularly pronounced with higher levels of prestressed steel corrosion. The corrosion of the prestressed reinforcements generated rust-induced expansive forces that contributed to concrete cracking and weakened the bond strength between the steel and concrete. Compared to the uncorroded test beams, the maximum crack width of the corroded beams increased with the corrosion rate under the same load level. Additionally, for a given fatigue load cycle count, the number of cracks decreased as the corrosion rate increased. During the loading process, the “breathing” of cracks in response to fatigue cycles was clearly visible to the naked eye. The final crack distribution on the test beams at the end of loading is illustrated in Figure 9, showing the crack distribution of beams F-0 and F-4 after 2 million fatigue cycles.

4.1. Strain Analysis of Steel Reinforcements During Fatigue Experiment

4.1.1. Law of Development of Strain in Ordinary Steel Reinforcements

The strain variation curve of the ordinary reinforcements under fatigue loading is shown in Figure 10. Both existing standards and recent studies indicate that the fatigue life of ordinary and prestressed reinforcements is influenced by stress amplitude. Thus, Figure 10 also presents the maximum and minimum strain values of the ordinary reinforcements, corresponding to the upper and lower limits of fatigue loading, as well as the relationship between strain amplitude and fatigue loading cycles. The following patterns can be summarized from Figure 10:

After the test beam cracks, stress redistribution occurs within the beam, and the tensile concrete region ceases to carry load, transferring its stress entirely to the reinforcement. Consequently, during the initial static loading phase, the ordinary reinforcement strain exhibits a marked inflection point near the cracking load, demonstrating a two-stage variation pattern.
For specimen F-8, as fatigue loading progresses to failure, the prestressed tendon fractures first, causing a sudden change in strain in the ordinary reinforcement. The strain in the ordinary reinforcement shows a distinct three-stage development: a rapid increase in strain within the initial 10,000 cycles, a slower progression in the intermediate phase, and a sharp increase in the latter phase of fatigue loading. As the corrosion rate of the prestressed tendons increases, the strain (including strain amplitude) in the ordinary reinforcement within the test beam also increases, with an accelerated rate of change. For example, at 500,000 cycles, the maximum strain values for beams F-0, F-4, and F-8 were 785.7 με, 982.8 με, and 1215.8 με, respectively, and the strain amplitudes were 806.2 με, 900.8 με, and 1043.4 με.
Due to the presence of prestress in the test beams, the ordinary reinforcement at the bottom of the beam undergoes cyclic loading between tension and compression during the initial phase of fatigue loading. Significant residual strain develops in all three test beams over the course of fatigue loading, which may be attributed to fatigue damage in the concrete in the compression zone and the formation of non-closable cracks in the concrete around the ordinary reinforcement.

4.1.2. Laws of Strain Development in Prestressed Reinforcements

The strain behavior of the prestressed reinforcements under fatigue loading is illustrated in Figure 11. In Figure 11, a dual y-axis is used to depict the maximum and minimum strain values of the prestressed reinforcements corresponding to the upper and lower limits of fatigue loading, as well as the variation in strain amplitude with increasing fatigue cycles. The following observations can be made from Figure 11:

The strain in the prestressed reinforcements also exhibits a slope change at the cracking load, displaying a distinct three-stage pattern. As fatigue loading progresses, significant residual strain is observed, with a pattern similar to that of ordinary reinforcement, which will not be reiterated here. However, in the corroded beams, F-4 and F-8, there is a notable strain increase in the later stages of fatigue loading, particularly in strain amplitude, which reduces the fatigue life and raises the likelihood of fatigue fracture at pitting corrosion points in the prestressed reinforcements.
Compared to the strain increase observed in prestressing reinforcements during fatigue loading, corrosion has minimal impact on the initial strain (i.e., static load strain during the first cycle of fatigue) of the prestressed reinforcements.

4.1.3. Laws of Strain Amplitude Ratio Development of Steel Reinforcements

Based on the fatigue test results from the previous section, the strain amplitudes of the ordinary reinforcements and prestressed reinforcements were normalized, resulting in the variation in the ratio of the prestressed reinforcement strain amplitude

Δ ε^{p}

to the ordinary reinforcement strain amplitude

Δ ε^{s}

with the number of fatigue loading cycles, as shown in Figure 12. Figure 12 illustrates that the

Δ ε^{p}

Δ ε^{s}

ratio follows a three-stage pattern throughout the loading process. In the initial stage, cracks appear at the bottom of the test beam, and because the ordinary reinforcement is positioned significantly lower than the prestressed reinforcement, the strain in the ordinary reinforcement increases more rapidly than in the prestressed reinforcement, causing the

Δ ε^{p}

Δ ε^{s}

ratio to decrease. In the second stage, a stable phase is observed, with the

Δ ε^{p}

Δ ε^{s}

ratio remaining relatively constant. During the final phase of fatigue loading, as the corrosion rate of the prestressed reinforcement increases, the strain amplitude in the prestressed reinforcement rises significantly, resulting in an increase in the

Δ ε^{p}

Δ ε^{s}

ratio. Although the corroded test beam F-4 did not fail, the

Δ ε^{p}

Δ ε^{s}

ratio also increased in the later loading stages, with all three fatigue test beams exhibiting ratios generally within the range of 0.65–0.75.

Overall, as the corrosion rate of the prestressed reinforcements increases, the

Δ ε^{p}

Δ ε^{s}

ratio also rises, indicating that tendon corrosion impacts the stress distribution within the test beam, resulting in an increased strain amplitude in the prestressed reinforcements and potentially leading to fatigue failure in the prestressed reinforcements prior to that in the ordinary reinforcements.

4.2. Strain Analysis of Concrete in the Compression Zone During Fatigue

4.2.1. Laws of Concrete Strain Development in the Compression Zone

The strain in the concrete compression zone at the top of the beam’s pure bending section under fatigue loading is shown in Figure 13. The following observations can be drawn from Figure 13:

Under fatigue loading, the strain in the concrete compression zone exhibits a three-stage progression. In the initial 10,000 cycles, the strain in the compression zone changes rapidly, with this effect being more pronounced as the corrosion rate increases. In the second stage of fatigue loading, the strain curve becomes denser, and the strain rate in the compression zone slows down. In the third stage of fatigue development, specimen F-8 shows an accelerated strain increase in the concrete compression zone.
Under high-cycle fatigue loading, as the number of cycles increases, the plastic deformation in the compression zone of the concrete gradually diminishes, eventually stabilizing. The stress–strain relationship of the concrete becomes increasingly linear, reflecting the internal crack propagation in the concrete. Consequently, the load–strain curve of the concrete in the compression zone of the test beams gradually approaches a linear form. Due to material damage from fatigue, the elastic modulus of the concrete continues to decrease, resulting in a gradual reduction in the slope of the load–strain curve for the concrete in the compression zone.
By the final loading stage (2 million cycles for beams F-0 and F-4, and fatigue failure for beam F-8), the strain growth in the compression zone of the concrete relative to the initial state is 143.8 με, 209.9 με, and 305.6 με, respectively. This indicates that as the corrosion rate of the prestressed reinforcements increases, the concrete strain also increases. Throughout fatigue loading, significant residual strain accumulates in the concrete, with total strain increases in the compression zone primarily attributed to residual strain accumulation. Further analysis of the difference between the total strain growth and residual strain growth in the compression zone shows values of 62.7 με, 93.4 με, and 145.7 με for the three beams, demonstrating that the increase in total strain is primarily due to residual strain in the concrete compression zone.
By the final stage of loading (2 million cycles for beams F-0 and F-4, and fatigue failure for beam F-8), the strain increases in the concrete compression zone relative to the initial state are 143.8 με, 209.9 με, and 305.6 με for the respective beams. This indicates that as the corrosion rate of the prestressed tendons increases, the strain in the concrete also increases. During fatigue loading, significant residual strain accumulates progressively within the concrete. Further analysis reveals that the difference between the total strain increase and the residual strain increase in the compression zone is 62.7 με, 93.4 με, and 145.7 με for the three beams, respectively. This observation suggests that the overall increase in concrete strain in the compression zone is primarily attributable to the accumulation of residual strain.

When the accumulated fatigue residual strain of the concrete

ε_{cr} (n)

reaches 0.4 times, its ultimate compressive strain under static loading, the concrete sustains severe damage and can no longer be used safely [23]. Therefore, studying the residual strain behavior of concrete during fatigue loading is an effective approach to understanding material damage in concrete. An analysis of the experimental data produced the curve shown in Figure 14, which illustrates the variation in the accumulated residual strain of the concrete in the compression zone of the test beams as a function of fatigue load cycles.

As shown in Figure 14, the accumulated residual strain in the concrete compression zone of the test beams generally follows a three-stage progression: in the first and third stages, the residual strain in the compression zone increases rapidly and exhibits a nonlinear trend, while in the second stage, the growth rate is slower and approximately linear. The magnitude of accumulated residual strain in the concrete for the three test beams is roughly proportional to the corrosion rate. Figure 14 also indicates that the accumulated residual strain in the concrete compression zone remains well below 0.4 times the ultimate compressive strain under static loading, or 563 με. This further supports the conclusion that fatigue failure in corroded prestressed concrete beams during the fatigue process is unlikely to be due to concrete failure.

4.2.2. Calculation of Concrete Strain in the Compression Zone

Based on studies [14,15,16] in the literature and the extensive fatigue testing of concrete prisms, the expression for the accumulated residual strain of concrete after n cycles under constant-amplitude fatigue loading is derived as follows:

ε_{cr} (n) = α n^{t}

(1)

where

α

is a coefficient related to the upper and lower stress limits of the fatigue load sustained by the concrete, and

t

is a constant value derived from the regression of the experimental data.

Holmén [16] comprehensively considered the effects of the upper and lower stress limits (

σ_{\max}^{c}

σ_{\min}^{c}

) of concrete and calculated the cumulative residual strain of concrete using the following formula.

ε_{cr} (n) = [\frac{f_{c}}{E_{c}} \lg^{- 1} (p_{1} α_{r} + q_{1})] \cdot n^{v_{1}}

(2)

where

f_{c}

is the initial compressive strength of concrete,

E_{c}

is the initial elastic modulus of concrete, and

p_{1}

q_{1}

, and

v_{1}

are fitting coefficients. In addition, the value of

α_{r}

is calculated using the following formula:

α_{r} = \frac{σ_{\max}^{c} - σ_{\min}^{c}}{f_{c} - σ_{\min}^{c}}

(3)

Although the upper and lower limits of the fatigue load on the tested beams remain the same, due to the corrosion of the prestressed reinforcements, which leads to a reduction in the effective area of the tendons and a subsequent decrease in effective prestress, the stress sustained by the concrete inevitably varies. Based on the above research and analysis, and considering that the cumulative residual strain of concrete in the compressive zone of corroded prestressed concrete beams exhibits a log-linear relationship with the number of fatigue loading cycles [24], this paper describes the impact of the corrosion rate of prestressed reinforcements on the cumulative residual strain of concrete. The calculation formula for the cumulative residual strain of concrete is derived as follows:

ε_{cr} (n) = [\frac{f_{c}}{E_{c}} \lg^{- 1} (p_{2} α_{r} + q_{2})] \cdot n^{a_{5} + b_{5} η_{0}}

(4)

where p₂, q₂, a₅, b₅ are fitting factors.

By fitting the experimental results of the residual strain in the compressive zone of concrete presented in Section 4.2.1, the following parameters were obtained: p₂ = −4.99963, q₂ = 4.13827, a₅ = 0.24875, and b₅ = 0.91486. A comparative analysis between the calculated cumulative residual strain curve of concrete derived from Equation (4) and the experimental data is shown in Figure 15. It can be observed that the calculated curve aligns well with the experimental data, meeting the accuracy requirements for engineering applications.

5. Conclusions

The fatigue lives of test beams F-0 and F-4 both exceeded 2 million cycles. However, with an increase in the prestressed reinforcement corrosion rate to 6.86%, the fatigue life of test beam F-8 sharply decreased to 860,200 cycles, losing the typical characteristics of non-prestressed tendon failure. The failure of F-8 was marked by the fracture of an individual steel wire within the prestressed reinforcement, rather than complete tendon fatigue rupture. The fracture surface exhibited typical macroscopic brittle characteristics without any observable necking deformation.
Compared to the uncorroded test beams, at the same number of fatigue load cycles, the width of the main cracks increased with the increase in the corrosion rate of the prestressed reinforcements, while the number of cracks decreased. By the time fatigue loading reached 10,000 cycles, the cracks on the test beams were fully developed, with the number of cracks remaining constant thereafter. Only the height and width of the cracks gradually increased, a trend that became more pronounced as the corrosion rate of the prestressed reinforcements increased.
With the increase in the corrosion rate of the prestressed reinforcements, the coupling effect with fatigue becomes more pronounced, resulting in greater cumulative fatigue damage and consequently a more significant reduction in the overall fatigue performance of the test beams. During fatigue loading, the strain in the ordinary reinforcements, prestressed reinforcements, and compressive-zone concrete of the test beams displayed a three-stage development trend: rapid development in the initial stage of fatigue loading and just before fatigue failure, with a relatively stable progression in the intermediate stage.
During fatigue loading, the ratio of strain amplitude in the prestressed reinforcements $Δ ε^{p}$ to that in the ordinary reinforcements $Δ ε^{s}$ generally remained between 0.65 and 0.75. This ratio tended to increase with the corrosion rate of the prestressed reinforcements.
Throughout fatigue loading, the increase in the total strain in the compressive zone of the concrete was primarily due to the accumulation of residual strain. Based on the pattern of residual strain development and considering factors such as the corrosion rate of the prestressed reinforcements and the number of fatigue loading cycles, a method for calculating the cumulative residual strain in the compressive zone of the concrete of corroded prestressed concrete box beams was established. The calculated values showed good agreement with the experimental values, meeting the accuracy requirements for engineering applications.

Author Contributions

Methodology, H.-B.H.; Formal analysis, P.C.; Investigation, P.W.; Data curation, Z.-Y.Z.; Writing—original draft, Z.-Y.Z.; Writing—review & editing, H.-B.H.; Visualization, P.W.; Supervision, P.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

Authors Zhao-Yuan Zhang and Ping Wei were employed by CCCC Third Highway Engineering Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Nomenclature

PTFE	Polytetrafluoroethylene
P_u	Ultimate bearing capacity
N^f	Fatigue life (ten thousand times)
Δε^p	Prestressed reinforcement strain amplitude
Δε^s	Ordinary reinforcement strain amplitude
ε_cr(n)	Accumulated fatigue residual strain of concrete

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Figure 1. Arrangement of prestressed reinforcement in the test beam (cm). (a) Half elevation of vertical arrangement of longitudinal prestressed reinforcement in the test girder. (b) Distribution of prestressed reinforcement in the section of the pivot point. (c) Distribution of prestressed reinforcement in mid-span section.

Figure 2. Arrangement of ordinary reinforcement in the test beam (cm). (a) Half elevation of ordinary reinforcement in test beam. (b) Distribution of ordinary reinforcement in the pivot section. (c) Distribution of ordinary reinforcement in mid-span section.

Figure 3. Structural drawing of corrosion tank.

Figure 4. CAD schematic diagram of the loading experiment (cm).

Figure 5. Test beam load–deflection curve at mid-span.

Figure 6. Schematic diagram of test beam S1’s elevation cracks.

Figure 7. Fracture surface of corroded prestressed strand wire in this test.

Figure 8. All fracture surfaces and fracture modes of the strand wires at the breakage location.

Figure 9. Crack distribution in the final stage of fatigue loading of test beams. (a) F-0. (b) F-4. (c) F-8.

Figure 10. Strain changes in ordinary steel reinforcements under fatigue loading. (a) F-0: load–ordinary reinforcement strain curve. (b) F-0: variation in strain with number of fatigue loadings in ordinary steel reinforcement. (c) F-4: load–ordinary reinforcement strain curve. (d) F-4: variation in strain with number of fatigue loadings in ordinary steel reinforcement. (e) F-8: load–ordinary reinforcement strain curve. (f) F-8: variation in strain with number of fatigue loadings in ordinary steel reinforcement.

Figure 11. Strain variation in prestressed reinforcements under fatigue loading. (a) F-0: load–prestressed reinforcement strain curve. (b) F-0: relationship between strain and number of fatigue loadings of prestressed reinforcement. (c) F-4: load–prestressed reinforcement strain curve. (d) F-4: relationship between strain and number of fatigue loadings of prestressed reinforcement. (e) F-8: load–prestressed reinforcement strain curve. (f) F-8: relationship between strain and number of fatigue loadings of prestressed reinforcement.

Figure 12. The ratio between the strain amplitude of prestressed reinforcements and ordinary reinforcements under fatigue loading.

Figure 13. Concrete strain changes in the compression zone of test beams during fatigue loading. (a) F-0: relationship between load and concrete strain in the compression zone. (b) F-4: relationship between load and concrete strain in the compression zone. (c) F-8: relationship between load and concrete strain in the compression zone.

Figure 14. Relationship between cumulative residual strain of concrete in the compression zone and the amount of fatigue loading.

Figure 15. Comparison between calculated and test data curves of cumulative residual strain of concrete in compression zone.

Table 1. Results of fatigue tests.

No.	Designed Corrosion Rate (%)	Actual Corrosion Rate (%)	Lower Fatigue Load Limit (kN)	Upper Fatigue Load Limit (kN)	$Fatigue Life N^{f}$ (Ten Thousand Times)	Type of Damage
F-0	0	0	100	700	$N^{f}$ > 200	Destruction by static loading
F-4	4	3.23	100	700	$N^{f}$ > 200	Destruction by static loading
F-8	8	6.86	100	700	86.02	Prestressed strand breakage

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MDPI and ACS Style

Zhang, Z.-Y.; Wei, P.; Cao, P.; Huang, H.-B. The Effect of the Corrosion Degree of Prestressed Steel Reinforcements on the Strain of Concrete Box Girders: An Experimental Fatigue Study. Buildings 2025, 15, 655. https://doi.org/10.3390/buildings15050655

AMA Style

Zhang Z-Y, Wei P, Cao P, Huang H-B. The Effect of the Corrosion Degree of Prestressed Steel Reinforcements on the Strain of Concrete Box Girders: An Experimental Fatigue Study. Buildings. 2025; 15(5):655. https://doi.org/10.3390/buildings15050655

Chicago/Turabian Style

Zhang, Zhao-Yuan, Ping Wei, Peng Cao, and Hai-Bin Huang. 2025. "The Effect of the Corrosion Degree of Prestressed Steel Reinforcements on the Strain of Concrete Box Girders: An Experimental Fatigue Study" Buildings 15, no. 5: 655. https://doi.org/10.3390/buildings15050655

APA Style

Zhang, Z.-Y., Wei, P., Cao, P., & Huang, H.-B. (2025). The Effect of the Corrosion Degree of Prestressed Steel Reinforcements on the Strain of Concrete Box Girders: An Experimental Fatigue Study. Buildings, 15(5), 655. https://doi.org/10.3390/buildings15050655

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