Experimental study on the effect of initial crack damage on the capacity degradation of RC eccentric columns

Abstract

This study investigates the degradation of bearing capacity in cantilever-casting arch bridges due to construction-induced cracking. An equivalent conversion method is proposed to model the arch ring segment as an eccentric compression column. Reinforced concrete (RC) columns with constant cross-sections are designed to simulate eccentric column specimens, with crack width serving as the damage quantification index. Various initial crack widths (0 mm, 0.05 mm, 0.10 mm, and 0.15 mm) are introduced through different loading methods, and load-bearing capacity tests are performed for various damage states. The results show that initial cracks on the tensile side significantly reduce the load-bearing capacity of the eccentric columns, with the largest reductions being 18.91% and 8.33% for large and small eccentric columns, respectively. A negative correlation is observed between crack width and bearing capacity, while cracks on the compressive side have a minimal effect on the load-bearing capacity. Cracks in large eccentric columns result in reduced elastic stiffness, early yielding of reinforcement, and a deterioration in ductility, while small eccentric columns fail in a brittle manner due to concrete crushing. The strain distribution in the damaged section still approximately follows the plane-section assumption, with crack propagation controlled by the initial crack face. Finally, a damage reduction factor model is developed, linking crack width to bearing capacity degradation, and the calculated results align well with experimental findings. This research provides experimental evidence and theoretical tools for assessing the load-bearing capacity of cracked arch bridges.

Keywords

concrete eccentric columns initial crack failure mechanism bearing capacity degradation damage reduction factor

Introduction

Reinforced concrete arch bridges, known for their superior spanning capacity and cost-effectiveness, play a crucial role in bridge construction in mountainous regions (Chen and Liu, 2020; Chen et al., 2021). In recent years, the cantilever casting method has gained widespread application in the construction of large-span arch bridges (over 200 m), offering advantages in maintaining the integrity and geometric accuracy of the arch ring (Liu et al., 2021; Tian et al., 2019, 2023). However, before closure, the arch ring is in a cantilever state, making it susceptible to factors like cable force error, temperature variation, and shrinkage creep. These factors can cause tensile stresses in the cross-section to exceed limits, potentially leading to concrete cracking (He et al., 2024; Tian et al., 2024). Current regulations (JTG/T 3650-2020, 2020) stipulate that tensile stresses should not occur in the main arch ring during the cantilever casting process. However, practical engineering experience indicates that it is still challenging for the upper and lower edges of the arch ring cross-section to meet the requirement of no tensile stress as specified in the regulations (Han et al., 2020; Xu et al., 2024).

For reinforced concrete arch bridges, the arch ring transforms into a hinge-free arch structure after closure, with full section primarily carrying axial pressure. Although cracks that appear during construction often partially or fully close under compressive stress upon closure, they nevertheless constitute initial damage within the structure and pose a potential risk to the load-bearing capacity. Currently, research on arch rings primarily focuses on assessing ultimate bearing capacity (Jiang et al., 2012), the influence of steel bar corrosion (Ma et al., 2016) and reinforcement and repair technologies (Yang et al., 2023). However, no in-depth research has been conducted on how initial cracks that occur during construction and close after closure affect the arch ring’s load-bearing performance, particularly the extent to which crack damage contributes to load-bearing capacity degradation.

From the perspective of the essence of force application, the force characteristics of an arch ring section under the combined action of bending moment and axial force are fundamentally consistent with the internal force state of the eccentrically compressed column section subjected to the same combination of bending moment and axial force. Therefore, based on the principle of equivalent beam-column (Lin and Chen, 2016), the key force-bearing sections of the arch structure are equivalent to eccentrically compressed columns, and the critical load or ultimate bearing capacity of the arch is calculated by using the relevant theoretical formulas of the eccentric column. This has become a widely applied research method. For example, Xin et al. (2019) investigated RC arches by fabricating 15 RC columns and utilizing DIC technology to examine crack development, bearing capacity, and strain field evolution during the failure of corroded reinforced concrete compression and bending members. Their findings lay the groundwork for analyzing the bearing capacity decay of RC arch bridges using the equivalent beam-column method. Yang et al. (2019) conducted two sets of eccentric column compression tests from the perspective of arch ring reinforcement, using super-strong, high-toughness resin steel wire mesh concrete (HTRCS) for reinforcement. The experimental studies of Liu et al. (2016) and Wang et al. (2023) demonstrated that, despite differences in internal force transmission mechanisms among tunnel linings, arch structures, and eccentrically compressed columns, their bearing capacity can be effectively analyzed using an eccentric column model. Their findings provide a theoretical foundation for the equivalent force-bearing analysis of arches and columns.

Currently, research on concrete eccentric compression columns primarily focuses on the use of high-strength materials (Fathi et al., 2024; Alqawzai et al., 2025), rust expansion cracking (Chao et al., 2023; Luo et al., 2025; Jiang et al., 2023) and reinforcement methods (Si et al., 2023; Torabian and Mostofinejad, 2025; Zhong et al., 2024). However, research into the mechanical properties of reinforced concrete compression and bending members, particularly with regard to the degradation law and failure mode of bearing capacity due to initial crack damage remains relatively scarce (e.g. cracks generated during construction that close afterwards). Miao et al. (2013) investigated the effect of crack width on the fire resistance of eccentric columns, but did not address the specific impact of cracks on bearing capacity. Pang et al. (2017) research indicates that the yield load of RC beams with initial damage exceeding 0.5 Pu decreases by 33.7% after undergoing a dry-wet cycle in seawater. Sathe and Devsale (2025) and Sathe and Patil (2024) conducted a systematic study of the weakening effect of corrosion on the reinforcement-concrete bond strength in concrete mixed with fly ash. As with corrosion damage, construction cracks have been shown to have a similar influence pattern on the bearing capacity of components. This research suggests that the combined effect of initial damage and environmental factors can significantly accelerate the degradation of bearing capacity. However, it is unclear whether such influencing factors also apply to arch rings or compressed RC columns.

While previous research has predominantly focused on the effects of corrosion, high-strength materials, or strengthening techniques on the behavior of eccentric columns, the impact of cracks induced specifically during the construction phase has received limited attention. To address this gap, this study investigates the cantilever-cast arch ring by proposing an equivalent transformation of arch segments into eccentric columns. Employing the equivalent beam-column principle, reinforced concrete (RC) eccentric columns with uniform cross-sections are designed, using crack width as a quantitative indicator of construction-induced damage. A series of static failure tests are systematically conducted on columns with varying degrees of initial damage. This research aims to elucidate the influence of different initial crack severities on the failure mode, bearing capacity, and ductility of eccentric columns. The findings are expected to provide experimental evidence and theoretical support for assessing the potential degradation in load-bearing capacity of RC arch bridges due to construction-related cracking.

Experimental program

Equivalence principle

As the primary load-bearing component in a cantilever-cast concrete arch bridge, the main arch ring under service conditions is typically subjected to a combination of bending moment (M) and axial force (N). This mechanical state is highly consistent with that of a reinforced concrete (RC) eccentric column. Although geometrically scaled full-arch model tests can most comprehensively reflect the performance of an arch ring with crack damage, they are often large-sized, complex to fabricate, time-consuming, and costly, making them difficult to implement. In contrast, tests based on the equivalent beam-column principle, which idealizes arch ring segments as eccentrically compressed columns, offer significantly enhanced operability and efficiency (Zhong et al., 2024).

Figure 1(a) illustrates the loading on the arch ring of a reinforced concrete arch bridge, which primarily carries the self-weight, q, and the concentrated force, F, from the columns. This represents a typical loading condition involving combined bending moment and axial force. When a segment is taken at Section Ⅰ-Ⅰ of the arch ring, it is under the combined action of bending moment (M), axial force (N), and shear force (Q), as shown in Figure 1(b). By rotating this segment to a vertical orientation (Figure 1(c)), its current force state can be considered equivalent to that of an eccentric column (Figure 1(d)), with the influence of shear force (Q) neglected.

Figure 1.

Schematic diagram of force conversion of the arch ring.

Specimen preparation

Based on a review of design parameters for existing cantilever-cast reinforced concrete arch bridges, the typical cross-section of the main arch ring has a height ranging from 2.8 to 4.6 m and a width between 6 and 10 m. These dimensions align with the general principle that the rib depth is typically 1/40 to 1/60 of the span, and the rib width is approximately 0.5 to 2.0 times the rib depth. Furthermore, the width-to-span ratio of the structure falls between 1/18.75 and 1/30.32, satisfying the common structural requirement that this ratio should not be less than 1/20 (Chen and Liu, 2020; Liu et al., 2021; Tian et al., 2023). Accordingly, a scale arch bridge model with a span of 3000 mm, a rise-to-span ratio of 1/5, and an arch axis coefficient m = 1.988 was designed, employing a solid rectangular section of 150 mm × 150 mm (b × h) for the arch rib. Thus, to maintain consistency and enable a systematic study, the cross-sectional dimensions of all eccentric columns tested in this work were determined accordingly.

The test specimens were eccentrically compressed reinforced concrete short columns, measuring 150 mm × 150 mm × 800 mm (b × h × l). To induce controllable initial crack damage in the tensile and compressive zones, 100-mm-high corbels were installed at both ends of the columns. The cross-section of these corbels was enlarged to 350 mm × 150 mm. To prevent local failure during testing, the corbel regions were reinforced with closely spaced stirrups. The mid-height section of the column was symmetrically reinforced with HRB400 steel bars. The longitudinal reinforcement and stirrups had diameters of 8 mm and 6 mm, respectively. Stirrup detailing was Ф6@60/80 mm, indicating 6-mm-diameter stirrups spaced at 60 mm within the corbel regions and 80 mm elsewhere along the column height. The reinforcement ratio was 1.06%, and the concrete cover thickness was 20 mm. Detailed dimensions, reinforcement layouts, and fabrication procedures of the specimens are illustrated in Figures 2 and 3.

Figure 2.

Schematic diagram of specimen dimensions (unit: cm).

Figure 3.

Specimen fabrication process.

The concrete mix ratio was Water: cement (42.5PO): Fly Ash: Mineral Powder: Sand: Crushed Stone = 1:1.9:0.2:0.56:5.3:5.9. In accordance with the Chinese standard (GB/T 50081-2019, 2019), 150-mm cubic specimens and 150 mm × 150 mm × 300 mm prismatic specimens were fabricated and cured for compressive strength tests and for measuring the axial compressive strength and elastic modulus, respectively. The reinforcement employed was HRB400-grade steel bar with a diameter of 8 mm. The yield strength of the bar was 458 MPa, and its mechanical properties were determined following the relevant Chinese standard (GB/T 28900-2012, 2012). The test results are summarized in Table 1, and the experimental setup is shown in Figure 4.

Table 1.

Test results of concrete material properties (unit: MPa).

Material	Cube strength	Axial compressive strength	Elastic modulus	Yield strength	Tensile strength
Concrete	51.5	42.6	3.27 × 10⁴	/	3.2
HRB400	/	/	2.01 × 10⁵	458	/

Figure 4.

Material test.

Specimen grouping

To systematically investigate the influence of initial crack damage on eccentric column performance, crack width (w) was adopted as the damage index. The selection of crack widths complied with the Chinese standard (GB 50010-2010, 2010), which specifies a maximum allowable width of w ≤ 0.2 mm. Specimens were precracked to introduce target initial crack widths of 0 mm (no damage), 0.05 mm (slight), 0.10 mm (moderate), and 0.15 mm (severe). The specimen designations and test matrix are given in Table 2. For instance, S-0.05t-70 denotes a specimen tested at an eccentricity (e) of 70 mm with a 0.05 mm wide initial crack on the tensile (t) side. Similarly, S-0.15t/c-35 refers to a specimen with e = 35 mm and 0.15 mm wide cracks on both the tensile (t) and compressive (c) sides.

Table 2.

Grouping table of test conditions.

Specimen number		Step-1	Step-2
1	S-wt-70	0 mm	Large eccentric loading failure. (Eccentricity, e = 70 mm)
2		0.05 mm
3		0.1 mm
4		0.15 mm
5	S-wc-70	0.05 mm
6		0.1 mm
7		0.15 mm
8	S-wt/c-70	0.15 mm
9	S-wt-35	0 mm	Small eccentric loading failure. (Eccentricity, e = 35 mm)
10		0.05 mm
11		0.1 mm
12		0.15 mm
13	S-wt/c-35	0.15 mm

Loading and measurement scheme

A 4000 kN servo-hydraulic testing machine was used for static loading, following the Chinese standard (GB/T 50152-2012, 2012). Each load increment was maintained for 10 min. Steel rollers were installed at the top and bottom of the specimen to simulate hinge supports; lubricating oil was applied to the interfaces to minimize frictional resistance. The test setup is shown in Figure 5, and the loading procedure was as follows:

(1) Step 1. Pre-cracking Test: A pre-cracking load was applied with an initial increment of 10 kN per step. As the theoretical cracking load (F_cr) was approached, the increment was reduced to 5 kN. Crack width was monitored in real time using an HC-CK103 crack detector (accuracy: 0.01 mm). Loading was suspended once the target crack width (0.05 mm, 0.10 mm, or 0.15 mm) on the tensile side was achieved, and the corresponding load and crack pattern were recorded before unloading.

(2) Step 2. Failure Test: A static failure test was conducted on each specimen according to Table 2. The load was increased in 20 kN increments until the specimen failed completely.

Figure 5.

Specimen loading layout diagram.

The arrangement of concrete and steel strain gauges on the specimen is shown in Figure 6. Two and six strain gauges were attached to the concrete surface on the tensile and compressive sides, respectively. To comprehensively analyze the strain distribution across the section height after damage, three additional concrete strain gauges were arranged vertically along the column. On the longitudinal reinforcement, Sections A-A, B-B, and C-C were instrumented with 2, 4, and 2 strain gauges, respectively. The lateral displacement of the column was measured using three dial gauges positioned along its height.

Figure 6.

Schematic diagram of the layout of the test specimen measurement points.

Analysis of test results

Pre-crack test

In order to achieve the research objective of utilising crack width as the damage quantification index, and in accordance with the crack control grade requirements stipulated in the Chinese standard (GB 50010-2010, 2010), the specimens were subjected to pre-crack loading conditions under the eccentricity e = 70 mm. Therefore, three primary crack widths of 0.05 mm, 0.10 mm and 0.15 mm are meticulously introduced on the tensile and compressive sides of the specimen. The load values corresponding to the specified crack width for each specimen, along with the crack test records, are presented in Table 3 and Figure 7, respectively.

Table 3.

Shows the initial crack width of some specimens.

Specimen number	Cracking load/kN	Specified crack load/kN			The number of cracks
Specimen number	Cracking load/kN	0.05 mm	0.1 mm	0.15 mm	The number of cracks
S-0-70	71	–	–	–	–
S-0.05t-70	73	84	–	–	1
S-0.1t-70	72	83	95	–	3
S-0.15t-70	74	85	97	115	3

Figure 7.

Shows the development of different initial cracks.

The crack patterns after pre-cracking are presented in Figure 8. The consistency of the initial cracking load (approximately 72 kN) across all specimens indicated low variability in concrete strength and high material uniformity, thereby supporting the reliability of subsequent tests. Upon initial loading, fine micro-cracks were observed near the column mid-height at approximately 70 kN, with initial widths of 0.01–0.02 mm. With further loading, these micro-cracks developed into transverse cracks that extended along the column shaft, their length and width growing concurrently. These transverse cracks then propagated towards the compression zone. The target crack widths of 0.05 mm, 0.10 mm, and 0.15 mm were achieved at loads of 81 kN, 95 kN, and 115 kN, respectively. Crack distributions (Figure 8) show that S-0.05t-70 had a single tensile crack, whereas S-0.10t-70 and S-0.15t-70 each developed three cracks with similar distributions and maximum widths near mid-height. After unloading, all cracks narrowed and became undetectable (w < 0.01 mm), confirming full closure.

Figure 8.

Schematic diagram of crack distribution in different specimens.

Load-bearing capacity

Figure 9 shows the final failure modes of the damaged specimens. Observation of these modes reveals that initial crack damage in the tensile or compressive zones did not alter the fundamental failure mode category, regardless of eccentricity. Failure was tensile-controlled under large eccentricity and compressive-controlled under small eccentricity. For undamaged specimens, the failure process involved concrete cracking, crack propagation, yielding of the tensile steel, and finally, crushing of the compressive concrete. No specimens exhibited out-of-plane bending or a sharp increase in lateral deflection, indicating that instability did not occur. The overall failure process for pre-damaged specimens was similar but with key differences:

Figure 9.

Failure mode of the specimen.

Under large eccentric loading, the initial cracks propagated rapidly, causing the tensile reinforcement to yield prematurely. Final failure was characterized by the widening of the initial tensile crack. In contrast, under small eccentric loading, crack propagation was slower, and failure was predominantly due to concrete crushing in the compression zone, with the initial tensile crack exerting only a limited influence on the failure location.

As shown in Figure 10, the bearing capacities of specimens S-0.05t-70, S-0.10t-70, and S-0.15t-70 were 291 kN, 269 kN, and 253 kN, respectively. In comparison with the 312 kN capacity of the undamaged specimen (S-0-70), this represents a decrease of 6.73%, 13.78%, and 18.91%. The results indicate that initial tensile cracks significantly impair the mechanical performance of large-eccentricity columns. The cracked concrete on the tensile side ceases to contribute, reducing the local stiffness. Although the stiffness of the tensile side gradually decreases with increasing crack width, the total reduction in bearing capacity does not exceed 20%. These findings confirm that initial tensile damage significantly weakens the bearing capacity, with the effect becoming more pronounced as the damage level increases.

Figure 10.

Comparison diagram of the bearing capacity of the specimens.

The bearing capacities of specimens S-0.05c-70, S-0.10c-70, and S-0.15c-70 were 318 kN, 305 kN, and 310 kN, respectively, showing no significant reduction compared to S-0-70. The capacity of specimen S-0.15t/c-70 was 255 kN, which is close to that of S-0.15t-70. This demonstrates that initial compressive-side cracks have a relatively small impact on bearing capacity. Under compressive stress, these cracks tend to remain closed or interlocked, thus having a limited effect on the ability of the core concrete to carry and transfer compressive stresses. Although large eccentric loading may lead to an earlier onset of nonlinearity, the overall bearing capacity is primarily governed by the damage state in the tension zone. Therefore, damage confined to the compression zone does not cause a significant reduction in bearing capacity.

For the small eccentricity specimens, the bearing capacities of S-0.05t-35, S-0.10t-35, S-0.15t-35, and S-0.15t/c-35 were 602 kN, 590 kN, 567 kN, and 561 kN, respectively. Compared to the 612 kN capacity of the undamaged specimen (S-0-35), the degradation rates were 1.63%, 3.59%, 7.35%, and 8.33%, respectively. Notably, all these values are below 10%. Under small eccentric loading, most column sections are under compression, resulting in relatively low tensile stress in the tensile zone. This phenomenon slows the propagation of initial cracks. Consequently, initial tensile damage has a more limited influence on the overall bearing capacity of small eccentricity specimens.

Crack development

Figure 11 shows the crack development during the complete failure process of representative eccentric specimens, with red and blue lines indicating the initial pre-cracks and the loading-induced cracks, respectively. For specimen S-0-70, micro-cracks first appeared on the tensile surface at a load of 71 kN and gradually extended laterally with further loading. During this stage, crack propagation was relatively slow. When the load increased to 210 kN (0.7F_u), the main crack fully developed and propagated toward the compression zone. The height of the compression zone decreased, and the crack widening rate increased significantly. For the pre-damaged specimens, crack propagation during the initial loading phase was concentrated at the location of the initial damage. As the load increased and a small number of new cracks formed, the maximum crack width at failure was invariably located at the initial damage site. Nevertheless, the final crack distribution pattern was similar to that of the undamaged specimens. For specimen S-0-35, cracks first appeared at a load of 300 kN, with subsequent slow propagation and few new cracks. In the pre-damaged small eccentricity specimens, crack development was predominantly governed by the propagation of pre-existing initial cracks, with minimal formation of new cracks.

Figure 11.

Schematic diagram of crack development in the specimen.

As the load increased, the initial cracks on the compressive side of specimens S-0.05c-70, S-0.10c-70, and S-0.15c-70 gradually closed. As illustrated in Figure 12(a), the crack development in the large eccentricity specimens shows that the growth rate of the main crack width is positively correlated with the degree of damage in the tensile zone. Furthermore, a comparison between specimens S-0.15c-70 and S-0.15t/c-70 reveals a consistent trend in the development of the maximum crack width. This observation indicates that tensile cracks directly weaken the bond stress between steel reinforcement and concrete at the cracked section. Under an applied load, significant stress concentration occurs at the crack tip, thereby making it the preferred site for further propagation. As a result, the main crack can extend preferentially along this pre-existing path without needing to overcome the tensile strength of intact concrete. In contrast, initial cracks on the compression side tend to remain closed or tightly interlocked under axial compressive stress. Consequently, the stress concentration effect at their crack tips is far less pronounced than in the tensile region.

Figure 12.

Comparison of crack development trends.

Figure 12(b) shows the development trend of crack width in small eccentric compression specimens. When subjected to small eccentric loading, the middle section of the column is dominated by compressive stress, and the crack width in the tensile zone increases slightly with the load. For the damaged specimens designated S-0.05t-35, S-0.1t-35, S-0.15t-35 and S-0.15t/c-35, the initial crack propagation initiation loads were 140 kN, 100 kN, 100 kN and 80 kN, respectively. The width of the crack initiation was found to be 0.02 mm for all specimens. The maximum crack widths recorded in the vicinity of failure were found to be 0.05 mm, 0.06 mm, 0.07 mm, 0.07 mm and 0.08 mm, respectively. The intensification of damage in the tensile zone has been shown to significantly reduce the cracking load, and the maximum crack width at the time of failure does not return to the initial damage level. This finding suggests that the transformation of large-scale eccentric compression damage into small-scale eccentric compression exerts a regulatory effect on crack propagation.

Load-vertical displacement curve

Figure 13 presents the load-vertical displacement curves of specimens with varying degrees of initial damage when subjected to both large and small eccentricities.

(1) Elastic stage: The load-displacement curve of specimen S-0-70 exhibited a steep initial slope, indicating high sectional stiffness. With increasing initial crack width (e.g., from S-0.05t-70 to S-0.15t/c-70), the initial slope decreased significantly, demonstrating that the damage reduced sectional stiffness and accelerated crack development from the onset of loading. A similar, though less pronounced, trend was observed in small-eccentricity specimens due to the dominance of compressive stress.

(2) Cracking and yielding stage: In the case of large eccentric loading, as evidenced by specimens S-0.15t-70 and S-0.15t/c-70, an increase in the initial crack width results in a heightened nonlinear behaviour of the curve, leading to an earlier occurrence of the yielding of the reinforcing bars. At this stage, the nonlinear region of the small eccentric specimens is relatively small, and the overall response remains relatively stable.

(3) Stage of failure: For specimens with large eccentric loading, as the initial crack damage increases, the curve demonstrates a rapid decline after reaching the maximum load. In comparison with the S-0-70 specimen, the ductility stage is not evident. In the case of small eccentric compression specimens, brittle failure is relatively obvious in the failure stage, and the initial damage has a relatively small influence on the failure mode of small eccentric specimens.

Figure 13.

Load - vertical displacement curve of the specimen.

In summary, increasing the initial crack width reduced the stiffness and bearing capacity in the elastic, cracking, and yielding stages. A small tensile crack (0.05 mm) had a limited impact on structural performance, whereas larger cracks (0.10–0.15 mm) caused significantly enhanced nonlinearity and stiffness degradation. During failure, a larger tensile crack led to faster load decay and a greater reduction in bearing capacity. Cracks on the compression side had a negligible effect on the load-displacement curve, similar to that observed in undamaged specimens.

Reinforcement strain

As illustrated in Figure 14, the effect of varying initial damage levels on the load-reinforcement strain curve of the specimen is demonstrated.

Figure 14.

Load - reinforcement strain curve of the specimen.

During the elastic stage, the load was linearly related to the rebar strain. The undamaged specimen S-0-70 showed the steepest curve slope, indicating the highest initial stiffness. The slopes for specimens S-0.05t-70, S-0.10t-70, and S-0.15t-70 decreased significantly, demonstrating that tensile-side initial cracks substantially reduce initial stiffness. In contrast, specimens with compressive-side damage (S-0.05c-70, S-0.10c-70, S-0.15c-70) exhibited elastic behavior highly similar to S-0-70. In the cracking stage, the curve slope for S-0-70 changed abruptly when its tensile concrete cracked, accompanied by a sharp increase in tensile rebar strain. For specimens pre-damaged on the tensile side, this cracking point was less distinct. The tensile reinforcement carried more load earlier, resulting in a smoother transition of the curve into the nonlinear stage. The strain development in specimens with compressive-side damage remained analogous to S-0-70. At yielding, the yield load of S-0.15t-70 was significantly lower than that of S-0-70, and its tensile rebar strain increased rapidly, reflecting a considerable loss of bearing capacity.

For small eccentricity specimens, the overall trend of the load-strain curves was similar. However, as the section is compression-dominated, the influence of tensile-side initial damage was less pronounced, and the tensile reinforcement did not yield at failure. Among them, specimen S-0.15t-35 showed the highest tensile stress, indicating that damage prompts earlier engagement of the tensile steel. Compared to S-0-35, S-0.15t-35 also exhibited the most rapid increase in compressive rebar strain as damage intensified. The initial crack propagated faster toward the neutral axis, leading to a more significant reduction in the compression zone height than in S-0-35.

In conclusion, initial damage significantly affects the load–rebar strain response of eccentric columns. Increasing tensile-side damage reduces the elastic slope, shortens the yield plateau, and lowers the failure load. Tensile-side damage has a more profound impact on column performance, whereas compressive-side damage has a relatively minor influence on rebar stresses.

Section strain in the column

A substantial body of research confirms that the mean strain distribution across a control section in reinforced concrete flexural and eccentric compression members generally adheres to the plane-section assumption from initial loading up to the ultimate state. Nevertheless, in eccentrically compressed columns with load-induced cracks, the presence of these cracks can lead to uneven local stiffness, disrupted material continuity, and potential nonlinearities in the sectional strain distribution.

To quantify the influence of initial cracking damage on strain distribution, a comparative analysis was conducted between undamaged specimens (S-0-70, S-0-35) and damaged specimens (S-0.15t-70, S-0.15t-35, S-0.15t/c-70, S-0.15t/c-35). The results are presented in Figure 15.

Figure 15.

Shows the strain distribution of concrete in the middle section of the column.

As shown in Figure 15(d) and (f), the strain distributions across the section height for specimens S-0.15t-35 and S-0.15t/c-35 remain linear. Under small eccentric compression, the dominant compressive stress causes tensile cracks to develop slowly and remain tightly closed. This degrades the local section stiffness but does not disrupt the overall linear strain gradient. Furthermore, cracks in the compression zone have a negligible effect on the compressive stress path. For large eccentricity specimens S-0.15t-70 and S-0.15t/c-70 (Figure 15(b) and (c)), the strain distributions also largely comply with the plane-section assumption. This occurs because the pre-existing crack interfaces from Step-1 loading serve as preferred paths for crack propagation in Step-2, inhibiting the formation of new cracks. The intact concrete between cracks maintains deformation compatibility across the section. Consequently, although the slope of the strain distribution changes, the cross-section approximately satisfies the plane-section assumption.

Bearing capacity of the damaged column

Basic assumptions

(1) The damaged specimen exhibits a linear strain distribution across its section under load, satisfying the plane section assumption.

(2) After concrete cracking, the cracked concrete contributes negligibly to load resistance, and the stress is entirely resisted by the steel reinforcement.

Undamaged specimens

Based on the aforementioned assumptions, the stress state at the mid-height cross-section of the specimen column is shown in Figure 16. Utilizing the equilibrium conditions of force and bending moment, the ultimate axial load capacities (N_u) under eccentric loading for both large and small eccentricity cases can be expressed by equations (1) and (2), respectively.

{\begin{cases} N_{u} = f_{c d} b x + f_{s d}^{'} A_{s}^{'} - f_{s d} A_{s} \\ f_{c d} b x (e_{s} - h_{0} + x / 2) = f_{s d} A_{s} e_{s} - f_{s d}^{'} A_{s}^{'} e_{s}^{'} \end{cases}

(1)

{\begin{cases} N_{u} e_{s}^{'} = - f_{c d} b (x / 2 - a_{s}^{'}) + σ_{s} A_{s} (h_{0} - a_{s}^{'}) \\ σ_{s} = ε_{c u} E_{s} (\frac{β h_{0}}{x} - 1) \end{cases}

(2)

where: f_cd represents the axial compressive strength of concrete; b represents the width of the cross-section; x represents the height of the concrete compression zone; f’_sd and f_sd respectively represent the yield strength of the reinforcing bars on the compressive side and the tensile side; A’_s and A_s respectively represent the cross-sectional areas of the compressed and tensioned reinforcing bars; e’_s and e_s respectively represent the distances from the point of action of the eccentric force Nu to the point of action of the resultant force A’_s and A_s of the reinforcing bars; h₀ represents the effective height of the cross-section; a_s represents the thickness of the protective layer of the reinforcing bar; ℇ_cu represents the ultimate compressive strain of concrete; E_s represents the elastic modulus of the reinforcing bar; β represents the coefficient related to the strength of concrete, as 0.8.

Figure 16.

Schematic diagram of the force on the bias column.

Damage reduction coefficient η

The tensile side cracks of the large eccentric compression column, as indicated by the bearing capacity test results of the specimens, have been shown to lead to a significant decrease in bearing capacity, and the tensile reinforcement has been demonstrated to yield prematurely. In the case of small eccentric compression specimens, the influence of cracks on the tensile side is relatively weakened, and the reinforcing bars on the tensile side do not yield. Consequently, the load-bearing capacity of each specimen exhibits a negative correlation with the increase of the initial crack, and essentially conforms to the linear law. It is possible to define a calculation method that takes the damage reduction coefficient into consideration. The introduction of the damage reduction coefficient, denoted by η, establishes a relationship with the initial crack width (w), as illustrated in equation (3).

η = {\begin{cases} η_{t} \begin{array}{l} = 1 - k_{t} w_{t} & 0 < η_{t} \leq 1; \end{array} \\ η_{c} \begin{array}{l} = 1 - k_{t} w_{c} & 0 < η_{c} \leq 1; \end{array} \end{cases}

(3)

where: η_t and η_c represent the damage reduction coefficients caused by the initial cracks on the tensile side and the compressive side respectively, 0 < η ≤ 1, and η = 1 indicates no damage, k represents the damage sensitivity coefficient, w represents the crack widths on the tensile side and the compressive side.

In the case of large eccentricity specimens, the existence of initial damage on the tension side has been shown to result in impaired interfacial bond stress transfer between concrete and reinforcing steel. This degradation leads to premature yielding of the tensile reinforcement at the crack interfaces, thereby effectively reducing its contribution to the overall load resistance. Consequently, the damage reduction factor η is applied to modify the tensile reinforcement term (f_sd) in equation (1), accounting for this diminished effectiveness. For small eccentricity specimens, the primary cause of failure is the crushing of the concrete in the compression zone. Initial cracks have been shown to exert a more pronounced influence on the strength of the compression concrete. These fissures have the potential to induce premature crushing of the concrete on the compression side. To model this effect, the damage reduction factor η is applied to modify the concrete axial compressive strength term (f_cd) in equation (2). The specific mathematical expressions incorporating the damage reduction factor η for both cases are given by equations (4) and (5), respectively.

{\begin{cases} N_{u} = f_{c d} b x + f_{s d}^{'} A_{s}^{'} - η \cdot f_{s d} A_{s} \\ f_{c d} b x (e_{s} - h_{0} + x / 2) = η \cdot f_{s d} A_{s} e_{s} - f_{s d}^{'} A_{s}^{'} e_{s}^{'} \end{cases}

(4)

{\begin{cases} N_{u} e_{s}^{'} = - η \cdot f_{c d} b (x / 2 - a_{s}^{'}) + σ_{s} A_{s} (h_{0} - a_{s}^{'}) \\ σ_{s} = ε_{c u} E_{s} (\frac{β h_{0}}{x} - 1) \end{cases}

(5)

The damage reduction coefficient η of the eccentric column under different damage conditions can be obtained through the bearing capacity test value Nut of the specimen. The calculation results are shown in Table 4.

Table 4.

Calculation results of the reduction coefficient.

Specimen number	Bearing capacity (kN)	w-t (mm)	w-c (mm)	η _t	η _c
S-0-70	312	–	–	1	1
S-0.05t-70	291	0.05	–	0.894	-
S-0.1t-70	269	0.1	–	0.686	-
S-0.15t-70	235	0.15	–	0.588	-
S-0-35	612	–	–	1	1
S-0.05t-35	602	0.05	0	0.9769	–
S-0.1t-35	590	0.1	0	0.9563	–
S-0.15t-35	567	0.15	0	0.9174	–

As illustrated in Table 4, the tensile damage coefficient is negatively correlated with the initial crack width. By grouping and fitting the reduction coefficient with the initial crack width, the damage sensitivity coefficient k can be obtained. As demonstrated in Figure 17, subsequent to the occurrence of cracking and damage to the tensile and compressive sides of the eccentric column, the damage reduction coefficient is exhibited in equation (5). It has been determined that the damage on the compressive side of the large eccentric specimen exerts minimal influence on the reduction of the bearing capacity. Consequently, in the calculation of the reduction coefficient, it is permissible to take η_c = 1.

\begin{array}{l} η_{t} = {\begin{cases} 1 - 2.857 w_{t} ξ \leq ξ_{b} \\ 1 - 0.512 w_{t} ξ > ξ_{b} \end{cases} \begin{array}{l} w \in [0, 0.15] \end{array} \\ \begin{array}{l} η_{c} = 1 \end{array} \end{array}

(6)

where: ξ represents the height of the relative compression zone and is used to determine the eccentric state of the compression column size.

Figure 17.

Damage reduction coefficient of the specimen.

Verification

The substitution of the reduction coefficient, denoted by η, into the respective equations, i.e. Equations (4) and (5), results in the determination of the reduced bearing capacity, N_u,p. The calculation results are displayed in Table 5. The predicted value is in close agreement with the test value, with a relative error of less than 5%. The mean and coefficient of variation of the ratio between the two are 1.03 and 0.012, respectively. This indicates that the calculation formula has high accuracy. Consequently, the established η-w relationship serves as a practical tool for the rapid preliminary assessment of bearing capacity loss due to construction cracks, providing a critical basis for arch bridge safety classification and maintenance decision-making.

Table 5.

Comparison of predicted and tested values of cracking damage on the tensile side (kN).

Specimen number	Damage type	w/mm	Test value/N_u,t	Predicted value/N_u,p	N_u,t/N_u,p
S-0-70	Undamaged	0	312	306	1.02
S-0.05t-70	The side under tension	0.05	291	286	1.02
S-0.1t-70		0.1	269	266	1.01
S-0.15t-70		0.15	253	243	1.04
S-0-35	Undamaged	0	612	592	1.03
S-0.05t-35	The side under tension	0.05	602	579	1.04
S-0.1t-35		0.1	590	565	1.04
S-0.15t-35		0.15	567	552	1.03

Conclusion

This study proposes a novel equivalence method converting cantilever-casting arch ring segments into eccentrically loaded columns, and systematically investigates the effect of initial cracking damage on the failure mechanisms of reinforced concrete columns through experimental tests. Key findings are summarized as follows:

(1) The initial damage in the tensile zone significantly weakens the bearing capacity of the eccentric column, with the crack width exhibiting a nearly linear negative correlation with the bearing capacity. When the initial crack width is 0.15 mm, the bearing capacity of the large eccentric compression column decreases by 18.91%, while that of the small eccentric column decreases by 8.33%. In contrast, cracks on the compression side have a negligible effect on the reduction of bearing capacity.

(2) Comparison with undamaged column, the stiffness of the initially damaged large eccentric column decreases during the elastic stage, thereby accelerating the nonlinear development in the cracking stage. The tensile reinforcement yielded at an earlier stage, and the yield plateau shortened, which ultimately led to ductility deterioration during the failure stage. The behaviour of small eccentric columns is dominated by compression, and the nonlinear stage changes are relatively gentle. The tensile reinforcement does not yield, resulting in brittle failure of the concrete crushing.

(3) In the case of eccentrically compressed columns, it has been demonstrated that the strain distribution of the damaged section conforms to the assumption of a flat section. The primary fissures exhibit preferential expansion along their initial crack positions, while the concrete between the cracks remains undisturbed, thereby preserving the collective deformation coordination of the section.

(4) The established damage reduction coefficient model quantifies the degree of damage through crack width. The predicted bearing capacity was found to be in close agreement with the test value, with a relative error within 5%, thus demonstrating a high degree of accuracy in predicting bearing capacity. This model provides a quantitative tool for the preliminary safety assessment of cantilever-casting concrete arch bridges based on construction crack width.

The conclusions of this study are derived from short-term static tests with specific design parameters. Future work should investigate the coupling effects of environmental corrosion and long-term creep and shrinkage, and expand the scope to include a wider range of design parameters, such as reinforcement ratios, to build a more universal damage assessment framework.

Footnotes

ORCID iDs

Ye Dai

Zujun Zhang

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article. It is financially supported by the National Natural Science Foundation of China (Grant Nos. 51478049, 52078058), the Doctoral Research Start-up Project of Hunan University of Arts and Science (Grant Nos. 24BSQD45), the Jiangxi Provincial Department of Transport Science and Technology Project (Grant No. 2023C0009).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Alqawzai

Yang

Chen

, et al. (2025) Testing and strength prediction of polygonal UHPCFDST short columns under concentric and eccentric compression. Engineering Structures 325: 119473.

Chao

Hao

Xiang

Lin (2023) Failure mode-based calculation method for bearing capacities of corroded RC columns under eccentric compression. Engineering Structures 285.

Chen

Liu

(2020) A review of world arch bridge construction and technology development. Journal of Transportation Engineering 20(1): 27–41, (in Chinese).

Chen

Zhang

Liu

, et al. (2021) Current situation and prospect of concrete arch bridge application in China. Journal of Fuzhou University 49(5): 716–726, (in Chinese).

GB 50010-2010 (2010) Code for Design of Concrete Structures. China Architecture & Building Press.

GB/T 28900-2012 (2012) Test Methods for Steel Bars for the Reinforcement of Concrete. General Administration of Quality Supervision of China.

GB/T 50081-2019 (2019) Standard for Test Methods of Concrete Physical and Mechanical Properties. China Architecture & Building Press.

GB/T 50152-2012 (2012) Standard for Test Method of Concrete Structures. China Architecture & Building Press.

Han

Gou

Zhang

, et al. (2020) Technical advances of temporary facilities for the failure prevention of large-span cantilever casting construction of mountainous concrete box-type arch bridges. Advances in Civil Engineering 2020(4): 1–20.

10.

Xiang

, et al. (2024) Research on construction risk assessment of long-span cantilever casting concrete arch bridges based on triangular fuzzy theory and Bayesian networks. Buildings 14(9): 2627.

11.

Fathi

Ghali

MKN

Shanour

, et al. (2024) Experimental and analytical study on eccentrically loaded fiber concrete columns reinforced longitudinally with GFRP bars. Engineering Structures 312: 118251.

12.

Jiang

Liu

Zhang

(2012) Load carrying capacity prediction of existing RC arch ribs based on the change rule of whole process stiffness. Journal of Computational Mechanics 29(4): 532–537.

13.

Jiang

Ding

, et al. (2023) Failure mode-based calculation method for bearing capacities of corroded RC columns under eccentric compression. Engineering Structures 285: 116038.

14.

JTG/T 3650-2020 (2020) Technical Specifications for Construction of Highway Bridges and Culverts. Ministry of Transport of the People’s Republic of China.

15.

Lin

Chen

(2016) Calculation of the bearing capacity of reinforced concrete arch by equivalent beam-column method. Journal of Fuzhou University (Natural Science Edition) 44(1): 110–114, (in Chinese).

16.

Liu

Huang

Yue

, et al. (2016) Behaviour of tunnel lining strengthened by textile-reinforced concrete. Structure and Infrastructure Engineering 12(8): 964–976.

17.

Liu

Zhou

, et al. (2021) Linear control method for arch ring of oblique-stayed buckle cantilever pouring reinforced concrete arch bridge. Advances in Civil Engineering 2021: 6633717.

18.

Luo

Pan

, et al. (2025) Eccentric compression behaviour of corroded H-section column: testing, simulation and theoretical analysis. Journal of Constructional Steel Research 226: 109234.

19.

Wang

, et al. (2016) Influence of corrosion-induced cracking on structural behavior of reinforced concrete arch ribs. Engineering Structures 117: 184–194.

20.

Miao

Gong

Chen

, et al. (2013) Experimental research and numerical simulation analysis on fire resistance performance of RC columns with damages caused by service loading. Journal of Building Structures 34(8): 56–64, (in Chinese).

21.

Pang

Diao

, et al. (2017) Seawater dry-wet circulation on the influence of the initial damage RC structural behavior. Journal of Beijing University of Aeronautics and Astronautics 43(5): 1004–1012, (in Chinese).

22.

Sathe

Devsale

(2025) Influence of corrosion on bond strength in reinforced recycled aggregate concrete with fly ash. European Journal of Environmental and Civil Engineering 29(10): 1953–1986.

23.

Sathe

Patil

(2024) Corrosion effects on bond strength in reinforced concrete with fly ash. Journal of Adhesion Science and Technology 38(24): 4467–4495.

24.

Zeng

, et al. (2023) Effect of size on the eccentric compression performance of damaged square RC columns strengthened with CFRP: an experimental study. Advances in Structural Engineering 26(1): 168–182.

25.

Tian

Peng

Zhang

, et al. (2019) Determination of initial cable force of cantilever casting concrete arch bridge using stress balance and influence matrix methods. Journal of Central South University 26(11): 3140–3155.

26.

Tian

Cai

Peng

, et al. (2023) Multi-loop nesting algorithm and response analysis of cable forces of long span cantilever cast arch bridges during construction. KSCE Journal of Civil Engineering 28(2): 699–714.

27.

Tian

Zhang

, et al. (2024) Experimental and numerical study of the three-dimensional temperature field in the arch ribs of the reinforced concrete ribbed arch bridge during construction. Advances in Structural Engineering 27(6): 995–1015.

28.

Torabian

Mostofinejad

(2025) On load-displacement behavior of RC columns strengthened with longitudinal CFRP strips under eccentric loading: ductility and effect of secondary moment. Structures 79: 109533.

29.

Wang

Liu

, et al. (2023) Corrigendum: calculation model of concrete-filled steel tube arch bridges based on the “arch effect”. Frontiers in Materials.

30.

Xin

Zhou

, et al. (2019) Experimental study on bearing capacity evolution of reinforced concrete compression and bending members considering material deterioration. Materials Review 33(14): 2362–2396, (in Chinese).

31.

Tian

Xiao

SXP

, et al. (2024) Reliability evaluation of reinforced concrete arch bridges during construction based on LGSSA‐SVR hybrid algorithm. Structural Concrete 25(6): 4150–4166.

32.

Yang

Wang

, et al. (2019) Experimental study of RC eccentric compression columns with side reinforcement by high toughness resin concrete with steel mesh. Bridge Construction 49(3): 23–28, (in Chinese).

33.

Yang

Chen

Zhang

, et al. (2023) Experimental study on the ultimate bearing capacity of damaged RC arches strengthened with ultra-high performance concrete. Engineering Structures 279: 115611.

34.

Zhong

Peng

, et al. (2024) The effect of section enlargement with cementitious grout on the eccentric compression behavior of RC columns. KSCE Journal of Civil Engineering 28(8): 3378–3393.