Experimental study with DIC technique on the bond failure of structural concrete under repeated reversed loading with different amplitude

Abstract

The bond between deformed steel rebar and concrete plays a critical role against seismic action, thus it is important to capture the dynamic bond loss and establish the bond-slip model with cyclic loading. To explain the macroscale performance such as bond-slip relationship and establish the bond strength model, it is meaningful to capture the mesoscale and local behaviors between ribs and concrete. In this paper, pull-out specimens with rebar embedded in concrete and small windows excavated in the cover concrete are adopted with DIC technique to monitor the strain variation and crack development along the interfaces under static and reversed loading of different amplitude. From the test, it is found that DIC is an effective approach to obtain the localized characteristics including the normal and shear deformations. Through parametric study, the effects of concrete cover depth and the existence of stirrups on bond deterioration in terms of both global and local behaviors are studied. Interestingly, the global slip and local crack-width show synchronically increase under the pulling-out action, which demonstrates that the macroscale behaviors could be clarified from mesoscale measurement with the aid of DIC technique.

Keywords

bond digital image correlation reversed loading concrete deformed rebar

Introduction

Reinforced concrete is one of the most popular construction materials all over the world and many studies have been conducted to assess its material and structural performance against various factors (Gong et al., 2023; Li et al., 2023; Wang et al., 2023). The reversed bond-slip model between concrete and steel bars is essential to evaluate the deformation and capacity of the reinforced concrete structures under seismic loading (Faraone et al., 2022; Fawaz and Murcia-Delso, 2021; Frappa and Pauletta, 2022; Lu et al., 2022; Lemcherreq et al., 2023; Miani et al., 2020; Rashedi et al., 2022). In case of cyclic reversed loading with constant amplitude, the bond resistance is determined by the cyclic number and the value of the prescribed displacement (Eligehausen et al., 1983; Harajli, 2010; Harajli and Gharzeddine, 2007; Xiao et al., 2022). When the slip exceeds the critical value, the bond resistance will significantly decrease during the first cycle and gradually decrease with subsequent cycles (Eligehausen et al., 1983). Previous research has demonstrated that this critical value is closely related to the concrete cover depth (Li et al., 2018), strength and type of concrete (Alavi-Fard and Marzouk, 2002; Campione et al., 2005; Hota and Naaman, 1997), and hoop confinement (Eligehausen et al., 1983) etc. Moreover, the deterioration of the bond strength is also related to the geometry and diameter of the steel bars (Li et al., 2007; Murcia-Delso et al., 2013; Zuo and Darwin, 2000), lateral pressure on the concrete (Li et al., 2018, 2022), level of corrosion (Kivell et al., 2015; Wang et al., 2019; Zhou et al., 2015) and environmental conditions (Hu et al., 2019; Xu et al., 2017). During the service life of the reinforced concrete structures, the steel bars may experience cyclic reversed loading with arbitrary amplitude (Zhang et al., 2021), and the hysteretic bond-slip relationship under reversed loading with variable amplitude shall be revealed to establish the bond stress-slip model. Using pull-out specimens, Li et al. (2022) systematically studied effect of lateral pressure on the bond response of the deformed bars under reversed loading with variable amplitude. During this study, the bond stress-slip model is based on the macro tests with the assumption that the bond stress is uniformly distributed along the interface as the bond length is smaller than 5 times the diameter of the steel rebar. However, owing to the existence of the transverse ribs between the interfaces, the failure process along the interfaces is very complex, especially for specimens with different bar diameters and lateral confinement, and the damage threshold with variable amplitude reversed loading remains unclear.

To experimentally capture the bond deterioration under cyclic loading, one typical way is to use strain gauges or displacement sensors so that to measure the strain of steel bars and the slip between concrete and rebar. However, it is still particularly difficult to follow the entire pull-out process from the onset of the crack in the concrete cracking to the final failure stage. As widely known, there are two types of failure with respect to the pulling-out test using deformed bar: one is the crushing of concrete in front of ribs, which leads to the pulling-out of rebar; the other is the initiation and propagation of radial cracks from the bond interface towards the concrete surface, which eventually results in the splitting of the specimen. Therefore, it is rather essential to observe the behavior of the bond interface physically and dynamically throughout the pull-out process, and thus achieve a deeper understanding of the bond failure mechanism under reversed loading.

Different from the measurement with gages or sensors, a non-interferometric optical technique has been widely adopted to capture the continuous process of bond deterioration and crack initiation/propagation, which is the Digital Image Correlation (DIC) technique (Avadh et al., 2021; Leibovich et al., 2016, 2018; Okeil et al. 2020). By opening a window in the cover concrete of pull-out specimen, DIC is applied to measure the local concrete deformation and strain in the vicinity of the rib during the pull-out process (Leibovich et al., 2016). It is found that when the height of the window is limited, the impact on the global load-displacement response is neglectable (Leibovich et al., 2016, 2018). With this technique, it indicates that the first rib plays the predominant role against monotonic load rather than all ribs sharing the overall load evenly (Leibovich et al., 2018). Okeil et al. (2020) adopted DIC to uniaxial tensile specimens with embedded deformed bars in both concrete and cement paste, where the crack direction in concrete is found to be around 60° while the one in cement paste is almost axial to the bar direction. Furthermore, uniaxial tension test on specimens with corroded rebars embedded in intact concrete was conducted, and DIC was used to observe the deteriorated rebar-concrete interface (Avadh et al., 2021). The diagonal cracks at the tips of the ribs disappeared with higher levels of corrosion. The above studies show the huge potential of DIC to observe the continuous bond-slip behavior. However, they are still constrained under monotonic loading conditions such as pull-out or uniaxial tension.

Therefore, this paper conducts an experimental study using DIC technique to capture the bond failure process under cyclically reversed loading. The test is conducted with different rebar diameters and amplitudes of reversed loads. The DIC technique was used to dynamically observe the crack initiation and propagation at the bond interface between rebar and concrete, as well as the failure mode of the specimen. VIC-2D was used to analyze the deformation and strain distribution of the pulling-out specimen so that to reveal the bond failure mechanism. The test results indicate that the bond stresses are uniformly distributed along the interface during the initial loading phase. However, with increasing reversed loading, the stress concentration occurs at the tip of the bar and then the bond stress is gradually distributed heterogeneously near the interface, especially for bars with small diameters. After that, the shear cracks can be firstly observed for specimen failure by pullout with a small bar diameter. For specimen failure by splitting, the splitting crack appears near the peak bond point. The presence of the stirrups mitigates the degradation of the bonding strength, especially for specimens with large bar diameters. The results of this study can provide a basis for establishing the bond stress-slip model.

Digital image correlation

In this section, a brief introduction of the DIC technique is described. Digital Image Correlation, widely known as DIC, is an innovative non-contact optical technique for measuring strain and displacement. The technique is originally developed by the researchers at the University of South Carolina in the 1980s (Peters and Ranson, 1982; Peters et al., 1983). By comparing digital photographs of an object at various phases of deformation, tracking and recording blocks of pixels, from which 2D or even 3D deformation vector fields and contours can be created. Research has shown that the speckle pattern is a critical factor (McCormick and Lord, 2010), as it should be random and unique, exhibiting a range of contrast and intensity levels. In general, two types of speckle patterns exist: laser-based and artificial white-light-based (Pan, B et al., 2009). The former is produced by illuminating the object's surface with a coherent light source, such as a laser beam. However, decorrelation may occur if the target exhibits rigid movement, excessive strain, or out-of-plane displacement. The latter one is more robust and widely adopted in previous studies (Pan, B et al., 2009). The DIC technique offers several merits, including a simple setup and specimen preparation, low requirements regarding the ambient environment, and flexible sensitivity and measurement resolution. Meanwhile, the technique also has some defects such as the requirement of gray intensity distribution, imaging system-dependent quality, lower accuracy compared to interferometric methods. In all, the DIC technique has been widely adopted as an effective methodology for analyzing surface strain and deformation in the field of civil engineering.

Figure 1 shows the schematic and photo of DIC set-up adopted in this paper. As mentioned earlier, a random grey intensity distribution (speckle pattern) is applied to the surface of the specimen, perpendicular to the direction of the Charge-Coupled Device (CCD) sensor in the camera. Instead of relying on the natural texture of the specimen surface, this study utilizes dot painting, which will be introduced later. Two axisymmetric lighting sources are adopted to brighten the area of measurement to capture clear digital images. Using images of the region of interest (calculation area) before and after the deformation of the object, the computer calculates the motion of each dot in the region to derive values for deformation and strains.

Figure 1.

Schematic and photo of DIC set-up used in current study.

During the calculation, the entire region is divided into sub-areas or subsets. The change in the location of the central point is then compared, and its deformation is calculated accordingly, as illustrated in Figure 2. The reason for using a subset comprising multiple pixels rather than just a single targeted pixel (the central one in the sub-set) is that a wider variation in gray levels enables more unique identification and easier distinction from other sub-sets (Pan et al., 2009). Based on the assumption of deformation continuity, the adjacent pixels in the same reference sub-set with the central pixel should remain in the deformed sub-set (target sub-set in the target image). Therefore, a shape function or displacement mapping function (zero-order, first-order, second-order) is adopted to determine the location of adjacent pixels considering the rigid movement or deformed cases of the sub-set. To distinguish the similarity between reference and deformed sub-sets, correlation criteria are required which include two main types: cross-correlation (CC) and sum of squared difference (SSD) (Giachetti, 2000; Tong, 2005). VIC-2D is a powerful technology that enables the measurement of full-field displacement and strain data during mechanical testing of flat specimens. This innovative approach utilizes digital scatter correlation to accurately determine the actual displacement of the object, providing valuable insights into its mechanical behavior. Moreover, VIC-2D facilitates the computation of the Lagrangian strain tensor at every point on the object's surface, enabling a comprehensive strain analysis. Applying VIC-2D is straightforward, requiring only a simple calibration procedure and the introduction of random scatter on the object being measured. These steps enable precise measurements without extensive setup or complex instrumentation. In the present study, VIC-2D is employed to analyze deformation and strain patterns based on high-resolution digital images. By utilizing VIC-2D, detailed displacement and strain information can be extracted, offering a comprehensive understanding of the mechanical response of flat specimens.

Figure 2.

Region of interest and sub-set in the reference and deformed images.

Experiment preparation

Materials

The detailed configuration of rebar is given in Table 1. Ordinary Portland Cement (PO 42.5), river sand and crushed stone were adopted to cast concrete, where a water-to-cement ratio of 0.50 was used (JGJ55-2011, 2011). Cubic specimens are adopted with dimensions of 150 mm × 150 mm × 150 mm and maximum aggregate size of 20 mm (GB/T14685-2011, 2011), with the concrete specimens exhibiting a compressive strength of 37 MPa (Frappa et al., 2022) and an elastic modulus of 31.7 GPa. The mix proportion, based on density, each cubic meter of concrete consisted of 412 kg of cement, 206 kg of water, 610 kg of sand, and 1133 kg of coarse aggregate. Three rebars with different diameter (12, 16, 22 mm) were used in the specimens to reflect common adoption in medium-scale engineering applications. The test involved three distinct diameters of rebar with a crescent pattern, with corresponding bond lengths in the concrete set to be five times the direct length of the rebar. The selected bond lengths were 60 mm, 80 mm, and 110 mm, respectively. As stirrups, plain bars with a diameter of 6 mm were utilized, which were bent into square shapes of 60 mm x 60 mm.

Table 1.

Configuration and properties of rebar (GB/T 28,900-2012, 2012).

Grade	D (mm)	h_t (mm)	C_s (mm)	α (°)	f_y (MPa)	E_s (GPa)
D12	12	0.92	8.50	61.9	460	200
D16	16	0.70	10.45	62.1	399	200
D22	22	1.60	11.17	61.7	374	200

D: diameter; h_t: height of rib; C_s: rib spacing; α: angle of rib; f_y: yield strength of rebar.

Specimen

As shown in Figure 3, the pulling-out specimens were cast with special steel mold. The rebar was fixed in the middle of mold with covering removable tape at the un-bonding zones. To create a window for DIC observation, wood blocks with a semicircle groove (having the same diameter as the rebar) on the bottom were made and fixed on the top of the rebar, as seen in Figure 4. The wood block was wedge-shaped, not prismatic, for two reasons: 1. To allow light to be easily shed into the window so that to ensure the brightness for DIC observation; 2. To reduce the stress concentration during pulling-out induced by hole-opening and thus introduce a smaller impact on the bond-slip behaviors. After all these arrangements were completed, concrete was poured into the mold to cast specimens. The mold and wood block were removed 1 day after the casting and then the specimens were cured with constant temperature and humidity. To avoid steel corrosion, all the exposed parts of the rebar (loading end, inside the DIC window) were covered with waterproof tape. After 28 days of curing, all the tapes (from the un-bonding zone and waterproofing) were removed for further processing. Since there were still some pastes penetrating through the narrow gap between wood block and rebar, polishing was conducted to remove all the hardened paste on the surface of rebar. Afterwards, as required for applying the DIC technique, speckle patterns of white painting with black dots (density of around 5-10 dots/mm²) were randomly sprayed inside the window. Additionally, it is worth noting that prefabricated windows generally have three rebar ribs. For this study, 6 mm diameter stirrups were used and positioned on both sides of the mold, with a distance of 40 mm from the mold's edge, see Figure 4(c).

Figure 3.

Schematic of specimen and the mold before concrete pouring.

Figure 4.

(a) Wood blocks (b) casting (c) molds and stirrups (d) polishing (e) dots spraying.

Loading and DIC setting

A uniaxial electrohydraulic servo testing machine was adopted as the loading apparatus, which possesses a single vertical loading axis, as shown in Figure 5. The loading axis has a capacity of 50 tons with an attached load sensor (with a maximum capacity of 300 kN and an accuracy of 0.1 kN). A spherical hinge was used to eliminate eccentric loading. A schematic of the loading frame is depicted in Figure 5. The loading plates were fastened with bolts to provide a counterforce for extraction and to accommodate LVDTs (with a maximum range of 30 mm and an accuracy of 0.01 mm) for deformation measurements. The surface of specimen with window was set to face the camera with lightening system. After securely attaching the concrete block to the central plate, a loading rate of 0.02 mm/s, with a prescribed displacement, was applied to the deformed bar, following the recommendation of Solomos and Berra (Solomos and Berra, 2010).

Figure 5.

Picture of loading apparatus and schematic of loading frame.

All the specimen and loading conditions are summarized in Tables 2 and 3 for static and cyclic loading, respectively. “S” and “C” mean static and cyclic loading; “D” followed by the number indicates the diameter of the rebar; “W” means that the window-opening is adopted; The final “S” stands for whether the stirrup is used or not. For static loading, six specimens were prepared with rebar diameters of 12 mm, 16 mm, and 22 mm, along with the consideration of whether the window was opened for DIC observation. The static test aims to investigate the influence of window opening on bond-slip behavior. For dynamic loading, all six specimens had the windows opened, and the varying parameters were the rebar diameter and the presence of stirrups. After six cycles of repeated loading, the monotonic load was applied until failure.

Table 2.

Specimens for static loading.

Specimen	Window	Rebar diameter [mm]	c/D	A _sw /A _s
S-D12	No	12	5.75	0.25
S-D12W	Yes	12	5.75	0.25
S-D16	No	16	4.19	0.14
S-D16W	Yes	16	4.19	0.14
S-D22	No	22	2.9	0.074
S-D22W	Yes	22	2.9	0.074

c/D: the ratio between depth of concrete cover and diameter of rebar diameter; A_sw/A_s: area of stirrups relative to the area of longitudinal reinforcement.

Table 3.

Specimens for cyclic loading.

Specimen	Stirrup	Cycles	Prescribed displacement [mm]	Rebar diameter [mm]
C-D12W	No	6	±0.5,±1.0,±2.0,±3.0,±4.0,±5.0	12
C-D12W-S	Yes	6	±0.5,±1.0,±2.0,±3.0,±4.0,±5.0	12
C-D16W	No	6	±0.5,±1.0,±2.0,±3.0,±4.0,±5.0	16
C-D16W-S	Yes	6	±0.5,±1.0,±2.0,±3.0,±4.0,±5.0	16
C-D22W	No	6	±0.5,±1.0,±2.0,±3.0,±4.0,±5.0	22
C-D22W-S	Yes	6	±0.5,±1.0,±2.0,±3.0,±4.0,±5.0	22

Result and discussion

Static loading

The relationships between bond stress and slip during static loading are plotted in Figure 6. The solid lines represent the specimen without window-opening, and the dashed lines stand for the specimen with window-opening. It is found that the window-opening may lead to a slight reduction (less than 10%, as shown in Table 4) in bond strength, which is nearly negligible. However, the stiffness is somehow influenced by the window excavation. Since this paper focuses on the peak stress, the window-excavation is believed to be acceptable. The comparison demonstrates the feasibility of using this window-opening method with the DIC technique to capture bond-slip properties without introducing additional damage, similar to the previous studies (Leibovich et al., 2016, 2018).

Figure 6.

Bond stress-slip curves under static loading.

Table 4.

Peak Stress and Stiffness of the bond Stress-slip Curves Under Static Loading.

Specimen	τ_max [MPa]	Difference (%)	Stiffness [N/mm³]	Difference (%)
D12	11.06	4.61	21.38	17.49
D12-W	10.55	4.61	17.64	17.49
D16	10.38	6.07	15.78	11.79
D16-W	9.75	6.07	13.92	11.79
D22	9.33	5.68	18.01	19.88
D22-W	8.8	5.68	14.43	19.88

Table 5.

Bond Stress and Slip at Peak Point Under Cyclic Load.

	D12W	D12WS		D16W	D16WS		D22W		D22WS
s (mm)	τ (MPa)	τ (MPa)	s (mm)	τ (MPa)	τ (MPa)	s (mm)	τ (MPa)	s (mm)	τ (MPa)
0.5	8.52	14.48	0.5	11.99	16.89	0.224	10.31	0.25	13.3
−0.5	−7.34	−12.28	−0.5	−8.87	−13.37	/	/	−0.3	−7.42
1	5.37	11.32	1	8.95	11.28	/	/	1	6.01
−1	−4.24	−9.35	−1	−5.77	−8.16	/	/	−1	−4.29
2	2.82	8.56	2	5.65	5.96	2	1.45	2	6
−2	−1.88	−6.26	−2	−3.7	−3.68	−2	−0.75	−2	−4.08
3	1.13	3.3	3	2.27	2.46	3	0.53	3	4
−3	−0.74	−2.09	−3	−1.66	−1.46	−3	0.54	−3	−2.51
4	0.36	0.94	4	0.84	1.01	4	0.33	4	2.58
−4	−0.27	−0.64	−4	−0.82	−0.45	−4	−0.4	−4	−1.37
5	0.21	0.42	5	0.32	0.33	5	0.18	5	1.41
−5	−0.2	−0.5	−5	−0.5	−0.29	−5	−0.16	−5	−0.83

Furthermore, the failure mode of deformed bar pullout is primarily governed by the ratio of the depth of concrete cover “C” to the diameter of the rebar “D” (Li et al., 2016, 2022; Wu et al., 2013; Xu et al., 2012): when c/D is less than 4.5, shear cracking initiates, leading to concrete failure; when c/D is greater than 4.5, the rebar typically gets pulled out from the concrete. In this study, for the D12 case, the ratio is calculated as (75-6)/12=5.75, which is greater than 4.5. Consequently, the rebars were observed to be pulled out, causing the concrete between the ribs to crush, as shown in the red curves. In the case of D22, where the ratio of c/D is less than 4.5, pronounced splitting failure occurs, resulting in a sharp decline in bond stress, as depicted by the blue curves in Figure 6. Corresponding to the failure mode, the bond strength also decreases as the value of c/D increases (from D12 to D22).

Cyclic loading

Failure mode

Similar to static loading, the failure modes under cyclic reversed loading also have two types, depending on the confinement provided by stirrups and concrete cover, which include rebar pullout and concrete splitting cracks. Figure 7 illustrates the failure modes of all specimens. For D12 cases in Figure 7(a), the failure mode is similar to that in the static test, where the rebar was pulled out from the concrete regardless of whether stirrups were used or not; For the D16 case in Figure 7(b), (a) mixed failure mode is observed when no stirrups were placed inside the concrete (D16W), in which the rebar was pulled out along with some observed splitting cracks in the concrete. When stirrups were used (D16W-S), the rebar was pulled out without any splitting cracks, owing to the strong confinement provided by the stirrups and the enhanced properties of the concrete; For the D22 case in Figure 7(c), the depth of concrete cover was even smaller, leading to an increased loss of confinement from the surrounding concrete when no stirrups were used. As a result, the typical splitting failure of concrete is observed for D22W. When stirrups were added in the concrete, the confinement was enhanced, causing the failure mode of D22W-S to become mixed, involving both rebar pullout and concrete splitting cracks. In other words, when the rebar diameter is large enough to cause splitting failure during pulling-out test, the stirrup ratio (Asw/As) will have an obvious impact on the failure mode. Otherwise, when the pulling-out failure happens with small rebar diameter, the enhancement of stirrup ratio on the failure mode is not significant.

Figure 7.

Failure modes under cyclic loading (a) D12, (b) D16, (c) D22.

Bond stress-slip curves

In addition to the failure modes, the bond stress-slip curves of specimens during cyclic loading are presented in Figure 8, and the values of peak bond stress with corresponding slip are summarized in Table 5. As mentioned in Table 3, the cyclic load was applied using displacement control ranging from 0.5 mm to 5 mm. Generally, the bond properties (i.e., peak bond stress, loading stiffness) degrade with increased reversed loading cycles and increased prescribed displacement. The envelope of the ascending branch in the first loading cycle is the same as that in the static loading case. Unloading occurs very quickly, resulting in the same slip value as the peak bond stress in each loading cycle. A frictional phase is clearly noticeable before the onset of the reverse loading phase. Furthermore, it can be observed that within one forward-backward loading cycle, both the bond strength and stiffness exhibit degradation during the latter part. For D22W, due to the large ratio between rebar’s diameter and concrete cover as well as the lack of stirrup and confinement, severe splitting crack appears during the first loading cycle as also shown in Figure 7(c). As a result, the bond strength deteriorated significantly, and almost no bond stress was observed during the second loading cycle.

Figure 8.

Bond stress-slip curves under cyclic loading (a) D12, (b) D16, (c) D22.

Mechanism

The mechanism of bond deterioration under cyclic loading is plotted in Figures 9 and 10. Figure 9 depicts the macroscale constitutive relationship between bond stress and slip of the deformed bar under cyclic loading. The model encompasses several phases within one cycle: forward loading phase (oab), forward unloading phase (bcd), reverse friction phase (de), reverse loading phase (efg), reverse unloading phase (gh), forward friction phase (hi). When the loading cycles reach a certain count and the damage accumulates to a certain extent, the rebar will be pulled out and follow the subsequent phase (pq). Figure 10 illustrates the mesoscale interaction between ribs and the surrounding concrete during the initial loading cycle: as the pulling-out load on the rebar increases, the ribs push against the concrete, leading to crushing of the concrete in front of the rib (in the forward loading direction). Simultaneously, the force acting on the concrete can be divided into two components: the shear force along the longitudinal direction of the rebar and the expansive force in the radial direction. The former term will cause diagonal cracking at the tip of ribs, while the latter term will be confined by the circumferential stress of concrete. When the circumferential confinement is strong enough, the rebar will be pulled out from the concrete. When the confinement is weak, splitting cracks may propagate towards the edge of the concrete, resulting in splitting failure. Unloading is assumed to occur within a very short period (bcd in Figure 9), and a frictional phase (de in Figure 9) precedes the reattachment of the ribs to the concrete in the reverse direction. As the reverse loading increases, diagonal cracking occurs in the reverse direction (on the left side), while the crack induced by forward loading (on the right side) closes. Furthermore, if the prescribed displacement in the loading cycle exceeds the slip value at the peak bond stress, the bond stress exhibits a significant decay (τ_sn⁺).

Figure 9.

Macroscale and global bond stress-slip constitutive relationship under cyclic loading.

Figure 10.

Mesoscale and local mechanism of bond-slip behaviors under cyclic loading.

DIC observation

Principal strain

The principal strains of D12W and D12W-S captured by DIC technique are plotted in Figures 11 and 12. Each row represents the loading phase as described in section 4.2.3 and Figure 9, and each column stands for the number of loading cycles in terms of prescribed displacement.

Figure 11.

Principal strain of specimen D12W.

Figure 12.

Principal strain of specimen D12W-S.

From Figure 11, it is evident that no obvious diagonal crack is observed at the tip of the ribs. Instead, a longitudinal crack between the rebar and concrete is visible, and the crack width increases with the applied load (prescribed displacement). In fact, immediately after the first loading cycle (±0.5 mm), this longitudinal crack occurred, peeling off the speckle patterns and making it difficult for DIC to capture the behaviors at the rebar-concrete interface. Figure 12 illustrates the principal strains observed when stirrups were employed (D12W-S), resulting in a delayed bond failure due to the confinement provided by the stirrups. Towards the end of the reverse unloading phase in the third loading cycle (±2.0 mm), the longitudinal crack became evident, leading to the removal of speckle patterns at the interface region. Prior to this, strain concentration was identified near the ribs, as indicated by the red region in the contours.

The principal strains of D16W and D16W-S, captured using the DIC technique, are presented in Figures 13 and 14. For D16W in Figure 13, no splitting crack towards the edge of concrete cover was observed and the failure mode was pulling-out of rebar. For the initial two loading cycles (±0.5 mm and ±1.0 mm), the principal strain mainly showed up in the concrete between two ribs, and no obvious diagonal crack was captured. When the prescribed displacement increased to ±2.0 mm (around b point), one diagonal crack shows up at the right side of rebar. With repeated loading, the concrete between ribs were pressed by shear force while the diagonal crack became wider through cyclic opening-closure. The crushed concrete kept peeling off, especially at the 4^th and 5^th loading cycles (±3.0 mm and ±4.0 mm), which made the DIC observation of bond interface ineffective. For D16W-S in Figure 14, with confinement by stirrup, the diagonal crack did not take place as for D16W. Instead, the longitudinal crack between rebar and concrete happened, which was similar as the case for D12W. The strain concentration (red region) shown up near the ribs at initial loading cycles were released by the crack opening at later loading cycles.

Figure 13.

Principal strain of specimen D16W.

Figure 14.

Principal strain of specimen D16W-S.

The principal strains of D22W and D22W-S captured by DIC technique are plotted in Figures 15 and 16. For D22W, a splitting crack happened at the third loading cycle (±2.0 mm) and the specimen came to failure accordingly. Similar as D12 and D16 cases, the strain concentration was clearly shown between the ribs. Furthermore, the contour of D22W up to loading of ±2.0 mm indicated the shape of diagonal crack as plotted in Figure 10. After shear failure took place (g point of ±2.0 mm), concrete inside the window was peeled off, which made the DIC ineffective. For D22W-S where stirrup was adopted, a splitting crack happened above the window soon after the prescribed displacement reached −0.5 mm (g point). But the concrete below the window remained intact. With the loading cycles increased and the loading amplitude became larger, this splitting crack was slightly widened. But a crack going through the concrete from top edge to bottom edge did not appear as for D22W. Finally, the D22 rebar was pulled out from the concrete block. Similar as D12W-S and D16W-S, the longitudinal crack was observed with failure of DIC to capture the interface behavior.

Figure 15.

Principal strain of specimen D22W.

Figure 16.

Principal strain of specimen D22W-S.

Crack opening (normal direction)

The contour maps of principal strain shown in section 4.3.1 could help to judge the strain distribution and crack propagation qualitatively. In order to conduct quantitative evaluation, VIC-2D analytical results were described in this section. As shown in Figure 17, two reference lines were marked at same height, where one was placed along the longitudinal rib of rebar and the other was placed parallelly on concrete at 5 mm from the bond interface. Through VIC-2D system, the reference line is divided into 200 points, and the horizontal distance between two corresponding points at different reference lines was recorded and regarded as the crack width. The crack width up to the end of first forward loading (b point of +0.5 mm in Figure 9) was recorded and analyzed considering the fact that maximum bond stress was reached (see Figure 8) and specimen D12W failed before +0.5 mm.

Figure 17.

Reference lines L0 (along rebar) and L1 (along concrete).

The crack width of different specimens up to a prescribed displacement of +0.5 mm is plotted in Figure 18

Figure 18.

Crack width of different specimens up to prescribed displacement reached +0.5 mm. (a)D12W. (b)D12W-S. (c)D16W. (d)D16W-S. (e)D22W. (f)D22W-S.

, where 10 point-couples at the same interval of distance are selected from among the 200 point-couples. Horizontal axis means the position of each point-couple (distance to the top of window) inside the window, and vertical axis stands for the crack width (distance between two reference lines). The region between two ribs is also clearly indicated as the dashed lines. For each specimen, 10 lines are plotted depending on the stress ratio to the bond strength. From the figures, it indicates that with the increased bond stress, the crack mainly initiated and enlarged in the concrete between two ribs. In addition, the maximum crack width is plotted in Figure 19

Figure 19.

Maximum crack width along the rebar.

. If comparing the specimen with and without stirrups, it is found that the stirrup could significantly reduce the crack happening and propagation. For specimens with different bar size, the crack initiation took place at bond stress ratio reached 20% for D12W and the crack width reached maximum when bond stress ratio became 90%. If keep loading (e.g., b point, +0.5 mm), there is a break in the curve which means the concrete crushing at the interface and DIC became ineffective. When stirrup was added (D12W-S), the sudden propagation of crack took place at bond stress ratio of 70%. Even when the prescribed displacement reached +0.5 mm, the curve is still continuous which means the concrete along the bond interface remained effective. For D16 and D22 cases, similar failure was captured at +0.5 mm of loading when no stirrup was adopted.

Shear strain (shear direction)

In addition to the normal behavior, the shear behavior is also focused since it has close relationship with the bond-slip characteristics. Figure 20

Figure 20.

Shear strain contours for (a) D12 (b) D16 and (c) D22 without stirrup.

shows the shear strain of specimens without stirrup during the first forward loading, which was captured by DIC technique. It can be seen that the shear strain usually enlarges faster at one side (right side). Along the longitudinal direction, the shear strain is not uniformly distributed for D12 but more evenly distributed in terms of larger bar size (D16 and D22). For D12, the shear strain initiates at very early stage (bond stress ratio=20%); while for D16 and D22, the shear strain initiates at later loading stage, such as 60% and 40% of bond stress ratio. Through strain measurement of rebar’s strain with embedded gauges, it is found that bonding length of 5D will lead to an uniform strain distribution. However, with DIC observation, it indicates that the deformation of concrete (interface) is not uniform. The shear strain of specimens with stirrup is plotted in Figure 21, where the strain of D12 becomes more uniform with the confinement by stirrup.

Figure 21.

Shear strain contours for (a) D12 (b) D16 and (c) D22 with stirrup.

Using the reference lines as shown in Figure 17, the shear strain of each line was recorded, and the difference was calculated. This factor represents the shear strain difference between concrete and rebar, and the values are given in Figure 22. For D12, the shear strain distributes uniformly at early loading stage (bond stress ratio up to 50%) and concentrates in the region between two ribs at later loading stage. For D16 and D22, this critical value becomes 60%–70%. Compared to the specimen without stirrups where the shear strain is between 0.005 and 0.02, 0-0.026, 0-0.015 for D12, D16 and D22, the specimen with stirrups has the shear strain between 0 and 0.026, -0.01-0.02, 0-0.04. It means that the shear strain (also stress) is enlarged by the confinement of stirrup. Thus, the usage of stirrup could effectively enhance the bond performance between rebar and concrete.

Figure 22.

Shear strain difference between rebar and concrete. (a)D12W. (b)D12W-S. (c)D16W (d)D16W-S. (e)D22W. (f)D22W-S.

Relationship between DIC and cyclic bond-slip

In section 4.3.1, the time-dependent strain distribution is described to show the localized behaviors of bond interface, where most contours after the second loading cycle (2.0 mm) have become ineffective as shown in Figures 11 –16. With the method of referencing lines (dots) to analyze the normal crack and shear strain by VIC-2D as presented in sections 4.3.2 and 4.3.3, the time-dependent performance of cyclic bond-slip could be roughly derived from the DIC measurement even after the contours along interface becomes blurry. Referencing points are set at two positions (at the rib and between two ribs), see Figure 23(a). The global slip at the initiation of local cracking is plotted for both locations as shown in Figure 24. From Figure 24, it indicates that the local crack takes places at later loading stage (with higher global slip) when it comes to the rebar with larger diameters for both cases (with or without stirrups), but the difference is almost neglectable. Comparing the case with and without stirrups, the stirrup is found to postpone the local crack-initiation, which corresponds well with the findings by the contour maps shown in section 4.3.2.

Figure 23.

Referencing points for the analysis of (a) global slip indicated by initiation of local crack (b) time-dependent local crack at different global loading stage.

Figure 24.

Relationship between global slip and local crack widths. (a) D12W. (b) D12WS. (c) D16W. (d) D16WS. (e) D22W. (f) D22WS.

In addition, to overcome the occurrence of ineffective contours after second loading cycles, two referencing points are set at specified regions after processing the whole loading process with VIC-2D, see Figure 23 (b). The absolute displacement of two points at different loading stages for all cases are shown in Figure 25

Figure 25.

Time-dependent displacement of referencing points (local crack widths). (a) D12W. (b) D12WS. (c) D16W. (d) D16WS. (e) D22W. (f) D22WS.

. From the figures, it yields that the width of local cracks increases with the prescribed displacement, which shows a more significant change at early loading stages (before 2 mm) rather than the later ones (after 2 mm). This correlates to the change of bond strength that decreases more rapidly at early loading cycles, see Figure 8. In each loading cycle, the crack at forward and backward branches may largely vary, in which obvious differences are found for certain cases (a, b, d, e) while same for rest cases (c, f). In addition, the residual crack keeps accumulate, which shows consistency with the decay of global residual bond strength, as shown in Figures 8 and 9. It shall be noted the results in both Figures 24 and 25 has close relationship with the referencing points selected as Figure 23. Therefore, although big potential is shown regarding the quantitative link between the global index (bond strength or slip) and local index (crack width), quantitative relationship requires more precise analysis with more referencing points at different location, which will be conducted in the future work.

Conclusion

This paper presents an experimental study with DIC technique to investigate the macroscale and global bond behaviors of pulling-out of steel rebar embedded in concrete cubes under the cyclic reversed loading. Small window is excavated in the cover concrete for DIC observation of mesoscale and local behaviors between rebar and concrete, where the excavation has neglectable impact on the entire bond performance. From this paper, following conclusions could be drawn:

1. The dimension of rebar compared to the depth of cover concrete and usage of stirrups have significant impact on the failure modes of pulling-out test. When the cover concrete is thick and stirrup is adopted, satisfied confinement will be provided so that the rebar is pulled out from the concrete. Visa-versa for the thin cover concrete and no stirrup is adopted, diagonal crack initiates from the tip of ribs and propagates to the concrete surface to cause splitting failure. The macroscale bond characteristics could be clarified well by the mesoscale crack initiation and propagation observed by the digital images.

2. The mesoscale and local mechanism is proposed to explain the macroscale and global cyclic bond behaviors according to the DIC observation. The schematic of the bond-slip characteristics is revealed.

3. At mesoscale level, from the data analysis of bond interface along both normal and shear direction by VIC-2D, failure mode of pulling-out test mainly happens at the tip of ribs as well as the region between the ribs. The former one causes the diagonal cracking (splitting failure) and the latter one results in the shear sliding of rebar from concrete.

4. From the DIC observation, it is found that the shear strain distributes evenly at the early age of cyclic loading. But at specific point where the micro-crack initiates, the shear strain is concentrated around the ribs, which breaks the uniformity and thus lead to the final failure. This is different from the observation of uniform strain distribution of rebar obtained from embedded gage with respected bonding length of 5 times of rebar diameter.

5. The macroscale properties (global slip) are found to correspond well to the mesoscale factors (normal displacement between two reference points), which shows the huge potential of using DIC technique to measure the entire process of the bond characteristics under cyclic reversed loading. Parametric study will be conducted in the future to derive the empirical model of the bond-slip constitutive relationship with mesoscale parameters for further analysis.

Footnotes

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the National Natural Science Foundation of China (No. 51809025, 51978630), Chongqing Natural Science Foundation of China (CSTB2022NSCQ-MSX0509), and the Chongqing Transportation Science and Technology Project (Grant No. 2022-06).

Correction (November 2024):

Reference “Frappa G and Pauletta M (2022)” has been updated to include the correct proceeding dates and page numbers.

ORCID iD

Zhao Wang

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