A reassessment of the existing literature has shown considerable effort to understand the mechanism behind bond deformation of RC structures under loading. It has been proven that when a deformed bar is used as tensile reinforcement, the rebar ribs are bonded with the surrounding concrete. Concrete cracks around reinforcement are mainly connected to the durability effect and the binding mechanism problem between RC members. Cracks can lower the life expectancy of RC structures by allowing carbonation, chloride ion ingress, moisture migration, and oxygen to enter the reinforcement area (8, 16). Even while cracks accelerate corrosion, their effects are limited to the length of the bar parallel to the crack’s width. As a result, concrete quality and cover thickness are critical criteria for preventing steel corrosion in concrete (17).

Therefore, this study considers the investigation of bond loss of RC by pullout reinforcement in cylindrical concrete to understand the essence of concrete cover in RC members under tension load with bond deterioration in lieu of corrosion and the residual bond interaction. PVC hollow pipes created the bond loss between the concrete and the reinforcing bar. Silicon gum was infused between the bar and the PVC hollow pipe to prevent free movement of the bar during testing. Moreover, structural members such as beam-column, corbel, dapped end beams (RCDEBs), and members with a sudden change in geometry often experience bond deterioration at the recess sections under loading due to the concentration of stresses at that point. To understand the behaviour of these structural members under loading, the author selected RCDEBs that exhibit tension damage at the dapped section. The bond loss was created at the nib of the dapped section of the beam and loaded monotonically till failure.

Furthermore, experimental evaluation and computational simulation of reinforced concrete structures are frequently used to analyze the nonlinear behaviour of concrete structures. Although the former yields accurate results, it can only explain occurrence under specific geometries, loading, boundary conditions, and cost (17). The latter involves creating computer models of reinforced concrete, which frequently has no boundaries. Numerical analysis is an alternative to the rigorous and expensive experimental study. The adaptability of the bond loss system in the experiment was then modelled in the Concrete Model of 3 Dimension (COM 3D) finite element software system to evaluate the efficiency of the software for large-scale adoption of structural members exhibiting bond deterioration.

Tepfers (18) used finite element analysis to describe the radial components of bond forces balanced against tensile rings in concrete (FEA). Independent of the rib face angle, the angle was 45^o along a perimeter touching the ribs of reinforcing bars. The rib face angle influences the bond behaviour of bars with rib face angles (19). The bond behaviour changes when the rib face angle is less than 30o. Bond strength is reduced in bars with small rib spacing and height. Goto (8) tested the propagation of various cracks around tensile reinforcing bars. Internal cracks form around the reinforcing bars in concrete, as illustrated in Figure 2. The internal cracks are categorized as primary and secondary cracks. The former is generated at an angle perpendicular to the bar lug and propagated outward on the account of increasing stress; the latter is formed due to the slipping. Internal crack inclination and compressive force direction on bar ribs vary between 45^o and 80^o.

RCDEBs increase the lateral flexibility of structural support members, can also reduce the total height distance of precast concrete frameworks, and often has a lower self-weight due to a change in the cross-section of the reentrant portion (20, 21). They have also been used in precast bridge girder members. They have recessed ends supported by cantilevers, columns, corbels, or inverted T-beams (22). Nevertheless, RCDEBs are weakened at the reentrant corner because the flow of internal stresses is disrupted by the change in the cross sections, resulting in zones of non-uniform stress distribution near the reentrant corner and the nib (23). Due to the high bearing reaction and the alteration in geometry, the reentrant corner has a high-stress intensity. These discontinuities in a member are referred to as disturbed regions (D-regions) (24-26). The formation of diagonal tension cracks will reduce the strength of the full-depth part of the dapped end under the yielding of the hanger reinforcing bars, as shown in Figure 3. Mattock and Chan (27), and Aswin et al. (28) identified different cracks leading to failure of the RCDEBs. The failure includes; the diagonal tension cracks at the reentrant corner, nib and undapped critical portion, flexural and axial tension at the extended end, and direct vertical shear between the nib and the undapped end. The shear strength performance of the RCDEBs depends on the nib-to-full depth ratio and spacing of the hanger bar close to the dapped end (29). Changes in nominal shear span and height of the nib will give different diagonal tension strength capacities of RCDEBs. Mohammed et al., (30) evaluated the performance of RC and R-ECC DEB on the role of stirrups and the diagonal reinforcing bar, although the investigation was remarkable with an increase in failure load while there was a delayed in crack initiation, the reentrant portion lost its confining strength which resulted in damage at the tension zone. Due to anchorage deterioration and overloading, the failure of bridges with dapped ends has been rampant in the last decade. Failure of the De la Concorde bridge in Canada was reported in 2006 due to bond deterioration of the anchorage zone (31). The collapse of the Annone overpass in Italy was reported recently due to corrosion of prestressed tendons at the anchorage zone (32-34). Maintenance of the dapped section (anchorage zone) of RCDEBs in the bridge girder requires excellent effort due to this recess portions that sit on other structural members; water or eroded materials can amass on this part, which can hasten the deterioration of the beam by causing corrosion concern (17). It is thus necessary to understand the damage mode of the RCDEBs subjected to increasing monotonic load under bond deterioration to proffer strategies for monitoring and maintenance for practical engineering.

The FEM of the specimen was carried out with the aid of the COM 3D system, under the multi-fixed crack approach, COM3D focuses on the full model of the reinforcement inside the concrete material to form the RC mesh. The reinforcing bar in Figure 5 was modelled in one dimension with the yield stress of the bar. The mesh density was accounted for here to avoid the coarseness of the FEM mesh, which could lead to unreliable output during loading. The exact dimension in Figure 4 was considered for the analytical model of pullout specimen. The hollow PVC plastic pipe properties were inserted into the mesh at the vicinity of the rebar where necessary, with a bond interface applied between the mesh and the embedded reinforcing bars. When investigating the response of RC structure under loading, it is essential to consider the bond interaction between the composites. COM3 permits the model of the bond interface between the composite to ensure adequate bonding. Figure 6 shows the bond interface element model used in place of steel and concrete properties under Mohr-Coulomb’s frictional law (34). Table 1 shows some of the properties of concrete, steel PVC plastic materials and the interface element considered during the analysis of the bond loss.

Figure 7 is the constitutive model of RC considered under the active fixed crack approach, where the stresses generated from the RC are a simple summation of the concrete crack model and the embedded reinforcing bar. The combination of the tension softening-stiffening model normal to cracks, compression-tension model along cracks, and shear transfer along cracks is required to develop the stress-strain relationship of cracked concrete in the elastoplastic domain. Some governing equations have been presented under the active fixed crack approach (35, 36).

M35 concrete mix grade was designed to achieve a 28-day characteristic cylindrical compressive strength of 35 MPa. Ordinary Portland cement, fine aggregate, and coarse aggregate with a maximum aggregate size of 20 mm are the constituents of the concrete mix, as presented in Table 2. The water-cement ratio (w/c) was 0.43, and the air-entraining water-reducing agent was 0.3% by weight of cement. In addition to the cast specimens, cylindrical sizes of 100 mm diameter and 200 mm height were cast to determine the concrete’s compressive strength and split tensile strength. The slump and air entrainment test results are 110 mm and 1.75%, respectively. The tensile strength of the reinforcing bars was determined in the laboratory using a universal testing machine with a capacity of 1000 kN. Figure 8 shows the plot of stress versus strain of the tensile test results of the 22 mm and 10 mm diameter bars and concrete compressive strength. The strains were captured with the strain gauges attached to the data logger machine. The test results made part of the input data in the analysis. The yield stress and ultimate strength of the 22 mm diameter bar are 410 MPa and 544 MPa, respectively, while the yield stress and ultimate strength of the 10 mm diameter bar are 500 MPa and 614 MPa, respectively.

Six specimens of the pull out tests were prepared in total (two for each series). Table 3 describes all the specimens, the compressive strength and splitting test for experimental investigation and analysis. The prepared pullout molds with the rebar centrally placed inside and the steel strain gauges affixed to the steel in Figure 9 were cast in three layers, each layer was compacted twenty-five times with a tamping rod, and the top surface smoothened. The binding wire was used to support the rebar at the upper part of the mold to achieve a persistent condition, while the lower part was guided with polystyrene material. The specimens were covered with a wet curing sheet and cured continuously for 7 days. After the seventh day, the cast specimens were demolded and wrapped in a wet curing sheet for the remaining 28 days, where water was constantly provided for curing. Concrete strain gauges were attached to all the specimens in the transverse direction to measure the concrete strain development during loading.

A universal testing machine (UTM) of 1000 kN capacity was used for the pullout test, as shown in Figure 9 (right side). The pullout specimen was put into the machine such that the movable part of the machine held the unintegrated length of the deformed bar to pull it out of concrete during testing, while the static part held the concrete in position. A hollow base plate with a 50 mm centrally bore-hole was provided on top of the static part where the concrete sat, and the unintegrated length of the steel was passed through the hollow base plate and anchored on the movable part. Gypsum flakes were prepared to balance the concrete so that the applied load could be evenly distributed during testing. The steel strain gauges and that of concrete were connected to the data logger to retrieve the strain response of the RC during the pullout. A displacement transducer (LVDT) was also mounted on the movable part to measure the amount of displacement up to the maximum load. The top surface of the concrete was fixed in the case of FEM loading of the pullout analysis, while the tensile load was applied at the tip of the steel (Figure 5). The bottom of the specimen was not supported to imitate the exact circumstances in the experiment.

The cracking load, load at failure and the deflection/slip of the pullout specimens for both experimental investigation and analysis are presented in Table 4. The load that generated the initial concrete cracks was considered since it signified the emergence of RC nonlinearity. The equivalent displacement, δ _y , was also assessed. The ductility ratio, ∆ u δ y , defines the ratio of initial crack displacement to the failure load displacement (37). Generally, the pullout analysis revealed a significant increase in capacity with high stiffness and deformation over the experiment in each group except for C1, as shown in Figure 11. This could result from increased concrete compressive and splitting strength (see Table 3). There is a reduction in slip displacement when the bond loss is considered at the bottom since the concrete crack emerged from the weak bond zone. When comparing the failure capacity of the experimental specimen, C1 increases by 10% and 11% over BB1 and BM1, respectively, and 2% and 8% over the analyses of BMA and BBA. While the failure capacity of the control analysis CA is the same as that of the BMA, it increases by 6% over the BBA.

Figures 12 and 13 show the load versus strain generated from reinforcement and concrete. The strain was measured by strain gauges mounted on both the surface of the reinforcement and concrete in the case of the experiment. In contrast, the space average of the strains under the active crack approach of the most stressed portion of the specimen was examined in the case of the analysis investigation. Apparently, a linear-elastic relationship initially occurred before concrete cracking. The reinforcement strain moderately increased as soon as the micro-cracks was generated, and a further increase in load resulted in the nonlinearity of the RC. Although there is no yielding point of reinforcement in all the specimens up to the failure load, as presented in Figure 12 (at a yield value of 2000µ), concrete began to crack as soon as the tensile stress generated exceeded the tensile strength of concrete. The concrete strain of -200µ has fairly been exceeded as indicated in Figure 12, except in BB2, due to the detachment of the strain gauge during loading.

The struts and Ties approach was adopted to model the reinforcing bars detailing the RCDEB. Figure 14 depicts the strut-and-Tie flow chart model as well as the specimen’s reinforcement detailing. The chosen dimensions are 1600 mm × 200 mm × 400 mm in length, width, and depth. The dapped end’s length, width, and depth are 300 mm × 200 mm × 200 mm. All stirrups were made of 10 mm diameter deformed bars with 150 mm centre-to-centre spacing close to the dapped portion and 210 mm centre-to-centre spacing in the middle. The nib longitudinal tensile and flexural bars were reinforced with 22 mm diameter reinforcing bars. Two series of RCDEBs specimens were considered, the control specimen and the bond loss specimen made with the PVC plastic hollow pipe was infused at the recessed corner, as shown in Figure 15. The same diameter of PVC pipe considered for the pullout specimen was used, with a length of 140 mm. steel strain gauges of 5 mm were mounted on both the stirrup bars close to the reentrant section and the longitudinal bar at the nib section, while 60 mm concrete strain gauges were mounted on the concrete.

Steel formwork was set up for RCDEB casting with plywood used to create the dapped-ends, detailed reinforcement was placed inside the formwork, and freshly prepared concrete was poured inside the formwork and vibrated with a vibrating machine to achieve workable concrete as shown in Figure 17 (left side). Four beams were cast, two for control and the others for bond loss, using PVC hollow pipe.

The RCDEB specimens were instrumented to obtain enough data recorded by the data logger, particularly at the dapped section where the bond loss occurred. The steel strains were measured with 5 mm electrical resistance steel strain gauges mounted to the longitudinal reinforcement at the nib and flexure zones. The strain gauges were also attached to the hanger reinforcement on the left and right sides of the beam to evaluate the strain values developed during loading. 60 mm concrete strain gauges were also attached to the concrete surface close to the dapped end. Three 25 mm capacity LVDTs were placed on the beam at the lower portion of the loading point and the top side of the supports to measure the vertical displacement of the beam. The test beams were subjected to three-point bending on a UTM with a capacity of 2000 kN in Figure 17 (right side), where the load was applied at a shear span to depth ratio (a/d) of 1.5 and the midpoint for the two series considered. A top steel rigid plate 200 mm × 200 mm was employed to transfer the load from the machine head to the beam. The load was applied in 5 kN increments till failure. In the case of the RCDEB FEM study, the incremental static load was applied at the transverse nodes, either at the midpoint or a/d, as the case may be (Figure 16).

Figures 18 and 19 show the damage patterns of RCDEB subjected to increasing monotonic load at a/d=1.5 and the midpoint. The first crack generally started at the reentrant corner and spread towards the compression zone as the monotonic loading increased. Loading at a/d=1.5 resulted in quick failure compared with loading at the midpoint because the hanger reinforcement near the dapped end and the nib longitudinal reinforcement sustained the increasing stresses. However, the tensile reinforcement aided in resisting the crack alongside the hanger reinforcement in the case of loading at the midpoint. In the case of control beams, the diagonal tension cracks formed were relatively between 45^o and 60^o when measured with a protractor. There was a separation between the bond loss zone at the nib section and the remaining part of the full depth of the RC close to the reentrant portion. The measured crack angle ranged between 25 and 40^o. At fairly high stress, diagonal cracks were formed at the full critical depth of the recess portion, resulting in the failure of beams BLE and BEM. This indicates that stresses tend to concentrate at the weak zone under high static loading.

On observing the maximum principal strain of the damage mode of RCDEB under FEM analysis as presented in Figure 20. The loading was gradually applied here at an increment of 5 kN. There is a close conformity between the experiment and the analysis. The crack was initiated at the reentrant corner and propagated with crack width extension. Another diagonal tension crack formed at the full depth travelled to meet the previous cracks at an incremental loading. In the case of the bond loss specimens BLA and BAM, the reentrant cracks travelled parallel to the longitudinal nib reinforcement indicating the separation of the nib sections from the remaining part of the beam due to the increasing slip action. Flexural cracks culminated in the failure of CAM and BAM when loaded at the midpoint.

As a result of the response under increasing monotonic load, cracking occurs when the induced tensile stress in concrete reaches its ultimate tensile strength near the bond loss region. Due to the loss of tensile stresses in the concrete at the crack position, the stresses in the concrete are subsequently transferred to the reinforcing bars through the bond formed between the concrete and the reinforcement during the cracking stage. Following that, the hanger reinforcement near the recessed corner absorbs additional tensile stresses released by the cracked concrete.