FE analysis of pulled-out eccentrically spliced longitudinal headed bars for precast beam-footing connections

ABSTRACT Load transfer in structural elements of RC constructions and the behavior of such constructions are basically dependent on the detailing of both the structural elements and their connections. Assessing analytically the characteristics and behavior of such structural elements and their connections under likely occurring loads is an important issue. For common detailing of footings in steel and precast structures, longitudinal reinforcement of foundation beams is bent horizontally and spliced with reinforcement of cast-in-place footings to insure an adequate juncture for load transfer. In this study, as concerned with reducing construction time and cost, instead of bending longitudinal reinforcement bars of both, beams and footings, headed reinforcement bars are adopted. By doing so, a discontinuity region is created where longitudinal bars of footings become eccentric to those of beams that are embedded in the footings. To allow the flow of tensile forces from longitudinal bars of beams to longitudinal bars of footings, a set of reinforcing ties is provided between them. As such setting of headed reinforcement bars is not common, thorough investigations have been carried out to confirm the relevance of the proposed tie reinforcement. In this paper, results of a finite element numerical investigation of pulled-out eccentrically spliced longitudinal headed bars with different detailing of transverse reinforcement, proposed for precast beam-cast-in-place footing connection, are presented and compared to test results. The elaborated modeling could fairly reproduce the global behavior of the six specimens, where the numerical results acceptably approached the experimental results in terms of initial stiffness, ultimate strength, crack pattern and strain of reinforcement.


Introduction
Precast concrete structures have become more and more popular in construction resulting from the demand for economical and safe design, as connection methods and hardware (devices) for precast structural elements had known important developments. In common practice, when precast concrete or steel columns are adopted, or when avoiding congestion problems, longitudinal bars of foundation beams are horizontally bent around columns and spliced to longitudinal bars of footings to insure an adequate juncture for load transfer from beams to footings (Figure 1). Such way of doing, although simple, may slow the construction process due to additional tasks and/or may result in some unusual forms of formworks and then, increase labor cost. For ease of construction, a range of novel splice methods were developed as an alternative for lap splices. Various studies have been carried out to confirm the relevance of these methods for structural elements and their influence on the response of structures, particularly those to be constructed in earthquake-prone areas. Tazarv and Saiidi (2015) studied the performance of a grouted corrugated duct connection for reinforced concrete bridge column-footing in high seismic zones and confirmed that the suggested connection was emulative of the conventional cast-in-place elements. Similarly, Belleri and Riva (2012) investigated grouted corrugated duct connections with and without partial unbonded length outside the footing for the spliced bars of column-to-foundation connections in seismic regions, in comparison to cast-in-place concrete and pocket foundation connections. The study revealed that using the duct connections resulted in a little damage in the column outside the base section. The study also showed that more damage reduction in the column was obtained for the element with partially unbonded spliced bars. Cogurcu and Uzun (2022) investigated, through tests, a new bolt-anchor connection for precast column-foundation and showed that the anchor connection had larger load capacity and energy dissipation than the non-spliced connection and socket connection. Orlando and Piscitelli (2018) showed experimentally that a good performance could be obtained for precast columns with dry connection joints where one type was achieved by welding column's longitudinal bars to its steel base plate, and the other type was achieved by overlapping column's longitudinal bars with sufficient length to rebar dowels welded to the steel column base plate. Mohebbi, Saiidi, and Itani (2018) studied the seismic behavior of a pocket connection in precast bridge column connected to a precast footing and showed that such connection was effective in forming the plastic hinge in the column with no damage at the connection and with negligible residual displacement. Jones et al. (2020) compared, through shaking table tests, the seismic performance of socket and pocket connections for reinforced concrete bridge columns and confirmed that both configurations exhibited satisfactory behavior and were appropriate for use in heigh seismic areas. Based on existing literature, Dabiri, Kheyroddin, and Dall'Asta (2022) made a review on lap, welded and mechanical splices and enumerated their benefits and shortcomings. Whereas they mentioned that the use of welded splices would solve the problem of congestion of reinforcement and allow more room for concrete pouring and vibrating, it would require preparation of steel bar ends, special equipments, skilled operators and thoroughly inspections. Furthermore, they cited that grouted mechanical splices, especially slim ones, have become the most common alternative for lap splices and mentioned, similarly to Nguyen and Mutsuyoshi (2015), that the influence of the quality of mechanical splicing on the behavior of structural elements would be a concern for improper splice installations. Ameli and Pantelides (2017) investigated the effect of mechanical splice location (sleeves arranged on column side with partially unbonded spliced bars in the footing or sleeves arranged on footing side) on the behavior of precast concrete bridge columns. The study confirmed that whereas both arrangements resulted in ductile performance comparable to the performance of a similar cast-in-place element, the later arrangement was more stable and experienced larger deformation capacity without strength degradation than the previous arrangement.
Whereas the previously mentioned studies focused on the structural performance when using the various splicing methods, the cost issue was rarely addressed. Concerned with reducing material cost, reducing construction tasks, use small capacity cranes at sites, shorten construction time of buildings and avoid reinforcement congestion problems at their foundations, the authors have proposed a simple structural system for foundations, which consists of precast foundation beams and cast-inplace footings.
As an alternative to using weld splicing or mechanical splicing or bending longitudinal reinforcement of foundation beams and footings, the authors adopted non-contact splicing and conceived their precast beams with protruding longitudinal headed bars at their ends ( Figure 2). To use small capacity cranes at site, each beam is partitioned, transversally, into 2 or 3 prefabricated sub-beam elements of smaller width, as depicted by discontinuous lines in the plane view of Figure 2. By adopting straight headed bars, a discontinuity region is created, where the longitudinal bars of the footings become laterally eccentric to those of the beams that are embedded in the footings. To allow the flow of tensile forces from longitudinal bars of beams to longitudinal bars of footings, providing an appropriate set of reinforcing ties becomes a challenge, though various ways and combinations that satisfy detailing regulations can be implemented. For instance, but not limited to: in case of normal shear reinforcement, setting up lapped U-shaped bars, or one side hooked and one side headed bars, or two sides headed bars, and in case of bent shear reinforcement, setting up above and below, respectively, the upper and lower longitudinal steel bar layers of each side (compression and tension), and if any obstacles exist, such bent bars can be partitioned and then lap spliced within the footing along the beam width. As the proposed foundation system and its connections are intended for moderate to high seismic regions, and as foundations should be over-resistant compared to the structure, sufficient safety margin against brittle failure should be confirmed.
For regulations, whereas some requirements, such as the minimum ratio for confining reinforcement and limit for concrete cover, specified in some codes, like in AIJ (2018), AIJ (2010) and ACI-314 (2019), for noncontact splicing (spaced splicing) of longitudinal reinforcement can generally be fulfilled for common detailing of structural elements, the limit specified for the spacing of non-contact splices might not be satisfied when the arrangement of longitudinal reinforcement becomes uncommon where non-alternated longitudinal reinforcement and/or columns of large size (width) be adopted, as illustrated in Figure 2.
When non-contact splicing was investigated experimentally, as in the studies carried out by Chamberlin (1952, 1958) on bent beams, Sagan, Gergely, and White (1991) on tensioned wall-like elements and Hamad and Mansour (1996) on bent slab elements, the transverse spacing of spliced bars was within the limits specified by regulations and the bars were arranged in a way that force transfer occurred between the spliced bars without being intensely affected by the developed forces in the other adjacent bars.
When eccentric and/or wide beam elements were dealt with in some studies like the ones carried out by Rafaelle et al. (1992), Burak and Wight (2004), Shin and Lafave (2004), Lam et al. (2011) and Luk and Kuang (2012), because longitudinal beam bars of the studied connections were mainly anchored in the beam column joint's core or placed closely at beam ends, issues related to region/reinforcement discontinuities were not addressed. Furthermore, when headed bars were used as in the studies carried out by Thompson et al. (2003aThompson et al. ( ), 2003bThompson et al. ( , (2006, Ishikawa et al. (2004), Lee andYu (2009), Yang et al. (2010) and Tagawa et al. (2011), headed bars in opposite directions were arranged alternately and closely within the considered connection zones. Whereas such arrangement of headed bars addressed the issue of reinforcement discontinuity (non-contact), eccentricity of sets of headed bars and stress flow between such eccentric reinforcement sets have not sufficiently been investigated.
As the proposed setting of headed reinforcement bars is not common and not explicitly presented by design regulations, a preliminary experimental study was carried out on six specimens, representing the tensile part of the foundation beam-footing connection. The pull-out performance of the eccentrically spliced longitudinal headed bars with different detailing of transverse reinforcement was investigated and a simple method, based on the friction shear theory, was suggested for the strength capacity evaluation of the proposed reinforcement arrangement. The test results and simple evaluation model can be found in detail in Ousalem and Takatsu (2021). Subsequently, a three-dimensional finite element simulation was performed to reproduce the results of the preliminary experimental program, understand the behavior and failure modes of the test specimens and validate a numerical model. Parameters of the validated numerical model of the tensile part of the foundation beamfooting connection would be used in a future study to investigate the seismic performance of the whole body of the foundation beam-footing connection and ensure its appropriateness. This paper presents a brief outline of the test and reports the results of the finite element analysis of the tested specimens.

Specimens and materials
To grasp the behavior of the proposed beam-footing connection and observe the likely developing failure mechanisms under cyclic bending, at first, a preliminary pull-out test of eccentrically spliced longitudinal headed bars with different arrangements of transverse reinforcement was carried out. Test results can be found in detail in Ousalem and Takatsu (2021).
Specimens constructed for testing, do not include the concrete part of the precast beams. The specimens represent only a part of the footing, which includes the longitudinal bars protruding from the precast beams that would undergo a tensile force due to bending of the beams (Figure 2). The geometry, detailing and main characteristics of the specimens are shown in Figure 3 and Table 1. As illustrated in the plane view of Figure 2, the distance between the closest eccentric longitudinal bars of the beam and footing was decided, according to the beam width (herein 250 mm) and, mainly, the size of the column (herein 300 mm). Such spacing was beyond the requirement prescribed in AIJ (2010AIJ ( , 2018 and ACI-314 (2019) which would be the minimum of 150 mm and onefifth the splicing length of the non-contact bars.  Alternation of opposed headed bars of beam and footing* Not Implemented Implemented *: When "Alternation" is implemented, one part of beam-headed bars are set up between footing headed bars, as shown in Figure 3(e-f) Splicing length of the eccentric longitudinal bars in all the specimens was fixed to 20 times the diameter of the beam longitudinal bars. These eccentric bars were tied by transverse reinforcement, distributed along the splicing length with a shear reinforcement ratio of 0.8% (relative to the area of Section C in Figure 3) and satisfying the minimum requirements of AIJ (1996). When bent shear reinforcement were added, half of the amount of the transverse reinforcement was considered. Conditioned by the size of the footing, the inclination from the beam axis of the bent shear reinforcement bars was 50 deg. for the specimen No-2 and 62 deg. for the specimens No-5 and No-6. When footing longitudinal reinforcement in the orthogonal direction was added, only 2/3 of the amount of the footing longitudinal bars in the specimen's axial direction were considered, assuming a less reinforced footing in the orthogonal direction. All the specimens (specimens No-1 to No-5) were designed to experience shear failure, except one (specimen No-6), which was designed to experience yielding of beam longitudinal steel bars and would be recommended for construction in actual buildings. Shear strength of the specimens was evaluated using a simple model, considering shear friction along presumed failure concrete surfaces between beam headed bars and footing headed bars, as well as tensile forces of the bent shear bars and dowel bearing forces of the orthogonal bars crossing the presumed failure surfaces. The design process and strength evaluation of the specimens can be found in detail in Ousalem and Takatsu (2021). Normal concrete was used to construct all the specimens. Table 2 lists the characteristics of materials obtained by laboratory test. Mean values of a set of three test pieces for each type of material are presented in the table. The slight difference between the Young's Modulus of different steel bars might be explained by the different origins of the class steel bars and thought to be caused by some dissimilarity in the manufacturing practices and quality control procedures followed by different manufacturers.
The parameters investigated in this test concerns the effect of bent shear reinforcement (comparison of specimen No-1 with specimen No-2 and specimen No-4 with specimen No-5), effect of longitudinal reinforcement of footings in the transverse direction (comparison of specimen No-1 with specimen No-3) and effect of alternating some of beam longitudinal reinforcement with footing longitudinal reinforcement (comparison of specimen No-1 with specimen No-4 and specimen No-2 with specimens No-5 and No-6).

Loading procedure and instrumentation
The loading setup is shown in Figure 4. Specimen's stub was fixed by high strength bolts to a rigid floor of the testing facility. The loading setup was accommodated for tensile forces to be applied vertically through the protruding beam longitudinal reinforcement, which were fixed at their end to a loading beam that was pushed upward using hydraulic jacks. A non-reversed cyclic tensile loading pattern with three successive cycles followed by a monotonic phase until failure was planned. Total and relative displacements at different locations, particularly at the concrete upper face on the axis of each specimen ("CF" location in Figure 4) and at the lower face on the axis of the loading steel beam ("SF" location in Figure 4) were measured. Strain gauges were placed at several locations on the longitudinal and transverse reinforcement (Figure 3). The hydraulic jacks were fitted with load  cells, and data were processed through a computerized data acquisition system.

Test results
Under the applied loading, several differences had appeared on the specimens, in terms of crack progression, reinforcement deformation and failure type.
Behaviors and failure modes of the tested specimens occurred as expected. All the specimens experienced shear failure and yielding of their footing longitudinal reinforcement, except the specimen No-6, which experienced a ductile failure and yielding of its beam longitudinal bars without any yielding of the footing longitudinal reinforcement. Figure 5 shows the relationship between the tensile strength (applied load) and displacement of the concrete upper surface on the axis of each specimen during test ("CF" location in Figure 4). For all the specimens, the load transfer was achieved through bond at first and then through compression struts that developed from the anchor heads of the beam longitudinal bars to those of the footing longitudinal bars and shear failure was triggered when transverse reinforcement close to the anchor heads of the footing longitudinal bars reached their yield strength, except for the specimen No-6. Measured tensile strengths of the specimens are listed in Table 3.
Damage and crack patterns undergone by the specimens are illustrated by the drawings in Figure 10 at the peak of the loading cycles P = F 1 and P = F 2 , and at the  maximum strength (P = P max ). Cracks progression during loading was almost similar for all the specimens within the loading range P = 0~ F 1 , where only cracks perpendicular to the axis of each specimen occurred below the beam anchor heads (at the level of the upper surface of the fixing concrete stab). Shear cracks were observed in all the specimens at around the peak of the second loading cycle (P = F 2 ), except for the specimen No-1, where it appeared soon after the perpendicular cracks. Since the loading level P = F 2 , in all the specimens, the compressive strut formed clearly, where the crack shape suggested that the applied load was mainly resisted by the compressive strut action between the anchor heads of the longitudinal bars of the beam and footing, inducing a transverse displacement of the footing side-parts away from the beam part. Concomitantly, the transverse shear reinforcement resisted the applied load and provided a clamping action on the developed cracks but when these transverse reinforcement bars reached their yield level, the cone shape became evident and when some shear cracks between the most adjacent longitudinal bars of the beam and footing joined, the load ceased to increase, except in the specimen No-6 where the cracks did not sufficiently develop to form a cone shape and a clear failure surface. Whereas the footing longitudinal reinforcement (D16 bars) in the orthogonal direction was not very effective, alternation of the opposed bars of beams and footings and bent shear reinforcement restrained, beyond the loading level P = F 2 , the crack progression.

Model, loading and boundary conditions
The outline of the elaborated 3D FE models (quartermodel adopted owing to symmetry) is depicted in Figure 6. The non-linear analyses were conducted using the commercial general-purpose finite element software Ls-Dyna R11.1.0 (LSTC 2019). Concrete and head anchors were modeled as solid elements (8-node brick elements) where a relatively highdensity mesh was used at the location of the head anchors. The aspect ratio of solid elements was between 1.0 and 2.5 for the upper part of the model (aimed part for investigation) and between 1.1 and 4.9 for the lower part of the model (concrete stub, fixed part). Longitudinal and transverse steel reinforcing bars were explicitly modeled as beam elements incorporated into the concrete mesh. The total length of the beam longitudinal reinforcement until their fixation on the loading beam was considered. For simplicity, the circular shape of the head anchor was made square by considering equivalent surfaces, whereas the length dimensions of the head anchors were not modified.
Material data from the test were used in the analyses. Models concerned the tested specimens and did neither include the whole loading setup nor the fixing bolts and their forces. The concrete stub of each specimen was restrained against all movements (vertical and horizontal displacements and all rotations). Along the symmetry planes, normal displacements and rotations were appropriately constrained. Similar load conditions as in the test were reproduced in the models. Loading was increased at a slow rate to avoid any dynamic amplification and ensure a static response. Displacement-controlled monotonic loading was applied, in the upward direction, at the tips of the beam longitudinal steel bars, while all the other movements of the bars' tips were restrained.

Material modeling
The continuous surface cap model (CSCM) was used for the constitutive material behavior for concrete (Figure 7(a-c)). This cap model is characterized by a smooth and continuous intersection between the shear yield surface and hardening cap. For setting up the model input, in this study, default material parameters were requested based on the unconfined compressive strength and maximum gravel size as input.
The derived Young's modulus and tensile strength of concrete are based on CEB-fib's equations (Fib, 2010).
The plastic-kinematic model was used for the constitutive material behavior for head anchors and steel bars (Figure 7(d)). This elastic-plastic model is suited to model hardening plasticity. Whereas default material parameters were requested, the input values were Young's modulus, the yield strength and tangent modulus.

Bond and interface modeling
The interaction between the steel bars and surrounding concrete was considered in the analyses (Figure 8 (a)). The constrained-beam-in-solid option was used to model the bond along the steel bars based on CEB-fib's bond stress-slip relationship (Fib (CEB-fip) 2010). The considered parameters of the stress-slip curve were those prescribed by the mentioned code for the pullout case (All other bond conditions) of deformed bars.
To treat the interaction at the interface between concrete and head anchors and tie their solid  elements, tie-break surface contact elements were used, where surfaces which are initially in contact are tied and their tangential motion is inhibited until failure occurs (interface tension is lost), as shown in Figure 8(b). The failure criterion, given by Eq. (1), has normal and shear components. The needed input was the friction coefficient μ, normal failure stressσ t and shear failure stressτ 0 . Both, the normal failure stress and shear failure stress were considered negligible taking into account the study of Rabbat and Russell (1985), therefore, a value of 0.1 MPa was used as input. The friction coefficient was taken equal to 0.5, which is slightly lower than the value reported in the test study of Rabbat and Russell (1985) but very close to the average value of the test study of Bui, Kabeyasawa, and Kabeyasawa (2012).
whereσ and τ are, respectively, the applied normal and shear stresses at the interface.

Analysis results
The numerical results in terms of the tension force and displacement at the concrete upper surface (coinciding with "CF" location in Figure 4) of the models are illustrated in Figure 9 and a summary of the maximum strength values is presented in Table 3 simultaneously with the test results. The distribution of the numerical maximum principal strains of the models at the time of maximum strength is illustrated in Figure 10. The axial strain evolution of some reinforcement of the models is shown in Figure 11, corresponding mainly to the location of the strain gauges of the longitudinal bars (one location each for close bars of beam and footing far from the anchor heads, Figure 3) and transverse steel bars (one location, Figure 3).Comparison of crack pattern and maximum principal strain distribution at the peak of the loading cycles P = F 1 and P = F 2 , and at maximum strength.
Whereas the analysis was carried out for the models No-1 to No-5 for a while beyond the maximum  Similarly in all models, at almost the same load level (Table 3), the first initial crack developed horizontally at the investigated lower part below the head anchors of the beam longitudinal reinforcement. That load level corresponded to the tensile strength of concrete on the surface between the most interior longitudinal bars of the footing. As to the numerical failure mode, that of the models No-1 to No-5 was characterized by a pull-out of a concrete cone ( Figure 10) that had basically initiated from the anchor heads of the longitudinal bars of the beam toward the anchor heads of the longitudinal bars of the footing. The cone shape completely formed when the transverse reinforcement reached yielding (Figure 11), soon followed by yielding of the longitudinal reinforcement of the footing (Figure 11). On the contrary, for the model No-6, although a cone shape was initiated, it did not fully develop as the longitudinal bars of the beam yielded whereas the transverse reinforcement did not. Such behavior of the model No-6, in comparison to the model No-5, was simply due to the change of steel strength of beam's longitudinal bars as it was confirmed by the analysis of the same model (No-6) with SD390 class bars for the beam and SD685 class bars for the footing. The analysis showed that the curves of the analyses were closely similar, as illustrated at the bottom right side of Figures 9 and in Figure 11(f). Results of both analyses of the model No-6 are also listed in Table 3.
The numerical results showed that, in combination with the distributed shear reinforcement, the most effective detailing to improve the strength would be by simultaneously providing bent shear reinforcement and alternating some of the beam longitudinal bars with those of the footing (as for the model No-5). Furthermore, to prevent the cone failure mode, selecting lower grade steel for the beam longitudinal reinforcement would result in a ductile behavior of the eccentric connection (as for the model No-6).

Comparison of analysis and test results
A comparison of the load-displacement curves obtained from the analysis and experiment showed that, in total, the analysis could fairly reproduce the global behavior of the six specimens. The numerical results acceptably approached the experimental results in terms of initial stiffness, ultimate strength, crack pattern and strain of reinforcement. Therefore, some discrepancies can still be noticed at some parts of the curves, due to some reasons more likely: ①nonuniformity in the actual bond characteristics along every bar and non-similarity on all bars, especially for parts subjected to confining compression or tension (contrary to the analysis in which uniformity and similarity of characteristics along every single bar and on all bars was considered), ②the mesh size and variation of the size ratio conditioned mainly by the size of the anchor heads, and ③some deformation discrepancies at the fixation of the beam longitudinal bars on the loading beam which might have induced some difference in deformation at their tips (contrary to the analysis in which the tips of the longitudinal bars of the model moved simultaneously all together). Whereas more accurate results would be expected by a more refined analysis, the presented one seems encouraging as it could predict the failure modes and the strength values with an acceptable safety margin, especially for the proposed reinforcement arrangement.
Although the numerical models were, in general, relatively stiffer than the tested specimens, which might be due to the assumptions (Sections 3.1~3.3) on the loading setup and fixing bolts and plates (not modeled but assumed in the analysis as fixed points) of the specimens as well as on the bond modeling or to some reasons, unfortunately, not clearly grasped by the authors besides the ones presented in ①~③, the models could predict well the load level at which the initial crack initiated. Therefore, whereas the numerical ultimate strengths of models No-2 and No-3 occurred almost at the same deformation levels as in the test, those of the other models occurred relatively earlier than in the test. As to the numerical values, they were very close to the test values (Table 3) where the ratios of the test value to the numerical value ranged from 0.98 to 1.17.
Based on both, the distribution of the numerical maximum principal strains and steel axial strains, the analysis produced similar failure modes as in the test. Comparison of schemes of recorded cracks during testing and the distribution of the numerical maximum principal strains of the models at the peak of the loading cycles P = F 1 and P = F 2 , and at the time of maximum strength is illustrated in Figure 10. For each model, the distribution of the numerical maximum principal strains was reasonably compatible with the crack pattern observed on the corresponding tested specimens. The initial crack (horizontal) that occurred at the investigated lower part could be reproduced by the model at almost the same load level as in the test. The numerical maximum principal strain distribution schemes show that the failure mode of the models No-1 to No-5 was characterized by a clear pull-out cone shape as observed in the test, whereas the cone shape of the model No-6 was not completely formed when the maximum load was attained as observed also in the test. Furthermore, the axial strain evolution of the reinforcement of the models, shown in Figure 11, presented similar trend as in the test. Although some differences in values can still be seen, especially beyond the peak strength, the axial strains of the longitudinal bars (one location each for close bars of beam and footing far from the anchor heads, Figure 3) and transverse steel bars (one location, Figure 3) were, in general, reasonably reproduced in the analysis until the maximum strength.
This erased text part should be displaced and set below the figures of cracks for the specimens No-4 to No-6

Conclusions
For common detailing of footings in steel and precast structures, when welding or mechanical splicing is not used, longitudinal reinforcement of foundation