Behavior of Precast Segmental Beams Made of High-strength Concrete and Ultra-high Performance Fiber Concrete Connected by Shear Keys Technique

The segments of the precast concrete beams can be assembled by joints have interlaced shear keys. This paper presents an experimental and numerical study of ten samples, six of them were tested under the influence of direct shear; these samples represent reinforced and non-reinforced shear keyed joints made of high-strength concrete (HSC) and ultra-high performance fiber concrete (UHPFC) under the influence of different levels of confining stress. In addition, four beams were tested under the influence of bending, two of them are unconnected control beams made of HSC and UHPFC, and the other two beams are precast segmented and were assembled using reinforced shear keyed joints of the same joints tested under direct shear. All the details of the shear keyed joints are fixed in all samples and they are dry non-epoxy joints, the external prestressing technique was used. Also, Abaqus program was used for numerical modeling of all samples that were tested in the experimental program using the 3D solid element model. The success of the modeling process was verified by comparing the experimental and numerical results as the results of the relationship between load and displacement and also the failure pattern. From the experimental and numerical study, it was found that by reinforcing the shear keys and/or by increasing the confining stress of the joints made of HSC and UHPFC, the shear capacity of the joints is increased. If the value of the used confining stress is constant at a value of 3 N/mm2 and by reinforcing the shear keys with reinforcement, the maximum load increases by 18% and 48%, respectively, than its non-reinforced counterparts joints. It was also found that by increasing the confining stress of the reinforced shear keyed joints from 3 N/mm2 to 6 N/mm2, the maximum load value is increased by 18% and 16%, for HSC and UHPFC shear keyed joints, respectively.


Introduction
In the last decades, some new types of concrete have appeared, such as high-strength concrete (HSC) and ultrahigh performance fiber concrete (UHPFC). These types of concrete are used to design concrete sections that have small dimensions or have a high ability to sustain large values of stresses resulting from external loads or resulting from prestressing technology or the need to make beams with large spans. This is because these types of concrete have high other factors affecting the behavior of HSC beams such as beams of small depth, which cause large deflection and ductility. The ductility is one of the most important points that must be taken into account when designing sections of HSC beams, as it indicates the ability of the element to deform at or near the maximum capacity of the element without a noticeable loss in the maximum load value (Ashour [18]; Shin et al. [19]).
UHPFC is a newfangled cement-based material unveiling a compressive strength of more than 100 MPa, higher tensile and flexural strengths, ductility as well as admirable durability. Based on experimental and numerical studies, Graybeal [20], Chen and Graybeal [21] studied the structural behavior of full-scale prestressed UHPC I-and Pi-girders subjected to bending. Yuguang et al. [22] have studied experimentally the bending behavior of UHPFC bridge decks. Yang et al. [23,24] carried out many experimental tests to study the bending behavior of UHPC beams. Fujikake et al. [25] and Yoo et al. [26] performed a drop-weight impact test for UHPC beams reinforced with prestressing tendons and steel rebars and suggested analytical models for predicting their deflection responses.
Due to the need sometimes to construct reinforced concrete bridges quickly without disrupting the movement of vehicle or trains tracks under these bridges for a long time or without waiting for the concrete to fully harden. Therefore, the idea of precast segmental reinforced concrete beams, which are assembled on field, appeared.
The segments of the precast concrete beams can be assembled by joints have interlaced shear keys, either dry or using an epoxy bonding material. It is also possible to increase the friction resistance between the segments of these beams by the prestressing technique.
Many researchers have studied the direct shearing behavior of the shear keyed joints by push-off test. Jiang et al. [27] experimentally tested twenty six joints of steel fiberreinforced concrete under direct shear. The study variables were the type of the joint (one-piece joints without using shear keys or joints with shear keys), the types of concrete used in the joints (conventional concrete or concrete with steel fibers), the number of shear keys, the type of contact between the two segments of the joint (full contact or partial contact) and the level of confining stress used. From the study, it was found that the use of steel fiber concrete in the shear keyed joints improves the shear resistance and ductility of these joints; with an increase in the level of confining stress, the stiffness and shear resistance of the shear keyed joints increases; by increasing the number of shear keys in the joint or by using partial contact between the two segments of the joint, the ductility of the joint increases.
Jang et al. [28] experimentally tested twelve joints under direct shear action. The joints were divided into two groups.
The first group represents joints between two UHPC segments and the second group represents joints between UHPC and normal strength concrete (NSC). The study variables were the type of joint (connected segments or monolithic one piece), the joint shape (flat or with grooves), the type of contact surface treatment (without treatment or treated with water jet) and the dimensions of the grooves used. From the study, it was found that by treating the contact surface using water jet, the shear resistance of the joint increases and this effect increases more clearly in the samples of the second group due to the effect of the interlocking mechanism of coarse aggregates existing in ordinary concrete. Also, the samples of the first group have a higher shear capacity and a greater ductility due to the high tensile strength of the UHPC and by increasing the dimensions of the grooves used, the shear joint resistance increases.
Kassem et al. [29] experimentally tested and analyzed nine joints. The first joint is without shear keys (flat joint) and the second joint has overlapping shear keys, but it is banned from sticking by placing 5 mm of foam between the facing surfaces. The rested joints are divided into three groups. The first group is concerned with studying the effect of different types of concrete, and it consists of two joints made of ordinary concrete and strain hardening cementitious composites (SHCC) concrete, with an angle of inclination of 45 degrees for the shear keys. The second group is concerned with studying the effect of changing the angle of inclination of the shear keys, it consists of two joints made of ordinary and SHCC concrete, one with a key angle of 60 degrees and the other at an angle of 90 degrees. The third group is concerned with studying the effect of the initial confining stress value, it consists of three joints made of SHCC with shear keys having an inclination of 45 degrees and subjected to different values of prestressing. From the study, it was found that the joints made of SHCC are stronger in shear stiffness and shear strength, have better behavior after cracking and have a ductile failure pattern when compared to the joints made of ordinary concrete. It was also found that the angle of inclination of the shear keys and the initial confining stress strongly affect the shearing stiffness and shear strength. It was found that the proposed analytical model is able to predict the shear capacity of shear keyed joints made of SHCC.
Sangkhon and Pisitpaibool [30] experimentally tested twelve shear keyed joints made of ordinary concrete. The study variables were the number of shear keys in the joint (single or triple shear keys), the shape of the shear keys used (triangular, trapezoidal or semicircular) and the level of confining stress used. From the study, it was found that the joint with triple keys has a final load greater than the single-key shear joint, but the single-key shear joint has a greater load when compared to the load per one shear key in the joint with triple keys. Semicircular shear keyed joints have a large shearing capacity, but the disadvantage is that its collapse is a brittle.
Liu et al. [31] experimentally tested twenty-five joints under the influence of direct shear and the study variables were the type of joint (flat joints without shear keys-with small or large single shear key-with small triple shear keys), the type of concrete used and the confining stress level applied. It was clear from the study that the maximum shear strength of the joints made of UHPC can be reached by increasing the level of confining stress used and by adding steel fibers that have a high resistance. Also, the joints with fibers concrete exhibited a limited area of concrete crushing compared with joints without fibers and it was found that the large single-key shear joints had a slight increase in shear strength when compared with the small triple-key shear joints.
Liu et al. [32] experimentally tested sixteen joints under the influence of direct shear. The study variables were the use of different types of concrete within the same joint and different shapes of facing surfaces of the joints such as bubble groove interfaces, flat-surface interfaces and waterjet-surface interfaces, and study the effect of existence of the dowel rebar and casting sequence of UHPC and NSC. From the study it became clear that for the connections between the UHPC and the NSC, most of the collapses occurred in the NSC and therefore the shear behavior is strongly affected by the NSC and the shear behavior of the joints changes strongly with the different priority of the casting sequence between the UHPC and the NSC.
Semendary et al. [33] studied the shear behavior of joints between precast HSC and casted in-situ UHPC. Therefore, they experimentally tested four samples, two of them were improved with reinforcement to increase the resistance of the contact surface to shear. From the study, it was found that the shear reinforcement gives greater ductility and greater strength even after the contact surface reaches adhesion capacity. It also confirmed the superior adhesion ability of UHPC concrete when poured on precast concrete.
Jiang et al. [34] experimentally tested five beams, including four segmental beams and one unsegment beam, to study the bending behavior of segmental concrete beams assembled using dry shear keys and hybrid tendons, and they found that the bending resistance of segmental beams with hybrid tendons is 30% less than the capacity of the unsegment beam with hybrid tendons.
Le et al. [35] experimentally tested three precast segmental reinforced concrete beams assembled using internally prestressed carbon fiber-reinforced polymer (CFRP) or steel tendons. The joints were dry or epoxied shear keyed joints. The aim of the study was to study the bending behavior of precast segmented beams. From the study, they found that it is possible to replace the steel tendons with tendons from CFRP, as the beams with CFRP tendons gave greater capacity and greater ductility compared to the beams with steel tendons. They also found that the type of joint of the shear keys either dry or epoxy greatly affects the initial stiffness of the beam.
Ahmed and Aziz [36] experimentally tested thirteen precast segmental reinforced concrete box beams to study the shear behavior of the joints and the results showed that increasing the confining stress to 4.5 MPa with or using a number of 6 to 10 shear keys can clearly improve the elastic stiffness, plasticity ductility and change of the brittle collapse pattern of epoxy joints.
Afefy et al. [37] experimentally tested seven T-shaped beams, five of them were precast segmental and assembled by dry shear keyed joints that internally prestressed, in addition to two reference beams for comparison. The segmented beams were strengthened at the joint location on the compression side by pouring half the depth of the upper flange with a layer of HPC. The joints were strengthened at the tension side by using a special steel assembly encapsulated in a layer of SHCC. The results showed that strengthening joints of segmental beams in the compression and tension side makes the assembled beams capable to reach 96% of the resistance of the prestressed control beam.
This research presents an experimental and numerical study using the Abaqus program [38] to study the shear behavior of reinforced and non-reinforced shear keyed joints made of HSC and UHPFC under the influence of different levels of confining stress. It also presents the behavior of these joints when they are used to connect segmented reinforced concrete beams under the influence of bending loads.
Among the objectives of this research is to get a successful numerical analysis model based on the finite element method used to analyze the shear keys joints, which may be used to model the connected precast segmental beams, in order to make a future parametric study to save the cost and effort that may be made in the experimental studies.

Geometry, Reinforcement and Material Properties
To study the behavior of joints with dry shear keys made of HSC and UHPFC under the influence of direct shear and under the influence of bending so an experimental program consisting of two groups was prepared, the first group represents joints tested under the influence of direct shear and consists of six samples, and the second group consists of four beams were tested under the influence of bending. The first group consists of six shear keyed joints with the dimensions shown in Fig. 1a, which are 100 mm wide, 300 mm high and 600 mm assembled total length. Each joint consists of three parts, the right part, the left part, and the middle part, the length of each part is 200 mm, and they are connected to each other using the technique of shear keys. The details of the shear keys used are shown in Fig. 1b, which is a surface with two trapezoidal shear keys, the length of the short base of the trapezoidal is 45 mm, the length of the long base is 101 mm, and the height is 40 mm. Three of the tested joints are made of HSC, where the first represents the shear keyed joint, which is non-reinforced and subjected to a confining stress of 3 N/mm 2 , the second is reinforced and subjected to a confining stress of 3 N/mm 2 , and the third is reinforced with the same specifications as the reinforcement of the second joint, but subjected to a confining stress of 6 N/mm 2 . The remaining three joints are of the same specifications as the first three joints but are made of UHPFC. Figure 1c shows a description of the reinforcement of shear key used. In the case of reinforcing the shear keys located in the central part, the reinforcing mechanism is a reinforcing steel bar with a diameter of 16 mm welded at the start and at the end with a steel skewer of thickness 5 mm, 30 mm wide and with length equal to the width of the joint, which is 100 mm. While this reinforcing steel bar is welded with a steel wicker on one side only, and the other end is hooked at an angle of 90 degrees in the case of reinforcing the rest of the parts. All joints before testing will be assembled with external prestressing technique.
The second group consist of four beams. The first and second beam are unconnected beams (one-piece beams) and are shown in Fig. 2a. The first beam is made of HSC and the second beam is made of UHPFC. All beams are 200 mm wide, 300 mm deep, 1960 mm total length, and 1860 mm effective length (length between the supports). The longitudinal reinforcement of the beams is two steel deformed bars with a diameter of 16 mm in the tension side (bottom side of the beam) and two reinforcing bars with a diameter of 10 mm in the compression side (top side of the beam). The shear strength of the beams has been enhanced by using stirrups with a diameter of 8 mm spaced 100 mm with two branches, and it was ensured that the concrete cover was fixed with a thickness of 25 mm.
The third and fourth beam are segmented beams and are assembled using a reinforced shear key technique. The details of the shear keys are identical to what was mentioned in the shear keys of the first group, except that two steel bars of 16 mm diameter per key were used to reinforcing the shear keys in this group. The third beam is made of HSC while the fourth beam is made of UHPFC. Details of these beams are shown in Fig. 2b and 2c. Before testing, the third and fourth beam will be assembled using an external prestressing technique by exposing them to a force of 150 kN that affects at the position of the rebar in the tension direction. All samples tested in this study are full-scale. Table 1 shows the details of all samples used in the experimental study. Figure 3 shows the wooden formwork and the blacksmithing processes of all samples where the wooden formwork is first prepared, then the rebar are placed in the right and left parts, if any. Then the right and left part is casted, then wait for these parts to harden, after that, the barrier wood parts between the three parts (right, left and the middle part) are  removed and aluminum foil for insulation is placed between the three parts then put the rebar, if any, in the middle part, then cast the middle part. Table 2 shows the quantities of each component used for the preparation of HSC and UHPFC. HSC consists of ordinary Portland cement (Type-I), fly ash, silica fume, sand, crushed basalt, superplasticizer and water for mixing while UHPFC consists of ordinary Portland cement (Type-I), silica fume, sand, steel fibers, superplasticizer and water for mixing. Three standard cylinders with a diameter of 150 mm and a height of 300 mm were casted for each type of concrete and used to be tested after its complete hardening after 28 days under the same conditions of treatment processing of the samples previously mentioned to determine the concrete's compressive strength. The longitudinal reinforcement, shear key reinforcement and stirrups were also tested under the Fig. 3 The wood formwork, blacksmithing and casting processes   Table 3 shows the mechanical properties of all types of rebar used.

Test Setup
All the beams were placed at their ends on two steel supports so that the effective length of the beams (the length between the supports) was 1860 mm and two loading plates were placed at equal distances from the middle of the beams so that the distance between the two loading plates was 620 mm. A steel distribution beam exposed to a hydraulic loading cylinder in the middle was placed on the two loading plates to apply a vertical load. A load cell was connected to the hydraulic loading cylinder to measure the value of the load. Also, a set of strain gauges was attached to a number of elements as steel bars used to make the external prestressing on the beams, in order to measure the value of the pretension in them while tightening. A skewer threaded on both ends is passed into the three parts to be assembled, then a piece of metal responsible for distributing stress is passed so that it confines the three concrete parts, then a nut is tightened at the two ends of the skewer over this piece of metal. With the nut tightened, the strain value inside this skewer is read by means of a strain gauge located on the surface of the skewer until the required force value is reached. Strain value is not noticed after this stage.
Also, strain gauges were attached to the nearest point to the middle of the beam in bottom reinforcing bars. A linearly variable differential transducer (LVDT) was also installed to measure the displacement of the beam vertically with loading and placed near the middle of the beam. Data from the load cell, strain gauges and LVDT were fed into a data acquisition system connected to a computer. The load was gradually increased by displacement control technique.
The same method mentioned above was used in the preparation of the direct shear test except that there was no beam to distribute the load, as the load was affected in the middle of the middle part directly. Figure 5 shows the test setup and details of instrumentations used. All tests were carried out at the reinforced concrete laboratory, Faculty of Engineering, Kafrelsheikh University.

Direct Shear Tests
Load-displacement curves for direct shear tests are shown in Fig. 6a and 6b. It is noticed from the load-displacement curves shown in Fig. 6a that with increasing loading of the samples made of HSC, the curves passes through three stages: the first stage, which is a linear stage and starts from the beginning of the loading and ends with the occurrence of the first crack in the sample and expresses the shear stiffness of the joint. The second stage is a nonlinear stage and begins with the occurrence of the first crack and ends with reaching the maximum load (P u ) and then the third stage, which is the stage of sample collapse, where the load decrease begins.
It is noticed in HSC samples that the shear capacity drops suddenly, and this indicates the possibility of sudden collapses. It is also noted that the clear effect of the confining stress on the joints where the shear stiffness and the shear strength increase (shear stiffness is the slope of the linear part in the load-displacement curve) with the increase in the effective confining stress value. The ductility gives an indicator that expresses the ability of the structural element to show deformations and warnings before the collapse occurs and the ductility of the direct shear samples will be calculated as the ratio between the displacement corresponding to the maximum load ( u ) to the displacement corresponding to the half-maximal load ( 0.5Pu ).
The sample NRKHSC3 is the control sample for samples made of HSC, and it was able to reach a maximum load value of 456 kN at a displacement of 0.47 mm and collapsed by shearing. It is noted that some of the shear keys are completely separated (see Fig. 7a) and by calculating the ductility of this sample it was found that it is 3.6. RKHSC3 is a sample made of HSC with reinforced shear keys and subjected to a confining stress of 3 N/mm 2 . This sample was able to reach a load of 536 kN, which represents an increase of 18% over the control sample. It gave a ductility value close to that of the control sample (98%), and it is noticeable that the shear keys maintain their cohesion even after collapse (see Fig. 7b).
RKHSC6 is a sample made of HSC with reinforced shear keys and subjected to a confining stress of 6 N/mm 2 , the behavior of this sample is similar to the previous sample (RKHSC3), where it reached a maximum load of 633 kN, which represents an increase of 39% over the control sample and also represents an increase of 18% over the sample with a confining stress of 3 N/mm 2 and this sample gave a ductility of 92% of the ductility of the control sample. The collapse pattern of this sample is shown in Fig. 7c.
The behavior of the samples RKHSC3 and RKHSC6 confirms that by reinforcing the shear keys and by increasing the confining stress, the shear capacity of the joint increases and that the failure pattern is shear. It is noted from all joint samples made of HSC that the number of cracks is limited.    oad-displacement curves for UHPFC shear keyed joints are shown in Fig. 6b. It is noticed that there is a significant difference in the behavior of the joints made of UHPFC from that of the joints made of HSC, where shear failure occurs but is ductile in contrast to the aforementioned shear failures of the joint samples made of HSC.
NRKUHPFC3 is the control sample for joints made of UHPFC. The maximum load for this sample is 682 KN and its ductility is 7.72, which represents an increase of 50% and 114%, respectively, over that made of HSC. This joint has also collapsed by shear (see Fig. 7d).
RKUHPFC3 is similar to RKHSC3 but is made of UHPFC. It is noted that the maximum load of this sample increased by 48% over the control sample and increased by 89% over the maximum load of that made of HSC. The ductility of this sample decreased by 30% from that of the control sample, but increased by 55% from RKHSC3.
By increasing the confining stress to 6 N/mm 2 in the sample RKUHPFC6, the maximum load increased and reached 1172 KN, which represents an increase of 16% over the sample with a confining stress of 3 N/mm 2 , noting that the ductility of 93% and 216% of that of the control sample and that made of HSC, respectively, was obtained. The RKUH-PFC3 and RKUHPFC6 joints collapsed by shearing (see Fig. 7e and f).
It is noted that by reinforcing the shear keys with reinforcement and with a constant confining stress of 3 N/mm 2 for joints made of HSC and UHPFC (samples RKHSC3 and RKUHPFC3), the maximum load increases than that of nonreinforced joints by 18% and 48%, respectively. Whereas, by increasing the confining stress from 3 N/mm 2 to 6N/mm 2 for reinforced shear keyed joints, the maximum load value increases by 18% and 16%, respectively. The behavior of samples NRKUHPFC3, RKUHPFC3, and RKUHPFC6 confirms that the shear keyed joints made of UHPFC give greater strength, better ductility and an increase in the number of cracks than shear keyed joints made of HSC.

Bending Tests
With the loading of the HSCB beam gradually, it is noticed that some bending cracks appear in the middle of the beam in the tension side. These cracks start from the bottom and extend upwards. A yield of the lower rebar was observed in the middle of the beam at a displacement of 4.04 mm. With increasing loading, the number of cracks increases, widens and extends upwards until the beam was able to reach a maximum load value of 177 kN and the beam continued to bear a value close to this load for a large displacement until the collapse of the compression side of the beam, which represents a ductile bending collapse pattern (see Fig 8a). The ductility of beams subjected to bending will be defined as the ratio between the displacement corresponding to the maximum load ( u ) to the displacement corresponding to the yield load ( y ). The ductility of the HSCB beam is 5.49.
The behavior of the UHPFCB beam is similar to the HSCB beam, where the maximum load reached a value of 276 KN and the ductility of 10.2, which represents an increase of 56% and 86%, respectively, if compared to the HSCB beam, but a greater number of cracks is observed, perhaps due to the effect of the steel fibers (see Fig 8b).  The behavior of the RHSCB and RUHPFCB beams is similar as these beams were only able to reach 74% and 48%, respectively, of the maximum load value of the control beams. It was also not observed recording any yielding with bottom rebar. The two beams collapsed by concrete crushing at the top of the beam at the joint location, followed by a gapping of the distance between the opposite surfaces at the joint location in the tension side. From the numerical study that will be mentioned later, it became clear that the ductile collapse behavior of these samples is due to the coincidence of the locations of the loading steel plates. The behavior of the RHSCB and RUHPFCB beams confirms the importance of reinforcing the shear keyed joints in the compression side if these joints are used in the reinforced concrete beams. The collapse patterns of the RHSCB and RUHPFCB samples are shown in Fig. 8c and d. Since there is no yield occurred to rebar on the tension side of the beams RHSCB and RUHPFCB, therefore, the ductility parameter could not be calculated (Ductility u / y ). The toughness can be defined as the area under the load-deflection curve, it also gives an indication for ductility so it was calculated for all samples and given in Table 4. Figure 6 shows the load-displacement curves, while Figs 7 and 8 show the failure patterns for all samples tested in the experimental program. Figure 9a and 9b shows the amount of change in the maximum load and toughness, respectively, Table 4 gives a summary of all experimental results.

Finite Element Analysis
To save the financial costs, effort and trouble spent in experimental work, the importance of numerical analysis using the finite element method appears. Numerical analysis allows studying more variables and predicting the outcome, but it is required to verify the accuracy of the modeling process used. For this purpose, the Abaqus program [38] will be used to study the behavior of reinforced and non-reinforced shear keyed joints made of HSC or UHPFC under the influence  of different values of confining stress, as well as study the behavior of beams subjected to bending made from these joints.
The concrete damaged plasticity model was used to model the behavior of both HSC and UHPFC. This model needs to define the elastic behavior of concrete represented by the Young's modulus and Poisson's ratio. It also needs to define the plastic behavior of concrete by introducing some variables as: Dilation angle ψ, Eccentricity ε, Shape parameter K c , Maximum compression axial/biaxial stresses (f bo /f co ) and Viscosity parameter μ. The definition of these variables is at the bottom of Table 5. To define the behavior of HSC in compression and tension, the models presented by Han et al. [39] and Hillerborg et al. [40], respectively, were used while the behavior of concrete prepared by Al-Osta et al. [41] was relied upon to represent the behavior of UHPFC this is due to the similarity of the same components of concrete used. Table 5 shows the values of the required concrete damaged plasticity variables that have been entered to define all types of concrete used and Fig 10 shows the stress-strain curves that were relied upon. The elastic-perfect plastic behavior was imposed to model all types of reinforcing steel used, whether in reinforcing shear keys or reinforcing beams, the data in Table 3 mentioned above were used. The material of the loading plates, supporting plates, prestressing bars and metal fittings used for applying prestressing was considered as an elastic material only without plasticity.
To model the interaction behavior of reinforcing steel (whether used to reinforce the shear keys or to reinforce the beams) with the surrounding concrete, the embedded region constraint technique (full bond contact) was used while to represent the contact behavior between the opposite surfaces for separated segments at the location of the shear key joint, the hard contact allow separation technique was used in the normal direction combined with the penalty technique with friction coefficient in the tangential direction and a value of 0.6 for the friction coefficient is imposed.
• ψ* is the dilation angle, measured in p-q plane and should be defined to calculate the inclination of the plastic flow potential in high confining pressures. The dilation angle is equal to the friction angle in low stresses. In higher level of confinement stress and plastic strain, dilation angle is decreased. Upper values represent a more ductile behavior and lower values show a more brittle behavior. • ε* is the flow potential eccentricity defines the range that the plastic potential function closes to the asymptote. • Kc* is the ratio of the second stress invariant in the tensile meridian to compressive meridian for any defined value of the pressure invariant at initial yield. It is used to define the multi-axial behavior of concrete. • (fbo/fco)* is the proportion of initial equibiaxial compressive yield stress and initial uniaxial compressive yield stress. • μ* is the viscosity parameter and contributes to converge.
The total length of all samples was modeled, symmetry was not taken into account, and the analysis was carried out in two steps. The first step is by applying prestressing using the bolt load command available in the Abaqus program [38] for the external prestressing bars. The second step is by loading by displacement control in the places where the loading points are located.
For beams samples subjected to bending moments, the modeling of concrete elements, loading plates, supporting plates and prestressed bars was carried out using C3D8R (three-dimensional reduced integration linear brick element with eight nodes) while the element C3D4 (threedimensional quadratic tetrahedron element with four nodes) was used in modeling of shear keys samples subjected to direct shear. The element T3D2 (three-dimensional linear truss element with two nodes) is used to represent the reinforcing steel. Figure 11 shows the details of the modeling process. Table 6 shows the model size for all analyzed samples. Figure 12 shows the experimental and numerical load-displacement curves which shows a great match in the stiffness (the linear part at the beginning of the curves). There is also a large affinity for the maximum load value. By comparing Figs 13 and 14 with Figs 7 and 8, it is clear that there is a great similarity in the failure patterns. It is necessary to note that the plastic strain index (the legend) shown in Fig 14 was used for all plastic strain distributions in recent study. Tables 7 and  8 give a comparison between the experimental and numerical maximum load value and initial stiffness, respectively. It is clear from the results of the numerical study the accuracy and success of the modeling process, the ability of the elements, materials models and interaction properties used to model the behavior of reinforced and non-reinforced shear keyed joints made of HSC or UHPFC under the influence of different values of confining stress, as well as study the behavior of beams subjected to bending made of these joints.

Shear capacity of shear keyed joints analytically
AASHTO [42] gave the following equation to calculate the shear capacity of the single-shear keyed joints, taking into account the reduction of the results by 25%. The compressive strength of concrete (MPa). σ n The effective normal compressive stress in concrete at the centroid of the cross section (MPa). μ 1 The friction coefficient between concrete segments. A sm The area of contact between smooth surfaces on the failure plane. μ 1 The friction coefficient of shear reinforcement used. A s The area of shear reinforcement used. f y The yield stress of shear reinforcement.
Applying this equation to the previously mentioned shear keyed joints, it was found that there is a discrepancy reached to 30% in the case of UHPFC joints, it may be due to AASHTO does not take into account the effect of fibers on the shear strength of joint. Table 9 gives a comparison between experimental and AASHTO failure loads.

Conclusions
This research aims to study the direct shear and bending behavior of reinforced and non-reinforced dry shear keyed joints made of HSC and UHPFC. From the experimental and numerical study, it becomes clear that: • By reinforcing the shear keys and/or by increasing the confining stress of the joints made of HSC and UHPFC, the shear capacity of the joints is increased. If the value of the used confining stress is constant at a value of 3 N/mm2 and by reinforcing the shear keys with reinforcement, the maximum load increases by 18% and 48%, respectively, than its non-reinforced counterparts joints (samples RKHSC3 and RKUHPFC3). By increasing the confining stress of the reinforced shear keyed joints from 3 N/mm2 to 6 N/mm2, the maximum load value is increased by 18% and 16%, respectively (samples RKHSC6 and RKUHPFC6). • Shear keyed joints and beams made of UHPFC give greater capacity, better ductility and an increase in the number of cracks than their counterparts made of HSC. • Strengthening of the shear keyed joints used in the reinforced concrete beams in the compression side should be studied to avoid the collapse of the concrete in the joint place, as happened with the beams RHSCB and RUH-PFCB. • The success of the modeling process using the finite element method to model the shear keyed joints and segmented beams made of HSC and UHPFC confirms the suitability of the models of materials and elements and the contacting method used and the ability of this model to make a study of other variables in the future.
Funding Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).
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