Fatigue and Ultimate Strength Evaluation of GFRP-Reinforced, Laterally-Restrained, Full-Depth Precast Deck Panels with Developed UHPFRC-Filled Transverse Closure Strips

Abstract

A depth precast deck panel (FDDP) is one element of the prefabricated bridge element and systems (PBES) that allows for quick un-shored assembly of the bridge deck on-site as part of the accelerated bridge construction (ABC) technology. This paper investigates the structural response of full-depth precast deck panels (FDDPs) constructed with new construction materials and connection details. FDDP is cast with normal strength concrete (NSC) and reinforced with high modulus (HM) glass fiber reinforced polymer (GFRP) ribbed bars. The panel-to-girder V-shape connections use the shear pockets to accommodate the clustering of the shear connectors. A novel transverse connection between panels has been developed, featuring three distinct female-to-female joint configurations, each with 175-mm projected GFRP bars extending from the FDDP into the closure strip, complemented by a female vertical shear key and filled with cementitious materials. The ultra-high performance fiber reinforced concrete (UHPFRC) was selectively used to joint-fill the 200-mm transverse joint between adjacent precast panels and the shear pockets connecting the panels to the supporting girders to ensure full shear interaction. Two actual-size FDDP specimens for each type of the three developed joints were erected to perform fatigue tests under the footprint of the Canadian Highway Bridge Design Code (CHBDC) truck wheel loading. The FDDP had a 200-mm thickness, 2500-mm width, and 2400-mm length in traffic direction; the rest was over braced steel twin girders. Two types of fatigue test were performed: incremental variable amplitude fatigue (VAF) loading and constant amplitude fatigue (CAF) loading, followed by monotonically loading the slab ultimate-to-collapse. It was observed that fatigue test results showed that the ultimate capacity of the slab under VAF loading or after 4 million cycles of CAF exceeded the factored design wheel load specified in the CHBDC. Also, the punching shear failure mode was dominant in all the tested FDDP specimens.

1. Introduction

Precast full-depth deck panels (FDDPs) have recently been used in new accelerated bridge construction (ABC) or for the rapid bridge replacement (RBR) of existing deteriorated bridge decks. FDDPs are considered an effective means of reducing traffic disruption [1]. While the Canadian Highway Bridge Design Code (CHBDC) [2] permits using GFRP-reinforced FDDPs in bridge construction, it does not provide specific guidelines regarding the joint details for these precast systems.

By 1974, FDDPs were made composite with the superstructure by extending the steel shear stud into the deck. FDDP was supported on girders and secured using shear studs embedded in the shear pockets normally filled with non-shrink grout to eliminate stress concentrations in the panels [3]. The transverse panel-to-panel connection has shear keys to protect adjacent panels from relative vertical movement due to traffic load. The panel-to-panel connection has several shapes, including the male–female shear key. However, cracking, spalling, and leakage were observed in such joints. Other panel-to-panel connections included a female-to-female shear key, which comes in bulb and diamond shapes [4,5,6,7]. The incorporation of longitudinal reinforcement was achieved using overlapping U-bars and HS spirals, or employing open or closed steel tubes [8,9]. Grouting materials have to be used to fill the shear pockets and transverse joints [10]. UHPFRC, as the filling material of the closure strip between connected FDDPs, has numerous benefits, including reduction of joint size, improved durability, speed of construction, and prolonged usage life [11,12,13,14,15].

GFRP reinforcement is a composite material made of polymer matrix reinforced with fibers. It has a high strength-to-weight ratio, is corrosion-free, and lasts longer [16]. A GFRP bar has relatively weak interlaminar shear strength governed by the weak matrix. The bond force in the GFRP bar is transferred to concrete by friction, adhesion, and mechanical interlock, provided that adequate concrete cover is available. GFRP bars as an internal reinforcement are a practical choice for replacing deteriorated concrete bridge deck slabs owing to reinforcing steel bar corrosion [17,18,19,20,21].

AASHT-LRFD design specifications [22] consider the design of the deck slab as a continuous strip of 1000 mm width resting freely over the bridge beams. The load-carrying capacity of such a slab, which is based on the bending moment capacity, makes such a design over-conservative [23]. CHBDC specifies two different design methods for the slab-on-girder type: (i) the flexural design method and (ii) the empirical method that accounts for the arching action of the laterally restrained slabs. The laterally restrained concrete bridge slab deck fails in punching shear failure mode due to the effect of the concentrated wheel load causing the arching or compressive membrane action. Laterally restrained precast FDDP under arching action should exhibit higher load-carrying capacity than one-way precast FDDP failed under pure flexural loading or combined flexural shear failure. Thus, it was deemed necessary to investigate the behavior of the laterally-restrained precast FDDP under the effect of truck wheel load.

Researchers have assessed fatigue on steel-reinforced deck slabs [24,25,26,27,28]. Additionally, investigations were carried out on two-way concrete bridge decks reinforced with GFRP bars and subjected to concentrated wheel loads, resulting in failures characterized by punching shear [29,30,31,32,33,34,35]. Furthermore, studies [36,37,38,39,40,41,42,43] were conducted on one-way bridge deck slabs, supported by girders and reinforced with GFRP bars, incorporating carbon fiber fabric [44] in their design. A small group of researchers has investigated cast-in-place deck slabs reinforced with GFRP bars subjected to fatigue loading conditions [45,46,47,48] and those that employ a CFRP grid [49]. Moreover, some researchers have performed static and fatigue load tests on jointed slabs reinforced with steel bars and supported by girders [50,51]. Similar evaluations were also performed on FRP-reinforced jointed deck slabs [11,46,52]. Hassan et al. [29] concluded that the upper FRP reinforcement in the bridge deck slab has a minimal impact on the punching shear capacity. Overall, investigations into the fatigue performance of bridge deck slabs indicated negligible deterioration in the loaded slabs.

Traditionally, bridges are designed using static loads that include the dynamic load allowance (DLA) due to passing trucks at the ultimate, serviceability, and fatigue limit states. It is important to examine the structural behavior of the jointed precast FDDPs under different fatigue loading conditions, which lead to progressive, internal, and permanent structural changes in the materials. Two types of fatigue loading are considered in testing: constant amplitude fatigue loading (CAF) and variable amplitude fatigue loading (VAF). Fatigue loading is known to reduce the life span of the bridge deck [53]. Constant amplitude fatigue (CAF) is a classical method for fatigue analysis of the material to obtain the three fatigue resistance components for a structure, namely: stress-life (S-N) known as the Wöhler curve, strain-life (ԑ-N), and fatigue crack growth (FCG). CAF limit is the safe stress level under elastic deformation for the design that can take a very large number of cycles, more than one million cycles. The variable amplitude fatigue (VAF) limit investigates the effect of periodic overloading cycles. VAF is based on the same concepts, with the addition of cycle counting and damage summation due to increased step loading. However, the resulting stresses are high enough for plastic deformation to occur within the number of cycles, which is much less than one million cycles.

A small group of researchers has investigated the fatigue strength of reinforced concrete slabs subjected to fixed-point pulsating and repetitive moving loads. Experimental tests showed that moving loads produce more fatigue deterioration than pulsating loads, and the influence of transverse reinforcement enhances fatigue performance [28]. Reduced-scale model deck slabs were tested under both pulsating and moving loads; although the moving load produced more fatigue deterioration, all slabs developed punching failure [23]. Under fatigue loading, plain concrete exhibits increasing strain at the beginning, forming initial cracks followed by a steady state for a longer time before it crushes. Typical fatigue damage mechanisms for the FRP bars subjected to fatigue include matrix cracking, fiber-matrix debonding, void growth, and fiber breakage. FRP bar concrete under fatigue loading may result in abrasion of the bar surface due to shear lag [54,55]. A 52.08-m two-equal-span bridge was constructed in Quebec, Canada, named Cookshire-Eaton Bridge, with one span reinforced with steel bars and another with GFRP bars [37]. After one year, the bridge passed the service performance test using a calibrated CHBDC truck. Field test results showed no cracks, and deflection was within the allowable limits. In Vermont, USA, Morristown Bridge was reinforced with GFRP bars. Field test results revealed the good performance of the GFRP bars [36]. Full-scale deck slabs reinforced with GFRP bars were tested under pulsating concentrated loading up to failure, showing superior performance [27,47].

This paper reports the experimental test program of three developed joint details in a real-world situation. Two precast FDDPs were constructed for each developed joint detail and connected to an available braced twin-steel girder system. For each joint detail, one precast FDDP system was tested under CAF loading followed by loading it monotonically to collapse, and the other one was tested under VAF loading directly to collapse. Test results are analyzed to examine the fatigue performance and the ultimate load-carrying capacity of the developed jointed precast slabs.

2. Proposed Closure Strip Details

Three details for the joints between precast panels were proposed incorporating GFRP bars, as depicted in Figure 1. The first proposed joint has a 200-mm-wide closure strip, as shown in Figure 1a. In this joint, the top and bottom GFRP bars in the precast slab project into the joint with a 175-mm anchorage length. The precast panel has a projected slab of 90 mm in length at the bottom of the joint to hold UHPFRC within the closure strip during casting. A foam-type packing rod is inserted in the 20-mm gap between the two projected slabs at the bottom of the closure strip to avoid material leakage. This joint is called the “Angle-shape” joint or “A-joint” in this research. Figure 1b shows a view of the angle-joint cast for testing.

The second proposed joint has a 200-mm-wide closure strip, as shown in Figure 1c. This joint is identical to the proposed joint but without the 90-mm projecting slab. The top and bottom GFRP bars in the precast slab project into the joint with a 175-mm anchorage length. It is assumed that temporary formwork will close the bottom of the closure strip to hold UHPFRC materials before hardening. This joint is called “C-shape” or “C-joint” in this research. Figure 1d shows a view of the C-joint cast for testing. The vertical shear key is expected to provide vertical shear friction resistance between the precast concrete and the UHPFRC filling, allowing for vertical shear continuity of the slab across the joint.

Figure 1e depicts the trapezoidal zigzag-shaped panel-to-panel connection with a vertical female-to-female shear key. The slab thickness of 200 mm is divided vertically into equally four layers. The clear joint width between the ends of the jointed panels is 100 mm, while the zigzag shape (i.e., trapezoidal tooth shape) allows for an extension of the joint width of the other 100 mm into the precast panel. So, a GFRP bar from the end of one panel at its wide width of the trapezoidal shape will project into the joint with a length of 175 mm in 200 mm joint width in the same bar direction (i.e., 100 into the closure strip and 75 mm into the grooved trapezoidal shape in the adjacent panel). The pullout strength of the embedded GFRP in the joint will be resisted by the bond between its surface and the surrounding UHPFRC filling, in addition to the bearing pressure between the UHPFRC filling and the precast concrete at the included surface of the trapezoidal shape at the interface between the two concretes. Such bearing pressure is expected to be resisted by the concrete surface normal to the joint at the narrow end of the trapezoidal shape and the GFRP bar projecting through it from the adjacent panel. A vertical shear key is introduced along the side of the precast panel, while the expanded polystyrene foam is cut and used to form the zigzag connection. Figure 1f shows the GFRP bar arrangement in the zigzag joint and a view of the joint cast for testing. More details about the new connection details can be found elsewhere [56]

3. Experimental Program

The experimental program included testing two laterally restrained precast FDDPs supported over a braced twin-steel girder bridge system shown in Figure 2a. The steel I-girders were 7500 mm in length and made of W610 × 241. They were placed over 330 × 330 × 25 mm elastomeric pads supported over steel pedestals, making the clear spacing of the girder equal to 7000 mm. Transverse cross-type bracings were installed at the two ends of the steel girders to provide lateral restraints to the deck slab as specified in the CHBDC empirical design method. The spacing of the twin girders was 2000 mm, measured center-to-center of the girders. Figure 2b shows cross-section details of the precast FDDP resting over the twin girders and connected to it using shear connectors. The M25 high-strength bolts are used for the panel-to-girder connection. The precast FDDP’s width was 2500 mm so that it could be supported over the twin girders to produce a slab span of 2000 mm, as depicted in Figure 2c. The precast FDDPs had a 200 mm thickness and were made of 35 MPa normal strength concrete (NSC) with a 10 mm nominal size aggregate, a 150 mm slump with added superplasticizer, and no air-entrant.

Straight-ended, 16M ribbed-surface HM GFRP bars reinforced the precast FDDP, per CHBDC requirements. The slab’s bottom and top transverse reinforcement were taken 16M bars @ 140 mm and 16M bars @ 200 mm, respectively. The slab was reinforced with 16M bars @ 200 mm in the bottom and top longitudinal direction (i.e., parallel to the girder). The properties of the materials of the HM GFRP bars are listed in

Table 1. Mechanical properties of GFRP bars used in this study.

Product Type	Bar Size	Bar Area (mm2)	Guaranteed Tensile Strength (MPa)	Modulus of Elasticity (GPa)	Strain at Failure
Ribbed-surface	15M (#5)	201	1188	64	2.6%

. The specified ultimate tensile strength and modulus of elasticity of the GFRP bars were 1188 MPa and 64 GPa, respectively [57]. Two precast FDDPs were formed first to form the joint between the precast FDDPs. The first precast FDDP was of 200 mm thickness, 2400 mm length in the girder direction, and 2500 mm width, while the second precast FDDP was of 200 mm thickness, 1000 mm length in the girder direction, and 2500 width. Those two FDDP segments are shown as FDDP 1 and FDDP 2 in Figure 2c. This made the final length of the jointed slab 3700 mm in the direction of traffic. It should be noted that the short precast FDDP of 1000 mm was introduced beside the large precast FDDP in Figure 2c to ensure deck slab continuity beyond the joint. Figure 3 shows some images of the construction and detailing of the tested FDDPs with the three types of adopted joints.

The panel-to-girder connection was made using shear pockets to achieve the full composite action. Shear bolts were used to establish such full composite action between the girder and the precast panel every 1200 mm. Figure 4 shows cross-sections and views of the shear pockets between and at the transverse closer strips. UHPFRC (Ductal joint-fill JS1000 produced and supplied by Lafarge Canada Inc., Stoney Creek, ON, Canada) was used as filling material for the shear pockets and the closure strips [58]. Typical UHPFRC composition and material properties are available elsewhere [51], while a state-of-the-art report on UHPFRC for the bridge community was produced by Russell and Graybeal (2013) [59]. The authors used Ductal JS1000 in this research since it was approved by the Ontario Ministry of Transportation for use in Ontario bridge construction. The ultimate strengths of the UHPFRC were 140, 30, and 8 MPa in compression, flexural, and direct tension, respectively, while its modulus of elasticity was 50 GPa.

Using the available force-control hydraulic actuator system, the experimental program tested two precast FDDPs supported over a twin-steel girder bridge. The first precast FDDP system was tested under constant amplitude fatigue (CAF) loading, followed by increasing static loading to collapse. To collapse, the second precast FDDP system was tested under incremental step fatigue loading of variable amplitude (VAF).

Table 2. Summary of fatigue-tested slab configurations.

Slab Name			Transverse Reinforcement (Normal to Girder)		Longitudinal Reinforcement (Parallel to Girder)
Slab Number	Joint Type	Test Type *	Bottom	Top	Bottom	Top
S1	A	CAF	Straight end No. 16 @ 140 mm	Straight end No. 16 @ 200 mm	Straight end No. 16 @ 200 mm	Straight end No. 16 @ 200 mm
S2		VAF
S3	C	CAF	Straight end No. 16 @ 140 mm	Straight end No. 16 @ 200 mm	Straight end No. 16 @ 200 mm	Straight end No. 16 @ 200 mm
S4		VAF
S5	Z	CAF	Straight end No. 16 @ 140 mm	Straight end No. 16 @ 200 mm	Straight end No. 16 @ 200 mm	Straight end No. 16 @ 200 mm
S6		VAF

* CAF = constant amplitude fatigue loading; VAF = variable amplitude fatigue loading.

presents a summary of fatigue-tested slab configurations. The constant-amplitude fatigue test is intended to examine whether the jointed slab can accommodate a minimum of two million cycles of fatigue loading without significant damage as an acceptance criterion per the Canadian Highway Bridge Design Code [2]. After the fatigue testing, the slab was statically loaded to collapse to determine its ultimate load-carrying capacity and compare it with the design wheel load for ultimate limit state design. The variable amplitude fatigue load test is meant to obtain fatigue test data to assist in developing a fatigue prediction model.

The actuator system generates sinusoidal harmonic force, $p_t=p_{avg}+p_o\sin 2\pi ƒt$, where $p_{avg}=p_{static}$ is the average load of the maximum and minimum load, $p_o$ is the amplitude of applied load, ƒ is the frequency of the applied load, and t is the time. Before performing the fatigue tests, a flexural crack was initiated at the bottom of the tested slab by applying a static load equal to three times the applied wheel load for serviceability limit state design per CHBDC (SLS₁ = 87.5 kN × 1.4 × 0.9 = 110.25 kN). The 87.5 kN equals the heaviest wheel load in the CHBDC truck, multiplied by 1.4 to include the dynamic load allowance (DLA) and 0.9 as the fatigue limit state design load factor. This load is three times SLS₁ = 110.25 × 3 = 330.75 kN. The footprint of the wheel load on the top surface of the tested slab measured 600 mm wide by 250 mm long, and it was decided to locate it just beside the edge of the joint, as depicted in Figure 2c.

The constant amplitude fatigue (CAF) loading was applied under force control with a sinusoidal shape to represent the fatigue limit state (FLS) load specified into the CHBDC as FLS = 87.5 × 1.4 × 1.0 = 122.5 kN at the frequency of 4 Hz for 4 million cycles. To prevent rattling of the test setup under cyclic loading, the loading cycle started with a 15 kN applied load that increased by 122.5 kN. Thus, the sinusoidal cyclic CAF ended up with a loading range of upper and lower absolute values of 137.5 kN and 15 kN, respectively, with a sample rate of 20.013 Hz. Figure 5a shows the CAF loading history applied to the test specimens. A static load test at 1.5 times the applied FLS load (i.e., 122.5 kN × 1.5 = 183.75 kN) was performed every 250,000 cycles to assess the degradation of the jointed slab due to fatigue loading. The force-control monotonic test had a ramp segment shape at a loading and unloading rate of 5 kN/min. and 10 kN/min, respectively, collecting data points every 0.049967 s, per

Table 3. Static load configuration.

Loading	Unloading
Segment shape: ramp function	Segment shape: ramp function
Rate: 5 kN/min	Rate: 10 kN/min
Control mode: Force	Control mode: force
Absolute end level (machine max. load for test purposes): 183.75 kN	Absolute end level: zero kN

. After the 4 million cycles of CAF loading, the FDDP system was monotonically loaded to collapse using a 1300 kN capacity hydraulic jack. The resulting ultimate load was compared to the CHBDC factored design load that was taken as P_f = 87.5 × 1.4 × 1.7 = 208.25 kN, where 87.5 kN is the heaviest wheel load in the CHBDC truck, the 1.4 is the dynamic load allowance and 1.7 is the live load factor for ultimate limit state design.

The incremental step variable amplitude fatigue (VAF) loading was applied under force control with sinusoidal shape to different seven absolute peak levels of 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 times the FLS load of 122.5 kN plus 15 kN as the absolute load lower level. The corresponding peak loads of the seven incremental steps of VAF loading were 137.5, 198.75, 260, 321.25, 382.5, 443.75 and 505 kN. Each load level was applied for 100,000 cycles at the range of 2 Hz to 0.5 Hz, depending on the stiffness of the FDDP system and the steel loading frame system, with the lowest frequency used when approaching failure of the slab. Figure 5b shows the VAF loading history considered in this study. Data were collected at a sample rate of 20.013 Hz. A monotonic test was performed after each 100,000 cycles with the same setting as the CAF monotonic test. After finishing with the seven absolute peak levels mentioned earlier, the VAF loading testing continued with the highest peak value till collapse. Figure 6 shows images for the test setup used to conduct the fatigue loading tests under VAF and CAF, and the monotonic loading to collapse tests for all panels.

4. Experimental Test Results

This section discusses the structural behavior of the tested specimens in the form of slab vertical deflection and crack pattern. As mentioned earlier, fatigue pre-cracking was conducted under force control. The first hair flexural crack was observed at about 2.5 times the FLS loading (275.625 kN) underneath the wheel footprint area at the mid-span in the longitudinal direction (parallel to the supporting girders). The load was increased to three times the FLS load (330.75 kN) to increase the crack propagation beyond the wheel footprint area. The flexural crack width was 80 µm at that static load. CHBDC specifies that the design-factored ultimate limit state (ULS) load of the deck slab is the multiplication of the CHBDC truck wheel load of 87.5 kN, load factor of 1.7, and dynamic load allowance of 1.40. This makes the factored design applied load ULS₁ = 87.5 × 1.4 × 1.7 = 208.25 kN. Interestingly, the pre-cracking monotonic load of 330.75 kN, at which a minor flexural crack appeared, is about 59% greater than the CHBDC factored design load of 208.25 kN.

4.1. Constant Amplitude Fatigue Loading

4.1.1. Behavior of the A-Jointed Precast FDDP under CAF

For the tested specimen S1 under CAF loading, the compressive strength of the concrete cylinders taken from the concrete mix were 60.76, 59.83, and 54.26 MPa, with an average value of 58.28 MPa. The tested cylinders for the UHPFRC resulted in compressive strengths of 161.94, 163.30, 170.54, and 159.20 MPa, with an average value of 161.48 MPa. During the initiation of the fatigue pre-cracking procedure, at a static load of 220.5 kN, the flexural crack propagated from underneath the mid-point of the wheel footprint about 100 mm towards the middle shear pockets shown at the middle of the precast slab segment. When the applied load increased to 275.625 kN, the flexural crack propagated further another 300 mm. However, when the applied load reached 330.75 kN, the flexural crack propagated diagonally from underneath the mid-point of the wheel footprint to the closest corner of the middle shear pocket. The maximum recorded flexural crack width at that point measured 80 µm. No more flexural cracks were observed during the CAF test that lasted over 16 days.

After each 250,000 cycles, the slab was subjected to monotonic loading to observe the change in slab flexural stiffness through deflection measurements. Figure 7a depicts the load-deflection relationship for the slab at the center of the footprint of the wheel load. It can be observed that the slope of the curves after each group of fatigue cycles appeared unchanged and stayed linear. After the 4 million fatigue cycles, the slab was subjected to a monotonic load that caused it to collapse. The precast FDDP failed due to punching shear at a jacking load of 930.92 kN. Figure 7b depicts the recorded slab deflection at the mid-length of the free edge of the short slab shown as the location of LVDT 1 in Figure 2c, noted as the “Free end” curve in Figure 7b. Such deflection reached 10.68 mm at failure. On the other hand, deflection under the wheel footprint shown as the location of LVDT 2 in Figure 2c, denoted as “Point load” in Figure 7b, was recorded as 23.05 and 23.88 mm at failure since two LVDTs were installed at this location. The deflection at the center of the long precast slab shown at the location of LVDT 3 in Figure 2c, denoted as “Mid-span” in Figure 7b, was recorded as 13.09 mm. The maximum deflection of the long precast slab at the mid-length of the edge joint shown as the location of LVDT 4 in Figure 2c, denoted as “Fixed end” in Figure 7b, was recorded as 6.80 mm at failure.

Interestingly, such a failure load is about 4.47 times the CHBDC factored design wheel load. Figure 8a presents the top view of the slab showing punching shear failure at the footprint of the wheel load. Figure 8b shows the bottom view of the slab showing a crack pattern after failure due to the fan mechanism. One may observe the radial cracks starting from the location of the footprint of the wheel load and propagating toward the support line in a fan shape. At failure, concrete spalling appeared in some parts of the bottom side of the slabs as signs of punching shear failure. However, such concrete spalling appeared only in the large FDDP slab, but it did not extend to the short FDDP segment on the other side of the closure strip.

4.1.2. Behavior of the C-Jointed Precast FDDP under CAF

For the tested specimen S3 having C-joint under CAF loading, the compressive strengths of the concrete cylinders on the testing day were 58.10, 57.08, and 54.87 MPa, with an average value of 56.68 MPa. The tested cylinders for the UHPFRC, which were cast ten days before the start of the fatigue testing, resulted in compressive strengths of 168.03, 162.33, 170.54, and 149.22 MPa, with an average value of 162.53 MPa.

During the initiation of the fatigue pre-cracking procedure, at a static load of 220.5 kN, the flexural crack propagated from underneath the mid-point of the wheel footprint about 100 mm towards the middle shear pockets shown at the middle of the precast slab segment. When the applied load increased to 275.625 kN, the flexural crack propagated further another 300 mm. However, when the applied load reached 330.75 kN, the flexural crack propagated diagonally from underneath the mid-point of the wheel footprint to the closest corner of the middle shear pocket. The maximum recorded flexural crack width at that point measured 80 µm. No more flexural cracks were observed during the CAF test that lasted over 16 days.

After each 250,000 cycles, the slab was subjected to monotonic loading to observe the change in slab flexural stiffness through deflection measurements. Figure 9a depicts the load–deflection relationship for the slab at the center of the footprint of the wheel load. It can be observed that the slope of the curves after each group of fatigue cycles appeared unchanged and stayed linear. After the 4 million fatigue cycles, the slab was subjected to a monotonic load that caused it to collapse. The precast FDDP failed due to punching shear at a jacking load of 973 kN. It can be noted that such a failure load is about 4.67 times the CHBDC factored design wheel load. Figure 8c shows the top view of the slab showing punching shear failure at the footprint of the wheel load, while Figure 8d presents the bottom view of the slab showing a crack pattern after failure. It can be observed that the radial cracks start from the location of the footprint of the wheel load and propagate toward the support line in a fan shape. At failure, concrete spalling appeared in some parts of the bottom side of the slabs on one side of the closure strip as a sign of punching shear failure. However, this concrete spalling did not extend through the closure strip to the adjacent FDDP. Figure 8d shows that a concrete diagonal crack at the end of the bottom perimeter of the punching shear plane appeared, passing through UHPFRC on one side of the closure strip. In addition, fan-shaped cracks at the bottom surface of the slab passed through the UHPFRC but were less intensive than those in the precast slab. Figure 9b depicts the load-deflection relationship for the tested slab under static loading to collapse. Deflection values were recorded at the mid-length of the free edge of the short slab, noted as a “Free end” curve that reached 2.54 mm at failure. On the other hand, deflection under the wheel footprint, denoted as “Point load”, was recorded as 25.98 mm at failure. The deflection at the center of the long precast slab, denoted as “Mid-span”, was recorded as 17.83 mm. The maximum deflection of the long precast slab at the mid-length of the edge joint, denoted as “Fixed end”, was recorded as 3.73 mm at failure.

4.1.3. Behavior of the Z-Jointed Precast FDDP under CAF

For the tested specimen S5 under CAF loading, the NSC cylinders’ average compressive and splitting tensile strengths were 37 MPa and 3.23 Mpa, respectively. The tested cylinders for the UHPFRC, which were cast 10 days before the fatigue testing, resulted in an average compressive strength of about 127 Mpa. During the initiation of the fatigue pre-cracking procedure, at a static load of 220.5 kN, the flexural crack propagated from underneath the mid-point of the wheel footprint about 100 mm towards the middle shear pockets. When the applied load increased to 275.625 kN, the flexural crack propagated further another 300 mm. However, when the applied load reached 330.75 kN, the flexural crack propagated diagonally from the mid-point of the wheel footprint to the closest corner of the middle shear pocket. The maximum recorded flexural crack width at that point measured 80 µm. No more flexural cracks were observed during the CAF test that lasted over 16 days.

After each 500,000 cycles, the slab was subjected to monotonic loading to observe the change in slab flexural stiffness through deflection measurements. Figure 10a depicts the load-deflection relationship for the slab at the center of the footprint of the wheel load. It can be observed that the slope of the curves after each group of fatigue cycles appeared unchanged and stayed linear. After the 4 million fatigue cycles, the slab was subjected to increasing monotonic load to collapse. The precast FDDP failed due to punching shear at a jacking load of 931 kN, which corresponded to about 4.47 times the CHBDC factored design wheel load. Figure 10b depicts the load-deflection relationship for the tested slab under static loading to collapse. The deflection value was recorded at the mid-length of the free edge of the short slab, noted as a “Free end” that reached 1.78 mm at failure. On the other hand, deflections under the wheel footprint, denoted as “Under load 1 and load 2”, were recorded as 30.29 and 28.94 mm at failure, respectively. The deflection at the center of the long precast slab, denoted as “Mid-span”, was recorded as 19.30 mm. The maximum deflection of the long precast slab at the mid-length of the edge joint, denoted as “Fixed end”, was recorded as 2.65 mm at failure. Figure 8e presents the top view of the slab showing punching shear failure at the footprint of the wheel load, while Figure 8f presents the bottom view of the slab showing the crack pattern after failure.

4.2. Variable Amplitude Fatigue Loading

4.2.1. Behavior of the A-Jointed Precast FDDP under VAF

The precast FDDP specimen S2 underwent sinusoidal waveform fatigue load cycles with incremental step low cycle fatigue loading. The compressive strengths of concrete cylinders for the normal strength concrete (NSC) used to cast S2 were 54.29, 57.22, 59.98, 46.54, 65.84, and 64.7 MPa, with an average value of 58.10 MPa. The splitting tensile test for the NSC resulted in tensile strengths of 3.53, 5.73, 5.31, 4.3, and 4.7 MPa, with an average value of 4.71 MPa. The compressive strengths of the concrete cylinder used to fill the joints of the UHPFRC were 154.17, 188.12, 184.61, and 181.91 MPa, with an average value of 179.52 MPa. The splitting tensile test for the UHPFRC resulted in tensile strengths of 15.12, 12.14, and 15.76 MPa, with an average value of 14.42 MPa.

The first 501,002 fatigue load cycles were performed at a frequency of 2 Hz, then followed by 160,242 cycles at 1 Hz, and finally by 130,139 cycles at 0.5 Hz, leading to punching shear failure at a total number of cycles of 809,493. Figure 11a depicts the 60-mm-deep punching shear failure at the wheel footprint on top of the slab, while Figure 11b depicts the crack pattern at the bottom surface of the slab at failure. One may observe the radial cracks starting from the location of the footprint of the wheel load and propagating toward the support line in a fan shape. At failure, concrete spalling appeared in some parts of the bottom side of the large slab on one side only of the closure strip as a sign of punching shear failure. However, concrete spalling appeared to deviate from the traditional shape for punching failure (close to circular shape at the end of diagonal cracks through slab thickness). However, a major flexural crack appeared at failure just under the wheel load, extending in the direction of the girder towards the free end of the small FDDP segment while crossing the closure strip, as depicted in Figure 11b. This precast FDDP failed at a jacking load of 487.50 kN and a maximum slab deflection of 32.46 mm. It is worth mentioning that such a failure load is about 2.34 times the CHBDC factored design wheel load. Figure 12 depicts the monotonic load-deflection relationship of the slab S2 after each 100,000 fatigue load cycles. It can be observed that the slope of the curve decreased, leading to a reduction in slab flexural stiffness, with an increase in the number of VAF load cycles.

Table 4. Test results: loading data.

Slab Number	Joint Type	Test *	Peak Cyclic Load (kN)	Frequency (Hz)	No. of Load Cycles	Ultimate Load (kN)	Ultimate Deflection (mm)	Failure Mode
S1	A	CAF + SUL	137.5	4	4,000,000	930.92	23.47	Punching
	A	VAF	500.0	2–0.5	809,493	487.50	32.46	Punching
S2	C	CAF + SUL	137.5	4	4,000,000	973.00	26.09	Punching
	C	VAF	500.0	2–0.5	692,866	495.69	40.89	Punching
S3	Z	CAF + SUL	137.5	4	4,000,000	931.00	29.62	Punching
	Z	VAF	500.0	2–0.5	961,540	488.43	37.03	Punching

* CAF = constant amplitude fatigue loading; SUL = static ultimate load; VAF = variable amplitude fatigue load.

and

Table 5. Test results: deflection data.

Monitoring Direction	Deflection, mm			Comments
Longitudinal Direction	A-Shape	C-Shape	Z-Shape
Free-end	7.48	8.78	9.00	Small segment
Point-load 1	23.05	25.98	30.29	Actual segment
Point-load 2	23.88	26.20	28.94	Actual segment
Mid-span	13.39	16.03	18.06	Actual segment
Fixed-end	2.44	8.28	7.47	Rear joint
Transverse direction
Steel-girder 1	10.68	2.54	1.78	Twin girder
0.25 Transverse-span	13.09	17.86	19.32	Actual segment
Point-load 1	23.05	25.98	30.29	Actual segment
Point-load 2	23.88	26.20	28.94	Actual segment
Steel-girder 2	6.8	3.73	2.65	Twin girder

summarize the test data for all specimens with A-joints, C-joints, and Z-joints under CAF and VAF loading.

4.2.2. Behavior of the C-Jointed Precast FDDP under VAF

The compressive strengths of concrete cylinders for the NSC used to cast the second precast FDDP specimen with C-joint S4 were 67.78, 64.93, 65.63, and 67.81 MPa, with an average value of 66.54 MPa. The compressive strengths of the concrete cylinder for the UHPFRC used to fill the joints were 147.60, 150.69, and 151.45 MPa, with an average value of 149.91 MPa.

The first 500,000 fatigue load cycles were performed at a frequency of 2 Hz, then by 100,000 cycles at 1 Hz, and finally by 92,866 cycles at 1 Hz, leading to punching shear failure at a total number of cycles of 692,866. Figure 11c depicts the punching shear failure at the wheel footprint on top of the slab, while Figure 11d depicts the crack pattern at the bottom surface of the slab at failure. A fan-shaped crack pattern was observed at the bottom surface similar to those developed for the slab tested to collapse after passing the CAF loading. However, Figure 11d shows greater concrete spalling along the perimeter on the punching shear plane at the bottom of the slab but only from one side of the closure strip. At failure of S4, a major flexural crack appeared at the wheel load location and extended to the free edge of the short FDDP segment, as depicted in Figure 11d. This led to the conclusion that the failure mode is primarily punching shear combined with flexural failure in the adjacent short FDDP. It should be noted that very few flexural cracks appeared at the bottom of UHPFRC in slab S4 tested under VAF loading when compared to intensive cracks through UHPFRC in slab S3 tested under CAF loading, as depicted in Figure 8d. Slab S4 failed at a jacking load of 495.69 kN and a maximum slab deflection of 40.89 mm. It is worth mentioning that such a failure load is about 2.38 times the CHBDC factored design wheel load. Figure 12 depicts the monotonic load-deflection relationship of the slab after each 100,000 fatigue load cycle. It can be observed that the slope of the curve decreased, leading to a reduction in slab flexural stiffness, with an increase in the number of VAF load cycles.

4.2.3. Behavior of the Z-Jointed Precast FDDP under VAF Loading

The compressive strengths of concrete cylinders for the NSC used to cast slab S6 were 43.26, 68.16, 64.99, and 65.74 MPa, with an average value of 60 MPa. The compressive strengths of the concrete cylinder for the UHPFRC used to fill the joints were 163.35, 183.31, and 153.28 MPa, with an average value of 167 MPa. The splitting tensile test for the UHPFRC resulted in tensile strength of 18.30, 20.47, and 21.69 MPa, with an average value of 20 MPa.

The first 895,000 fatigue load cycles were performed at a frequency of 2 Hz, then 21,736 cycles at 1 Hz, and finally followed by 44,804 cycles at 0.5 Hz, leading to punching shear failure at a total number of cycles of 961,540. Figure 11e depicts the punching shear failure at the wheel footprint on top of the slab, while Figure 11f depicts the crack pattern at the bottom surface of the slab at failure. A fan-shaped crack pattern was observed at the bottom surface similar to those developed for the slab tested to collapse after passing the CAF loading. However, greater concrete spalling appeared along the perimeter on the punching shear plane at the bottom of the slab but only from one side of the closure strip when compared to the failure mode shown in Figure 8f for slab S5 subjected to CAF loading. This precast FDDP slab S6 failed at a jacking load of 488.43 kN, about 2.35 times the CHBDC factored design wheel load, and a maximum slab deflection of 37.03 mm. Figure 13 depicts the monotonic load-deflection relationship of the slab after each 100,000 fatigue load cycle. It can be observed that the slope of the curve decreased, leading to a reduction in slab flexural stiffness, with an increase in the number of VAF load cycles.

To obtain a comprehensive overview of the punching shear failure at each side of the loaded area, slabs S1, S2, S3, S4, S5, and S6 were sliced at the load location in both the transverse direction (normal to the steel girders) and the longitudinal direction. Figure 14 shows schematic diagrams of the punching shear failure in the tested slab when sliced longitudinally and transversally at the wheel load location observed after saw-cutting the slabs.

4.3. Stiffness Degradation

The stiffness degradation of precast FDDPs under flexural-shear loading was calculated as spring stiffness, k. k is the ratio between the applied monotonic load, F, in kN, and the corresponding slab deflection, d, in mm. Stiffness degradation in reinforced concrete elements results from cracking, loss of bond, and interaction with higher shear or flexural stresses. The level of stiffness degradation depends on the characteristics of the structure, such as material properties (P-delta effect), geometry level, level of connection ductility, loading history, and their combination.

Table 6. Stiffness degradation of the tested slabs.

Joint Type	Slab S1 with CAF Loading *				Slab S2 with VAF Loading *
	Cumulative Cycles (N)	Load (kN)	Deflection (mm)	k = F/d **	Cumulative Cycles, N	Load (kN)	Deflection (mm)	k = F/d **
A-type	0	183.75	1.40	131.25	0	183.75	1.24	148.19
	250,000	183.75	2.90	63.36	100,000	183.75	2.37	77.53
	500,000	183.76	2.89	63.58	200,000	183.76	2.47	74.39
	750,000	183.75	2.91	63.14	300,000	183.76	2.76	66.58
	1,000,000	183.75	2.92	62.92	400,000	183.76	3.80	48.35
	1,250,000	183.76	2.93	62.71	500,000	183.76	5.38	34.15
	1,500,000	183.76	2.94	62.50	600,000	183.78	7.41	24.80
	1,750,000	183.76	2.95	62.29	715,381	183.76	9.44	19.46
	2,000,000	183.77	2.96	62.08	809,493
	2,250,000	183.76	2.97	61.87
	2,500,000	183.75	2.99	61.45
	2,750,000	183.76	3.01	61.05
	3,000,000	183.75	2.99	61.45
	3,250,000	183.76	3.02	60.84
	3,500,000	183.76	3.02	60.84
	3,750,000	183.75	3.01	61.04
	4,000,000	183.76	3.03	60.64
C-type	Slab S3 with CAF loading *				Slab S4 with VAF loading *
	0	183.75	1.35	136.11	100,000	183.75	3.58	51.32
	500,000	183.76	2.65	69.34	200,000	183.76	3.72	49.39
	1,000,000	183.76	2.67	68.82	300,000	183.75	4.09	44.92
	1,250,000	183.76	2.66	69.08	400,000	183.75	5.43	33.84
	1,500,000	183.76	2.68	68.56	500,000	183.76	6.89	26.67
	1,750,000	183.76	2.72	67.56	600,000	183.75	9.74	18.86
	2,000,000	183.76	2.7	68.05	692,866
	2,250,000	183.76	2.71	67.80
	2,500,000	183.75	2.73	67.31
	2,750,000	183.76	2.74	67.06
	3,000,000	183.75	2.71	67.80
	3,250,000	183.75	2.77	66.33
	3,500,000	183.76	2.77	66.34
	3,750,000	183.76	2.76	66.58
	4,000,000	183.76	2.74	67.06
Z-shape	Slab S5 with CAF loading *				Slab S6 with VAF loading *
	0	184.55	1.78	103.68	100,000	183.74	3.12	58.89
	500,000	183.76	1.99	92.34	200,000	183.76	3.2	57.42
	1,000,000	183.75	2.07	88.77	300,000	183.76	3.5	52.5
	1,250,000	183.75	2.09	87.92	400,000	183.75	4.55	40.38
	1,500,000	183.76	2.06	89.2	500,000	183.76	6.19	29.68
	1,750,000	183.75	2.14	85.86	600,000	183.75	7.64	24.05
	2,000,000	183.77	2.14	85.87	700,000	183.75	8.77	20.95
	2,250,000	183.75	2.15	85.46	800,000	183.83	10.88	16.89
	2,500,000	183.75	2.17	84.68	895,000	--
	2,750,000	183.75	2.18	84.29	916,736	--
	3,000,000	183.75	2.71	67.80
	3,250,000	183.75	2.77	66.33
	3,500,000	183.76	2.77	66.34
	3,750,000	183.76	2.76	66.58
	4,000,000	183.76	2.74	67.06

* CAF = constant amplitude fatigue loading; VAF = variable amplitude fatigue load. ** k is the spring constant in kN per mm, F is the ultimate load in kN, and d is the deflection in mm.

summarizes the results for the CAF loading and for the VAF loading for precast A-Jointed FDDPs S1 and S2. Figure 15a,b depict the relationship between the spring stiffness and the number of fatigue cycles and slab deflection, respectively. One may observe that the specimen’s stiffness of S1 degraded by about 53.8% after 4 million cycles of constant amplitude fatigue loading. On the other hand, the specimen’s stiffness of S2 degraded by 86.86% when subjected to variable amplitude fatigue loading before complete collapse. Table 6 also summarizes the results for the CAF loading and the VAF loading for C-jointed precast FDDPs S3 and S4. Figure 15c,d depicts the relationship between the spring stiffness and the number of fatigue cycles and slab deflection, respectively, for S3 and S4. It can be observed that the first specimen’s stiffness (S3) degraded by about 50.73% after 4 million cycles of constant amplitude fatigue loading. On the other hand, the second specimen’s stiffness (S4) degraded by 63.24% when subjected to variable amplitude fatigue loading before complete collapse.

Furthermore, Table 6 summarizes the results for the CAF loading and for the VAF loading for Z-jointed precast FDDPs S5 and S6. Figure 15e,f depict the relationship between the spring stiffness and the number of fatigue cycles and slab deflection, respectively. One may observe that the specimen’s stiffness of S5 degraded by about 21.9% after 4 million cycles of constant amplitude fatigue loading. On the other hand, the specimen’s stiffness of S6 degraded by 71.32% when subjected to variable amplitude fatigue loading before complete collapse. Figure 16 shows a comparison of slab degradation under CAF and VAF loading.

4.4. Life Estimation of Fatigue of GFRP-Reinforced Precast FDDP

A realistic representation of the service loads is usually variable amplitude, which should consider the accurate measure of the applied load on the existing structure and predict loads on the structure that do not exist yet. Loads can be obtained from real-life histories or through simplified segmental loading. The fatigue cycle counting method compares the effect of the variable amplitude fatigue load histories to the fatigue data and curves obtained with the simple constant amplitude fatigue loading cycles. Applying the linear damage rule where cumulative linear damage, D = 1.0 requires the knowledge of the mean and amplitude of the load to which the damaging event is compared. One approach to the variable load histories is the concept of the damage, known as fraction life or cycle ratio. These fractions are added together with the sum of 1.0 as defined in Equation (1) by the linear damage rule as proposed by Palmgren [60] and later again by Miner [61].

$$D=\sum {\displaystyle \frac{n_i}{N_{fi}}}=1$$

(1)

where n is the number of cycles and N_f is the number of repetitions of the same cycle that equals life to failure. The damaging effect of n₁ cycles at P₁ load amplitude is assumed to be $n_1{D}_1=n_1/N_{f1}$, while the damaging effect of n₂ cycles at P₂ load amplitude is assumed to be $n_2{D}_2=n_2/N_{f2}$. Similarly, the cycle ratio or damage caused by n_i cycles at P_i load amplitude is $n_i{D}_i=n_i/N_{fi}$. Failure is predicted when the sum of all ratios becomes 1 or 100%. The assumption of the linear damage depends on the rate of damage accumulation and load amplitude, which leads to $n_i/N_{fi}\ne 1$ for a low-to-high or a high-to-low loading sequence. Miner’s Rule does not account for overload or high stress, which may occur in compressive residual stress that leads to retarding of the crack growth. High-to-low stresses may have less damage due to compressive residual stress. However, it is widely used for simplicity and hardly to achieve better agreement with the current experimental data. Non-linear damage theories proposed $D=\sum {\left(n_i/N_{fi}\right)}^{{\alpha }_l}$ where ${\alpha }_l$ depends on the load level. When considering the change of load level to be $P/P_u$, the authors propose the non-linearity of the damaging effect on the step loading through Equation (2) as a result of the observed stiffness degradations, keeping the linearity of $D=1$ and solving for the $\eta$ using the non-linear least square regression analysis (NLREG).

$$N_f=e^{\eta (1-P/P_u)}$$

(2)

where $\eta$ equals 25.86, 24.32, and 25.609 for the A-Joint, C-Joint, and Z-Joint, respectively.

Table 7. Fatigue parameters.

Joint Pattern	H	K
A-Jointed Precast FDDP	25.86	0.039
C-Jointed Precast FDDP	24.32	0.041
Z-Jointed Precast FDDP	25.61	0.039

,

Table 8. Loading history of the tested slab S2 of type A-joint with equivalent constant amplitude fatigue load segments.

Segment	Pu	FLS			Pmin	Pmax	Pamp	Pmean	R	A	Pmax/Pu	n	Nf	n/Nf
		MF	WL	FLS1
1	930.92	1.0	87.5	122.5	15	137.50	61.25	76.25	0.109	0.803	0.148	100,000	3,740,491,266	2.673 × 10−5
2	930.92	1.5	87.5	183.8	15	198.75	91.88	106.88	0.075	0.860	0.213	100,000	682,217,686	0.0001466
3	930.92	2.0	87.5	245.0	15	260.00	122.50	137.50	0.057	0.891	0.279	100,000	124,427,766	0.0008037
4	930.92	2.5	87.5	306.3	15	321.25	153.13	168.13	0.046	0.911	0.345	100,000	22,694,030	0.0044064
5	930.92	3.0	87.5	367.5	15	382.50	183.75	198.75	0.039	0.925	0.411	100,000	4,139,100	0.0241598
6	930.92	3.5	87.5	428.8	15	443.75	214.38	229.38	0.034	0.935	0.477	100,000	754,919	0.1324646
7	930.92	4.0	87.5	490.0	15	505.00	245.00	260.00	0.030	0.942	0.542	115,381	137,688	0.8379916
8	930.92	4.0	87.5	490.0	15	505.00	245.00	260.00	0.030	0.942	0.542	94,112	137,688	0.6835187
											Total	809,493	Σn/N	0.9999995

Notes: P_mean = (P_max + P_min)/2; R = P_min/P_max; A = P_a/P_m; P_a = (P_max − P_min)/2.

,

Table 9. Loading history of the tested slab S4 of type C-joint with equivalent constant amplitude fatigue load segments.

Segment	Pu	FLS			Pmin	Pmax	Pamp	Pmean	R	A	Pmax /Pu	n	Nf	n/Nf
		MF	WL	FLS1
1	973	1.0	87.5	122.5	15	137.50	61.25	76.25	0.109	0.803	0.141	100,000	1,176,908,558	8.497 × 10−5
2	973	1.5	87.5	183.8	15	198.75	91.88	106.88	0.075	0.860	0.204	100,000	254,549,386	0.0003929
3	973	2.0	87.5	245.0	15	260.00	122.50	137.50	0.058	0.891	0.267	100,000	55,055,586	0.0018163
4	973	2.5	87.5	306.3	15	321.25	153.13	168.13	0.047	0.911	0.330	100,000	11,907,778	0.0083979
5	973	3.0	87.5	367.5	15	382.50	183.75	198.75	0.039	0.925	0.393	100,000	2,575,491	0.0388275
6	973	3.5	87.5	428.8	15	443.75	214.38	229.38	0.034	0.935	0.456	100,000	557,044	0.1795191
7	973	4.0	87.5	490.0	15	505.00	245.00	260.00	0.030	0.942	0.519	92,886	120,481	0.7709595
											Total	692,886	Σn/N	0.9999981

Notes: P_mean = (P_max + P_min)/2; R = P_min/P_max; A = P_a/P_m; P_a = (P_max − P_min)/2.

and

Table 10. Loading history of the tested slab S6 of type Z-joint with equivalent constant amplitude fatigue load segments.

Segment	Pu	FLS			Pmin	Pmax	Pamp	Pmean	R	A	Pmax/Pu	n	Nf	n/Nf
		MF	WL	FLS1
1	931	1.0	87.5	122.5	15	137.50	61.25	76.25	0.109	0.803	0.147	100,000	3,015,323,194	3.316 × 10−5
2	931	1.5	87.5	183.8	15	198.75	91.88	106.88	0.075	0.860	0.213	100,000	559,277,378	0.0001788
3	931	2.0	87.5	245.0	15	260.00	122.50	137.50	0.057	0.890	0.279	100,000	103,733,884	0.000964
4	931	2.5	87.5	306.3	15	321.25	153.13	168.13	0.046	0.911	0.345	100,000	19,240,397	0.0051974
5	931	3.0	87.5	367.5	15	382.50	183.75	198.75	0.039	0.925	0.411	100,000	3,568,678	0.0280216
6	931	3.5	87.5	428.8	15	443.75	214.38	229.38	0.034	0.935	0.477	100,000	661,913	0.1510773
7	931	4.0	87.5	490.0	15	505.00	245.00	260.00	0.030	0.942	0.542	100,000	122,771	0.8145276
8	931	4.0	87.5	490.0	15	505.00	245.00	260.00	0.030	0.942	0542	100,000	122,771	0.8145276
9	931	4.0	87.5	490.0	15	505.00	245.00	260.00	0.030	0.942	0.542	95,000	122,771	0.7738013
10	931	4.0	87.5	490.0	15	505.00	245.00	260.00	0.030	0.942	0.542	21,736	122,771	0.1770457
11	931	4.0	87.5	490.0	15	505.00	245.00	260.00	0.030	0.942	0.542	44,804	122,771	0.364941
											Total	961,540	Σn/N	0.9999999

Notes: P_mean = (P_max + P_min)/2; R = P_min/P_max; A = P_a/P_m; P_a = (P_max − P_min)/2.

illustrate the fatigue data where D = 1 for all types of joints of the precast FDDPs. The proposed model to determine the P-N effect is shown in Equation (3), where K equals 0.039, 0.041, and 0.039 for the A-Joint, C-Joint, and Z-Joint, respectively. For static failure N = 1, the model yields to $P/P_u=1$.

$${\displaystyle \frac{P}{P_u}}=-K\ln \left(N_f\right)+1$$

(3)

Figure 17 shows the P-N fatigue curves for the developed model compared to the recently developed models on log-scale graphs compared to other fatigue models [46,47,62,63]. Equations (4)–(11) summarize the recent fatigue models.

Khalafalla’s model [46]

$${\displaystyle \frac{P}{P_u}}=1-{\displaystyle \frac{\ln \left(N\right)}{29}}$$

(4)

$$N=e^{-29\left(P/P_u\right)+29}$$

(5)

El-Ragaby et al.’s model [47]

$${\displaystyle \frac{P}{P_u}}=0.0034{(\log \left(N\right))}^2-0.1187\log \left(N\right)+1.0752$$

(6)

$$N=e^{40.19-0.0147\sqrt{-2.826\times {10}^5+7.21\times {10}^6\left(P/P_u\right)}}$$

(7)

Memon’s model [62]

$$LogN=5.737\sqrt{{\displaystyle \frac{1-R}{R}}}$$

(8)

$$N={10}^{5.737\sqrt{{\displaystyle \frac{1-R}{R}}}}$$

(9)

Mufti et al.’s model [63]

$${\displaystyle \frac{P}{P_u}}=1-{\displaystyle \frac{\ln \left(N\right)}{30}}$$

(10)

$$N=e^{-30\left(P/P_u\right)+30}$$

(11)

The common observation is that these models, by their current parameters, are overestimating the fatigue life since $D\ne 1$.

In summary, one may conclude that the three UHPC-filled closure strips in Figure 1 had almost identical behavior, given the very close experimental ultimate loads shown in Table 4, the punching shear failure pattern shown in Figure 8, and the developed fatigue parameters for the fatigue prediction model in Table 7.

5. Conclusions

Three joint details were developed for transverse closure strips between precast FDDPs to accelerate bridge construction. Actual-size FDDPs were constructed and tested under CAF and VAF loading. Also, the panels tested under CAF loading were loaded under static loading to collapse. The experimental results yield several significant conclusions.

The experimental findings regarding the A-Jointed precast FDDP indicate that the newly developed transverse panel-to-panel connection, which incorporates projecting straight-ended high-modulus GFRP bars, can facilitate continuous force transfer across the transverse joints of the FDDPs. The experiments demonstrated exceptional fatigue performance, as no fatigue damage was detected after exposure to 4,000,000 cycles under a high-cyclic CAF loading of 122.5 kN, as outlined in the CHDBC. The precast FDDP subjected to high-cyclic CAF loading achieved a failure load approximately 4.47 times greater than the CHBDC-factored design wheel load of 208.25 kN. In contrast, the precast FDDP tested under low-cyclic incremental step VAF loading reached a failure load roughly 2.34 times the CHBDC factored design wheel load. The two laterally restrained precast FDDPs ultimately failed in a punching shear mode. Additionally, the stiffness of specimen S1 experienced a degradation of approximately 53% following 4 million cycles. In contrast, specimen S2 degraded by 86.86% when subjected to low-cyclic variable amplitude fatigue (VAF) loading before complete failure.

The experimental findings regarding the C-Jointed precast FDDP lead to the conclusion that the newly designed transverse panel-to-panel C-shaped joint, which incorporates projecting straight-end high-modulus GFRP bars, effectively facilitates continuous force transfer across the transverse joint in precast FDDPs. The results further demonstrated that the precast FDDP, reinforced with high-modulus GFRP, exhibited exceptional fatigue performance, as no fatigue damage was detected after enduring 4,000,000 cycles of high-cyclic constant amplitude fatigue (CAF) loading at 122.5 kN, as outlined in the CHBDC. When subjected to CAF loading followed by an incrementally increasing monotonic wheel load until failure, the tested precast FDDP achieved a failure load approximately 4.67 times greater than the CHBDC factored ultimate limit state (ULS) design wheel load. In contrast, the precast FDDP under low-cyclic incremental step variable amplitude fatigue (VAF) loading reached a failure load roughly 2.38 times the CHBDC factored ULS1 design wheel load. Both precast FDDPs ultimately failed in a punching shear mode. Additionally, the stiffness of specimen S3 diminished by approximately 50.73% after 4 million cycles of high-cyclic CAF loading, while specimen S4 experienced a stiffness reduction of 63.42% under low-cyclic VAF loading before complete failure.

The experimental findings regarding the Z-Jointed precast FDDP lead to the conclusion that the newly designed transverse panel-to-panel connection, which incorporates projecting straight-ended high-modulus GFRP bars, effectively facilitates continuous force transfer across the transverse joints of the FDDPs. The results further demonstrated that the precast FDDP, reinforced with high-modulus GFRP ribbed-surface bars, exhibited exceptional fatigue performance, showing no signs of fatigue damage after enduring 4,000,000 cycles under high-cyclic constant amplitude fatigue (CAF) loading of 122.5 kN, as stipulated in the CHBDC. The precast FDDP tested under high-cyclic CAF loading achieved a failure load approximately 4.47 times greater than the CHBDC factored design wheel load of 208.25 kN. In contrast, the same precast FDDP, when subjected to low-cyclic incremental step variable amplitude fatigue (VAF) loading, sustained a failure load roughly 2.35 times the CHBDC factored design wheel load. The two laterally restrained precast FDDPs ultimately failed due to punching shear mode. Additionally, the stiffness of specimen S5 decreased by approximately 21.9% following 4 million cycles of constant amplitude fatigue (CAF) loading, whereas specimen S6 experienced a significant stiffness reduction of 71.32% under low-cyclic variable amplitude fatigue (VAF) loading before complete failure.

A mathematical model has been developed, grounded in experimental results, to assess the cumulative fatigue damage (CFD) and fatigue resistance (P-N effect) of GFRP-reinforced FDDPs featuring transverse joints. It is observed that the amplification factor related to fatigue loading is inversely related to the frequency of repeated cycles, which corresponds to the lifespan until failure.

The three developed UHPC-filled closure strips with projecting GFRP bars exhibited almost identical behavior given their similar punching shear failure pattern and very close experimental ultimate loads. They also developed fatigue parameters for the fatigue prediction model.

Based on the outcome of this research, the following recommendations for future research can be made:

• Study the monotonic and cyclic pushover effect of the shear pockets and shear stud distribution for the GFRP-reinforced panel-to-girder connection.
• Conduct static and fatigue tests on a composite girder incorporating the developed zigzag-shaped joint as a transverse joint subjected to pure tension resulting from a global negative bending moment at the piers on the continuous bridge girders.