Fatigue performance and residual capacity of UHPC-reinforced simply supported-to-continuous concrete box beams in negative moment zone: experimental study

ABSTRACT

This study investigated the effects of reinforcement ratio and fatigue load level on the fatigue performance and residual capacity of ultra-high performance concrete (UHPC) continuous box beams in the negative moment region. Six UHPC specimens were designed and fabricated, with some tested statically and others subjected to fatigue loading. The research specifically examined how reinforcement ratio and fatigue loading influence structural performance parameters, including mid-span deflection and reinforcement strain, during fatigue testing. And the accuracy of the experimental results was further verified through finite element numerical simulations. The experimental results demonstrated that: During static loading tests, beams B1 and B2 demonstrated an increase in flexural capacity of 8% and 25%, respectively, relative to the reference beam B0. These findings indicate that the application of UHPC in the negative moment region of simply supported-to-continuous box beams significantly enhances flexural performance. This enhancement is attributed to optimized stress distribution within the cross-section, which improves ductility and damage tolerance. Following 2 million fatigue cycles, no observable fatigue damage was detected in beams PLB0, PLB1, or PLB2. Post-fatigue static failure tests were subsequently conducted on these beams. Compared to their corresponding reference beams (B0, B1, B2), PLB0, PLB1, and PLB2 exhibited reductions in maximum mid-span deflection of 30%, 16.1%, and 5.8%, respectively, along with markedly lower reinforcement stress amplitudes. Beam PLB0 exhibited a 10% reduction in residual capacity relative to the static ultimate capacity of reference beam B0. Conversely, beams PLB1 and PLB2 demonstrated residual capacity increases of 4% and 21%, respectively, surpassing the static ultimate capacity of their corresponding reference beams (B1 and B2). These findings demonstrate that UHPC implementation enhances flexural stiffness, retards fatigue damage accumulation, and effectively increases residual capacity in bridge components.

Keywords:
UHPC; Negative moment zone; Box beam; Fatigue performance

1. INTRODUCTION

The simply supported-to-continuous bridge system integrates the advantages of both simply supported and continuous beam configurations [¹, ²]. This structural system is commonly employed in small-to-medium-span bridges owing to its ease of construction and economic efficiency [³]. During their service life, bridges are subjected to dynamic loads such as repetitive, impact, and harmonic forces [⁴, ⁵]. These dynamic effects lead to progressive damage accumulation and generate transient stress peaks [⁶]. Recent finite element studies have highlighted the effectiveness of advanced materials, including Glass Fiber Reinforced Polymer (GFRP) and Reactive Powder Concrete (RPC), in enhancing bridge performance under various dynamic loads.Simulation-based finite element modeling demonstrated improved load-bearing capacity and crack resistance of beams subjected to various dynamic stresses, preventing structural damage in bridges induced by dynamic effects [⁷,⁸,⁹,¹⁰]. However, under cyclic loading, progressive fatigue damage accumulates in the structure, with the negative moment zone near abutment tops exhibiting heightened susceptibility to premature crack initiation and propagation. This damage progression causes significant degradation in both structural durability and load-carrying capacity, ultimately accelerating concrete fatigue failure and substantially reducing bridge service life [¹¹,¹²,¹³].

Current engineering practice typically addresses this issue through prestressing tendon installation in critical zones. However, this approach leads to structural congestion, reduced construction efficiency, and may result in over-reinforced sections due to excessive reinforcement ratios [¹⁴]. Consequently, optimizing wet-joint materials presents a critical research direction for enhancing structural performance while mitigating these limitations [¹⁵,¹⁶,¹⁷]. DINESHKUMAR and RAMKUMAR [¹⁸] investigated the fatigue behavior of reinforced concrete beams incorporating mineral admixtures. Their research demonstrated that optimally dosed mineral admixtures enhance concrete’s mechanical properties and fatigue strength, with fatigue life governed primarily by stress amplitude and cycle count.

Since 2000, material innovations have enabled successful applications of ultra-high performance concrete (UHPC) in complex structural systems, including building facilities and long-span bridges [¹⁹,²⁰,²¹]. Its dense microstructure facilitates synergistic optimization of tensile strength, fracture toughness, and durability, effectively mitigating the low tensile strength and poor ductility inherent in conventional concrete. Current research on UHPC fatigue performance in bridge applications remains limited. Critical knowledge gaps persist regarding the generalizability of UHPC’s fatigue response mechanisms and the influence of key parameters on structural durability indices [²²,²³,²⁴]. Consequently, researchers globally have initiated targeted investigations. ZHENG et al. [²⁵] investigated the static and fatigue performance of lightweight composite bridge deck system (LCBD) composed of lightweight UHPC and orthotropic anisotropic steel bridge deck (OSD) under negative bending moments. The effects of different reinforcement spacing on cracking stress, bending stiffness, and fatigue life of UHPC layers were investigated by full-scale modeling tests. NIU et al. [²⁶] examined how steel fiber volume fraction influences fatigue crack propagation in UHPC. Their findings revealed reduced crack propagation rates during stable growth phases with increasing steel fiber content. However, significant knowledge gaps persist in understanding how reinforcement ratios and fatigue load levels affect UHPC beam fatigue performance, impeding broader engineering implementation [²⁷, ²⁸].

Current research has predominantly focused on UHPC material properties and bridge applications [²⁹,³⁰,³¹], while fatigue performance in negative moment zones of simply supported-to-continuous box beams remains critically understudied. Existing international fatigue design codes, primarily developed for conventional concrete or prestressed structures [³²], lack adequate provisions for UHPC applications. Crucially, the interactive effects of reinforcement ratios and fatigue loading on durability mechanisms in UHPC structures remain unquantified. Current design approaches exhibit significant limitations: The American Association of State Highway and Transportation Officials (AASHTO) restricts fatigue stress to 20% of rebar yield strength without considering UHPC’s fiber-reinforcement mechanism. The fatigue stress limits stipulated in conventional design codes are often conservatively constrained to ensure structural safety under cyclic loading. These provisions are primarily derived from empirical data of traditional concrete and prestressed members, neglecting the unique fatigue resistance mechanisms of UHPC. In practice, such limitations may unnecessarily restrict the utilization of UHPC’s superior performance in negative moment regions. Highway Reinforced Concrete and Prestressed Reinforced Concrete Bridges and Culverts (TG D62-2012) acknowledges UHPC applications but omit specific fatigue design methods for negative moment zones.

In this paper, UHPC-reinforced simply supported-to-continuous concrete box beams in negative moment zone static and fatigue tests are carried out. Reinforcement ratio and fatigue load magnitude were used as the main parameters to investigate the quantitative influence law of residual load capacity of UHPC-reinforced box beams. To fill the gap in the study of fatigue performance of UHPC in the negative moment region. The structural performance parameters such as mid-span deflection and reinforcement strain of the test beams were collected. Comparative analysis of the effects of different reinforcement rates and fatigue load levels on the static and fatigue performance of UHPC-reinforced simply supported-to-continuous concrete box beams in the negative moment region.

2. PILOT PROGRAM

2.1. Design of test beam

This research is based on the Kunting-Tangxi section of the Shenhai Expressway connecting line in Ningbo Zhoushan Port’s Meishan Port Area. Building on actual engineering practice, UHPC implementation eliminated prestressed tendons and rebar welding in negative moment zones. This innovation established a non-prestressed simply supported-to-continuous system, effectively mitigating cracking susceptibility in pier-top negative moment zones. Three 1:2 scale model beams were designed for testing. These specimens replicated material compositions from the actual structure. Table 1 details the scaling relationships between test girder parameters and prototype bridge dimensions.

Table 1
Physical similarity between test beams and actual beams.

PARAMETER	LONGITUDINAL RATIO OF NEGATIVE MOMENT ZONE	VERTICAL RATIO	STRESS	STRAIN	BENDING MOMENT
Proportion	1/2	1/6	1	1	1/8

The test specimen consisted of a 5 m long reinforced concrete box beam with a 4.6 m effective span. Its asymmetric cross-section had a total height of 450 mm, with top and bottom flange widths of 1200 mm and 700 mm respectively. Flange and base plate thicknesses measured 120 mm, web thickness 150 mm, and flange overhang 250 mm. Transverse bulkheads featured graded thicknesses (200 mm at midspan, 300 mm at end panels). This study examined the influence of reinforcement ratios for conventional steel bars and UHPC on structural performance. Control beams B0 and PLB0 were simply supported-to-continuous conventional concrete box beams. UHPC-reinforced beams (B1/PLB1 and B2/PLB2) utilized simply-supported-to-continuous configurations. UHPC was cast over 1.6 m segments in critical zones. Basic parameters are provided in Table 2, with detailed dimensions and reinforcement ratios illustrated in Figures 1 to 5.

Table 2
The scheme of test.

TEST BEAM NUMBER	UHPC LENGTH L (mm)	TENSILE STEEL BARS IN THE TOP PLATE (mm)	UHPC THICKNESS (mm)	REINFORCEMENT RATIO OF ORDINARY STEEL BARS (%)
B0`PLB0	–	11Φ12	–	0.43
B1`PLB1	1600	5Φ12+6Φ10	60	0.36
B2`PLB2	1600	11Φ12	60	0.43

Figure 1
Elevation of test beams B0, PLB0 (unit: mm).

Figure 2
Elevation of test beams B1, B2, PLB1, PLB2 (unit: mm).

Figure 3
Section diagram of beams B0 and PLB0 (unit: mm). (a) Section A-A, (b) Section B-B.

Figure 4
Section diagram of beams B1, B2, PLB1, PLB2 (unit: mm). (a) Section A-A (b) Section B-B.

Figure 5
Test beam reinforcement diagram (A-A section) (unit: mm). (a) PLB0, PLB2 (b) PLB1.

2.2. Design of test beam

The tests were conducted using a resistive strain gauge monitoring system, with strain gauges deployed at critical nodes of the reinforcement to capture the axial deformation response. To facilitate subsequent identification, the monitoring section codes were defined as A (central part of the beam), B (5 cm proximal zone of the transverse bulkhead), and C and D (5 cm transition zone on both sides of the UHPC-NC interface).

This test was configured with seven sets of displacement gauges to monitor the real-time displacement response of key nodes. Layout points cover the mid-span and quarter-point areas, the bearing area, and the UHPC-NC interface transition zone. First test the displacement gauge to see if it is working properly. The displacement gauge is then fixed to the magnetic support and adjusted to the appropriate position. Finally, zero the displacement meter reading. The exact arrangement of the displacement meter is shown in Figure 6.

Figure 6
The arrangement of the displacement meter (unit: mm).

Reinforcing steel strain monitoring points were deployed in four critical cross-section areas, A, B, C, and D. Among them, there are 4 reinforcing steel strain gauges in the top plate of A section, which is set on both sides of the flange, and both sides of the beam ribs. A total of five locations were set up in sections B, C, and D, which is one more intermediate location than in section A. The bottom plate reinforcement strain gauges were set at 3 locations, on both sides of the beam ribs and in the center. The location of specific rebar strain measurement points is shown in Figure 7.

Figure 7
The arrangement of reinforcement strain gauge (unit: mm). (a) Bar strain gauge paste section position (b) A-A section reinforcement strain gauge layout (c) B-B, C-C, D-D sectional reinforcement strain gauge layout.

2.3. Material performance

2.3.1. Mechanical performance of normal concrete

C40 concrete was utilized in this study, with mixed proportions detailed in Table 3. Three standard cubic compression specimens and prismatic flexural specimens were prepared. Key mechanical properties of the concrete matrix were determined, including compressive strength, flexural tensile strength, and elastic modulus. Following curing completion, mechanical properties were tested according to Standard Test Methods for Mechanical Properties of Ordinary Concrete (GB/T 50081-2019). Results are presented in Table 4.

Table 3
C40 concrete mix ratio.

MATERIAL	QUALITY RATIO (kg/m3)
Water	0.33
Concrete	1
Sand	1.15
Rock	2.26
Water reducer	0.004

Table 4
Results of mechanical properties of C40 concrete materials.

TYPE OF CONCRETE	COMPRESSIVE STRENGTH (MPa)	FLEXURAL STRENGTH (MPa)	MODULUS OF ELASTICITY (MPa)
C40	40.9	2.47	26500

2.3.2. Mechanical performance of rebar

HRB400 rebar was selected for the tensile tests in the lab. Measurement of yield strength and ultimate tensile strength of rebar. The mechanical properties are shown in Table 5.

Table 5
Mechanical performance of rebar.

REBAR DIAMETER (MM)	YIELD STRENGTH (MPA)	TENSILE STRENGTH (MPA)	MODULUS OF ELASTICITY (MPA)
10	432	578	2 × 105
12	453	597	2 × 105

2.3.3. Mechanical performance of UHPC

End-hooked steel fibers were incorporated into the UHPC matrix at a 2% dosage. Mix proportions are detailed in Table 6. Three specimens of each type were cast: cubic compression, prismatic flexural, and dog-bone tensile specimens. All specimens underwent identical curing conditions before testing UHPC compressive strength, flexural strength, and tensile strength. The resultant mechanical properties are presented in Table 7.

Table 6
UHPC material mixing ratio.

MATERIAL	QUALITY RATIO (kg/m3)
Concrete	956
Alumina	214.2
Grit	856.8
Silica fume	159
Quartz powder	159
Water reducer	25.5
Water	216.7

Table 7
Mechanical performance of rebar.

COMPRESSIVE STRENGTH (MPa)	FLEXURAL STRENGTH (MPa)	TENSILE STRENGTH (MPa)
122	23.3	7.91

2.4. Loading system configuration

2.4.1. Experimental loading setup

The test was conducted in the structural laboratory of Liaoning Chase Highway Engineering Company Limited. Static and fatigue tests were conducted using an electro-hydraulic servo fatigue testing machine (Jinan Lizhi Test Systems Co., Ltd.). Key specifications included: 1500 kN static/dynamic capacity; 2–8 Hz operating frequency; 10 mm maximum amplitude; 120 mm actuator stroke. The test system comprised: a bearing frame assembly; servo-hydraulic actuators; a hydraulic power unit; and a digital controller with dedicated software. The experimental loading configuration is illustrated in Figure 8. Due to the relative simplicity of positive moment testing, negative moment effects were equivalently simulated through specimen inversion. The distance between the loading points (purely bending region) is 600 mm, locating the effective span at 4600 mm. To suppress the stress concentration effect, the top support area of the test beam was equipped with a rectangular steel distribution beam.

Figure 8
Test loading device. (a) Test loading device (b) Elevation diagram (c) Test loading diagram.

2.4.2. Experimental loading scheme

The fatigue tests were performed using sinusoidal equal amplitude loading with a loading frequency of f = 5 Hz. According to the relevant provisions of the Design Code for JTG D62-2012. For the test beam fatigue load lower limit P_min should meet not less than 3% of the maximum loading capacity of the fatigue testing machine. The principle of not making the test beam jump during the fatigue test was also considered, and this fatigue test was loaded by controlling the stress amplitude. So there is a difference between the upper and lower fatigue load limits. The lower limit value of fatigue load P_min is taken as 90 kN for beams PLB0 and PLB1, and the lower limit value of fatigue load P_min is taken as 110 kN for beam PLB3. In bridge structures, the upper limit of fatigue load is generally between 0.5 and 0.8 P_u. P_u is the ultimate load capacity of each test beam. The upper fatigue load limit P_max is taken as 185 kN for beams PLB0 and PLB1, and the upper fatigue load limit P_max is taken as 205 kN for beam PLB2, as detailed in Table 8.

Table 8
Loading parameters of fatigue test.

TEST BEAM NUMBER	UPPER LIMIT OF FATIGUE LOAD Pmax (KN)	LOWER LIMIT OF FATIGUE LOAD Pmin (KN)	FATIGUE LOAD LEVELS = Pmax/Pu
PLB0	185	90	0.66
PLB1	185	90	0.6
PLB2	210	105	0.6

• Note: P_u is the ultimate bearing capacity of each test beam.

The applied fatigue load levels exceeded the conventional ranges specified in AASHTO provisions. In contrast, the AASHTO fatigue design provisions for plain concrete structures are based on conventional material properties, which are primarily for plain reinforced concrete or prestressed structures. UHPC has greater fatigue resistance due to its high tensile strength. Li used S = 0.6 in the fatigue tests of prestressed UHPC beams. However, the fatigue life of the UHPC beams still meets the requirement of 2 million cycles, and their residual bearing capacity decreases significantly less than that of ordinary concrete [³³].

Fatigue testing comprised three sequential stages: pre-fatigue static testing, cyclic fatigue loading, and post-fatigue static failure testing, as shown in Figure 9.

Figure 9
Schematic diagram of fatigue loading scheme.

(1) Static load test phase

Before testing, a 15 kN static preload eliminated contact interface gaps and calibrated the measurement system. A graded 10 kN loading protocol advanced to the upper fatigue limit, with 5–10 min holds between increments for crack marking. Stepwise unloading at 10 kN intervals followed until zero load. Strain and displacement data were continuously recorded.

(2) Fatigue test phase

Following static testing, the load was increased to the median fatigue stress level. Cyclic loading commenced immediately, with real-time adjustments ensuring compliance with prescribed load limits. Stop and unload at 1, 2, 5, 10, 20, 50, 1, and 1.5 million cycles respectively. Specimens rested 5–10 min until residual deformation stabilized, followed by static reloading to the upper limit with synchronized data acquisition.

(3) Static load test failure phase

If no damage occurs after loading the test beam 2 million times, switch to the static loading mode for loading until damage occurs in the test beam. Ultimate load, mid-span deflection at failure, and maximum tensile reinforcement strain were documented.

3. ANALYSIS OF TEST RESULTS

3.1. Crack analysis

The test beams were not damaged after 2 million fatigue loadings, so the test beams were statically loaded until they were damaged. Crack distributions during failure are depicted in Figures 10 to 12. PLB0 beams showed 19 cracks in the static load test phase before fatigue, mainly in the pure bending section and in the shear span area near the loading point. The maximum crack height was about 200 mm, and the cracks were finished after 10,000 fatigue loadings, totaling 24 cracks. PLB1 beams showed 14 cracks during the pre-fatigue static load test phase, which were mainly located at the UHPC-NC longitudinal interface and nearby areas. There are 4 cracks in the UHPC area. One of them extended from the UHPC to the upper concrete area, one started at the UHPC-NC lateral interface, and the remaining two did not develop to the concrete interface. The maximum crack height was about 205 mm. After 50,000 fatigue loadings, the cracks were basically out of the end, with a total of 17 cracks. PLB2 beams showed 14 cracks during the pre-fatigue static load test phase, which were mainly located at the UHPC-NC longitudinal interface and nearby areas. There are six cracks in the UHPC area. One of these extends into the upper concrete area, three begin at the UHPC-NC transverse interface, and the remaining two did not progress to the concrete interface. After 50,000 fatigue loadings, the cracks were basically out of the finish, with a total of 23 cracks.

Figure 10
Distribution of cracks in beam PLB0.

Figure 11
Distribution of cracks in beam PLB1.

Figure 12
Distribution of cracks in beam PLB2.

3.2. Analysis of static load test results

3.2.1. Static failure mode

Comparative analysis of flexural failure processes in conventional concrete (B0) and UHPC-reinforced box beams (B1/B2) revealed three characteristic failure phases: The elastic phase precedes crack initiation load thresholds. Load-deflection curves exhibited essentially linear behavior, with structural stiffness maintained at undamaged state levels; Upon exceeding the crack initiation threshold, tensile stresses in concrete surpassed its tensile capacity, inducing cracks propagating through the section depth. This initiated sectional stiffness degradation with a progressive decline in load-deflection curve slopes; After yielding of the longitudinal tensile reinforcement, the test beam enters the damage phase. The structural stiffness produces a substantial attenuation, the load increase slows down, the crack width increases exponentially, and the slope of the load-deflection curve decreases further.

The cracking load, yield load, and ultimate load of each test beam are shown in Table 9.

Table 9
Cracking load, yield load and ultimate load of each test beam.

BEAM NUMBER	CRACKING LOAD PCR(KN)	YIELD LOAD Py(KN)	ULTIMATE LOAD Pu(KN)
B0	60	240	280
B1	85	230	303
B2	95	270	350

3.2.2. Mid-span deflection analysis

The load versus mid-span deflection comparison curves for the test beams are presented in Figure 13. Before reaching the yield critical load, the sectional stiffness of B1 and B2 significantly exceeded that of B0. This enhancement stems from the bridging system formed by steel fibers within the UHPC matrix. When initial cracks develop in the concrete tensile zone, steel fibers redistribute stress through interfacial adhesion and mechanical interlock, transferring localized tensile stresses to adjacent uncracked matrix regions. Consequently, crack propagation is suppressed, resulting in fine, densely distributed cracks. Upon entering the damage stage, the high tensile strength of UHPC synergizes with the crack-arresting effect of steel fibers. The counteracting restraint generated by the fiber bridging action reduced crack propagation rates, enabling the test beams to maintain structural integrity. Ultimate failure exhibited progressive characteristics: steel fiber bonds at major cracks exceeded their limiting values, accelerating crack penetration through the compression zone and consequently causing loss of load-bearing capacity. These results demonstrate significantly enhanced flexural stiffness in UHPC-reinforced beams, confirming their advantageous application in simply supported-to-continuous beam bridge systems.

Figure 13
Load-midspan deflection relation curve. (a) Beam B0 (b) Beam B1 (c) Beam B2 (d) Comparison curve of each test beam.

3.2.3. General tensile reinforcement strain analysis

Analysis of the tensile reinforcement strain evolution in the B-section (data up to the yielding stage) is presented in Figure 14. The mechanical responses of the test beams exhibited significant divergence. During initial loading, the load-strain curves maintained linear and synchronous growth, indicating consistent material constitutive relationships in the elastic stage. Upon exceeding the cracking load, strain curves developed divergent characteristics. The slope reduction magnitude was negatively correlated with the reinforcement ratio, and inflection point occurrence was significantly delayed at higher reinforcement ratios. For the beam B0—constructed with full-section C40 concrete without UHPC reinforcement—sectional resistance transferred entirely to longitudinal tensile reinforcement after cracking, resulting in a substantially increased reinforcement strain rate. In contrast, UHPC-reinforced beams benefited from stress compensation in the negative moment zone. Post-cracking formation of a steel fiber-matrix synergistic stress system enabled the UHPC layer to absorb tensile stresses, thereby reducing the strain rate in the main reinforcement of beams B1 and B2. Experimental data confirm that the UHPC reinforcement layer enhances ductile properties and damage tolerance in reinforced concrete structures through optimized sectional stress distribution.

Figure 14
Load-strain relationship curve. (a) Beam B0 (b) Beam B1 (c) Beam B2(d) Comparison curve of each test beam.

3.3. Analysis of fatigue test results

3.3.1. Fatigue failure mode

Under fatigue loading, the damage mechanisms of different beam types exhibit distinct behaviors. Conventional reinforced concrete (RC) beams exhibit accelerated damage accumulation during the initial fatigue stages owing to the absence of ultra-high-performance concrete (UHPC) reinforcement. A pronounced increase in mid-span deflection and reinforcement stress amplitude, coupled with rapid crack propagation and cross-sectional penetration, results in severe structural stiffness degradation. Ultimately, the accelerated propagation of primary cracks induces a complete loss of bearing capacity. In contrast, UHPC-reinforced beams effectively suppress crack progression and mitigate damage accumulation, leveraging the superior tensile strength of UHPC. During the initial fatigue phase, although reinforcement strain and stress amplitude rise sharply, their growth rate diminishes considerably beyond 200,000 cycles, accompanied by a limited increase in mid-span deflection. At failure, crack penetration is significantly delayed due to the synergistic reinforcement effect of UHPC.

After 2 million fatigue loadings, the beams PLB0, PLB1 and PLB2 showed no significant damage. The fatigue life of each fatigue test beam is shown in Table 10.

Table 10
Fatigue life of test beams in fatigue test.

NUMBER	UPPER LIMIT OF FATIGUE LOAD Pmax (KN)	LOWEr LIMIT OF FATIGUE LOAD Pmin (KN)	FATIGUE LOAD LEVEL Smax = Pmax/Pu	FATIGUE LIFE NF (IN TEN THOUSAND CYCLES	FATIGUE MODE
PLB0	185	90	0.66	200	Did not fail after 2 million cycles of fatigue; Static ultimate bearing capacity PuF = 251 kN.
PLB1	185	90	0.6	200	Did not fail after 2 million cycles of fatigue; Static ultimate bearing capacity PuF = 290 kN.
PLB2	205	110	0.6	200	Did not fail after 2 million cycles of fatigue; Static ultimate bearing capacity PuF = 340 kN.

3.3.2. Deflection analysis

The beam PLB0 exhibits upper and lower fatigue load limits of 185 kN and 90 kN, respectively. The evolution of mid-span deflection under cyclic loading is illustrated in Figure 15. As shown in Figure 15(b), the load-displacement response of beam PLB0 exhibits a pronounced hysteresis loop during the initial loading cycle. The peak mid-span deflection reached 11.63 mm, with a residual deflection of 5.4 mm. With increasing load cycles, the load-displacement hysteresis gradually diminishes, approaching a linear response. Figure 15(a) reveals that mid-span displacements increase markedly during the first 100,000 fatigue cycles, demonstrating cycle-dependent growth. By 100,000 cycles, the peak mid-span displacement had increased by 2.6 mm (22.4%) relative to the initial loading. Between 100,000 and 200,000 cycles, the reduced growth rate of mid-span displacements suggests decelerated damage accumulation. Beyond 200,000 cycles, the displacement-cycle curve transitions to a stable phase, persisting until the fatigue test concludes at 2 million cycles.

Figure 15
Change and development curve of mid-span deflection of beam PLB0. (a) Variation curve of mid-span deflection (b) Mid-span deflection development curve.

The beam PLB1 exhibits fatigue load limits of 185 kN (upper) and 90 kN (lower), with Figure 16 illustrating its displacement characteristics under cyclic loading. The load-displacement response by Figure 16(b) demonstrates a pronounced hysteresis loop during initial loading, recording peak and residual mid-span deflections of 11.36 mm and 5.2 mm respectively. With progressive cycling, the hysteresis behavior gradually diminishes toward linear elasticity. Figure 16(a) reveals that mid-span displacement undergoes significant growth during the initial 100,000 cycles, increasing by 2.07 mm (18.2%) relative to the first cycle. The subsequent 100,000 cycles (100,000–200,000) show markedly reduced displacement growth rates, indicating decelerated damage accumulation. Beyond 200,000 cycles, the displacement-cycle relationship stabilizes, maintaining minimal growth throughout the remaining test duration until 2 million cycles.

Figure 16
Change and development curve of mid-span deflection of beam PLB1. (a) Variation curve of mid-span deflection (b) Mid-span deflection development curve.

The beam PLB2 demonstrates upper and lower fatigue load limits of 210 kN and 110 kN, respectively. Figure 17 presents their displacement evolution under cyclic loading conditions. As evidenced in Figure 17(b), the initial loading cycle produces a distinct hysteresis loop in the load-displacement response, with peak and residual mid-span deflections measuring 11.22 mm and 3.68 mm, respectively. Progressive cycling leads to gradual hysteresis reduction, ultimately approaching linear elastic behavior. Figure 17(a) indicates substantial displacement growth during the initial 100,000 cycles, with the peak deflection increasing by 2.12 mm (18.9%) relative to the first cycle. The subsequent 100,000 cycles (100,000–200,000) exhibit markedly reduced displacement growth rates, suggesting negligible damage accumulation. Beyond 200,000 cycles, the displacement-cycle relationship stabilizes, maintaining near-constant values throughout the remaining test duration of up to 2 million cycles.

Figure 17
Change and development curve of mid-span deflection of beam PLB2. (a) Variation curve of mid-span deflection (b) Mid-span deflection development curve.

Figure 18 presents the comparative evolution of maximum mid-span deflection under fatigue loading for the three test beam configurations (PLB0, PLB1, and PLB2). As you can see in the graph: During the initial 200,000 loading cycles, beam PLB0 exhibited significantly faster development of mid-span deflection compared to beams PLB1 and PLB2. The deflection-fatigue number curves of beams PLB1 and PLB2 showed nearly identical progression, indicating similar deformation behavior. These observations demonstrate substantially greater damage accumulation in beam PLB0 relative to beams PLB1 and PLB2 during this loading stage. Between 200,000 and 500,000 cycles, the mid-span displacements of beams PLB0 and PLB1 continued to increase slowly, while beam PLB2 remained almost level. After 500,000 cycles, the deflection-fatigue number curves of beams PLB1 and PLB2 leveled off, while the deflection-fatigue number curves of beam PLB0 still showed a clear increasing trend. It shows that the damage accumulation in beam PLB0 continues in this phase, while the relative growth of damage accumulation in beams PLB1 and PLB2 tends to slow down.

Figure 18
Relationship between mid-span deflection and fatigue cycles of each test beam.

3.3.3. General tensile reinforcement strain analysis

Figure 19 illustrates the strain evolution pattern of tensile reinforcement in the B-section under fatigue loading. All three test beam specimens (PLB0, PLB1, and PLB2) exhibited a two-stage strain development process, with the inflection point occurring at approximately 200,000 loading cycles. During the initial fatigue phase (0-200,000 cycles), this behavior is attributed to the combined effects of material damage accumulation and microcrack propagation. Under P_max loading, the reinforcement strains in beams PLB0, PLB1, and PLB2 increased rapidly by 14.6%, 15.3%, and 15.9%, respectively, compared to those during the first static loading. The strain-cycle number curves of PLB0 and PLB2 exhibited close overlap. Beyond the critical threshold of 200,000 cycles, the reinforcement strain increment decreased significantly and stabilized until the completion of 2 million fatigue loading cycles. Upon reaching 2 million cycles, the cumulative reinforcement strain under the upper fatigue load limit increased by 23.1%, 20.5%, and 19.2% for beams PLB0, PLB1, and PLB2, respectively, compared to the first static load. Notably, the strain curves of beams PLB0 and PLB2 began to diverge significantly after 200,000 fatigue cycles, indicating faster damage accumulation in the plain concrete beam (PLB0) under prolonged fatigue loading. In contrast, the reinforced beams (PLB1, PLB2) demonstrated superior fatigue resistance, attributable to the enhanced properties of UHPC materials.

Figure 19
Relation between strain and load cycles of ordinary tensile reinforcement of each test beam. (a) Beam PLB0 (b) Beam PLB1 (c) Beam PLB2 (d) Strain comparison of each test beam at the upper limit of fatigue load.

Figure 20 presents the stress amplitude of longitudinal tensile reinforcement in the B-section for each test beam, defined as the stress difference between the upper and lower limits of the fatigue load. Similar to the reinforcement strain behavior, the stress amplitude exhibits a two-stage evolution characterized by rapid initial development followed by slower progression, with the inflection point likewise occurring at 200,000 loading cycles. During initial static loading, the stress amplitudes at P_max were measured as 221 MPa, 189 MPa, and 219 MPa for beams PLB0, PLB1, and PLB2, respectively. At the 200,000-cycle threshold, the reinforcement stress amplitudes in beams PLB0, PLB1, and PLB2 increased by 5.2%, 10.4%, and 5.8%, respectively, relative to their initial static load values. Beyond 200,000 loading cycles, the reinforcement stress amplitude in all test specimens transitioned to a stable growth phase. Comparing the B0 and B1 beams, it can be found that in the case of a smaller reinforcement ratio of the beam B1, although the upper fatigue load limit and the lower fatigue load limit of the two beams are the same, the stress amplitude of the beam B1 is significantly smaller than that of the beam B1 due to UHPC reinforcement in the negative moment region of the beam B1. Comparing the B0 and B2 beams, it can be found that the upper fatigue load limit of beam B2 is larger than that of beam B1, but its stress amplitude under the upper fatigue load limit is also smaller than that of beam B1. This inverse relationship between load capacity and stress amplitude provides strong evidence for the superior fatigue resistance of UHPC-reinforced concrete box beams.

Figure 20
Relation between stress amplitude and number of load cycles of each test beam. (a) Beam PLB0 (b) Beam PLB1 (c) Beam PLB2 (d) Comparison of stress amplitude of each test beam.

3.4. Residual bearing capacity analysis

No evident fatigue damage was observed in the PLB0, PLB1, and PLB2 specimens upon completion of 2 million loading cycles. Subsequently, static load tests were conducted on three specimens to evaluate their post-fatigue performance, enabling precise determination of the residual load-bearing capacity (Table 11). The test results demonstrate that the PLB0, PLB1, and PLB2 specimens exhibited reductions of 10%, 4%, and 3%, respectively, relative to the ultimate loads of the control specimens (B0, B1, and B2).

Table 11
Static properties after fatigue loading.

TEST BEAM NUMBER	NUMBER OF FATIGUE CYCLES (MILLION)	RESIDUAL BEARING CAPACITY MF (KN)	ORIGINAL STATIC ULTIMATE BEARING CAPACITY MS (KN)	MF/MS
PLB0	200	251	280	90%
PLB1	200	290	303	96%
PLB2	200	340	350	97%

The results of the residual bearing capacity of beams PLB0, PLB1 and PLB2 are shown in Figure 21. As illustrated in the figure, the mid-span deflection of PLB0 decreased significantly from 37.3 mm to 26.1 mm, representing a 30% reduction relative to the control beam (B0). Similarly, PLB1 exhibited a reduction in mid-span deflection from 28 mm to 23.5 mm, corresponding to a 16.1% decrease compared to B1. In contrast, PLB2 showed a more moderate 5.8% decrease in mid-span deflection (from 38.8 mm to 36.5 mm) relative to B2. The experimental results demonstrate that UHPC incorporation enhances the flexural stiffness of the beams considerably. Due to the failure of most strain gauges during the advanced loading phase, only the pre-yield load-strain relationships are presented. The experimental data indicate that the load-rebar strain relationships of PLB1 and PLB2 closely align with those of the B1 and B2 control beams, whereas PLB0 demonstrates progressive divergence in its load-strain behavior as yielding approaches.

Figure 21
Static load failure of each test beam after fatigue. (a) Load-midspan deflection comparison of each test beam (b) Load-reinforcement strain comparison of each test beam.

Compared with beam PLB0, the reinforcement ratio of beam PLB1 is smaller than that of beam PLB0, but their upper fatigue load limit and load amplitude are the same as those of PLB0 beams. The mid-span deflections and reinforcement strains of beam PLB1 are less than those of beam PLB0 under the same loads; Compared to beam PLB2, beam PLB1 has the same reinforcement rate as beam PLB0, but their upper fatigue load limit is greater than that of beam PLB0. Both mid-span deflections and reinforcement strains of beam PLB2 are also smaller than those of beam PLB0 under the same loads. This reinforces the fact that the incorporation of UHPC significantly improves the flexural and fatigue performance of the test beams compared to the simply supported-to-continuous plain reinforced concrete box beams.

The above discusses the comparison of the mechanical properties of each fatigue test beam with its corresponding static load test beam. A comparison of the mechanical properties of each fatigue test beam with those of the B0 beams is carried out. As shown in Table 12, the residual load capacity of PLB0 beams is reduced by 10% compared to the static load ultimate capacity of B0 beams after 2 million fatigue loadings. While PLB1 and PLB2 beams showed 4% and 21% improvement over B0 beams respectively. It is shown that the incorporation of UHPC significantly improves the fatigue performance of simply supported-to-continuous concrete box beams.

Table 12
Residual bearing capacity of PLB0, PLB1 and PLB2 beams.

TEST BEAM NUMBER	RESIDUAL BEARING CAPACITY MF (KN)	STATIC ULTIMATE BEARING CAPACITY OF BEAM B0 MS (KN)	MF/MS
B0	–	280	–
PLB0	251	280	90%
PLB1	290	280	104%
PLB2	340	280	121%

Design Code for Concrete Structures (GB 50010-2010) requires that the residual bearing capacity after fatigue should not be less than 90% of the original bearing capacity. The remaining capacity of the PLB0 beam in the test was 90% of the original capacity, which just met the code requirements. The UHPC reinforced beams (PLB1, PLB2) reached 96%-97% of the original bearing capacity, which fully meets and outperforms the specification requirements. The tests showed a 21% and 4% increase in the residual load capacity of the UHPC beams, far exceeding the 10% drop in plain concrete. This phenomenon is consistent with the qualitative description in TG D62-2012 that UHPC can improve durability. The residual load-carrying capacity is increased by 10-15% compared to the study of prestressed UHPC beams by LI et al. [³³]. The performance in this test was even better, with UHPC simplifying the structure while still guaranteeing long-term performance [³³].

3.5. Finite element numerical simulation analysis

To validate the experimental findings, this study employs ABAQUS software to simulate the static and fatigue behaviors of the test beam. The simulation results are compared with experimental data to verify the accuracy of the test results.

3.5.1. Finite Element Modeling (FEM)

In ABAQUS, a quarter-model was established for analysis to improve computational efficiency, taking advantage of the test beam’s symmetry. The concrete material was modeled using 8-node linear brick (C3D8R) solid elements, while the reinforcement bars were simulated with 2-node linear truss (T3D2) wire elements. The supports and bearing blocks were modeled as solid elements. The concrete model was connected to the supports, bearing blocks, and UHPC layers via Tie constraints. The longitudinal and stirrup rebars were embedded into the model using the Embedded region method. A reference point (RP) was defined on the top surface of the bearing block and coupled with the surface using kinematic coupling constraints. Displacement-controlled loads were then applied to the RP to simulate static and fatigue loading on the test beam.For mesh generation, the UHPC overlay zone of the test beam was locally refined to ensure computational accuracy, while coarser meshes were adopted elsewhere to optimize efficiency. The resulting mesh configuration and reinforcement layout are illustrated in Figures 22 and 23, respectively.

Figure 22
Finite element mesh of the 1/4 symmetry box beam model.

Figure 23
Rebar configuration in the FEM model.

3.5.2. Comparison between experimental and finite element simulation results

Finite element analysis was conducted on test beams B0, B1, and B2 under static loading conditions. Figure 24 presents a comparison between the experimentally measured and numerically simulated load-displacement curves for beams B0, B1, and B2. The results demonstrate excellent agreement in the slope variation between experimental and simulation curves throughout the entire loading process. Notably, during the advanced loading stages, the numerical simulations successfully captured both the yield load and ultimate load with high synchronization to the experimental data, thereby validating the reliability of the test results. A comprehensive comparison of cracking loads and ultimate loads between the experimental beams and finite element models is provided in Table 13.

Figure 24
Comparison of experimental and simulated load-deflection curves for beams (B0, B1, B2) under static loading.

Table 13
Comparison of cracking loads and ultimate loads between the experimental beams and finite element models.

TEST BEAM NUMBER	EXPERIMENTALLY MEASURED CRACKING LOAD (KN)	FEM-SIMULATED CRACKING LOAD (KN)	DISCREPANCY	EXPERIMENTALLY OBTAINED ULTIMATE LOAD (KN)	FEM-SIMULATED ULTIMATE LOAD (KN)	DISCREPANCY
B0	60	58	3.3%	280	276	1.4%
B1	85	82	3.5%	303	292	3.6%
B2	95	87	8.4%	350	341	2.6%

Finite element simulation analysis was performed on the test beams (PLB0, PLB1, PLB2) under fatigue loading. The results are shown in Figure 25. The experimentally measured load-displacement curves at different fatigue cycles were compared with the finite element modeling results, showing consistent trends between the two. As the number of fatigue cycles increased, the midspan deflection at the upper limit of the fatigue load also exhibited progressive growth. Overall, the stiffness of the test beams gradually decreased with the accumulation of fatigue cycles. For the same number of fatigue cycles, the error in reaching the maximum load amplitude remained within 1.5 mm.

Figure 25
Comparison of experimental and simulated load-deflection curves for beams (PLB0, PLB1, PLB2) under fatigue loading. (a) Beam PLB0 (b) Beam PLB1 (c) Beam PLB2.

After completing 2 million loading cycles, no significant fatigue damage was observed in specimens PLB0, PLB1, and PLB2. Static loading simulations were subsequently performed on these beams to evaluate their residual bearing capacity. The FEM-predicted residual capacities demonstrate close agreement with experimental test results (Table 14), with a maximum discrepancy of as low as 1.7%. This further validates the accuracy of the experimental methodology.

Table 14
Comparison of residual bearing capacity between test beams (PLB0, PLB1, PLB2) and finite element models.

TEST BEAM NUMBER	EXPERIMENTALLY MEASURED RESIDUAL BEARING CAPACITY (KN)	FEM-SIMULATED RESIDUAL BEARING CAPACITY (KN)	DISCREPANCY
PLB0	251	258	2.7%
PLB1	290	301	3.7%
PLB2	340	346	1.7%

4. CONCLUSION

In this paper, UHPC-reinforced simply supported-to-continuous concrete box beams in negative moment zone static and fatigue tests are carried out. An experimental research method was used to investigate the effects of reinforcement rate and fatigue load level on the fatigue performance of the test beams. And the accuracy of the experimental results was further verified through finite element numerical simulations. It ensures performance in critical areas and simplifies the construction process, effectively extending the service life of the box beams. The main conclusions are as follows:

• (1)

  During static loading tests, beams B1 and B2 demonstrated an increase in flexural capacity of 8% and 25%, respectively, relative to the reference beam B0. These findings indicate that the application of UHPC in the negative moment region of simply supported-to-continuous box beams significantly enhances flexural performance. This enhancement is attributed to optimized stress distribution within the cross-section, which improves ductility and damage tolerance.

• (2)

  Following 2 million fatigue cycles, no observable fatigue damage was detected in beams PLB0, PLB1, or PLB2. Post-fatigue static failure tests were subsequently conducted on these beams. Compared to their corresponding reference beams (B0, B1, B2), PLB0, PLB1, and PLB2 exhibited reductions in maximum mid-span deflection of 30%, 16.1%, and 5.8%, respectively, along with markedly lower reinforcement stress amplitudes. The significant effect of UHPC in improving the flexural strength of the structure was verified.

• (3)

  The application of UHPC to the negative moment zone of simply supported-to-continuous concrete box beams can effectively improve the residual bearing capacity of the test beams. After 2 million fatigue cycles, Beam PLB0 exhibited a 10% reduction in residual capacity relative to the static ultimate capacity of reference beam B0. Conversely, beams PLB1 and PLB2 demonstrated residual capacity increases of 4% and 21%, respectively, surpassing the static ultimate capacity of their corresponding reference beams (B1 and B2).

5. ACKNOWLEDGMENTS

The authors are grateful for the financial support of the Basic Scientific Research Project of Colleges and Universities of Liaoning Province Education Department (Project No. LJ212410153032), the Doctoral Start-up Foundation of Liaoning Province (Project No. 2021-BS-168), and Shenyang Science and Technology Project Fund (Project No. 23-407-3-19).

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Publication Dates

• Publication in this collection
  25 July 2025
• Date of issue
  2025

History

• Received
  30 Apr 2025
• Accepted
  09 June 2025