Experimental Study on Flexural Fatigue Performance of Steel-Fiber-Concrete-Layered Beams

Abstract

Fatigue cracking and stiffness degradation remain critical challenges for concrete flexural members used in bridge decks, crane beams, pavements, and other structures subjected to repeated loading. Layered beams that combine normal concrete in the compression zone with steel-fiber concrete in the tension zone offer a promising route to reduce self-weight while retaining crack resistance and ductility. However, the coupled influence of layer depth and fiber dosage on the flexural fatigue response of such members is still insufficiently quantified for reliable engineering design. Unlike previous studies that mainly focused on homogeneous SFRC members, UHPC-based members, or layered beams under static loading, the present study addresses a more practice-oriented but less explored problem, namely the flexural-fatigue behavior of cast-in-place layered beams composed of normal concrete in compression and steel-fiber concrete in tension. More importantly, the study does not examine fiber effect or layer geometry separately, but quantifies within one unified framework how lower-layer height ratio and fiber dosage jointly govern fatigue life, stiffness retention, crack development, and failure transition. A calibrated nonlinear finite-element model with damage-plasticity constitutive laws and cycle-block degradation was further established to reproduce the experiments and to conduct a broader parametric study. The results show that no horizontal crack formed at the cast interface and that the strain-deflection response preserved the typical three-stage fatigue evolution. Increasing either the steel-fiber volume fraction from 0.8% to 1.6% or the lower-layer height ratio from 0.5 to 0.7 markedly prolonged fatigue life and improved crack control. A practical fatigue-life relation, a stiffness-degradation law, and a numerical response surface are proposed, indicating that a height ratio of 0.6–0.7 combined with a fiber dosage of 1.2%–1.6% provides the best balance between fatigue durability, stiffness retention, and failure ductility.

1. Introduction

In recent years, concrete structures with longer spans, higher load frequencies, and stricter durability requirements have been increasingly used in transportation and industrial engineering. The increase in loading frequency in practical concrete members is mainly associated with dense traffic flow, repeated wheel passages, crane operation cycles, pavement service under continuous vehicle loading, and other industrial actions involving short-interval repeated flexural demand. Compared with ordinary reinforced concrete members, layered concrete beams have great potential as an efficient structural form because the compressive zone and the tensile zone can be tailored by different materials according to the actual stress demand. When normal concrete is placed in the upper compression zone and steel-fiber concrete is arranged in the lower tension zone, the beam can simultaneously benefit from the economy and compressive strength of normal concrete, the reduced self-weight of aggregate concrete, and the crack-bridging ability of steel fibers. The use of layered beams has two direct structural consequences. On the one hand, material zoning improves structural efficiency by assigning normal concrete to the compression zone and fiber-reinforced concrete to the tension zone, thereby reducing self-weight while improving crack control. On the other hand, the layered form introduces an interface and changes the internal force redistribution after cracking, so its fatigue behavior cannot be directly inferred from that of homogeneous reinforced concrete beams. However, the design theory and engineering experience are still insufficient for predicting the response of layered beams under repeated flexural loading, especially with respect to fatigue life, crack evolution, and post-cracking stiffness.

There have been many studies on the fatigue behavior of steel-fiber concrete and layered concrete members. Existing fatigue studies have mainly concentrated on homogeneous SFRC members, UHPC-based members, or material-level fatigue mechanisms, where the beneficial role of fibers in restraining crack propagation and delaying stiffness degradation has been well demonstrated [1]. In parallel, studies on layered or functionally graded beams have mainly emphasized static flexural behavior, serviceability improvement, or tensile-zone optimization [2,3,4]. Recent nonlinear studies further confirmed that calibrated constitutive models can reproduce the cyclic response of fiber-reinforced members and can support parametric analysis [5,6]. However, a direct fatigue-oriented evaluation of cast-in-place layered beams made of conventional normal concrete and steel-fiber concrete is still scarce. More importantly, previous studies have seldom quantified, within one unified framework, how the lower-layer height ratio and fiber dosage jointly govern fatigue life, stiffness retention, crack evolution, and failure transition [7]. Against this background, the contribution of the present study is not merely to report another layered-beam test, but to establish a fatigue-centered experimental–numerical assessment for a practical cast-in-place layered configuration. Compared with previous studies, the novelty of this work lies in three aspects: (1) it focuses specifically on cast-in-place layered beams composed of normal concrete in compression and steel-fiber concrete in tension under repeated flexural loading; (2) it quantifies, within the same test framework, the coupled influence of lower-layer height ratio and fiber dosage rather than examining these parameters separately; and (3) it translates the observed trends into a fatigue-life relation and a numerical response surface that can directly support preliminary design comparison for layered beams within the tested domain. Admittedly, the present study does not introduce a new material system or a fundamentally new analytical theory. Its novelty is instead incremental and problem-oriented. However, the work is clearly differentiated from most existing studies in that it targets a practical cast-in-place layered beam configuration under repeated flexural loading, explicitly separates the roles of tensile-zone depth and fiber dosage at the section level, and converts the observed trends into design-oriented fatigue indicators within the tested parameter range. In this sense, the contribution of the study lies in the clear identification of the engineering problem and response mechanism, rather than in claiming a disruptive conceptual innovation.

This paper aims to solve the fatigue-performance assessment problem of cast-in-place layered beams subjected to bending. In this paper, fatigue experiments were first performed on nine layered beams with two variables, namely steel-fiber volume fraction and lower-layer height ratio, and it was found that the interface remained intact while crack distribution, rebar stress amplitude, and fatigue life were strongly affected by material gradation. Then, a nonlinear numerical model was established which can consider the concrete damage, steel yielding, and fatigue-induced degradation of tensile-zone properties. Later, a series of numerical studies based on the calibrated model were performed to investigate the combined influence of layer depth and fiber dosage beyond the tested parameter range. Accordingly, the main contribution of this work is a unified experimental–numerical framework that reveals how lower-layer height ratio and fiber dosage interact to control the fatigue response of cast-in-place layered beams. On this basis, the derived fatigue-life relation and numerical response surface provide not only mechanistic interpretation, but also practical guidance for comparing alternative layered configurations within the tested parameter range. It is pointed out that the fatigue resistance of layered beams is controlled by the stress amplitude of longitudinal reinforcement and by the ability of the fiber-reinforced lower layer to retard the upward migration of the neutral axis.

2. Experimental Scheme

2.1. Experimental Introduction

The experimental program was carried out on cast-in-place layered reinforced concrete beams composed of a top normal-concrete layer (C50) and a bottom steel-fiber concrete layer (LC40). The lower layer was prepared with expanded-shale aggregate and milled steel fibers, whereas the upper layer adopted crushed stone and natural sand. The steel fibers used in the lower-concrete layer were milled steel fibers with a nominal length of 36 mm, an equivalent diameter of 1.35 mm, and an aspect ratio of 26.7. These geometric properties are now explicitly stated to better characterize the fiber reinforcement adopted in the SF-WC layer. The nominal tensile strength of the milled steel fibers was 600 MPa, according to the manufacturer’s specification.

The longitudinal tensile reinforcement consisted of two HRB400 rebars with a nominal diameter of 18 mm, and HPB300 stirrups with a diameter of 6 mm were arranged at 120 mm spacing. The beam reinforcement layout consisted of two 18 mm diameter HRB400 tensile bars at the bottom, 6 mm diameter HPB300 stirrups at 120 mm spacing, and two 8 mm diameter top longitudinal bars. The top reinforcement was mainly used to complete the reinforcement cage and to ensure stable sectional behavior during casting and loading. The beams were tested on an MTS servo-hydraulic fatigue machine (Beijing Hangtian Keyu Testing Instrument Co., Ltd., Beijing, China) under four-point bending, while strain gauges, displacement transducers, and crack microscopy were used to record the fatigue response. The material properties and mixture proportions are summarized in

Table 1. Mechanical properties of the constituent concretes used in the layered beams.

Material	Vf (%)	Cube Strength (MPa)	Axial Compressive Strength (MPa)	Axial Tensile Strength (MPa)	Elastic Modulus (GPa)	Specimen Type and Size	Test Purpose/Method
NC (C50)	0	68.4	63.8	2.83	37.2	Cube, 150 × 150 × 150 mm/ Prism, 150 × 150 × 300 mm/ Prism, 100 × 100 × 500 mm/ Prism, 150 × 150 × 300 mm	Cube compressive strength/ Axial compressive strength/ Axial tensile test/ Elastic modulus
SF-WC (LC40)	0.8	43.6	40.8	3.18	22.95	Cube, 150 × 150 × 150 mm/ Prism, 150 × 150 × 300 mm/ Prism, 100 × 100 × 500 mm/ Prism, 150 × 150 × 300 mm	Cube compressive strength/ Axial compressive strength/ Axial tensile test/ Elastic modulus
SF-WC (LC40)	1.2	39.2	38.0	3.39	22.35	Cube, 150 × 150 × 150 mm/ Prism, 150 × 150 × 300 mm/ Prism, 100 × 100 × 500 mm/ Prism, 150 × 150 × 300 mm	Cube compressive strength/ Axial compressive strength/ Axial tensile test/ Elastic modulus
SF-WC (LC40)	1.6	42.7	41.1	3.81	23.88	Prism, 150 × 150 × 300 mm/100 × 100 × 500 mm/150 × 150 × 300 mm	Axial compressive strength/axial tensile test/elastic modulus

Note: Companion specimens were cast together with the beams and cured under the same conditions. The loading areas of the specimens were adjusted to ensure uniform stress transfer during testing. The elastic modulus reported in this table was determined from the measured compressive stress–strain response of the prism specimens. In addition, the beam reinforcement layout consisted of two 18 mm bottom tensile bars, 6 mm stirrups at 120 mm spacing, and two 8 mm top longitudinal bars.

and

Table 2. Mix proportions of normal concrete and steel-fiber concrete (kg/m³).

Mixture	Cement	Fly Ash	Water	Coarse Aggregate	Fine Aggregate	Steel Fiber	SP
NC-C50	368.20	92.05	176.40	1118.60	612.30	-	4.60
SF-WC, Vf = 0.8%	438.00	112.00	210.82	470.10	375.20	62.4	5.40
SF-WC, Vf = 1.2%	438.00	112.00	210.35	465.90	374.80	93.6	5.40
SF-WC, Vf = 1.6%	438.00	112.00	209.88	461.70	374.20	124.8	5.40

, respectively. According to the material tests, the normal concrete used in the upper layer had a cube compressive strength of 68.4 MPa and an axial compressive strength of 63.8 MPa. For the lower SF-WC layer, the cube compressive strengths were 43.6 MPa, 39.2 MPa, and 42.7 MPa for V_f = 0.8%, 1.2%, and 1.6%, respectively, while the corresponding axial compressive strengths were 40.8 MPa, 38.0 MPa, and 41.1 MPa. For the three lower-layer height ratios of η_h = 0.5, 0.6, and 0.7, the corresponding lower SF-WC layer heights were 150 mm, 180 mm, and 210 mm, whereas the upper normal-concrete layer heights were 150 mm, 120 mm, and 90 mm, respectively. This layered division was selected to systematically examine how the effective depth of the fiber-reinforced tensile zone influences fatigue resistance while retaining a normal-concrete compression zone. The load was applied through a four-point bending arrangement, in which the actuator force was distributed into two symmetric concentrated loads by a loading beam, thereby creating a constant-moment region in the mid-span zone.

The basic properties of the steel fibers used in the SF-WC layer are summarized in

Table 3. Basic properties of the steel fibers used in the SF-WC layer.

Fiber Type	Length (mm)	Equivalent Diameter (mm)	Aspect Ratio	Tensile Strength (MPa)
Milled steel fiber	36	1.35	26.7	600

Note: The nominal geometric parameters and tensile strength of the milled steel fibers were taken from the manufacturer’s specification. The tensile strength of the fibers will be supplemented according to the manufacturer’s specification.

.

The beam geometry and the loading arrangement are shown in Figure 1. All specimens had an overall length of 3000 mm, a clear span of 2700 mm, and a rectangular cross-section of 150 mm × 300 mm. The lower steel-fiber concrete layer was cast first, and the normal concrete layer was placed before the lower layer reached final set, so that a monolithic cast interface could be formed. No additional surface roughening, chiseling, or bonding-agent treatment was applied before casting the upper layer. Instead, the interface integrity relied on the fresh-on-fresh sequential casting procedure, in which the upper normal-concrete layer was placed before the lower SF-WC layer reached final set, so that mechanical interlock and early chemical bonding could be developed under continuous casting conditions.

2.2. Experimental Design and Procedures

The objective of the test matrix was to quantify the influence of two variables on flexural fatigue resistance: the steel-fiber volume fraction, V_f = 0.8%, 1.2%, and 1.6%, and the lower-layer height ratio, η_h = 0.5, 0.6, and 0.7. The fiber volume fractions V_f = 0.8%, 1.2%, and 1.6% were selected to represent a practical low-to-moderate dosage range for SF-WC, so that both the strengthening effect and the possible diminishing-return tendency could be identified while maintaining workable mixture proportions. The steel fibers used in the lower layer were milled steel fibers with a nominal length of 36 mm, an equivalent diameter of 1.35 mm, an aspect ratio of 26.7, and a nominal tensile strength of 600 MPa, according to the manufacturer’s specification.

A total of nine beams were arranged in a two-factor, three-level matrix, while all other geometric and reinforcement parameters were kept unchanged. It should be noted that the present program was designed as a comparative two-factor parametric study, and only one beam was tested for each parameter combination because of specimen-fabrication and long-duration fatigue-testing constraints. Therefore, the current results are intended primarily to identify the relative influence of V_f and η_h, rather than to establish statistical descriptors such as standard deviation or coefficient of variation. Future work should include repeated specimens for each condition. Accordingly, the present dataset should be interpreted as a comparative two-factor dataset rather than a statistically representative fatigue database. Because no replicated specimens were tested for the same parameter combination, statistical descriptors such as variance, confidence interval, and probability distribution of fatigue life could not be established. This lack of replication is therefore one of the major limitations of the present study. The fatigue load was applied in the form of a constant-amplitude sinusoidal wave with a frequency of 10 Hz and a stress ratio of 0.10. The loading frequency of 10 Hz was selected as a practical compromise between testing efficiency and stable operation of the servo-hydraulic system. During the fatigue tests, no abnormal vibration, impact-like response, or visually observable instability was identified under the adopted specimen size, loading configuration, and stress level. In addition, no macroscopic damage feature that could be directly associated with severe heat accumulation, such as local softening or abnormal interface deterioration, was visually observed during the loading process. However, it should be emphasized that the thermal effect associated with the adopted loading frequency was not quantitatively verified in the present study because the specimen temperature was not instrumentally monitored. Therefore, the present results should be interpreted as fatigue responses obtained under the specific loading protocol adopted herein, rather than as direct evidence that frequency-related heating was negligible. Future studies should combine direct temperature measurement with comparative tests at different loading frequencies to clarify the possible thermal influence of loading frequency on the fatigue response of layered beams. The upper limit, Pmax, for each beam was selected as the load corresponding to a crack width of 0.20 mm at the centroid level of the tensile reinforcement under a preliminary static loading stage. To clarify the fatigue loading level relative to the static flexural resistance, the monotonic ultimate flexural capacity of the corresponding layered beams was first determined from a preliminary static-loading stage. The fatigue load range was then expressed as P_min–P_max, with P_min/P_max = 0.10. For the tested beams, the applied upper fatigue load corresponded to a sub-ultimate loading regime, and the ratio P_max/P_u should be reported together with the measured fatigue parameters to indicate the proximity of the fatigue loading to the static flexural limit. Here, P_u denotes the ultimate flexural capacity under monotonic four-point loading.

Measurements were taken at 5 × 10³, 1 × 10⁴, 5 × 10⁴, 1 × 10⁵, 2 × 10⁵, and subsequent cycle blocks until failure. The specimen matrix and the key fatigue results are listed in

Table 4. Test matrix and measured fatigue performance of the nine layered beams.

Beam	Vf (%)	ηh	Lower-Layer Height (mm)	Pmax (kN)	Pmax/Pu	Fatigue Life, Nf	Rebar Stress Amplitude (MPa)	Equivalent Stress Level, Seq
B0.8-150	0.8	0.5	150	95	95/Pu, 0.8-150	189,540	236.7	0.8348
B0.8-180	0.8	0.6	180	94	94/Pu, 0.8-180	234,860	231.9	0.7956
B0.8-210	0.8	0.7	210	93	93/Pu, 0.8-210	286,430	227.0	0.7956
B1.2-150	1.2	0.5	150	96	96/Pu, 1.2-150	221,780	235.6	0.8088
B1.2-180	1.2	0.6	180	96	96/Pu, 1.2-180	279,640	231.1	0.8088
B1.2-210	1.2	0.7	210	95	95/Pu, 1.2-210	332,510	226.0	0.8138
B1.6-150	1.6	0.5	150	97	97/Pu, 1.6-150	255,360	234.1	0.8138
B1.6-180	1.6	0.6	180	98	98/Pu, 1.6-180	317,580	231.8	0.788
B1.6-210	1.6	0.7	210	97	97/Pu, 1.6-210	389,760	224.9	0.788

Note: P_u denotes the ultimate flexural capacity obtained from the corresponding monotonic four-point bending test, and P_max/P_u represents the fatigue upper-load level relative to the static flexural resistance. The rebar stress amplitude listed in Table 4 was determined from the measured strain response at the centroid level of the tensile reinforcement during fatigue loading.

. It should be noted that the present test matrix included only one beam for each parameter combination. Therefore, statistical descriptors of fatigue-life scatter, such as standard deviation, could not be established from repeated tests under identical conditions. In this study, the measured fatigue lives are mainly used as comparative indicators to reveal the relative influence of steel-fiber dosage and lower-layer height ratio under the same loading protocol, rather than as statistically representative population values.

Figure 2 rearranges the same test matrix in a fatigue-life response map to better show the coupled role of the two variables. The matrix already suggests a monotonic increase in fatigue life with higher fiber dosage and larger lower-layer height ratio, but the magnitude of improvement is not identical for the two variables, which justifies a subsequent coupled analysis.

2.3. Experimental Results

All beams failed in flexure and none exhibited a premature horizontal crack along the cast interface, which confirms that the layered section behaved monolithically during most of the fatigue process, in agreement with observations reported for several graded and layered composite beams [8,9,10]. This observation indicates that, within the present fatigue-life range and loading level, the cast interface retained sufficient bond and shear-transfer capacity and did not become the governing weak plane. Nevertheless, the present tests do not prove that the interface would remain unaffected under much longer fatigue duration, more severe stress levels, or adverse environmental actions. In other words, although no interface deterioration was identified before failure in the current program, possible long-term interfacial weakening cannot be completely excluded and should be investigated in future work through dedicated interface-fatigue tests and long-duration monitoring. Three representative failure characteristics were observed as the lower-layer height and fiber dosage increased: brittle rupture concentrated along a dominant flexural crack, compressive crushing of the upper normal concrete accompanied by rebar fracture, and a more ductile crushing-dominated mode with suppressed sudden tensile-bar failure. The observed rebar fracture was attributed to fatigue damage accumulation in the tensile reinforcement under repeated high stress amplitude. After crack localization, the stress concentration in the longitudinal bar near the dominant flexural crack increased progressively, and microcracks initiated at rib roots or local surface imperfections. With continued cyclic loading, these fatigue cracks propagated through the bar section, eventually leading to sudden tensile-bar fracture after yielding had already developed in the local cracked region. Figure 3 summarizes the characteristic failure morphologies redrawn in a publication-style schematic.

The measured fatigue lives are presented in Figure 4. In addition, the stress level in the tensile reinforcement during fatigue loading was evaluated by the measured rebar stress amplitude and the equivalent stress level S_eq, as summarized in Table 4. The measured rebar stress amplitude ranged from 224.9 MPa to 236.7 MPa, indicating that the fatigue response was governed by a relatively high but still sub-yield cyclic stress state in the longitudinal reinforcement. At the same fiber dosage, increasing the lower-layer height ratio from 0.5 to 0.7 increased fatigue life by approximately 51.1%, 49.9%, and 52.6% for V_f = 0.8%, 1.2%, and 1.6%, respectively. At the same height ratio η_h = 0.6, increasing the fiber dosage from 0.8% to 1.6% increased fatigue life from 2.35 × 10⁵ to 3.18 × 10⁵ cycles, corresponding to an increase of about 35.2%. These results indicate that the two parameters acted synergistically, and that a thicker tensile zone delayed crack coalescence while the fibers improved stress redistribution after cracking. It should also be emphasized that fatigue data inherently exhibit scatter, whereas only one specimen was tested for each case in the present experimental program. As a result, statistical descriptors such as the standard deviation, coefficient of variation, and confidence interval of fatigue life could not be established for the current dataset. The monotonic trends observed across the nine beams, together with the compatible evolution of crack width, compressive strain, and stiffness degradation, improve the interpretability of the experimental observations, but they should not be regarded as evidence of statistical reliability. In other words, internal consistency among different response indicators supports the comparative reading of the present results, yet it cannot replace replicated testing for quantifying specimen-to-specimen scatter. Therefore, the reported fatigue lives should be interpreted primarily as comparative observations under the present loading protocol rather than as statistically representative population values. Repeated tests and probabilistic evaluation remain necessary in future work.

To improve academic readability, characteristic serviceability indicators at 1.0 × 10⁵ cycles were consolidated from the measured response curves and their interpolated envelopes, as listed in

Table 5. Characteristic response indices at 1.0 × 10⁵ cycles for comparative discussion.

Beam	Mid-Span Deflection at 1 × 105 Cycles (mm)	Top Compressive Strain at 1 × 105 Cycles (με)	Maximum Crack Width at 1 × 105 Cycles (mm)	B100k/B0
B0.8-150	12.2	1380	0.37	0.718
B0.8-180	12.55	1297	0.329	0.742
B0.8-210	12.9	1228	0.281	0.753
B1.2-150	11.65	1449	0.34	0.726
B1.2-180	12.0	1362	0.303	0.743
B1.2-210	12.35	1290	0.259	0.754
B1.6-150	11.25	1490	0.326	0.733
B1.6-180	11.6	1401	0.29	0.747
B1.6-210	11.95	1326	0.247	0.759

. Here, B_100k/B₀ denotes the ratio of the beam flexural stiffness at 1.0 × 10⁵ cycles to the initial flexural stiffness before fatigue loading. The general tendency is clear: a larger lower-layer height ratio reduced the top compressive strain and the maximum crack width, whereas a higher fiber dosage reduced crack width and improved stiffness retention but, owing to the slightly higher admissible upper fatigue load, could produce a somewhat larger top compressive strain at the same cycle number.

The evolution of the top-surface compressive strain for beams with V_f = 1.2% is shown in Figure 5. All beams exhibited the classical three-stage fatigue development, namely a rapid initial growth stage, a long quasi-stable accumulation stage, and a final accelerated stage near failure. This trend is qualitatively consistent with the fatigue evolution laws reported in previous studies on steel-fiber concrete and other high-performance cementitious flexural members, which is consistent with previous studies [11,12,13]. When η_h increased from 0.5 to 0.7, the compressive strain at the same relative fatigue life decreased because more steel-fiber concrete remained effective in the tension zone, thereby delaying the upward migration of the neutral axis.

Figure 6 shows that the mid-span deflection followed a similar three-stage law, which agrees well with the evolution pattern reported in related studies on fiber-reinforced concrete flexural members [14,15,16]. In the early stage, approximately 5%–10% of the total fatigue life was consumed by rapid crack initiation and redistribution of internal force; in the middle stage, which occupied about 80% of the fatigue life, damage accumulated steadily; and in the final stage the deflection accelerated abruptly until failure. At the same fiber dosage, the beam with a higher lower-layer height ratio presented a slightly larger deflection under the same upper fatigue load because its initial flexural stiffness was marginally lower, but its fatigue life was still longer owing to better crack control and slower stiffness loss.

The influence of fiber dosage on crack development is illustrated in Figure 7 for η_h = 0.6. The maximum crack width and the average crack width again exhibited a three-stage evolution. In the steady stage, increasing the fiber dosage from 0.8% to 1.2% reduced the characteristic crack width by about 13%, and increasing it further to 1.6% produced an additional but smaller improvement. These observations are consistent with previous studies on the flexural fatigue behavior of steel-fiber-reinforced concrete (SFRC) members, which have shown that increasing fiber dosage improves crack control and ductility, although the marginal benefit gradually decreases beyond a certain fiber content [17,18]. Compared with previously published fatigue studies on steel-fiber-reinforced concrete beams and other fiber-reinforced cementitious flexural members, the present layered beams exhibited the same qualitative three-stage evolution in compressive strain, mid-span deflection, and crack width, namely an initial rapid development stage, a long quasi-stable accumulation stage, and a final accelerated deterioration stage close to failure. This agreement suggests that the fundamental fatigue-damage mechanism of the present members is still governed by cumulative flexural cracking and stiffness degradation, rather than by a different deterioration mode induced by the layered configuration itself. At the same time, the present results also reveal a feature specific to the cast-in-place layered beams: increasing the lower-layer height ratio reduced the compressive strain at the same relative fatigue life by delaying the upward migration of the neutral axis, whereas increasing the fiber dosage mainly improved crack control and slowed the transition from the stable stage to the accelerated stage. Therefore, the present results are qualitatively consistent with the fatigue-evolution trends reported for conventional SFRC beams, while also clarifying how tensile-zone depth and fiber dosage interact in a layered section. More importantly, this comparison indicates that the layered configuration does not simply reproduce the fatigue behavior of conventional SFRC beams. Instead, it introduces a section-level design effect in which tensile-zone depth and fiber dosage play different roles: increasing the lower-layer height ratio mainly delays neutral-axis migration and reduces compressive-strain demand, whereas increasing fiber dosage mainly improves crack bridging and slows stiffness deterioration. This distinction is not explicitly available from most previous studies on homogeneous SFRC members or layered beams under predominantly static loading, and it is one of the key findings of the present work.

Following the classical semi-logarithmic fatigue format, the equivalent stress level and fatigue life of the layered beams can be described by:

Seq = 1.613 − 0.148 log10(N_f)

(1)

For the present test domain, a complementary two-parameter regression directly linking fatigue life with layer geometry and fiber dosage was obtained as:

log10(N_f) = 4.700 + 0.164V_f + 0.898η_h, R² = 0.998

(2)

Equation (1) is consistent with the measured trend in Figure 8, while Equation (2) is convenient for preliminary design comparison within the tested range. The regression confirms that the lower-layer height ratio had a slightly stronger influence than the fiber dosage on fatigue life under the adopted loading protocol. The applicability of Equations (1) and (2) should be interpreted with caution. Equation (2) is an empirical regression derived only from the present nine-beam test matrix, namely cast-in-place layered beams with the current section size, reinforcement arrangement, material system, loading mode, and the parameter ranges of V_f = 0.8%–1.6% and η_h = 0.5–0.7. Therefore, it should be used only for preliminary comparison within this tested domain and should not be directly extrapolated to other beam geometries, reinforcement ratios, loading protocols, or environmental conditions. By contrast, Equation (1) has the same semi-logarithmic stress–life format as a classical S–N relation because it links an equivalent stress level to fatigue life. However, unlike conventional reinforced-concrete S–N curves, which are usually established for a given member type under multiple stress levels, Equation (1) was calibrated specifically for the tested cast-in-place layered beams and therefore reflects the coupled influence of the layered material configuration under the adopted loading protocol.

3. Numerical Model

3.1. Definition of the Numerical Model

A three-dimensional nonlinear finite-element model was established in ABAQUS (version 2021) to reproduce the flexural fatigue response of the layered beams. The concrete layers were modeled by eight-node reduced-integration solid elements (C3D8R), while the longitudinal rebars and stirrups were modeled by embedded truss elements (T3D2), following common nonlinear simulation strategies adopted for layered or fiber-reinforced concrete beams [19,20,21,22]. Because the test beams were cast in sequence before the lower layer reached final set and no interface crack was observed in the experiments, the interface was modeled as a tied contact in the baseline analysis; a cohesive sensitivity check was also introduced to confirm that the interface traction remained below the calibrated limit in the tested parameter range. Therefore, the baseline numerical treatment reflects the experimentally observed monolithic behavior within the present test range, but it should not be interpreted as evidence that interface fatigue degradation would remain negligible under all long-term service scenarios. Fatigue loading was simulated by a cycle-block strategy in which each block was represented by a quasi-static solution followed by stiffness and tensile-damage updates in the cracked tension zone [23]. A supplementary mesh-sensitivity check was carried out using the representative beam B1.2-180, whose parameter combination is located near the center of the present test domain. Three characteristic solid-element sizes, namely 30 mm, 20 mm, and 15 mm, were examined, with local refinement introduced in the constant-moment region and near the cast interface. The predicted fatigue life changed from 2.607 × 10⁵ cycles for the coarse mesh to 2.701 × 10⁵ cycles for the medium mesh and 2.734 × 10⁵ cycles for the fine mesh, while the corresponding characteristic stiffness at 1.0 × 10⁵ cycles changed from 2.655 × 10¹² to 2.692 × 10¹² and 2.705 × 10¹² N·mm², respectively. Relative to the medium mesh, the fine mesh altered the predicted fatigue life and characteristic stiffness by only 1.22% and 0.48%, respectively. Therefore, the 20 mm mesh was adopted in the subsequent simulations as a compromise between computational efficiency and prediction accuracy.

3.2. Parameters of the Model and Calibration

The normal concrete and the steel-fiber concrete were both described by the concrete damage plasticity framework, but different tensile-softening and fracture-energy parameters were adopted to account for steel-fiber bridging. The elastic modulus, compressive strength, and tensile strength were taken from the material tests, whereas the residual tensile factors and fracture energies were calibrated by matching the measured post-cracking stiffness and crack-development trend. The tensile reinforcement was assigned a bilinear elastoplastic law with isotropic hardening, and fatigue damage in the steel bars was represented through a Miner-type cumulative rule driven by the stress amplitude obtained from the sectional response [24,25,26]. The principal calibrated parameters are listed in

Table 6. Calibrated constitutive parameters used in the nonlinear numerical model.

Component	Element/Law	Elastic Parameters	Strength Parameters	Fatigue-Related Calibration
NC (C50)	CDP solid, C3D8R	E = 37.2 GPa, ν = 0.20	fc = 63.8 MPa; ft = 2.83 MPa	Gf = 0.11 N/mm; dilation = 36°
SF-WC, Vf = 0.8%	CDP solid, C3D8R	E = 22.95 GPa, ν = 0.21	fc = 40.8 MPa; ft = 3.18 MPa	Residual tensile factor = 0.55; Gf = 0.20 N/mm
SF-WC, Vf = 1.2%	CDP solid, C3D8R	E = 22.35 GPa, ν = 0.21	fc = 38.0 MPa; ft = 3.39 MPa	Residual tensile factor = 0.63; Gf = 0.25 N/mm
SF-WC, Vf = 1.6%	CDP solid, C3D8R	E = 23.88 GPa, ν = 0.21	fc = 41.1 MPa; ft = 3.81 MPa	Residual tensile factor = 0.72; Gf = 0.31 N/mm
Rebar HRB400	Embedded truss, T3D2	E = 200 GPa, ν = 0.30	fy = 462 MPa; fu = 635 MPa	Miner-based fatigue accumulation
Cast interface	Surface tie/cohesive check	Kn = 5 × 105 MPa/mm	ft, int = 2.3 MPa; τint = 3.8 MPa	No significant slip before failure

. The Poisson’s ratios listed in Table 6 were adopted as representative values for the corresponding concretes and steel because they were not directly measured in the present test program, and only a small difference was introduced between NC and SF-WC to reflect their different aggregate systems. The fracture energy ${\mathrm{G}}_{\mathrm{f}}$ was calibrated by matching the measured post-cracking stiffness degradation and crack-development trend of the beams, whereas the interface normal stiffness ${\mathrm{K}}_{\mathrm{n}}$ was assigned a sufficiently large value to ensure stable contact transfer without unrealistic penetration and was further checked through cohesive sensitivity analysis. Therefore, these parameters should be regarded as calibration-based model inputs rather than directly measured material constants in the present study.

3.3. Model Verification with Test Results

The credibility of the numerical study depends primarily on the calibration and verification procedure. It should be clarified that the comparison reported here is not a fully independent external validation based on a separate test series. Owing to the limited number of available specimens, the same experimental program was used for parameter calibration and for consistency checking of the calibrated model, with representative beams selected to cover different lower-layer height ratios and fiber dosages.

Table 7. Experimental–numerical comparison for representative beams.

Beam	Exp. Nf	FE Nf	Error in Nf (%)	Exp. B100k (×1012 N·mm2)	FE B100k (×1012 N·mm2)	Error in B100k (%)
B0.8-150	189,540	197,800	+4.4	2.579	2.507	−2.8
B0.8-180	234,860	227,600	−3.1	2.610	2.519	−3.5
B0.8-210	286,430	292,900	+2.3	2.593	2.510	−3.2
B1.2-180	279,640	270,100	−3.4	2.792	2.692	−3.6
B1.6-180	317,580	329,400	+3.7	2.903	2.777	−4.3
B1.6-210	389,760	401,800	+3.1	2.880 *	2.765 *	−4.0

* B100k denotes the characteristic beam flexural stiffness at 1.0 × 10⁵ fatigue cycles; for beam B1.6-210, the marked value was extracted from the corresponding stiffness-degradation curve at 1.0 × 10⁵ cycles for consistency of comparison.

compares the experimental and numerical results. Here, B_100k represents the characteristic beam flexural stiffness at 1.0 × 10⁵ fatigue cycles. For the selected cases, the absolute error in fatigue life was within ±5%, and the error in characteristic stiffness at 1.0 × 10⁵ cycles was below about 4.5%. These deviations are acceptable for nonlinear fatigue analysis of concrete members and indicate that the proposed modeling route can capture the main deterioration mechanisms. Nevertheless, because no separate hold-out specimen group was available, the present agreement should be interpreted as evidence of internal consistency within the tested domain rather than as fully independent predictive validation. Accordingly, the numerical results are used here as calibrated trend-supporting evidence, while broader predictive applicability still requires independent validation and repeated experimental specimens.

Figure 9 compares the measured and calculated stiffness-degradation curves. Both the test and the simulation show a clear three-stage evolution. This stable deterioration pattern qualitatively indicates that the measured fatigue response was mainly governed by cumulative flexural damage under the adopted loading protocol. However, because no direct temperature monitoring or comparative frequency tests were conducted, the possible influence of frequency-related thermal effects was not quantitatively assessed in the present study. In practical terms, the layered beam retained about 72%–76% of its initial flexural stiffness after 1.0 × 10⁵ cycles, and the model reproduced this band with good fidelity. The agreement supports the use of the numerical model for broader parametric exploration.

3.4. Simulation Cases and Procedures

After validation The simulated lower-layer height ratio ranged from 0.40 to 0.80, the fiber dosage ranged from 0.0% to 2.0%, and the equivalent stress level covered the practical interval of 0.76–0.86. For each case, the model output included the evolution of mid-span deflection, compressive-zone strain, rebar stress amplitude, interface traction, and predicted fatigue life. To avoid excessive computational cost, one fatigue block represented 5000–20,000 cycles depending on the current damage stage, and the constitutive parameters were updated adaptively according to the calculated damage index, which is similar to the accelerated numerical fatigue procedures reported in recent studies [27,28]. Within each fatigue block, the equilibrium response was solved using the ABAQUS implicit procedure with automatic time incrementation. The initial pseudo-time increment, minimum increment, and maximum increment were set to 0.05, 1 × 10⁻⁵, and 0.10, respectively, and up to 80 equilibrium iterations were allowed for each increment. To ensure reproducibility of the cycle-block procedure, the block size was linked to the current damage level, namely 20,000 cycles/block for D < 0.30, 10,000 cycles/block for 0.30 ≤ D < 0.70, and 5000 cycles/block for D ≥ 0.70. When rapid stiffness degradation caused convergence difficulty during the later fatigue stage, the increment size was automatically reduced, while the fatigue-block length was maintained at the conservative lower bound.

3.5. Analysis of Simulation Results

Figure 10 synthesizes the numerical model and the resulting response surface of fatigue-life prediction. The simulated damage contour confirms that tensile damage remained concentrated in the lower layer and in the vicinity of the major flexural cracks, whereas the interface remained largely undamaged, which is fully consistent with the experimental observation that no interface crack formed before final failure. The parametric surface shows that the fatigue life increased nonlinearly with both η_h and V_f, but the improvement rate gradually diminished when V_f exceeded about 1.6% or when η_h exceeded about 0.7, which is broadly consistent with the diminishing-return tendency reported for fiber dosage and graded tensile-zone enhancement in related studies [29,30,31]. In other words, excessively increasing the fiber dosage or the lower-layer height will not proportionally increase fatigue life, because the response eventually becomes controlled by rebar stress amplitude and by crushing of the upper normal-concrete zone. Therefore, in practical structural design, the most efficient region is a lower-layer height ratio of η_h = 0.6–0.7 with a steel-fiber dosage of V_f = 1.2%–1.6%, which provides effective crack control, acceptable deflection, and improved failure ductility. This result indicates that the steel-fiber concrete layer does not need to occupy the entire section, but should instead be concentrated in the effective tensile zone, while the upper compression zone can remain normal concrete for better economy and compressive efficiency. For the present 150 mm × 300 mm beam section, this corresponds to a lower-layer depth of 180–210 mm, which is sufficient to cover the main flexural cracking zone without excessively increasing the amount of the fiber-reinforced layer. Since the fatigue-life gain becomes gradually non-proportional when the fiber dosage exceeds about V_f = 1.2%–1.6%, the above range should be regarded as a practical material-efficiency recommendation rather than a strict economic optimum. No formal economic model, life-cycle cost analysis, or cost-performance optimization was established in the present study. Therefore, the recommended ranges of lower-layer height ratio and fiber dosage should be interpreted only as fatigue-performance-oriented and material-efficiency-oriented guidance within the tested domain, rather than as an economically optimal solution.

4. Conclusions

This study investigated the flexural-fatigue behavior of cast-in-place layered beams composed of normal concrete in the compression zone and steel-fiber concrete in the tension zone through experiments and calibrated numerical analysis. Although the present work represents an incremental contribution rather than a disruptive innovation, it is clearly differentiated from most previous studies in three respects: it focuses on a practical cast-in-place layered beam system under repeated flexural loading, it reveals the coupled section-level roles of lower-layer height ratio and fiber dosage, and it translates the observed fatigue trends into design-oriented comparative indicators within the tested domain. In this respect, the study extends the existing literature from material-level observations or static layered-beam behavior to a more explicit fatigue-oriented assessment for conventional cast-in-place layered members. The main conclusions can be drawn as follows:

• No premature horizontal crack formed at the interface between the two concretes, which indicates that the cast-in-place layered section can work monolithically under flexural fatigue when proper casting continuity is ensured. The global response of the beams, including compressive strain and mid-span deflection, followed the classical three-stage fatigue-development law.
• Increasing the lower-layer height ratio from 0.5 to 0.7 markedly prolonged fatigue life, reduced compressive-zone strain, and reduced crack width because more steel-fiber concrete remained effective in the tension zone and delayed the upward movement of the neutral axis.
• Increasing the steel-fiber volume fraction from 0.8% to 1.6% improved crack distribution, reduced crack width, enhanced stiffness retention, and shifted the failure mechanism toward a more ductile compression-dominated mode. The marginal benefit became smaller once the dosage exceeded approximately 1.2%–1.6%, indicating that unlimited fiber addition is not the most economical strategy.
• Within the present loading protocol and tested parameter range, the fatigue response can be represented by the empirical relations Seq = 1.613 − 0.148log10(N_f) and log10(N_f) = 4.700 + 0.164V_f + 0.898η_h. The former is an S–N-type stress-life relation for the tested layered beams, whereas the latter is a design-oriented regression for comparing alternative layered configurations within the present experimental domain. Therefore, these relations should be used only as preliminary engineering references for this beam type and should not be regarded as universally applicable fatigue design equations.
• The proposed numerical model reproduced the measured fatigue life and stiffness degradation with satisfactory accuracy and indicated that a lower-layer height ratio of η_h = 0.6–0.7 combined with a steel-fiber volume fraction of V_f = 1.2%–1.6% provides a balanced combination of fatigue durability, stiffness retention, crack control, and failure ductility. Because only one beam was tested for each parameter combination, the present conclusions mainly establish comparative fatigue-performance trends rather than statistical fatigue-life distributions. Future studies should include repeated specimens for each test condition so that standard deviations, confidence intervals, and probabilistic fatigue analyses can be reported. In addition, because the fatigue tests were conducted at 10 Hz without direct temperature measurement, the possible thermal influence associated with loading frequency was not quantitatively verified. Accordingly, the present conclusions should be understood as being applicable to the adopted loading protocol, and further temperature-monitored fatigue tests are needed for a more rigorous assessment of frequency effects.