1. Introduction
Ultra-high-performance concrete (UHPC) is a relatively novel fibrous cementitious composite. It is characterized by its ultra-high compressive strength, low water to cement content (usually less than 25%), superior packing density, impact resistance, flowability, and long-lasting characteristics [
1,
2,
3]. The generally acknowledged minimum compressive strength level of UHPC is 150 MPa. However, it is practical to allow for the broader domain of UHPC’s strengths, as investigators employ various standardized methods for strength assessment [
4]. The compact microstructure of UHPC is obtained by optimizing its packing density. The latter significantly affects the compressive strength and waterproofness (i.e., enhances the permanency features) [
2]. UHPC normally incorporates steel fibers to enhance its ductility response to tensile forces [
5]. The technology for developing UHPC involves properly mixing Portland and other types of cement with an optimized aggregate size distribution, fibrous reinforcement, and employment of chemical admixtures (superplasticizers) [
6,
7].
The scientific community has devoted significant efforts to explore the applicability of UHPC in various structures (e.g., slab on grade, highway bridges, abutments, super-ductile structural elements, rehabilitation of existing structures, etc.) [
8,
9,
10]. UHPC, in addition to its superior compressive strength, has a higher Young’s modulus than conventional concrete that enables the design of slender structural elements. The high tensile and flexural strength of UHPC obtained by the inclusion of fibrous systems enable its potential usage in special structural features. In previous research, many investigators have studied the use of UHPC in beam elements due to its remarkable merits with regard to entire mechanical responses. It is worth noting that the balanced reinforcement area for the UHPC beam is significantly larger than the comparable high-performance concrete, due to the higher strength class. This behavior results in a more ductile flexural response in the condition of ultimate loading and increased bar reinforcement conditions [
11,
12].
The use of discontinuous fibers in UHPC can cause improved cracking resistance and therefore higher tensile and flexural strength. Fractured UHPC has the capacity to resist higher loading, with strain-hardening (multiple cracking) responses [
13]. Research evidence has shown that the use of fiber reinforcement in UHPC increases its tensile strength. It reduces the amount of mild steel bars needed and the total cost of materials [
14]. Additionally, the higher strength-to-weight ratio of UHPC generates a substantial decrease in the dead-weight of UHPC elements. Under analogous loading conditions, the use of UHPC instead of normal strength concrete to design a structural element reduces the dead load of structures by 50–67% [
15]. In light of these aspects, UHPC has received attention from builders who strive to develop slenderer structures, especially in bridges, to provide cost-effective construction. Therefore, UHPC has been extensively used in various structural members (e.g., precast girders, deck (infill) connections, railway slab systems, tiny elements, deck sheets, permanent formwork, and functionally categorized materials) for road and walkway bridges [
16,
17,
18,
19,
20,
21,
22].
The guidelines for designing normal concrete structures have been successfully developed by many building codes such as ACI (American Concrete Institute), IBC (International Building Code), Eurocode, etc., which have been utilized in design practice for many years [
10]. Nevertheless, these guidelines do not apply for recently developed UHPC structural members, since its intrinsic mechanical properties (i.e., tensile, compressive, and fracture energy) are quite different from normal concrete. It is noteworthy that some references on the prediction of the ultimate moment of UHPC structural elements are available in [
23,
24,
25]; however, these methods have not yet been adopted in the international design codes. Additionally, many prediction formulas have been developed that incorporate the inelastic response of UHPC [
12,
26,
27,
28,
29,
30]. These references have been fundamentally employed in the moment–curvature prediction. It involves the utilization of the tensile and compressive constitutive stress–strain models with experimental investigations, which are problematic for design purposes. For these purposes, the establishment of simplified prediction models for the ultimate moment is therefore of great importance. Significant research efforts have been devoted to structural elements developed by high- and ultra-high-performance reinforced concrete. Such studies are conducted to investigate the sectional stress and strain distributions, the physicomechanical characteristics (i.e., tensile strength, shape, aspect ratio, etc.), and content, dispersion, the bonding strength of fibers, and other factors impacting the tensile behavior of UHPC [
30,
31,
32,
33,
34,
35,
36,
37,
38]. However, these investigations have only addressed the use of single-kind fibers, and very little information (e.g., [
10]) is obtainable on the use of a hybrid system of fibers in UHPC.
In the current research, the primary goal was to study the structural performance of shear-deficient UHPC hybrid fiber-reinforced beams and to develop a reliable prediction model for their ultimate moment strength. Thus, 12 beams with various longitudinal bar arrangements were developed with low-to-high reinforcement percentages (0%, 0.54%, 0.84%, 1.21%, 2.14%, and 3.35%). All beams were prepared using a UHPC mixture containing 2.58% (vol.) of a hybrid system of smooth-coated fibers with various lengths and a unified diameter (0.2 mm), and tested under four-point loading conditions. In this work, the observed structural response (load–deflection and moment–curvature curves, ductility, crack response, and failure patterns) of beams is presented and discussed. In addition, a step-by-step analytical model for the prediction of the UHPC beam’s moment capacity is described.
4. Prediction of Beam’s Load Capacity
The prediction capability of the proposed analytical model for the ultimate moment capacity of the UHPC beams (0) is summarized in
Table 7. This table establishes the validity of the proposed analytical approach for predicting the ultimate moment capacity of UHPC beams. For all beams, the proportion of the calculated moment capacity to the experimentally observed one was very close to unity. This mean ratio was above one by 0.6% with a fairly insignificant standard deviation of 0.52%. According to
Table 7, the moment capacities for B1 through B5 were fairly accurate, suggesting that reasonable safety levels were attained. Nevertheless, the ACI 544 [
41] approach (
Section 2.2.4) overestimated B6’s moment capacity by a relatively higher margin (+12%). As a result, this approach might be appropriate for UHPC beams with longitudinal reinforcement ratios approaching the balanced ratio (see
Section 2.2.2). It is noteworthy that the common analytical data for all beams were
15.123 mm,
1.934%,
0.548%,
0.097%,
2.578%,
15.126 mm,
0.2 mm, and
0.0015.
The capacity of the proposed analytical model to reproduce the ultimate moment of UHPC beams is also displayed in
Figure 15. It can be seen from this figure that all predicted–observed data points are fairly close to the line of equality. Moreover, all the predicted–observed results were in between (or close to B3) the ±90% accuracy zone.
UHPC is a zero-permeable composite whose preparation relies on the interstitial transition zone with maximal packing density and surface hydration products, rather than full chemical hydration. The main concept of UHPC production is, therefore, to lower water content below 0.2 as it is the primary cause of porosity, which should be avoided in order to achieve zero permeability with high packing density. The effective development of a self-flowable UHPC mix with a very low w/c ratio, even below 0.18, has been enabled by the utilization of optimized content of silica fume, fly ash, and fine powders, and a higher dosage of superplasticizer with cement. As a result, compressive strength of 280 MPa has been achieved using a compacted granular cementitious matrix reinforced with steel fibers.
The mix composition specifies the proportion of each individual constituent that provides the most optimal packing density. The optimal superplasticizer dosage for improved workability was also determined. The functionality of the individual and hybridized microfibers was taken into consideration when they were inserted into the final mix, shown in
Table 4. The optimization phase that precedes the hybridization process identified and accounted for the influence of each type of fiber on the load–deflection curves. From
Table 2, it is evident that type A is the shortest, with excellent dispersibility and stability in the mixture, followed by type B, which settles down faster than type A as its content rises. When type C is added at a high content, it causes agglomeration and precipitation and thus compromises the fresh and hardened properties. The limitations of each type were then established. The best hybridized mix of the three types of microfibers was then experimentally determined. The combination described in
Table 4 is the optimal hybridization for maximum effect on the flexural properties due to the integrated sequential elongation that takes place during the fiber pullout mechanism. This paper presents the flexural properties of the optimal UHPC mix. The flexural properties results confirmed the validity of design principles.
5. Conclusions and Perspectives
The intertwining of the three types of fibers has enabled an enhanced pullout mechanism in a cementitious matrix with low water content. Based on the fact that fibers with shorter aspects become more numerous than longer fibers under the same proportion, shorter microfibers are more likely to be unidirectional and compactly distributed in the axial axis of the highly compacted and flowable cementitious matrix under the concrete pouring direction. Accordingly, short microfibers become more effective in controlling the initiation and propagation of microcracks while the longer fibers control the macrocracks. As a result, this ternary combination would prevent micro- and macro-crack growth in the generated cementitious matrix. The concept of high packing density and highly distributed microfibers due to the selected additives with optimal proportions is validated through the performance-based approach relied on post-cracking strength and toughness.
In the current research, the experimental mechanical response (load–deflection and moment–curvature curves, ductility, crack response, and failure patterns) to the four-point loading condition of UHPC beams was accordingly discussed. Furthermore, analytical prediction formulas for the calculation of the UHPC beam’s moment capacity were presented. Based on this study, the following conclusions were drawn:
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The inclusion of the fibrous system of fibers in the UHPC concrete increased its compressive and flexural strengths by 31.5% and 237.8%, which indicated the significance of fibers in promoting the tensile and flexural properties of UHPC.
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The investigation of the load–deflection curves of beams revealed that the UHPC beams with low failed by a sudden brittle flexural failure; however, the beams with medium to high altered this failure behavior to semi-ductile to ductile ones. This conclusion implies that better safety could be achieved by optimizing the tensile reinforcement for a UHPC beam. Additionally, the entire load–deflection behavior was enhanced by the introduction of more bar reinforcement (especially after yielding the bar reinforcement).
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The analysis of the moment–curvature curves demonstrated that most of the UHPC beams were prospective under reinforcement (tension-controlled). Additionally, the slope of the pre- and post-steel yielding was almost typical for all beams. This was due to the efficient hybrid fibrous system in the UHPC that controls the post-cracking curvatures of beams.
In the current study, and were calculated to investigate the ductility behavior of UHPC beams with different The percentage differences of these ductility parameters for the duplicate samples were 1.95–11.12% and 30.44–76.21%, respectively. The relatively high percentage difference for was likely due to the bilinearization hypothesis of the curve. Moreover, it was concluded that as increases, the exponentially increases; however, the relation between and showed a robust third-order polynomial trend. According to this analysis, B3 and B4 had inferior curvature ductility with respect to B1, which was attributed to the compressive failure of their concrete at the top surface or tensile failure of bars prior to achieving high ductility. The cracking response of the UHPC beams demonstrated that increasing notably decreased the crack opening width of the UHPC beams at the same service loading. Moreover, increasing the bar reinforcement ratio contributed to stabilizing the crack propagation. The cracking pattern beams showed that increasing the bar reinforcement percentages notably enhanced their initial stiffness and deformability. The existence of bar reinforcement helped to enhance the failure pattern, as more flexure shear cracks were observed as its existence increased. These flexural cracks were the main cause of failure for all beams; however, flexure shear cracks were observed in moderately reinforced beams. The prediction efficiency of the proposed analytical model was established by performing a comparative study on the experimental and analytical ultimate moment capacity of the UHPC beams. For all beams, the percentage of the mean calculated moment capacity to the experimentally observed ones nearly approached 100%. Future studies could provide more insight into the reinforcement conditions (tension-, balance-, or compression-controlled) of UHPC beams. Additionally, different features of loading, spans, reinforcement locations, sectional dimensions, and plain UHPC (with fibers) could be explored.