Behavior of Non-Shear-Strengthened UHPC Beams under Flexural Loading: Influence of Reinforcement Percentage

Abstract

In the present work, the structural responses of 12 UHPC beams to four-point loading conditions were experimentally and analytically studied. The inclusion of a fibrous system in the UHPC material increased its compressive and flexural strengths by 31.5% and 237.8%, respectively. Improved safety could be obtained by optimizing the tensile reinforcement ratio ($\rho$) for a UHPC beam. The slope of the moment–curvature before and after steel yielding was almost typical for all beams due to the inclusion of a hybrid fibrous system in the UHPC. Moreover, we concluded that as $\rho$ increases, the deflection ductility exponentially increases. The cracking response of the UHPC beams demonstrated that increasing $\rho$ notably decreases the crack opening width of the UHPC beams at the same service loading. The cracking pattern the beams showed that increasing the bar reinforcement percentages notably enhanced their initial stiffness and deformability. Moreover, the 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 capacity approached 100%.

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.

2. Experimental Program

2.1. Materials

Ordinary Portland cement (PC) complying with ASTM C150 specifications was used as the main constituent for the binder formulated with silica fume (SF) and class F fly ash (FA) as supplementary cementitious materials.

Table 1. Physicochemical properties of PC and SCMs.

Oxides (%)	PC	FA	SF
SiO2	20.41	55.23	86.20
Al2O3	5.32	25.95	0.49
Fe2O3	4.10	10.17	3.79
CaO	64.14	1.32	2.19
MgO	0.71	0.31	1.31
SO3	2.44	0.18	0.74
TiO2	0.30	-	-
Na2Oeq	0.10	0.86	2.80
L.O.I.	2.18	5.00	2.48
Relative density	3.15	2.70	2.20

lists the physicochemical properties of the employed types of cement. The specific gravities of PC, SF, and FA were 3.15, 2.2, and 2.7, respectively. Furthermore, Arabian Peninsula-based sands [characterized as red dune (RS) and white (WS)] were employed as fine aggregates. The specific gravities of RS and WS at saturated surface dry conditions (SSD) were 2.65 and 2.74, respectively. An Axios Max X-ray fluorescence (XRF) machine was utilized to determine the chemical composition of the binder constituting powders. The particle-size distribution (PSD) analysis of the fine powders was conducted using a laser diffraction particle size analyzer (LA-950). Microstructural analysis was conducted employing a Versa 3D dual beam field emission scanning electron microscope (SEM). Figure 1a depicts the grain size distribution curves for PC, FA, and SF, whereas Figure 1b and

Table 2. Physical properties of RS and WS.

Property	RS	WS
Bulk specific gravity (OD basis)	2.64	2.73
Apparent specific gravity	2.67	2.76
Absorption, %	0.30	0.37
Fineness modulus (range of 2.3–3.1)	1.11	1.46

illustrate the particle size distribution analysis and physical properties of the employed aggregates.

In this experimental investigation, a hybrid system of three fibers (designated as A, B, and C) bright high-carbon and high-performance strength microsteel straight fibers were used as discontinuous reinforcement of the developed UHPC mixes. The physical and mechanical properties (as received) of the microsteel fibers are given in

Table 3. Physicomechanical properties of microsteel fibers.

Type		Length (mm)	Diameter (µm)	Unit Weight (kg/m3)	Tensile Strength (MPa)
A		13	200	7850	2600
B		20
C		30

. The mix design of the UHPC is detailed in

Table 4. Mix proportions of the developed UHPC (in kg/m³).

PC	SF	FA	WS	RS	Water	SP	Fiber
							A	B	C
1123.1	239.1	66.1	481.2	160.9	212.7	39.7	151.8	43.0	7.6

. It is worth noting that a polycarboxylate ether-based water reducer superplasticizer [commercially recognized as Master Glenium 51 (Master Builders Solutions UK Ltd, Manchester, UK)] was identified as SP and employed in the current study to control the workability of the prepared mixes. This SP had a density and water content of 1080 kg/m³ and 65.19%, respectively. To this end, the quantity of water contained in the SP was corrected in the calculation of the amount of mixing water after the water-to-binder ratio was optimized as 0.165.

2.2. Methods

2.2.1. Mixing, Casting, and Curing

In the current study, the UHPC was prepared using a dissolver mixer [MischTechnik, UEZ ZZ 50-S with 95 L capacity (UEZ Mischtechnik GmbH, Stuttgart, Germany)]. Firstly, all the dry materials (PC, FA, SF, WS, and RS) were mixed for 5 min at high rotation speed (about 743 rpm) to achieve their highest analogy. Secondly, the mixing water, which was blended with SP, and the aggregates’ absorption water were added during mixing for 10 min until the flowability of the mix was in the range of 180–220 mm. The flowability was measured following the ASTM C 1437. Afterward, the weighed hybrid system of fibers was gradually poured into the wet mix in slight dosages for ideal diffusion at a slow rotation pace (about 371 rpm) for 2 min. After the addition of fibers, the mixing speed was converted to intermediate. This last stage of mixing took 3–8 min to develop satisfactory homogenization of the UHPC. Eventually, the produced UHPC was poured (in 50 mm layers) into the beam’ molds, which included the pre-placed steel bars. To investigate the compressive and flexural strength of the UHPC, 50 mm cubes and (75 mm × 75 mm × 300 mm) prism samples were additionally prepared. All UHPC specimens were cured for 28 days under standard saturated curing conditions (21 ± 2 °C temperature and 100% relative humidity).

2.2.2. Beam Specimen Details

In this study, 12 mini-scale UHPC rectangular beams were prepared for the experimental investigation. The size of beam test specimens was 150 mm × 150 mm × 600 mm. Figure 2 shows the geometry and reinforcement properties. It is noteworthy that the bottom and side cover of bars were 20 mm. Moreover, a set of prefabricated concrete spacers (20 × 20 × 20 mm) was used to fix the single-layer reinforcing bars.

Table 5. Reinforcement details for beam specimens.

No.	Code	$\varnothing$ (mm)	Reinforcement Ratio $\mathit{\rho }$ (%)
1	B1	-	-
2	B1-R
3	B2	8	0.54
4	B2-R
5	B3	10	0.84
6	B3-R
7	B4	12	1.21
8	B-R
9	B5	16	2.14
10	B5-R
11	B6	20	3.35
12	B6-R

lists the details of the beam’s bars and their percentages of reinforcement. In the current investigation, the key variable between the various beam sets was the percentage of the tensile reinforcement. The maximum employed percentage of reinforcement was designed to be less than the balance threshold (${\rho }_b$), which was calculated by following Equation (1), which has been recently proposed by Yao et al. [39] for singly reinforced beams. It is noteworthy that the balance failure is a state of simultaneous concrete compressive and steel tensile strains approaching the crushing and yielding thresholds, respectively.

$${\rho }_b=\frac{2\mu \left[{\lambda }_{cu}\left(\alpha -1\right)+\alpha -\psi \right]+\alpha \gamma \psi \left(2{\lambda }_{cu}-\omega \right)-\alpha }{2n\psi \left({\lambda }_{cu}+\psi \right)}.$$

(1)

where,

$\mu$	:	${\sigma }_p/{\sigma }_{cr}$ (a normalized residual tensile strength of the UHPC);
${\lambda }_{cu}$	:	UHPC’s peak compressive strain;
$\alpha$	:	$d/h$;
$\psi$	:	${\epsilon }_{sy}/{\epsilon }_{cr}$ (a normalized yielding strain of steel);
$\gamma$	:	$E_c/E$ (UHPC’s normalized compressive modulus);
$\omega$	:	${\epsilon }_{cy}/{\epsilon }_{cr}$ (UHPC’s normalized compressive yielding strain);
$n$	:	$E_s/E$ (modular ratio);
${\sigma }_p$	:	residual tensile strength of UHPC;
${\sigma }_{cr}$	:	UHPC’s cracking stress;
${\epsilon }_{sy}$	:	yielding strain of steel;
${\epsilon }_{cr}$	:	UHPC’s cracking strain;
$E_s$	:	steel Young’s modulus;
$E_c$	:	UHPC’s Young’s modulus of concrete unr compression;
$E$	:	UHPC’s Young’s modulus of concrete under tension;
$d$	:	beam’s effective depth; and
$h$	:	beam’s overall depth.

In the preliminary design of the UHPC beams, the material properties presented in [12] (with elasticity modulus and compressive and tensile strengths of 46.4 GPa, 194 MPa, and 30.6 MPa, respectively) were selected due to their proximity to the current investigation. Therefore, the previous material and structural parameters were taken as $\mu =0.55$, ${\lambda }_{cu}=11.7$, $\alpha =0.83$, $\psi =11.7$, $\omega =11.2$, $n=4.55$, and $\gamma =1.0$ Hence, ${\rho }_b$ of practically 4.1% was calculated for the UHPC beams of this investigation.

2.2.3. Testing Details

Material Properties

The compressive strength of the UHPC samples was determined using a universal compression testing machine [Instron (Norwood, MA, USA), with a capacity of 3000 kN, Figure 3a]. This test was accomplished in compliance with ASTM C109 specifications of a constant loading rate of 0.2 MPa/s. The test control unit is shown in Figure 3b. It is worth noting that previous studies on the compressive behavior of UHPC using the ASTM C109 standard and cubic specimens have shown closely comparable results to the response obtained by the ASTM C39 by employing cylindrical specimens. Accordingly, the cubic concrete samples that do not require preparation of their ends have the potential to effectively substitute for the cylindrical ones [40].

The flexural test (Figure 3c,d) was conducted according to ASTM C1609. Beneath the sample, two linear variable differential transformers [LVDTs, Tokyo Sokki, model FDP 50A with 300 × 10⁻⁶ strain/mm sensitivity (Tokyo, Japan)] were installed to measure the mid-span displacement of the samples during the test. Moreover, a 30 kN universal testing machine [INSTRON, Model 3367 (Norwood, Massachusetts, US)] was employed to conduct the flexural test at a loading rate of 0.2 mm/min. It worth noting that the two LVDTs were connected to a data acquisition system (Tokyo Sokki, model TDS-630 with a speed of 1000 channels in 0.1 s) to synchronize and acquire the test data. The compressive and flexural tests were conducted on UHPC samples with and without fibers (UHPC-C) for comparison purposes.

In the current research, the mechanical properties of the steel bars were evaluated by performing the uniaxial tensile test using 600 mm (length) specimens as per ASTM A370 specifications. The test was conducted under displacement-controlled conditions at a rate of 0.0187 mm/s. From this test, the stress–strain behavior of the high-strength steel was obtained and utilized to evaluate the material’s yield strength and Young’s modulus. It is worth noting that the result for the earlier material tests represents the average of three samples.

Structural Response

In the current investigation, the structural behavior of the control and reinforced UHPC beams (Figure 2 and Table 5) was investigated under four-point loading conditions. The test’s schematic diagram is shown in Figure 4a. This test was performed by utilizing Toni Technik’s servo-controlled hydraulic universal testing machine (Model 2073, 3000-kN capacity). The instrumentation during the test included three strain gauges (Figure 4b) attached to the specimen’s top and front faces to measure the strain response of concrete. Two strain gauges were additionally attached to the embedded reinforcement of B2–B6 in order to acquire the tensile strain of steel bars.

Moreover, two linear variable differential transformers (LVDTs—Tokyo Sokki, model FDP 50A with 300 × 10⁻⁶ strain/mm sensitivity) (Figure 4b) were attached at the specimen’s mid-span to obtain its real-time mean defection. Moreover, two horizontal/inclined LVDTs were fixed to measure the crack width after its initiation. In the current experimental testing, displacement-controlled loading conditions were applied at a rate of 0.4 mm/min to the beam’s top surface (Figure 4a) until final failure. It is worth mentioning that all the earlier-described accessories (LVTDs, strain gauges, and load cell) were synchronized to a data acquisition system (Tokyo Sokki, model TDS-630 with a speed of 1000 channels in 0.1 s) to gain the test data. Additionally, high-resolution photographs were taken for the 12 beams after the accomplishment of each test to assess their failure pattern.

2.2.4. Prediction of the Ultimate Moment Capacity

In the current research, an ACI 544-based approach [41] was used to predict the ultimate moment capacity of hybrid fiber-reinforced UHPC beams. This method is, however, initially recommended for conventional fiber-reinforced concrete. This method employs uniform tensile and compressive stress blocks. In this prediction model, the tensile properties of the UHPC were evaluated in terms of the fiber’s characteristics and fiber–matrix bonding strength. The fundamentals of this approach have been employed by different investigators [10,31,35,36,37,38] for calculating the capacity of singly reinforced beams prepared by fiber-reinforced concrete. The ultimate load of the beam was predicted based on the assumption that it is governed by the yielding of reinforcement bars.

Moreover, the idealization of the sectional compression and tensile stress distributions by the uniform stress blocks was adopted in this approach (Figure 5). In ACI 544 [41], the uniform tensile stress is evaluated by Equation (1). This equation assumes that the composite’s tensile strength ($f_{t_1}^{\prime }$) is a function of the fiber-matrix bonding strength. It is noteworthy that this strength (${\tau }_f$) has been assumed by the ACI 544 [41] as 2.3 MPa for conventional fiber-reinforced concrete. Generally, ${\tau }_f$ is in the range of 1 to 9 MPa for normal and high-strength concrete and various fibrous configurations [42]. Imam et al. [38] have employed a fiber–matrix interfacial shear strength of 4.15 MPa for high-performance concrete, as suggested by Al-Ta’an [43]. The factor of $7.72\times {10}^{-3}$ in Equation (2) was thus increased to $20\times {10}^{-3}$ in Equation (3). For UHPC beams, Khalil and Tayfur [37] adjusted Equations (2)–(4), where ${\tau }_f$ was adopted as 7.7 MPa for UHPC with a mean compressive strength of 136 MPa. It is worth noting that this adjustment (Equation (4)) was recently employed by Turker et al. [10], when they assumed ${\tau }_f$ as 8.15 MPa for hybrid fiber-reinforced UHPC beams. In the current study, ${\tau }_f$ was taken as 3.7 MPa, due to the use of hybrid smooth fibers.

$$f_{t_1}^{\prime }=7.72\times {10}^{-3}\left[a_f{\rho }_f{F}_{be}\right]$$

(2)

$$f_{t_2}^{\prime }=20\times {10}^{-3}\left[a_f{\rho }_f{F}_{be}\right].$$

(3)

$$f_{t_3}^{\prime }=0.85\left[a_f{\rho }_f{\tau }_f\right]$$

(4)

where,

$a_f$	=	the fiber’s aspect ratio (= $l_f/d_f$), and $l_f$ and $d_f$ are the fiber’s length and diameter, respectively;
${\rho }_f$	=	the content of fiber (vol.); and
$F_{be}$	=	the fiber–matrix bonding efficiency factor.

In the current investigation, the tensile strength of the UHPC was predicted by Equation (5), originally developed by Ahmed and Pama [44] and then adopted by Kahlil and Tayfur [37] and Turker et al. [10]. This formula (Equation (5)) accounts for the different fiber properties (e.g., dispersion, cohesion, dosage, etc.). In this equation, the efficiency coefficients ${\zeta }_o$, ${\zeta }_b$, and ${\zeta }_l$ stand for the fiber’ dispersion, bond, and length, considered as 0.86, 1.0, and 0.41, respectively [10,41,45,46]. It is noteworthy that these coefficients do not depend on the concrete strength class, but rely on the properties of the fibrous reinforcement. According to ACI 544 [41], the tensile stress distribution starts at a distance $e$ from the sectional extreme compression fiber (Figure 5) to the ultimate fibrous strain position. This distance can be estimated using Equation (6), in which ${\epsilon }_s{}_{\left(\mathrm{fiber}\right)}$ is the fiber’s strain that is conventionally determined from a single-fiber pullout test (assumed as 0.0015 in this study). The former equations were basically developed for the mono-fibrous system. Thus, for UHPC with hybrid fibers, the fibers’ lumping coefficients were adopted (Equations (7) and (8)). In these equations, $l_{f_i}$, $d_{f_i}$, and $V_{f_i}$ represent the fibers’ length, diameter, and volume fraction for fiber $i$, respectively.

$$f_t^{\prime }=2{\zeta }_o{\zeta }_b{\zeta }_l{V}_f{\tau }_f{a}_f.$$

(5)

$$e=\frac{c[{\epsilon }_s{}_{\left(\mathrm{fiber}\right)}+0.004]}{0.004}.$$

(6)

$$l_f={\displaystyle \sum }_{i=1}^3{l}_{f_i}\left(\frac{V_{f_i}}{V_f}\right).$$

(7)

$$d_f={\displaystyle \sum }_{i=1}^3{d}_{f_i}\left(\frac{V_{f_i}}{V_f}\right).$$

(8)

In the current investigation, an MS Excel sheet was developed for the prediction of the ultimate moment capacity of the UHPC beams by applying the following steps ((a)–(c)). The program’s solver added application (add-ins) was used to preserve the equilibrium of tensile and compressive forces ($F_c=F_f+F_s$ (Equations (8)–(10)).

(a)

The concrete’s tensile strength ($f_t^{\prime })$ was predicted using Equations (5)–(8).

(b)

The depth of the sectional neural axis $\left(c\right)$ was calculated by the governing equilibrium condition of Equations (9)–(11).

(c)

The ultimate moment capacity was calculated by taking moments around the sectional neutral axis (Equation (12)).

$$F_c=0.65\left(0.85f_c^{\prime }\right)bc$$

(9)

$$F_f=f_t^{\prime }\left(h-e\right)b$$

(10)

$$F_s=A_s{f}_y$$

(11)

$$M_u=F_c\left(\frac{c}{2}\right)+F_f\left(h-\frac{e}{2}\right)+F_s\left(d-\frac{c}{2}\right)$$

(12)

3. Results and Discussion

3.1. Material Properties

The observed average 28-day compressive strength of UHPC mixes (Table 4) with and without fibers (UHPC-C) under normal curing conditions were 143 and 188 MPa, respectively. Figure 6 shows the flexural load–displacement details for the plain and fiber-reinforced UHPC. This figure illustrates the significant contribution of the hybrid system of fiber on the strength and entire deformability of the concrete mix. Accordingly, the calculated mean flexural strengths for UHPC-C and UHPC were 4.3 and 15.2 MPa, respectively. Additionally, the uniaxial testing of steel bars showed that the ultimate yield strength and Young’s modulus of the employed steel bars for longitudinal reinforcement of beams were 520 MPa and 210 GPa, respectively. Here, the tensile strength of the UHPC was calculated as 5.07 MPa using Equation (5).

3.2. Structural Response

3.2.1. Load–Defection Curves

The load–deflection responses of B1–B6 and their replicas are presented in Figure 7, obtained from the four-point loading test (described in Section 2.2.3). For all beams, this figure demonstrated that repeatability of acceptable results has been accomplished, as close curves were obtained for the duplicated specimens. Figure 7 demonstrated that increasing the amount of tensile reinforcement in the UHPC beams could increase the load-bearing capacity and change the failure pattern from brittle to ductile. In this context, B6 (Figure 7f) represents a typical reinforced concrete beam behavior. According to this finding, fibers are likely of marginal importance in accelerating the load-bearing of shear-deficient UHPC beams.

Figure 8a displays a comparison of the representative load–deflection curves for the tested UHPC beams. As expected, for the beams with low reinforcement percentages (0–0.84% (B1–B3)), a sudden brittle flexural failure was observed. However, the use of the medium to high $\rho$ (1.21–3.35% (B4–B6)) altered this failure behavior to semi-ductile to ductile ones. Figure 8a also shows the loading and energy absorption capacities (especially after yielding the bar reinforcement), as would be anticipated. Moreover, the ultimate midspan deflection of the UHPC beams with low reinforcement percentages (B1–B3) was almost constant (about 8 mm) and increased as their reinforcing content increased; however, it notably increased as it reached higher reinforcement levels (B4 to B6). This displacement response could be attributed to the brittle behavior of the first three beams (failure occurred right after the ultimate loading) compared to the improved deformability of the latter beams. Figure 8b shows the relation between the beam’s ultimate load and reinforcement ratio. The trend of this relation was fairly linear, with a 96% confidence level (coefficient of correlation).

3.2.2. Moment–Curvature Curves

In the current experimental program, the moment–curvature ($M-\varnothing$) curves were also analyzed taking into consideration the pure flexural region of the beam, while Equations (13) and (14) were used to calculate the corresponding curvature ($\varnothing$) values. In these equations, ${\epsilon }_{c_1}$ and ${\epsilon }_{c_3}$ are the concrete’s peak compressive strain at 0.02 m from the top of the beam (obtained through the experiment from the concrete’s top strain gauges, Figure 4) and $c$ = the depth of the sectional neutral axis (in meters).

$$c=\frac{0.020}{\left[1-\frac{{\epsilon }_{c_3}}{{\epsilon }_{c_1}}\right]}$$

(13)

$$\varnothing =\frac{{\epsilon }_{c_1}}{c}$$

(14)

By applying the above formulas, Figure 9 shows the $M-\varnothing$ behavior of B1–B6. The moment–curvature for B6 had a premature termination due to the crushing of the extremely stressed UHPC (at top face). It is worth noting that the calculation of the beam’s strains was not attainable if cracks extended to the beam’s top surface, as they disturb the measurement of the concrete strains. This issue could be handled by the use of horizontal LVDTs for curvature measurements.

Figure 10a depicts a representative moment–curvature response for B1–B6. This figure demonstrated that all bar-reinforced beams, except B6, were likely under-reinforced (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. The relation between the moment capacity and bar reinforcement ratio is presented in Figure 10b. This figure shows the robust linearity of this relation (with a 99% correlation coefficient).

3.2.3. Ductility Analysis

The ductility property of a structural element is an important factor that reveals its reliability. This property can be described as the capability of a structural element to plastically resist loading between its yield to ultimate points [47]. The evaluation of the yield point can be made by graphical and equivalent toughness approaches [48].

In the current study, the deflection (${\mu }_D$) and curvature ductility parameters were calculated to investigate the ductility behavior of beams with different $\rho$. Here, ${\mu }_D$ was evaluated as the ratio of the ultimate deflection (${\delta }_u$) to yield deflection (${\delta }_y$). The beam’s load–deflection curves were employed to estimate these deflections. According to the widely used approach [49,50,51], a straight line was created between the origin point and 50% of the ultimate load ($P_u$) that extended to 80% $P_u$, as depicted in Figure 11a. The deflection at this load (0.8 $P_u$) was defined as involving the beam’s yield of reinforcement (${\delta }_y$), while defection corresponds to the same load but on the descending branch, which was assumed to be equal to the ultimate deflection, ${\delta }_u$ The rationale for this assumption is that all UHPC beams exhibited flexural stability issues when the strength of the beams reduced by 20% $P_u$ after the ultimate load.

Figure 11b shows the method for evaluating the curvature ductility ($\mu$), which is an energy-based approach. Here, $\mu$ was calculated by Equation (15). This method has been employed by various investigators (e.g., [48]) in the past.

$$\mu =\frac{A_u}{A_y}=\frac{0.375M_u{\varnothing }_y+0.875M_u\left({\varnothing }_u-{\varnothing }_y\right)}{0.375M_u{\varnothing }_y}$$

(15)

Table 6. Ductility analysis of the reinforced UHPC beams.

Beam	Deflection Ductility				Curvature Ductility
	$\delta$ (mm)		${\mu }_D$		$M_u$ (kNm)		$\varnothing$ (×10−6/mm)		$\mu$
	${\delta }_y$	${\delta }_u$	$=\frac{{\delta }_u}{{\delta }_y}$	Average ${\mu }_D$	$M_u$	Average	${\varnothing }_y$	${\varnothing }_u$	Equation (15)	Average
B1	1.094	3.882	3.548	3.226	16.5	16.7	28.0	105.2	7.429	6.3
B1-R	1.040	3.020	2.904		16.9		28.5	79.4	5.167
B2	1.385	4.41	3.184	3.340 (+3.5%)	21.9	23.1 (+38.1%)	27.2	178.3	13.948	9.3 (+47.7%)
B2-R	1.440	5.035	3.497		24.3		76.2	195.6	4.660
B3	1.178	4.295	3.646	3.749 (+16.2%)	24.8	25.1 (+50.3%)	29.8	92.8	5.923	4.2 (−32.6%)
B3-R	1.324	5.099	3.851		25.3		34.6	57.9	2.567
B4	1.641	6.181	3.767	3.293 (+2.1)	29.8	30.3 (+81.7)	36.2	163.9	9.238	7.6 (+20.5%)
B4-R	1.662	4.687	2.820		30.8		39.3	122.5	5.941
B5	1.838	17.556	9.552	7.460 (+131.2)	41.7	42.4 (+154.1)	34.2	149.7	8.868	12.2 (+94.5)
B5-R	2.053	11.02	5.368		43.1		28.9	209.9	15.626
B6	2.051	27.201	13.262	14.536 (+350.6)	50.7	48.6 (+191.0%)	30.5	83.1	5.028	6.1 (−3.6)
B6-R	1.885	29.803	15.811		46.5		38.7	140.3	7.119

summarizes the results of the performed ductility analysis of the UHPC beams. This table shows that the percentage difference of ${\mu }_D$ for the duplicated samples were between 1.95% and 11.12%; it was in the range of 30.44% to 76.21 for $\mu$. The relatively high percentage difference for $\mu$ was likely due to the bilinearization assumptions of the $M-\varnothing$ curve, as it exhibited high material nonlinearity. With respect to the control beam, the means of ${\mu }_D$ and $\mu$ for the two duplicated samples of each beam set were evaluated (as given in parenthesis in Table 6) to emphasize the influence of $\rho$ on the ductility of UHPC beams. This table suggested that as $\rho$ increases, the ${\mu }_D$ exponentially increases (Figure 12). Table 6 illustrates that both B3 and B4 had inferior curvature ductility with respect to B1. The reason for this phenomenon would be the quick closure of the $M-\varnothing$ curve for these beams due to compressive failure of their concrete at top surface or tensile failure of bars prior to achieving high ductility.

3.2.4. Load–Crack Opening Curves

The cracking response of a concrete structural member plays a significant role in its survivability state. The serviceability phase is related to the crack propagation stage when the service loading is less than the yielding one of the UHPC elements. Figure 13 displays the load vs. the maximum crack width for all investigated UHPC beams, after the initiation of the crack propagation stage. As expected, the load–cracking response of the UHPC beams becomes very similar to the descending branch of the load–deflection curve (Figure 7). Additionally, this figure demonstrated that increasing $\rho$ notably decreases the crack opening width of the UHPC beams at the same service loading. It is worth noting that this finding is inconsistent with that reported by Qiu et al. [52]. Another significant observation is that increasing the bar reinforcement ratio contributed to stabilizing the crack propagation, as the slope of the UHPC beam’s load–crack curve increases as its bar reinforcement increases. In other words, the initiation and development of cracking are considerably delayed as the tensile continuous reinforcement of the beam increases. A similar pattern of results was obtained in [53].

3.2.5. Crack Pattern and Failure Modes

Figure 14 indicates the experimental cracking pattern of the control and bar-reinforced UHPC beams. This figure depicts that increasing the bar reinforcement percentages notably enhances the deformability of the UHPC beams. Moreover, the significant cracks of these beams were observed at loading levels close to their ultimate loads; however, B3 and B6 are exceptions. As discussed in Section 3.2.2 and Section 3.2.3, the reason behind this behavior was likely due to the concrete’s compressive failure that expedited the major crack development. Typically, the beginning of the pullout process of the fibers from the UHPC matrix initiates the failure mechanism of the UHPC beams [54]. The existence of bar reinforcement helps to enhance the failure pattern as more flexure shear cracks were observed as its presence increased. The flexure cracks were introduced at the beam’s bottom surface and near its midspan and then extended along at an angle of 60°–90°. These cracks were the main cause of failure for all beams; nevertheless, flexure shear cracks were observed in moderately reinforced beams. The failure mode of B3 (with 0.81% of bar reinforcement) was due to tensile failure of reinforcement bars, which is possibly due to the higher bond with the UHPC that decreases the length of the plastic hinge and increases the stress concentration in the bars. Moreover, the concrete crushing at the top surface of the midspan of B6 ($\rho =$ 3.35%) was accompanied by its flexure mode of failure, which could be attributed to the reinforcement ratio of this beam approaching the balanced threshold (${\rho }_b$, as given in Section 2.2.2). It is worth noting that the load–deflection curves and failure pattern of B6 (the beam with larger diameters) indicate that no damage was caused by bar slippage.

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. Prediction data of the UHPC beams.

Beam	${\mathit{A}}_{\mathit{s}}$ (mm2)	$\mathit{e}$ (mm)	$\mathit{c}$ (mm)	${\mathit{F}}_{\mathit{c}}$ (kN)	${\mathit{F}}_{\mathit{f}}$ (kN)	${\mathit{F}}_{\mathit{s}}$ (kN)	Moment Capacity (kNm)		${\mathit{M}}_{\mathit{p}}/{\mathit{M}}_{\mathit{o}}$
							Tested $\left({\mathit{M}}_{\mathit{o}}\right)$	Predicted $\left({\mathit{M}}_{\mathit{p}}\right)$
B1	-	7.266	5.284	108.9	108.9	-	16.700	16.232	0.972
B2	100.5	12.450	7.697	158.7	106.4	52.3	23.100	22.236	0.963
B3	157.1	12.450	9.055	186.7	105.0	81.7	25.100	25.778	1.027
B4	226.2	14.731	10.714	220.9	103.2	117.6	30.300	29.980	0.989
B5	402.1	20.538	14.937	307.9	98.8	209.1	42.400	40.926	0.965
B6	628.3	28.003	20.366	419.8	93.1	326.7	48.600	54.451	1.120
								Means	1.006
								Std.	0.052

. 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 $L_f=$15.123 mm, $V_{f_1}=$1.934%, $V_{f_2}=$0.548%, $V_{f_3}=$0.097%, $V_f=$2.578%, $L_f=$ 15.126 mm, $d_f=$0.2 mm, and ${\epsilon }_f=$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 $\rho$ failed by a sudden brittle flexural failure; however, the beams with medium to high $\rho$ 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, ${\mu }_D$ and $\mu$ were calculated to investigate the ductility behavior of UHPC beams with different $\rho$ 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 $\mu$ was likely due to the bilinearization hypothesis of the $M-\varnothing$ curve. Moreover, it was concluded that as $\rho$ increases, the ${\mu }_D$ exponentially increases; however, the relation between $\rho$ and $\mu$ 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 $\rho$ 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.