Behavior of Non-Shear-Strengthened UHPC Beams under Flexural Loading: Influence of Reinforcement Percentage
Behavior of Non-Shear-Strengthened UHPC Beams under Flexural Loading: Influence of Reinforcement...
Khan, Mohammad Iqbal;Fares, Galal;Abbas, Yassir M.;Alqahtani, Fahad K.
2021-11-30 00:00:00
applied sciences Article Behavior of Non-Shear-Strengthened UHPC Beams under Flexural Loading: Influence of Reinforcement Percentage Mohammad Iqbal Khan * , Galal Fares , Yassir M. Abbas and Fahad K. Alqahtani Department of Civil Engineering, King Saud University, Riyadh 800-11421, Saudi Arabia; galfares@ksu.edu.sa (G.F.); yabbas@ksu.edu.sa (Y.M.A.); bfahad@ksu.edu.sa (F.K.A.) * Correspondence: miqbal@ksu.edu.sa; Tel.: +966-1-46-76-920 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 (r) 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 r increases, the deflection ductility exponentially increases. The cracking response of the UHPC beams demonstrated that increasing r 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 Citation: Khan, M.I.; Fares, G.; capacity to the experimentally observed capacity approached 100%. Abbas, Y.M.; Alqahtani, F.K. Behavior of Non-Shear-Strengthened UHPC Keywords: ultra-high-performance concrete (UHPC); moment capacity; RC beams; hybrid fiber; Beams under Flexural Loading: ductility Influence of Reinforcement Percentage. Appl. Sci. 2021, 11, 11346. https:// doi.org/10.3390/app112311346 1. Introduction Academic Editor: Doo-Yeol Yoo Ultra-high-performance concrete (UHPC) is a relatively novel fibrous cementitious Received: 10 October 2021 composite. It is characterized by its ultra-high compressive strength, low water to cement Accepted: 24 November 2021 content (usually less than 25%), superior packing density, impact resistance, flowability, Published: 30 November 2021 and long-lasting characteristics [1–3]. The generally acknowledged minimum compressive strength level of UHPC is 150 MPa. However, it is practical to allow for the broader domain Publisher’s Note: MDPI stays neutral of UHPC’s strengths, as investigators employ various standardized methods for strength with regard to jurisdictional claims in assessment [4]. The compact microstructure of UHPC is obtained by optimizing its packing published maps and institutional affil- density. The latter significantly affects the compressive strength and waterproofness iations. (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 Copyright: © 2021 by the authors. (superplasticizers) [6,7]. Licensee MDPI, Basel, Switzerland. The scientific community has devoted significant efforts to explore the applicability of This article is an open access article UHPC in various structures (e.g., slab on grade, highway bridges, abutments, super-ductile distributed under the terms and structural elements, rehabilitation of existing structures, etc.) [8–10]. UHPC, in addition conditions of the Creative Commons to its superior compressive strength, has a higher Young’s modulus than conventional Attribution (CC BY) license (https:// concrete that enables the design of slender structural elements. The high tensile and flexural creativecommons.org/licenses/by/ strength of UHPC obtained by the inclusion of fibrous systems enable its potential usage in 4.0/). Appl. Sci. 2021, 11, 11346. https://doi.org/10.3390/app112311346 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 11346 2 of 21 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 [16–22]. The guidelines for designing normal concrete structures have been successfully de- veloped by many building codes such as ACI (American Concrete Institute), IBC (Inter- national 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 [23–25]; however, these methods have not yet been adopted in the interna- tional design codes. Additionally, many prediction formulas have been developed that incorporate the inelastic response of UHPC [12,26–30]. These references have been funda- mentally 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 [30–38]. 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 con- taining 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. Appl. Sci. 2021, 11, 11346 3 of 21 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 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 Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 22 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 2. Exp powders erimental was Progr conducted am using a laser diffraction particle size analyzer (LA-950). Microstructural analysis was conducted employing a Versa 3D dual beam field emission 2.1. Materials scanning electron microscope (SEM). Figure 1a depicts the grain size distribution curves Ordinary Portland cement (PC) complying with ASTM C150 specifications was used for PC, FA, and SF, whereas Figure 1b and Table 2 illustrate the particle size distribution as the main constituent for the binder formulated with silica fume (SF) and class F fly ash analysis and physical properties of the employed aggregates. (FA) as supplementary cementitious materials. Table 1 lists the physicochemical proper- ties of the employed types of cement. The specific gravities of PC, SF, and FA were 3.15, Table 1. Physicochemical properties of PC and SCMs. 2.2, and 2.7, respectively. Furthermore, Arabian Peninsula-based sands [characterized as red dune Oxides (RS (%) ) and white (WS)] we PC re employed as fine FA aggregates. The specific SF gravities of RS and WS at saturated surface dry conditions (SSD) were 2.65 and 2.74, respectively. SiO 20.41 55.23 86.20 Al O 5.32 25.95 0.49 2 3 An Axios Max X-ray fluorescence (XRF) machine was utilized to determine the chemical Fe O 4.10 10.17 3.79 2 3 composition of the binder constituting powders. The particle-size distribution (PSD) anal- CaO 64.14 1.32 2.19 ysis of the MgO fine powders was con0.71 ducted using a laser di0.31 ffraction particle size an 1.31 alyzer (LA- SO 2.44 0.18 0.74 950). Microstructural analysis was conducted employing a Versa 3D dual beam field emis- TiO 0.30 - - sion scanning electron microscope (SEM). Figure 1a depicts the grain size distribution Na Oeq 0.10 0.86 2.80 curves for L.O.I. PC, FA, and SF, wherea 2.18 s Figure 1b and Table 5.00 2 illustrate the partic2.48 le size distri- Relative density 3.15 2.70 2.20 bution analysis and physical properties of the employed aggregates. WS RS PC FA SF 0.01 1 100 0.01 0.1 1 10 Particle size (µm) Particle Size (mm) (a) (b) Figure 1. Grain size distribution of (a) types of cement and (b) aggregates. Figure 1. Grain size distribution of (a) types of cement and (b) aggregates. Table 2. Physical properties of RS and WS. Table 1. Physicochemical properties of PC and SCMs. Property RS WS Oxides (%) PC FA SF SiO2 20.41 55.23 86.20 Bulk specific gravity (OD basis) 2.64 2.73 Apparent specific gravity 2.67 2.76 Al2O3 5.32 25.95 0.49 Absorption, % 0.30 0.37 Fe2O3 4.10 10.17 3.79 Fineness modulus (range of 2.3–3.1) 1.11 1.46 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 Passing (%) Passing (%) Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 22 Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 22 Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 22 Table 2. Physical properties of RS and WS. Table 2. Physical properties of RS and WS. Table 2. Physical properties of RS and WS. Property RS WS Property RS WS Property RS WS Bulk specific gravity (OD basis) 2.64 2.73 Bulk specific gravity (OD basis) 2.64 2.73 Bulk specific gravity (OD basis) 2.64 2.73 App Appar arent ent spe specific gr cific gravi avity ty 2.67 2.67 2.76 2.76 Apparent specific gravity 2.67 2.76 Appl. Sci. 2021, 11, 11346 Absorption, % 0.30 4 of 0.37 21 Absorption, % 0.30 0.37 Absorption, % 0.30 0.37 Fi Finene neness ss mo mod dul ulu us s (r (range ange o of 2. f 2.3 3– –3.1) 3.1) 1.11 1.11 1.46 1.46 Fineness modulus (range of 2.3–3.1) 1.11 1.46 In In th this is exp experi erimen mental tal inve investiga stigat tion, ion, a a hyb hybrid rid s system ystem of of th three ree fi fiber bers s ( (designated designated as as A, A, In this experimental investigation, a hybrid system of three fibers (designated as A, 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 B, and C) bright high-carbon and high-performance strength microsteel straight fibers B, and C) bright high-carbon and high-performance strength microsteel straight fibers 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 were used as discontinuous reinforcement of the developed UHPC mixes. The physical were used as discontinuous reinforcement of the developed UHPC mixes. The physical 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. The and mechanical properties (as received) of the microsteel fibers are given in Table 3. The and mechanical properties (as received) of the microsteel fibers are given in Table 3. The and mechanical properties (as received) of the microsteel fibers are given in Table 3. The mix design of the UHPC is detailed in Table 4. It is worth noting that a polycarboxylate mix design of the UHPC is detailed in Table 4. It is worth noting that a polycarboxylate mix design of the UHPC is detailed in Table 4. It is worth noting that a polycarboxylate mix design of the UHPC is detailed in Table 4. It is worth noting that a polycarboxylate eth ether er- -bas based water ed water re reduce ducer r s superpl uperplas astic ticiz ize er r [ [com commer mercially cially reco recogni gnize zed d as as M Mas aster ter Gleni Glenium um ether-based water reducer superplasticizer [commercially recognized as Master Glenium ether-based water reducer superplasticizer [commercially recognized as Master Glenium 51 51 51 (M (Mas aster ter B Bui uil lders ders Solut Soluti ions ons UK UK Ltd Ltd, , Ma Manch nche ester, ster, UK)] UK)] w was as ide ident ntif ifie ied d as as SP SP and and em- em- 51 (Master Builders Solutions UK Ltd, Manchester, UK)] was identified as SP and em- (Master Builders Solutions UK Ltd, Manchester, UK)] was identified as SP and employed ployed in the current study to control the workability of the prepared mixes. This SP had ployed in the current study to control the workability of the prepared mixes. This SP had ployed in the current study to control the workability of the prepared mixes. This SP had in the current study to control the workability of the prepared mixes. This SP had a density 3 3 a density and water content of 1080 kg/m3 and 65.19%, respectively. To this end, the quan- a density and water content of 3 1080 kg/m and 65.19%, respectively. To this end, the quan- a density and water content of 1080 kg/m and 65.19%, respectively. To this end, the quan- and water content of 1080 kg/m and 65.19%, respectively. To this end, the quantity of tity of water contained in the SP was corrected in the calculation of the amount of mixing tity of water contained in the SP was corrected in the calculation of the amount of mixing tity of water contained in the SP was corrected in the calculation of the amount of mixing water contained in the SP was corrected in the calculation of the amount of mixing water water after the water-to-binder ratio was optimized as 0.165. water after the water-to-binder ratio was optimized as 0.165. water after the water-to-binder ratio was optimized as 0.165. after the water-to-binder ratio was optimized as 0.165. Table Table 3. 3. Physi Physic comechanical omechanical pr propertie operties s o of f m micr icros osteel fi teel fibers bers.. Table 3. Physicomechanical properties of microsteel fibers. Table 3. Physicomechanical properties of microsteel fibers. Leng Length th Diame Diamete ter r Uni Unit t W Weigh eight t Tensi Tensile le Length Diameter Unit Weight Tensile Length Diameter Unit Weight Tensile Strength Type Type Type Type 3 3 3 (mm) (µm) (kg/m3) Strength (MPa) (mm (mm) ) ( (µ m) m) (kg/m (kg/m ) ) Str (MPa) ength (MPa) (mm) (µm) (kg/m ) Strength (MPa) A 13 A A 13 13 A 13 200 7850 2600 B 20 200 7850 2600 B 20 200 7850 2600 B B 20 20 200 7850 2600 C 30 C 30 C C 30 30 3 3 Table 4. Mix proportions of the developed UHPC (in kg/m3). Table 4. Mix proportions of the developed UHPC (in kg/m ). Table 4. Mix proportions of the developed UHPC (in kg/m ). Table 4. Mix proportions of the developed UHPC (in kg/m ). Fiber Fiber Fiber PC SF FA WS RS Water SP PC SF FA WS RS Water SP PC SF FA WS RS Water SP Fiber A B C A B C A B C PC SF FA WS RS Water SP A B C 1123.1 239.1 66.1 481.2 160.9 212.7 39.7 151.8 43.0 7.6 1123.1 239.1 66.1 481.2 160.9 212.7 39.7 151.8 43.0 7.6 1123.1 239.1 66.1 481.2 160.9 212.7 39.7 151.8 43.0 7.6 1123.1 239.1 66.1 481.2 160.9 212.7 39.7 151.8 43.0 7.6 2.2. Methods 2.2. Methods 2.2. Methods 2.2.1. Mixing, Casting, and Curing 2.2. 2.2.1. Methods Mixing, Casting, and Curing 2.2.1. Mixing, Casting, and Curing 2.2.1. Mixing, Casting, and Curing In the current study, the UHPC was prepared using a dissolver mixer [MischTechnik, In the current study, the UHPC was prepared using a dissolver mixer [MischTechnik, In the current study, the UHPC was prepared using a dissolver mixer [MischTechnik, UEZ UEZ ZZ ZZ 50 50- -S S with with 95 95 L L c cap apaci acity ty ( (UEZ UEZ M Mis ischt chtechn echni ik k G Gmb mbH, H, Stutt Stuttgart gart, , Germ Germany)] any)]. . F Firs irst tly ly, , 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 UEZ all ZZ th50-S e drywith materials 95 L capacity (PC, FA, (UEZ SF, WS, Mischtechnik and RS) weGmbH, re mixed Stuttgart, for 5 minGermany)]. at high rotati Firstly on spee , d 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 all the (abo dry ut 743 materials rpm) (PC, to achiev FA, SF e th , WS, eir hi and ghest analogy RS) were mixed . Secofor ndly, 5 min the at mix high ing rw otation ater, w speed hich was (about 743 rpm) to achieve their highest analogy. Secondly, the mixing water, which was (about blended 743 rpm) with to SP, achieve and th their e aggreg highest ates’ analogy absorpt . ion Secondly water , were the mixing addedwater during , which mixinwas g for 10 blended with SP, and the aggregates’ absorption water were added during mixing for 10 blended with SP, and the aggregates’ absorption water were added during mixing for 10 blended min unti with l th SP e ,fl and owabi the lity aggr of egates’ the mix absorption was in the ra water nge o wer f 18e 0– adde 220 mm d during . The fmixing lowability forwas min until the flowability of the mix was in the range of 180–220 mm. The flowability was min until the flowability of the mix was in the range of 180–220 mm. The flowability was 10 min meas meas until ured ured the following following flowability th the e of A ASTM STM the mix C C 14 14 was 37. 37. in Afterw Afterw the range ar ard, d, th th of e e 180–220 weighe weighed d mm. hy hybrid brid Thesy sy flowability stem stem of of f fibers ibers measured following the ASTM C 1437. Afterward, the weighed hybrid system of fibers was measured following the ASTM C 1437. Afterward, the weighed hybrid system of was was gradu graduall ally y po poured ured into into th the e wet wet mix mix i in n slight slight dos dosages ages for for i idea deal l diffu diffusi sion on at at a a sl slow ow ro ro- - was gradually poured into the wet mix in slight dosages for ideal diffusion at a slow ro- fibers tation was pace gradually (about pour 371 ed rpm into ) for the2 wet min. mix After in slight the add dos iti ag on esof for fiideal bers, dif the fusion mixing at speed a slowwas tation pace (about 371 rpm) for 2 min. After the addition of fibers, the mixing speed was tation pace (about 371 rpm) for 2 min. After the addition of fibers, the mixing speed was 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 converted to intermediate. This last stage of mixing took 3–8 min to develop satisfactory converted to intermediate. This last stage of mixing took 3–8 min to develop satisfactory 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 homogenization of the UHPC. Eventually, the produced UHPC was poured (in 50 mm homogenization of the UHPC. Eventually, the produced UHPC was poured (in 50 mm 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 layers) into the beam’ molds, which included the pre-placed steel bars. To investigate the layers) into the beam’ molds, which included the pre-placed steel bars. To investigate the layers) into the beam’ molds, which included the pre-placed steel bars. To investigate the com compressive pressive and fl and flexur exural s al stren trength of gth of the UH the UHPC, PC, 50 m 50 mm cubes m cubes and (7 and (75 5 mm mm × × 75 75 mm mm × × 300 300 compressive and flexural strength of the UHPC, 50 mm cubes and (75 mm × 75 mm × 300 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 experi- mental 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 Appl. Sci. 2021, 11, 11346 5 of 21 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 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 (r ), 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. 2m l a 1 + a y + agy 2l w a [ ( ) ] ( ) cu cu r = . (1) 2ny(l + y) cu where, m : s /s (a normalized residual tensile strength of the UHPC); p cr l : UHPC’s peak compressive strain; cu a : d/h; y : # /# (a normalized yielding strain of steel); sy cr Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 22 g : E /E (UHPC’s normalized compressive modulus); w : # /# (UHPC’s normalized compressive yielding strain); cy cr n : E /E (modular ratio); s : residual tensile strength of UHPC; 6 B3-R s : UHPC’s cracking stress; cr 7 B4 # : yielding strain of steel; sy 12 1.21 8 B-R # : UHPC’s cracking strain; cr E : steel Young’s modulus; 9s B5 16 2.14 E : UHPC’s Young’s modulus of concrete unr compression; 10 B5-R E : UHPC’s Young’s modulus of concrete under tension; 11 B6 d : beam’s effective depth; and 20 3.35 12 B6-R h : beam’s overall depth. (a) (b) Figure 2. The details of (a) B1 and (b) B2–B6 (Dimensions are in mm). Figure 2. The details of (a) B1 and (b) B2–B6 (Dimensions are in mm). 2.2.3. Testing Details 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 Material Properties 30.6 MPa, respectively) were selected due to their proximity to the current investiga- The compressive strength of the UHPC samples was determined using a universal tion. Therefore, the previous material and structural parameters were taken as m = 0.55, compression testing machine [Instron (Norwood, MA, USA), with a capacity of 3000 kN, l = 11.7, a = 0.83, y = 11.7, w = 11.2, n = 4.55, and g = 1.0 Hence, r of practically cu Figure 3a]. This test was accomplished in compliance with ASTM C109 specifications of a 4.1% was calculated for the UHPC beams of this investigation. 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 ob- tained by the ASTM C39 by employing cylindrical specimens. Accordingly, the cubic con- crete 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 test- ing 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. Appl. Sci. 2021, 11, 11346 6 of 21 Table 5. Reinforcement details for beam specimens. No. Code Æ (mm) Reinforcement Ratio r (%) 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 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 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. Appl. Sci. 2021, 11, 11346 7 of 21 Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 22 (a) (b) Point load LVDT Concrete prism Two-point support (c) (d) Figure 3. Compressive test (a) machine and (b) control unit. Flexural test (c) schematic diagram and (d) setup (dimensions Figure 3. Compressive test (a) machine and (b) control unit. Flexural test (c) schematic diagram and (d) setup (dimensions are in mm). are in mm). Structural Response Moreover, two linear variable differential transformers (LVDTs—Tokyo Sokki, model FDP 50A with 300 10 strain/mm sensitivity) (Figure 4b) were attached at the speci- In the current investigation, the structural behavior of the control and reinforced men’s mid-span to obtain its real-time mean defection. Moreover, two horizontal/inclined UHPC beams (Figure 2 and Table 5) was investigated under four-point loading condi- LVDTs were fixed to measure the crack width after its initiation. In the current experimental tions. The test’s schematic diagram is shown in Figure 4a. This test was performed by testing, displacement-controlled loading conditions were applied at a rate of 0.4 mm/min utilizing Toni Technik’s servo-controlled hydraulic universal testing machine (Model to the beam’s top surface (Figure 4a) until final failure. It is worth mentioning that all the 2073, 3000-kN capacity). The instrumentation during the test included three strain gauges earlier-described accessories (LVTDs, strain gauges, and load cell) were synchronized to (Figure 4b) attached to the specimen’s top and front faces to measure the strain response a data acquisition system (Tokyo Sokki, model TDS-630 with a speed of 1000 channels in of concrete. Two strain gauges were additionally attached to the embedded reinforcement 0.1 s) to gain the test data. Additionally, high-resolution photographs were taken for the of B2–B6 in order to acquire the tensile strain of steel bars. 12 beams after the accomplishment of each test to assess their failure pattern. Moreover, two linear variable differential transformers (LVDTs—Tokyo Sokki, −6 model FDP 50A with 300 × 10 strain/mm sensitivity) (Figure 4b) were attached at the 2.2.4. Prediction of the Ultimate Moment Capacity specimen’s mid-span to obtain its real-time mean defection. Moreover, two horizontal/in- In the current research, an ACI 544-based approach [41] was used to predict the ulti- clined LVDTs were fixed to measure the crack width after its initiation. In the current mate moment capacity of hybrid fiber-reinforced UHPC beams. This method is, however, experimental testing, displacement-controlled loading conditions were applied at a rate initially recommended for conventional fiber-reinforced concrete. This method employs of 0.4 mm/min to the beam’s top surface (Figure 4a) until final failure. It is worth mention- uniform tensile and compressive stress blocks. In this prediction model, the tensile prop- ing that all the earlier-described accessories (LVTDs, strain gauges, and load cell) were erties of the UHPC were evaluated in terms of the fiber ’s characteristics and fiber–matrix synchronized to a data acquisition system (Tokyo Sokki, model TDS-630 with a speed of bonding strength. The fundamentals of this approach have been employed by different 1000 channels in 0.1 s) to gain the test data. Additionally, high-resolution photographs investigators [10,31,35–38] for calculating the capacity of singly reinforced beams prepared were taken for the 12 beams after the accomplishment of each test to assess their failure by fiber-reinforced concrete. The ultimate load of the beam was predicted based on the pattern. assumption that it is governed by the yielding of reinforcement bars. Appl. Sci. 2021, 11, 11346 8 of 21 Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 22 Strain gauges Center-line of the beam Load-cell LVDT Loading points Support (a) (b) Figure Figure 4. 4. T Testing estingof of beams beams under under four four -point -point loading: loading: (a) (a schematic ) schematic diagram diagraand m and (b)(setup b) setup and and instr inst umentatio rumentatio ns (dimensions ns (dimen- sions are in mm). are in mm). Moreover, the idealization of the sectional compression and tensile stress distributions 2.2.4. Prediction of the Ultimate Moment Capacity by the uniform stress blocks was adopted in this approach (Figure 5). In ACI 544 [41], In the current research, an ACI 544-based approach [41] was used to predict the ulti- the uniform tensile stress is evaluated by Equation (1). This equation assumes that the mate moment capacity of hybrid fiber-reinforced UHPC beams. This method is, however, composite’s tensile strength ( f ) is a function of the fiber-matrix bonding strength. It initially recommended for conventional fiber-reinforced concrete. This method employs is noteworthy that this strength (t ) has been assumed by the ACI 544 [41] as 2.3 MPa uniform tensile and compressive stress blocks. In this prediction model, the tensile prop- for conventional fiber-reinforced concrete. Generally, t is in the range of 1 to 9 MPa for erties of the UHPC were evaluated in terms of the fiber’s characteristics and fiber–matrix normal and high-strength concrete and various fibrous configurations [42]. Imam et al. [38] bonding strength. The fundamentals of this approach have been employed by different have employed a fiber–matrix interfacial shear strength of 4.15 MPa for high-performance investigators [10,31,35–38] for calculating the capacity of singly reinforced beams pre- concrete, as suggested by Al-Ta’an [43]. The factor of 7.72 10 in Equation (2) was pared by fiber-reinforced concrete. The ultimate load of the beam was predicted based on thus increased to 20 10 in Equation (3). For UHPC beams, Khalil and Tayfur [37] the assumption that it is governed by the yielding of reinforcement bars. adjusted Equations (2)–(4), where t was adopted as 7.7 MPa for UHPC with a mean Moreover, the idealization of the sectional compression and tensile stress distribu- compressive strength of 136 MPa. It is worth noting that this adjustment (Equation (4)) tions by the uniform stress blocks was adopted in this approach (Figure 5). In ACI 544 was recently employed by Turker et al. [10], when they assumed t as 8.15 MPa for hybrid [41], the uniform tensile stress is evaluated by Equation (1). This equation assumes that fiber-reinforced UHPC beams. In the current study, t was taken as 3.7 MPa, due to the use the composite’s tensile strength (𝑓 ) is a function of the fiber-matrix bonding strength. It of hybrid smooth fibers. h i is noteworthy that this strength (𝜏 ) has been assumed by the ACI 544 [41] as 2.3 MPa for 0 3 f = 7.72 10 a r F (2) f f be conventional fiber-reinforced concrete. Generally, 𝜏 is in the range of 1 to 9 MPa for nor- h i mal and high-strength concrete and various fibrous configurations [42]. Imam et al. [38] 0 3 f = 20 10 a r F . (3) t f f be have employed a fiber–matrix interfacial shear strength of 4.15 MPa for high-performance h i −3 concrete, as suggested by Al-Ta’an [43]. The factor of 7.72 × 10 in Equation (2) was thus f = 0.85 a r t (4) t f f f −3 3 increased to 20 × 10 in Equation (3). For UHPC beams, Khalil and Tayfur [37] adjusted Equations (2)–(4), where 𝜏 was adopted as 7.7 MPa for UHPC with a mean compressive where, the fiber ’s aspect ratio (= l /d ), and l and d are the fiber ’s length and diameter, strength of 136 MPa. It is worth not f ing f that f this adj f ustment (Equation (4)) was recently a = respectively; employed by Turker et al. [10], when they assumed 𝜏 as 8.15 MPa for hybrid fiber-rein- r = the content of fiber (vol.); and forced UHPC beams. In the current study, 𝜏 was taken as 3.7 MPa, due to the use of F = the fiber–matrix bonding efficiency factor. be hybrid smooth fibers. ′ −3 𝑓 = 7.72 × 10 [𝑎 𝜌 𝐹 ] (2) 𝑡 𝑓 𝑓 𝑏𝑒 Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 22 ′ −3 𝑓 = 20 × 10 [𝑎 𝜌 𝐹 ] (3) 𝑡 𝑓 𝑓 𝑓 = 0.85[𝑎 𝜌 𝜏 ] (4) 𝑡 𝑓 𝑓 𝑓 where, the fiber’s aspect ratio (=𝒍 /𝒅 ), and 𝒍 and 𝒅 are the fiber’s length and di- 𝒇 𝒇 𝒇 𝒇 ameter, respectively; Appl. Sci. 2021, 11, 11346 9 of 21 𝜌 = the content of fiber (vol.); and 𝐹 = the fiber–matrix bonding efficiency factor. Figure 5. Strain and stress profiles. Figure 5. Strain and stress profiles. In the current investigation, the tensile strength of the UHPC was predicted by 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 Equation (5), originally developed by Ahmed and Pama [44] and then adopted by Kahlil and and T T ayfur ayfur[ 37 [37] ] and and TT urker urker etet al al. [.10 [10] ]. This . This formula formul(Equation a (Equation (5)) (5accounts )) account for s for theth dif e di fer ffer- ent fiber ent fipr ber operti propes erties (e.g., (e.g. dispersion, , dispersion cohesion, , cohesion, dosage, dosage, etc.). etc.)In . In this this equation, equation,the the ef efficienc ficiency y coefficients z , z , and z stand for the fiber ’ dispersion, bond, and length, considered as coefficients 𝘁 , 𝘁 , and 𝘁 stand for the fiber’ dispersion, bond, and length, considered as o b l 𝑜 𝑏 𝑙 0.86, 1.0, and 0.41, respectively [10,41,45,46]. It is noteworthy that these coefficients do not 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 reinforce- depend on the concrete strength class, but rely on the properties of the fibrous reinforce- ment. According to ACI 544 [41], the tensile stress distribution starts at a distance e from ment. 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. the sectional extreme compression fiber (Figure 5) to the ultimate fibrous strain position. This distance can be estimated using Equation (6), in which # is the fiber ’s strain that This distance can be estimated using Equation (6), in which (fiber 𝘀 ) is the fiber’s strain (fiber) is conventionally determined from a single-fiber pullout test (assumed as 0.0015 in this that is conventionally determined from a single-fiber pullout test (assumed as 0.0015 in study). The former equations were basically developed for the mono-fibrous system. Thus, this study). The former equations were basically developed for the mono-fibrous system. for UHPC with hybrid fibers, the fibers’ lumping coefficients were adopted (Equations (7) Thus, for UHPC with hybrid fibers, the fibers’ lumping coefficients were adopted (Equa- and (8)). In these equations, l , d , and V represent the fibers’ length, diameter, and f f f i i i tions (7) and (8)). In these equations, 𝑙 , 𝑑 , and 𝑉 represent the fibers’ length, diame- 𝑓 𝑓 𝑓 𝑖 𝑖 𝑖 volume fraction for fiber i, respectively. ter, and volume fraction for fiber 𝑖 , respectively. f = 2z z z V t a . (5) t 𝑓 = 2𝘁 b 𝘁 l 𝘁 f 𝑉 f 𝜏 f𝑎 (5) 𝑡 𝑜 𝑏 𝑙 𝑓 𝑓 𝑓 𝑐 [𝘀 + 0.004] c[# + 0.004] (fiber) (fiber) (6) 𝑒 = e = . (6) 0.004 0.004 V 𝑉 f 𝑓 i 𝑖 l = 𝑙 = ∑ l 𝑙 ( .) (7) (7) f 𝑓 å f 𝑓 i 𝑖 V 𝑉 f 𝑓 i=1 𝑖 =1 d = d . (8) f å f (8) 𝑑 = ∑ 𝑑 ( ) 𝑓 𝑓 f 𝑉 i=1 𝑖 =1 In the current investigation, an MS Excel sheet was developed for the prediction of the In the current investigation, an MS Excel sheet was developed for the prediction of ultimate moment capacity of the UHPC beams by applying the following steps ((a)–(c)). the ultimate moment capacity of the UHPC beams by applying the following steps ((a)– The program’s solver added application (add-ins) was used to preserve the equilibrium of (c)). The program’s solver added application (add-ins) was used to preserve the equilib- tensile and compressive forces (F = F + F (Equations (8)–(10)). c s rium of tensile and compressive forces (𝐹 = 𝐹 + 𝐹 (Equations (8)–(10)). 𝑐 𝑓 𝑠 (a) The concrete’s tensile strength ( f ) was predicted using Equations (5)–(8). (a) The concrete’s tensile strength (𝑓 ) was predicted using Equations (5)–(8). (b) The depth of the sectional neural axis c 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 = 0.65 0.85 f bc (9) F = f (h e)b (10) F = A f (11) s s y 𝑏𝑒 𝑏𝑒 Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 22 (b) The depth of the sectional neural axis (𝑐 ) was calculated by the governing equilib- rium condition of Equations (9)–(11). (c) The ultimate moment capacity was calculated by taking moments around the sec- tional neutral axis (Equation (12)). ( ) 𝐹 = 0.65 0.85𝑓 (9) 𝑐 𝑐 𝐹 = 𝑓 (ℎ − 𝑒 )𝑏 (10) 𝑓 𝑡 𝐹 = 𝐴 𝑓 (11) 𝑠 𝑠 𝑦 Appl. Sci. 2021, 11, 11346 10 of 21 𝑐 𝑒 𝑐 𝑀 = 𝐹 ( ) + 𝐹 (ℎ − ) + 𝐹 (𝑑 − ) (12) 𝑢 𝑐 𝑓 𝑠 2 2 2 c e c M = F + F h + F d (12) u c s 2 2 2 3. Results and Discussion 3. Results and Discussion 3.1. Material Properties 3.1. Material Properties The observed average 28-day compressive strength of UHPC mixes (Table 4) with 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, 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- respectively. Figure 6 shows the flexural load–displacement details for the plain and reinforced UHPC. This figure illustrates the significant contribution of the hybrid system fiber-reinforced UHPC. This figure illustrates the significant contribution of the hybrid of fiber on the strength and entire deformability of the concrete mix. Accordingly, the cal- system of fiber on the strength and entire deformability of the concrete mix. Accordingly, culated mean flexural strengths for UHPC-C and UHPC were 4.3 and 15.2 MPa, respec- the calculated mean flexural strengths for UHPC-C and UHPC were 4.3 and 15.2 MPa, tively. Additionally, the uniaxial testing of steel bars showed that the ultimate yield 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 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 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). was calculated as 5.07 MPa using Equation (5). 30 30 UHPC-C#1 UHPC#1 UHPC-C#2 UHPC#2 25 25 UHPC-C#3 UHPC#3 20 20 15 15 10 10 5 5 0 0 0 2 4 6 8 0 2 4 6 8 Mid-span Deflection (mm) Mid-span Deflection (mm) (a) (b) Figure 6. Flexural load displacement response: (a) UHPC-C, (b) UHPC. Figure 6. Flexural load displacement response: (a) UHPC-C, (b) UHPC. 3.2. Structural Response 3.2. Structural Response 3.2.1. Load–Defection Curves 3.2.1. Load–Defection Curves The load–deflection responses of B1–B6 and their replicas are presented in Figure 7, 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 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 figure demonstrated that repeatability of acceptable results has been accomplished, as curves were obtained for the duplicated specimens. Figure 7 demonstrated that increasing close curves were obtained for the duplicated specimens. Figure 7 demonstrated that in- the amount of tensile reinforcement in the UHPC beams could increase the load-bearing creasing the amount of tensile reinforcement in the UHPC beams could increase the load- 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 r (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, Load (kN) Load (kN) 𝑏𝑐 Appl. Sci. 2021, 11, 11346 11 of 21 Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 22 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 bearin after g capa the city ultimate and chang loading) e the fcompar ailure patt ed ern to the from impr britt oved le todeformability ductile. In this ofco the ntext latter , B6 beams. (Figure Figur 7f) ree present 8b shows s a ty the pica relation l reinfo between rced conthe cretbeam’s e beam ultimate behaviorload . Accor and ding reinfor to th cement is find- ratio. ing, fiThe bers tr ar end e liof kely this of rmar elation gina was l impo fairly rtan linear ce in , with acceler a 96% ating confidence the load-bear level ing (coef of sh ficien ear- tde- of corr ficient UH elation). PC beams. 500 500 500 B1 B2 B3 B2-R 400 B1-R 400 400 B3-R 300 300 200 200 100 100 0 0 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32 Deflection (mm) Deflection (mm) Deflection (mm) (a) (b) (c) 500 500 500 B4 B5 B4-R 400 400 400 B5-R 300 300 300 200 200 200 B6 100 100 100 B6-R 0 0 0 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32 Deflection (mm) Deflection (mm) Deflection (mm) (d) (e) (f) Figure 7. Load–deflection responses of (a) B1, (b) B2, (c) B3, (d) B4, (e) B5, and (f) B6. Figure 7. Load–deflection responses of (a) B1, (b) B2, (c) B3, (d) B4, (e) B5, and (f) B6. Figure 8a displays a comparison of the representative load–deflection curves for the 3.2.2. Moment–Curvature Curves tested UHPC beams. As expected, for the beams with low reinforcement percentages (0– In the current experimental program, the moment–curvature (M ?) curves were 0.84% (B1–B3)), a sudden brittle flexural failure was observed. However, the use of the also analyzed taking into consideration the pure flexural region of the beam, while Equa- medium to high 𝜌 (1.21–3.35% (B4–B6)) altered this failure behavior to semi-ductile to tions (13) and (14) were used to calculate the corresponding curvature (?) values. In these ductile ones. Figure 8a also shows the loading and energy absorption capacities (especially equations, # and # are the concrete’s peak compressive strain at 0.02 m from the top of c c after yielding the bar reinforcement), as would be anticipated. Moreover, the ultimate 1 3 the beam (obtained through the experiment from the concrete’s top strain gauges, Figure 4) midspan deflection of the UHPC beams with low reinforcement percentages (B1–B3) was and c = the depth of the sectional neutral axis (in meters). almost constant (about 8 mm) and increased as their reinforcing content increased; how- ever, it notably increased as it reached higher reinforcement levels (B4 to B6). This dis- 0.020 h i placement response could be attribute c = d to the brittle behavior of the first three be(13) ams (failure occurred right after the ultimate loading) compared to the improved deformabil- ity 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 ? = (14) level (coefficient of correlation). By applying the above formulas, Figure 9 shows the M ? 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. Load (kN) Load (kN) Load (kN) Load (kN) Load (kN) Load (kN) Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 22 B1 B2 𝑃 = 86.3𝜌 + 156.1 200 𝑢 B3 B4 B5 B6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 4 8 12 16 20 24 28 32 Reinforcement ratio (%) Deflection (mm) (a) (b) Figure 8. (a) Load–deflection of beams and (b) peak load-reinforcement ratio relation. Appl. Sci. 2021, 11, 11346 12 of 21 Appl. Sci. 2021, 11, x FOR PEER REVIEW 3.2.2. Moment–Curvature Curves 12 of 22 In the current experimental program, the moment–curvature (𝑀 − ∅) curves were also analyzed taking into consideration the pure flexural region of the beam, while Equa- tions (13) and (14) were used to calculate the corresponding curvature (∅) values. In these equations, 𝘀 and 𝘀 are the concrete’s peak compressive strain at 0.02 m from the top 𝑐 𝑐 1 3 of the beam (obtained through the experiment from the concrete’s top strain gauges, Fig- ure 4) and 𝑐 = the depth of the sectional neutral axis (in meters). 0.020 𝑐 = (13) [1 − ] B1 B2 𝑃 = 86.3𝜌 + 156.1 200 1 𝑢 B3 ∅ = (14) B4 B5 By applying the above formulas, Figure 9 shows the 𝑀 − ∅ behavior of B1–B6. The B6 moment–curvature for B6 had a premature termination due to the crushing of the ex- 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 4 8 12 16 20 24 28 32 tremely stressed UHPC (at top face). It is worth noting that the calculation of the beam’s Reinforcement ratio (%) Deflection (mm) strains was not attainable if cracks extended to the beam’s top surface, as they disturb the (a) (b) measurement of the concrete strains. This issue could be handled by the use of horizontal LVDTs for curvature measurements. Figure 8. (a) Load–deflection of beams and (b) peak load-reinforcement ratio relation. Figure 8. (a) Load–deflection of beams and (b) peak load-reinforcement ratio relation. 60 60 3.2.2. Moment–Curvature Curves B3 B1 B2 50 B3-R 50 50 In the current experimental program, the moment–curvature (𝑀 − ∅) curves were B2-R B1-R also analyzed taking into consideration the pure flexural region of the beam, while Equa- 40 40 tions (13) and (14) were used to calculate the corresponding curvature (∅) values. In these 30 30 equations, 𝘀 and 𝘀 are the concrete’s peak compressive strain at 0.02 m from the top 𝑐 𝑐 1 3 20 20 20 of the beam (obtained through the experiment from the concrete’s top strain gauges, Fig- 10 10 10 ure 4) and 𝑐 = the depth of the sectional neutral axis (in meters). 0 0 0 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0.020 Appl. Sci. 2021, 11, x FOR PEER REVIEW 13 of 22 𝑐 = Curvature (µrad) Curvature (µrad) 𝘀 Curvature (µrad) 𝑐 (13) [1 − ] (a) (b) (c) 60 60 B4 50 ∅ = 50 (14) B4-R 40 40 By applying the above formulas, Figure 9 shows the 𝑀 − ∅ behavior of B1–B6. The 30 30 30 moment–curvature for B6 had a premature termination due to the crushing of the ex- 20 20 tremely stressed UHPC (at top face). It is worth noting that the calculation of the beam’s B5 B6 10 10 strains was not attainable if cracks extended to the beam’s top surface, as they disturb the B5-R B6-R 0 measurement of the concrete strains. This issue could be handled by the use of horizontal 0 0 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 LVDTs for curvature measurements. Curvature (µrad) Curvature (µrad) Curvature (µrad) (d) (e) (f) 60 60 B3 B2 B1 50 B3-R 50 Figure 9. Moment–curvature 50 responses of (a) B1, (b) B2, (c) B3, (d) B4, (e) B5, and (f) B6. Figure 9. Moment–curvature responses of (a) B1, (b) B2, (c) B3, (d) B4, (e) B5, and (f) B6. B2-R B1-R 40 40 Figure 10a depicts a representative moment–curvature response for B1–B6. This Figure 10a depicts a representative moment–curvature response for B1–B6. This fig- 30 30 30 figur ure demo e demonstrated nstrated ththat at all all bar bar -re -rinf einfor orce ced d beams, beams, exc except ept B6, B6, wer were e likely likely under under-r -reinf einfor orce ced d 20 20 20 (tension-controlled). Additionally, the slope of the pre- and post-steel yielding was almost (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 10 typical for all beams. 10 This was due to the efficient hybrid 10 fibrous system in the UHPC that that controls the post-cracking curvatures of beams. The relation between the moment controls the post-cracking curvatures of beams. The relation between the moment capacity 0 0 0 capacity and bar reinforcement ratio is presented in Figure 10b. This figure shows the 0 50 100 150 and 200 bar reinforcement 0 rati 50o is 100 prese150 nted in 200 Figure 10b. This 0figur50 e show 100 s the 150 robust 200line- Curvature (µrad)robust linearity of this relation Curvature (with (µrad a )99% correlation coefficient).Curvature (µrad) arity of this relation (with a 99% correlation coefficient). (a) (b) (c) B1 B2 B3 B4 B5 B6 𝑀 = 10.57𝜌 + 16.68 (𝑅 = 0.99) 0 50 100 150 200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Reinforcement ratio (%) Curvature (µrad) (a) (b) Figure 10. (a) Moment–curvature of beams and (b) ultimate moment–reinforcement ratio relation. 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 plas- tically 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 (𝜇 ) and curvature ductility parameters were cal- culated to investigate the ductility behavior of beams with different 𝜌 . Here, 𝜇 was eval- uated as the ratio of the ultimate deflection (𝛿 ) to yield deflection (𝛿 ). The beam’s load– 𝑢 𝑦 deflection curves were employed to estimate these deflections. According to the widely used approach [49–51], a straight line was created between the origin point and 50% of the ultimate load (𝑃 ) that extended to 80% 𝑃 , as depicted in Figure 11a. The deflection 𝑢 𝑢 at this load (0.8 𝑃 ) was defined as involving the beam’s yield of reinforcement (𝛿 ), while 𝑢 𝑦 defection corresponds to the same load but on the descending branch, which was assumed Moment (kNm) Moment (kNm) Moment (kNm) Moment (kNm) Load (kN) Load (kN) Moment (kNm) Moment (kNm) Moment (kNm) Peak load (kN) Peak load (kN) Peak load (kN) Moment (kNm) Moment (kNm) Moment (kNm) Appl. Sci. 2021, 11, x FOR PEER REVIEW 13 of 22 60 60 B4 50 50 B4-R 40 40 40 30 30 30 20 20 20 B5 B6 10 10 10 B5-R B6-R 0 0 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 Curvature (µrad) Curvature (µrad) Curvature (µrad) (d) (e) (f) Figure 9. Moment–curvature responses of (a) B1, (b) B2, (c) B3, (d) B4, (e) B5, and (f) B6. Figure 10a depicts a representative moment–curvature response for B1–B6. This fig- ure 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 Appl. Sci. 2021, 11, 11346 13 of 21 and bar reinforcement ratio is presented in Figure 10b. This figure shows the robust line- arity of this relation (with a 99% correlation coefficient). B1 B2 B3 B4 B5 B6 𝑀 = 10.57𝜌 + 16.68 (𝑅 = 0.99) 0 10 0 50 100 150 200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Reinforcement ratio (%) Curvature (µrad) (a) (b) Figure 10. (a) Moment–curvature of beams and (b) ultimate moment–reinforcement ratio relation. Figure 10. (a) Moment–curvature of beams and (b) ultimate moment–reinforcement ratio relation. 3.2.3. Ductility Analysis 3.2.3. Ductility Analysis The The ductility ductilitypr pro operty perty of of aa str struct uctural ural element element is isan animportant important factor factor that that reveals reveals its its reliability reliability . . This This pro property perty ccan an be bede described scribed as as ththe e cap capability ability of a of str austr ctural uctural elemen element t to plas- to plastically resist loading between its yield to ultimate points [47]. The evaluation of the tically resist loading between its yield to ultimate points [47]. The evaluation of the yield yield point can be point can made by be made gr by apgraphical hical and e and quivalent equivalent tough toughness ness approac appr hes oaches [48].[ 48]. In the current study, the deflection (m ) and curvature ductility parameters were In the current study, the deflection (𝜇 ) and curvature ductility parameters were cal- calculated to investigate the ductility behavior of beams with different r. Here, m was culated to investigate the ductility behavior of beams with different 𝜌 . Here, 𝜇 was eval- evaluated as the ratio of the ultimate deflection (d ) to yield deflection (d ). The beam’s uated as the ratio of the ultimate deflection (𝛿 ) tou yield deflection (𝛿 ). Th y e beam’s load– 𝑢 𝑦 load–deflection curves were employed to estimate these deflections. According to the deflection curves were employed to estimate these deflections. According to the widely widely used approach [49–51], a straight line was created between the origin point and 50% used approach [49–51], a straight line was created between the origin point and 50% of of the ultimate load (P ) that extended to 80% P , as depicted in Figure 11a. The deflection u u the ultimate load (𝑃 ) that extended to 80% 𝑃 , as depicted in Figure 11a. The deflection 𝑢 𝑢 at this load (0.8 P ) was defined as involving the beam’s yield of reinforcement (d ), while u y at this load (0.8 𝑃 ) was defined as involving the beam’s yield of reinforcement (𝛿 ), while 𝑢 𝑦 defection corresponds to the same load but on the descending branch, which was assumed defection corresponds to the same load but on the descending branch, which was assumed to be equal to the ultimate deflection, d The rationale for this assumption is that all UHPC beams exhibited flexural stability issues when the strength of the beams reduced by 20% P after the ultimate load. Figure 11b shows the method for evaluating the curvature ductility (m), which is an energy-based approach. Here, m was calculated by Equation (15). This method has been employed by various investigators (e.g., [48]) in the past. 0.375M ? + 0.875M ? ? u y u u y m = = (15) A 0.375M ? y u y Table 6 summarizes the results of the performed ductility analysis of the UHPC beams. This table shows that the percentage difference of m for the duplicated samples were between 1.95% and 11.12%; it was in the range of 30.44% to 76.21 for m. The relatively high percentage difference for m was likely due to the bilinearization assumptions of the M ? curve, as it exhibited high material nonlinearity. With respect to the control beam, the means of m and m for the two duplicated samples of each beam set were evaluated (as given in parenthesis in Table 6) to emphasize the influence of r on the ductility of UHPC beams. This table suggested that as r increases, the m 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 ? curve for these beams due to compressive failure of their concrete at top surface or tensile failure of bars prior to achieving high ductility. Moment (kNm) Moment (kNm) Moment (kNm) Peak load (kN) Moment (kNm) Appl. Sci. 2021, 11, x FOR PEER REVIEW 14 of 22 to be equal to the ultimate deflection, 𝛿 . The rationale for this assumption is that all Appl. Sci. 2021, 11, 11346 14 of 21 UHPC beams exhibited flexural stability issues when the strength of the beams reduced by 20% 𝑃 after the ultimate load. (a) Curvature Curvature (b) Figure 11. Ductility calculated by (a) deflection (𝜇 ) and (b) moment–curvature area (𝜇 ). Figure 11. Ductility calculated by (a) deflection (m ) and (b) moment–curvature area (m). Table 6. Ductility analysis of the reinforced UHPC beams. Figure 11b shows the method for evaluating the curvature ductility (𝜇 ), which is an energy-based approach. Here, 𝜇 was calculated by Equation (15). This method has been Deflection Ductility Curvature Ductility employed by various investigators (e.g., [48]) in the past. d (mm) m M (kNm) ? (10 /mm) m Beam D 𝐴 0.375𝑀 ∅ + 0.875𝑀 (∅ − ∅ ) 𝑢 𝑢 𝑦 𝑢 𝑢 𝑦 𝜇 = = d (15) d d Average m M Average ? ? Equation (15) Average y u D u y u 𝐴 0.375𝑀 ∅ y 𝑦 𝑢 𝑦 B1 1.094 3.882 3.548 16.5 28.0 105.2 7.429 Table 6 summarizes the results of the performed ductility analysis of the UHPC 3.226 16.7 6.3 B1-R 1.040 3.020 2.904 16.9 28.5 79.4 5.167 beams. This table shows that the percentage difference of 𝜇 for the duplicated samples B2 1.385 4.41 3.184 3.340 21.9 23.1 27.2 178.3 13.948 9.3 were between 1.95% and 11.12%; it was in the range of 30.44% to 76.21 for 𝜇 . The relatively B2-R 1.440 5.035 3.497 (+3.5%) 24.3 (+38.1%) 76.2 195.6 4.660 (+47.7%) high percentage difference for 𝜇 was likely due to the bilinearization assumptions of the B3 1.178 4.295 3.646 3.749 24.8 25.1 29.8 92.8 5.923 4.2 𝑀 − ∅ curve, as it exhibited high material nonlinearity. With respect to the control beam, B3-R 1.324 5.099 3.851 (+16.2%) 25.3 (+50.3%) 34.6 57.9 2.567 ( 32.6%) the means of 𝜇 and 𝜇 for the two duplicated samples of each beam set were evaluated B4 1.641 6.181 3.767 29.8 36.2 163.9 9.238 7.6 3.293 (+2.1) 30.3 (+81.7) (as given in parenthesis in Table 6) to emphasize the influence of 𝜌 on the ductility of B4-R 1.662 4.687 2.820 30.8 39.3 122.5 5.941 (+20.5%) UHPC beams. This table suggested that as 𝜌 increases, the 𝜇 exponentially increases B5 1.838 17.556 9.552 7.460 41.7 34.2 149.7 8.868 12.2 42.4 (+154.1) B5-R 2.053 11.02 5.368 (+131.2) 43.1 28.9 209.9 15.626 (+94.5) (Figure 12). Table 6 illustrates that both B3 and B4 had inferior curvature ductility with B6 2.051 27.201 13.262 14.536 50.7 48.6 30.5 83.1 5.028 6.1 respect to B1. The reason for this phenomenon would be the quick closure of the 𝑀 − ∅ B6-R 1.885 29.803 15.811 (+350.6) 46.5 (+191.0%) 38.7 140.3 7.119 ( 3.6) 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 Moment Moment Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 22 Table 6. Ductility analysis of the reinforced UHPC beams. Deflection Ductility Curvature Ductility 𝜹 𝑴 ∅ 𝝁 𝝁 −6 Beam (mm) (kNm) (× 10 /mm) 𝒖 Average 𝜹 = ∅ 𝜹 𝑴 Average ∅ Equation (15) Average 𝒚 𝒚 𝒖 𝒖 𝒖 Appl. Sci. 2021, 11, 11346 15 of 21 B1 1.094 3.882 3.548 16.5 28.0 105.2 7.429 3.226 16.7 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 21.9 23.1 27.2 178.3 13.948 9.3 UHPC beams becomes very similar to the descending branch of the load–deflection curve B2-R 1.440 5.035 3.497 (+3.5%) 24.3 (+38.1%) 76.2 195.6 4.660 (+47.7%) (Figure 7). Additionally, this figure demonstrated that increasing r notably decreases the B3 1.178 4.295 3.646 3.749 24.8 29.8 92.8 5.923 4.2 25.1 (+50.3%) crack opening width of the UHPC beams at the same service loading. It is worth noting B3-R 1.324 5.099 3.851 (+16.2%) 25.3 34.6 57.9 2.567 (−32.6%) that this finding is inconsistent with that reported by Qiu et al. [52]. Another significant B4 1.641 6.181 3.767 29.8 36.2 163.9 9.238 7.6 3.293 (+2.1) 30.3 (+81.7) observation is that increasing the bar reinforcement ratio contributed to stabilizing the B4-R 1.662 4.687 2.820 30.8 39.3 122.5 5.941 (+20.5%) crack propagation, as the slope of the UHPC beam’s load–crack curve increases as its B5 1.838 17.556 9.552 7.460 41.7 34.2 149.7 8.868 12.2 42.4 (+154.1) bar reinforcement increases. In other words, the initiation and development of cracking B5-R 2.053 11.02 5.368 (+131.2) 43.1 28.9 209.9 15.626 (+94.5) are considerably delayed as the tensile continuous reinforcement of the beam increases. B6 2.051 27.201 13.262 14.536 50.7 48.6 30.5 83.1 5.028 6.1 A similar pattern of results was obtained in [53]. B6-R 1.885 29.803 15.811 (+350.6) 46.5 (+191.0%) 38.7 140.3 7.119 (−3.6) Appl. Sci. 2021, 11, x FOR PEER REVIEW 16 of 22 Figure 12. Reinforcement ratio and deflection–ductility relations. Figure 12. Reinforcement ratio and deflection–ductility relations. 500 500 3.2.4. Load–Crack Opening Curves B2 B3 B1 The cracking response of a concretB2-R e structural member plays a significant role in its 400 400 B3-R 400 B1-R survivability state. The serviceability phase is related to the crack propagation stage when 300 300 the service loading is less than the yielding one of the UHPC elements. Figure 13 displays 200 200 the load vs. the maximum crack width for all investigated UHPC beams, after the initia- tion of the crack propagation stage. As expected, the load–cracking response of the UHPC 100 100 beams becomes very similar to the descending branch of the load–deflection curve (Figure 0 0 7). Additionally, this figure demonstrated that increasing 𝜌 notably decreases the crack 0 4 8 12 16 20 0 4 8 12 16 20 0 2 4 6 8 10 12 opening width of the UHPC beams at the same service loading. It is worth noting that this Crack opening (mm) Crack-opening (mm) Crack opening (mm) finding is inconsistent with that reported by Qiu et al. [52]. Another significant observa- (a) (b) (c) tion is that increasing the bar reinforcement ratio contributed to stabilizing the crack prop- 500 500 500 B4 agation, as the slope of the UHPC beamB5 ’s load–crack curve increases as its bar reinforce- B4-R 400 400 B5-R 400 ment increases. In other words, the initiation and development of cracking are considera- bly delayed as the tensile continuous reinforcement of the beam increases. A similar pat- 300 300 300 tern of results was obtained in [53]. 200 200 100 100 B6 B6-R 0 0 0 4 8 12 16 20 0 4 8 12 16 20 0 4 8 12 16 20 Crack opening (mm) Crack opening (mm) Crack opening (mm) (d) (e) (f) Figure 13. Load crack opening responses of (a) B1, (b) B2, (c) B3, (d) B4, (e) B5, and (f) B6. Figure 13. Load crack opening responses of (a) B1, (b) B2, (c) B3, (d) B4, (e) B5, and (f) B6. 3.2.5. Crack Pattern and Failure Modes 3.2.5. Crack Pattern and Failure Modes Figure 14 indicates the experimental cracking pattern of the control and bar-rein- Figure 14 indicates the experimental cracking pattern of the control and bar-reinforced forced UHPC beams. This figure depicts that increasing the bar reinforcement percentages UHPC beams. This figure depicts that increasing the bar reinforcement percentages notably notably enhances the deformability of the UHPC beams. Moreover, the significant cracks enhances the deformability of the UHPC beams. Moreover, the significant cracks of these of these beams were observed at loading levels close to their ultimate loads; however, B3 beams were observed at loading levels close to their ultimate loads; however, B3 and B6 are and B6 are exceptions. As discussed in Sections 3.2.2 and 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 bot- tom 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 rein- forcement) 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 (𝜌 = 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 (𝜌 , 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. B1 B1-R (a) Load (kN) Load (kN) Load (kN) Load (kN) Load (kN) Load (kN) Appl. Sci. 2021, 11, x FOR PEER REVIEW 16 of 22 500 500 B2 B3 B1 B2-R 400 400 B3-R 400 B1-R 300 300 200 200 100 100 100 0 0 0 0 4 8 12 16 20 0 4 8 12 16 20 0 2 4 6 8 10 12 Crack opening (mm) Crack-opening (mm) Crack opening (mm) (a) (b) (c) 500 500 500 B4 B5 B4-R 400 400 400 B5-R 300 300 200 200 100 100 B6 B6-R 0 0 0 4 8 12 16 20 0 4 8 12 16 20 0 4 8 12 16 20 Crack opening (mm) Crack opening (mm) Crack opening (mm) (d) (e) (f) Figure 13. Load crack opening responses of (a) B1, (b) B2, (c) B3, (d) B4, (e) B5, and (f) B6. 3.2.5. Crack Pattern and Failure Modes Figure 14 indicates the experimental cracking pattern of the control and bar-rein- Appl. Sci. 2021, 11, 11346 16 of 21 forced 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 Sections 3.2.2 and 3.2.3, the reason behind this exceptions. As discussed in Sections 3.2.2 and 3.2.3, the reason behind this behavior was behavior was likely due to the concrete’s compressive failure that expedited the major likely due to the concrete’s compressive failure that expedited the major crack development. crack development. Typically, the beginning of the pullout process of the fibers from the Typically, the beginning of the pullout process of the fibers from the UHPC matrix initiates UHPC matrix initiates the failure mechanism of the UHPC beams [54]. The existence of the failure mechanism of the UHPC beams [54]. The existence of bar reinforcement helps bar reinforcement helps to enhance the failure pattern as more flexure shear cracks were to enhance the failure pattern as more flexure shear cracks were observed as its presence observed as its presence increased. The flexure cracks were introduced at the beam’s bot- increased. The flexure cracks were introduced at the beam’s bottom surface and near its tom surface and near its midspan and then extended along at an angle of 60°–90°. These midspan and then extended along at an angle of 60 –90 . These cracks were the main cause cracks were the main cause of failure for all beams; nevertheless, flexure shear cracks were of failure for all beams; nevertheless, flexure shear cracks were observed in moderately observed in moderately reinforced beams. The failure mode of B3 (with 0.81% of bar rein- reinforced beams. The failure mode of B3 (with 0.81% of bar reinforcement) was due to forcement) was due to tensile failure of reinforcement bars, which is possibly due to the tensile failure of reinforcement bars, which is possibly due to the higher bond with the higher bond with the UHPC that decreases the length of the plastic hinge and increases UHPC that decreases the length of the plastic hinge and increases the stress concentration the stress concentration in the bars. Moreover, the concrete crushing at the top surface of in the bars. Moreover, the concrete crushing at the top surface of the midspan of B6 the midspan of B6 (𝜌 = 3.35%) was accompanied by its flexure mode of failure, which (r = 3.35%) was accompanied by its flexure mode of failure, which could be attributed to could be attributed to the reinforcement ratio of this beam approaching the balanced the reinforcement ratio of this beam approaching the balanced threshold (r , as given in threshold (𝜌 , as given in Section 2.2.2). It is worth noting that the load–deflection curves Section 2.2.2). It is worth noting that the load–deflection curves and failure pattern of B6 and failure pattern of B6 (the beam with larger diameters) indicate that no damage was (the beam with larger diameters) indicate that no damage was caused by bar slippage. caused by bar slippage. B1 B1-R Appl. Sci. 2021, 11, x FOR PEER REVIEW 17 of 22 (a) B2 B2-R 195 141 160 110 141 (b) B3 B3-R (c) B4 B4-R 265 220 (d) B5 B5-R 330 315 (e) B6 B6-R 330 330 (f) Figure 14. Failure patterns of (a) B1, (b) B2, (c) B3, (d) B4, (e) B5, and (f) B6. Figure 14. Failure patterns of (a) B1, (b) B2, (c) B3, (d) B4, (e) B5, and (f) B6. 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 va- lidity 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 ex- perimentally 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 mo- ment 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) overesti- mated B6’s moment capacity by a relatively higher margin (+12%). As a result, this ap- proach might be appropriate for UHPC beams with longitudinal reinforcement ratios ap- proaching the balanced ratio (see Section 2.2.2). It is noteworthy that the common analyt- ical data for all beams were 𝐿 = 15.123 mm, 𝑉 = 1.934%, 𝑉 = 0.548%, 𝑉 = 0.097%, 𝑓 𝑓 𝑓 𝑓 1 2 3 𝑉 = 2.578%, 𝐿 = 15.126 mm, 𝑑 = 0.2 mm, and 𝘀 = 0.0015. 𝑓 𝑓 𝑓 𝑓 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 pre- dicted–observed data points are fairly close to the line of equality. Moreover, all the pre- dicted–observed results were in between (or close to B3) the ±90% accuracy zone. Load (kN) Load (kN) Load (kN) Load (kN) Load (kN) Load (kN) Appl. Sci. 2021, 11, 11346 17 of 21 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 L =15.123 mm, V =1.934%, V =0.548%, V =0.097%, V =2.578%, f f f f f 1 2 3 L = 15.126 mm, d =0.2 mm, and # =0.0015. f f f Appl. Sci. 2021, 11, x FOR PEER REVIEW 18 of 22 Table 7. Prediction data of the UHPC beams. Moment Capacity (kNm) F (kN) F (kN) F (kN) M /M Beam A (mm ) e (mm) c (mm) f p o s Table 7.c Prediction data of the UH s PC beams. Tested (M ) Predicted M o p B1 - 7.266 5.284 108.9 108.9 - Momen 16.700 t Capacity 16.232 (kNm) 0.972 𝒆 𝒄 𝑭 𝑭 𝒄 𝒔 B2 100.5 12.450 7.697 158.7 106.4 52.3 23.100 22.236 0.963 Beam 𝑨 (mm ) 𝑴 /𝑴 𝒔 Tested 𝒑 𝒐 B3 157.1 12.450 (mm) 9.055 (mm) 186.7 (kN) 105.0 (kN) 81.7 25.100 25.778 1.027 (kN) Predicted (𝑴 ) (𝑴 ) 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 B1 - 7.266 5.284 108.9 108.9 - 16.700 16.232 0.972 B6 628.3 28.003 20.366 419.8 93.1 326.7 48.600 54.451 1.120 B2 100.5 12.450 7.697 158.7 106.4 52.3 23.100 22.236 0.963 Means 1.006 B3 157.1 12.450 9.055 186.7 105.0 81.7 25.100 25.778 1.027 Std. 0.052 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 The capacity of the proposed analytical model to reproduce the ultimate moment B6 628.3 28.003 20.366 419.8 93.1 326.7 48.600 54.451 1.120 of UHPC beams is also displayed in Figure 15. It can be seen from this figure that all Means 1.006 predicted–observed data points are fairly close to the line of equality. Moreover, all the Std. 0.052 predicted–observed results were in between (or close to B3) the 90% accuracy zone. Figure 15. Predicted vs. observed 𝑀 . Figure 15. Predicted vs. observed M . 𝑢 u UHPC is a zero-permeable composite whose preparation relies on the interstitial UHPC is a zero-permeable composite whose preparation relies on the interstitial transition zone with maximal packing density and surface hydration products, rather than 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 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 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 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 pro- vides the most optimal packing density. The optimal superplasticizer dosage for im- proved workability was also determined. The functionality of the individual and hybrid- ized 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 identi- fied 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 pre- cipitation 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 Appl. Sci. 2021, 11, 11346 18 of 21 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 mecha- nism 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 pre- diction formulas for the calculation of the UHPC beam’s moment capacity were presented. Based on this study, the following conclusions were drawn: - The inclusion of the fibrous system of fibers in the UHPC concrete increased its com- pressive and flexural strengths by 31.5% and 237.8%, which indicated the significance of fibers in promoting the tensile and flexural properties of UHPC. - The investigation of the load–deflection curves of beams revealed that the UHPC beams with low r failed by a sudden brittle flexural failure; however, the beams with medium to high r 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). - 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. Appl. Sci. 2021, 11, 11346 19 of 21 In the current study, m and m were calculated to investigate the ductility behavior of UHPC beams with different r 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 m was likely due to the bilinearization hypothesis of the M ? curve. Moreover, it was concluded that as r increases, the m exponentially increases; however, the relation between r and m 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 r 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. Author Contributions: Conceptualization, M.I.K. and G.F.; methodology, M.I.K. and F.K.A.; software, Y.M.A.; validation, F.K.A. and M.I.K.; investigation, G.F.; resources, M.I.K.; data curation, G.F. and Y.M.A.; writing—original draft preparation, G.F., Y.M.A. and F.K.A.; writing—review and editing, M.I.K.; supervision, M.I.K.; project administration, M.I.K.; funding acquisition, M.I.K. All authors have read and agreed to the published version of the manuscript. Funding: This research and the APC were funded by National Plan for Science, Technology and Innovation (MAARIFAH), King Abdulaziz City for Science and Technology, Kingdom of Saudi Arabia grant number 14-BUI2262-02. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: All research data are available and can be provided upon request. 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