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Material BehaviorIn the past, UHPC carried high material and construction costs, hindering wide-scale adoption in structural applications. Developments in the past decade have led to open-source formulations that are more economical than proprietary versions and perform just as well. One of the earliest open-source mixes in the United States was published by Wille et al. (2011a, b, c). This was subsequently followed by a number of related and other mixes documented in Wille et al. (2012), Wille and Boisvert-Cotulio (2013), Alkaysi et al. (2016), Berry et al. (2017), El-Tawil et al. (2018), Alsalman et al. (2018), Tai and El-Tawil (2020), Mendonca et al. (2020), and El-Tawil et al. (2020). These mixes are generally made of components readily available on the US open market and do not require any special mixing or placing equipment.When properly formulated and reinforced with fibers, UHPC can display compressive and direct tensile strengths as high as 255 MPa and 37 MPa, respectively (Wille et al. 2011b, 2014). Changes in the type and quantity of fibers directly affect the ductility and strength of the material (Pyo and El-Tawil 2015; Pyo et al. 2016). UHPC also exhibits exceptional toughness prior to crack localization and self-consolidation properties (Pyo and El-Tawil 2015), and generally develops a high early strength in the range of 70–95 MPa within 24 h (Karmacharya and Chao 2019).The compressive and tensile responses of UHPC are quite different from those of regular concrete, and must be adequately modeled for realistic analysis or design. In general, UHPC exhibits an almost linear compressive stress–strain response up to the strain at the peak stress. Strain softening usually commences right after the peak is reached and the descending slope is controlled by the amount and type of fiber reinforcement. Fig. 1(a) shows a compressive stress–strain curve proposed by Sritharan et al. (2003) for analysis and design purposes, compared with the experimentally measured response in Acker and Behloul (2004).As a fiber-reinforced cementitious material, UHPC resists tensile stress through composite action between the matrix and embedded fibers. The transmission of forces between these two components occurs through interfacial bond. After cracking, fibers bridge the cracks, providing resistance to crack opening and enhancing structural behavior and durability. As shown in Fig. 1(b), UHPC’s tensile response can be generally characterized by an elastic portion, followed by strain-hardening, a plateau, and then a long strain-softening phase. Aaleti et al. (2013) proposed the idealized tensile response shown in Fig. 1(b) for analysis and design purposes.The linear portions of the tensile and compressive regimes are characterized by an elastic modulus, E. Several equations have been proposed to link the elastic modulus to compressive stress. For example, Sritharan et al. (2003) proposed E (MPa)=4,150fc′(MPa) [E (psi)=50,000fc′(psi)], while Garcia and Graybeal (2007) used a similar equation but with a slightly reduced coefficient (3,835 instead of 4,150 or 46,200 instead of 50,000). Rather than providing an explicit equation, ACI 239R (ACI 2018) just lists a range of values from 6,000–7,200 Ksi (40–50 MPa).The ACI 318 (ACI 2019) and AASHTO codes (AASHTO 2020) use a strain of 0.003 as the crushing strain (or maximum design compressive strain), εcu, at a postpeak compressive stress of 0.8fc′ for plain concrete. Chao et al. (2019) observed εcu of 0.015 and 0.003 for UHPC with 3% microsteel fiber by volume and plain concrete, respectively, in large-scale beam testing, where the strains were measured by a digital image correlation (DIC) system. The high compressive strain capacity of UHPC is not unusual for a high-performance fiber-reinforced cementitious material, as noted by Naaman (2018). The discrepancy between the response depicted in Fig. 1(a) and values noted in Chao et al. (2019) is attributed to the differences in UHPC fiber content. Further research is needed to specify values suitable for design.Longitudinal reinforcement is typically used in UHPC structural members subjected to bending. Previous research shows that, because of their tension-stiffening effect, reinforcing bars or prestressing strands used in structural members enhance the cracking distribution and tensile ductility of fiber-reinforced concrete. Fig. 2 illustrates the results of an investigation by Aghdasi et al. (2016), which provides the total (UHPC + #10M rebar) and pure (UHPC only) tensile stress–strain curves, as well as the tensile stress–strain curve of UHPC specimen with no rebar. The results indicate that, while the tensile strength remained nearly the same (7.7 MPa), the presence of rebar considerably enhanced the tensile ductility of the UHPC. In the UHPC specimen, tensile strain-hardening was maintained up to a strain of 1.3%, nearly 7.5 times larger than the specimen with no rebar.To date, most of the studies on UHPC material response have focused on monotonic behavior. There is a marked scarcity of data on high- and low-cycle fatigue loading. Although initial indications are that the high-cycle fatigue resistance of UHPC is extremely high (Ocel and Graybeal 2007; Fitik et al. 2008, 2010; Carlesso et al. 2019), future research studies are needed to confirm this finding and fully characterize the tensile and compressive response of fatigue-loaded UHPC, especially in high-demand applications such as wind towers and bridges. To the knowledge of the authors, there are no studies that have developed models of the low-cycle response of UHPC, and therefore research into this area is urgently needed.In addition, unlike plain concrete, because UHPC’s tensile capacity may be largely utilized in the strength design of a UHPC structural member, its long-term behavior can have an impact on the performance of the member. It has been shown that UHPC can experience tensile creep under long-term loading; however, tensile creep of UHPC can be decreased approximately 65% when thermal treatment of 60°C (140°F) for 72 h or 90°C (194°F) for 48 h is applied, respectively, prior to loading (Garas et al. 2010). Further research is warranted to investigate this effect on the long-term performance of UHPC members. In compression, UHPC is known to have much less creep than conventional concrete. As in tension, the use of heat treatment appears to decrease creep even further (Russell and Graybeal 2013).References Aaleti, S., B. Petersen and S. Sritharan. 2013. Design guide for precast UHPC waffle deck panel system, including connections. Rep. No. FHWA-HIF-13-032. Washington, DC: USDOT. Aaleti, S., and S. Sritharan. 2017. Investigation of a suitable shear friction interface between UHPC and normal strength concrete for bridge deck applications. Rep. No. InTrans Project 10-379. Ames, IA: Iowa DOT. AASHTO. 2008. 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