PSI - Issue 47

Luciano Feo et al. / Procedia Structural Integrity 47 (2023) 800–811 Author name / Structural Integrity Procedia 00 (2019) 000–000

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conventional one. Ultra-high performance concrete is one of the possible alternatives that, thanks to the high compressive strength and the hardening strain response under tensile loading, described by a multiple cracking behavior, is characterized by a remarkable resistance to severe loading and environmental actions (Habel & Gauvreau (2008)). Furthermore, the high density of the matrix guaranteed by the presence of fibers, implies low permeability, increased ductility and energy absorption capacity (Cuenca et al. (2023)). However, particularly if the number of fibers is limited, the large spacing between fibers makes UHPFRC ineffective in controlling the inception and initial growth of microcracks (Libya Ahmed Sbia et al. (2014)). To overcome this problem, in the last decade, advances in nanotechnology have provided opportunities to improve the microstructure of nanoscale cementitious composites incorporating several types of nanofillers in UHPFRCs cement paste (i.e., carbon nanofibers (CNFs), graphite nanoplatelets (GNPs), carbon nanotubes (CNTs)). The narrow spacing between nanofillers limits the formation and propagation of microcracks in concrete and improves its mechanical properties. In fact, Meng and Khayat (2016) found that the incorporation of 0.3% graphite nanoplates into UHPFRC elements increases the tensile strength and the energy absorption capacity by 56% and 187%, respectively. Kononova et al. (2015) have shown that a small amount of MWCNT can improve the pull-out behavior thanks to the bridging effect offered by both carbon nanotubes and short carbon fibers. In addition, Chen et al. (2023) found that the thermal conductivity at high temperature improved by addicting nanotubes in UHPFRC. Based on our knowledge, some theoretical models available in the literature are able to predict the cracking and post-cracking behavior of Fiber Reinforced Cementitious Composites, which can be divided in ( i ) a discrete crack approach, such as interface elements by Caggiano et al. (2012), lattice and particle approaches by El-Helou et al. (2014) and in ( ii ) smeared fracture approaches, i.e., continuum damage theories by Li et al. (2001) and microplane formulations by Beghini et al. (2007). In the present study, the meso-scale based model initially formulated in Martinelli et al. (2020,2021) and recently extended in Penna et al. (2022), is here enriched to capture the mechanical response of UHPFRC doped with nanofibers. For this end, the model has been enhanced by introducing a new parameter, , in the tensile concrete constitutive law and a modified bond-slip law for steel fibers has been calibrate, in order to take in to account the presence of nanofiller in the concrete mixture. T he validation of the new proposed model has been obtained by comparing the numerical results with those available in the literature. The work is structured as follows. An enriched formulation of the Meso-Mechanical Cracked-Hinge Model is described in Section 2. In Section 3 the model calibration and results are reported. Finally, the main conclusions are reported in Section 4. An enriched formulation of the Meso-Mechanical Cracked-Hinge Model The original formulation of the cracked-hinge model developed by Martinelli et al. (2020) is here enriched with the aim of predicting the effect of nanofibers on the mechanical response of UHPFRC specimens under four-point bending tests. In particular, the kinematics of the meso-mechanical cracked-hinge model and the modified constitutive laws of both UHPC matrix and steel fibers are presented. Then, the proposed modified model is validated by using the experimental results obtained by Meng and Khayat (2016). 3.1 Model kinematic As widely discussed in Martinelli et al. (2020), the meso-scale based model is able to take into account the behavior of the cement matrix and the spread fibers as well as their interaction. In addition, the random spatial distribution and the orientation of the reinforcement phase are simulated with statistical considerations, while the crack-bridging effect is considered by evaluating the total number of fibers in the mid-span section as: � � � � , � � � � � , � � � � � � �� 4 � � (1) 2.