Coupled Experimental and Computational Investigation
of the Interplay between Discrete and Continuous
Reinforcement in Ultrahigh Performance Concrete
Beams. II: Mesoscale Modeling
Tathagata Bhaduri, S.M.ASCE
1
; Shady Gomaa
2
; and Mohammed Alnaggar, M.ASCE
3
Abstract: The first experimental campaign presented in the preceding Part I of this study is used to calibrate and validate a comprehensive
computational framework called the lattice discrete particle model for fiber-reinforced concrete (LDPM-F). The model is then used to design
the second experimental campaign that was also presented in the preceding Part I so that all beams fail in shear. Finally, the model is used to
investigate and explain the observed failure modes, validate the fiber/reinforcement interplay effects postulated in Part I, and to analyze
comprehensively the load-transfer mechanisms in the reinforced ultra-high performance concrete (R-UHPC) beams in both shear and flexural
failure. This two-part study proves the effectiveness of coupling experimental analysis with comprehensive computational modeling to under-
stand the behavior of structural members made from complex materials. Using this coupled understanding, detailed explanations of load-
transfer mechanisms in shallow and deep beam shear failure as well as flexural failure are discussed and compared to simplified sectional
analysis models showing the places of needed improvement in such models. These detailed discussions show the ability of the presented
coupled approach to accurately predict these failure mechanisms and their dependence on fiber/reinforcement contents and their interplay.
The presented accurate probing of different load-transfer mechanisms within the structural elements and how they vary during failure pro-
gression paves the road towards developing rigorous design formulations based on fundamental understanding of the complex mechanical
behavior of these structural members. DOI: 10.1061/(ASCE)EM.1943-7889.0001941. © 2021 American Society of Civil Engineers.
Introduction
Numerical modeling of concrete class materials may range from the
use of classical continuum-based finite-element modeling to a dis-
crete class of models (Rena et al. 2008). As the main objective in
current work revolves around understanding the intricacies of fail-
ure mechanisms and the corresponding load-transfer mechanisms
in reinforced ultra-high performance concrete (R-UHPC) members,
high-fidelity models are required to capture phenomena unique to
concrete as a particulate composite that is reinforced with short fiber
and continuous rigid reinforcement. Concrete belongs to the cat-
egory of quasi-brittle materials (Bazant and Planas 1997); hence,
concrete exhibits specific fracture mechanisms like friction shearing
and damage localization, which lead to strain-softening behavior.
Early developments in fracture mechanics–based modeling of con-
crete behavior utilized the classical cohesive crack law (Hillerborg
et al. 1976) in which stresses are transmitted through a fictitious
crack as a function of crack opening displacements. Another popu-
lar approach known as crack band theory (Bažant and Oh 1983a)
considers the width of fracture process zone in the formulation of
fracture using continuum mechanics. Later, to simulate dynamic
fracture behavior in concrete considering gradual strain-softening,
Bažant and Oh (1983b) introduced a microplane model in which
stress and strain are expressed as vectors on each microplane instead
of tensors and invariants (Bažant and Oh 1985). In this model, mi-
croplane strains are kinematically constrained by the macroscopic
strain tensor while the macroscopic stress tensor is connected to mi-
croplane stress through the principle of virtual work. Although the
latest versions of microplane models incorporate robust features
with capabilities for large-scale finite-element simulations (Caner
and Bažant 2012), spurious mesh sensitivity remains a problem that
needs mesh selection to be in compliance with crack band theory
(Bažant and Oh 1983a). Furthermore, nonlocal models (Bažant
and Ožbolt 1990) and gradient-based formulations (Bažant and
Di Luzio 2004) were able to diminish mesh sensitivity with finer
mesh and increased cost of computation.
In simulating fiber-reinforced concrete (FRC), classical con-
tinuum damage formulations had been a popular choice among re-
searchers (Fanella and Krajcinovic 1985; Peng and Meyer 2000; Li
and Li 2001). Among other significant developments, the micro-
plane model was also extended to simulate the behavior of FRC in
two of the subsequent variants (Beghini et al. 2007; Caner et al.
2013) where the latest model M7f (Caner et al. 2013) takes care of
the fiber pullout and breakage in a more realistic way. However,
one of the main challenges with continuum-based models for FRC
is its inability to capture explicitly different mesoscale mechanisms
of load transfer occurring during fiber-matrix interactions. Hence,
such models are prone to postulated failure surfaces that approxi-
mate the macroscopic response without physically capturing mes-
oscale interactions.
Another class of models that has been extensively utilized
in concrete damage modeling is the discrete class models such
1
Graduate Student, Dept. of Civil and Environmental Engineering,
Rensselaer Polytechnic Institute, Troy, NY 12180.
2
Graduate Student, Dept. of Civil and Environmental Engineering,
Rensselaer Polytechnic Institute, Troy, NY 12180; Assistant Lecturer,
Dept. of Structural Engineering, Zagazig Univ., Zagazig, Eygpt.
3
Assistant Professor, Dept. of Civil and Environmental Engineering,
Rensselaer Polytechnic Institute, Troy, NY 12180 (corresponding author).
ORCID: https://orcid.org/0000-0002-3320-7652. Email: alnagm2@rpi.edu
Note. This manuscript was submitted on October 23, 2020; approved on
February 16, 2021; published online on June 25, 2021. Discussion period
open until November 25, 2021; separate discussions must be submitted for
individual papers. This paper is part of the Journal of Engineering Me-
chanics, © ASCE, ISSN 0733-9399.
© ASCE 04021050-1 J. Eng. Mech.
J. Eng. Mech., 2021, 147(9): 04021050
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