  In this paper, five different approaches for reduced-order modeling of
brittle fracture in geomaterials, specifically concrete, are presented and
compared. Four of the five methods rely on machine learning (ML) algorithms to
approximate important aspects of the brittle fracture problem. In addition to
the ML algorithms, each method incorporates different physics-based assumptions
in order to reduce the computational complexity while maintaining the physics
as much as possible. This work specifically focuses on using the ML approaches
to model a 2D concrete sample under low strain rate pure tensile loading
conditions with 20 preexisting cracks present. A high-fidelity finite
element-discrete element model is used to both produce a training dataset of
150 simulations and an additional 35 simulations for validation. Results from
the ML approaches are directly compared against the results from the
high-fidelity model. Strengths and weaknesses of each approach are discussed
and the most important conclusion is that a combination of physics-informed and
data-driven features are necessary for emulating the physics of crack
propagation, interaction and coalescence. All of the models presented here have
runtimes that are orders of magnitude faster than the original high-fidelity
model and pave the path for developing accurate reduced order models that could
be used to inform larger length-scale models with important sub-scale physics
that often cannot be accounted for due to computational cost.
