  This article proposes a weighted-variational model as an approximated
surrogate model to lessen numerical complexity and lower the execution times of
brittle fracture simulations. Consequently, Monte Carlo studies of brittle
fractures become possible when energy release rates are modelled as a random
field. In the weighed-variational model, we propose applying a Gaussian random
field with a Mat\'ern covariance function to simulate a non-homogeneous energy
release rate ($G_c$) of a material. Numerical solutions to the
weighed-variational model, along with the more standard but computationally
demanding hybrid phase-field models, are obtained using the FEniCS open-source
software. The results have indicated that the weighted-variational model is a
competitive surrogate model of the hybrid phase-field method to mimic brittle
fractures in real structures. This method reduces execution times by 90\%. We
conducted a similar study and compared our results with an actual brittle
fracture laboratory experiment. We present an example where a Monte Carlo study
is carried out, modeling $G_c$ as a Gaussian Process, obtaining a distribution
of possible fractures, and load-displacement curves.
