  Numerical simulations of concrete fracture performed with a probabilistic
mesoscale discrete model are presented. The model represents a substantial part
of material randomness by assigning random locations to the largest aggregates.
The remaining part of randomness is introduced by causing material parameters
to fluctuate randomly via a homogeneous random field. An extensive numerical
study performed with the model considers prisms loaded in uniaxial tension with
both fixed and rotating platens, and also beams with and without a notch loaded
in three point bending. The results show the nontrivial effect of (i)
autocorrelation length and (ii) variance of the random field on the fracture
behavior of the model. Statistics of the peak load are presented as well as the
size and shape of the fracture process zone at the moment when the maximum load
is attained. Local averaging within the fracture process zone and weakest-link
are identified as underlying mechanisms explaining the reported results. The
companion paper, Part II [64], introduces an analytical model capable of
predicting the distribution of the peak load obtained with the probabilistic
discrete model via the simple estimation of extremes of a random field obtained
as moving average of local strength.
