  In this report we present a study on the strength of rocks which are
partially fractured from before. We have considered a two dimensional case of a
rock in the form of a lattice structure. The fiber bundle model is used for
modelling the $2-D$ rock. Each lattice site is considered to be a fiber which
has a breaking threshold. Fractures in this system will be of the form a
cluster of sites and the length is defined as the number of sites belonging to
a single cluster. We introduce fractures in the system initially and apply load
until the rock breaks. The breaking of a rock is characterized by a horizontal
fracture which connects the left side of the lattice to the right side. The
length distribution and the strength of such systems have been measured.
