  We study the effect of grain polydispersity on the bulk modulus in
non-cohesive two dimensional granular solids. Molecular dynamics simulations in
two dimensions are used to describe polydisperse samples that reach a
stationary limit after a number of hysteresis cycles. For stationary samples,
we obtain that the packing with the highest polydispersity has the lowest bulk
modulus. We compute the correlation between normal and tangential forces with
grain size using the concept of {\it branch vector/contact length}. Classifying
the contact lengths and forces by their size compared to the average length and
average force respectively, we find that strong normal and tangential forces
are carried by large contact lengths, generally composed of at least one large
grain. This behavior is more dominant as polydispersity increases, making force
networks more anisotropic and removing the support, from small grains, in the
loading direction thus reducing the bulk modulus of the granular pack. Our
results for two dimensions describe qualitatively the results of three
dimensional experiments.
