A methodology was developed to predict pressure and temperature regimes achieved during detonation of RDX/TNT compositions with inert granular inclusions. The predicted pressures and temperatures are used as inputs for thermochemical simulations to design detonation synthesis experiments that utilize shock-induced chemical reactions to produce ceramic nanomaterials. This study computationally assessed the effects of inert spherical sand inclusions and porosity produced by inert additives on the sensitivity of the explosive composition during the shock-to-detonation transition using a limited scope approach through Lee-Tarver ignition and growth modeling. On the continuum scale, the effects of inert additives on pressure generation behind the detonation wave and within the reaction zone were parameterized through numerical modeling using Jones-Wilkins-Lee equations of state coupled with programmed burn and ignition and growth burn models. The developed model predicted convergent shock loading within the sand inclusions producing localized pressures as great as 135 GPa with associated superheating to temperatures greater than 5000 Kelvin. These results imply that phase formation in an inert inclusion will depend on the location of the material relative to the point of shock convergence where pressures and temperatures can far exceed the Chapman-Jouguet values for the explosive matrix used in the tests.