The Hertz-Mindlin (HM) contact model has been one of the most widespread tool for numerical simulations on granular matter behavior. Inter-granular contact forces are predicted using this approach relying on space distribution of the grains and
the equation of motions are numerically integrated. However, the basic assumptions of this mean field approximation have showed several pitfalls on the elastic description of shear phenomenon in granular packings. In this work we present an acoustic consistent contact model which scales the tangential stiffness components from the HM model. The scaling factors
are obtained by means of the numerical and empirical ultrasonic multi-component wave propagation comparison. Energy
partition between affine and non-affine particle motion seemed to explain the acoustic wave velocities differences between HM simulations and laboratory data. A pressure dependant HM pre-factor is proposed to achieve more accurate simulated results. This refined model could give new insights on rock mechanics modeling and hydrocarbon seismic exploration.