The Hertz-Mindlin (HM) contact model has been a cornerstone for the development of several effective medium theories (EMTs) aimed at describing the mesoscopic and macroscopic mechanical behavior of granular materials like unconsolidated sands. In addition, this model is at the core of most of the discrete particle method designs used to numerically solve for the responses of these heterogeneous materials to external perturbations, like acoustic and stress-strain experiments. However, this model has shown shortcomings in the description of the shear response characterization of granular materials, partly due to the non-affine motions experienced by the grains. We have developed a correction of the model based on a detailed calibration of our acoustic numerical results with previous empirical data. Using a microscopic approach to the grain-grain contact surfaces, the nature of the corrections found appear to be related to the shear resistant asperities and the smaller scale of the grain-grain contact areas compared to the total area assumed by the HM model. An improved HM model characterized by a tangential stiffness weakening is based on these surface corrections. Using this observation an enhanced EMT theory emerges based not only on the tangential stiffness modification but also on the velocity-pressure dependence obtained during the calibration of our numerical model.