In this paper a generalization of the well known endochronic densification law for dry sand under dynamic loading is presented, taking into account the dependence of its parameters on some measured and calculated sand properties and the variation of these parameters with time. This new generalized law needs the calibration of only one numerical coefficient. For this purpose two sets of reported experimental data of dry sand under cyclic shear strain controlled tests have been used. For non-harmonic loading a new method to determine the equivalent number of cycles has been developed. Finally, the proposed law is implemented in a one-dimensional FEM code to simulate the behavior of a sand layer subjected to the San Fernando earthquake (February 9, 1971), in order to compare the computed results with previous researches and field observations.