Data-Driven (DD) Mechanics [1] is a novel paradigm in Computational Mechanics that intends to do away with the need to define involved phenomenological constitutive laws to represent the material behavior that is later used in further analyses. This groundbreaking discipline has attained remarkable results already, in particular when it comes to performing efficient multi-scale calculations of Granular Media, a field where the limitations of phenomenological regression-based relations are evident [2]. In order to perform data-driven simulations, the strain-stress phase space must be densely populated with results from either experiments or micro-scale simulations, where the micro-constituents of the material are fully resolved. The phase space of complex materials will depend not only on the magnitude of the stresses (non-linearity) but also on past stress states (history-dependence). The DD paradigm has proved itself able of handling these two [3], but the influence of loading rate (another crucial parameter) has not been addressed yet. Our work aims to incorporate this influential parameter in the DD framework. We take advantage of an application of relevance in Geotechnical Earthquake Engineering to serve as testbed: 1D Site Response Analysis (1D-SRA) [4]. A classic scenario studied in 1D-SRA consists of a soil column being subjected to a base shake representing an incoming earthquake; the variable of interest is the dynamic amplification between the column bottom (where displacements can be inputted as a boundary condition) and the upper free surface. We compare the response of the a realistic model of the column (e.g. fully resolved using the Discrete-Element Method) to the one obtained via DD calculations and to the one obtained using a phenomenological constitutive law.