In this work, we present a general numerical framework to include mesoscale physics into constitutive modelling of granular materials. In particular, we combine DEM simulations at the scale of a few grains to account for the interplay between fine and coarse grains in gap-graded materials. This work extends the range of validity of the H-model — a micromechanical model for granular materials, originally proposed by Nicot and Darve [1] and further developed in the last decade [2, 3]. The change from discrete to continuum framework utilizes statistical homogenization by computing the mechanical response of a collection of enriched mesostructures through the mesoscale discrete element method (DEM). It bridges mesostructural interactions with continuum models in a physically consistent manner. The meso-DEM simulations rely on the open-source software YADE, to simulate hexagonal patterns of coarse grains (the original H-cell) filled with fine grains, all of them interacting through linear elasto-frictional contacts laws [4]. The meso-DEM multiscale framework is benchmarked by comparing the DEM response of the H-model with those of the original analytical model under a constant volume biaxial undrained loading. It is worth highlighting that both models are able to simulate the liquefaction response of a loose sample during a constant volume biaxial test. Subsequently, the meso-DEM approach is extended to the enriched H-model incorporating fine content with the aim of accounting for gap-graded materials sensitive to internal erosion and changes in their fine content over time. The presence of fine content notably influences the liquefaction behavior, leading to a shorter liquefaction duration compared to cases without fines. This highlights the importance of taking fine contents into consideration for accurately predicting the behavior of gap-graded granular materials. Overall, this enhanced mesoscale DEM framework provides a powerful and flexible tool for accurately capturing and predicting the complex behaviors observed in granular media.