The detailed Martian Energetic Radiation Environment Model (dMEREM) is a Geant4 based model developed for the European Space Agency, which enables to predict the radiation environment expected at different locations on the Martian orbit, atmosphere and surface, as a function of epoch, latitude and longitude, taking into account the specific atmospheric and soil composition, based on different particle propagation codes for primary Galactic Cosmic Rays or Solar Particle Events. This work describes the validation of dMEREM with differential proton fluxes measured with the NASA Curiosity rover Radiation Assessment Detector (RAD) at the Gale Crater, at the surface of Mars, from 15 November 2015 to 15 January 2016 and in the beginning of September 2017, using two different Galactic Cosmic Ray (GCR) models, the ISO-15 390 and the Badhwar-O’Neill 2014 models. This work includes a comparative study of the available Geant4 physics lists in describing the RAD measured proton spectrum, and an investigation of the proton directional spectrum at the Martian surface, and on its effect on the comparisons between models and data, which are necessarily measured within a limited field-of-view. For both GCR models and data periods there was a good agreement between the proton fluxes in the energy range between 10 and 90 MeV measured at the surface of Mars with RAD and the corresponding dMEREM predictions. Therefore, although the RAD only measures a limited field-of-view in zenith angle of the Martian Particle Radiation Field, and this effect has to be taken into account, the results obtained constitute an important benchmark in the use of dMEREM in the assessment of the expected ionising radiation field on the surface of Mars.