A planned array of 200,000 antennas covering an area of 200,000 km$^2$ the GRAND project is proposed to detect cosmic-ray, gamma-ray, and neutrino primaries in the energy range beyond 10$^{17}$eV. The GRAND array will be able to detect upward-going air showers initiated by neutrino interactions in the rocks on its mountainous site, furthermore, it may also detect very inclined and atmosphere-skimming air showers initiated by cosmic rays. So the corresponding shower geometry differs from the other experiments and asks for a detailed investigation. To meet the requirements of GRAND, we develop an update of CORSIKA7 for the simulation of upward-going air showers. Furthermore, we apply today’s best knowledge of parameters of the GRAND project, in particular realistic on-site atmospheres, in an extensive library of inclined air showers. Finally, we evaluate expected signal-to-noise ratios and detection thresholds for the GrandProto300 (GP300) phase of GRAND.