[en] Cosmic rays are charged particles, as well as coproducts like photons and neutrinos, originated in cosmic-ray sources inside or outside the Galaxy. They arrive at the top of the Earth's atmosphere with primary energies of up to a few 10 EeV. When the cosmic rays enter the atmosphere, they interact with the molecules in the air and produce a large number of secondary particles, creating an extensive air shower (EAS). The ground-based observation of the EAS can be used to deduce the energy, the arrival direction, and the mass composition of cosmic rays. The Pierre Auger Observatory and the Large High Altitude Air Shower Observatory (LHAASO) are both EAS observatories aiming at solving open questions of cosmic-ray studies but focusing on different energy ranges, the highest-energy and the so-called knee (around few PeV) regions. Based on the experience gained during the operation of the Pierre Auger Observatory for more than 10 years, the Auger collaboration has proposed an upgrade project, called 'AugerPrime', with the aim of increasing the sensitivity of the surface detector array to the primary mass of cosmic rays. Both observatories employ the so-called 'hybrid detector arrays' composed of optical telescopes overlooking the longitudinal development and ground detector arrays sampling the signal densities in the lateral direction of the EAS. The ground detector arrays of both observatories are being constructed or upgraded to have various types of particle detectors (scintillator and water-Cherenkov detectors), which allow us to decompose the electromagnetic and muonic components of the EAS. In this thesis, a series of studies contributing to the AugerPrime and LHAASO projects are presented. Concerning the AugerPrime project, the present study includes R and D work of the scintillator detector and data analysis of the engineering array. For the LHAASO project, simulations of the wide field of view Cherenkov telescope array and a multivariate analysis of LHAASO-hybrid observations for the primary mass identification are presented. (author)