  The sources of cosmic rays with energies above 55 EeV are still mysterious. A
guaranteed associated flux of ultra high energy neutrinos known as the
cosmogenic neutrino flux will be measured by next generation radio facilities,
such as the proposed Giant Radio Array for Neutrino Detection (GRAND). By using
the orthogonal information provided by the cosmogenic neutrino flux, we here
determine the prospects of GRAND to constrain the source redshift evolution and
the chemical composition of the cosmic ray sources. If the redshift evolution
is known, independently on GRAND's energy resolution, GRAND with 200,000
antennas will constrain the proton/iron fraction to the $\sim5-10\%$ level
after one year of data taking; on the other hand, if hints on the average
source composition are given, GRAND will measure the redshift evolution of the
sources to a $\sim 10\%$ uncertainty. However, the foreseen configuration of
GRAND alone will not be able to break the degeneracy between redshift evolution
of the sources and their composition. Our findings underline the discriminating
potential of next generation radio array detectors and motivate further efforts
in this direction.
