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Gamma-ray bursts (GRBs) are one of the candidates of ultra-high-energy(around 10^18.5 eV) cosmic-ray (UHECR) sources. We investigate high-energycosmic-ray acceleration including heavy nuclei in GRBs by using Geant 4, anddiscuss its various implications, taking both of high-luminosity (HL) andlow-luminosity (LL) GRBs into account. This is because LL GRBs may also make asignificant contribution to the observed UHECR flux if they form a distinctpopulation. We show that not only protons but also heavier nuclei can beaccelerated up to ultra-high energies in the internal, (external) reverse andforward shock models. We also show that the condition for ultra-high-energyheavy nuclei such as iron to survive is almost the same as that for about TeVgamma-rays to escape from the source and for high-energy neutrinos not to bemuch produced. The multi-messenger astronomy by neutrino and GeV-TeV gamma-raytelescopes such as IceCube and KM3Net, GLAST and MAGIC will be important to seewhether GRBs can be accelerators of ultra-high-energy heavy nuclei. We alsodemonstrate expected spectra of high-energy neutrinos and gamma rays, anddiscuss their detectabilities. In addition, we discuss implictaions of theGRB-UHECR hypothesis. We point out, since the number densities of HL-GRBs andLL-GRBs are quite different, its detemination by UHECR observations is alsoimportant.

High-energy cosmic-ray nuclei from high- and low-luminosity gamma-ray bursts and implications for multi-messenger astronomy