Fragmentation of relativistic $^{16}$O in nuclear emulsions and in future runs at the LHC was simulated with the Abrasion-Ablation Monte Carlo for Colliders (AAMCC) model. The calculated probabilities of production of specific elements as spectators in $^{16}$O--Em collisions were found in general agreement with measurements. However, the calculated multiplicity distributions of $^4$He fragments have demonstrated the underestimation of channels with single $^4$He and, especially with two and three $^4$He. Such a deficiency of multiple production of $^4$He can be attributed to $\alpha$-clustering in initial $^{16}$O. The cross sections of production of given numbers of spectator neutrons and nucleons as well as certain spectator nuclei were also calculated with AAMCC for $^{16}$O--$^{16}$O collisions at the LHC.