The Siegel modular variety, which is the moduli space of abelian varieties, is compactified by Faltings-Chai. Recently, Kajiwara-Kato-Nakayama realized this compactification as the moduli space of log abelian varieties which are degenerated objects in the world of logarithmic geometry. In the study of the mod p fiber of this compactified moduli space, log p-divisible groups occur as degenerated objects of p-divisible groups. In this talk, we explain the various stratifications on the mod p fiber of Siegel modular variety, and describe the partial compactifications of these strata by using log p-divisible groups.