  In this paper, we prove compatibilities of various definitions of relatively
unipotent log de Rham fundamental groups for certain proper log smooth integral
morphisms of fine log schemes of characteristic zero. Our proofs are purely
algebraic. As an application, we give a purely algebraic calculation of the
monodromy action on the unipotent log de Rham fundamental group of a stable log
curve. As a corollary we give a purely algebraic proof to the transcendental
part of Andreatta-Iovita-Kim's article: obtaining in this way a complete
algebraic criterion for good reduction for curves.
