  Let $X={\rm Spec}\: B$ be a factorial affine variety defined over an
algebraically closed field $k$ of characteristic zero with a nontrivial action
of the additive group $G_a$ associated to a locally nilpotent derivation
$\delta$ on $B$. Suppose that $A={\rm Ker}\: \delta$ is an affine $k$-domain.
The quotient morphism $\pi : X \to Y={\rm \Spec}\: A$ splits to a composite
${\rm pr} \circ p$ of the projection ${\rm pr} : Y\times \mathbb A^1 \to Y$ and
a $G_a$-equivariant birational morphism $p : X \to Y\times \mathbb A^1$ where
$G_a$ acts on $\mathbb A^1$ by translation. In this article, we study $X$ of
dimension $\ge 3$ under the assumption that the plinth ideal $\delta(B)\cap A$
is a principal ideal generated by a non-unit element $a$ of $A$. By decomposing
$p : X \to Y\times \mathbb A^1$ to a sequence of $G_a$-equivariant affine
modifications, we investigate the structure of $X$. We show in algebraic way
that the general closed fiber of $\pi$ over the closed set $V(a)$ of $Y$
consists of a disjoint union of affine lines. The $G_a$-action on $X$ and the
fixed-point locus $X^{G_a}$ are studied with particular interest.
