Additive group scheme actions on integral schemes defined over discrete valuation rings

Let (O,t) be a discrete valuation ring of equi-characteristic zero and let B be an integral domain which is finitely generated over O and equipped with a locally nilpotent O-derivation δ on B such that the associated Ga-action is free from fixed points. We shall describe the structure of such an O-algebra B in terms of generators and relations when B has relative dimension one over O and B/tB is an integral domain.