  In this paper we prove that the $r$-th ADO polynomial of a knot, for $r$ a
power of prime number, can be expanded as Vassiliev invariants with values in
$\mathbb{Z}$. Nevertheless this expansion is not unique and not easily
computable. We can obtain a unique computable expansion, but we only get $r$
adic topological Vassiliev invariants as coefficients. To do so, we exploit the
fact that the colored Jones polynomials can be decomposed as Vassiliev
invariants and we tranpose it to ADO using the unified knot invariant
recovering both ADO and colored Jones defined in arXiv:2003.09854. Finally we
prove some asymptotic behavior of the ADO polynomials modulo $r$ as $r$ goes to
infinity.
