  We investigate $D$-dimensional gravitational model with curvature-quadratic
and curvature-quartic correction terms: $R+R^2+R^4$. It is assumed that the
corresponding higher dimensional spacetime manifold undergos a spontaneous
compactification to a manifold with warped product structure. Special attention
is paid to the stability of the extra-dimensional factor space for a model with
critical dimension D=8. It is shown that for certain parameter regions the
model allows for a freezing stabilization of this space. The effective
four-dimensional cosmological constant is negative and the external
four-dimensional spacetime is asymptotically AdS.
