We consider a partially hyperbolic set $K$ on a Riemannian manifold $M$ whose
tangent space splits as $T_K M=E^{cu}\oplus E^{s}$, for which the
centre-unstable direction $E^{cu}$ expands non-uniformly on some local unstable
disk. We show that under these assumptions $f$ induces a Gibbs-Markov
structure. Moreover, the decay of the return time function can be controlled in
terms of the time typical points need to achieve some uniform expanding
behavior in the centre-unstable direction. As an application of the main result
we obtain certain rates for decay of correlations, large deviations, an almost
sure invariance principle and the validity of the Central Limit Theorem.