The speed of a biased random walk on a percolation cluster at high density

We study the speed of a biased random walk on a percolation cluster on ${\mathbb{Z}}^d$ in function of the percolation parameter $p$. We obtain a first order expansion of the speed at $p=1$ which proves that percolating slows down the random walk at least in the case where the drift is along a component of the lattice.