  The tunnel current of a Luttinger liquid with a finite density of strong
impurities is calculated using an instanton approach. For very low temperatures
$T$ or electric fields $E$ the (nonlinear) conductivity is of variable range
hopping (VRH) type as for weak pinning. For higher temperatures or fields the
conductivity shows power law behavior corresponding to a crossover from multi-
to single-impurity tunneling. For even higher $T$ and not too strong pinning
there is a second crossover to weak pinning. The determination of the position
of the various crossover lines both for strong and weak pinning allows the
construction of the global regime diagram.
