  We quantitatively investigate how collisional avalanches may developin debris
discs as the result of the initial break-up of a planetesimal or comet-like
object, triggering a collisional chain reaction due to outward escaping small
dust grains. We use a specifically developed numerical code that follows both
the spatial distribution of the dust grains and the evolution of their
size-frequency distribution due to collisions. We investigate how strongly
avalanche propagation depends on different parameters (e.g., amount of dust
released in the initial break-up, collisional properties of dust grains and
their distribution in the disc). Our simulations show that avalanches evolve on
timescales of ~1000 years, propagating outwards following a spiral-like
pattern, and that their amplitude exponentially depends on the number density
of dust grains in the system. We estimate a probability for witnessing an
avalanche event as a function of disc densities, for a gas-free case around an
A-type star, and find that features created by avalanche propagation can lead
to observable asymmetries for dusty systems with a beta Pictoris-like dust
content or higher. Characteristic observable features include: (i) a brightness
asymmetry of the two sides for a disc viewed edge-on, and (ii) a one-armed open
spiral or a lumpy structure in the case of face-on orientation. A possible
system in which avalanche-induced structures might have been observed is the
edge-on seen debris disc around HD32297, which displays a strong luminosity
difference between its two sides.
