A collisional avalanche is set off by the breakup of a large planetesimal, releasing small unbound grains that enter a debris disc located further away from the star, triggering there a collisional chain reaction that can potentially create detectable transient structures. We explore this mechanism, using for the first time a code coupling dynamical and collisional evolutions, and investigate if avalanches could explain the short-term luminosity variations observed in some extremely bright discs. We consider two set-ups: a cold disc case, with a dust release at 10au and an outer disc extending from 50 to 120au, and a warm disc case with the release at 1au and a 5-12au outer disc. We find that avalanches could leave detectable structures on resolved images, for both cold and warm disc cases, in discs with optical depth $tau$ of a few $10^{-3}$, provided that large dust masses ($gtrsim$10$^{20}$-5$times$10$^{22}$g) are initially released. The integrated photometric excess due to an avalanche is limited, less than 10% for these released dust masses, peaking in the mid-IR and becoming insignificant beyond $sim$40-50$mu$m. Contrary to earlier studies, we do not obtain stronger avalanches when increasing $tau$ to higher values. Likewise, we do not observe a significant luminosity deficit, as compared to the pre-avalanche level, after the passage of the avalanche. These two results concur to make avalanches an unlikely explanation for the sharp luminosity drops observed in some extremely bright debris discs. The ideal configuration for observing an avalanche would be a two-belt structure, with an inner belt of fractional luminosity >10$^{-4}$ where breakups of massive planetesimals occur, and a more massive outer belt, with $tau$ of a few $10^{-3}$, into which the avalanche chain reaction develops and propagates.
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