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The form of the failure probability distribution for discrete and continuum percolation in the critical region is obtained. The existence of bond-strength fluctuations in continuum percolation changes the distribution from a very steep form (at least an exponential of an exponential) to a Weibull-like form (exponential of a powerlaw). Futhermore, a size effect of the typical failure strength analogous to that of brittle materials is derived.
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Didier Sornette (1988) studied this question.
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