The piping flow erosion process, which involves the enlargement of a continuous tunnel from upstream to downstream levels, is a major cause of the degradation of water retaining structures. Such pipes can be imputed to roots or burrows. The erosion coefficient must be known in order to estimate the remaining time to failure and downstream flooding. The Hole Erosion test is a laboratory experiment particularly well-adapted for estimating this geotechnical parameter. We therefore propose simplified expressions for the remaining time to breaching by accounting for this erosion parameter. We established that the evolution of the pipe radius obeys a two-parameter scaling law. The first parameter is the critical stress while the second parameter is the characteristic time of piping erosion, which is a function of the initial hydraulic gradient and the erosion coefficient. Here, we establish new mechanically based relations for water retaining structures. The time to failure and peak flow are related to the two basic parameters of piping failure: the coefficient of erosion and the maximum pipe diameter prior to roof collapse and breaching. Orders of magnitude of the coefficient of erosion and the erosion rate are finally inferred from 18 case studies.