A semi-theoretical model is available to estimate the effect of backward erosion piping by underseepage in a dike by computing the critical head. The model accounts for the groundwater flow through the subsoil, pipe flow through the erosion channel and a limited particle equilibrium at the bottom of the channel. This model is extended and updated with the results of a wide range of tests presented in the paper of (Van Beek et al., 2011). The smallscale tests are analyzed by means of a multivariate regression in order to identify the level of influence of each variable. The regression outcome for the permeability corresponds precisely with the outcome of the prediction rule. The effect of relative density, uniformity and particle roundness is empirically dealt with. The role of the particle size is adapted in the new empirical formulation. RÉSUMÉ. Les conséquences d'une érosion régressive par écoulement interne sous une digue peuvent être évaluées en calculant la charge hydraulique critique à l'aide d'un modèle semithéorique. Le modèle tient compte de l'écoulement dans le sous-sol, de l'écoulement de conduit dans le chenal d'érosion et de l'équilibre des particules à la base du chenal. Ce modèle est généralisé et actualisé avec les résultats obtenus sur une large gamme d'essais publiés par Van Beek et al. (2011). Les essais à petite échelle sont analysés par régression multivariée afin de quantifier le niveau d'influence de chaque variable. Le résultat de la régression pour la perméabilité correspond précisément au résultat du modèle. Les effets de la densité relative, de l'uniformité et de la rondeur des particules sont traités de façon empirique. Le rôle de la taille des particules est adapté à la nouvelle formulation empirique.

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The process of backward erosion piping poses a threat to dams and dikes on foundations of nonplastic sands and silts. The available models for design and predictions focus predominantly on the progression of the pipe. However, sand boils in the field will occur as a result of the initiation of sand transport. Although criteria are available for predicting sand boiling and heaving in columns, there is no model describing the initiation of piping in situations where the exit flow is not uniform, as is the case in most backward erosion experiments and situations in the field. This study compared laboratory experiments in which the process of initiation leads directly to failure with analytical and numerical groundwater flow calculations and heave criteria. The aim was to develop a model for the onset of pipe formation. It emerged that the sand bed needs to be fluidised over a distance of at least 20 times the grain diameter from the toe of the structure for a pipe to initiate. The proposed model explains the scale effects of grain size and configuration on a critical gradient. This approach clarifies the processes governing pipe initiation and progression and it can be used to establish a conservative estimate of the critical head in uniform sands, which is essential for laboratory work on this topic and for the appraisal of sand boils in practice.

One of the failure mechanisms that can affect the safety of a dyke or another water-retaining structure is backward erosion piping, a phenomenon that results in the formation of shallow pipes at the interface of a sandy or silty foundation and a cohesive cover layer. The models available for predicting the critical head at which the pipe progresses to the upstream side have been validated and adapted on the basis of experiments with two-dimensional (2D) configurations. However, the experimental base for backward erosion in three-dimensional (3D) configurations in which the flow concentrates towards one point, a situation that is commonly encountered in the field, is limited. This paper presents additional 3D configuration experiments at two scales with a range of sand types. The critical gradients, the formed pipes and the erosion mechanism were analysed for the available experiments, indicating that the erosion mechanism is more complex than previously assumed, as both erosion at the tip of the pipe (primary erosion) and in the pipe (secondary erosion) are relevant. In addition, a 3D configuration was found to result in significantly lower critical gradients than those predicted by an accepted calculation model calibrated on the basis of 2D experiments, a finding that is essential for the application of the model in the field.