A mathematical model for piping

Sellmeijer, J. B.; Koenders, M. A.

doi:10.1016/s0307-904x(09)81011-1

Cited by 60 publications

(30 citation statements)

References 2 publications

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“…Based on these observations (Sellmeijer, 1988;Sellmeijer et al, 1991) proposed a conceptual model, resulting in a piping rule analogous to relation [1]. The model covers three essential areas: groundwater flow through the subsoil, pipe flow through the erosion channel and limit equilibrium of sand particles at the bottom of the channel.…”

Section: Relationmentioning

confidence: 99%

Fine-tuning of the backward erosion piping model through small-scale, medium-scale and IJkdijk experiments

Sellmeijer¹,

Cruz²,

Beek³

et al. 2011

European Journal of Environmental and Civil Engineering

101

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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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Section: Relationmentioning

confidence: 99%

Fine-tuning of the backward erosion piping model through small-scale, medium-scale and IJkdijk experiments

Sellmeijer¹,

Cruz²,

Beek³

et al. 2011

European Journal of Environmental and Civil Engineering

101

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“…Originally developed by Sellmeijer (1989); Sellmeijer and Koenders (1991) and Koenders and Sellmeijer (1992), the equation for critical water height difference did not consider thickness of the sand layer (D s ): κ is calculated according to Eq. (21):…”

Section: Probability Of Pipingmentioning

confidence: 99%

Development of dike fragility curves for piping and micro-instability breach mechanisms

Vorogushyn

Merz

Apel

2009

Nat. Hazards Earth Syst. Sci.

117

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Abstract. The paper analyses the prevailing breach mechanisms of fluvial dikes. Piping in the dike foundation and slope failure as a consequence of seepage flow through a dike core (micro-instability) were identified as two of the dominant breach mechanisms for historically-grown dikes along with overtopping and slope macro-instability. For the former two mechanisms the physically-based and empirical process descriptions were reviewed and led to the formulation of the reliability functions. Evaluation of these functions in the Monte Carlo framework for the time dependent load led to the development of fragility functions. These functions indicate the probability of failure of a dike section upon loading and can be computed for each spatially discretised dike section. The probability of breaching is conditioned by the uncertainty in geometrical and geotechnical dike parameters. This uncertainty is explicitly taken into account during computation of the fragility functions in a Monte Carlo simulation. Sensitivity analysis was carried out in order to identify the sensitive geotechnical parameters influencing the distribution of failure probability. The identification of sensitive parameters indicates the priorities in geotechnical measurement campaigns aimed at the assessment of dike stability. The newly developed fragility functions can be applied in flood hazard and risk assessment studies for modelling of dike failures in a probabilistic framework.

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“…Nowadays, Sellmeijer's prediction model is often used to estimate the critical gradient at which backward erosion piping leads to failure, see equation 1 (Sellmeijer and Koenders 1991;Sellmeijer 1988).…”

Section: Current Formulaementioning

confidence: 99%

3D character of backward erosion piping: Small-scale experiments

2014

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Backward erosion piping is an important failure mechanism for cohesive water retaining structures which are founded on a sandy aquifer. At present, the prediction models for safety assessment are often based on 2D assumptions. In this work, the 3D character of the phenomenon is demonstrated on the basis of small-scale experiments. Our approach reveals the correlation between the occurrence of piping initiation and progression and the width of the physical model, which is a measure for the inclusion of the third dimension (to be regarded in a real dike situation as the influence zone of a crater). In addition, it was found that the model width has an impact on pipe characteristics and pipe development. Therefore, our results enable a better understanding of the complex physical mechanism related to backward erosion piping and thus can lead to a significant improvement in the safety assessment of water retaining structures.

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A mathematical model for piping

Cited by 60 publications

References 2 publications

Fine-tuning of the backward erosion piping model through small-scale, medium-scale and IJkdijk experiments

Fine-tuning of the backward erosion piping model through small-scale, medium-scale and IJkdijk experiments

Development of dike fragility curves for piping and micro-instability breach mechanisms

3D character of backward erosion piping: Small-scale experiments

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