Backward erosion piping in numerical models: A literature review

Errors in finite element analysis of backward erosion piping

Multi-fidelity deep neural network with Monte Carlo dropout technique for uncertainty-aware risk recognition of backward erosion piping in dikes

Backward erosion piping (BEP) is an internal erosion mechanism by which erosion channels progress upstream, typically through cohesionless or highly erodible foundation materials of dams and levees. As one of the primary causes of embankment failures, usually during high pool events, the probability of BEP-induced failure is commonly evaluated by the U.S. Army Corps of Engineers for existing dams and levees. In current practice, BEP failure probability is quantitatively assessed assuming steady state conditions with qualitative adjustments for temporal aspects of the process. In cases with short-term hydraulic loads, the progression rate of the erosion pipe may control the failure probability such that more quantitative treatment of the temporal development of erosion is necessary to arrive at meaningful probabilities of failure. This report builds upon the current state of the practice by investigating BEP progression rates through a series of laboratory experiments. BEP progression rates were measured for nine uniform sands in a series of 55 small-scale flume tests. Results indicate that the pipe progression rates are proportional to the seepage velocity and can be predicted using equations recently proposed in the literature.

Backward erosion piping accounts for one of the leading threats to dams and levees throughout the world. A laboratory modeling program has been conducted to interpret pore pressure data and observations collected during backward erosion piping (BEP) initiation and progression in sandy soils. An analytical model has been applied to assess the development of BEP mechanisms as well as calculating the critical hydraulic conditions required for various BEP stages to initiate and progress. The results with the predicted model are produced by successively matching the hydraulic head regime surrounding the developing BEP stages based on observations and pore pressure measurements obtained from the laboratory models. Interpretation based on an analytical model allows assessment of the processes governing BEP initiation and progression, including: (1) substantial concentrations of seepage flow around the edge of the exit area resulting in increased gradients and BEP initiation (i.e., sand boiling); (2) soil particles collapsing leading to BEP progression (i.e., channel development). The findings of the study identified the criterion for governing channel progression that can be applied to the assessment of BEP mechanics.

Backward erosion piping is an internal erosion mechanism during which shallow pipes are formed in the direction opposite to the flow underneath water-retaining structures as a result of the gradual removal of sandy material by the action of water. It is an important failure mechanism in both dikes and dams where sandy layers are covered by a cohesive layer. Sand boils can indicate that backward erosion is present and they are observed regularly during high water and floods. Although failure resulting from backward erosion piping is not common, several dike failures in the US, China and the Netherlands have been attributed to this mechanism. Given the impact that climate change is expected to have, prediction models for backward erosion piping are becoming increasingly important in flood-risk assessment. The prediction models available until now, such as Bligh’s rule and the Sellmeijer model, were validated in the research programme ‘Strength and loads on flood defence structures’ (SBW: Sterkte en Belastingen Waterkeringen) in the period 2008-2010 using small-, medium- and large-scale experiments. These experiments showed that an empirical adjustment of the Sellmeijer model was required to take the effect of the sand type into account and that validation was not possible for loose sand types because the erosion mode is different in those conditions. However, the absence of a theoretical basis makes this proposed empirical adjustment unsatisfactory because it lacks robustness. The main question addressed by this dissertation is how to explain and predict the pipe-forming erosion processes in uniform sands. A review of the literature, in conjunction with additional experiments, showed that the critical head in pipe formation leading to dike failure depends on either pipe initiation or pipe progression. In some experiments, the critical head for pipe initiation exceeds that of pipe progression and equilibrium is therefore prevented. The experiments in which no equilibrium was observed allowed for the development of a model for pipe initiation. It was possible to relate the observed differences in critical gradient caused by scale, sand type and configuration to the fluidisation of sand very close to the exit, where the local gradients are high. In the field, pipe progression is likely to determine the critical gradient. The Sellmeijer model predicts the progression of the pipe on the basis of the equilibrium of particles on the bottom of the pipe. The literature, and an analysis of the pipe width, depth, gradient and erosion process in experiments, indicate that pipe progression relies on two processes: primary erosion, which causes the removal of particles at the pipe tip, and secondary erosion, which causes the erosion of the pipe walls and bottom. Although the Sellmeijer model does not include primary erosion, it does function well for sand layers with a 2D exit configuration in which there is no variation in the grain size along the pipe path. The adaptation of the Sellmeijer model that was found necessary to account for the effect of sand type can be replaced by using the original model in combination with a variable bedding angle based on incipient motion experiments from the literature. The Sellmeijer model does not predict the critical gradient well for 3D configurations such as flow towards a single point, or for heterogeneous soils. Variations in the grain size in the pipe path were found to result in significantly higher critical gradients than expected, whereas a strong concentration of the flow towards the exit led to a fall in the critical gradient. 3D numerical calculations and the inclusion of primary erosion in the Sellmeijer model are needed to predict piping under these conditions.

While the Backward Erosion Piping (BEP) form of internal erosion is one of the least understood mechanisms in geotechnical engineering, a precise, mechanism-based analysis method for backward erosion piping (BEP) remains elusive for geotechnical engineers. BEP is still generally analyzed with empirically-based methods that do not consider many of the complexities of the soil, the subsurface geometry, the seepage regime, and the exit face conditions. Furthermore, many of the analysis methods commonly used for BEP were actually developed for other forms of internal erosion and adapted to BEP by correlating with crude empirical data. This paper presents a laboratory testing program performed to investigate the mechanisms of BEP under two conditions often encountered in the field: 1) exiting on a sloping exit face, and 2) exiting into a constricted exit. The study builds upon previous research on the mechanisms of piping initiation performed at Utah State University using a similar apparatus. A variety of soils representing a range of grain size, grain shape, and gradations are subjected to increasing hydraulic gradients under a variety of exit face condition including sloped exit faces and a range of constricted seepage exits. The results are compared with three-dimensional finite element analyses in order to develop a better understanding of the BEP initiation process.

Backward erosion piping (BEP) is a form of internal erosion and common failure mode along levees. Despite over a century of study, predicting where BEP will initiate is still a considerable challenge. This study proposes a new model for predicting BEP initiation focused on the widest range of applicability. A logit model is trained using data from 15 sites along the Lower Mississippi Valley. The included parameters are independent of geography or geological regime and exhibit recorded or suspected correlations to BEP. Three significant factors (95% confidence interval) are retained for the final model: cumulative clay thickness within the blanket (odds ratio (OR) 0.520), critical gradient (OR 0.001) and exit gradient (OR 63.15). Receiver operating characteristics analysis indicates an area under the curve of 0.823. The model demonstrates 71% classification accuracy, a dramatic 10% increase over previous logit model attempts. Model results are most applicable within 150 m of the levee toe to predict new incidents of BEP initiation. The final model is a useful tool for BEP assessment and mitigation efforts.

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, a 3D numerical approach of the groundwater flow leading to the erosion mechanism of backward erosion piping is presented and discussed. Comparison of the 2D and 3D numerical results explicitly demonstrates the inherent 3D nature of the piping phenomenon. In addition, the influence of the seepage length is investigated and discussed for both piping initiation and piping progression. The results clearly indicate the superiority of the presented 3D numerical model compared to the established 2D approach. Moreover, the 3D numerical results enable a better understanding of the complex physical mechanism involved in backward erosion piping and thus can lead to a significant improvement in the safety assessment of water retaining structures.

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, a 3D numerical approach of the groundwater flow leading to the erosion mechanism of backward erosion piping is presented and discussed. Comparison of the 2D and 3D numerical results explicitly demonstrates the inherent 3D nature of the piping phenomenon. In addition, the influence of the dike length is investigated and discussed for both piping initiation and piping progression. The results clearly indicate the superiority of the presented 3D numerical model compared to the established 2D approach. Moreover, the 3D numerical results enable a better understanding of the complex physical mechanism involved in backward erosion piping and thus can lead to a significant improvement in the safety assessment of water retaining structures.

Backward erosion piping is a form of internal erosion that endangers the structural stability of levees and dams. Understanding the factors that influence this form of erosion can result in improved risk assessment and more appropriate modifications to new and existing structures. Historically, it has been assumed that the presence of silt size particles would reduce the gradient required for erosion. This study investigated the influence of fines content on backward erosion piping through a series of laboratory experiments on silty sands. Laboratory results show that as the fines content increased in the samples, so too did the gradient required to produce and progress piping to failure. The results indicate that a new factor is needed to properly account for silt content in backward erosion piping (BEP) risk assessment of silty sands.

Backward erosion piping is an important failure mechanism for water-retaining structures, a phenomenon that results in the formation of shallow pipes at the interface of a sandy foundation and a cohesive cover layer. This paper studies the effect of two sand types on backward erosion piping; both in case of a homogeneous sand layer, and in a vertically layered sand sample, where the pipe is forced to subsequently grow through the different layers. Two configurations with vertical sand layers are tested; they both result in wider pipes and higher critical hydraulic gradients, thereby making this an interesting topic in research on measures to prevent backward erosion piping failures. Grain size analysis shows that the finer fraction is more likely to be eroded and also indicates that grains usually do not settle once they are eroded.

Backward erosion piping is an important failure mechanism for water-retaining structures, a phenomenon that results in the formation of shallow pipes at the interface of a sandy or silty foundation and a cohesive cover layer. This paper studies the effect of two soil types on backward erosion piping; both in case of a homogeneous sand layer, and in a vertically layered sand sample, where the pipe is forced to subsequently grow through the different layers. Two configurations with vertical sand layers are tested; they both result in wider pipes and higher critical gradients, thereby making this an interesting topic in research on measures to prevent backward erosion piping failures.

Backward erosion piping (BEP), a form of internal soil erosion, often threatens the safety of dykes built on alluvial deposits. To reduce the risk of dyke failure due to piping, reliable and cost-effective mitigation measures are essential. For the first time, this paper proposes the use of nature-inspired low-permeability barriers to mitigate BEP. The potential of this novel solution is demonstrated in a series of laboratory physical tests. Low-permeability barriers are created by mixing sand either with aluminium–organic matter flocs, or clay. The results show that both kinds of barriers can significantly inhibit pipe progression and intercept the erosion channels. The hydraulic gradients required for pipes to reach the barrier are significantly higher than the critical gradient measured in the absence of barriers, ranging from 2·2 to 7·4 times greater than those in sand alone. The associated mitigating mechanisms include the dissipation of flow energy, resistance to internal erosion due to pore space clogging and prevention of sand fluidisation. The mitigating effect is affected by the reduction of hydraulic conductivity, the depths and the heterogeneity of barriers. The findings of this experimental work provide guidance for the design of low-permeability barriers in practice and contribute to the development of numerical models for BEP.

Backward erosion piping (BEP) is a type of internal erosion that typically involves the erosion of foundation materials beneath an embankment. BEP has been shown, historically, to be the cause of approximately one third of all internal erosion related failures. As such, the probability of BEP is commonly evaluated as part of routine risk assessments for dams and levees in the United States. Currently, average gradient methods are predominantly used to perform these assessments, supported by mean trends of critical gradient observed in laboratory flume tests. Significant uncertainty exists surrounding the mean trends of critical gradient used in practice. To quantify this uncertainty, over 100 laboratory-piping tests were compiled and analysed to assess the variability of laboratory measurements of horizontal critical gradient. Results of these analyses indicate a large amount of uncertainty surrounding critical gradient measurements for all soils, with increasing uncertainty as soils become less uniform.

Random finite element analysis of backward erosion piping