Backward Erosion Piping Research Articles

A physics-based approach for predicting time-dependent progression length of backward erosion piping

The progression length at various stages of backward erosion piping (BEP) in levee systems can serve as a key engineering demand parameter for reliability and risk assessments. The main goal of this study is to put forward a reliable and computationally efficient technique for predicting the progression length during BEP. Many existing modeling approaches for predicting progression lengths of BEP are either computationally expensive or consider a constant, time-independent amplification factor for the permeability coefficient. In contrast, the model developed here considers the underlying physical phenomena to properly capture the amplification of the permeability coefficient during the progression of BEP. The proposed model is derived considering the rolling threshold condition, which is obtained from the moment equilibrium of erodible particles. This modeling approach with time-varying permeability coefficients has been implemented in FLAC3D, and the derived BEP paths are validated for three flume experiments. The impact of material properties including porosity, tortuosity, and coefficient of uniformity on the amplification factor are investigated. These analyses show that the permeability amplification factor and the progression length increase with low rates at the initial stages of piping. Following the formation of the piping path, they both increase at a generally greater rate over time.

Predicting backward erosion piping hazard, Lower Mississippi Valley, USA

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.

Inverse analysis of laboratory data and observations for evaluation of backward erosion piping process

Abstract An inverse analysis procedure has been developed to interpret collected pore pressure data and observations during backward erosion piping (BEP) initiation and progression in sandy soils. The procedure has been applied to laboratory models designed to mimic the initiation and progression of BEP through a constricted vertical outlet. The inverse analysis uses three-dimensional (3D) finite element method (FEM) to successively produce models of the hydraulic head regime surrounding progressive stages of BEP based on observations at the sample surface and pore pressure measurements obtained from the laboratory models. The inverse analysis results in a series of 3D contour plots that represent the hydraulic-head regime at each stage of the BEP development, allowing for assessing the development of BEP mechanism as well as calculating the critical hydraulic conditions required for various BEP stages to initiate and progress. Interpretation of the results identified four significant stages of the piping process: (1) loosened zone initiation, (2) channel initiation and progression, (3) riser sand fluidization, and (4) loosened zone progression. Interpretation of the hydraulic head contour plots allows assessment of the critical hydraulic gradients needed to initiate and progress various components of the BEP development.

Analysis of development and depth of backward erosion pipes in the presence of a coarse sand barrier

Backward erosion piping (BEP) is a failure mechanism that can affect the safety of water-retaining structures. It can occur when a local anomaly on the downstream side of an embankment causes a concentration of seepage flow at that location. Shallow pipes may then form, progressing in the upstream direction and leading to a collapse of the water-retaining structure. A novel and economically appealing measure against BEP is the coarse sand barrier (CSB), which is now being developed in a multiscale experimental programme in the Netherlands. The method involves placing a trench filled with coarse sand below the blanket layer on the downstream side of the embankment. The CSB prevents the upstream progression of the pipe and significantly enhances resistance to BEP. This paper presents medium-scale laboratory tests involving a range of sands, barrier depths and relative densities. The piping process and the observations of pipe progression in the presence of a CSB are presented, followed by a conceptual model. The presence of a CSB changed the erosion pattern. It resulted in pipe formation perpendicular to the flow direction over the entire width of the barrier before the barrier was damaged. The findings also demonstrate the effect of material properties on pipe initiation, progression and pipe depth. Measurements of the pipe depth are presented and analysed, revealing the significance of pipe depth for understanding the piping process. This analysis shows considerable erosion in the downstream background sand and demonstrates that erosion profiles and measured pipe depths are significantly larger than in BEP tests without a CSB.

Analyses of Backward Erosion Progression Rates from Small-Scale Flume Experiments

AbstractBackward erosion piping is a leading cause of levee failures, second only to overtopping, and is therefore of great concern to engineers involved in flood control. Backward erosion piping r...

Coupled backward erosion piping and slope instability performance model for levees

While backward erosion piping (BEP) and slope instability failure mechanisms have been investigated independently, they are not analyzed concurrently despite that the response of levees embankments to the BEP may likely impact the stability of the slope, especially if levees were to fail. This study presents a framework towards interfacing soil instability and BEP simulation with the goal of producing a performance model that considers the hydro-mechanical coupling between the material properties. This is afforded by updating the stiffness and strength properties of eroded zones based on the porosity changes that are determined according to a critical diameter model. The framework is then applied on a levee without a cutoff wall built on a silty sand foundation. The results show that the captured coupling between these two failure mechanisms crucially enhances our understanding of the performance of levee systems. Specifically, the results show that coupling effects are more substantial in cases where pipes extend to more than 50% of levee’s bottom width. Furthermore, the results indicate that ignoring the softening in the strength properties of the eroded zones due to BEP leads to overestimation of the slope’s factor of safety against instability by as much as 40%.

Measuring Critical Gradients for Soil Loosening and Initiation of Backward Erosion-Piping Mechanism

AbstractA laboratory modeling program has been conducted to evaluate the hydraulic conditions required for backward erosion piping (BEP) to initiate and progress in sandy soils. The first stage of ...

Assessment of centrifuge modelling of internal erosion induced by upward flow conditions

A series of centrifuge modelling tests was performed in this study to evaluate the internal erosion induced by upward flow that typically occurs during the initiation phase of backward erosion piping. The study focuses on the assessment of the centrifuge scaling behaviour of models under different levels of centrifuge gravity. Tests were performed by maintaining the same model dimensions, soil and fluid properties and at centrifuge gravity ranging from 10g to 30g. The results from centrifuge tests are also compared with results under Earth's gravity or 1g. Two critical hydraulic gradients associated with the first visible movement of sand particles and the total heave were obtained. The critical hydraulic gradients obtained for the first visible movement of grains agree with the theoretical scaling law. However, the theoretical scaling is not applicable to the total heave due to the expansion of the models. Regardless, the critical gradients for first visible movement and total heave were 0.56–0.99 and 1.16–2.44, respectively, and these results agree with numerical and experimental values available in the literature. The seepage-induced stresses at the granular level were estimated and it was found that 16% of the critical total seepage stress was contributed by the viscous shear stress, while the remaining 84% was contributed by differential pressure across the grain.

Statistical analysis of experimentally determined critical hydraulic gradients for heave

Heave is a type of deformation that occurs due to seepage, which may evolve into backward erosion piping and eventually lead to the total collapse of a hydraulic structure. It may occur downstream of the hydraulic structure when uniform non-cohesive soil is subjected to upward seepage. In this study, the limit state condition for heave was formulated based on the equilibrium of acting forces and with the use of corresponding partial factors. During extensive laboratory research, glass beads of 0·2, 0·5 and 1·0 mm in diameter, three natural and three artificially prepared sands with grain diameters ranging from 0 to 4 mm and a uniformity coefficient CU ranging from 1·4 to 5 were subjected to upward seepage in cylindrical permeameter. The hydraulic gradient was gradually raised until heave of the material occurred. The porosity of specimens varied from 0·31 to 0·54 according to the method of placement and compaction degree. In total, 425 experiments were carried out. The results were statistically processed for nine sets of materials and partial factors were derived for a selected structure reliability. The values obtained for the factors may be used by practitioners during the safety assessment of the hydraulic structures exposed to potential heave.

Field measurements of sand boil hydraulics

A sand boil is a cone of granular material deposited on the ground surface around concentrated points of vertical seepage. Sand boils often form downstream of embankments during flood events, creating unfiltered seepage exits that may lead to initiation of backward erosion piping (BEP) in the foundation materials. Further progression of the backward erosion process may undermine the embankment, ultimately leading to collapse and breach. As the progression of BEP is dependent on the horizontal hydraulic gradient in the foundation, it is also impacted by the head loss occurring through the sand boil. In this study, the head loss occurring in sand boils along the Mississippi River and Waal River were measured and compared to predictions from a simple theoretical model. The measured head loss compared favourably with the predictions, indicating that the head loss is not constant but rather a function of grain size, sand boil throat diameter and flow rate.

Modelling seepage flow near the pipe tip

Backward erosion piping is an important failure mechanism in both dikes and dams where uniform silts and sands are covered by a cohesive layer. It is an internal erosion mechanism during which shallow pipes are formed at the interface of the aquifer and the cohesive top layer in the direction opposite to the flow. The hydraulic conditions near the pipe tip determine the onset of erosion near the pipe tip, which causes pipe lengthening. The seepage field near the pipe tip was analysed using the analytical solutions. The two-dimensional (2D) analytical solution available for calculating the seepage field at the vertical section of the pipe tip in three-dimensional (3D) groundwater flow has been validated on the basis of experiments with 3D configurations. The motion characteristics of particles at the pipe tip were explained on the basis of the analysis of the effect of the ditch at the toe of the pipe tip on the hydraulic conditions near the pipe tip. The equilibrium of the soil in front of the pipe tip was analysed to determine the pressure distribution on the top of the sand layer in front of the pipe tip. The unified method for calculating the local critical hydraulic gradient at the pipe tip in both 2D and 3D experiments was proposed. The local critical hydraulic gradients at the pipe tip were analysed for the available experiments, indicating that the influences of grain diameter and scale on the local critical hydraulic gradient are limited, a finding that is essential for the development of a new model.

A numerical experiment of backward erosion piping: kinematics and micromechanics

We report on a numerical experiment by which we investigated the propagation of an erosion pipe in a water saturated granular soil. The simulation was performed with a two-dimensional implementation of the coupling between the discrete element method and the lattice Boltzmann method. A synopsis of the numerical scheme is provided. The specimen and testing conditions were designed as representative of the pipe front region. The kinematics of mobilisation and fluidisation of the granular mass were investigated based on the physically-motivated definition of particle velocity thresholds. We measured a constant mass erosion rate, up to a clogging event. The study includes a micromechanical analysis of the response of the granular skeleton. We emphasise the influence of the unloading-induced damage on the erosion path, and the relevance of force chain arching as a self-organised resistance mechanism.

Multiscale modeling of backward erosion piping in flood protection system infrastructure

AbstractThis article presents a novel multiscale modeling approach to simulate the evolution of the backward erosion piping (BEP) process in flood protection systems (FPSs). A multiphase description of the BEP phenomenon is proposed for the numerical solution at the local scale and validated by means of full‐scale experimental results available in the literature. Results of the local scale simulations are used as the training set for a multilayer machine learning (ML) model to bridge the information between the local and system scales. Accuracy of the trained ML algorithms is demonstrated by comparing results obtained from detailed physics‐based numerical models. The novelty of the proposed methodology lies in its capability of real‐time predictions of the overall response at the system scale. A case study is presented where a portion of the Nashville Metro Levee System is analyzed over the span of a year, to assess the likelihood of BEP in the infrastructure. The capability of the model to accept water height data obtained from field measurements is exploited in the numerical simulations.

Evaluation of environmental predictors for sand boil formation: Rhine–Meuse Delta, Netherlands

During high-water events, backward erosion piping poses a serious threat to the stability of artificial levee structures. Sand boils forming on the land-side of levees are presently the best indicator of active backward erosion piping, but surveying these features across extensive levee works during flood events is time and resource intensive. Using geographic information system (GIS) technology and a probabilistic statistical analysis, this study assimilates geologic, environmental, and spatial relationship data to generate models to predict the likelihood of sand boil development. Data such as unfavorable geologic orientation, normalized difference vegetation index (NDVI), and blanket thickness are assigned to over 100 km of levees along the Waal and IJssel rivers of the Netherlands. A binary logistic regression is then applied to identify factors with statistically significant relationships to historical sand boil locations, and generate a predictive model using the significant factors. The logit models generally support previous findings indicating unfavorable orientation of geologic deposits and NDVI have a significant relationship with the spatial occurrence of sand boils. Despite this statistical significance, the best predictive model yields an accuracy only 10.83% higher than a random prediction model. Given variance in factors between models, sand boil formation appears to be dependent on a combination of conditions experienced on a local scale. Furthermore, attempting to predict sand boils using a single logit model across multiple geologic environments reduces the influence of region-specific conditions, yielding a less effective model than evaluating the systems individually.

Use of incipient motion data for backward erosion piping models

Backward erosion piping involves the gradual removal of granular material under the action of water flow from the foundation of a dam or levee, whereby shallow pipes are formed that grow in the direction opposite to the flow. This pipe-forming process can ultimately lead to failure of a water-retaining structure and is considered one of the most important failure mechanisms for dikes and levees in the Netherlands and the United States. Modeling of this mechanism requires the assessment of hydraulic conditions in the pipe, which are controlled by the particle equilibrium at the pipe wall. Since the pipe׳s dimensions are controlled by the inflow to the pipe from the porous medium, the flow through the pipe is thought to be laminar for fine- to medium-grained sands. The literature provides data for incipient motion in laminar flow, which is reviewed here and complemented with data from backward erosion experiments. The experiments illustrate the applicability of the laminar incipient motion data to determine the erosion pipe dimensions and corresponding pipe hydraulics for fine- to medium-grained sands, for the purpose of backward erosion piping modeling.

Experimental investigation of the backward erosion mechanism near the pipe tip

Backward erosion piping is a prominent failure mechanism in water-retaining structures. It is a phenomenon in which shallow pipes are formed in an upstream direction at the interface of a sandy aquifer and an impermeable top layer. Experiments were conducted at two different scales to investigate the erosion mechanism near the pipe tip that causes the pipe to lengthen at the grain scale. The erosion process of grains at the tip of the pipe was filmed from the top and the side. The observations and video recordings allowed for a better understanding of the features of the pipe tip. A zone of loosened sand grains was formed around the pipe during the pipe development. The extent of the loosened zone was determined by analysing the images captured during the lengthening of the pipe. The motion characteristics of particles at the pipe tip and the erosion mechanism near the pipe tip were obtained by analysing the erosion process observed. The findings can serve as a basis for the establishment of a criterion for pipe progression and the development of a novel piping prediction model.

Progression rate of backward erosion piping in laboratory experiments and reliability analysis

Backward erosion piping is an important failure mode of dikes and dams. The time required for the backward erosion process to result in dike failure is expected to be an important factor in the safety of dikes. This holds especially in coastal and estuarine areas which are dominated by storm surge, and pipes may not fully develop during a storm. Furthermore, insight in the duration of the various piping stages can assist in developing effective emergency mitigation measures. However, the temporal development of piping is hardly studied quantitatively, as most experimental and modelling studies focus on the critical head. Also data of real breaches is generally insufficient to determine the time to failure. As a result, currently the contribution of time required for pipe growth cannot be quantified in a deterministic and reliability analysis. In this study, it is investigated how the pipe progression rate can be predicted and applied to dike reliability. The data analysis is based on a composition of 45 small, medium and large scale experiments from six studies. Advancement rates are related to the applied hydraulic gradient and soil properties using a multivariate analysis. From the analysis we derive an empirical model for the advancement rate, including a quantification of the uncertainty. This model is applied in a reliability analysis of a hypothetical coastal and riverine dike. The results of our analysis may be used to validate transient numerical piping models, perform time-dependent probabilistic dike safety analysis and support emergency response.

Flow behaviour and piping potential at the soil–structure interface

The piping phenomenon that occurs at a soil–structure interface, referred to as backward erosion piping, is often observed beneath hydraulic structures such as conduits buried in levees. In this study, the flow behaviour and piping characteristics at the soil–structure interface were investigated by theoretical analysis using ideal uniform spherical particles and simple experiments. The factors influencing backward erosion piping beneath a structure were evaluated, with the void characteristics of the soil particles and the roughness of the structure surface identified as significant factors that affected the phenomena and the interface flow behaviour.

The effect of sudden critical and supercritical hydraulic loads on backward erosion piping: small-scale experiments

Backward erosion piping is an important failure mechanism for cohesive water-retaining structures which are founded on a sandy aquifer. This paper studies the effect of the sudden application of critical and supercritical hydraulic loads in small-scale experiments. For supercritical loads, it is clear that a part of the upper sand bed goes in suspension before being eroded, resulting in a relatively dense sand–water mixture being transported through the eroded pipe. A linear relation is found between the average velocity at which the pipe grows from downstream to upstream and the applied supercritical load. The pipe cross section is measured at the end of each test. The variations in pipe width, depth and cross section give more insight into the hydraulic regime within the pipe. The clear correspondence for gradual loading and sudden critical loading, and a smooth transition to higher supercritical loads, indicates that the fundamental erosion mechanism may be the same. Finally, grain size analysis of the eroded sand shows that the finer portion of the sand is eroded in case of subcritical or critical loading, while the coarse grains are eroded in case of supercritical loads.

A finite element method for localized erosion in porous media with applications to backward piping in levees

SummaryThis paper presents a computational method able to effectively model both the simultaneous processes typically observed in backward erosion piping, ie, the pipe tip propagation and the conduit cross‐section enlargement. The numerical method is based on the novel formulation of a problem of localized erosion along a line propagating in a multidimensional porous medium. In this line, a conduit with evolving transverse size is embedded, which conveys a multiphase flow. The two systems, porous medium and pipe, are bridged by exchange terms of multiphase fluid mass and by a shared fluid pressure field. On the contrary, different fields are considered to describe flows, which are assumed as Darcian in the porous medium and turbulent in the conduit. These two flows drive pipe propagation and enlargement, respectively, as modeled by means of proper erosion kinetic laws. The corresponding numerical formulation is based on the combination between one‐ and multidimensional finite elements, to model the erosion conduit and the porous medium, respectively. Several simulations are proposed to demonstrate the ability of the proposed approach in reproducing available experimental data of real‐scale tests on levees. Our results point out the crucial role played by the combined influence of pipe propagation and enlargement, as well as of three‐dimensional (3D) effects. We also assess the mesh independence of the proposed numerical solution, particularly as concerns the calculated pipe propagation history.