Dike Slope Research Articles

Characterization of Overtopping Volumes from Focused Wave Groups over Smooth Dikes with an Emerged Toe: Insights from Physical Model Tests

This research examines the overtopping volumes associated with focused wave groups on smooth dikes with an emerged toe. Focused wave groups are employed to represent the highest waves of random sea states in a compact form, obviating the need to model the entire irregular wave train. This study investigates how overtopping volumes are affected by focus location and phase. A total of 418 experimental tests were gathered and analyzed. Data with overtopping volumes below 600 L per meter (prototype conditions) were excluded in order to focus on extreme overtopping events, resulting in 324 relevant test cases. The experiments used first-order wave generation theory to analyze structural response. Subsequent studies will address the errors induced by this approximation and compare it with second-order wave generation. The experiments simulated extreme wave impacts on an idealized coastal layout, comprising a 1:6.3 foreshore slope and three different dike slopes, including vertical structures, with the initial still water level set below the dike toe. This study employed the NewWave theory to generate focused wave groups, with the objective of extending recent research on wave overtopping under varied conditions. The results, analyzed in both dimensional and non-dimensional forms, indicate that overtopping volumes are significantly influenced by the focus phase. Critical focus locations were identified at a distance of one-third of the deep-water wavelength from the toe.

A New Numerical Method to Evaluate the Stability of Dike Slope Considering the Influence of Backward Erosion Piping

Backward erosion piping, a soil erosion phenomenon induced by seepage, compromises the stability of water-retaining structures such as dikes. During floods, the seepage in the dike body increases due to high water levels, which directly affects the progression of the piping channel. The formation of the piping channel then impacts the stability of the dike. In this paper, an improved piping model that considers the impact of seepage in the dike body is proposed based on Wewer’s model. Specifically, we added a seepage field of the dike body to the original model to account for the impact of dike-body seepage on the evolution of piping. The seepage field of the dike body is solved using Darcy’s law and the continuity equation for unsaturated porous media. In addition, this approach also incorporates the coupling effect of seepage stress. The accuracy of the model was verified through comparing the calculated results with the IJkdijk experiment and Wewer’s results. The effects of BEP on dike stability were investigated using the proposed improved piping model. The two major conclusions of the study are that (1) the incorporation of unsaturated seepage enhanced the performance of the piping model, allowing it to more accurately simulate the development of pipe length and the changing of pore pressure; and (2) the formation of the pipe impacted dike stability, leading to a substantial reduction in the safety factor of the dike slope.

Numerical study of wave run-up on sea dikes with vegetated foreshores

Integrating coastal vegetation into sea dikes is a nature-based approach aimed at combining disaster prevention with ecological sustainability in coastal areas. This study investigates the impact of vegetation on the wave run-up on dikes through numerical analysis. The numerical model used in the study solves the Reynolds-averaged Navier–Stokes equations by adding a vegetation resistance force to account for momentum loss. A stabilized k–ω shear stress transport model considering the vegetation effect was adopted for turbulence closure. A series of numerical simulations was carried out on the wave run-up (Ru) on dikes, focusing on the effects of different vegetation heights, densities, zone lengths, and dike slopes under various wave conditions. The results indicate that vegetation can significantly decrease Ru and may cause the wave to change from breaking to nonbreaking on dikes. The Ru behaviors depend on whether waves break and can be well characterized by the Iribarren number and dimensionless wave momentum flux parameter under breaking and nonbreaking conditions, respectively. Finally, the multivariate non-linear regression (MNLR) and artificial neural network (ANN) methods were adopted to explore a prediction model for evaluating Ru. Comparisons showed that the prediction performance of the ANN model is superior to that of the MNLR model. The ANN model has the potential as a promising predictive tool for obtaining wave run-up on dikes with vegetated foreshores under breaking and nonbreaking conditions.

Pre- and post-failure behaviour of a dike after rapid drawdown of river level based on material point method

The rapid drawdown of river level is very detrimental to the stability of dikes. In this paper, the entire slope failure process of a real dike with sandy soil interlayer after rapid river drawdown is accurately reproduced using the material point method (MPM). The analysis of pre-failure behaviour, in combination with field test results, reveals the triggering mechanism of such dike slope failure, demonstrating that the presence of sandy soil interlayer is the leading cause of dike instability. By tracking the response of the dike slope from failure initiation to runout termination, the failure mode of the dike slope with sandy soil interlayer is identified as a progressive and retrogressive failure mode, with shallow and deep-seated slip surfaces appearing successively. Parametric studies indicate the friction angle, cohesion, dilatancy, and permeability of the sandy soil play significant roles in dike slope stability. A relationship between the permeability of sandy soil and the maximum sliding displacement is also found. In the face of rapid river drawdown, river-facing slope surface protection is the most effective protection measure for such dike slopes with sandy soil interlayer, while traditional riprap protection at the slope toe has a limited protecting effect.

Strategic coastal dike shape for enhanced tsunami overflow reduction.

Coastal dikes are an essential social infrastructure to mitigate tsunami damage. However, there are no clear guidelines on effective dike shapes for reducing tsunami overflow. To examine effective dike shapes, numerical simulations of the amount of tsunami overflow at coastal dikes are conducted with reference to tsunami waveforms caused by the Great East Japan Earthquake. Results reveal the relationship between the dike shape and the amount of the overflow; the mechanism of overflow reduction based on the velocity and water level distribution is also verified. The comparison of the seaward and landward slopes of coastal dikes reveals that the seaward slope has a greater impact on the overflow, and the seaward slope with a vertical wall or a wave return structure reduces the overflow by 5%-30% compared to the 1:2 (26.6°) seaward slope. The landward slope should be determined based on the tsunami scale and the scour related to the dike stability. Since tsunami inflow damages human life and social infrastructure, achieving the overflow reduction without increasing dike height is vital. Our work contributes to rational design guidelines for coastal dikes.

Effects of flood wave shape on probabilistic slope stability of dikes under transient groundwater conditions

ABSTRACT The time-dependent response of pore water pressures during floods largely determines the safety against geotechnical failure of dikes, which is deemed to be highly dependent on the uncertain shape (duration, maximum height, etc.) of the flood discharge wave. This paper derives the uncertainty of flood wave shape from a database of precalculated hydrographs (GRADE) and evaluates the effect of shape variability on probabilistic safety estimates of slope stability, using a modelling chain consisting of a transient hydrological model (MODFLOW) and a probabilistic dike slope safety assessment (FORM). Accounting for flood wave uncertainty with transient groundwater flow generally leads to higher reliability estimates for slope stability, compared to the steady-state groundwater condition and other conservative assumptions, but to lower reliability estimates compared to a single design flood wave. Furthermore, the uncertainty of the flood wave shape can be as important as the uncertainty in geotechnical properties. For landside dike slope stability, the volume of the flood wave is the most important factor, while riverside slope stability depends mainly on the total water level drop after the peak. These two waveform characteristics are thus essential uncertainties to consider in probabilistic assessments of dike safety with transient groundwater conditions.

Overflow Tests on Grass-Covered Embankments at the Living Lab Hedwige-Prosperpolder: An Overview

In regions with a temperate climate, a well-maintained grass sod on a clay layer is considered a reliable protection for dams and dikes. In the Living Lab Hedwige-Prosperpolder, on the left bank of the Scheldt river straddling the border between Belgium and the Netherlands, a series of 27 overflow tests with a purpose-built overflow generator has been executed to determine the strength of the protective layer against erosion at various conditions. The goal of this paper is to inform on the executed test program and the initial results. From the results, it was concluded that in general, a high-quality grass cover on the landside dike slope can withstand high overflow discharges well for 12 to 30 h, without severe erosion damage. Anomalies, such as the presence of animal burrows, reed vegetation, and already present deformations can strongly reduce the resistance of the cover layer and may lead to failure within a couple of hours.

Assessing lithological uncertainty in dikes: Simulating construction history and its implications for flood safety assessment

AbstractDikes often have a long history of reinforcement, with each reinforcement adding new material resulting in a heterogeneous dike. As data on the dike internal heterogeneity is sparse, it is generally overlooked in the stability assessment of dikes. We present an object‐based and process‐based model simulating dike construction history on archeological dike cross, yielding similar patterns of heterogeneity as observed in real dikes, and apply it in a dike safety assessment. Model predictions improve when being based on more accurate statistics of dike buildup, or when being conditioned to ground truth data. When incorporated in a dike stability assessment, multiple model runs can be coupled to hydrological simulations and dike slope stability calculations, resulting in a probabilistic stability assessment considering internal dike heterogeneity. While high‐resolution observations are still sparse, good model accuracies can be reached by combining regional information on dike buildup with local point observations and this model provides a parsimonious basis to include information of internal dike heterogeneity in safety assessments.

Wave Run-Ups and Overtopping Affected by Oblique Wave Approaches and Currents

Abstract To quantify the effect of a current on the height of a wave’s run-up and overtopping combined with an oblique wave approach, the “FlowDike” hydraulic research project was carried out. Tests were performed on two dike slopes of 1:3 and 1:6. Waves were generated across (perpendicular to) the physical model and also inclined in-plane to the stream axis. Oblique waves were generated both towards and along the flow’s direction. The effect of the current and of the wave direction on the height of the wave run-up and amount of the wave overtopping was expressed by means of a combined correction factor for the wave’s inclination and flow velocity. The results of the research confirmed that the flow velocity had only a small effect.

Global Sensitivity Analysis of Groundwater Related Dike Stability under Extreme Loading Conditions

With up to 15% of the world’s population being protected by dikes from flooding, climate-change-induced river levels may dramatically increase the flood risk of these societies. Reliable assessments of dike stability will become increasingly important, but groundwater flow through dikes is often oversimplified due to limited understanding of the important process parameters. To improve the understanding of these parameters, we performed a global sensitivity analysis on a comprehensive hydro-stability model. The sensitivity analysis encompassed fifteen parameters related to geometry, drainage conditions and material properties. The following three sensitivity settings were selected to characterize model behavior: parameter prioritization, trend identification and interaction qualification. The first two showed that dike stability is mostly dependent on the dike slope, followed by the type of subsurface material. Interaction quantification indicated a very prominent interaction between the dike and subsurface material, as it influences both groundwater conditions and dike stability directly. Despite our relatively simple model setup, a database containing the results of the extensive Monte Carlo analysis succeeded in finding most of the unsafe sections identified by the official inspection results. This supports the applicability of our results and demonstrates that both geometry and subsurface parameters affect the groundwater conditions and dike stability.

Method to assess the interplay of slope, relative water depth, wave steepness, and sea state persistence in the progression of damage to the rock layer over impermeable dikes

The objective of this research was to develop a new methodology to assess the progression of damage to sloped coastal structures such as revetments, dikes, and mound breakwaters by applying dimensional analysis. The adequacy of the derived functional relationship was verified with the same experimental data (rock layer over impermeable dikes under irregular waves and four dike slopes) originally used to obtain the Van de Meer stability formula. The method addresses the epistemic uncertainty of the damage evolution model and its dependence on the experimental design and technique, the non-dimensional incident sea-state characteristics at the foot of the slope, relative water depth, relative wave height, wave steepness, sea-state persistence, and number of waves. It is specific to each dike slope. Specifically, the scarcity of experimental data in shallow water conditions are considered. Accordingly, the sigmoid function is proposed as an alternate model to quantify the progression. In the current state of knowledge, it is uncertain how the formulas based on lab-experiments perform for real-world design conditions. More research in the form of further test series is thus necessary to explore this new approach in greater depth.

Overtopping‐Induced Failure of Non–Cohesive Homogeneous Fluvial Dikes: Effect of Dike Geometry on Breach Discharge and Widening

AbstractLaboratory experiments were conducted to assess the influence of dike geometry on the breaching of non‐cohesive homogeneous fluvial dikes. Both the channel‐side and floodplain‐side dike slopes and the crest length were varied systematically. The time‐evolution of the breach discharge and breach width was monitored. Dikes having a larger volume per unit width lead to a more gradual increase in breach discharge and in breach width during the first stage of breach expansion (i.e., phase of rapid erosion). In contrast, the later stage of gradual breach widening is less influenced by the dike geometry. The breach hydrographs were observed to follow three distinct patterns, which are explained based on the relative magnitude of two characteristic time scales and of a normalized form of the dike unit volume.

Calibration and preparation of field measurements of oblique wave run-up and overtopping on dikes using laser scanners

Wave overtopping is typically measured in the field using overtopping tanks. In this paper, an alternative system is developed that uses two laser scanners. The system also measures wave run-up, as well as run-up depths and velocities, both during perpendicular and oblique waves on a dike in the field. The paper considers the first calibration tests with the system in the field, with perpendicular and oblique waves generated by the wave run-up simulator on a grass dike slope. Furthermore, simulations are performed with the numerical wave model SWASH, to gain more insight in the potential performance of the system during actual oblique wave attack during a storm. The run-up is determined from the measured elevation and reflection intensity, which agrees well with the visually observed run-up. Run-up depths and front velocities can be determined accurately as well. The (virtual) wave overtopping discharge can be calculated from the data, which agrees well with the most commonly used overtopping equations for perpendicularly incident waves. Finally, from the simulated run-up data of obliquely incident waves, it is concluded that an estimate can be obtained of the incident wave period and wave angle of incidence at the toe of the structure.

A physical model simulation of combination of a geo-bag dike and mangrove vegetation as a natural coastal protection system for the Indonesian shoreline

To mitigate coastal erosion, coastal regions worldwide focus on sustainable coastal development practices. To this end, many countries use natural protective methods, including the use of vegetation such as mangroves. However, this practice is challenging. For example, mangrove seedlings are often damaged by sea waves before they can grow strong enough to protect coastal lines, and hence they require protection for at least two years after planting. In this study, a coastal protection system combining a main natural structure and a temporary artificial structure is proposed. The effectiveness of this method is related to the deep-water steepness of the incoming waves and the transmitted wave parameters. The transmitted waves consist of two parts: waves transmitted after the water has passed through the artificial system, and those transmitted after it has passed through the mangroves. The first part affects the juvenile mangroves, whereas the latter affects the shoreline. To identify natural coastal protection methods applicable to Indonesia, wave steepness data specific to Indonesian waters were derived using data from an online open database. After weighing the alternatives for temporary human-made structures, the geo-bag dike was chosen. The effects of various geo-bag-dike configurations and geo-bag unit weights on wave height reduction were quantified. Laboratory experiments were conducted on a narrow wave flume using a mangrove model as the main structure and geo-textile-geo-bag models as temporary artificial structures. Based on the dimensionless wave steepness data, the wave conditions of Indonesian waters were produced in the laboratory. This study determined the most effective geo-bag-dike configuration to reduce the wave height, which affects juvenile mangroves, and to decrease the height of transmitted waves after they have passed through mangroves, which cause shoreline erosion. The results reveal that the effectiveness of a temporary geo-bag-dike structure significantly depends on the incoming wave height and the dimensionless wave steepness. The steeper the waves are, the greater the reduction in the transmitted wave height. The results also showed that the reduction in wave height due to the presence of a geo-bag-dike structure varied between 2% and 65% in front of the juvenile mangroves and between 8% and 71% after the waves passed through them. The most effective geo-bag-dike configuration uses relatively heavy geo-bag units with a moderate dike slope of 1:2.0. The reduction significantly depended on the wave parameters, slope, and unit weight.

Determination of Semi-Empirical Models for Mean Wave Overtopping Using an Evolutionary Polynomial Paradigm

The present work employs the so-called Evolutionary Polynomial Regression (EPR) algorithm to build up a formula for the assessment of mean wave overtopping discharge for smooth sea dikes and vertical walls. EPR is a data-mining tool that combines and integrates numerical regression and genetic programming. This technique is here employed to dig into the relationship between the mean discharge and main hydraulic and structural parameters that characterize the problem under study. The parameters are chosen based on the existing and most used semi-empirical formulas for wave overtopping assessment. Besides the structural freeboard or local wave height, the unified models highlight the importance of local water depth and wave period in combination with foreshore slope and dike slope on the overtopping phenomena, which are combined in a unique parameter that is defined either as equivalent or imaginary slope. The obtained models aim to represent a trade-off between accuracy and parsimony. The final formula is simple but can be employed for a preliminary assessment of overtopping rates, covering the full range of dike slopes, from mild to vertical walls, and of water depths from the shoreline to deep water, including structures with emergent toes.

Relative Magnitude of Infragravity Waves at Coastal Dikes with Shallow Foreshores: A Prediction Tool

Despite the widely recognized role of infragravity (IG) waves in many often-hazardous nearshore processes, spectral wave models, which exclude IG-wave dynamics, are often used in the design and assessment of coastal dikes. Consequently, the safety of these structures in environments where IG waves dominate remains uncertain. Here, we combine physical and numerical modeling to: (1) assess the influence of various offshore, foreshore, and dike slope conditions on the dominance of IG waves over those at sea and swell (SS) frequencies; and (2) develop a predictive model for the relative magnitude of IG waves, defined as the ratio of the IG-to-SS-wave height at the dike toe. Findings show that higher, directionally narrow-banded incident waves; shallower water depths; milder foreshore slopes; reduced vegetated cover; and milder dike slopes promote IG-wave dominance. In addition, the empirical model derived, which captures the combined effect of the varied environmental parameters, allows practitioners to quickly estimate the significance of IG waves at the coast, and may also be combined with spectral wave models to extend their applicability to areas where IG waves contribute significantly.

Experimental Study on Sand Dike Breaching by Wave Overtopping

A series of large-scale experiments are conducted to investigate the breaching process of sand dikes under wave overtopping. The dikes are constructed with uniform sand, covered with a thin clay layer on the upstream slope to prevent seepage during breaching. Wave height, wave period and dike slopes are systematically varied to examine their effects on the breaching process. Morphological development of the breach is recorded using a 3D laser scanner. The results indicate that erosion starts at the downstream edge of dike crest and the downstream dike slope gradually flattens. The breach cross-section is observed to be of a trapezoidal shape. Breach flow increases at an accelerating rate after initial overtopping until a peak flow is attained. The breach dimension and peak flow rate increase with increasing wave height, wave period, and upstream and downstream dike slopes. A dimensionless dike breach parameter is proposed to establish regression relations for the breach geometry and flow characteristics.

Stability Analysis of Flood Spreading Systems in Arid Regions, Iran

Water spreading projects by controlling the floodwater, infiltrating to subsurface and recharging the groundwater, will result in a reliable source of water in dry seasons. In this study, an arid region in Ilam province of Iran was chosen and after careful evaluation, three water spreading projects, including mechanical and water structures, were selected to be executed in the area, and while estimating the discharge in each site using HEC-HMS model, the stability condition of the structures was studied using Geo-Slope software. Also, the stability and instability factors of the structures and dikes were analyzed in flood spreading systems using various methods at the end of construction, steady seepage, and rapid drawdown stages. Results showed that in both static and quasi-static stability analysis of downstream and upstream slopes of dikes based on the calculated safety factors compared to the allowed safety factor, the slopes of embankment dams in all three stages possess the required safety factor.

Utilization of a pond in East Jakarta for a sustainable urban drainage system model

High population growth in the area of East Jakarta has led to more construction of settlements, including in several areas of East Jakarta, which includes Jalan Pengantin Ali in Ciracas Sub-District. When very heavy rains fall in the rainy season, this place is often flooded, while in the dry season there is a scarcity of raw water or clean water. This study examines the application of sustainable drainage systems with the technique of making a retention pond as a flood control alternative. The purpose is to hold water runoff during the rainy season so that it does not enter the river directly, and so that some of the collected water could be used to meet the clean water supply needs of the people. The calculation of rainwater potential used the height of the monthly average rainfall. The retention pond capacity was determined by the pool simulation method during the rainy season. The planned flood discharge was calculated using the Nakayasu HSS method. The obtained results indicated a peak discharge value with a return period of 2 years that amounted to 8.84 m3/sec. The planned retention pond area is 6380.94 m2, with a retention pond height of 4 m, a dike slope of 1:1, and the elevation of the overflow base being at an altitude of 38.5 meters above sea level (masl). From the results of the HEC-RAS 5.0.6 software, an optimal overflow width of 2 m was obtained, with an outflow discharge of 4.55 m3/sec and a pond volume of 19530 m3. With the retention pond, flood peak discharge could be reduced by 4.29 m3/sec. This will allow the flood discharge in the rainy season to be reduced and increased clean water needs in the dry season to be met.

Numerical simulations of overflow experiments on a model dike

Dike failure due to overtopping is one of the important factors, which should be considered in the dike designing process. Although the overflow is characterized by the relatively low risk of occurrence, in many cases dikes are totally destroyed or seriously damaged. An interesting phenomenon occurring during overflow is the trapping of air in pores of the unsaturated soil material. As the infiltration progresses from all sides, the air pressure in the unsaturated region increases, which may ultimately lead to damage of the dike structure. It happens when the air is expulsed in form of bursts and forms large macropores. Such a behaviour evidenced in laboratory experiments. In this study we attempt to simulate the evolution of stress field in the model dike subjected to overtopping. The results are in qualitative agreement with observations, showing that formation of the first macropores occurs in the direction perpendicular to the minor principal stress in the soil mass along the dike slope edge.