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Yi Pan - One of the best experts on this subject based on the ideXlab platform.
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An analysis of the downward-flushing flow on the crest of a levee under Combined Wave and surge overtopping
Coastal Engineering, 2020Co-Authors: Yi Pan, Zhou Zijun, Yongping ChenAbstract:Abstract In extreme storm conditions, a levee would be subject to a combination of Wave overtopping and surge overflow, namely Combined Wave and surge overtopping, which is easier to induce catastrophic levee failures than common Wave overtopping. One of the significant differences between Combined Wave and surge overtopping and Wave overtopping is that downward-flushing flows are formed on the levee crest during Combined Wave and surge overtopping due to plunging breakers. Downward-flushing flow might induce lining damage and thus lead to the failure of levees. In this paper, the downward-flushing flow on the levee crest are investigated based on the measurements of full-scale flume tests on Combined Wave and surge overtopping. Firstly, the occurrence probabilities and velocity magnitudes of downward-flushing flow are analyzed on the basis of the time series of instantaneous two-dimensional flow velocity measured on the levee crest. A general portray of the downward-flushing flow is given based on the analysis. Furthermore, the individual downward-flushing flow processes induced by individual Waves are distinguished from the time series of flow velocity and studied in different flow directions. Empirical formulae are proposed to estimate the occurrence probabilities, mean velocities and velocity distributions of individual downward-flushing flow processes. The results can provide references for laboratory and field tests on levee linings under extreme overtopping conditions.
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Combined Wave and surge overtopping erosion failure model of HPTRM levees: Accounting for grass-mat strength
Ocean Engineering, 2015Co-Authors: Saiyu Yuan, Yi Pan, Hongwu Tang, Farshad AminiAbstract:Abstract High performance turf reinforcement mat (HPTRM) has emerged as an effective and flexible strengthening system to protect earthen levees against the erosion caused by overtopping flows. The purpose of this study is to characterize the erosion and failure processes of HPTRM-strengthened levees under Combined Wave and surge overtopping. The Erosion Function Apparatus (EFA) is used to analyze the erodibility of HPTRM-strengthened clay. The erodibility parameters such as critical shear stress and erodibility coefficient are then obtained. A HPTRM-element model is proposed to account for the mechanism of HPTRM in protecting cohesive soil with the help of EFA results in the characterization of the grass mat strength parameter. At last, a failure model is developed based on the excess stress equation, and the durations of HPTRM-strengthened levees against Combined overtopping with different Wave heights and freeboards are presented.
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Erosion Resistance of HPTRM Strengthened Levee from Combined Wave and Surge Overtopping
Geotechnical and Geological Engineering, 2014Co-Authors: Yi Pan, Farshad Amini, Kuang Cuiping, Jean-louis BriaudAbstract:Post-Katrina investigations revealed that most earthen levee damage occurred on the levee crest and land-side slope as a result of either Wave overtopping, storm surge overflow, or a combination of both. This study addresses erosion resistance performance of a levee strengthening technique—high performance turf reinforcement mat under Combined Wave and surge overtopping conditions using full-scale flume tests as well as erosion function apparatus (EFA) tests. Based on the results of full-scale flume tests, an “upper limit” of soil loss is observed for certain flow conditions. Erosion rate was presented as a function of velocity and freeboard. The effect of duration of overtopping on the erosion depth is also determined. The results of EFA tests indicate that the presence of grass roots substantially improve the critical velocity and soil erodibility.
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Stability Monitoring of Articulated Concrete Block Strengthened Levee in Combined Wave and Surge Overtopping Conditions
Geo-Congress 2014 Technical Papers, 2014Co-Authors: Farshad Amini, Yi PanAbstract:Most earthen levee damages have occurred on the levee crest and downstream after Hurricane Katrina as a result of Combined Wave and surge overtopping. This study was to investigate the performance of one of the levee strengthening methods, namely, articulated concrete block (ACB) system and its stability during the Combined Wave and surge overtopping. A full-scale experimental study on Combined Wave and surge overtopping of a levee strengthened by ACB was conducted in a two-dimensional laboratory Wave/flow flume. Geotechnical instrumentation was installed for slope stability analysis and also for an assessment of change in soil parameters and embankment conditions. Piezometers, soil strain meters, soil moisture content meters, and pressure cells were used to monitor changes in pore water pressures, magnitude and location of the strains, change in moisture contents, and total pressure change. This information can be used to determine the condition of the embankments during and after construction. Movement of ACB was checked after each test. Total stress, pore water pressure, effective stress, soil strain, and soil moisture content were analyzed. The stability of ACB strengthened levee in the Combined Wave and surge overtopping was studied.
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Influence of Three Levee-Strengthening Systems on Overtopping Hydraulic Parameters and Hydraulic Equivalency Analysis between Steady and Intermittent Overtopping
Journal of Waterway Port Coastal and Ocean Engineering-asce, 2013Co-Authors: Yi Pan, Farshad Amini, Cuiping KuangAbstract:AbstractDifferent types of strengthening systems were introduced to protect the crest and land-side slope of the levees against surge overflow and Wave overtopping after Hurricane Katrina. Three levee-strengthening systems, roller-compacted concrete, articulated concrete block, and high-performance turf reinforcement mat, were investigated through full-scale laboratory tests in this study. Hydraulic performances of these three levee-strengthening systems were compared to determine the effect of strengthening systems and to provide the equivalency analysis between surge-only overflow and Combined Wave and surge overtopping. The findings of this study indicate that the high-performance turf reinforcement mat system has the strongest effect in reducing and smoothing the overtopping discharge and in reducing the flow velocity and Wavefront velocity on the land-side slope, whereas roller-compacted concrete has the weakest effect. Equivalency analysis between surge-only overflow and Combined Wave and surge over...
Farshad Amini - One of the best experts on this subject based on the ideXlab platform.
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Numerical study of Combined Wave overtopping and storm surge overflow of HPTRM strengthened levee
Ocean Engineering, 2015Co-Authors: Saiyu Yuan, Farshad Amini, Hongwu TangAbstract:Overtopping of earthen levees produces fast-flowing, turbulent water velocities on the land-side slope that can damage the protective grass covering and expose the underlying soil to erosion. High performance turf reinforcement mat (HPTRM) is one of the most advanced flexible armoring technologies for severe erosion challenges. In this study, Combined Wave overtopping and storm surge turbulent overflow of a HPTRM strengthened levee was studied in a three-dimension numerical modeling. The primary objective was to investigate the hydrodynamics of the Combined overtopping turbulent flow on the land-side levee slope. Thirty Combined overtopping cases with different freeboards and significant Wave heights were simulated. After verifying the numerical model with full-scale overtopping experimental data and previous equations, new equations were developed to estimate average overtopping discharge, mean flow thickness, characteristic parameters of Wave height and flow thickness, and Wave front velocity at the toe of the land-side levee slope for the HPTRM strengthened levee. The range of the application of these equations is discussed.
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Combined Wave and surge overtopping erosion failure model of HPTRM levees: Accounting for grass-mat strength
Ocean Engineering, 2015Co-Authors: Saiyu Yuan, Yi Pan, Hongwu Tang, Farshad AminiAbstract:Abstract High performance turf reinforcement mat (HPTRM) has emerged as an effective and flexible strengthening system to protect earthen levees against the erosion caused by overtopping flows. The purpose of this study is to characterize the erosion and failure processes of HPTRM-strengthened levees under Combined Wave and surge overtopping. The Erosion Function Apparatus (EFA) is used to analyze the erodibility of HPTRM-strengthened clay. The erodibility parameters such as critical shear stress and erodibility coefficient are then obtained. A HPTRM-element model is proposed to account for the mechanism of HPTRM in protecting cohesive soil with the help of EFA results in the characterization of the grass mat strength parameter. At last, a failure model is developed based on the excess stress equation, and the durations of HPTRM-strengthened levees against Combined overtopping with different Wave heights and freeboards are presented.
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Erosion Resistance of HPTRM Strengthened Levee from Combined Wave and Surge Overtopping
Geotechnical and Geological Engineering, 2014Co-Authors: Yi Pan, Farshad Amini, Kuang Cuiping, Jean-louis BriaudAbstract:Post-Katrina investigations revealed that most earthen levee damage occurred on the levee crest and land-side slope as a result of either Wave overtopping, storm surge overflow, or a combination of both. This study addresses erosion resistance performance of a levee strengthening technique—high performance turf reinforcement mat under Combined Wave and surge overtopping conditions using full-scale flume tests as well as erosion function apparatus (EFA) tests. Based on the results of full-scale flume tests, an “upper limit” of soil loss is observed for certain flow conditions. Erosion rate was presented as a function of velocity and freeboard. The effect of duration of overtopping on the erosion depth is also determined. The results of EFA tests indicate that the presence of grass roots substantially improve the critical velocity and soil erodibility.
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Stability Monitoring of Articulated Concrete Block Strengthened Levee in Combined Wave and Surge Overtopping Conditions
Geo-Congress 2014 Technical Papers, 2014Co-Authors: Farshad Amini, Yi PanAbstract:Most earthen levee damages have occurred on the levee crest and downstream after Hurricane Katrina as a result of Combined Wave and surge overtopping. This study was to investigate the performance of one of the levee strengthening methods, namely, articulated concrete block (ACB) system and its stability during the Combined Wave and surge overtopping. A full-scale experimental study on Combined Wave and surge overtopping of a levee strengthened by ACB was conducted in a two-dimensional laboratory Wave/flow flume. Geotechnical instrumentation was installed for slope stability analysis and also for an assessment of change in soil parameters and embankment conditions. Piezometers, soil strain meters, soil moisture content meters, and pressure cells were used to monitor changes in pore water pressures, magnitude and location of the strains, change in moisture contents, and total pressure change. This information can be used to determine the condition of the embankments during and after construction. Movement of ACB was checked after each test. Total stress, pore water pressure, effective stress, soil strain, and soil moisture content were analyzed. The stability of ACB strengthened levee in the Combined Wave and surge overtopping was studied.
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Turbulence Measurement of Combined Wave and Surge Overtopping of a Full-Scale HPTRM-Strengthened Levee
Journal of Waterway Port Coastal and Ocean Engineering, 2014Co-Authors: Saiyu Yuan, Farshad Amini, Hongwu TangAbstract:AbstractA combination of storm surge and extreme Waves may cause overtopping of coastal protection structures such as levees, dikes, and seawalls, resulting in structural damage and flooding behind these structures. High turbulence of the overtopping flow is an important or even critical factor in soil erosion, and may be responsible for the destruction of levees during Combined overtopping. The goal of this study was to observe and measure the turbulence on the crest and landside of levees strengthened by high performance turf reinforcement mats (HPTRMs). A full-scale laboratory study of the Combined Wave and surge overtopping of a levee strengthened with HPTRMs was conducted in a two-dimensional (2D) laboratory Wave/flow flume. During a total of 11 trials, the authors recorded and processed three-dimensional (3D) velocity and water depth. They developed a new formula to estimate the average overtopping discharge. This paper presents turbulent fluctuations of the three components of flow velocity on the ...
Steven A. Hughes - One of the best experts on this subject based on the ideXlab platform.
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Earthen Levee Shear Stress Estimates for Combined Wave Overtopping and Surge Overflow
Journal of Waterway Port Coastal and Ocean Engineering, 2012Co-Authors: Steven A. Hughes, Justin M. Shaw, Isaac L. HowardAbstract:AbstractA total of 25 small-scale laboratory experiments simulating Combined Wave overtopping and storm-surge overflow on a trapezoidal levee were conducted at a nominal prototype-to-model scale of NL=25. Time series measurements of irregular and unsteady flow thickness and velocity were acquired at two locations on the landward-side, 1V : 3H slope. These measurements were used to calculate the time series of instantaneous shear stress representing the average over a 4.8-m-long (prototype scale) levee slope between the two measurement locations. Empirical relationships are presented for estimating the mean shear stresses for steady overflow and for Combined Wave and surge overtopping. For the latter case, additional formulas are given for estimating representative parameters of the irregular shear stress peaks associated with individual overtopping Waves. The collected data were intended primarily for the design of rapidly deployable levee armoring systems; however, the data could also be used to evaluate...
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Laboratory study of Combined Wave overtopping and storm surge overflow of a levee
Coastal Engineering, 2009Co-Authors: Steven A. Hughes, N.c. NadalAbstract:Combined Wave overtopping and storm surge overflow of a levee with a trapezoidal cross section was studied in a two-dimensional laboratory Wave/flow flume at a nominal prototype-to-model length scale of 25-to-1. The goal of this study was to develop design guidance in the aftermath of Hurricane Katrina. Time series of water depth at two locations on the levee crown and flow thickness at five locations on the landward-side slope were measured along with horizontal velocity near the landward edge of the crown. New equations are presented for average overtopping discharge, distribution of instantaneous discharge, and distribution of individual Wave volumes. Equations are also given for mean flow thickness, RMS Wave height, mean velocity, and velocity of the Wave front down the landward-side slope.
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Combined Wave and Surge Overtopping of Levees: Flow Hydrodynamics and Articulated Concrete Mat Stability
2008Co-Authors: Steven A. HughesAbstract:A 1-to-25 scale physical model of a typical cross section of the levee along the Mississippi River Gulf Outlet (MRGO) was con-structed at the U.S. Army Engineer Research and Development Centers Coastal and Hydraulics Laboratory in Vicksburg, MS. The purpose of the physical model was to obtain hydrodynamic measurements of unsteady flow conditions caused by Combined Wave and surge overtopping of the levee, and to examine the feasibility of using articulated concrete mats (ACMs) for levee protection during this type of overtopping event. Specifically, the U.S. Army Engineer District, New Orleans, was interested in determining whether the same ACMs used by the Corps Mat Sinking Unit to protect river banks could be used to protect the MRGO levee against surge and Wave overtopping. When the storm surge elevation was 0.75 ft above the levee crest, the stability tests indicated the ACMs were prone to uplift on the lower portion of the levee protected-side slope for even relatively mild Wave overtopping. An increase in Wave height created mat roll-up instability at the toe of the flood-side levee slope, indicating the need to bury or anchor the leading and tailing edges of the mats. Mat stability could be increased with additional anchoring or increasing mat thickness. Tests were also conducted to document the hydrodynamics associated with Combined Wave and surge over-topping. The primary parameters were three overtopping surge levels (+1, +3, and +5 ft); three significant Wave heights (3, 6, and 9 ft); and three peak Wave periods (6, 10, and 14 sec) for a total of 27 unique conditions. Measurements included the incident irregular Waves and time series of water elevations at seven locations on the crest and protected-side slope of the levee. Horizontal flow velocity was recorded near the leeward levee crest shoulder, and the velocity was then Combined with water elevation to estimate the unsteady instantaneous discharge over the levee. Discharge cumulative probability distributions were determined using the Weibull probability distribution, and a predictive equation was developed for the distribution of overtopping discharge as a function of Wave and surge parameters.
Dong-sheng Jeng - One of the best experts on this subject based on the ideXlab platform.
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Combined Wave-current induced excess pore-pressure in a sandy seabed: Flume observations and comparisons with theoretical models
Coastal Engineering, 2019Co-Authors: Dong-sheng Jeng, Fu-ping Gao, Zuodong LiangAbstract:Abstract Waves are coexisting with currents in coastal zones; nevertheless, previous experimental studies for excess pore-pressure responses in a porous seabed were predominantly limited to the Wave-only condition. In this study, the Combined Wave-current induced excess pore-pressures in a sandy seabed were experimentally simulated with a specially-designed flume, which can concurrently generate periodic Waves and a following/opposing co-directional current. The effect of a current on the Wave profile is firstly examined. The Wave steepness is decreased by a following current, but enhanced by an opposing current. Flume observations indicate that, under Combined Wave-current loading, the Wave-induced pore-pressure is increased for the following-current case, but reduced for the opposing-current case. Such Wave-current combination effect becomes more significant for shorter Wave periods. The variation trend of the excess pore-pressure distribution in the present flume observations is consistent with that of the existing analytical solutions. Nevertheless, due to the existence of Wave and/or current boundary layer and non-lineartiy of Wave-current interactions as indicated by the flume observations, certain deviations exist between the flume results for excess pore-pressure and the analytical solutions, which can not be ignored especially for the opposing-current case. The effects of the boundary layer on the Combined Wave-current induced pore-pressures in the seabed are further highlighted by supplementary numerical simulations. A favorable prediction by the analytical solution would be expected for following-current cases and smaller pore-pressure amplitudes would be obtained for opposing-current cases.
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Liquefaction of a poro-elastoplastic seabed under Combined Wave and current loading
2015Co-Authors: Dong-sheng Jeng, Song Cui, Jian LengAbstract:Combined Wave and current loading is a very common and important situation for sandy seabeds. The dynamic seabed response under Combined these loadings, including the change of excess pore water pressure and the stress, is of great significance to the coastal structures design and construction In this paper, based on two-phase u-p theory for saturated soil, a new constitutive model, which is developed from the concept of superloading and sub-loading, is proposed to analyze the dynamic responds in a sandy seabed under the Combined Wave and current loadings. Firstly, a poro-elastoplastic model for a sandy seabed is established. The seabed soils parameters are obtained from the un-drained triaxial cyclic loading tests. The mechanics of oscillatory excess pore water pressure and residual excess pore pressure due to Waves/currents are discussed and the liquefaction depth which changes correspondingly is obtained. A comparison between the dynamic responds of elastic and elatoplastic sandy seabeds to Waves/currents loading is presented. Then, a parametric study is carried out to investigate the effects of currents on the pore pressures and liquefaction.
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Numerical Modeling of Seabed Response to Combined Wave-Current Loading
Journal of Offshore Mechanics and Arctic Engineering, 2013Co-Authors: Jisheng Zhang, Yu Zhang, Chi Zhang, Dong-sheng JengAbstract:In this paper, a numerical model is developed to study the dynamic response of a porous seabed to Combined Wave-current loadings. While the Reynolds-averaged Navier–Stokes equations with k-ε turbulence closure scheme and internal Wave-maker function are solved for the phenomenon of Wave-current interaction, Biot's poro-elastic “u-p” model is adopted for the seabed response. After validated by the laboratory measurements, this model is applied for the investigation of the effects of Waves and currents on the Wave-current induced pore pressures. Furthermore, the effects of currents on maximum liquefaction depths of a porous seabed is examined, and it is concluded that the opposite currents will increase the liquefaction depth up to 30% of that without currents.
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Dynamic Response in a Porous Seabed of Finite Depth to Combined Wave and Current Loadings
Journal of Coastal Research, 2013Co-Authors: Bo Liu, Dong-sheng Jeng, J.-s. ZhangAbstract:ABSTRACT Liu, B.; Jeng, D.S., and Zhang, J.S., 2014. Dynamic response in a porous seabed of finite depth to Combined Wave and current loadings. In this study a u-p approximation for the dynamic response of a porous seabed to nature dynamic loadings is proposed. Unlike most previous research, the effects of currents are considered in the new analytical solution. Based on the numerical examples, the significant influence of Combined Wave and current loadings on seabed response in shallow water is concluded. This influence affects not only the amplitudes of the seabed response but also the distributions of the space region. The relative difference of the maximum pore pressure between different direction currents can reach 8% of the static water pressure. In addition, the relative difference of maximum liquefaction depth between the previous model (without currents) and the present model can reach 19% of the maximum liquefaction depth of the case without currents.
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an analytical solution for response of a porous seabed to Combined Wave and current loading
Ocean Engineering, 2013Co-Authors: Yufang Zhang, Dong-sheng Jeng, Jisheng ZhangAbstract:In this paper, an analytical approximation for the evaluation of the pore pressure and effective stresses in marine sediments under Combined Wave and current loadings is derived. Unlike previous investigations, non-linear interactions between Waves and currents are considered in this study. An analytical solution for the Wave-current induced oscillatory soil response in marine sediment is presented first. Based on the proposed analytical solution, a parametric study for the liquefaction potential will be carried out. Parametric study results indicate that the influence of current and non-linear Waves on the maximum liquefaction depth is significant.
Hongwu Tang - One of the best experts on this subject based on the ideXlab platform.
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Numerical study of Combined Wave overtopping and storm surge overflow of HPTRM strengthened levee
Ocean Engineering, 2015Co-Authors: Saiyu Yuan, Farshad Amini, Hongwu TangAbstract:Overtopping of earthen levees produces fast-flowing, turbulent water velocities on the land-side slope that can damage the protective grass covering and expose the underlying soil to erosion. High performance turf reinforcement mat (HPTRM) is one of the most advanced flexible armoring technologies for severe erosion challenges. In this study, Combined Wave overtopping and storm surge turbulent overflow of a HPTRM strengthened levee was studied in a three-dimension numerical modeling. The primary objective was to investigate the hydrodynamics of the Combined overtopping turbulent flow on the land-side levee slope. Thirty Combined overtopping cases with different freeboards and significant Wave heights were simulated. After verifying the numerical model with full-scale overtopping experimental data and previous equations, new equations were developed to estimate average overtopping discharge, mean flow thickness, characteristic parameters of Wave height and flow thickness, and Wave front velocity at the toe of the land-side levee slope for the HPTRM strengthened levee. The range of the application of these equations is discussed.
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Combined Wave and surge overtopping erosion failure model of HPTRM levees: Accounting for grass-mat strength
Ocean Engineering, 2015Co-Authors: Saiyu Yuan, Yi Pan, Hongwu Tang, Farshad AminiAbstract:Abstract High performance turf reinforcement mat (HPTRM) has emerged as an effective and flexible strengthening system to protect earthen levees against the erosion caused by overtopping flows. The purpose of this study is to characterize the erosion and failure processes of HPTRM-strengthened levees under Combined Wave and surge overtopping. The Erosion Function Apparatus (EFA) is used to analyze the erodibility of HPTRM-strengthened clay. The erodibility parameters such as critical shear stress and erodibility coefficient are then obtained. A HPTRM-element model is proposed to account for the mechanism of HPTRM in protecting cohesive soil with the help of EFA results in the characterization of the grass mat strength parameter. At last, a failure model is developed based on the excess stress equation, and the durations of HPTRM-strengthened levees against Combined overtopping with different Wave heights and freeboards are presented.
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Turbulence Measurement of Combined Wave and Surge Overtopping of a Full-Scale HPTRM-Strengthened Levee
Journal of Waterway Port Coastal and Ocean Engineering, 2014Co-Authors: Saiyu Yuan, Farshad Amini, Hongwu TangAbstract:AbstractA combination of storm surge and extreme Waves may cause overtopping of coastal protection structures such as levees, dikes, and seawalls, resulting in structural damage and flooding behind these structures. High turbulence of the overtopping flow is an important or even critical factor in soil erosion, and may be responsible for the destruction of levees during Combined overtopping. The goal of this study was to observe and measure the turbulence on the crest and landside of levees strengthened by high performance turf reinforcement mats (HPTRMs). A full-scale laboratory study of the Combined Wave and surge overtopping of a levee strengthened with HPTRMs was conducted in a two-dimensional (2D) laboratory Wave/flow flume. During a total of 11 trials, the authors recorded and processed three-dimensional (3D) velocity and water depth. They developed a new formula to estimate the average overtopping discharge. This paper presents turbulent fluctuations of the three components of flow velocity on the ...
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Smoothed Particle Hydrodynamics Modeling of Combined Wave and Surge Overtopping and Hydraulic Erosion of an Articulated Concrete Block-Strengthened Levee System
Journal of Coastal Research, 2012Co-Authors: Xin Rao, Farshad Amini, Hongwu TangAbstract:Abstract Rao, X.; Li, L.; Amini, F., and Tang, H., 2012. Smoothed particle hydrodynamics modeling of Combined Wave and surge overtopping and hydraulic erosion of an articulated concrete block-strengthened levee system. Combined Wave and surge overtopping may cause damage on earthen levees. Levee strengthened on the levee crest and landward-side slope can provide protection against the erosion damage induced by the Combined Wave and surge overtopping. In this paper Combined Wave overtopping and storm surge overflow of a levee with a trapezoidal cross section strengthened by an articulated concrete block (ACB) system was studied in a purely Lagrangian and meshless approach, two-dimensional smoothed particle hydrodynamics (SPH) model. By comparing with the results of full-scale experiment data, the model was verified, and the erosion parameters were calibrated. Time series of overtopping discharge and flow thickness at six locations on the levee crest and landward-side slope were calculated. New equations we...
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Numerical study of Combined Wave and surge overtopping over RCC strengthened levee systems using the smoothed particle hydrodynamics method
Ocean Engineering, 2012Co-Authors: Xin Rao, Farshad Amini, Hongwu TangAbstract:Abstract Most earthen levee damages occurred on the levee crest and landward-side slope after Hurricane Katrina as a result of either Wave overtopping, storm surge overflow, or a combination of both. It is important to understand the overtopping hydraulics in the Combined Wave and surge overtopping condition for levees strengthened by roller compacted concrete (RCC). In this paper, Combined Wave overtopping and storm surge overflow of a levee with a trapezoidal cross section, strengthened by RCC, were studied in a purely Lagrangian and meshless approach, two-dimensional smoothed particle hydrodynamics (SPH) model. After verifying the developed SPH model in this study with full-scale overtopping experimental data and previous equations, time series of discharge, and water depths at two locations on the levee crest and flow thickness at five locations on the landward-side slope, 27 combinations of Wave/surge overtopping cases were simulated. New equations are presented for average overtopping discharge, mean flow thickness, RMS Wave height, mean velocity, and velocity of the Wave front down the landward-side slope. The range of the application of these equations is discussed.