Prediction of scour depth at breakwaters due to non-breaking waves using machine learning approaches

Coastal structures may cease to function properly due to seabed scouring. Hence, prediction of the maximum scour depth is of great importance for the protection of these structures. Since scour is the result of a complicated interaction between structure, sediment, and incoming waves, empirical equations are not as accurate as machine learning schemes, which are being widely employed for the coastal engineering modeling. In this paper, which can be regarded as an extension of Pourzangbar et al. (2016), two soft computing methods, a support vector regression (SVR), and a model tree algorithm (M5′), have been implemented to predict the maximum scour depth due to non-breaking waves. The models predict the relative scour depth (S_max/H₀) on the basis of the following variables: relative water depth at the toe of the breakwater (h_toe/L₀), Shields parameter (θ), non-breaking wave steepness (H₀/L₀), and reflection coefficient (Cr). 95 laboratory data points, extracted from dedicated experimental studies, have been used for developing the models, whose performances have been assessed on the basis of statistical parameters. The results suggest that all of the developed models predict the maximum scour depth with high precision, the M5′ model performed marginally better than the SVR model and also allowed to define a set of transparent and physically sound relationships. Such relationships, which are in good agreement with the existing empirical findings, show that the relative scour depth is mainly affected by wave reflection.     

Developing empirical formulas for assessing the scour of vertical and inclined piers

Abstract

Because scour is one of the main reasons for bridge failure, this study focuses on accurately predicting the maximum scour depth around different vertical and inclined piers. Scouring is an issue of concern in the bridge design process, as most existing equations for predicting local scour near bridge piers suffer from over- or underprediction issues, resulting in higher foundation costs or bridge failure and inaccurate predictions of the scour around piers. The dimensionless maximum scour depths (y_s/D) of vertical and inclined piers were investigated for seven pier shapes with different L/D ratios and four inclination angles (θ) under shallow flow conditions. The inclined pier configuration reduced the y_s/D of the piers. The maximum y_s/D was observed for a rectangular pier with an L/D of 4.5 in both vertical and inclined configurations (θ of 10, 15 and 21°, respectively). The y_s/D was significantly decreased by increasing the angle of the pier from 10 to 30°. The y_s/D of the inclined rectangular piers decreased as θ decreased from 30 to 10° and the L/D ratio increased from 1 to 4.5. The best y_s/D results were obtained for inclined rectangular piers at a θ value of 30° and an L/D ratio of 7.5 compared to other shapes and inclination angles. New equations were developed to predict the local scour depth for circular, square and rectangular bridge piers. The equations yielded excellent results for predicting the maximum clear water scour depth around vertical and inclined piers with inclination angles of 10, 15, 21 and 30°, respectively.     

Relevance of transition turbulent model for hydrodynamic characteristics of low Reynolds number propeller

The propeller of an Autonomous Underwater Vehicle (AUV) operates at low Reynolds number in laminar to turbulent transition region. The performance of these propellers can be calculated accurately using RANSE solver with γ − Re_θ transition model. In this study, the global and local hydrodynamic characteristics of open and ducted propeller are investigated using the γ − Re_θ transition model. The capability of the γ − Re_θ transition model to capture laminar to turbulent transition on the surface of the open propeller is demonstrated by comparison with published experimental results. The application of transition model for the propeller K_a-4-70 inside the duct 19A shows that the centrifugal forces are dominant at low Reynolds number and the flow is mainly directed in the radial direction. The transition model is able to predict complex flow physics such as leading-edge separation, tip leakage vortex, and the separation bubble on outer surface of the duct. The accurate prediction of these flow phenomenon can lead to correct calculation of global hydrodynamic forces and moments acting on the propeller at low Reynolds number.     

A numerical model for onset of scour below offshore pipelines

A numerical model is developed to predict the onset of local scour below offshore pipelines in steady currents and waves. The scour is assumed to start when the pressure gradient underneath the pipeline exceeds the floatation gradient of the sediments. In this model, the water flow field above the bed is determined by solving the two-dimensional (2-D) Reynolds-averaged Navier–Stokes equations with a k-ω turbulence closure. The seepage flow below the seabed is calculated by solving the Darcy's law (Laplace's equation) with known pressure distribution along the common boundaries of the flow domains-seabed. The numerical method used for both the turbulent flow around the pipeline and Darcy's flow in the seabed is a fractional finite element method. The average pressure gradient along the buried pipe surface is employed in the evaluation of onset condition with a calibration coefficient. The numerical model is validated against experimental data available in literature. A unified onset condition for steady currents and waves is proposed. Influences of flow parameters, including water depth, embedment depth, boundary layer thickness, Reynolds number (Re) and Keuleagan–Carpenter (KC) number, on the pressure drop coefficient over the pipeline are studied systematically.     

Experimental study of vortex-induced vibrations of a pipeline near an erodible sandy seabed

Based on similarity analyses, a series of experiments have been conducted with a newly established hydro-elastic facility to investigate the transverse vortex-induced vibrations (VIVs) of a submarine pipeline near an erodible sandy seabed under the influence of ocean currents. Typical characteristics of coupling processes between pipe vibration and soil scour in the currents have been summarized for Case I: pipe is laid above seabed and Case II: pipe is partially embedded in seabed on the basis of the experimental observations. Pipe vibration and the corresponding local scour are usually two coupled physical processes leading to an equilibrium state. The influence of initial gap-to-diameter ratio (e₀/D) on the interaction between pipe vibration and local scour has been studied. Experimental results show that the critical values of V_r for the initiation of VIVs of the pipe near an erodible sand bed get bigger with decreasing initial gap-to-diameter ratio within the examined range of e₀/D (−0.25<e₀/D<0.75). The comparison of the pipe vibrations near an erodible soil with those near a rigid boundary and under wall-free conditions indicates that the vibration amplitudes of the pipe near an erodible sand bed are close to the curve fit under wall-free conditions; nevertheless, for the same stability parameter, the maximum amplitudes for the VIV coupled with local scour increase with the increase of initial gap-to-diameter ratio.     

An experimental study of seabed responses around a marine pipeline under wave and current conditions

Experiments on three types of soil (d₅₀=0.287, 0.057 and 0.034 mm) with pipeline(D=4 cm) either half buried or resting on the seabed under regular wave or combined with current actions were conducted in a large wave flume to investigate characteristics of soil responses. The pore pressures were measured through the soil depth and across the pipeline. When pipeline is present the measured pore pressures in sandy soil nearby the pipeline deviate considerably from that predicted by the poro-elasticity theory. The buried pipeline seems to provide a degree of resistance to soil liquefaction in the two finer soil seabeds. In the silt bed, a negative power relationship was found between maximum values of excess pore pressure p_max and test intervals under the same wave conditions due to soil densification and dissipation of the pore pressure. In the case of wave combined with current, pore pressures in sandy soil show slightly decrease with time, whereas in silt soil, the current causes an increase in the excess pore pressure build-up, especially at the deeper depth. Comparing liquefaction depth with scour depth underneath the pipeline indicates that the occurrence of liquefaction is accompanied with larger scour depth under the same pipeline-bed configuration.     

Scour depth under pipelines placed on weakly cohesive soils

We here study the scouring processes that evolve around a submarine pipeline placed on a weakly cohesive seabed. We first analyze some laboratory tests carried out by Vijaya Kumar et al. [21], Xu et al. [25] and Zhou et al. [28] that focused on the scouring around a horizontal cylinder lying on a cohesive bed, subject to waves and currents. The specific purpose is that of finding a new formula for the prediction of the equilibrium scour depth under submarine pipelines. After a theoretical analysis of the main parameters, the sought formula has been found to be a function of: (i) the hydrodynamic forces acting on the cylinder (through the Keulegan–Carpenter parameter KC), (ii) the clay content of the soil C_c, and (iii) the burial depth e₀/D. In the presence of small amounts of clay (C_c< 5 %), the scour depth depends directly on KC (as confirmed by many literature works for pipelines lying on sandy soils, e.g. [18]) and inversely on C_c (as already seen for bridge abutments on cohesive soils, e.g. [1]), the best-fit law being characterized by a coefficient of determination R² = 0.62. If some burial depth is accounted for, this being a novelty of the present work, a more general formulation can be used, valid in the presence of weakly-cohesive soils and with burial depths of the pipe smaller than 0.5 (R² = 0.79). For large clay-content ranges (2% < C_c < 75 %), the scour depth depends directly on both KC and C_c, this giving R² = 0.79 (no burial depth) and 0.91 (some burial depth). However, this finding is at odds with the main literature, because, for large amounts of clay, it is fundamental to consider the liquidity index LI, which accounts for some important clay properties, like the plasticity. We argue that the absence of LI is balanced by the direct dependence of the scour depth on C_c. Notwithstanding the small number of available data, a formula for the prediction of the scour depth under pipelines lying on cohesive soils is fundamental for several engineering applications. The present contribution represents the first attempt to build such a formula, when the pipeline is subject to the wave-current forcing and the seabed is characterized by a relatively small clay content.     

Inertial and tidal shear variability above Reykjanes Ridge

Yearlong 75 kHz acoustic Doppler current profiler (ADCP) data were obtained well above Reykjanes Ridge (northern extension of the Mid-Atlantic Ridge (MAR)). The area is characterized by relatively large semidiurnal tidal (‘D₂’) currents that have (at lunar M₂) more than half a decade larger variance than inertial (f) currents. However, despite the relatively weak near-inertial kinetic energy, its vertical current shear shows larger magnitudes than at M₂ in an otherwise flat f−D₂ band limited between frequencies 0.74 and 1.35f, which equals the inertio-gravity wave bounds [σ_min, σ_max](N=f). N represents the buoyancy frequency. The shear in this band dominates all shear computed at 20 m effective vertical scale. As the kinetic energy spectrum peaks at M₂, but not (significantly) at S₂ and N₂, a difference in tidal (and inertial) scales and hence sources is observed. M₂-tides contribute mostly to large-scale coherent motions. The dominant incoherent f−D₂ shear is highly variable in time (∼2-day periodicity). Furthermore, inertial and tidal shear are more or less completely separated in space and time, each occurring in different layers in the vertical. The thin shear layers reflect the rapidly varying short vertical scale N_s profile, to within the ∼20 m limitation of ADCP data, rather than the large-scale smooth N_L. In each of large-N_s layers Ri≈1, probably. The yearlong smoothed shear magnitude follows N_L, but only as stable Ri≈5. The shear polarization is more circular than rectilinear, albeit varying with time, and highly symmetric around f. During transitions, e.g., between stratified and homogeneous layers and between waves from varying sources, near-circular motions can generate near-rectilinear shear in the direction of wave propagation (in the direction of the minor axis of the current ellipse). This contrasts with the possibility of near-rectilinear barotropic oscillatory motions generating near-circular shear under viscosity in shallow seas.     

波流共同作用下海底子母管线水动力的物理模型试验研究

通过物理模型试验研究海底子母管线分别在规则波加流和不规则波加流作用下的水动力特性。基于Morison方程,采用"等效直径法"分析得到子母管线拖曳力系数C_D,惯性力系数C_M和升力系数C_L(C_D+,C_L-)。试验分别考察了流速比U_c/U_w,母管与海床间隙比e/D及子母管间的相对缝隙G/D对海底子母管线水动力系数的影响。结果表明水动力系数随U_c/U_w的增大而减小;当e/D<0.5时,海床对子母管线受力的影响比较明显,C_D,C_M及C_L+均随e/D增大而减小,|C_L-|随e/D增大而增大;对子母管间的相互影响也不可忽略,C_D,C_M和|C_L-|均随G/D增大而减小,C_L+值随G/D增大而增大。     

GMDH to predict scour depth around a pier in cohesive soils

This study presents new application of group method of data handling (GMDH) to predict scour depth around a vertical pier in cohesive soils. Quadratic polynomial was used to develop GMDH network. Back propagation algorithm has been utilized to adjust weighting coefficients of GMDH polynomial thorough trial and error method. Parameters such as initial water content, shear strength, compaction of cohesive bed materials, clay content of cohesive soils, and flow conditions are main factors affecting cohesive scour. Performances of the GMDH network were compared with those obtained using several traditional equations. The results indicated that the proposed GMDH-BP has produced quite better scour depth prediction than those obtained using traditional equations. To assign the most significant parameter on scour process in cohesive soils, sensitivity analysis was performed for the GMDH-BP network and the results showed that clay percentage was the most effective parameter on scour depth. The error parameter for three classes of IWC and C_p showed that the GMDH-BP model yielded better scour prediction in ranges of IWC = 36.3–42.28% and C_p = 35–100%. In particular application, the GMDH network was proved very successful compared to traditional equations. The GMDH network was presented as a new soft computing technique for the scour depth prediction around bridge pier in cohesive bed materials.     

波流共同作用下海底子母管线水动力的物理模型试验研究

通过物理模型试验研究海底子母管线分别在规则波加流和不规则波加流作用下的水动力特性。基于Morison方程,采用"等效直径法"分析得到子母管线拖曳力系数C_D,惯性力系数C_M和升力系数C_L(C_D⁺,C_L^-)。试验分别考察了流速比U_c/U_w,母管与海床间隙比e/D及子母管间的相对缝隙G/D对海底子母管线水动力系数的影响。结果表明水动力系数随U_c/U_w的增大而减小;当e/D<0.5时,海床对子母管线受力的影响比较明显,C_D,C_M及C_L⁺均随e/D增大而减小,|C_L^-|随e/D增大而增大;对子母管间的相互影响也不可忽略,C_D,C_M和|C_L^-|均随G/D增大而减小,C_L⁺值随G/D增大而增大。     

New expression-based models to estimate scour depth at clear water conditions in rectangular channels

Scouring in the channel contractions occurs due to the flow concentration within them inducing excessive bed shear stress. This is a complex process, so it is difficult to describe it through a general empirical model, the present research work describes contemporary conceptual relationships to estimate the local scour depth under equilibrium and clear water conditions in rectangular channels. Incidentally, gene-expression programming (GEP), evolutionary polynomial regression (EPR), and model tree (MT)-based formulations were utilized to predict the scour depth at long contractions. The input variables comprising average flow velocity, critical threshold velocity of sediment movement, flow depth, median particle diameter, geometric standard deviation, and uncontracted and contracted channel widths were used to feed the applied models. The performances of the developed approach were compared with those calculated using existing scour prediction equations. The results showed that the developed MT approach in terms of linear relationships could predict the scour depth more precisely than GEP, EPR, and the traditional equations. What is more, dimensionless parameter of h₁/b₁ (ratio of upstream flow depth to uncontracted channel width) was determined as the most influential variable in predicting the scour depth in long contractions.     

Numerical evaluation of passive control of VIV by small control rods

Flow past a circular cylinder with multiple small control rods is studied by numerical simulation for Re_D ranging from 1161.3 to 6387.1. The Reynolds-Averaged-Navier–Stokes (RANS) equations and shear stress transport (SST) k − ω turbulence model are used to calculate the vortex field, while a fourth-order Runge–Kutta method is employed for evaluating the structure dynamics of the cylinder group. Comparisons with experimental results demonstrate the validation of this method. This study is concerned with the vortex induced vibration (VIV) suppression efficacy of small control rods placed around a main cylinder. The effects of control rod number, diameter ratio, spacing ratio and Reynolds number on the hydrodynamics and vibration responses of the main cylinder are investigated. The reduced percents of in-line and cross-flow amplitudes and the increased percents of the whole cross-sectional area of cylinders and the drag coefficient are used to give a comprehensive evaluation. Results of simulation indicate that placing small rods with appropriate number at appropriate locations can achieve good suppression effectiveness at a wide range of Reynolds number. The numerical result for the case with nine control rods, diameter ratio of 0.15 and spacing ratio of 0.6 shows the best suppression effect among the cases investigated in this study.     

Evaluation of hydraulic conductivity through particle shape and packing density characteristics of sand–silt mixtures

Abstract

This study aims to evaluate the relationship between saturated hydraulic conductivity with particle shape and packing density characteristics of silty sand soils. The article presents a series of hydraulics tests performed on three kinds of sand with different particles shapes (Chlef rounded sand, Fontainebleau sub-rounded sand and Hostun sub-angular sand) mixed with low plastic rounded Chlef silt in the range of 0–30% fines content. The sand–silt mixture samples were tested in the constant-head permeability device at a loose relative density (D_r = 18%) and a constant room temperature (T?=?20?°C). The obtained results indicate that the measured saturated hydraulic conductivity (K_s) correlates very well with the fines content (F_c), packing density in terms of [maximum void ratio “e_max,” minimum void ratio “e_min,” predicted maximum void ratio “e_max”_pr and predicted minimum void ratio “e_min”_pr] and particle shape characteristics ratios in terms of roundness ratio (R_r = R_hs/R_mixture) and sphericity ratio (S_r = S_hs/S_mixture) of the silty sand materials under consideration. Moreover, the analysis of the available data show a noticeable success in exploring the prediction of the saturated hydraulic conductivity (K_s) based on the particle shape and packing density characteristics (R_r, S_r, e_max, and e_min) of the studied sand–silt mixture samples.     

A lateral global buckling failure envelope for a high temperature and high pressure (HT/HP) submarine pipeline

Submarine pipelines are the primary component of an offshore oil transportation system. Under operating conditions, a pipeline is subjected to high temperatures and pressures to improve oil mobility. As a result, additional stress accumulates in pipeline sections, which causes global buckling. For an exposed deep-water pipeline, lateral buckling is the major form of this global buckling. Large lateral displacement causes a very high bending moment which may lead to a local buckling failure in the pipe cross-section. This paper proposes a lateral global buckling failure envelope for deep-water HT/HP pipelines using a numerical simulation analysis. It analyzes the factors influencing the envelope, including the thickness t, diameter D, soil resistance coefficient μ, calculating length L_f, imperfection length L and imperfection amplitude V. Equations to calculate the failure envelope are established to make future post-buckling pipeline failure assessment more convenient. The results show that (1) the limit pressure difference p_max (the failure pressure difference for a post-buckling pipeline when it suffers no difference in temperature) is usually below the burst pressure difference p_b (which is the largest pressure difference a pipeline can bear and is determined from the strength and sectional dimensions of the pipeline) and is approximately 0.62–0.75 times the value of p_b and (2) thickness t has little influence on the normalized envelopes, but affects p_max. The diameter D, soil resistance coefficient μ, and calculating length L_f influence the maximum failure temperature difference T_max (the failure temperature difference for a pipeline suffering no pressure difference). The diameter D also significantly affects the form of the normalized envelope.     

斜向波浪作用下双层水平板式防波堤波浪荷载试验研究

In this study, systematic physical model tests were performed to investigate the wave forces on the twin-plate breakwater under irregular waves. Based on the experimental results, the effects of the relative plate width B/L,wave height Hs/D and incident angle θ0 on the wave forces were analyzed and discussed. The results showed that:(1) The envelopes of the total wave pressure were generally symmetrical along the direction of plate width under the incident angles(θ0) being 0°, 15°, 30°, 45° and 60°. In particular, the envelopes of wave pressure atθ0=30° were larger than all other cases.(2) The synchronous pressure distribution of the breakwater under oblique wave action was more complicated comparing to the normal incident waves.(3) Based on data analysis, an empirical formula was obtained to estimate the total vertical force of the twin-plate breakwater.This empirical formula can be a good reference for the design basis of engineering applications under specified wave conditions.     

Modified McCormicks model for equilibrium shorelines behind a detached breakwater

Experimental data of equilibrium shorelines behind a detached breakwater obtained by previous investigators were collected and re-reviewed to investigate the major parameters affecting the shoreline shapes. The result shows that the equilibrium shorelines depend not only on the breakwater length B and the distance of the breakwater from the initial shoreline S, but also on the incident wave steepness H₀/L₀, beach slope S_b and the sand size D₅₀. Most of equilibrium shorelines behind a detached breakwater could be approximately described by a couple of elliptic curves as proposed by McCormick (Ports, Coastal & Ocean Engineering ASCE 119, 1993, p. 657). However, after re-examination, this paper shows that the dimensionless semiminor axis b/S and the dimensionless distance G/b in the McCormick’s elliptic-curve model should be modified, as compared with the available experimental data. The modified expressions of b/S and G/b were proposed, and the performances of the modified expressions were also detaily examined in this paper.