3D scour below pipelines under waves and combined waves and currents

This paper presents the results of an experimental investigation on three-dimensional local scour below a rigid pipeline subjected to wave only and combined wave and current conditions. The tests were conducted in a conventional wave flume. The major emphasis of the investigation was on the scour propagation speed (free span expansion rate) along the pipeline after local scour was initiated at a controlled location. The effects of flow ratio (steady current velocity vs. combined waves/current velocity), flow incidence angle and pipeline initial embedment depth on free span expansion rate were investigated. It was observed that the scour along the pipeline propagated at a constant rate under wave only conditions. The scour propagation rate decreased with increasing embedment depth, however, increased with the increasing Keuglegan–Carpenter (KC) number. Under combined wave and current conditions, the effect of velocity ratio on scour propagation velocity along the pipeline was quantified. Empirical relationships between the scour propagation rate (V_h) and key parameters such as the KC number and embedment depth (e/D) were established based on the testing results.     

Numerical study of the Reynolds-number dependence of two-dimensional scour beneath offshore pipelines in steady currents

A numerical model for local scour below pipelines is employed to investigate the Reynolds-number dependence of the two-dimensional scour beneath offshore pipelines in steady currents. A novel wall function is proposed in calculating the suspended sediment transport rate in the model. Scour developments beneath a model pipeline and the corresponding prototype pipeline are simulated under the same undisturbed Shields parameter but different values of Reynolds number. The effects of the Reynolds number difference on the scour profile development are investigated. It is found that scour depths for prototype pipelines are about 10–15% smaller than those for model pipelines. The flow phenomena that causes this difference are discussed by means of flow visualization. The normalized time scales are found to be approximately the same. The simulated scour profiles for the model pipelines agree well with the experimental results from an independent study.     

Onset of scour below pipelines and self-burial

This paper summarizes the results of an experimental study on the onset of scour below and self-burial of pipelines in currents/waves. Pressure was measured on the surface of a slightly buried pipe at two points, one at the upstream side and the other at the downstream side of the pipe, both in the sand bed. The latter enabled the pressure gradient (which drives a seepage flow underneath the pipe) to be calculated. The results indicated that the excessive seepage flow and the resulting piping are the major factor to cause the onset of scour below the pipeline. The onset of scour occurred always locally (but not along the length of the pipeline as a two-dimensional process). The critical condition corresponding to the onset of scour was determined both in the case of currents and in the case of waves. Once the scour breaks out, it will propagate along the length of the pipeline, scour holes being interrupted with stretches of soil (span shoulders) supporting the pipeline. As the span shoulder gets shorter and shorter, more and more weight of the pipeline is exerted on the soil. In this process, a critical point is reached where the bearing capacity of the soil is exceeded (general shear failure). At this point, the pipe begins to sink at the span shoulder (self-burial). It was found that the self-burial depth is governed mainly by the Keulegan–Carpenter number. The time scale of the self-burial process, on the other hand, is governed by the Keulegan–Carpenter number and the Shields parameter. Diagrams are given for the self-burial depth and the time scale of the self-burial process.     

泥沙突变理论在海底管线冲刷中应用

基于泥沙突变理论,针对海底管线冲刷下泥沙的运动特征,建立恒定流作用下的泥沙起动模式,确定希尔兹数、无量纲参数、冲刷坑深度之间相互作用的非线性方程,推导了恒定流作用下海底管线冲刷坑深度的预测公式。将相同条件下该公式的计算结果与前人的试验资料进行了对比,可发现尽管计算结果存在一定的误差,但也基本能满足对冲刷坑深度的预测和判断,从而证明了泥沙突变模型在预测海底管线冲刷坑深度中的适用性。     

Prediction of wave-induced scour depth under submarine pipelines using machine learning approach

The scour around submarine pipelines may influence their stability; therefore scour prediction is a very important issue in submarine pipeline design. Several investigations have been conducted to develop a relationship between wave-induced scour depth under pipelines and the governing parameters. However, existing formulas do not always yield accurate results due to the complexity of the scour phenomenon. Recently, machine learning approaches such as Artificial Neural Networks (ANNs) have been used to increase the accuracy of the scour depth prediction. Nevertheless, they are not as transparent and easy to use as conventional formulas. In this study, the wave-induced scour was studied in both clear water and live bed conditions using the M5’ model tree as a novel soft computing method. The M5’ model is more transparent and can provide understandable formulas. To develop the models, several dimensionless parameter, such as gap to diameter ratio, Keulegan-Carpenter number and Shields number were used. The results show that the M5’ models increase the accuracy of the scour prediction and that the Shields number is very important in the clear water condition. Overall, the results illustrate that the developed formulas could serve as a valuable tool for the prediction of wave-induced scour depth under both live bed and clear water conditions.     

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.     

Numerical simulation of a partially buried pipeline in a permeable seabed subject to combined oscillatory flow and steady current

Hydrodynamic forces exerting on a pipeline partially buried in a permeable seabed subjected to combined oscillatory flow and steady current are investigated numerically. Two-dimensional Reynolds-Averaged Navier-Stokes equations with a k−ω turbulent model closure are solved to simulate the flow around the pipeline. The Laplace equation is solved to calculate the pore pressure below the seabed with the simulated seabed hydrodynamic pressure as boundary conditions. The numerical model is validated against the experimental data of a fully exposed pipeline resting on a plane boundary under various flow conditions. Then the flow with different embedment depths, steady current ratios and KC numbers is simulated. The amplitude of seepage velocity is much smaller than the amplitude of free stream velocity as expected. The normalized Morison inertia, drag and lift coefficients based on the corresponding force coefficients of a fully exposed pipeline are investigated. The normalized Morison force coefficients reduce almost linearly with the increase of embedment depth and that the KC only has minor effect on the normalized Morison coefficients. It is also found that the permeable seabed condition causes a slight increase on the inline force and has a little effect on the lift force, compared with corresponding conditions in an impermeable bed.     

Burial and scour around short cylinder under progressive shoaling waves

The results of a laboratory experimental program aimed at better understanding the scour around and burial of heavy cylindrical objects under oscillating flow on a sandy bed are described. This study was motivated by its application to the dynamics of isolated cobbles/mines on a sandy floor under nonlinear progressive waves, such as that occur in shallow coastal waters beyond the wave-breaking region. In the experiments, nonlinear progressive waves were generated in a long wave tank of rectangular cross-section with a bottom slope. Model mines (short cylinders) were placed on the sandy bottom and the temporal evolution of the bed profile and the velocity field in the near field of the object were observed. Experiments were conducted at relatively high Reynolds numbers for a range of flow conditions, which can be characterized by the Keulegan–Carpenter number and Shields parameter. Depending on the values of these parameters, four different scour regimes around the cylinder including periodical burial of cylinder under migrating sand ripples were observed; they were classified as: (i) no scour/burial, (ii) initial scour, (iii) expanded scour, and (iv) periodic burial cases. A scour regime diagram was developed and the demarcation criteria between different regimes were deduced. Semi-empirical formulae that permit estimation of the scour depth with time, the equilibrium maximum scour depth and length, and conditions necessary for the burial of the cylinder as a function of main external parameters are also proposed.     

Characteristics of Parameters for Local Scour Depth around Submarine Pipelines in Waves

The purpose of this study is to investigate the characteristics of parameters for local scour depth around submarine pipes due to waves. Because it is impossible to consider all the factors that influence the scour, it is reasonable to investigate the correlations between parameters and scour. The experimental works about scour were performed for the conditions of 40, 60, 90 m pipe diameter, various wave periods, and wave height in the case of horizontal bed and 1/10 slope bed, respectively. Analyzing the results of experiments, the Reynolds number, Shields parameter, Keulegan-Carpenter number, Ursell number, and Modified Ursell number were estimated. The correlations between the relative scour depth, which is the maximum equilibrium local scour depth divided by the pipe diameter, and 5 parameters were analyzed. It was shown that there was hardly any correlation with the Reynolds number. In the case of a horizontal bed, the Keulegan-Carpent number had the highest correlation, but in the case of the slope bed the correlation was greatly reduced. The modified Ursell number showed a high correlation regardless of the type of bed.     

Scour and burial mechanics of conical frustums on a sandy bed under combined flow conditions

The scour and burial of conical frustums placed on a sandy bed under waves alone (WA) and combined flows (CF) conditions was investigated. The observations indicate that equilibrium burial depth is smaller than burial of other objects such as short cylinders laying on a sand bed under equivalent hydrodynamic conditions. Truncated cone offers less resistance to the flow field due to its more round shape when compared to a horizontally placed short cylinder characterized by sharp edges. A smaller disruption to the flow field translates to less turbulent intensity and to smaller sediment transport capacity of the flow around the object and less burial. The equilibrium burial depth shows a significantly weaker dependency on the Shields parameter than on the Keulegan-Carpenter number, contrary to the case of finite short cylinders. A new empirical predictor based on the relative strength of the wave to the wave plus current velocity, the Keulegan-Carpenter number, and the Shields parameter is proposed for estimating the equilibrium burial of truncated cones under combined flows. Both the Keulegan-Carpenter number and the Shields parameter determine the width of the scour hole around the cone. The former however, is the most dominant parameter influencing the length of the scour hole.     

轴线倾斜海底管道冲刷速率试验研究

通过物理模型试验研究水流作用下轴线倾斜海底管道的三维局部冲刷问题。利用超声波探头监测管道下部冲刷沿管轴线方向的扩展过程,分析海底管道三维局部冲刷的动态发展机理。由模型沙的冲蚀试验,建立沙床面剪切应力与泥沙表观侵蚀速率之间的关系式,并引入经验公式对沙床面剪切应力放大系数、泥沙表观侵蚀速率以及远场床面剪切应力之间的关系进行表达。由倾斜管道模型试验,在分析冲刷扩展位置随时间变化数据的基础上,结合上述经验公式以及沙床面剪切应力放大系数与管道埋深的关系,建立轴线倾斜海底管道冲刷扩展速率的预测公式。     

Numerical simulation of local scour around two pipelines in tandem using CFD–DEM method

In the field of offshore oil and gas engineering, the arrangement of multiple pipelines are becoming more common, the spacing between the pipelines and the incoming stream velocity will significantly affect the scouring process around the pipelines. In this study, the effect of space ratio (G/D) and the stream velocity on the scouring process around two pipelines in tandem are investigated using the coupled approach of computational fluid dynamics (CFD) and discrete element method (DEM). Here G is the spacing between the pipelines and D is the diameter of the pipeline. Specifically, the effect of space ratio and the stream velocity are discussed by simulating the gap ratio (G/D) between two pipelines ranging from 1 to 3 with an interval of 1, under the stream velocity U = 0.5,1 and 2 m/s, The results indicate that when G/D ≤ 2, the equilibrium scour depth below the upstream pipeline (S1) is slightly larger than that under the downstream pipeline (S2), S1 and S2 slightly increase as the gap ratio increases. Whereas for G/D > 2, the equilibrium scour depth beneath the upstream pipeline is slightly smaller than that under the downstream pipeline, S1 and S2 slightly decrease as the gap ratio increases. Furthermore, the scour depths are highly dependent on and positively related to the incoming stream velocity, the equilibrium bed profiles are similar under the same incident stream velocity with different gap ratios.     

Investigation on the Local Scour Beneath Piggyback Pipelines Under Clear-Water Conditions

A piggyback pipeline consists of two pipes such that the secondary line rides on the main pipe with a fixed distance between two pipes in length. The novel strategy is utilized in offshore areas instead of a single flow line. In this regard, there are only a handful of experimental and numerical studies investigating the effect of scour below a piggyback pipeline under steady current. Hence, this study focuses on examining the influential factors on scouring due to steady current including the pipe diameter and the gap between pipes through numerical simulations and experimental tests. Accordingly, at the first phase of the research, a single pipe was established and tested in laboratory to compare the results with those of an empirical equation. After finishing experimental verifications,piggyback pipelines were also assembled to study the scouring under steady current conditions. It was concluded that by increasing the gap distance between the pipes, the maximum scour depth decreases; however, an increase in the small pipe's diameter results in a larger maximum scour depth. Secondly, numerical simulations were carried out using the FLOW-3D software which was found to be a suitable tool for the numerical investigation of this study.Finally, the numerical results have been compared with the corresponding experimental data and a relatively good agreement was achieved between them.     

Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents

Local scour around a submerged vertical circular cylinder in steady currents was studied both experimentally and numerically. The physical experiments were conducted for two different cylinder diameters with a range of cylinder height-to-diameter ratios. Transient scour depth at the stagnation point (upstream edge) of the cylinder was measured using the so-called conductivity scour probes. Three-dimensional (3D) seabed topography around each model cylinder was measured using a laser profiler. The effect of the height-to-diameter ratio on the scour depth was investigated. The experimental results show that the scour depth at the stagnation point is independent on cylinder height-to-diameter ratio when the later is smaller than 2. The increase rate of equilibrium scour depth with cylinder height increases with an increase in Shields parameter.     

Numerical investigation of local scour below a vibrating pipeline under steady currents

Local scour below a vibrating pipeline under steady current is investigated by a finite element numerical model. The flow, sediment transport and pipeline response are coupled in the numerical model. The numerical results of scour depths and pipeline vibration amplitudes are compared with measured data available in literature. Good agreement is obtained. It is found that pipeline vibrations cause increases of scour depth below the pipeline. The scour pit underneath a two-degree-of-freedom vibrating pipeline is deeper than that under a pipeline vibrating only in the transverse flow direction. The effects of water depth are also investigated. The present numerical result shows that water depth has weak effect on the scour depth. However it does affect the time scale of the scour. The shallower the water depth is, the less time it requires to reaches the equilibrium state of scour. It is found that the vibration forces vortices to be shed from the bottom side of the pipeline. Then vortex shedding around a vibrating pipeline is closer to the seabed than vortex shedding around a fixed pipeline. This contributes to the increase of the scour depth.     

NF-GMDH-Based self-organized systems to predict bridge pier scour depth under debris flow effects

Existence of debris structures inevitably ascends the rate of scour process around bridge piers and flow area not only lead into remarkable deviation of flow but also increase the velocity around bridge piers. A myriad of experimental and field studies to understand effective parameters on the scour depth with debris effects were conducted. To reach permissible values of the scour depth for the practical uses, relationships extracted in previous investigations suffer from lack of generalization for experimental data ranges. In this way, neuro-fuzzy group method of data handling (NF-GMDH)-based self-organized models is applied to evaluate the pier scour depth. In this study, NF-GMDH network is implemented using evolutionary algorithms listed particle swarm optimization (PSO), gravitational search algorithm (GSA), and genetic algorithm (GA). In all, 243 experimental datasets including a wide range of input and output parameters to develop the proposed models were compiled from various literature. The efficiency of NF-GMDH networks for training and testing stages was perused. NF-GMDH-PSO model provided the scour depth with more precise predictions (root mean squared error (RMSE)?=?0.388 and scatter index (SI)?=?0.343) in comparison with NF-GMDH-GA (RMSE?=?0.402 and SI?=?0.361) and NF-GMDH-GSA (RMSE?=?0.456 and SI?=?0.407) networks. In addition, blockage ratio (ΔA) was taken into account as the most sumptuous parameter with utmost level of effectiveness using the sensitivity analysis.     

斜向波作用下斜坡海床上管线三维冲刷不均衡性研究

由于海床起伏不平,斜坡的存在必然改变波浪对管线及海床的作用特性,进而影响管线三维冲刷。基于波浪港池实验,考虑规则波的作用,采用中值粒径为0.22mm的原型沙铺设与波浪传播方向成45°夹角的斜坡,研究斜向波作用下斜坡上海底管线的三维冲刷特性。通过测量管线下方冲刷坑宽度和深度的差异,分析管线三维冲刷的不均衡性。实验表明:管线的存在使斜坡上的波高有所降低;斜向波作用下管线三维冲刷的不均衡性表现为深度不均衡性和宽度不均衡性,宽度不均衡性主要是管后淤积泥沙的后移引起的,周期对三维冲刷不均衡性的影响比波高对其的影响程度大;管线自深海向近岸延展时,随水深的减小,冲刷深度分为缓慢发展阶段和快速发展阶段。     

Physical Modeling of Localized Scour for the Yangtze Estuary Waterway Improvement Project,Phase Ⅰ

In order to examine the effectiveness of engineering protection against localized scour in frontof the south groin-group of the Yangtze Estuary Waterway Improvement Project,Phase I,an undistort-ed physical model on a geometric scale of 1:250 is built in this study,covering two groins and their adacentestuarine areas.By use of rinsing fix-bed model as well as localized mobile-bed model,the experiment isundertaken under bi-directional steady flow.According to the experimental results,waterway dredgingleads to the increase in steram velocity,the increase being larger during the ebb than during the flood.Con-struction of the upstream groin has some influence on the flow patterns near the downstream groin.Local-ized scour in front of the groin-heads is controlled mainly by ebb flow.In the case of a riverbed composedentirely of silt,the depths of localized scour in front of the two groin-heads are 27 m and 29 m,respectively.In reality,the underneath sediment of the prototype riverbed is clay whose threshold ve     

GMDH-GEP to predict free span expansion rates below pipelines under waves

ABSTRACT

In this research, group method of data handling (GMDH) as a one of the self-organized approaches is utilized to predict three-dimensional free span expansion rates around pipeline due to waves. The GMDH network is developed using gene-expression programming (GEP) algorithm. In this way, GEP was performed in each neuron of GMDH instead of polynomial quadratic neuron. Effective parameters on the three-dimensional scour rates include sediment size, pipeline geometry, and wave characteristics upstream of pipeline. Four-dimensionless parameters are considered as input variables by means of dimensional analysis technique. Furthermore, scour rates along the pipeline, vertical scour rate, and additionally scour rates in the left and right of pipeline are determined as output parameters. Results of the proposed GMDH-GEP models for the training stages and testing ones are evaluated using various statistical indices. Performances of the GMDH-GEP models are compared with artificial neural network (ANN), GEP, GMDH, and traditional equations-based regression models. Moreover, sensitivity analysis and parametric study are conducted to perceive influences of different input parameters on the three-dimensional scour rates.     

The effects of uniform and nonuniform pile spacing variations on local scour at pile groups

Pile groups are frequently used to support bridge decks. Scour in the vicinity of piles is the main cause for the bridges failure. In this research, to address the effects of uniform and nonuniform pile spacing on the equilibrium scour depth, laboratory experiments were carried out under steady clear-water conditions. For this purpose, scour depth produced by pile group with various pile spacing and arrangement was investigated using a laboratory flume. Flume bed was covered by uniform sediments with a median size of 0.9?mm and 0.2?m thickness. Flow discharge and velocity as well as scour depth were recorded in each experiment and the data were analyzed. The results showed that the pile spacing influences the local scour depth and with increase in uniform and transverse (perpendicular to the flow) spacing, the maximum scour depth was reduced. The pile spacing variation in line with the flow has a minor effect on scour depth. In addition, the pile spacing perpendicular to the flow was with the most influences on scour depth. The results of this research can be used by engineers to optimize the design of bridges.