Prediction of scour depth at piers with debris accumulation effects using linear genetic programming

Abstract

Exact evaluation of scour depth around piers under debris accumulation is crucial for the safe design of pier structures. Experimental studies on scouring around pier bridges with debris accumulation have been conducted to estimate the maximum scour depth using various empirical relationships. However, due to the oversimplification of a complex process, the proposed relationships have not always been able to accurately predict the pier scour depth. This research proposes linear genetic programming (LGP) approach as an extension of the genetic programming to predict the scour depth around bridge piers. Among the artificial intelligence techniques, LGP and locally weighted linear regression (LWLR) models have not been used to predict the scour depth at bridge piers. Literature experimental data were collected and used to develop the models. The performance of the LGP method was compared with gene-expression programming, LWLR, multilinear regression and empirical equations using rigorous statistical criteria. The correlation coefficient (R) and the root mean squared error (RMSE) were (R?=?0.962, RMSE =0.31) and (R?=?0.885, RMSE =0.542) for the LGP and LWLR, respectively. The results demonstrated the superiority of the LGP method for increasing the accuracy of the predicted scour depth in comparison with the other models.     

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.     

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.     

Current-induced scour around a vertical pile in cohesive soil

Stability of many ocean structures is affected by seabed scour induced by under-currents. The depth of scour is an important parameter for determining the minimum depth of foundations as it reduces the lateral capacity of the foundations. A review of the literature reveals that there is not much information available in the field of scour in cohesive soils. Hence, a detailed laboratory testing programme on model piles of diameters 50 mm to 110 mm embedded in soft silty clay soil was carried out in a wave flume of 30 m long, 2.0 m wide and 1.7 m deep, which has the capability of simulating steady currents. Scour around the pile due to steady streaming is monitored by using special instrumentation. A procedure has been suggested to predict the ultimate scour depths based on the observed variation in scour depth over a limited time period. The study indicates that the ultimate scour depth is controlled by diameter of obstruction, current velocity, model Reynolds number, flow Froude number, shear stress, and soil characteristics. Based on these results, a few functional relationships are suggested between scour depth and other parameters like Reynolds number, Froude number, and strength of the soil bed.     

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.     

港珠澳大桥青州航道桥桥墩基础冲刷试验研究

桥墩基础冲刷是桥梁毁坏的重要因素,是桥梁基础设计的关键指标之一。目前国内外对于桥墩基础在复杂动力条件下冲刷深度的研究常采用物理模型试验方法,利用正态系列模型方法,在波流水槽中研究了水流、潮流和波流共同作用下青州航道桥索塔基础周围流态变化和局部冲刷特征。研究结果表明,桥墩最大冲刷深度和冲淤范围与水流流速、桥墩轴线与水流夹角和波浪等因素有关;在潮流最大流速和恒定流流速一致情况下,桥墩局部冲刷深度达到平衡后,将会达到与恒定流基本一致的最大冲深;波流共同作用下的最大冲刷深度比恒定流增加10%左右。设计桥墩形状在100年一遇水流和波浪共同作用下桥墩基础局部最大冲刷深度为13.7 m。     

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.     

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.     

Prediction of local scour around circular piles under waves using a novel artificial intelligence approach

Abstract

The scour phenomena around vertical piles in oceans and under waves may influence the structure stability. Therefore, accurately predicting the scour depth is an important task in the design of piles. Empirical approaches often do not provide the required accuracy compared with data mining methods for modeling such complex processes. The main objective of this study is to develop three data-driven methods, locally weighted linear regression (LWLR), support vector machine (SVR), and multivariate linear regression (MLR) to predict the scour depth around vertical piles due to waves in a sand bed. It is the first effort to develop the LWLR to predict scour depth around vertical piles. The models simulate the scour depth mainly based on Shields parameter, pile Reynolds number, grain Reynolds number, Keulegan–Carpenter number, and sediment number. 111 laboratory datasets, derived from several experimental studies, were used for the modeling. The results indicated that the LWLR provided highly accurate predictions of the scour depths around piles (R?=?0.939 and RMSE = 0.075). Overall, this study demonstrated that the LWLR can be used as a valuable tool to predict the wave-induced scour around piles.     

Three-dimensional scour below offshore pipelines in steady currents

This paper presents the results of an experimental investigation on three-dimensional scour below offshore pipelines subject to steady currents. The major emphasis of the investigation is on the scour propagation velocity along the pipeline after the scour initiation. Physical experiments were conducted to quantify the effects of various parameters on scour propagation velocity along the pipeline in a water flume of 4 m wide, 2.5 m deep and 50 m long. Local scour depths directly below the model pipeline were measured using specifically developed conductivity scour probes. Effects of various parameters such as pipeline embedment depth, incoming flow Shields parameter and flow incident angle (relative to the pipeline) on scour propagation velocity along the pipeline were investigated. It was found that scour propagation velocity generally increases with the increase of Shields parameter but decreases with the increase of the pipeline embedment depth. A general predictive formula for scour propagation velocity is proposed and validated against the experimental results.     

Dynamic interaction between two parallel submarine pipelines considered vortex-induced vibration and local scour

Abstract

The mechanism of local scour under two vibrating pipelines is investigated numerically in this research. A sediment scour model is adopted to estimate the motion of sediment. The general moving objects model, which is dynamically coupled with fluid flow, is set up to simulate the vortex-induced vibration (VIV) of the pipeline. The sediment scour model and pipeline vibration model are verified with the previous experimental results and show good agreement. Then, the coupling effects between the pipeline vibration and the local scour are investigated numerically. The effects of G/D (the ratio of the distance between the two pipelines to the diameter of the pipelines) on the local scour and the VIV of the pipeline are examined. The results indicate that the maximum scour depth under the vibrating pipelines is much larger than the scour depth under the fixed pipelines. Due to the shadowing effect of the upstream pipeline, the maximum scour depth under the upstream pipeline is deeper than that under the downstream pipeline. The pipeline vibration magnitude is closely related to the strength of the vortex that sheds behind the pipeline. The effect of G/D on the shape and strength of the vortices that shed behind the pipelines is significant.     

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 modeling of flow and scour below a pipeline in currents: Part II. Scour simulation

A vertical two-dimensional (2D) numerical model for time dependent local scour below offshore pipelines subject to unidirectional steady flow is developed. The governing equations for the flow and sediment transport are solved by using finite difference method in a general curvilinear coordinate system. The performance of two turbulence models, the standard k–ɛ model and Smagorinsky subgrid scale (SGS) model, on modeling time dependent scour processes is examined. Both suspended load and bed load are considered in the scour model. The suspended-load model is verified against two channel sediment transport cases. The change of bed level is calculated from the continuity equation of total sediment transport. A new time marching scheme and a sand slide scheme are proposed for the scour calculation. It is found that the proposed time marching scheme and sand slide model work well for both clear-water and live-bed scour situations and the standard k–ɛ turbulence closure is more preferable than the SGS model in the 2D scour model developed in this study.     

基于Flow-3D的抗拖网海床基冲刷数值模拟

基于Flow-3D软件,建立抗拖网海床基沙土基床冲刷的三维数学模型,控制水流流速和泥沙粒径,对不同条件下抗拖网海床基周围沙土基床的冲刷进行数值模拟,并分析了抗拖网海床基最大冲刷深度随这两种因素改变的趋势。结果表明,抗拖网海床基沙土基床冲刷坑深度随海流流速增大而增加,在设定其他条件不改变的情况下,冲刷坑的加深速度随着流速增大会逐渐减缓,最终达到冲淤平衡。同时,由于海底环境复杂多变,导致模型与实际情况有一定的差异,还需在后续的研究中进一步进行优化。     

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.     

海流作用下海底管道局部冲刷数值分析

在任意拉格朗日-欧拉参考坐标系下,采用基于雷诺平均的Navier-Stokes方程组(RANS)、流线迎风有限元方法、泥沙输运模型以及底床变形方程,对海流引起的海底管道局部冲刷进行了数值模拟。着重讨论了均匀来流流速和海底管道直径对局部冲刷发展过程及平衡冲刷深度的影响作用。数值结果表明,在冲刷的初始阶段,冲刷深度随时间迅速增加,之后缓慢逼近极限平衡深度;在管径一定的情况下,管道附近的局部平衡冲刷深度与流速大致呈线性关系;当流速超过某一临界区域后,最大平衡冲刷深度出现的位置并不在管道正下方,而是随流速的增加向管道下游方向移动;另外,管道直径也会对平衡冲刷深度产生比较明显的影响,在相同流速下,平衡冲刷深度大致随管径呈线性增大。在本文的计算范围内,海底管道的相对局部平衡冲刷深度基本随雷诺数线性增加,但流速对冲刷深度的影响作用要比管径的影响作用更为明显。     

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.