Numerical analysis of a cylinder moving through rate-dependent undrained soil

Geo-hazard assessment of the potential damage to a pipeline caused by a submarine landslide requires a quantitative model to evaluate the impact forces on the pipeline. In contrast with typical geotechnical problems, the strain rate within the fast moving, flow-like submarine landslide is typically far higher, which will lead to enhancement of the soil strength and therefore result in larger impact forces. Generally, there are two possible predictive frameworks for strain-rate dependence: a fluid dynamics framework and a geotechnical framework. By comparison of common rheological models adopted in these two different approaches, a unified additive power-law model, a normalised form of the Herschel-Bulkley model from fluid mechanics, is explored in this paper. This model has been used in conjunction with a large deformation finite element approach to investigate the undrained limiting loads on a cylinder moving steadily through inertia-less soft rate-dependent material, in order to quantify the strain-rate effects.The flow mechanism and the effects of the shear-thinning index and Oldroyd number on the shear zones are explored. The calculated resistance factors are compared with the drag coefficients obtained from computational fluid dynamics analysis. The average rate of strain experienced by the soil flowing past the cylinder is estimated for a given flow velocity and an expression in the form of a conventional bearing capacity equation, but with shear strength linked directly to the normalised flow velocity, is proposed to predict the magnitude of the viscous force exerted by the debris flow.     

Numerical investigation on the penetration of gravity installed anchors by a coupled Eulerian–Lagrangian approach

Gravity installed anchors (GIAs) are released from a height of 30–150 m above the seabed, achieving velocities up to 19–35 m/s at the seabed, and embed to depths of 1.0–2.4 times the anchor length. Challenges associated with GIAs include the prediction of anchor initial embedment depth, which determines the holding capacity of the anchor. Based on the coupled Eulerian–Lagrangian approach, a numerical framework is proposed in this paper to predict the embedment depth of GIAs, considering the effects of soil strain rate, soil strain-softening and hydrodynamic drag (modeled using a concentrated force), with the anchor-soil friction described appropriately. GIAs are influenced by the hydrodynamic drag before penetrating into the soil completely, hence the anchor accelerates less than the previous investigations in shallow penetration, even decelerates directly at the terminal impact velocity. The hydrodynamic drag has more influence on OMNI-Max anchors (with an error of ∼4.5%) than torpedo anchors, and the effect becomes more significant with increasing impact velocity. An extensive parametric study is carried out by varying the impact velocity, strain rate and strain-softening parameters, frictional coefficient, and soil undrained shear strength. It is concluded that the dominant factor affecting the penetration is the soil undrained shear strength, then are the impact velocity, strain rate dependency and frictional coefficient, and the minimal is the strain-softening of soil. In addition, although the strain rate dependency is partly compensated by the softening, the anchor embedment depth accounting for the effects of strain rate and strain-softening is lower than that for ideal Tresca soil. Strain rate dependency dominates the combined effects of strain rate and strain-softening in the dynamic installation of GIAs, on which should pay more attention, especially for the calibration of the related parameters and the measured solutions. In the end, the theoretical model based on the bearing resistance method is extended by accounting for the hydrodynamic drag effect.     

Toward a quick evaluation of the performance of gravity installed anchors in clay: Penetration and keying

Gravity installed anchors (GIAs) are the most recent generation of anchoring solutions to moor floating facilities for deepwater oil and gas developments. Challenges associated with GIAs include predicting the initial embedment depth and evaluating the keying performance of the anchor. The former involves high soil strain rate due to large anchor penetration velocity, while the later influences the subsequent behavior and pullout capacity of the anchor. With the coupled Eulerian–Lagrangian method, three-dimensional large deformation finite element models are established to investigate the penetration and keying of GIAs in non-homogeneous clay. In the penetration model, a modified Tresca soil model is adopted to allow the effects of soil strain rate and strain softening, and user-defined hydrodynamic drag force and frictional resistance are introduced via concentrated forces. In the keying model, the anchor line effects are incorporated through a chain equation, and the keying, diving and pulling out behaviors of the anchor can all be replicated. Parametric studies are undertaken at first to quantify the effects of various factors on the performance of GIAs, especially on the penetration and keying behaviors. Based on the results of parametric studies, fitted formulae are proposed to give a quick evaluation of the anchor embedment depth after the installation, and the shackle horizontal displacement, shackle embedment loss and anchor inclination at the end of the keying. Comparative studies are also performed to verify the effectiveness of the fitted formulae.     

Axial friction response of full-scale pipes in soft clays

The axial friction response of subsea pipelines in soft clays is a very important aspect for designers of subsea pipelines but the response is not well understood so far. There is a pressing need for the comprehension of the response. In this paper, model tests are performed using full-scale pipes coated with polyethylene (PE) to study the effects of the set-up period, the pipe diameter, the buried depth of the pipe, the shear strength of soft clays and the loading rate on the axial friction response of pipelines in soft clays. The variations of the axial friction coefficient are analyzed using the effective stress method based on model test results. The results show that the axial friction resistance increases with the increasing pipe diameter but the effect of the pipe diameter on the axial friction coefficient can be neglected. The ultimate axial resistance also increases with the increase of the buried depth of pipelines, the undrained shear strength of soft clays and the loading rate. The axial friction coefficient increases with the increasing loading rate. However, the axial friction coefficient decreases with the increasing buried depth. The method to determine the axial friction coefficient is developed by analyzing model test results, which considers the effects of the diameter, the buried depth, the undrained shear strength of soft clays and the loading rate. The study results not only extend the industry data base but also supply a basis to determine the axial friction coefficient of PE-coated pipes in soft clays for ocean engineering geological investigations.     

内孤立波作用下竖直圆柱体的横向力研究

本文对内孤立波作用下圆柱体的水动力特性进行了数值研究。对不同直径、不同水深比、不同浸没深度的圆柱进行了水平方向受力分析,从多个因素出发,研究了内孤立波对水下竖直圆柱的水平作用情况。通过分析水平作用力和力矩的时程曲线,得到内孤立波行进过程中对于圆柱体的横向作用力和力矩与时间的关系。通过对比不同工况下内孤立波橫向作用力幅值,得到内孤立波作用力幅值与圆柱直径、水深比以及浸没深度的关系。结果表明,内孤立波横向作用力(力矩)幅值与圆柱直径呈线性相关关系,但与水深比相关关系不明显,随着圆柱浸没深度的增加,内孤立波横向作用力幅值呈现出先增大后减小的趋势。     

Wave forces acting on a vertical circular cylinder with a constant forward velocity

Wave forces acting on submerged circular cylinders moving forward with a constant velocity in regular waves are investigated experimentally. Hydrodynamic forces acting on the cylinder forced to surge in a steady are also measured and hydrodynamic coefficients were obtained. Wave force coefficients obtained from wave force measurements are compared with the hydrodynamic coefficients from surging tests, and the similarity and difference between them are discussed. Experiments show that these coefficients are quite different from those of the cylinder without a forward velocity.     

Estimation of Uplift Capacity of Rapidly Loaded Plate Anchors in Soft Clay

Plate anchors are extensively used in civil engineering constructions as they provide an economical alternative to gravity and other embedded anchors. The rate of loading is one of the important factors that affects the magnitude of soil resistance as well as soil suction force. This article outlines the effect of pullout rate on uplift behavior of plate anchors (70 mm diameter) buried in soft saturated clay by varying the pullout rate from 1.4 mm/min to 21.0 mm/min. The variation of breakout force and suction force with embedment depth and rate of pull are presented. A correlation between the rate of increase of undrained strength of clay and anchor capacity with rate of strain has been established. Finally an empirical equation has been proposed that includes the rate of pull in the estimation of breakout capacity of anchors.     

Estimation of Uplift Capacity of Rapidly Loaded Plate Anchors in Soft Clay

Plate anchors are extensively used in civil engineering constructions as they provide an economical alternative to gravity and other embedded anchors. The rate of loading is one of the important factors that affects the magnitude of soil resistance as well as soil suction force. This article outlines the effect of pullout rate on uplift behavior of plate anchors (70 mm diameter) buried in soft saturated clay by varying the pullout rate from 1.4 mm/min to 21.0 mm/min. The variation of breakout force and suction force with embedment depth and rate of pull are presented. A correlation between the rate of increase of undrained strength of clay and anchor capacity with rate of strain has been established. Finally an empirical equation has been proposed that includes the rate of pull in the estimation of breakout capacity of anchors.     

Wave drift enhancement effects in multi column structures

A theoretical assessment is made of mean wave drift forces on groups of vertical circular cylinders, such as the columns of a floating offshore platform. A complete analytical solution is obtained for two cylinders extending from seabed to free surface, and a long wave approximation is found to provide reliable predictions of the drift force in line with the waves at low frequencies. For moderate separation between the two cylinders, this force is found to tend at low frequencies to a value four times the force on an isolated cylinder.A numerical method is employed to study two surface piercing cylinders truncated below the free surface, and an arrangement of four vertical cylinders characteristic of a floating offshore platform. The mean vertical drift force is found to be reasonably well approximated, over the frequency range of practical interest, by the force on an individual cylinder considered in isolation multiplied by the number of cylinders in the group. Interaction effects, however, have a profound influence on the total horizontal drift force. At low frequencies this force is found to tend to the force on an isolated cylinder multiplied by the squate of the number of cylinders in the group.     

自由落体式球形贯入仪在硬-软黏土中的贯入响应

自由落体贯入仪（free falling penetrometer,简称FFP）通过自由下落贯入土层中,由于其高效便捷的特性,越来越广泛地被应用于海底浅层土体原位勘察。采用耦合欧拉-拉格朗日（Coupled Eulerian Lagrangian,简称CEL）方法,进行了球形FFP在硬-软双层黏土中贯入的大变形有限元分析,考虑了土体的应变率和应变软化效应。与离心机试验、现场试验和数值模拟结果进行了对比,验证了模型的可靠性。分析了成层土对贯入过程的影响,发现FFP在贯入过程中上部硬黏土层形成空腔,且底部会伴随着土塞。通过广泛的变参数分析结果,拟合了球形FFP最终贯入深度与总能量之间的归一化表达式,建立了土体不排水抗剪强度、FFP直径和贯入速度与FFP在硬-软黏土层中最终贯入深度的关系。     

An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections.This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum.The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.     

Solitary wave interactions with an array of two vertical cylinders

This paper addresses a numerical investigation of nonlinear waves interactions with an array of two surface-piercing vertical cylinders and the corresponding nonlinear hydrodynamic loads on each individual cylinder. The primary interest of this study is concentrated on the problem of three-dimensional scattering of solitary waves by cylinder arrays and the nonlinear interactions between scattered waves. The theoretical model adopted for simulation is the generalized Boussinesq two-equation model. The boundary-fitted coordinate transformation and multiple-grid technique are utilized here to simplify the computation domain and to facilitate the applications of the boundary conditions on the cylinder surfaces. The velocity potential, free-surface elevation and subsequent evolution of the scattered wave field are numerically evaluated. The hydrodynamic forces on each cylinder during wave impact are also determined. A study of the sheltering effect by the neighboring structures on wave loads is conducted. It is found that the presence of the neighboring cylinder has shown significant influence on the wave loads and the scattering of the primary incident waves. For two transversely arranged cylinders, the transverse force coefficient increases as the separation distance decreases.     

基于粘性流模型的筒型基础防波堤波浪力数值分析

筒型基础防波堤是一种新型港口海岸工程结构,其基础上部是由连续排列的圆筒构成的直立防浪墙.采用粘性流数值模型,研究连续圆筒防波堤上波浪力竖向分布、水平(沿圆筒环向)分布和波浪力合力特性,并对粘性流数值模型计算的平面直墙波浪力与海港水文规范方法计算结果;粘性流数值模型计算的连续圆筒墙面波浪力与平面直墙波浪力;无限长连续圆筒墙面波浪力与有限长连续圆筒墙面波浪力进行比较分析.针对所选工程算例,建议按<海港水文规范>中平面直墙波浪力计算方法确定连续圆筒防波堤上的波浪力时,波峰时考虑0.90左右的折减系数,波谷时考虑0.95左右的折减系数.     

Geotechnical Investigation of the Titanic Wreck Site

Abstract

Recent marine forensic investigations have largely unravelled the sequence of events concerning the sinking of the R.M.S. Titanic and its descent through nearly 3800 m of water to the seafloor on the morning of 15 April 1912. In particular, the velocity and attitude of the Titanic's bow section (at present lying upright, reasonably intact, and embedded by ～12 m at the prow) as it hit the bottom are of general interest to marine accident investigators. During the 1998 Titanic Science Expedition, a single sediment sample was retrieved from the seafloor (depth 20–30 cm) near the wreck by the deep water submersible, Nautile. Published geological studies suggest the seafloor in this area has remained largely undisturbed since 1912. Geotechnical analysis of the sediment sample reveals that the impact was probably a substantially undrained event and that the characteristic undrained shear strength of the sediment is ～25kPa within 10–16 m below the seafloor. A simple analytical model was used to calculate the embedment of a cuboid with dimensions and mass of the water-filled bow as a function of impact velocity, impact angle, and the undrained shear strength of the sediment. The results indicate the impossibility of a steep angle of impact and fast velocity. The most likely scenario is an impact velocity of 5–10 m/s at a fairly shallow angle (<40°), which corroborates the results of hydrodynamic investigations.     

Wave interaction with a concentric porous cylinder system

This is a theoretical investigation of wave interaction with a concentric surface-piercing two-cylinder system. The exterior cylinder is porous and considered to be thin in thickness and the interior cylinder is impermeable. Both cylinders are rigidly fixed at the sea bed. The fluid motion is idealized as a linearized potential flow. The free-surface elevation and the total net hydrodynamic forces acting on both cylinders are determined analytically. The wave-induced overturning moments are also evaluated. It is found that, with the existence of the exterior porous cylinder, the hydrodynamic force acting on the interior cylinder is reduced if compared to the force exerted on the interior cylinder by a direct wave impact. The reduction of the wave amplitude around the leeward side of the outer porous cylinder is shown from the free-surface computations. In this paper, results are also presented to illustrate the effects of wave parameter and structural porosity on this wave and cylinder interaction problem. The role played by the ratio of radii of the inner and outer cylinders is duscussed.     

Computation of the inertia-dominated forces on horizontal circular cylinders placed in oblique waves and near to a plane bed

Wave-force coefficients of horizontal circular cylinders inclined with respect to the incoming waves, are studied numerically under conditions when the effects of flow separation are insignificant. The mathematical model is set in terms of a boundary-value problem for the velocity potential of the wave, which is formulated under the assumption of the linear diffraction theory, and solved numerically by the boundary element method. The numerical calculations are performed in the vertical plane, assuming uniform water depths in the direction along the axis of the cylinder. A first-order correction to the pressures is introduced to take account of the asymmetry of the velocity field around the cylinder when it is close to the plane bed. The correction procedure is found to be highly effective in computing the transverse forces for small gap ratios. The numerical results show that irrespective of the values of the gap ratio, the in-line forces are always sensitive to the wave directionality. The transverse forces, however, show sensitivity only for the smaller gap ratios. It is also shown that by accounting for the wave directionality effects in the wave kinematics only, the forces could be estimated to a certain extent by using the hydrodynamic force coefficients of inertia and lift corresponding to the normal waves.     

Numerical Analyses of Caisson Breakwaters on Soft Foundations Under Wave Cyclic Loading

A caisson breakwater is built on soft foundations after replacing the upper soft layer with sand. This paper presents a dynamic finite element method to investigate the strength degradation and associated pore pressure development of the intercalated soft layer under wave cyclic loading. By combining the undrained shear strength with the empirical formula of overconsolidation clay produced by unloading and the development model of pore pressure, the dynamic degradation law that describes the undrained shear strength as a function of cycle number and stress level is derived. Based on the proposed dynamic degradation law and M-C yield criterion, a dynamic finite element method is numerically implemented to predict changes in undrained shear strength of the intercalated soft layer by using the general-purpose FEM software ABAQUS, and the accuracy of the method is verified. The effects of cycle number and amplitude of the wave force on the degradation of the undrained shear strength of the intercalated soft layer and the associated excess pore pressure response are investigated by analyzing an overall distribution and three typical sections underneath the breakwater. By comparing the undrained shear strength distributions obtained by the static method and the quasi-static method with the undrained shear strength distributions obtained by the dynamic finite element method in the three typical sections, the superiority of the dynamic finite element method in predicting changes in undrained shear strength is demonstrated.     

南中国海神狐海域天然气水合物上覆地层不排水抗剪强度预测

浅层沉积物不排水抗剪强度（Su）是深水作业的关键参数之一。为了获取南海神狐海域首次海域天然气水合物试采区W18-19框体的基本工程地质特征,试采工程准备阶段开展了原位孔压静力触探测试（CPTU）及大量的室内实验。本文将主要基于CPTU计算不排水抗剪强度的基本模型,采用微型十字板、电动十字板、袖珍贯入仪及不固结不排水三轴实验,确定该区域不排水抗剪强度的基本模式,并提出适用于南海神狐钙质黏土层的不排水抗剪强度纵向分布规律计算模型,对该区域水合物上覆层的不排水抗剪强度进行预测。 结果表明,基于总锥端阻力、有效锥端阻力、超孔隙压力的模型系数分为13.8、4.2、14.4。综合考虑地层压实效应和含气情况,本文提出的分段函数预测模型与室内结果的一致性较好,可用于工程设计阶段进行工区不排水抗剪强度纵向分布规律的预测。另外,基于有效锥端阻力的不排水抗剪强度经验模型适应于浅层极软-较硬压实的钙质粘土层,基于超孔隙压力的不排水抗剪强度模型适用于较硬-坚硬的不含气层,而基于总锥端阻力的不排水抗剪强度计算模型则适用于坚硬含气的钙质黏土层。本文提出的分段函数模型有效的提高了经验模型在南海神狐水合物赋存区的适用性,计算结果可为工程安全评价提供支撑。     

In-line force on a cylinder translating in oscillatory flow

Experiments were conducted with smooth and sand-roughened cylinders moving with constant velocity in a sinusoidally oscillating flow to determine the drag and inertia coefficients and to examine the effect of wake biasing on the modified Morison equation. The various flow parameters such as the relative cylinder velocity. Reynolds number, and the Keulegan-Carpenter number were varied systematically and the in-line force measured simultaneously. The principal results, equally valid for both smooth and rough cylinders, are as follows: the drag coefficient decreases with increasing relative current for a given Reynolds number and Keulegan-Carpenter number; the effect of wake biasing on the drag and inertia coefficients is most pronounced in the drag-inertia dominated regime; and the two-term Morison equation with force coefficients obtained under no-current conditions is not applicable to the prediction of wave and current induced loads on circular cylinders.