Hysteretic damping model for laterally loaded piles

Fatigue assessment is a critical design aspect for many offshore structures. Soil-foundation interaction has a direct impact on the system dynamic response of these structures. While the stiffness of the soil-foundation interaction influences the system's natural frequency, the damping influences the amplification of the structural response to environmental excitations. This paper presents a simplified model for estimating the soil damping due to nonlinear soil response for pile foundations, which have wide applications in the offshore industry, such as for supporting jacket platforms, wind turbines and wellhead facilities. The proposed model is fundamentally linked to the damping response of the soil measured at element level therefore it offers design engineers an efficient and accurate way to estimate soil-pile interaction damping based on site-specific soil data. Approaches to include the suggested model for structural analysis are also proposed.     

桩-土-承台相互作用的有限元简化模型

针对低桩承台结构计算中往往只考虑桩土作用,忽视承台与土相互作用的问题,通过工程实例,建立考虑桩-土-承台相互作用的低桩承台有限元简化模型,分析桩间土的承载作用对承台和桩内力的影响。结果表明:在简化模型中考虑桩间土的承载作用后,承台弯矩和桩基轴力可减少35%～40%;桩身弯矩和剪力主要受水平力和土体m值影响;桩基轴力随地基土基床系数的增大而逐渐减小,但减幅逐渐趋缓。     

Equivalent linear pseudostatic and dynamic modelling of vertically vibrating monopile

To optimize offshore wind turbine (OWT) design, an engineering tool has been developed allowing for a detailed investigation of the effects of nonlinear soil stiffness and damping on foundation dynamics. We have studied the response of a vertically oscillating offshore wind monopile foundation in a realistic soil profile subjected to loads between 1 and 200 MN in the frequency range 0–10 Hz with pseudo-static and equivalent linear dynamic model. The non-linear soil behaviour is modelled with an equivalent linear method with shear modulus reduction and damping curves as input. The tool is verified and validated by comparison with elasto-dynamic model and experiments. With increasing load amplitudes foundation stiffness increases and damping decreases. For large load amplitudes the lower part of the pile foundation contributes more to foundation damping. The results indicate the nonlinear foundation stiffness and damping can be modelled rationally by combining stiffness and hysteretic damping from nonlinear static tools with apparent mass and radiation damping from elasto-dynamic analysis. The tool can be used to compute soil springs and dampers based on laboratory-based soil stiffness and damping.     

桩土相互作用阻尼系数试验结果与其他结果的对比

当前如何考虑桩土之间的相互作用并将其定量化是限制基桩缺陷定量分析方法准确性的重要因素。低应变条件下将土对桩的作用以粘滞阻尼器考虑,通过桩土相互作用试验测定桩顶速度响应并结合理论分析结果确定桩侧土在不同状态下的桩土相互作用阻尼系数。在现有的一些研究中也有一些其他确定阻尼系数的方法,例如经过动力平衡分析得到桩侧土单位长度阻尼系数的理论表达式,实际测定表达式中各个参数即可确定相应阻尼系数;也有通过多次动静对比试验得到的阻尼系数经验值。由于各个阻尼系数定义并不相同,参考试验时的实际情况确定各个参数,进而将不同定义的阻尼系数转化为同一量纲,分析了不同阻尼系数的差距,发现通过多次动静对比试验得到的Case阻尼系数由于是在大应变情况下得到的,相对桩土相互作用试验得到的阻尼系数有较大差距,应用于低应变分析并不合适。而理论推导得到的阻尼系数相对试验结果虽然并不一致,但是他们之间存在一定的相关性,进而经过拟合分析发现两者之间的比值可以表示为剪切波速的函数。     

A simplified method to efficiently design steel fenders subjected to vessel head-on collisions

Steel fenders have been widely used to protect bridges from vessel collisions because of their relatively large plastic deformability and energy dissipation capacity. In the design of a steel fender, detailed finite element (FE) models are usually employed. However, detailed FE analysis involves complicated modeling and substantial computation time. This method is often not applicable, particularly during preliminary design iterations. For this reason, a simplified analytical method was developed in this paper with the aim to efficiently design steel fenders under vessel collisions. For primary individual members of steel fenders, the deformation mechanisms and models as well as participations during various collision scenarios were discussed in detail. By combining the contributions of primary members, a general analytical procedure was presented to rapidly estimate the force-deformation relationship of steel fenders under various bow impacts. For the fixed and floating steel fenders, several collision scenarios were simulated by FE models to verify the accuracy of the developed analytical method. The crushing resistances and energy dissipation capacities estimated by the developed analytical method were in good agreement with those obtained from the FE simulations. Based on the analytical method, an energy-based design approach was proposed for the efficient design of steel fenders. The developed design approach was demonstrated to be capable of predicting the crush depth and peak impact force of a steel fender with good accuracy.     

Dynamics of an ultra-deepwater mooring line with embedded chain segment

A code is developed to study the mooring tensions on a line with an embedded segment considered, based on lumped mass method. The accuracy of this code is validated by published results. The influence of soil-chain interaction on the static and dynamic behaviour of a 1500 m mooring line is studied under two operational situations: shallow embedded taut mooring line and deep embedded semi-taut mooring line. The shallow case has an embedded depth setting as 10 m under seafloor, while the embedded depth is 20 m for deep water. To study the influence of soil on mooring dynamics, three simplified cases without soil force considered are investigated and the results are compared with the dynamics of embedded mooring. These three cases include: i) Case MA has the same spread distance to embedded mooring anchored on seafloor; ii) Case MB is anchored on seafloor and it has the same pretension with embedded mooring; iii) Case MC is anchored to the same point to the embedded mooring but the soil force is not considered. Furthermore, the effects of effective width parameters of tangential and bearing soil resistance on mooring dynamics are also discussed. In this work, three different oscillations are forced on fairlead to study the mooring dynamics, which are low frequency oscillation, hybrid oscillation (low frequency and wave frequency) and wave frequency oscillation.     

Estimation of natural frequencies and damping using dynamic field data from an offshore wind turbine

The dynamic characteristics of offshore wind turbines are heavily affected by environmental loads from wave and wind action and nonlinear soil behaviour. In the design of the monopile structures, the fatigue load due to wind and wave loading is one of the most important problems to consider. Since the fatigue damage is sensitive to the foundation stiffness and damping, increasing the accuracy of analysis tools used in the design and optimization process can improve the reliability of the structure and reduce conservatism, thereby leading to a more cost-efficient design. In this context, analysis of field data is important for calibrating and verifying purposes. This paper presents analysis of measured accelerations and strains from a wind farm in the North Sea with monopile foundations. Field data during idling conditions, collected over long periods of operation, are analysed and the natural frequencies are determined, and damping is estimated. The measured natural frequencies are compared to calculated values using an aero-servo-hydro-elastic code, showing a good agreement in the frequency range below 2 Hz. Variation of the natural frequencies with intensity of loading may indicate effect of soil nonlinearity on the overall OWT response. Since the first natural bending modes have the largest potential to mobilize soil reactions, they are of primary interest in this context. The effect of load (wave, wind and dynamic bending moment) on the first natural frequency is investigated using different analysis techniques in the frequency domain and time domain. A clear correlation between load level and first natural frequency is demonstrated. A simple nonlinear SSI model of the tower/soil system is employed to numerically investigate the observed changes in the measured first natural frequency with the level of loading and increased overall damping. The simulated results reproduce the general trends in the observed reduction in the first natural frequency and increased damping ratio with the load level. However, the effect of the load level is less than that observed in the measurements, indicating contribution also from other factors than soil nonlinearity.     

高桩梁板式码头结构横梁内力影响分析

重点研究了不同荷载类型情况下不同地基条件、不同截面尺寸以及不同简化模型（横向排架系统和弹性支承连续梁）对横梁内力的影响及其规律。研究结果表明：较差的地基条件会使横梁出现较大的负弯矩;增大横梁尺寸也会使横梁弯矩增大;对于大桩帽排架,不同简化模型对横梁内力结果影响较大。     

Time domain approach for coupled cross-flow and in-line VIV induced fatigue damage of steel catenary riser at touchdown zone

Existing VIV prediction approaches for steel catenary riser (SCR) typically employ truncation model without considering the interaction between the SCR and soil, and only allow for cross-flow (CF) VIV. In this study, a time domain approach accounting for the SCR-soil interaction is proposed to predict the CF and in-line (IL) VIV induced fatigue damage of a SCR at touchdown zone (TDZ). The hydrodynamic force resulting from the vortex shedding is modeled using the forced oscillation test data of a rigid cylinder and an empirical damping model, which are defined as functions of the non-dimensional dominant frequency and amplitude of the SCR response. Due to the coupling effect, the IL VIV force is magnified based on the CF VIV amplitude. By combining a linear hysteretic interaction model with a trench shape model, some particular phenomena during the vertical SCR-soil interaction are captured and qualitatively discussed, while for the horizontal direction, the seabed is simplified as nonlinear spring model. Based on these models, parametric studies are conducted to broaden the understanding of the sensitivity of VIV induced fatigue damage to the seabed characteristic. The results indicate trench depth, vertical and lateral stiffness, and clay suction are significantly affect the VIV induced maximum fatigue damage at TDZ.     

考虑基础柔性的隔振系统功率流特性分析

根据舰船机械设备安装特性及隔振要求,建立包含机械设备、隔振器和柔性基础的数学模型并对其求解,得到隔振系统在简谐激励下的响应及传递功率流计算公式,讨论了隔振系统中设备质量、隔振器刚度和阻尼、柔性基础刚度和阻尼等参数对隔振能力的影响。理论表明,适当增大机械设备质量、隔振器阻尼及柔性基础阻尼能提高系统隔振能力,较大的隔振器刚度不利于隔振,而基础板柔性对隔振系统的影响与激励频率有关,并给出了柔性基础隔振设计中参数选取的一般规律。     

Influence of different topological variants on optimized structural scantlings of passenger ship

For a multi-deck ships with extensive superstructures (such as passenger and cruise ships, RoPax, mega yachts, etc.) the global structural response can be particularly complex. The influence of the superstructure to the primary strength for those multi-deck ships must be considered from an early design phase. Main global topological parameters (e.g. size of side openings, position and stiffness of longitudinal and transverse bulkheads, etc.) have dominant influence on the shape of hull girder stress distributions over the ship height. The Taguchi concepts and techniques (FFE, orthogonal arrays, ANOVA, etc.) could be used to systematically study influence of multiple topological parameters on the global structural response obtained by FEM analysis. It also enables rational identification of the most dominant parameters and provide designer with the near-optimal level of each topological parameter for the defined design objective. It has been demonstrated how different topological variants can lead to different optimal structural scantlings w. r.t chosen design objectives (mass, VCG, etc.), using simplified full ship 3D FE model of passenger ship as an example. Structural design software MAESTRO and in-house developed framework for the design support system DeMak – OCTOPUS Designer were used as a structural optimization tool. This paper aim to extend the standard scantling optimization by introducing topological aspects as a first STEP in overall optimization procedure.     

Time-domain coupled dynamic simulation for SFT-mooring-train interaction in waves and earthquakes

In this study, Submerged Floating Tunnel (SFT)-mooring-train coupled dynamics is solved in the time domain to investigate their dynamic and hydro-elastic interactions under wave and earthquake excitations. The SFT is modeled by the rod-FE (finite element) theory, and it is connected to mooring lines through dummy-connection-mass and linear and rotational springs. A 3D rigid-multi-body dynamic model is developed for train dynamics that consists of seven rigid bodies. The tunnel-train interaction is taken into consideration based on the wheel-rail correspondence assumption and the simplified Kalker linear creep theory. The developed computer simulation program is validated through comparisons with commercial programs and published results when possible. In the case of earthquake-induced dynamics of the coupled system, the effects of soil conditions, tunnel length, mooring interval, seismic-wave propagation, and seaquake are investigated. The magnitudes of the SFT downward motions induced by the moving train are small compared with the motions induced by earthquakes. The earthquake causes transient SFT responses especially at their lowest wet natural frequencies while high-frequency motions are induced by seaquake effect. Structural damping and seismic propagation play an important role in dynamic responses. The interaction of the tunnel and moving train is also evaluated for various train speeds in terms of the derailment and offload factors and riding-comfort criterion. For the given SFT and train designs, the offload factor and riding-comfort criterion can slightly exceed their limits at certain earthquake conditions with the speed as high as 70 m/s, which can be adjusted by reducing train speed.     

海洋平台井口管道布置与应力分析

从工程设计角度,通过井口管道布置与应力分析设计实例,分析井口管道布置的特殊性,并阐述影响井口管道布置设计合理性的关键因素.     

A multi-spring model for monopile analysis in soft clays

The offshore wind industry in China has seen a rapid development in recent years and is projected to account for half of global yearly installed capacity in the years to come. Monopiles are a popular foundation solution for supporting offshore wind turbines. However, due to challenging seabed soil conditions, which often feature thick normally consolidated soft clays and harsh environmental loading (i.e. frequent occurrence of typhoons), extremely long monopiles are often designed. The large monopiles are costly to fabricate and install and sometimes kills the viability of the concept in cases where the bedrock is relatively shallow and expensive piling in rock is otherwise required. However, the state-of-practice for designing these monopiles in clays is typically by using the API p-y springs, which are widely known to underestimate soil-pile interaction stiffness and capacity for large diameter monopiles. Improvement to the design method can therefore have significant economic implications to the industry. The paper presents an effort toward this direction. A multi-spring beam-column model suitable for monopile design in soil conditions in China is proposed. The model features three soil spring components, namely the lateral p-y spring, the pile tip base shear s-y spring and rotational m-θ springs along the pile shaft. The validity of the model is verified by a comprehensive suite finite element parametric analyses. Guidance for incorporating the cyclic loading effect into design is also provided. The model proposed in this paper has large potentials for application in design practice.     

Nonlinear dynamics of a submerged floating moored structure by incremental harmonic balance method with FFT

A submerged floating moored structure has a great potential in ocean engineering applications. The nonlinear dynamics of a submerged floating moored structure subjected to vertical excitation with possible slackness in the mooing system are investigated by incremental harmonic balance (IHB) method. Heaviside step function is introduced to describe the nonlinearity in axial stiffness arising from loss of mooring tension. The dimensionless governing equation is derived, and three parameters, frequency ratio η, damping ratio ζ and dimensionless net buoyancy W, are found to be independent. Due to the fact that the restoring force term is function of the unknown displacement and could barely be expressed in an explicit form of time, a fast Fourier transformation (FFT) is implemented in IHB method to simplify the Galerkin average procedure. Both stable and unstable solutions and both period-1 and bifurcated solutions are obtained by IHB method. The stability of the periodic solutions is investigated by Floquet theory. Parameter study is carried out. Results indicate that the system nonlinearity becomes stronger as dimensionless the net buoyancy W and damping ratio ζ decrease. A path to chaotic motions though a series of period doubling bifurcations is found. Multiple solutions are observed, and the domains of attraction are investigated by interpolated cell mapping (ICM) technique.     

Numerical simulation of the flow about self-propelling tanker models

A time-marching CFD simulation is performed for self-propelling ships. The flow about the hull is simulated by the finite-volume method, and the propeller action is approximated as a propeller disk for which the solution is given by a simplified propeller model. The interaction of two flow models is treated in a time-marching procedure converging towards the steady self-propelling condition. This method is applied to five tanker models, and detailed comparisons are made between the simulated results and corresponding experimental results. It is shown that the flow field in the self-propelling condition is qualitatively well reproduced in the simulation, and the estimated thrust deduction factors for the five hull forms agree well with measured ones. However, the effective wake factors are underestimated, since the Reynolds number in the simulations differs from that in the experiment.     

船舶横摇阻尼的CFD数值模拟研究

船舶横摇阻尼是影响参数横摇和瘫船稳性等大幅横摇运动的关键参数.文中基于非定常RANS方程在静水中对模型2792进行了自由横摇衰减的数值模拟,该模型是船舶第二代完整稳性衡准制定中瘫船稳性研究的国际标准船模,数值模拟中采用了两种网格类型,一种是滑移网格,另一种重叠网格.计算结果表明,数值模拟的自由横摇衰减曲线和模型试验结果吻合良好,另外CFD计算的横摇阻尼与试验值的误差小于Ikeda's经验公式计算的误差,证明非定常RANS方程可用于预报横摇阻尼.     

Fatigue analysis of water intake risers: Hydrodynamic damping effect and a hybrid frequency-time domain method

The fatigue performance is key to the design of water intake risers (WIRs), which is a novel concept used to convey cooling water for liquefaction of natural gas at sea. To estimate the fatigue life, it is crucial to accurately predict the response amplitude of the WIRs, which is dominated by hydrodynamic damping. In operational conditions, the motion amplitudes of WIRs are usually smaller than their diameter, and thus leading to a flow regime of KC < 5. It is found in this flow regime; the hydrodynamic damping largely depends on the motion magnitude of the risers. To consider this coupling effect, a hybrid frequency-time domain fatigue analysis method is proposed, where a nonlinear stress transfer function is adopted. The hybrid method accounts for the coupling effect between the hydrodynamic damping and the structural motion. Significantly reducing the computational cost, this method provides results as accurate as that from a time domain analysis based on the relative velocity model with a constant drag coefficient. Furthermore, recommendations for further simplification of the fatigue analysis recognizing the coupling effect are given.     

Foundation damping for monopile supported offshore wind turbines: A review

Today, an important challenge for offshore wind energy is to design efficient and reliable offshore wind turbines (OWTs). The overall damping of OWTs plays an important role in the design process as it limits the amplitude of the OWT dynamic response at frequencies near resonance. Therefore, an accurate estimation of OWTs damping is necessary for the efficient design of these systems. The foundation damping is one of the main sources overall turbine damping and is the least well understood. This paper presents a critical review of recently published studies on foundation damping for OWTs on monopiles and explains how soil damping contributes to the total damping of OWTs. It also reviews the main methods that have been used for the estimation of foundation damping in numerical and experimental studies. In addition, the importance of damping to the OWTs fatigue life is discussed. Finally, a discussion is provided on the challenges to be overcome and recommendations for the accurate estimation of foundation damping.     

Mechanical model and characteristics of deep-water drilling riser-wellhead system under internal solitary waves

Internal solitary waves with a huge amount of energy easily trigger the large dynamic responses of riser-wellhead system and threaten its structural safety. However, previous studies have only focused on the dynamic response of the riser under internal solitary waves. The riser may experience excessive traction from the platform, especially from the mooring platform, in response to the arrival of internal solitary waves. The bottom of the riser connects to the wellhead system, which in turn exerts a reaction force on the riser. To address this problem, a coupled dynamic model of deep-water drilling mooring platform-riser-wellhead system under internal solitary waves is developed in this paper. A dynamic response analysis method based on the fourth-order Runge-Kutta method and finite element method is also proposed for the mooring platform-riser-wellhead system. A dynamical solver for the coupled system is then developed using MATLAB. The dynamic response characteristics of the riser-wellhead system under internal solitary waves are calculated. Results show that the displacement and bending moment of the system initially increases and then decreases along with the propagation of internal solitary waves, and finally reach equilibrium position. The displacement and bending moment reach their peak before the trough of internal solitary waves passes through the riser-wellhead system. The dynamic responses of the riser-wellhead system under the influence of internal solitary wave loads are much larger than those without the effect of internal solitary wave loads. The riser system experiences shearing loads at the interface of internal solitary waves, which trigger a step-like bending moment variation. The bending moment of the conductor under the mudline is greatly increased by the internal solitary waves.