Heave Displacement Research Articles

Modeling and Simulation of Buoy Heave Response Under Electric Generator Load Using Simulink

According to the different links of energy transmission, the oscillating buoy wave energy converter is divided into mechanical mode and hydraulic mode. For the oscillating buoy wave energy converter with mechanical transmission, it’s requisite to consider the influence of electric generator and different transmission ratio on the heave response of buoy in its design process. Consequently, the Simulink toolbox is used to establish the simulation model of the buoy heave response under the electric generator load, and the heave response of the buoys with different diameters under the electric generator and transmission ratio is analysed. The results show that as the buoy diameter increases linearly, the heave displacement, heave velocity and generating power curve amplitude do not increase linearly which shows that the increment of amplitude becomes smaller. Therefore, buoys with different diameters have different load capacity.

Study on stability of cable-anchored underwater platform by parametric excitation

Aiming at the stability of the heaving–pitching coupling motion of the cable-anchored underwater platform in the nonlinear flow field, considering the change of its initial equilibrium position under the flow field, a coupled heaving–pitching motion equation is established; the transition curve of stability at frequency ratios of 0, 0.5, and 1 was obtained by using the virtual mass method and deformation parameter method. According to the Floquet theory, the stability characteristics under weak parameter excitation are studied. The stability and instability regions were identified and verified by time history response. The results show that the range of the stability region can be changed by adjusting the damping of the system. With the increase of damping, the range of stability gradually increases. Therefore, it is possible to take measures such as adding the helical damping side plate, changing the cross-sectional shape of the platform floating body, and increasing the cross-sectional diameter to suppress the heaving displacement and pitching range of the cable-anchored underwater platform.

Effects of free heave motion on wave resonance inside a narrow gap between two boxes under wave actions

Fluid resonance inside a narrow gap between two side-by-side boxes is investigated based on an open-source CFD package, OpenFOAM. An upstream box heaves freely under wave actions and a downstream box remains fixed. The focus of this work is to study the influence of the motion of the upstream box on the hydrodynamic behavior of the resonant fluid inside the gap. The hydrodynamic behavior considered in this study includes the wave height inside the gap, heave displacement and their harmonic components, and reflection, transmission and energy loss coefficients. For comparison, the configuration in which the two boxes are fixed is considered. It was found that the heave motion of the upstream box increases the fluid resonant frequency and significantly reduces the resonant wave height in the gap. The frequencies at which the maximum and minimum heave displacements of the upstream box are observed to obviously deviate from the fluid resonant frequency. For the wave height in the gap and heave displacement, the effects of the incident wave height on their harmonic components are different. The heave motion of the upstream box results in a larger reflection coefficient and smaller energy loss coefficient.

Helicopter Pilots Synchronize Their Altitude with Ship Heave to Minimize Energy When Landing on a Ship’s Deck

ABSTRACT Objective: This study aims at investigating helicopter pilots’ strategies to achieve ship deck landing. Background: Helicopter maritime operations are challenging, especially when it comes to landing on the moving decks of small ships, such as frigates, which can lead to dramatic accidents. Method: Expert pilots were requested to fly the full ship landing maneuver from approach to touchdown in an immersive simulator. Two sea states (3 and 4 on the Douglas Sea scale) and their resulting deck movements were used. Changes in helicopter altitude were correlated with deck heave movements throughout the maneuvers in order to scrutinize the helicopter-deck coupling. The energy at impact was measured. Results: The dynamics of helicopter-deck coupling evolved through two phases during the maneuver: Initially, no coupling then, coupling in phase between the helicopter vertical displacements and deck heave displacements. Moreover, the coupling reached higher values within the last 15 m to landing, corresponding to a hover phase and touchdown, and the correlation increased with sea level. This coupling might help in improving pilots’ safety since the greater the coupling at touchdown, the lesser the kinetic energy at impact. Conclusion: Coupling the helicopter vertical displacements with ship heave movements seems to be an efficient strategy to minimize energy at impact. Questions arise on both the rationale and the perceptual invariant behind such behavior and indicate the necessity of further investigation.

Analytical Solution of Three-Dimensional Heaving Displacement of Ground Surface during Tunnel Freezing Construction Based on Stochastic Medium Theory

Many studies indicate that the heaving displacement during tunnel freezing construction can be regarded as a plane strain problem. However, due to the fact that many of the frozen pipes are placed obliquely in practical engineering, it should be a three-dimensional problem. Therefore, considering stochastic medium theory, the analytical solution of three-dimensional heaving displacement of ground surface during tunnel freezing construction is established, and the analytical solution is applied to the project case in Beijing. The calculation results show that, considering the inclination angle between the freezing pipe and the center axis of the tunnel, the maximum heaving displacement of the ground surface occurs at the tunnel center. When the inclination angle is equal to 0°, the analytical solution of three-dimensional ground surface heaving displacement is in good agreement with that of the two-dimensional prediction model, which further verified the reliability of the established analytical solution of the three-dimensional frost heave prediction model.

CFD approach to heave damping of spar with heave plates with experimental validation

Spar, tension leg platform, and semi-submersibles use heave plates to reduce heave response by increasing heave damping and added mass. Conventional practice is to use a linear damping ratio, which is typically obtained from free heave decay tests or Computational Fluid Dynamics (CFD) simulations. However, with the addition of heave plates, the system damping becomes nonlinear. Understanding such nonlinear damping behavior of spar with circular heave plates in various configurations could be useful in the design of heave compensation devices. Experimental and numerical investigation on heave damping and added mass of a scaled model of spar with a variety of heave plate configurations have been carried out using free heave decay for a range of initial heave displacements. Applicability of the linear and quadratic damping models have been assessed for all configurations. The effects of parameters such as heave plate diameter, location of heave plate above the keel, and spacing between two plates on damping and added mass have also been studied. Flow fields obtained from numerical simulations are presented, and their implication on damping discussed.

Research on the swelling mechanism of high-speed railway subgrade and the induced railway heave of ballastless tracks

The ballastless track has been a widely-used track form in high-speed railway (HSR), however, its application is seriously hampered by the railway heave, which is mainly caused by subgrade swelling. In order to identify the mechanism of HSR subgrade swelling and the rules of swelling-induced railway heave response, long-term longitudinal-continuous deformation monitoring and layered deformation monitoring over a heaving-affected site have been carried out. Furthermore, a coarse-grained soil oedometer was applied to explore the correlations between swelling pressure and swelling ratio of the subgrade filler and mudstone foundation to the on-site water content. With the aid of FLAC3D-PFC3D coupled numerical simulation, the influence of different swelling ratios for subgrade filler and mudstone foundation on the railway heave response of a double-block ballastless track under was analyzed. According to the field monitoring results, swelling deformation occurred in both the filler layer and subgrade layer of the heave section, and this combined action within the two layers resulted in railway heave displacement. Laboratory tests indicated that the swelling ratios of the subgrade filler and mudstone foundation under in-situ water content reached 0.205% and 3.325%, respectively. The swelling pressure and swelling ratio in the subgrade filler and mudstone foundation both followed a logistic function relationship with the water content. Numerical results showed that the railway heave amount followed Expassoc and Nelder distribution relationships with the swelling ratios of the subgrade filler and mudstone foundation, respectively. The research results could provide some reference value for the study on the swelling potential of expansive soils and the prediction of railway deformation in railway engineering.

Efficiency and survivability analysis of a point-absorber wave energy converter using DualSPHysics

Abstract Smoothed Particle Hydrodynamics (SPH) method is used here to simulate a heaving point-absorber with a Power Take-Off system (PTO). The SPH-based code DualSPHysics is first validated with experimental data of regular waves interacting with the point-absorber. Comparison between the numerical and experimental heave displacement and velocity of the device show a good agreement for a given regular wave condition and different configurations of the PTO system. The validated numerical tool is then employed to investigate the efficiency of the proposed system. The efficiency, which is defined here as the ratio between the power absorbed by the point-absorber and its theoretical maximum, is obtained for different wave conditions and several arrangements of the PTO. Finally, the effects of highly energetic sea states on the buoy are examined through alternative configurations of the initial system. A survivability study is performed by computing the horizontal and vertical forces exerted by focused waves on the wave energy converter (WEC). The yield criterion is used to determine that submerging the heaving buoy at a certain depth is the most effective strategy to reduce the loads acting on the WEC and its structure, while keeping the WEC floating at still water level is the worst-case scenario.

Analysis of internal force and displacement of foundation pit pile anchor supporting structure based on soil frost heaving

In order to study the influence of soil frost heaving on the internal force and displacement of foundation pit supporting structure in seasonal frozen soil area in Northwest China, the field test of pile anchor supporting structure for deep foundation pit is carried out to monitor the change of internal force and displacement of supporting pile in winter. The interaction relationship between soil frost heaving and internal force and displacement of supporting pile is analyzed combined with temperature change conditions. The results show that: Under the condition of natural frost heaving in winter, the frost heaving effect is the most significant at 0.5 m of the upper part of the supporting pile, and the reinforcement stress value on both sides of the pile body is the largest. The change rate of bending moment of supporting pile above 3.25m is higher than that of the embedded section and the maximum bending moment is at 0.5m, while the blot has a certain constraint on the bending moment deformation. The displacement of supporting pile increases in proportion to the freezing time, and the final increase is 157.7% of the initial value. It can be seen that soil frost heaving has great influence on the internal force and deformation of the upper structure of the retaining pile. The research results can provide reference for the construction of foundation pit support engineering in similar areas in winter.

Analytical solution of frost heaving force and stress distribution in cold region tunnels under non-axisymmetric stress and transversely isotropic frost heave of surrounding rock

Accurate evaluation of the frost heaving force and stress distribution plays an essential role in frost damage prevention design of cold region tunnels. To ensure the safe operation of tunnels in cold regions and develop new practical method for their design, an analytical solution of frost heaving force and stress distribution in cold region tunnels under non-axisymmetric stress and transversely isotropic frost heave of surrounding rock is established. The solution is of urgent demand because the tunnel sites with significant difference between horizontal and vertical initial ground stresses are frequently encountered. In analysis, the mechanical process is considered as two steps based on the linear superposition principle of elasticity theory. In step 1, the frozen zone freezes and expands without constraint first, and in step 2 the frost heaving displacement of the frozen zone is then inhibited by lining and unfrozen surrounding rock to reach a final balance state. The stress and displacement distributions of the above two steps are derived first, and then the solution of frost heaving force and stress is determined by boundary conditions. The analytical solution is verified with the existing solution under the axisymmetric stress condition. Furthermore, the stress distribution and the increment of stress in lining and surrounding rock induced by frost heave are analyzed. Finally, the influence of the related factors on stress distribution is analyzed. Results show that the increment of the stress in lining and surrounding rock significantly vary with the lateral pressure coefficient and the anisotropic frost heave coefficient, which demonstrates that the non-axisymmetric stress and the transversely isotropic frost heave of surrounding rock have considerable impact on the stress distribution and should be considered.

Full Scale Modeling of Footing Supported on Expansive Soil using Concrete Pile Anchor Foundation (CPAF).

Buildings constructions over expansive soils are exposed to many problems and cracks. The most damaging issues occur due to differential heave displacements, which cause excessive deformations to the overlying structure up to and beyond its serviceability limit state and, in the worst cases, its ultimate limit state. A site investigation is performed for the study area at Tabuk University, Kingdom of Saudi Arabia. The geotechnical soil properties and swelling characteristics were determined. Visual observations of samples obtained from drilled boreholes at study area revealed reddish brown to grey thinly laminated weathered shale followed by shale formation, the subsurface formation is classified (CH) according to USCS. The research study is aimed at measuring the contact pressure at field and studying the efficiency of concrete pile anchor foundation (CPAF) system in reducing heave of footings constructed on expansive soil. In the field, two full scales reinforced concrete footings with and without concrete anchor piles were constructed on top of the expansive shale. After construction of field prototypes, the test area is wetted for 64 days. Monitoring of the footing movement indicated that the footing upward movement using CPAF system caused a 62% less than the footing constructed directly on expansive shale.

ANALYTICAL SOLUTION OF FROST HEAVING FORCE IN NON-CIRCULAR COLD REGION TUNNELS

A complex variable method is presented of stress and displacement problems for non-circular cold region tunnels. The complex variable method considers the non-circle tunnel support, the frost heaving circle and the unfrozen surrounding rock at the same time, making the problem from the single connected domain to multi connected domain problem, and can not directly apply the classical complex function theory to solve the problem of the stress and displacement of the non-circular tunnel. The analytical formula in Zeta plane orthogonal curvilinear coordinate system of non-circular tunnel lining to frozen surrounding rock to unfrozen surrounding rock system is derived by using classical complex variable method and continuity condition with power series and conformal transformation. Then, the frost heaving force and frost heaving deformation of the non-circular cold region tunnel are obtained by conformal transformation. This complex variable method is applied to Zhegushan tunnel research, and the analytical solution of Zhegushan tunnel openning frost heave stress and frost heave displacement is obtained. Comparing the analytical solution with the numerical solution to verify the correctness of the analytical solution. It can be seen from the results that frost heaving force has an obvious influence on the lining, and the additional circumferential stresses caused by frost heaving at the vault, arch foot and arch bottom are significantly increased. The additional normal stresses caused by frost heaving at the vault and both sides of arch shoulder are significantly increased. Because of the geometric configurations of lining, the frost heaving deformation is uneven, which leads to uneven distribution of frost heaving forces. Compared with previous studies, which consider the frost heaving ring as a single ring, the complex variable method is more practical. And the research results were expected to provide a referenced basis for elasto-plastic analysis of cold-region tunnel.

Factor’s Influence Analysis of Frost Heave during the Twin‐Tunnel Construction Using Artificial Horizontal Ground Freezing Method

In order to analyze the influence of different twin‐tunnel parameters on the frost heave of the ground, six tunnel clear distances (0.25 D, 1.00 D, 1.50 D, 2.00 D, 2.50 D, and 3.00 d), three tunnel buried depths (6 m, 12 m, and 18 m), and two freezing orders (simultaneous freezing and sequential freezing) are selected to establish the two‐dimensional numerical calculation models, using ABAQUS finite‐element program and the user subroutine of frost heaving deformation, and considering the orthotropic deformation characteristics of frozen soil. Numerical simulation results show that the interaction of twin‐tunnel freezing is weakened with the increase in tunnel clear distance. Correspondingly, the heaving displacement of the ground surface also decreases. Besides, the heaving displacement curve of the ground surface gradually changes from the unimodal N‐type to bimodal M‐type as the tunnel clear distance increases. However, the trough of the bimodal M‐type curve gradually disappears as the tunnel buried depth increases. SPSS mathematical analysis results show that tunnel clear distance has the highest significance, tunnel buried depth ranks the second, and freezing order ranks the last. It is important to select the appropriate tunnel clear distance during the design of the twin‐tunnel construction using the artificial horizontal ground freezing method.

Model test and numerical simulation of frost heave during twin-tunnel construction using artificial ground-freezing technique

Based on the actual twin-tunnel freezing project of the Shanghai Metro in China, this study aims to establish a model test system that can simulate horizontal ground freezing, and the temperature distribution and frost heave ‘displacement are investigated. The model test results show that the frost heaving displacement of the soil was closely related to the closure time of the frozen wall. When the sequential freezing mode was adopted in the model test, the frost heaving displacement during the freezing period of the downlink tunnel was smaller than that during the freezing period of the uplink tunnel under the influence of water migration. Considering two different freezing modes, namely, sequential freezing and simultaneous freezing of uplink and downlink tunnels, we conducted a numerical simulation of the horizontal ground freezing of the twin tunnels. Compared with simultaneous freezing, sequential freezing can reduce frost heave displacement to a larger extent. This study can provide a reference for the design and construction of twin tunnels using artificial ground-freezing technique.

Laboratory Investigation on Hydrodynamic Performance of an Innovative Aeration Device with a Wave-Driven Heaving Buoy

Coastal seawater quality is of significance for the environment, ecology and fisheries. In recent years, the hypoxia or anoxia problems of bottom seawater aggravated due mainly to the seawater stratification and eutrophication. This paper addresses an innovative aeration device with a wave-driven heaving buoy to enhance the dissolved oxygen concentration for bottom water. A series of physical experiments was conducted to investigate its hydrodynamic performance and air flow rate. The response amplitude of heaving components and the average value of air flow rate were examined with the related parameters, including incident wave height, incident wave steepness and aeration depth. It was found that with increasing incident wave height, the average heaving displacement and the average air flow rate increase respectively. With the increase of incident wave steepness, the relative value of average heaving displacement increases obviously for high wave period scenarios, it increases slightly for small wave period scenarios in comparison and the relative value of air flow rate increases evidently. With the increase of aeration depth, the average heaving displacement and the average air flow rate decrease respectively. With the increase of relative aeration depth, the relative value of average heaving displacement and the relative value of air flow rate decrease respectively. In addition, the dimensional analysis and the least squares methods were used to obtain the prediction formulas for the average heaving displacement and the average air flow rate, and they agreed well with the related experimental data.

Laboratory Investigation of the Effect of Nano-Silica on Unconfined Compressive Strength and Frost Heaving Characteristics of Silty Clay

In order to investigate the effect of nano-silica on the unconfined compressive strength and frost heaving characteristics of silty clay, a series of indoor tests of unconfined compressive strength, frost heaving, and mercury intrusion porosimetry (MIP) was done on silty clay with different nano-silica content. The unconfined compressive strength of silty clay increased with increases in nano-silica content, and increased by 6.65 times when the nano-silica content was 5.0%. However, the frost heaving displacement decreased with increases in the nano-silica content. The results of MIP tests illustrated that the volume and number of large pores decreased, and the volume and numbers of small pores increased with increases in the nano-silica content. An increase in the nano-silica content increased the porosity and decreased the average pore diameter. The formation of viscous gel by addition of nano-silica into silty clay enhanced the bonding and filled the gaps between particles of silty clay and blocked the migration of water in the soil. The microscopic pore structure of the sample was generally uniform with increasing nano-silica content, which resulted in an increase in unconfined compressive strength and a decrease in frost heaving displacement.

Slam Loads and Kinematics of Wave-Piercing Catamarans During Bow Entry Events in Head Seas

Centre bow (CB) design for wave-piercing catamarans (WPCs) is a critical compromise between minimization of slamming and protection against deck diving. To inform the design process, this article investigates the slam loads and kinematics during bow entry events in regular head seas for a 112-m WPC with systematic variations to its CB and wet-deck geometry. Model tests using a 2.5-m hydroelastic segmented catamaran considered five different CB configurations, designated as the parent, high, low, long, and short CB. The results indicated that changes in the CB length had little effect on the general kinematic trends obtained for the pitch, heave, and bow vertical displacement at the instant of slamming, but increasing the wet-deck height resulted in an increase in heave (but not pitch) at slamming. Two new design ratios are proposed. The CB immersion depth to arch height ratio showed slamming occurring in the range of 0.3–0.6 depending on the wave encounter frequency and the CB configuration. The CB buoyancy in the encountered waves was estimated by considering both immersion depth and area along the CB in waves through relative motion analyses. It was found that the buoyancy to slam force ratio increased with increasing wet-deck height but not with increasing CB length. This suggests that an optimal CB configuration could be achieved by first modifying the arched cross-structure to reduce the arch filling effect on slamming severity and then maximizing the CB buoyancy to slam force ratio by increasing either the wet-deck height or the CB length. 1. Introduction An above-water centre bow (CB) for improving seakeeping is a feature of modern wave-piercing catamarans (WPCs) (Soars 1993; Boulton 1998; Fang & Chan 2007; Dubrovsky 2014). Figure 1 shows a 112-m Incat WPC with the CB located between the two demihulls. There are several important factors to be considered when designing such a central bow. First, the reserve buoyancy offered by the CB is the primary design factor for providing a pitchrestoring moment and eliminating deck diving in the following waves (Davis & Whelan 2007). Second, the CB configuration can influence the slamming loads in WPCs during bow entry in waves (Lavroff et al. 2013). This is due to the complex fluid-structure interaction in the CB area. When the CB enters waves, the water gradually fills the spaces between the CB and demihulls, referred to here as archways, and may result in complete closure of the archways and slamming in excessive pitch conditions. Finally, the frequency of slamming occurrence is, to some extent, related to the CB design as it contributes to lateral jet flow during the CB entry. As a result, slamming may occur in even partial water entrapment below the arch wet-deck cross-structure, which could be the case in small pitch motions (Lavroff & Davis 2015).

Hydrodynamic responses and efficiency analyses of a heaving-buoy wave energy converter with PTO damping in regular and irregular waves

Abstract Experimental investigation on the power performance of a heaving-buoy wave energy converter (WEC) with power take-off (PTO) damping was conducted under regular and irregular waves. The effects of the main influential parameters, including the incident wave height, wave frequency and PTO damping, on the maximum heave displacement, phase difference between the buoy velocity and wave elevation, and capture width ratio were quantitatively studied. For regular waves, with decreasing incident wave height or increasing PTO damping, the nonlinearity between the heave motion and surrounding wave elevation became pronounced and three modes of the buoy, i.e., linear motion, non-linear motion and non-motion, can be found. Based on analyses of the capture width ratio in both regular and irregular waves, the present WEC can obtain an optimal power efficiency at frequency ratio of ω / ω n ≈ 0.8 and PTO damping ratio of ζ p ≈ 0.5. It has been examined that H 1/10 can generally provide better approximation of the incident wave energy than H 1/3 and H AVG for irregular waves based on the linear wave theory. The statistical power performance of the WEC in irregular waves generally has the same trend as that in regular waves. The capture width ratio in irregular waves is found to be (approximately 5–40%) higher than that in regular waves for the same wave parameters, though the absolute incident and absorbed wave power in irregular waves are only half of those in regular waves. Finally, the flow structures around the heaving buoy are analyzed. The formation of vortices around the bottom corner provides flow interpretation on the viscous loss of wave energy for a heaving-buoy WEC with a flat bottom.

Finite element modelling of the mechanical behaviour of unsaturated expansive soils subjected to wetting and drying cycles with shakedown concept

A simplified model based on the shakedown theory (Zarka method) has been developed in this study for unsaturated expansive soils subjected to wetting and drying cycles. This method determines directly the stabilised limit state. The parameters of the proposed shakedown-based model are calibrated by the suction-controlled odometer tests obtained for an expansive soil compacted at loose and dense initial states, and then validated for the same soil compacted at intermediate initial state by comparing the model predictions with the experimental results. Finally, the finite element equations for the proposed shakedown model are developed and these equations are implemented in the finite element code CAST3M to carry out the full-scale calculations. The performed simulation is on a 2D geometry, made up of the expansive soil at the intermediate state subjected to successive extremely dry and wet seasons for the different applied vertical loads. The results show the swelling plastic deformations for the lower vertical stresses and the shrinkage deformations for the higher vertical stresses. Only inelastic heaving displacement can be observed in the geometry after considering the residual field.

Heave Compensation System Design for Offshore Crane based on Input-Output Linearization

A heave motion of the offshore crane system with load is affected by unpredictable external factors. Therefore the offshore crane must satisfy rigorous requirements in terms of safety and efficiency. This paper intends to reduce the heave displacement of load position which is produced by rope extension and sea wave disturbance in vertical motion. In this system, the load position is compensated by the winch actuator control. The rope is modeled as a mass-damper-spring system, and a controller is designed by the input-output linearization method. The model system and the proposed control method are evaluated on the simulation results.