Stability of Artificial Subaqueous Slopes in Sandy Soils Under Wave Loads

2015 ◽  
Author(s):  
Julian Bubel ◽  
Marc-André Pick ◽  
Jürgen Grabe
Keyword(s):  
Surface Waves ◽  
Wave Length ◽  
Ground Surface ◽  
Sandy Soils ◽  
Wave Theory ◽  
Friction Angle ◽  
Shallow Foundation ◽  
Cohesionless Soil ◽  
Linear Wave ◽  
Wave Loads

Shallow foundation structures in marine environments can rarely be placed on top of the sea floor. Weak soils usually need to be excavated to place the structure on more stable ground. Steep but stable slopes of the resulting pit meet both economic and ecologic aims as they minimise material movement and sediment disturbance. This paper focuses changes of geometry of submarine slopes in non-cohesive soils (erosion, sedimentation, breach failure, liquefaction failure) due to surface waves. After Terzaghi the angle between slope and the horizontal of the ground surface of cohesionless soil is at most equal to the critical state friction angle, as obviously true for dry soil. However, it can be observed that natural submarine slopes of sandy soils are always mildly sloped. During the construction of artificial submarine pits under offshore conditions it should be considered that the long-term slope-inclination is less than onshore due to hydrodynamic actions (e. g. flow, waves, earthquakes). Large surface waves cause excess pore water pressures within the soil body, leading to a reduction of effective stresses and in case of submarine slopes to changes of the slope geometry depending on wave length L, wave height H, water depth h and soil properties (permeability k, relative density Dr). During our preliminary work we investigated such processes based on the coupling of linear wave theory and linear quasistatic consolidation theory (e.g. [1]). With the help of numerical modelling we solved corresponding equations considering also materially nonlinear consolidation. However, deformations were always limited by used Lagrangian-FEM. Recent developments at our Institute enable the use of an Eulerian-FEM approach with an u-p-Formulation for fully saturated soil [2]. This allows larger deformations of the subaqueous slope to be numerically investigated.

Stability of Submarine Foundation Pits Under Wave Loads

2012 ◽  
Author(s):  
Julian Bubel ◽  
Jürgen Grabe
Keyword(s):  
Ground Surface ◽  
Friction Angle ◽  
Shallow Foundation ◽  
Cohesionless Soil ◽  
Wave Loads ◽  
In Situ Tests ◽  
Sea Floor ◽  
The North ◽  
The Stability ◽  
Wave Induced

Shallow foundation structures offer ecological benefits compared to pile foundations as less noise is emitted at sea floor level during construction process. On the other hand, shallow offshore foundations can rarely be placed on top of the sea floor. Weak soils usually need to be excavated to place the foundation structure on more stable ground and thus, anthropogenic submarine pits result. Steep but stable slopes of the pit meet both economic and ecologic aims as they minimise material movement and sediment disturbance. According to Terzaghi [1] the angle β between slope and the horizontal of the ground surface of cohesionless soil is at most equal to the critical state friction angle φc. However, it can be observed that natural submarine slopes of sandy soils are always much more shallow. Artificial (temporary) slopes do not appear and behave as natural submarine slopes, since the latter are already shaped by perpetual loads of waves, tide and mass movements. Physical simulations of different scales were presented at the OMAE 2011 [2] to analyse the stability of artificial submarine slopes of sandy soil in the North Sea. The laboratory tests focused on gravitational forces and impacts from the excavation processes. This paper presents additional numerical simulations of wave-induced bottom pressure on the suggested submarine foundation pits. Furthermore, in-situ tests will be performed in 2012 and 2013. Both dredging process and resulted foundation pits will be considerably surveyed.

Numerical Simulation of Flows Past Partially-Submerged Horizontal Circular Cylinders in Free Surface Waves

2013 ◽  
Author(s):  
Hans Bihs ◽  
Muk Chen Ong
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Wave Theory ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Wave Forces ◽  
Linear Wave ◽  
Numerical Wave Tank ◽  
Linear Wave Theory ◽  
Free Surface Waves

Two-dimensional (2D) numerical simulations are performed to investigate the flows past partially-submerged circular cylinders in free surface waves. The 2D simulations are carried out by solving the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations with the k-ω turbulence model. The level set method is employed to model the free-surface waves. Validation studies of a numerical wave tank have been performed by comparing the numerical results with the analytical results obtained from the linear-wave theory. Wave forces on the partially-submerged cylinders have been calculated numerically and compared with the published theoretical and experimental data under regular-wave conditions. The free-surface elevations around the cylinders have been investigated and discussed.

Calculation of Wave Forces Acting on a Cylinder With a Porous Plate Fixed Inside

2009 ◽  
Author(s):  
Weiguang Bao ◽  
Fenfang Zhao ◽  
Takeshi Kinoshita
Keyword(s):  
Body Surface ◽  
Porous Body ◽  
Porous Plate ◽  
Wave Theory ◽  
Wave Forces ◽  
Linear Wave ◽  
Normal Velocity ◽  
Wave Loads ◽  
Eigen Values ◽  
Eigen Function

To evaluate wave forces and to estimate the motion of breakwater, a circular cylinder is investigated based on the linear wave theory in the present work. The cylinder possesses a porous sidewall, an impermeable bottom and a horizontal porous plate inside that is fixed in the cylinder to work as obstruct and make wave dissipation more effectively. To simplify the problem, the Darcy’s fine-pore model is applied to the boundary condition on the porous body surface. The boundary value problem is solved by means of the eigen-function expansion approach. The fluid domain is divided into three regions and different eigen-function series are used. The so-called dispersion relation for the region inside the cylinder is quite different from a conventional one due to the existence of the porous plate. It leads to eigen values of complex number. To obtain solutions for the radiation problems, particular solution should be constructed to take account of the normal velocity appearing on the porous boundary. The wave loads are evaluated by integrating the pressure difference on two sides of the wetted body surface. The theoretical works are in good consistence with the experimental results. The Haskind relations are examined for the porous body. It is found that the damping coefficient consists of two parts. In addition to the component of conventional wave-radiating damping, exists a second component caused by the porous effects.

scholarly journals EFFECT OF WAVE-CURRENT INTERACTION ON THE WAVE PARAMETER

1982 ◽  
Vol 1 (18) ◽  
pp. 28
Author(s):  
Yu-Cheng Li ◽  
John B. Herbich
Keyword(s):  
Wave Height ◽  
Wave Length ◽  
Wave Theory ◽  
Length Change ◽  
Numerical Calculations ◽  
Wave Parameter ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Wide Range ◽  
Non Linear

The interaction of a gravity wave with a steady uniform current is described in this paper. Numerical calculations of the wave length change by different non-linear wave theories show that errors in the results computed by the linear wave theory are less than 10 percent within the range of 0.15 < d/Ls s 0.40, 0.01 < Hs/Ls < 0.07 and -0.15 < U/Cs i 0.30. Numerical calculations of wave height change employing different wave theories show that errors in the results obtained by the linear wave theory in comparison with the non-linear theories are greater when the opposing relative current and wave steepness become larger. However, within range of the following currents such errors will not be significant. These results were verified by model tests. Nomograms for the modification of wave length and wave height by the linear wave theory and Stokes1 third order theory are presented for a wide range of d/Ls, Hs/Ls and U/C. These nomograms provide the design engineer with a practical guide for estimating wave lengths and heights affected by currents.

scholarly journals Wave-induced loads on a lock gate provided with an opening through the ballast tank

2020 ◽  
Vol 6 (4) ◽  
pp. 415-425
Author(s):  
Luca Cavallaro ◽  
Claudio Iuppa ◽  
Pietro Scandura ◽  
Enrico Foti
Keyword(s):  
Mathematical Model ◽  
Wave Theory ◽  
Maximum Load ◽  
Wave Number ◽  
Linear Wave ◽  
Vertical Force ◽  
Wave Loads ◽  
Wave Load ◽  
Ballast Tank ◽  
Lock Gate

AbstractThe wave loads on a navigation lock gate provided with an opening in the ballast tank are analyzed using a mathematical model based on the linear wave theory. The analysis focuses on the influence of the wave number and the geometrical characteristics of the structure on the applied load. It is shown that the maximum value of the vertical force mainly depends on the height of the ballast tank and on the width of the opening. The wave number for which the maximum load occurs significantly depends on the geometric characteristics of the structure except for the water depth above the ballast tank which has a negligible effect. An increase in the height of the ballast tank causes an increase in the wave load while an increase in the width of the opening causes a decrease in the wave load. Based on the results of the mathematical model an easy to use regression model has been developed which can be employed to evaluate the wave load.

scholarly journals TRANSMISSION OF REGULAR WAVES PAST FLOATING PLATES

1974 ◽  
Vol 1 (14) ◽  
pp. 112
Author(s):  
Uygur Sendil ◽  
W.H. Graf
Keyword(s):  
Water Depth ◽  
Wave Length ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Linear Wave ◽  
Regular Waves ◽  
Transmission Coefficients ◽  
Wave Flume ◽  
Wave Heights ◽  
Incident Waves

Theoretical solutions for the transmission beyond and reflection of waves from fixed and floating plates are based upon linear wave theory, as put forth by John (1949), and Stoker (1957), according to which the flow is irrotational, the fluid is incompressible and frictionless, and the waves are of small amplitude. The resulting theoretical relations are rather complicated, and furthermore, it is assumed that the water depth is very small in comparison to the wave length. Wave transmissions beyond floating horizontal plates are studied in a laboratory wave flume. Regular (harmonic) waves of different heights and periods are generated. The experiments are carried out over a range of wave heights from 0.21 to 8.17 cm (0.007 to 0.268 ft), and wave periods from 0.60 to 4.00 seconds in water depth of 15.2, 30.5, and 45.7 cm (0.5, 1.0 and 1.5 ft). Floating plates of 61, 91 and 122 cm (2, 3 and 4 ft) long were used. From the analyses of regular waves it was found that: (1) the transmission coefficients, H /H , obtained from the experiments are usually less than those obtained from the theory. This is due to the energy dissipation by the plate, which is not considered in the theory. (2) John's (1949) theory predicts the transmission coefficients, H /H , reasonably well for a floating plywood plate, moored to the bottom and under the action of non-breaking incident waves of finite amplitude. (3) a floating plate is less effective in damping the incident waves than a fixed plate of the same length.

scholarly journals An Experimental Investigation of Wave Forces on a Submerged Horizontal Plate over a Simple Slope

2020 ◽  
Vol 8 (7) ◽  
pp. 507
Author(s):  
Jie Dong ◽  
Leiping Xue ◽  
Kaiyu Cheng ◽  
Jian Shi ◽  
Chi Zhang
Keyword(s):  
Wave Length ◽  
Wave Forces ◽  
Linear Wave ◽  
Intermediate Water ◽  
Vertical Force ◽  
Wave Loads ◽  
Horizontal Plate ◽  
Flat Bottom ◽  
Simple Slope ◽  
Submerged Horizontal Plate

We experimentally investigated the forces induced by monochromatic and solitary waves on a submerged horizontal plate in a wave flume. The experimental results of two-dimensional wave forces on the plate over a 1:10 simple slope and a flat bottom are presented. The effects of the uneven bottom on wave loads are discussed by comparing the results with those in a constant water depth. The measured nonlinear wave forces exhibited considerable discrepancies with the theoretical results from the linear wave theory. The wave forces on the plate induced by monochromatic waves over the simple slope in intermediate water showed no appreciable difference with the flat-bottom results. The solitary wave forces in terms of the downward vertical force and overturning moment significantly decreased in the existence of the simple slope. Furthermore, the dependency of the wave length, wave height and the submergence depth on the wave loads is also discussed.

scholarly journals Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 320
Author(s):  
Dimitrios N. Konispoliatis ◽  
Ioannis K. Chatjigeorgiou ◽  
Spyridon A. Mavrakos
Keyword(s):  
Water Waves ◽  
Wave Attenuation ◽  
Three Dimensional ◽  
Cylindrical Body ◽  
Expansion Method ◽  
Wave Theory ◽  
Linear Wave ◽  
Wave Loads ◽  
Dimensional Solution ◽  
Eigenfunction Expansion Method

In the present study, the diffraction and the radiation problems of water waves by a surface-piercing porous cylindrical body are considered. The idea conceived is based on the capability of porous structures to dissipate the wave energy and to minimize the environmental impact, developing wave attenuation and protection. In the context of linear wave theory, a three-dimensional solution based on the eigenfunction expansion method is developed for the determination of the velocity potential of the flow field around the cylindrical body. Numerical results are presented and discussed concerning the wave elevation and the hydrodynamic forces on the examined body for various values of porosity coefficients. The results revealed that porosity plays a key role in reducing/controlling the wave loads on the structure and the wave run-up, hence porous barriers can be set up to protect a marine structure against wave attack.

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

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