Reflection of Oblique Incident Waves by Breakwaters with Partially-Perforated Wall

The reflection of oblique incident waves from breakwaters with a partially-perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigenfunction expansion method is applied to expand velocity potentials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with experimental data. The effect of porosity, the relative chamber width, the relative water depth in the wave absorbing chamber and the water depth in front of the structure are discussed.

The force of oblique incident wave on the breakwater with a partially perforated wall

Wave forces induced by the interaction between the oblique incident wave and the breakwater with a partially perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigen-function expansion method is applied to expanding velocity potentials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with other theories and a good agreement can be found between them. Experimental data have been compared with the present theoretical results. The effect of the traverse wall on wave forces has been discussed in detail. On the basis of the linear wave theory, it is shown that in the range Of engineering practice, the incident angle of wave has small influence on wave forces on the unit length of perforated caisson.

2.5-dimension soil seismic response to oblique incident waves based on exact free-field solution

With the three dimensional(3D)oblique incident waves exactly determined for the free field,the soil seismic responses in both frequency and time domains are studied by the 2.5 dimension(2.5D)finite/infinite element method.First,the free-field responses in frequency domain are solved exactly for 3D arbitrary incident P and SV waves,which requires no coordinate conversion or extra effort for SV waves with super-critical incident angles.Next,the earthquake spectra are incorporated by the concept of equivalent seismic forces on the near-field boundary,based only on the displacements input derived for unit ground accelerations of each frequency using the 2.5D approach.For the asymmetric 2.5D finite/infinite element model adopted,the procedure for soil seismic analysis is presented.The solutions computed by the proposed method are verified against those of Wolf’s and de Barros and Luco’s and for inversely calculated ground motions.Of interest is that abrupt variation in soil response occurs around the critical angle on the wave propagation plane for SV waves.In addition,the horizontal displacements attenuate with increasing horizontal incident angle,while the longitudinal ones increase inversely for 3D incident P and SV waves.

REFLECTION OF OBLIQUE INCIDENT WAVES BY PERFORATED CAISSONS WITH TRAVERSE WALL

The interaction of oblique incident waves with infinite number of perforated caissons is investigated. The fluid domain is divided into infinite sub-domains by the caissons, and eigen-function expansion is applied to expand velocity potentials in each domain. A phase relation is introduced for wave oscillation in each caisson, and the structure geometry is considered in constructing the models of reflection waves. The reflected waves with the present analysis include all of the waves traveling in different directions when incident wave period is short. Numerical examinations show that velocities at the inner and outer sides of the front walls of caissons ase close to each other, and reflection coefficients satisfy the energy conservation relation very well when porous effect parameter is infinite. Numerical results show that the reflection coefficients of oblique incident waves are smaller for shorter caissons at low frequency, and decrease with the increase of wave incident angle.

First-order approximate analytical expressions of oblique incident elastic wave at an interface of porous media saturated with a nonviscous fluid

The analysis technology of Amplitude Variation with Offset(AVO)is one of the important methods for oil and gas reservoir prediction.Zoeppritz equation and its approximations are the theoretical basis of AVO analysis,which assumes that the upper and lower media of a horizontal interface are single-phase media.Limited by this assumption,AVO analysis has limited prediction and identification accuracy for complex porous reservoirs.In view of this,the first-order approximate analytical expressions of oblique elastic wave at an interface of porous media are derived.Firstly,the incident and scattering characteristics of various waves at the interface of porous media are analyzed,and the displacement vectors generated by these elastic waves are described by exponential function.Secondly,the kinematic and dynamic boundary conditions at the interface of porous media are discussed.Thirdly,by substituting the displacement vectors of incident and scattered waves into boundary conditions,the exact analytical equation is derived.Then,considering the symmetry of scattering matrix in the equation,the exact analytical expressions of each scattered wave are obtained.Furthermore,under the assumptions of small incident angle,weak elasticity at an interface of porous media,and ignoring the second-and higherorder terms,the first-order approximate analytical expressions are derived.Establishing a model of sandstone porous media with different porosity in upper and lower media,the correctness of the approximate analytical expressions is verified,and the elastic wave response characteristics of lithology and pore fluids are analyzed.

Soil seismic analysis for 2D oblique incident waves using exact free-field responses by frequency-based finite/infinite element method

The seismic analysis of a viscoelastic half-space under two-dimensional(2D)oblique incident waves is carried out by the finite/infinite element method(FIEM).First,the frequency-domain exact solutions for the displacements and stresses of the free field are derived in general form for arbitrary incident P and SV waves.With the present formulation,no distinction needs to be made for SV waves with over-critical incident angles that make the reflected P waves disappear,while no critical angle exists for P waves.Next,the equivalent seismic forces of the earthquake(Taft Earthquake 1952)imposed on the near-field boundary are generated by combining the solutions for unit ground accelerations with the earthquake spectrum.Based on the asymmetric finite/infinite element model,the frequency-domain motion equations for seismic analysis are presented with the key parameters selected.The results obtained in frequency and time domain are verified against those of Wolf’s,Luco and de Barros’and for inversely computed ground motions.The parametric study indicated that distinct phase difference exists between the horizontal and vertical responses for SV waves with over-critical incident angles,but not for under-critical incident angles.Other observations were also made for the numerical results inside the text.

Seismic stability of jointed rock slopes under obliquely incident earthquake waves

Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction.To investigate the impact of obliquely incident earthquake excitations,the input method for SV and P waves with arbitrary incident angles is conducted,respectively,by adopting the equivalent nodal force method together with a viscous-spring boundary.Then,the input method is introduced within the framework of ABAQUS software and verified by a numerical example.Both SV and P waves input are considered herein for a 2 D jointed rock slope.For the jointed rock mass,the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum.Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes.The larger the incident angle,the greater the risk of slope instability.Furthermore,the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily.P waves induce weaker responses and SV waves are shown to be more critical.

Seismic analysis of underground tunnels subjected to 3D oblique incident P and SV waves by 2.5D approach

This paper presents,for the first time,the consideration of three-dimensional(3D)oblique incident P and SV waves in calculating the 3D seismic response of a lined tunnel embedded in a half-space by the 2.5D finite/infinite element method(FIEM).Firstly,the applicability of the 2.5D FIEM for 3D seismic analysis is summarized.With the exact solutions obtained for the free field in the Appendix,the equivalent seismic forces are rationally computed for the near-field boundary,considering the horizontal and vertical excitations of the Chi-Chi Earthquake.By performing seismic analysis of the half space embedded with a tunnel using the 2.5D FIEM,the time-domain responses of the tunnel are obtained.The accuracy of the present solutions is verified against those of de Barros and Luco.Conclusions drawn from the parametric study include:(1)Stress concentration for the principal stress under oblique incident seismic waves occurs at the polar angles of 0(vault),90,180(inverted arch),and 270of the lining wall.(2)The vault and inverted arch are the weakest parts of the tunnel during earthquakes.(3)The accelerations of the tunnel during earthquakes can be regarded as of the rigid body type.(4)The responses of the tunnel lining caused by SV waves of an earthquake are much more critical than those by P waves.(5)For arbitrary seismic waves,the maximum longitudinal acceleration azmax is of the same order of magnitude as the maximum horizontal acceleration axmax.

Wave Forces Acting on Vertical Walls

Regular and irregular wave forces acting on vertical walls are studied by a previously developed numerical model. The computed wave forces are compared with the available experimental data to verify the numerical model, and satisfactory agreements are obtained. The variation of wave forces with incident angles and the shape of simultaneous pressure distribution are investigated, and the comparisons between numerical results and Goda＇ s predictions are also carried out. It is concluded that the maximum wave forces acting on the unit length of vertical wall is often induced by the obliquely incident waves instead of normally incident waves, while Goda＇ s formula may be inapplicable for oblique wave incidence. The shape of simultaneous pressure distribution is not significantly influenced by incident angles, and it can be favorably predicted by Goda＇ s formula. When regular wave heights are taken as the same as irregular wave height H1%, the irregular wave forces Ph. 1% are slightly larger than regular wave forces in most cases.

具有阶梯状海底的表面穿透柔性多孔屏障结构斜波捕获（英文）

The present study deals with the oblique wave trapping by a surface-piercing flexible porous barrier near a rigid wall in the presence of step-type bottoms under the assumptions of small amplitude water waves and the structural response theory in finite water depth.The modified mild-slope equation along with suitable jump conditions and the least squares approximation method are used to handle the mathematical boundary value problem.Four types of edge conditions,i.e.,clamped-moored,clamped-free,moored-free,and moored-moored,are considered to keep the barrier at a desired position of interest.The role of the flexible porous barrier is studied by analyzing the reflection coefficient,surface elevation,and wave forces on the barrier and the rigid wall.The effects of step-type bottoms,incidence angle,barrier length,structural rigidity,porosity,and mooring angle are discussed.The study reveals that in the presence of a step bottom,full reflection can be found periodically with an increase in(i)wave number and(ii)distance between the barrier and the rigid wall.Moreover,nearly zero reflection can be found with a suitable combination of wave and structural parameters,which is desirable for creating a calm region near a rigid wall in the presence of a step bottom.

Hydrodynamic Performance of the Arc-Shaped Bottom-Mounted Breakwater

The problem of the hydrodynamic interaction with the arc-shaped bottom-mounted breakwaters is investigated theoretically. The breakwater is assumed to be rigid, thin, impermeable and vertically located in a finite water depth. The fluid domain is divided into two sub-regions of inner and outer by an auxiliary circular interface. Linear theory is assumed and the eigenfunction expansion approach is used to determine the wave field. In order to examine the validity of the theoretical model, the analytical solutions are compared to agree well with published results with the same parameters. Numerical results including wave amplitude, surge pressure, and wave force are presented with different model parameters. The major factors including wave parameters, structure configuration, and water depth that affect the surge pressure, wave forces, and wave amplitudes are discussed and illustrated by some graphs and cloud maps.