Effects of dynamic soil behavior and wave non-linearity on the wave-induced pore pressure and effective stresses in porous seabed

Most previous investigations for the wave-induced soil response have only considered the quasi-static soil behavior under linear wave loading. However, it is expected that the dynamic soil behavior and wave non-linearity will play an important role in the evaluation of wave-induced seabed response. In this paper, we include dynamic soil behavior and wave non-linearity into new analytical models. Based on the analytical solution derived, the effects of wave non-linearity on the wave-induced seabed response with dynamic soil behavior are examined. Numerical results demonstrate the significant effects of wave non-linearity and dynamic soil behavior on the wave-induced effective stresses. The applicable range of dynamic and quasi-static approximations is also clarified for engineering practice.     

An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: II. Breaking waves

The evaluation of the wave-induced liquefaction potential is particularly important for coastal engineers involved in the design of marine structures. Most previous investigations of the wave-induced liquefaction have been limited to two-dimensional non-breaking waves. In this paper, the integrated three-dimensional poro-elastic model for the wave-seabed interaction proposed by [Zhang, H., Jeng, D.-S., 2005. An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: I. A sloping seabed. Ocean Engineering 32(5/6), 701–729.] is further extended to simulate the seabed liquefaction potential with breaking wave loading. Based on the parametric study, we conclude: (1) the liquefaction depth due to breaking waves is smaller than that of due to non-breaking waves; (2) the degree of saturation significantly affects the wave-induced liquefaction depth, and no liquefaction occurs in full saturated seabed, and (3) soil permeability does not only significantly affect the pore pressure, but also the shear stresses distribution.     

Response of a porous seabed around breakwater heads

The evaluation of wave-induced pore pressures and effective stresses in a porous seabed near a breakwater head is important for coastal engineers involved in the design of marine structures. Most previous studies have been limited to two-dimensional (2D) or three-dimensional (3D) cases in front of a breakwater. In this study, we focus on the problem near breakwater heads that consists of incident, reflected and diffracted waves. Both wave-induced oscillatory and residual liquefactions will be considered in our new models. The mistake in the previous work [Jeng, D.-S., 1996. Wave-induced liquefaction potential at the tip of a breakwater. Applied Ocean Research 18(5), 229–241] for oscillatory mechanism is corrected, while a new 3D boundary value problem describing residual mechanism is established. A parametric study is conducted to investigate the influences of several wave and soil parameters on wave-induced oscillatory and residual liquefactions around breakwater heads.     

Wave dispersion equation in a porous seabed

The wave dispersion equation has played a very important role in the development of ocean surface wave theories. The evaluation of the length of a water wave is an essential example of solving the dispersion relation. Conventional ocean wave theories have been based on an assumption of a rigid impermeable seabed. Thus, the conventional wave dispersion equation can only be used in the case of a wave propagating over a rigid impermeable seabed. For waves propagating over a porous seabed (such as a sandy bed), the conventional dispersion relation is no longer valid because of the absence of the characteristics of the porous seabed. The objective of this study is to establish a new wave dispersion equation for waves propagating over a porous seabed. Based on the new relation, the effects of a porous seabed on wave characteristics (such as the wavelength and wave profile) are discussed in detail.     

Ocean waves propagating over a porous seabed of finite thickness

In the past few decades, considerable efforts have been devoted to the phenomenon of wave-seabed interaction. However, conventional investigations for determining wave characteristics have been focused on the wave nonlinearity. On the other hand, most previous works have been only concerned with the seabed response under the wave pressure, which was obtained from the assumption of a rigid seabed. In this paper, the inertia forces and employing a complex wave number are considered in the whole problem. Based on Biot’s poro-elastic theory, the problem of wave-seabed interaction is first treated analytically for a homogeneous bed of finite thickness and a new wave dispersion relationship is also obtained, in which the soil characteristics are included. The numerical results indicate that the effects of soil parameters significantly affect the wave characteristics (such as the damping of water wave, wave length and wave pressure). Furthermore, the effects of inertia forces on the wave-induced seabed response cannot always be ignored under certain combination of wave and soil conditions.     

Analysis on pore pressure in an anisotropic seabed in the vicinity of a caisson

This paper presents an analysis of pore pressure around a caisson-type breakwater subjected to dynamic wave loading. Unlike previous investigations for wave-seabed-caisson interaction, cross-anisotropic soil behaviour is considered in this paper. Based on a linear poro-elastic theory, a finite element model is developed. A parametric study related to the effects of wave parameters, soil characteristics and geometry of caisson and rubble mound base on the pore pressure around a caisson is performed. The numerical results indicate that the effects of anisotropic soil behaviour on the wave-induced pore pressure in a sandy bed beneath a caisson are not negligible.     

An experimental study of seabed responses around a marine pipeline under wave and current conditions

Experiments on three types of soil (d₅₀=0.287, 0.057 and 0.034 mm) with pipeline(D=4 cm) either half buried or resting on the seabed under regular wave or combined with current actions were conducted in a large wave flume to investigate characteristics of soil responses. The pore pressures were measured through the soil depth and across the pipeline. When pipeline is present the measured pore pressures in sandy soil nearby the pipeline deviate considerably from that predicted by the poro-elasticity theory. The buried pipeline seems to provide a degree of resistance to soil liquefaction in the two finer soil seabeds. In the silt bed, a negative power relationship was found between maximum values of excess pore pressure p_max and test intervals under the same wave conditions due to soil densification and dissipation of the pore pressure. In the case of wave combined with current, pore pressures in sandy soil show slightly decrease with time, whereas in silt soil, the current causes an increase in the excess pore pressure build-up, especially at the deeper depth. Comparing liquefaction depth with scour depth underneath the pipeline indicates that the occurrence of liquefaction is accompanied with larger scour depth under the same pipeline-bed configuration.     

Stability and liquefaction analysis of porous seabed subjected to cnoidal wave

Cnoidal wave theory is appropriate to periodic wave progressing in water whose depth is less than 1/10 wavelength. However, the cnoidal wave theory has not been widely applied in practical engineering because the formula for wave profile involves Jacobian elliptic function. In this paper, a cnoidal wave-seabed system is modeled and discussed in detail. The seabed is treated as porous medium and characterized by Biot's partly dynamic equations (u–p model). A simple and useful calculating technique for Jacobian elliptic function is presented. Upon specification of water depth, wave height and wave period, Taylor's expression and precise integration method are used to estimate Jacobian elliptic function and cnoidal wave pressure. Based on the numerical results, the effects of cnoidal wave and seabed characteristics, such as water depth, wave height, wave period, permeability, elastic modulus, and degree of saturation, on the cnoidal wave-induced excess pore pressure and liquefaction phenomenon are studied.     

Unfluidized soil responses of a silty seabed to monochromatic waves

A flume experimental study on unfluidized responses of a silty bed (d₅₀=0.05 mm) to monochromatic water waves had shown that pore pressure variations were generally poro-elastic in the bulk body and displayed two other characteristic features not found in previous laboratory sand tests. They were an immediately fluidized thin surface layer induced by wave stresses inside the seabed's boundary layer and a porous skeleton with internally suspended sediments due to channeled flow motions. The analyses verified that on soils beneath the measurement points, both features resulted in relatively small-step pore pressure build-ups, while the former played a primary role. Besides, laboratory observations confirmed that there were some near-bed sediment suspensions during wave actions resulting in a flat bed form over a silty bed compared to small-scaled ripples over a sandy bed with no clearly identified suspended sediments. These characteristic silt responses suggest that sediment transport is critically associated with the internal soil responses and some field-observed sediment suspensions near above sandy beaches can further be approached in the laboratory by utilizing fine-grained soils.     

A semi-analytical solution for random wave-induced soil response and seabed liquefaction in marine sediments

In this study, unlike most previous investigations for wave-induced soil response, a simple semi-analytical model for the random wave-induced soil response is established for an unsaturated seabed of finite thickness. Two different wave spectra, the B-M and JONSWAP spectra, are considered in the new model. The influence of random wave loading on the soil response is investigated by comparing with the corresponding representative regular wave results through a parametric study, which includes the effect of the degree of saturation, soil permeability, wave height, wave period and seabed thickness. The maximum liquefaction depth under the random waves is also examined. The difference on the soil response under the two random wave types, B-M and JONSWAP frequency spectra, is also discussed in the present work.     

浅水非线性波作用下沙质底床孔隙水压力响应数值分析

近岸水深较浅,波浪具有较强的非线性,海床破坏与波浪作用下孔隙水压力的分布有着密切的关系。波浪场控制方程采用雷诺时均方程和k-ε紊流模型,入射波采用椭圆余弦波,采用PLIC-VOF法追踪自由表面;海床域以Biot动力固结理论为基础,建立了非线性波浪与海床相互作用的弱耦合数学模型,获得椭圆余弦波作用下沙质海床中孔隙水压力响应规律。计算结果表明,与线性波浪相比,浅水非线性波作用下沙质海床中孔隙水压力幅值增大非常显著。     

Pore pressure within dipping reservoirs in overpressured basins

To predict reservoir pore pressure, we present a one-dimensional flow model that captures complicated two- and three-dimensional flow present in a dipping permeable reservoir encased in overpressured mudrock. The model incorporates the variation of mudrock permeability with effective stress and includes the effect of reservoir geometry. We find that reservoir pressure is lower when stress-dependent mudrock permeability is assumed relative to the case of constant mudrock permeability. Increased structural relief further reduces the reservoir pressure relative to the far-field pressure and increased effective stress (pore pressure is lower relative to the overburden) results in increased reservoir pressure relative to the far-field pressure. If a large fraction of the reservoir area is in deeper areas where the mudrocks are more overpressured, then the relative pressure is higher than cases where the reservoir area remains constant with depth. The model results compare favorably both to pressures predicted by a more complex numerical model that simulates basin evolution and to field observations in the Bullwinkle Basin (Green Canyon 65, Gulf of Mexico). Our model provides a quick workflow to predict excess pressures in dipping reservoirs encased in mudrock within mechanically-compacted basins. It can be used to analyze trap integrity, understand hydrocarbon migration, and improve drilling safety.     

Numerical study for waves propagating over a porous seabed around a submerged permeable breakwater: PORO-WSSI II model

The phenomenon of the wave, seabed and structure interactions has attracted great attentions from coastal geotechnical engineers in recent years. Most previous investigations have based on individual approaches, which focused on either flow region or seabed domain. In this study, an integrated model (PORO-WSSI II), based on the Volume-Averaged/Reynolds-Averaged Navier-Stokes (VARANS) equations and Biot's poro-elastic theory, is developed to investigate the mechanism of the wave-permeable structure-porous seabed interactions. The new model is verified with the previous experimental data. Based on the present model, parametric studies have been carried out to investigate the influences of wave, soil and structure parameters on the wave-induced pore pressure. Numerical results indicated: (i) longer wave period and larger wave height will obviously induce a higher magnitude of pore pressure at the leading edge of a breakwater; (ii) after a full wave-structure interaction, the magnitude of pore pressure below the lee side of a breakwater decreases with an increasing structure porosity while it varies dramatically with a change of structure height; and (iii) the seabed thickness, soil permeability and the degree of saturation can also significantly affect the dynamic soil behaviour.     

浅水区波浪非线性效应对砂质海床动力响应的影响

以广义Biot动力固结理论为基础,运用一阶椭圆余弦波和二阶Stokes波等非线性波浪理论考虑浅水区波浪荷载的非线性效应,在时域上采用有限元方法对非线性波浪力作用下饱和砂质海床的动力响应进行了数值求解,并与线性波浪作用下海床动力响应特性进行了对比分析。结果表明,随着波长与水深之比L／d及无量纲参数T(g/d)^1/2的增大,非线性波浪对海床动力响应的影响增大。与线性波浪理论相比,孔隙水压力与有效应力幅值的增大效应非常显著。因此在近海海洋建筑物设计与工程场地评价中,波浪力的非线性特性必须引起注意。     

粉砂质海床上建筑物周围局部冲刷的系列模型延伸法研究

系统介绍了泥沙冲刷系列模型试验的相似理论,同时利用系列模型试验结果对相似关系式中的参数进行了分析,指出:(1)系列模型试验是利用几何及水流运动相似而泥沙运动不相似的模型取得试验成果的一种有效方法;(2)采用原型沙进行系列模型试验也是适宜的;(3)系列模型试验只要作两个比尺差距较大的模型就能通过外延取得所需要的试验成果,并能保证一定的精度.     

Propagation of a solitary wave over rigid porous beds

The unsteady two-dimensional Navier–Stokes equations and Navier–Stokes type model equations for porous flows were solved numerically to simulate the propagation of a solitary wave over porous beds. The free surface boundary conditions and the interfacial boundary conditions between the water region and the porous bed are in complete form. The incoming waves were generated using a piston type wavemaker set up in the computational domain. Accuracy of the numerical model was verified by comparing the numerical results with the theoretical solutions. The main characteristics of the flow fields in both the water region and the porous bed were discussed by specifying the velocity fields. Behaviors of boundary layer flows in both fluid and porous bed regions were also revealed. Effects of different parameters on the wave height attenuation were studied and discussed. The results of this numerical model indicate that for the investigated incident wave as the ratio of the porous bed depth to the fluid depth exceeds 10, any further increase of the porous bed depth has no effect on wave height attenuation.     

Non-linear wave-induced transient response of soil around a trenched pipeline

Submarine pipelines are always trenched within a seabed for reducing wave loads and thereby enhancing their stability. Based on Biot's poroelastic theory, a two-dimensional finite element model is developed to investigate non-linear wave-induced responses of soil around a trenched pipeline, which is verified with the flume test results by Sudhan et al. [Sudhan, C.M., Sundar, V., Rao, S.N., 2002. Wave induced forces around buried pipeline. Ocean Engineering, 29, 533–544] and Turcotte et al. [Turcotte, B.R., Liu, P.L.F., Kulhawy, F.H., 1984. Laboratory evaluation of wave tank parameters for wave-sediment interaction. Joseph H. Defree Hydraulic Laboratory Report 84-1, School of Civil and Environmental Engineering, Cornell University]. Non-linear wave-induced transient pore pressure around pipeline at various phases of wave loading is examined firstly. Unlike most previous investigations, in which only a single sediment layer and linear wave loading were concerned, in this study, the influences of the non-linearity of wave loading, the physical properties of backfill materials and the geometry profile of trenches on the excess pore pressures within the soil around pipeline, respectively, were explored, taking into account the in situ conditions of buried pipeline in the shallow ocean zones. Based on the parametric study, it is concluded that the shear modulus and permeability of backfill soils significantly affect the wave-induced excess pore pressures around trenched pipeline, and that the effect of wave non-linearity becomes more pronounced and comparable with that of trench depth, especially at high wave steepness in shallow water.     

Simulation of wave breaking effects in two-dimensional elliptic harbor wave models

A technique is developed for including the effects of dissipation due to wave breaking in two-dimensional elliptic models based on the mild-slope wave equation. This involves exploration of convergence properties pertaining to iteration due to presence of the nonlinear wave breaking parameter in the governing equations as well as new boundary conditions that include wave-breaking effects. Five wave-breaking formulations are examined in conjunction with the resulting model, which is applied to tests involving a sloping beach, a bar-trough bottom configuration, shore-connected and shore-parallel breakwaters on a sloping beach, and two real-world cases. Model results show that three of the formulations, when used within the context of the modeling scheme presented here, provide excellent results compared to data.     

寒潮影响下江苏沿海风浪场数值模拟研究

基于第三代浅水波浪数值预报模型SWAN,建立自西北太平洋嵌套至东中国海、江苏沿海的三重嵌套模型,对2010年12月12日至15日江苏沿海寒潮大风引起的风浪过程进行了数值模拟研究。利用西北太平洋和江苏沿海实测数据对模型进行了验证,结果表明SWAN嵌套模型能较好地模拟江苏沿海寒潮风浪场的时空分布。通过响水站实测数据对江苏沿海底摩擦系数进行了率定,研究表明选取Collins拖曳理论中摩擦因数C_f=0.001时,有效波高模拟误差相对较小。寒潮风浪场的特征分析表明,有效波高分布与风场分布基本一致,寒潮风浪在江苏沿海北部影响较为显著,辐射沙洲附近由于其特殊地形影响相对较小。     

Effects of seabed properties on acoustic wave fields in a seismo-acoustic ocean waveguide

Acoustic wave fields in an ocean waveguide with a sediment layer having continuously varying density and sound speed overlying an elastic subbottom are considered in this analysis. The objective of this study is to investigate the effects of seabed acoustic properties, including the density and sound speed of the sediment layer and subbottom, on the characteristics of the wave fields. Examination of the reflection coefficient, wavenumber spectrum, and noise intensity of the sound field through numerical analysis has shown that the variation in the acoustic properties in the sediment layer is an important factor in determining the reflected or noise sound fields. In particular, the sediment thickness-to-wavelength ratio and the types of variation of acoustic properties inside the layer give rise to many characteristics that potentially allow for acoustic inversion of the seabed properties. With regard to the wave-field components in a shallow-water environment, the various types of waves existing in a seismo-acoustic waveguide have been illustrated. The results indicate that the effects of the sediment properties on the wavenumber spectrum are primarily on the continuous and evanescent regimes of the wave field. The noise intensity generated by distributive random monopoles at various depths, together with the effect of refractive sound-speed distribution in the water column, has been obtained and analyzed.