Wave‐induced seepage flux into anisotropic seabeds

Considerable effort has been devoted to quantifying the wave‐induced soil response in a porous seabed in the last few decades. Most previous investigations have focused on the analysis of pore pressure and effective stresses within isotropic sediments, despite strong evidence of anisotropic soil behaviour reported in the literature. Furthermore, the seepage flux, which is important in the context of contaminant transport, has not been examined. In this paper, we focus on water wave‐driven seepage in anisotropic marine sediments of finite thickness. The numerical results predict that the effects of hydraulic anisotropy and anisotropic soil behaviour on the wave‐driven seepage in marine sediment are significant. Copyright © 2001 John Wiley & Sons, Ltd.     

Wave-induced soil response in an unsaturated anisotropic seabed of finite thickness

An analytical solution for the wave-induced soil response is developed for a seabed of finite thickness subject to a three-dimensional (3-D) wave system produced by two intersecting waves of equal properties. These 3-D exact solutions for the pore pressure and effective stresses, proposed for a non-cohesive soil matrix of finite depth in a homogeneously unsaturated and anisotropic condition, are readily reducible to the limiting two-dimensional cases of progressive and standing waves, for which no explicit solutions are available for finite thickness. The effects of soil isotropy, degree of saturation, seabed thickness and grain size on the wave-induced pore pressure are discussed in detail. The explicit solutions presented in this study for the wave-induced pore pressure and effective stresses should benefit the laboratory experiments and field monitoring programs carried out in soil of finite depth.     

Breaking wave‐induced response and instability of seabed around caisson breakwater

Breaking‐wave‐induced dynamic response and instability of seabed around a caisson breakwater are investigated. A seabed‐rubble‐breakwater system is modeled using finite elements. The impact response of the porous seabed and rubble foundation is assumed to be governed by the coupled Biot equations, and three possible formulations are considered with respect to the inclusion of inertial terms. The response is presented in terms of shear stress and pore pressure distributions at three locations underneath the breakwater. The effect of seabed and wave parameters and the inertial terms on the impact response is investigated through parametric studies. Analyses show that usually partly dynamic formulation yields the largest response amplitudes as compared to the fully dynamic formulation, which is the most complete form. The instability of seabed and rubble mound as a result of instantaneous liquefaction is also studied. Breaking wave‐induced pressures in some cases are found to cause liquefaction in the rubble and the seabed. The effect of some parameters on the instability is found to be significant. Copyright © 2011 John Wiley & Sons, Ltd.     

Chemo‐thermo‐mechanically coupled seismic analysis of methane hydrate‐bearing sediments during a predicted Nankai Trough Earthquake

In the present study, we have developed a numerical method which can simulate the dynamic behaviour of a seabed ground during gas production from methane hydrate‐bearing sediments. The proposed method can describe the chemo‐thermo‐mechanical‐seismic coupled behaviours, such as phase changes from hydrates to water and gas, temperature changes and ground deformation related to the flow of pore fluids during earthquakes. In the first part of the present study, the governing equations for the proposed method and its discretization are presented. Then, numerical analyses are performed for hydrate‐bearing sediments in order to investigate the dynamic behaviour during gas production. The geological conditions and the material parameters are determined using the data of the seabed ground at Daini‐Atsumi knoll, Eastern Nankai Trough, Japan, where the first offshore production test of methane hydrates was conducted. A predicted earthquake at the site is used in the analyses. Regarding the seismic response to the earthquake which occur during gas production process, the wave profiles of horizontal acceleration and horizontal velocity were not extensively affected by the gas production. Hydrate dissociation behaviour is sensitive to changes in the pore pressure during earthquakes. Methane hydrate dissociation temporarily became active in some areas because of the main motion of the earthquake, then methane hydrate dissociation brought about an increase in the average pressure of the fluids during the earthquake. And, it was this increase in average pore pressure that finally caused the methane hydrate dissociation to cease during the earthquake. Copyright © 2016 John Wiley & Sons, Ltd.     

波浪作用下砂质海床孔隙水压力的响应规律实验研究

采用波流水槽模型试验的方法,研究了规则波和不规则波作用下砂质海床的孔隙水压力响应问题,其中主要考虑不同深度、波高及周期对孔隙水压力的影响,从而得出孔压变化规律。当周期和波高不变时,由波浪引起的孔隙水压力随水深的增加而逐渐减小。同一水深和波高条件下,由波浪引起的孔隙水压力随周期变大而变大;当水深和周期固定时,由波浪引起的孔隙水压力随波高的增加而增加。     

A simple analytical solution to one‐dimensional consolidation for unsaturated soils

This paper presents a simple analytical solution to Fredlund and Hasan's one‐dimensional (1‐D) consolidation theory for unsaturated soils. The coefficients of permeability and volume change for unsaturated soils are assumed to remain constant throughout the consolidation process. The mathematical expression of the present solution is much simpler compared with the previous available solutions in the literature. Two new variables are introduced to transform the two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved with standard mathematical formulas. It is shown that the present analytical solution can be degenerated into that of Terzaghi consolidation for fully saturated condition. The analytical solutions to 1‐D consolidation of an unsaturated soil subjected to instantaneous loading, ramp loading, and exponential loading, for different drainage conditions and initial pore pressure conditions, are summarized in tables for ease of use by practical engineers. In the case studies, the analytical results show good agreement with the available analytical solution in the literature. The consolidation behaviors of unsaturated soils are investigated. The average degree of consolidation at different loading patterns and drainage conditions is presented. The pore‐water pressure isochrones for two different drainage conditions and three initial pore pressure distributions are presented and discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

非线性波浪作用下海底管线-海床动力响应分析

确定波浪荷载作用下海底埋置管线和海床的响应是海底管线设计中的关键问题。目前大多数研究只是考虑了管线、海床在线性推进波作用下的响应,并没有考虑管线与海床之间的相互作用效应。采用接触摩擦理论,考虑管线与海床之间的相互作用效应,基于有限元方法研究了非线性波浪作用下海底埋置管线和多孔海床相互作用问题。数值计算结果表明,在计算中如果忽略波浪非线性项,既有可能低估海底管线内应力及管线周围海床中孔隙水压力,也有可能高估海底管线内应力及管线周围海床中孔隙水压力。     

随机波浪作用下海床动力响应及液化的理论分析

运用随机波浪理论,基于广义Biot动力固结理论,建立了能够考虑波浪荷载随机特性影响的计算海床动力响应及液化深度的解析数值模型,并从时域上进行求解分析.通过与传统线性规则波浪荷载作用下海床动力响应及液化深度的数值结果的对比分析,详细讨论了考虑波浪荷载的随机特性对于求解海床动力响应及液化深度的影响程度.结果表明,根据随机波浪理论计算得到的海床中的超孔隙水压力、水平有效应力、竖向有效应力、剪应力表现出较强的不规则性,其幅值沿着海床深度方向的变化趋势与根据线性规则波浪理论计算得到结果的变化趋势基本相同,但在同数量级上更大,同时计算得到的海床最大液化深度明显大于根据线性规则波浪理论计算得到的结果.因此,在海洋地基设计和自由场地安全评估时应该合理地考虑波浪荷载的随机特性.     

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method

This paper introduces an exact analytical solution for governing flow equations for one‐dimensional consolidation in unsaturated soil stratum using the techniques of eigenfunction expansion and Laplace transformation. The homogeneous boundary conditions adopted in this study are as follows: (i) a one‐way drainage system of homogenous soils, in which the top surface is considered as permeable to air and water, whereas the base is an impervious bedrock; and (ii) a two‐way drainage system where both soil ends allow free dissipation of pore‐air and pore‐water pressures. In addition, the analytical development adopts initial conditions capturing both uniform and linear distributions of the initial excess pore pressures within the soil stratum. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on the proposed boundary conditions. Besides, the Laplace transform method is adopted to solve the first‐order differential equations. Once equations with transformed domain are all obtained, the final solutions, which are proposed to be functions of time and depth, can be achieved by taking an inverse Laplace transform. To verify the proposed solution, two worked examples are provided to present the consolidation characteristics of unsaturated soils based on the proposed method. The validation of the recent results against other existing analytical solutions is graphically demonstrated. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytical solution to 1D coupled water infiltration and deformation in two‐layer unsaturated soils

An analytical solution to 1D coupled water infiltration and deformation in layered soils is derived using a Laplace transformation. Coupling between seepage and deformation, and initial conditions defined by arbitrary continuous pore‐water pressure distributions are considered. The analytical solutions describe the transient pore‐water pressure distributions during 1D, vertical infiltration toward the water table through two‐layer unsaturated soils. The nonlinear coupled formulations are first linearized and transformed into a form that is solvable using a Laplace transformation. The solutions provide a reliable means of comparing the accuracy of various numerical methods. Parameters considered in the coupled analysis include the saturated permeability (k_s), desaturation coefficient (α), and saturated volumetric water content (θ_s) of each soil layer, and antecedent and subsequent rainfall infiltration rates. The analytical solution demonstrates that the coupling of seepage and deformation plays an important role in water infiltration in layered unsaturated soils. A smaller value of α or a smaller absolute value of the elastic modulus of the soil with respect to a change in soil suction (H) for layered unsaturated soils means more marked coupling effect. A smaller absolute value of H of the upper layer soil also tends to cause more marked coupling effect. A large difference between the saturated coefficients of permeability for the top and bottom soil layers leads to reduced rainfall infiltration into the deep soil layer. The initial conditions also play a significant role in the pore‐water pressure redistribution and coupling effect. Copyright © 2011 John Wiley & Sons, Ltd.     

波流共同作用下多孔介质海床动力响应的解析解

本文提出一个评价波流共同作用下多孔介质海床的孔隙水压力和有效应力动力响应的u-p近似模型。与过去相关研究主要不同处是在于本文着重考虑了潮流在该问题解析解中的作用。本文提出的解析解首先分别与实测数据和COMSOL数值解对比验证。接着以此解析解为基础进行了一系列关于流的作用的参数分析。本文首先研究了潮流对于不同海床深度的影响以及不同波流荷载下海床的动力响应问题,数值结果显示了潮流和非线性波对孔隙水压力和有效应力的重要作用。本文最后研究了不同潮流方向对海床动力响应的影响,结果显示由不同的潮流方向引起的孔隙水压力的相对变化可以达到静水压力的15%。     

Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd.     

非饱和土拟二维平面应变固结问题的解析计算方法

基于Fredlund非饱和土一维固结理论,建立了二维平面应变条件下的固结方程组,并得到了单层非饱和土平面应变条件下的解析解。基于相关理论,假设体变系数和渗透系数都为常量,同时考虑到瞬时加载条件下,沿着土体深度方向上产生均匀或者线性分布的初始超孔隙压力,建立了二阶二元偏微分方程组。求解时,引入函数方法来降低方程的阶数,然后通过分离变量法获得方程的通解。在此基础上,结合一个针对单面排水条件下二维平面应变问题案例,通过与数值解对比,验证了所提方法的正确性。并采用所提方法计算获得了二维平面下超孔隙水压力、气压力沿垂直和水平方向消散的等时线,通过计算对比,分析了不同线性分布情况下,初始超孔隙压力对固结消散过程的影响。研究结果表明：初始超孔隙压力的不同分布对超孔隙气压力消散的影响几乎可以忽略,而对超孔隙水压力消散的影响更大。     

波浪作用下饱和砂质海床土体与管线相互作用规律研究

针对波浪引起的饱和砂质海床土体和管线相互作用问题,将Biot动力固结理论与笔者课题组提出的砂土液化变形弹塑性本构模型相耦合,较为合理地再现了简谐波浪作用下较浅饱和砂质海床中管线周围可液化海床土体的超静孔隙水压力瞬态累积变化规律与液化过程。数值计算结果与Sumer等的试验规律一致。结果表明：由于管线的存在,改变了饱和砂质海床液化区域的空间分布。液化首先由管线下部土体开始产生,随着波浪荷载的持续作用,液化区域沿着管线外壁向上演化;同时海床表层土体产生液化并向深层发展,最终管线周围土体都发生液化,这是导致空管上浮的主要原因。当饱和砂质海床中存在管线时,管线附近海床土体液化深度明显变深。超静孔压累积和渗透力变化的耦合作用是导致饱和砂质海床土体产生液化的原因。与将海床土体视为饱和弹性多孔介质相比,可考虑液化全过程的弹塑性动力分析能更为合理地揭示实际波浪作用下饱和砂质海床土体的渗流场和应力场的瞬态时空演变规律。     

Displacement ring load Green's functions for saturated porous transversely isotropic tri‐material full‐space

Based on the Biot's poroelastic theory and using scalar potential functions both the ring load and point load displacement Green's functions for a transversely isotropic saturated porous full‐space composed of an upper half‐space, a finite thickness middle layer and a lower half‐space is analytically presented for the first time. It is assumed that each region consists of a different transversely isotropic material. The equations of poroelastodymanics in terms of the solid displacements and the pore fluid pressure are uncoupled with the help of two scalar potential functions, so that the governing equations for the potential functions are either a second order wave equation or a repeated wave‐heat transfer equation of sixth order. With the aid of Fourier expansion with respect to circumferential direction and Hankel integral transforms with respect to the radial direction in cylindrical coordinate system, the response is determined in the form of line integrals in the real space, followed by theorem of inverse Hankel integral transforms. The solutions degenerate to a single phase elastic material, and the results are compared with previous studies, where an excellent agreement may be observed with the results provided in the literature. Some examples of displacement Green's functions are finally given to illustrate the solution. Copyright © 2016 John Wiley & Sons, Ltd.     

Oscillatory soil response and liquefaction in an unsaturated layered seabed

The subject of wave-induced soil response in a real seabed has attracted the attention of geotechnical and coastal engineers over the last three decades, for which several basic theories have been developed. However, the evaluation of soil liquefaction has not been attempted theoretically in a seabed with multiple sub-layers, in which homogeneity in soil properties can be assumed within each layer. In this study, a semi-analytical approach is presented for obtaining solutions for the pore pressure and effective stresses in a non-cohesive layered seabed of finite thickness subject to a system of three-dimensional waves. Based on the numerical results for a layered seabed, influences of soil characteristics (relative layer thickness, permeability ratio and shear modulus) on seabed responses are described. Special attention is given to the effect of placing a coarser material as a top layer for protecting an underlayer of finer sediment. Although only a three-layered seabed is explicitly solved in this study, the procedure outlined can readily be extended to a multi-layered soil system. The three-dimensional solutions can also be applied to the two-dimensional progressive or standing wave systems.     

波浪作用下黄河三角洲粉质土海床动力响应分析

应用饱和土动力固结理论和Pastor-Zienkiewicz III动力本构关系,对波浪作用下黄河三角洲粉质土海床的动力响应特征进行了有限元分析,应用总超孔压准则对海床进行了液化判别,并将计算结果与现场观测资料进行对比。结果表明：波浪导致的海床超孔压由瞬态孔压和累积孔压两部分组成;相比均质海床,拥有表面硬层的海床瞬态孔压沿深度衰减更快,累积孔压在表层增长速度更大;不同波浪条件下,瞬态孔压值及其变化趋势较为一致,累积孔压则具有较大的不同。年平均波浪条件下海床不会发生液化;5 a和50 a一遇极端波浪条件下,考虑三维效应和具有表面硬层的海床更容易液化,最大液化深度在海床表面以下2～3 m范围内。计算所得的海床最大液化深度与实测的黄河三角洲海底灾害地貌深度有较好的一致性,表明了文中方法的有效性和合理性。     

A new approximation for pore pressure accumulation in marine sediment due to water waves

The residual mechanism of wave‐induced pore water pressure accumulation in marine sediments is re‐examined. An analytical approximation is derived using a linear relation for pore pressure generation in cyclic loading, and mistakes in previous solutions (Int. J. Numer. Anal. Methods Geomech. 2001; 25 :885–907; J. Offshore Mech. Arctic Eng. (ASME) 1989; 111 (1):1–11) are corrected. A numerical scheme is then employed to solve the case with a non‐linear relation for pore pressure generation. Both analytical and numerical solutions are verified with experimental data (Laboratory and field investigation of wave– sediment interaction. Joseph H. Defrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, 1983), and provide a better prediction of pore pressure accumulation than the previous solution (J. Offshore Mech. Arctic Eng. (ASME) 1989; 111 (1):1–11). The parametric study concludes that the pore pressure accumulation and use of full non‐linear relation of pore pressure become more important under the following conditions: (1) large wave amplitude, (2) longer wave period, (3) shallow water, (4) shallow soil and (5) softer soils with a low consolidation coefficient. Copyright © 2006 John Wiley & Sons, Ltd.