Poroelastic Seabed Research Articles

Dynamic response in a transversely isotropic and layered nonlocal poroelastic seabed subjected to vertical P-waves

A novel model is put forward to characterize the seismic response excited by vertical P-waves in a transversely isotropic and layered nonlocal poroelastic seabed. The proposed model integrates nonlocal parameter, anisotropy, and stratification to accurately examine wave propagation behavior. The fundamental equations for the underlying seabed are formulated using Biot's poroelastodynamic theory and Eringen's nonlocal theory. The wave equation for the overlying water is expressed in terms of the velocity potential. General solutions in both the poroelastic seabed and water layer are derived by solving the involved ordinary differential equations. Employing the newly devised and unconditionally stable propagator matrix scheme, semi-analytical solutions are derived for the time-harmonic response in a layered poroelastic seabed subjected to vertical P-wave excitation within the frequency domain. The validity of the proposed solutions is confirmed through rigorous comparison with the previously established analytical solutions. The influence of key material properties of seabed on the velocities of P-waves and free-field response in the poroelastic seabed is estimated in detail, along with the free-field response in a nonhomogeneous poroelastic seabed.

Importance of sign conventions on analytical solutions to the wave-induced cyclic response of a poro-elastic seabed

This paper discusses the influence of different sign conventions for strains and stresses, i.e. the solid mechanics sign convention and the soil mechanics sign convention, on the form of governing partial differential equations (the static equilibrium equations and the continuity equation) used to describe the wave-induced cyclic response of a poro-elastic seabed due to propagation of a sinusoidal surface water-wave. Some selected analytical solutions, obtained by different authors and published in specialist literature in the form of complex functions describing the wave-induced pore-fluid pressure, effective normal stress and shear stress oscillations in the seabed, have been analysed and compared with each other mainly with respect to different sign conventions for stains and stresses and also with regard to different orientations of the positive vertical axis of the two-dimensional coordinate system and different directions of surface water-wave propagation. The performed analyses of the analytical solutions has indicated many inaccuracies, or even evident errors and exemplary mistakes of wrong-signed values of basic wave-induced response parameters (the shear stress in particular), thereby disqualifying these solutions and their final equations from practical engineering applications. Most of the mistakes found in the literature must be linked to authors’ lack of understanding and consistency in an uniform application of a certain sign convention for strains and stresses in the soil matrix at both stages of mathematical formulation of the governing problem and correct interpretation of equations of the final analytical solution. The present paper, based mostly on a thorough literature review, ought to draw attention and arouse interest among coastal scientists and engineers in proper identification and use of the existing analytical solutions to the wave-induced cyclic seabed response – solutions which differ very often in the applied sign convention for stresses in the soil matrix.

Dynamic response and liquefaction potential of porous seabed induced by partial standing ocean waves

The analysis of ocean wave-induced dynamic response of a porous seabed is particularly important for coastal and geotechnical engineers when designing and constructing maritime structures. In this study, an analytical solution is presented to analyze the dynamic response and liquefaction potential of a poro-elastic seabed induced by partial standing waves with arbitrary reflectivity. The porous seabed is modeled using Biot’s theory describing the propagation of elastic waves, and coupled deformation and water flow of porous media, whereas the ocean waves are described using linear ocean wave theory. Based on the mixed boundary-value conditions, explicit expressions of displacements, effective stresses and excess pore water pressure of seabed are derived with consideration of the effects of inertial forces, compressibility of solid and fluid, and arbitrary reflectivity of standing waves. The results of degenerated analytical solutions are compared with the existing ones to verify the correctness of the proposed method. The effects of several pertinent parameters of ocean wave-seabed system, including reflection coefficient, phase lag and period of standing waves, depth of water, permeability, degree of saturation, and shear modulus of seabed deposits, etc., on the dynamic response of seabed and liquefaction potential, are examined and discussed. It is found that the reflection of standing wave has a significant effect on the dynamic response and liquefaction potential of porous elastic seabed. Compared with that of no wave reflection, the liquefaction depth of seabed induced by fully-reflected standing waves increases 82.49% under certain conditions of wave-seabed system. In addition, phase lag, wave period, water depth and mechanical and physical properties of seabed soil such as saturation, permeability and shear modulus have different effects on the dynamic response and liquefaction potential of porous elastic seabed. The investigation of the dynamic response and liquefaction of the porous elastic seabed under partial standing ocean waves will help to better predict the influence of standing waves on breakwaters and seabed soil, and can provide some guidance for the design of offshore structures.

Integrated Model for Wave-Induced Oscillatory and Residual Soil Response in a Poro-Elastic Seabed: Partially Dynamic Model

The evaluation of wave-induced residual pore pressure in a porous seabed and associated seabed liquefaction is essential for designing marine infrastructure foundations. The strength and stiffness of the seabed could be weakened due to the build-up of pore pressures under cyclic wave action, further leading to residual liquefaction. Existing models for residual liquefaction are limited to the quasi-static uncoupled approaches, which do not account for the effect of oscillatory pore pressure on the accumulative pore pressure acceleration of solid particles, despite the mutual influence of these two mechanisms. To overcome these limitations, this paper proposes a new model for residual soil response with u−p approximation (partial dynamic model) that couples oscillatory and residual mechanisms. The proposed model is validated through wave flume tests and centrifuge tests. Based on the coupling model, a new criterion of liquefaction integrating both oscillatory and residual mechanisms is also proposed. Numerical examples demonstrate that the coupling effect significantly affects the wave-induced seabed liquefaction potential. Furthermore, a new parameter (Ω) representing the ratio of oscillatory and residual pore pressure is introduced to clarify which mechanism dominates the pore pressure development.

Second-order Stokes wave-induced dynamic response and instantaneous liquefaction in a transversely isotropic and multilayered poroelastic seabed

The ocean waves exhibit obvious non-linearity with asymmetric distribution of wave crests and troughs, which could induce significantly different effect on the seabed compared to the commonly used linear wave theory. In this paper, a semi-analytical solution for a transversely isotropic and multilayered poroelastic seabed under non-linear ocean wave is proposed by virtue of the dual variable and position (DVP) method. The ocean wave and seabed are, respectively, modelled using second-order Stokes theory and Biot’s complete poroelastodynamic theory. Then the established governing equations are decoupled and solved via the powerful scalar potential functions. Making use of the DVP scheme, the layered solutions are finally gained by combining the boundary conditions of the seabed. The developed solutions are verified by comparing with existing solutions. The selected numerical examples are presented to investigate the effect of main parameters on the dynamic response of the seabed and evaluate the corresponding liquefaction potential. The results show that the anisotropic stiffness and permeability, degree of saturation and stratification have remarkable influence on the dynamic response and liquefaction behavior of the seabed. The present solution is a useful tool to estimate the stability of transversely isotropic and layered seabed sediment in the range of non-linear ocean wave.

Poro-elastic and poro-elasto-plastic modeling of sandy seabed under wave action

The seabed could be liquefied due to the wave-induced accumulation of residual excess pore water pressure (EPWP), resulting in the instability of offshore and marine structures. Thus, it is of importance to consider both the buildup of EPWP and the associated deformation behavior of the seabed. In this study, a dynamic poro-elasto-plastic seabed model, integrated with a state-dependent plasticity model, is developed in COMSOL Multiphysics. The numerical model of seabed is validated against the analytical solutions and model tests. The elliptical trajectories of soil particle at different depths of the poro-elastic seabed under the progressive wave are illustrated. The ratio of the amplitude of vertical displacement to that of horizontal displacement generally decreases as the depth increases for the poro-elastic seabed. In the poro-elasto-plastic seabed, however, the soil particles tend to move following the direction of the wave propagation. Moreover, the soil particles at the shallow part of the seabed go downwards before the initial liquefaction, while the soil particles at the lower position initially go upwards and then turn to go downwards when the initial liquefaction occurs. Particularly, the surface seabed with lower relative density is more prone to lose the stability, resulting in a dramatic upward vertical displacement.

Transient wave-induced pore-water-pressure and soil responses in a shallow unsaturated poroelastic seabed

An analytical solution is developed for studying transient water wave-induced responses inside an unsaturated poroelastic seabed of finite thickness. The soil skeleton and the pore fluid are compressible and the constitutive relationship of the soil skeleton is described by Hooke's law. Assuming that the horizontal length scale of wave motion is much larger than the seabed thickness, the leading-order analytical solutions for the seabed responses, including pore fluid pressure and soil skeleton motion, are obtained. The present solutions are suitable for general transient wave loading and for the shear modulus of the soil skeleton being of the same order of magnitude as the effective bulk modulus of elasticity of the pore fluid. The present theory is first validated by checking the solutions with the experimental data for the pore pressure induced by periodic-wave loading. The present analytical solutions are then used to investigate the seabed responses under transient waves, including linear periodic wave, a solitary wave and a bore. The effects of the wave-induced effective stresses on the bed failure potential are further analysed. The results show that the shear failure potential and its duration are highly dependent on the soil properties, such as saturation degree, shear modulus and permeability. Sensitivity analyses are presented.

Dynamic Responses of a Multilayered Transversely Isotropic Poroelastic Seabed Subjected to Ocean Waves and Currents

In this study, a semi-analytical solution to the dynamic responses of a multilayered transversely isotropic poroelastic seabed under combined wave and current loadings is proposed based on the dynamic stiffness matrix method. This solution is first analytically validated with a single-layered and a two-layered isotropic seabed and then verified against previous experimental results. After that, parametric studies are carried out to probe the effects of the soil’s anisotropic characteristics and the effects of ocean waves and currents on the dynamic responses and the maximum liquefaction depth. The results show that the dynamic responses of a transversely isotropic seabed are more sensitive to the ratio of the soil’s vertical Young’s modulus to horizontal Young’s modulus (Ev/Eh) and the ratio of the vertical shear modulus to Ev (Gv/Ev) than to the vertical-to-horizontal ratio of the permeability coefficient (Kv/Kh). A lower degree of quasi-saturation, higher porosity, a shorter wave period, and a following current all result in a greater maximum liquefaction depth. Moreover, it is revealed that the maximum liquefaction depth of a transversely isotropic seabed would be underestimated under the isotropic assumption. Furthermore, unlike the behavior of an isotropic seabed, the transversely isotropic seabed tends to liquefy when fully saturated in nonlinear waves. This result supplements and reinforces the conclusions determined in previous studies. This work affirms that it is necessary for offshore engineering to consider the transversely isotropic characteristics of the seabed for bottom-fixed and subsea offshore structures.

Wave-induced dynamic response in a transversely isotropic and multilayered poroelastic seabed

The dynamic response of a transversely isotropic, multilayered and poroelastic seabed under the action of two-dimensional water waves is investigated via a recently developed semi-analytical method. The coupled governing equations of motion are based on the Biot's complete poroelastodynamic model, expressed in the (u,p) form. The potential-function method is introduced to express the unknown primary quantities such that the general solution in each layer is obtained with six undetermined coefficients. By virtue of the stable and efficient dual variable and position method, a general recursive relation for the displacements, stresses and pore pressure among different layers is established. The semi-analytical solutions for the layered seabed with two typical bottom boundary conditions are derived. Particularly, for the homogeneous transversely isotropic seabed, exact solutions are also derived for different bottom boundaries. The accuracy and reliability of the solutions are verified against existing solutions. Selected numerical examples are further presented to study the effect of anisotropic stiffness, anisotropic permeability and material layering on the wave-induced pore pressure and effective stresses.

Three-Dimensional Wave-Induced Dynamic Response in Anisotropic Poroelastic Seabed

This paper presents a novel analytical solution, which is developed for investigating three-dimensional wave-induced seabed responses for anisotropic permeability. The analytical solution is based on the assumption of the poroelastic and the u − p dynamic form, which considers the inertia force of the soil skeleton. In this paper, the problem is regarded as an eigenvalue problem through a first-order ordinary differential equation in matrix form. The problematic eigenvector involved in the solution is dealt with using numerical computation, and a process is proposed to implement the present solution for the desired dynamic response. A verification, which is compared with two existing solutions, demonstrates an agreement with the present solution. The results show that the amplitude profile of seabed response for a shorter wave period varies significantly. A comparison between the anisotropic and transverse isotropic, as well as isotropic permeabilities reveals that the error of vertical effective stress on the seabed bottom can reach 74 . 8 % for the isotropic case. For anisotropic permeability, when the wave direction is parallel to the higher horizontal permeability direction, the amplitude profiles of pore pressure and vertical effective stress exhibit the greatest dissipation and increment, respectively. For transverse isotropic permeability, the vertical effective stress is independent of the wave direction, which results in the two horizontal effective stresses on the seabed bottom being identical to each other and independent of the wave direction. Our comprehensive analysis provides insight into the effect of anisotropic permeability on different wave periods and wave directions.

Seepage Force on a Buried Submarine Pipeline Induced by a Solitary Wave

In this study, a finite element method was used to establish a two-dimensional numerical model to solve the problem of the Biot equation describing the poroelastic seabed, and to analyze the seepage force on a buried submarine pipeline under the propagation of a solitary wave. The model provides a solution to the displacement of the poroelastic seabed and the variation of the pore-water pressure. By means of numerical simulation, the effects of Young’s modulus and permeability coefficient of the soil on the pore-water pressure and seepage force are discussed. In the simulation of solitary waves passing through fully buried submarine pipelines, numerical results indicate that the smaller the permeability coefficient in dense sandy bed the greater the vertical force acting on the pipeline, and the smaller the permeability coefficient in loose sand bed the smaller the vertical force acting on the pipeline. In general, when the permeability coefficient is large, the smaller the Young’s modulus the more obvious the influence of the vertical force on the pipeline, and when the permeability coefficient is small, the larger the Young’s modulus the more obvious the influence of the vertical force on the pipeline.

Wave and current-induced dynamic response in a multilayered poroelastic seabed

Waves and currents often coexist in ocean, which significantly changes the pore pressure and stress state in the seabed. Besides, stratification is a basic feature of a seabed due to natural deposition or artificial construction. An analytical solution to the dynamic response of a multilayered seabed to combined wave and current loading is proposed in this study. The seabed is modeled using Biot’s fully dynamic theory, where the effects of inertia and the compressibility of solids and fluids are included. Unlike previous investigations, stratification of seabed and non-linear interactions between waves and the current are considered in this study. The present solution is firstly validated against an existing analytical solution and a model test. Comprehensive parametric study is then conducted to study the influences of soil layering, current and waves on the dynamic response of a multilayered seabed. A seabed with layered soil properties (e.g. shear modulus, permeability) has substantially different pore pressure and stress state from a homogeneous seabed under combined wave and current loading. The current significantly influences the seabed response. An opposing current is beneficial to prevent both soil liquefaction and shear failure, and a following current is more likely to cause seabed instability. The present solution is a practical tool to evaluate seabed stability in an ocean environment with multiple layers, especially where waves and currents are prevailing.

Influence of vertical shear stresses due to pile-soil interaction on lateral dynamic responses for offshore monopiles

It has recently been pointed out that the vertical shear stresses at pile-soil interface play an important role in static responses of offshore monopiles with large diameters, and traditional p - y curves cannot fully capture this influence. However, the influences of the vertical shear stresses on the dynamic response of monopiles are still not clear. This is the main focus of this study. The coupled horizontal and rocking vibration of a monopile embedded in a fully saturated poroelastic seabed is studied in this paper. The focus of the study is the difference between the responses with and without the vertical shear stresses on the pile. The monopile dynamic response is studied by the integral equation method, with both 3D elastodynamic theory and Euler-Bernoulli beam theory. Selected numerical results for highlighting the influence of the vertical shear stresses on the dynamic contact load distributions, pile displacements, and lateral dynamic impedance functions are examined for different length to diameter (l/d) ratios as well as poroelastic materials and frequencies of excitation. These results confirm that exclusion of the vertical shear stresses will lead to potentially very conservative design for monopiles with l/d < 6 in soft soil, and monopiles with l/d < 10 in medium to stiff soils. The computed dynamic responses of the monopile when the vertical shear stress is ignored can be up to 30% larger than the case when the vertical shear stress is considered.

Wave-Induced Dynamic Response in a Poroelastic Seabed

AbstractThis paper presents an analytical solution for the wave-induced dynamic response in a poroelastic seabed. The water waves are described by linear wave theory. The seabed was modeled using B...

Elastic rocking vibration of an offshore Gravity Base Foundation

Gravity Base Foundation is one of the main foundations in offshore wind turbine structure, and the foundation rocking stiffness mostly controls the structure fatigue life. This study models the rocking vibration of a rigid disc foundation on a poro-elastic seabed, covered by a compressible inviscid seawater half-space. The coupled rocking problem is solved using the 3-dimensional elastic wave theory. The behavior of seawater and soil are depicted with the Euler equations and the Biot's theory, respectively. The contact surface of the disc foundation with the soil and the water is assumed to be smooth. The solutions are expressed in Fredholm integral equations of the second kind and solved numerically. The obtained dynamic impedances are used to study the dynamic behavior of Gravity Base Foundations of offshore wind turbines, which are very sensitive to dynamic moments. It is found that foundation with a permeable surface has much smaller dynamic amplitudes, compared to the one with an impermeable surface. The existence of seawater half-space will also alleviate the dynamic amplitudes, but decreasing the natural frequency of the foundation.

Cnoidal wave induced seabed response around a buried pipeline

The evaluation of wave-induced pore pressures and effective stresses in a poroelastic seabed is important for coastal and ocean engineers in the design of marine structures. Most previous theoretical investigations have focused commonly on the Stokes wave induced seabed response. In this paper, a cnoidal wave–seabed–pipeline system is modeled using the finite element method. Taylor’s expression and the precise integration method are used to estimate the Jacobian elliptic function. The seabed is treated as a poroelastic medium and is characterized by Biot’s partly dynamic equations (u–p model). The pore water pressure and effective vertical stress on the poroelastic seabed around a buried pipeline are examined. Based on the numerical results, a parametric study is conducted to examine the effects of wave and seabed characteristics on the seabed response. Comparison with the cnodial wave and Stokes wave induced seabed response is also demonstrated here. It implies that the difference between the maximum pore pressure and vertical effective stress induced by the cnoidal wave and Stokes wave may reach 60–70%.

An analytical solution for wave-induced seabed response in a multi-layered poro-elastic seabed

In this study, a new analytical solution for the wave-induced seabed response in a multi-layered poro-elastic seabed is developed. The seabed is treated as a multi-layered porous medium and characterized by Biot’s theory. The displacements of the solid skeleton and the pore pressure are expressed in terms of two scalar potentials and one vector. Then, the Biot’s dynamic equation can be solved using Fourier transformation and reducing to Helmholtz equations. To obtain the general solutions for the multi-layered poro-elastic seabed in the frequency-wave-number domain, the transmission and reflection matrices (TRM) method is used to form the equivalent stiffness. Using the boundary conditions and continuous conditions, the frequency-wave-number domain solutions are obtained. Finally, the time-space domain solutions for the multi-layered poro-elastic seabed are obtained by means of the inverse Fourier transformation with respect to the horizontal coordinate. Based on the new solution, a parametric study is carried out to examine the effects of soil characteristics (number of layers, permeability and shear modulus) and wave characteristics (water depth and wave steepness) on seabed responses. The results indicate that the seabed response is affected significantly by permeability, shear modulus and relative water depth.

Analytical solution for wave-induced response of isotropic poro-elastic seabed

By use of separation of variables, the governing equations describing the Biot consolidation model is firstly transformed into a complex coefficient linear homogeneous ordinary differential equation, and the general solution of the horizontal displacement of seabed is constructed by employing a complex wave number, thus, all the explicit analytical solutions of the Biot consolidation model are determined. By comparing with the experimental results and analytical solution of Yamamoto etc. and the analytical solution of Hsu and Jeng, the validity and superiority of the suggested solution are verified. After investigating the influence of seabed depth on the wave-induced response of isotropic poro-elastic seabed based on the present theory, it can be concluded that the influence depth of wave-induced hydrodynamic pressure in the seabed is equal to the wave length.

Dynamic response of an offshore pile to pseudo-Stoneley waves along the interface between a poroelastic seabed and seawater

A coupled model is developed to investigate the dynamic interaction between an offshore pile, a porous seabed and seawater when subjected to the pseudo-Stoneley wave along the seabed and the seawater interface. The pile and the seabed are treated as the porous medium governed by Biot's theory, while the seawater is considered as an acoustic medium and is described by the conventional Helmholtz equation. The free field solution of the incident pseudo-Stoneley wave is obtained using Biot's theory and the potential method. Based on the boundary element method (BEM) for the porous medium and the acoustic medium, three BEM formulations are constructed for the pile, the seabed and the seawater, respectively, which are combined together using the continuity conditions between the pile, the seabed and the seawater to formulate the coupled model for the system. As shown in numerical examples, when the system is subjected to the pseudo-Stoneley wave, the maximum pore pressure of the seabed usually occurs at the region near the interfaces between the seabed and the seawater.

An enhanced Element-Free Galerkin method for dynamic response of poroelastic seabed

This study presents an effective numerical model for the dynamic response of poroelastic seabed under wave action with enhanced performance. The spatial discretization is based on the Element-Free Galerkin (EFG) method and the time integration based on the GN11 scheme. A stability strategy that adopts a smaller number of nodes for the pore water pressure compared with those for the displacements of the soil skeleton is suggested to resolve the similar difficulty as encountered in the finite element method for a problem with mixed formulation when the pore water is incompressible and the soil skeleton impervious. The accuracy of the numerical model is verified through applying it to a typical case with critical permeability. Good agreement between computational and analytical solutions is obtained.