Maximum Liquefaction Depth Research Articles

An analytical solution to the soil’s dynamic response induced by wave interaction with a marine current characterized by a non-uniform vertical profile

In this work, we obtain an analytical solution to the soil’s dynamic response induced by wave interaction with a marine current with a prescribed non-uniform vertical profile. The control volume used to analyze the present problem is divided into a water region and another composed of a poroelastic soil region. The governing equations for the water hydrodynamics are presented in its dimensionless version and they are simplified for the limit of linear water waves. The velocity field in the water region is determined from the continuity equation and the “inviscid Orr-Sommerfeld linear equation”. We obtain a dispersion equation for wave-current interaction. For modeling the soil’s dynamics response, we adopt the u-p approximation. Considering a characteristic criterion for soil liquefaction, the maximum liquefaction depth is obtained as an eigenvalue problem. The analytical estimations, valid for the limit of linear water waves, provided by the present analysis show that, marine currents traveling in the same direction to the wave propagation induces larger values of the liquefaction depth than those obtained for currents opposite to wave propagation. As a first approximation, the present analysis may help understand the dynamic response of poroelastic soil induced by the wave-non-uniform marine current interaction.

Dynamic Response Analysis and Liquefaction Potential Evaluation of Riverbed Induced by Tidal Bore

Tidal bores, defined by sudden upstream surges of tidal water in estuaries, exert significant hydrodynamic forces on riverbeds, leading to complex sedimentary responses. This study examines the dynamic response and liquefaction potential of riverbeds subjected to tidal bores in macro-tidal estuaries. An analytical model, developed using the generalized Biot theory and integral transform methods, evaluates the dynamic behavior of riverbed sediments. Key factors such as permeability, saturation, and sediment properties are analyzed for their influence on momentary liquefaction. The results indicate that fine sand reduces liquefaction risk by facilitating pore water discharge, while silt soil increases sediment instability. Additionally, the study reveals that pressure gradients induced by tidal bores can trigger momentary liquefaction, with the maximum liquefaction depth predicted based on horizontal pressure gradients being five times that predicted based on vertical pressure gradients. This research highlights the critical role of sediment characteristics in riverbed stability, providing a comprehensive understanding of the interactions between tidal bores and riverbed dynamics. The findings contribute to the development of predictive models and guidelines for managing the risks of tidal bore-induced liquefaction in coastal and estuarine environments.

3D numerical investigation of wave-induced seabed response around a tripod pile foundation with different arrangements

This paper developed an integrated numerical model for the dynamic response of the seabed around tripod turbine foundations under dynamic wave pressure. Three-dimensional (3D) numerical analysis is performed by applying an integrated multiphysics model developed in the finite volume method (FVM) based on the OpenFOAM framework. The present work adopts nonlinear wave model, linear elastic structure model, and anisotropic porous seabed model for wave-structure-seabed interactions. Accuracy of the wave-structure-seabed coupling process was ensured by comparing the numerical model with the numerical and experimental results. This study indicates: (1) the existence of tripods will significantly affect the consolidation results of the surrounding seabed; (2) wave force acting on the tripod structure varies with different arrangements, in which the maximum wave force under the wave crest decreases as the angle between wave and structure increases; and (3) the asymmetry 15° arrangement would significantly increase the maximum liquefaction depth of the seabed.

Dynamics of offshore wind turbine and its seabed foundation under combined wind-wave loading

Over the past two decades, a great number of offshore wind turbines (OWTs) have been built in offshore areas worldwide to harvest clean wind energy resources. The dynamic response and stability of OWTs under environmental loads, e.g., wind and wave, is a key technical problem that engineers are most concerned about. In this study, a wave-structure-foundation integrated numerical model OlaFlow–ABAQUS, which was independently developed through the secondary development, is used to study the dynamics characteristics of a thin-walled steel monopile offshore wind turbine and its seabed foundation under extreme wave and wind loads that would occur in typhoon weather. The wave-induced load imposed on the cylindrical tower of the OWT is determined by solving the VARANS (Volume Average Reynolds Average Navier-Stokes) hydrodynamic equation, the wind load on the turbine blades is estimated by applying the pulsating wind theory, and the mechanical behavior of seabed foundation soil is described by the ideal elastoplastic Mohr-Coulomb model. The computational results show that the OWT and its seabed foundation have a strong dynamic response under the combined action of extreme wind and wave, and there is intensive interaction between them. There is a transient liquefaction zone in the seabed foundation, and the maximum liquefaction depth, in this case, is approximately 2 m. Residual horizontal displacement with a magnitude of approximately 0.4 m occurs at the top of the cylindrical tower of the OWT, resulting in the overall tilting of the OWT. The maximum inclination angle of the cylindrical tower is approximately 0.51°. This angle of inclination may cause significant bending moment and stress concentration in some mechanical components such as the drive shafts and gearboxes that connect to the turbine blades. It reduces the service life of the OWT significantly and also is detrimental to the long-term service performance of the OWT.

Three-dimensional numerical simulation of wave-induced seabed response around a dumbbell-shaped cofferdam

The dumbbell-shaped cofferdam has a large-scale and complex geometric shape, which may result in a complicated fluid-structure-seabed coupling mechanism and sophisticated seabed response around the structure. To investigate the wave-induced oscillatory seabed response around a dumbbell-shaped cofferdam, this study simulates the wave-cofferdam-seabed interaction process using a numerical model within the OpenFOAM framework. In this study, the finite volume method is applied to both the wave model and seabed model, thus ensuring the computational accuracy of this study. Biot's poro-elastic theory (u-p approximation) is considered as the governing equation for the dynamic response of the porous seabed, and the fluid motions are simulated based on the Reynolds-averaged Navier–Stokes equation. First, the accuracy of the numerical model for simulating wave-induced soil response is validated against existing experiments. Next, the effects of the submerged depth, wave incidence angle, and wave height on the oscillatory pore pressure response are studied in detail. Finally, momentary liquefaction around the dumbbell-shaped cofferdam is examined. The numerical results indicate that the wave-induced oscillatory seabed response around the cofferdam is considerably affected by the wave height but less affected by the wave incident angle. Moreover, the distribution of the wave-induced pore pressure in the vicinity of the dumbbell-shaped cofferdam is complex, and the maximum liquefaction depth around the cofferdam occurs near the steel casing along the centerline of the cofferdam.

Experimental study on the dynamic response of a silty seabed under waves

Scouring and liquefaction of silty seabeds under waves have been recognized as two major modes of the seabed instability around marine structures. A series of wave experiments were conducted to investigate the wave-induced dynamic response in a silty seabed. The seabed was composed of light sand with and without geotextile covering under various wave conditions. When the seabed was not covered with geotextile, the seabed was liquefied under the action of waves, accompanied by sediment incipience and suspension. The results show that with increasing wave height, the seabed develops a series of processes such as sand ripples, ripple attenuation, sheet flow and seabed liquefaction. After seabed liquefaction occurs, an upward force gradient of the accumulated pore pressure is generated, which increases the suspended sediment concentration near the bottom and further enhances the scour of the seabed. When it is scoured, the sediment particles are continuously removed, and the stress in the soil is released, which intensifies seabed liquefaction. When the seabed is covered with geotextile, the concentration of suspended sediment near the bottom is zero. The maximum liquefaction depth of the seabed decreases along with the development rate of the liquefaction depth. The amplitude of the pore water pressure in the seabed decreases by approximately 5%–20% and seabed liquefaction is reduced. Experimental results clarify that liquefaction and scour promote each other.

Combined nonlinear wave and current induced instantaneously-liquefied soil depth in a non-cohesive seabed

Progressive waves usually coexist with a steady current in coastal environments. Superposing a following or opposite current onto the progressive waves could significantly alter the excess pore-water pressure distribution within the seabed. Unlike previous studies which were predominantly limited to the pure wave cases, the instantaneous liquefaction of a non-cohesive seabed is investigated analytically under the combined loading of 3rd order Stokes waves and a steady current. Explicit expressions are derived for the transient pore pressure distribution in a seabed with instantaneously-liquefied zone and the corresponding instantaneous liquefaction depth, which are verified by degradation analyses and comparisons with the existing offshore field observations. The phase lag of excess pore pressure is taken into account in the theoretical derivation. Parametric study is then performed to examine the effects of wave non-linearity and superimposing a current on the instantaneous liquefaction depth. It is indicated that wave-nonlinearity effects on the instantaneous liquefaction depth are not neglectable, especially when the wave height gets larger and the current velocity is reduced. The envelope for the variation of maximum instantaneous liquefaction depth with both wave period and current velocity is further constructed. To superimpose an opposing current onto the progressive waves with a relatively small wave period could be beneficial for the prevention of instantaneous liquefaction. Nevertheless, the variation trends of the maximum instantaneous liquefaction depth are attributed to the synthetical effect of the alternations of both wavelength and wave height during nonlinear wave-current interactions. • Analytical solutions for instantaneous liquefaction depth under combined Stokes 3rd order waves and a steady current. • To superimpose an opposing current onto waves could be beneficial for liquefaction prevention. • Variations of maximum liquefaction depth with wave number are attributed to the synthetical effect of wave-current interactions.

Numerical Analysis of Dynamics of Jack-Up Offshore Platform and Its Seabed Foundation under Ocean Wave

Jack-up offshore platform is a type of important marine structure, which is mainly used for satellite launch, oil exploitation, and other engineering tasks in the offshore area. The offshore platform is bound to be subjected to wave loading in the course of use. Whether it can withstand the wave impact is an important engineering problem. To solve this engineering problem, the self-developed fluid–structure–foundation interaction coupling model OlaFlow-ABAQUS is used to explore the dynamic response characteristics of a jack-up offshore platform and its seabed foundation under three conventional wave conditions (wave height is 3, 5, and 7 m, respectively) in a coupled way. The numerical results show that only a small amplitude of periodic sloshing occurs for the jack-up offshore platform under the three conventional wave conditions. The maximum sloshing amplitude is up to 8 cm, and there is no visible residual displacement. It is indicated that there is no plastic deformation zone in the seabed foundation near the pile legs of the jack-up platform. It can thus be concluded that the jack-up platform has excellent stability under conventional wave conditions. Under conventional wave loading, momentary liquefaction occurs in the seabed foundation around the pile legs of the platform, and the maximum liquefaction depth is about 1 m. This study indicates that the coupling model OlaFlow-ABAQUS for the fluid–structure–foundation interaction is feasible, and has some advantages to study the dynamic response and to evaluate the stability of large-scale marine structures and their seabed foundations under ocean waves.

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.

Numerical study of scour depth effect on wave-induced seabed response and liquefaction around a pipeline

Wave-induced liquefaction depth is a key factor in providing the safe design of submarine pipelines. However, existing numerical studies simplify the seabed as a flat foundation and ignore the effect of scour depth on wave-induced seabed response and liquefaction depth. The effects of scour depth on wave-induced seabed response and liquefaction depth around a submarine pipeline are investigated, and a three-dimensional hybrid model combining Reynolds-averaged Navier-Stokes (RANS) equations with Biot's poroelastic theory for wave propagation and anisotropic seabed is proposed in this study. Numerical results indicate that local scour leads to the redistribution of the initial effective stress within the seabed around the pipeline. With increasing scour depths, the maximum liquefaction depth beneath the pipeline simultaneously decreases. When the scour depth reaches a certain depth, the seabed seems to no longer liquefy. Parametric studies indicate that the liquefaction depth increases by either decreasing the saturation degree or increasing the wave height. Under anisotropic seabed conditions, a nonlinear relationship exists between the maximum liquefaction depth of the seabed and the seabed permeability.

Response of a Porous Seabed around an Immersed Tunnel under Wave Loading: Meshfree Model

Seabed instability surrounding an immersed tunnel is a vital engineering issue regarding the design and maintenance for submarine tunnel projects. In this study, a numerical model based on the local radial basis function collocation method (LRBFCM) is developed to evaluate the seabed behaviour in a marine environment, in which the seabed is treated as the porous medium and governed by Biot’s “ u − p ” approximation. As for the flow field above the seabed, the VARANS equations are used to simulate the fluid motion and properties. The present model is validated with analytical solutions and experimental data which show a good capacity of the integrated model. Both wave and current loading are considered in this study. Parametric studies are carried out to investigate the effects of wave characteristics and soil properties. Based on the numerical results, the maximum liquefaction depth around the immersed tunnel could be deeper under the wave loading with long wave period (T) and large wave height (H). Moreover, a seabed with lower permeability ( K s ) and degree of saturation ( S r ) is more likely to be liquefied.

Effect of vertical seismic motion on the dynamic response and instantaneous liquefaction in a two-layer porous seabed

The evaluation of seismic-induced responses in a porous seabed is a fundamental problem in geotechnical and coastal engineering. Although ground motions generally include both horizontal and vertical components, a majority of previous theoretical investigations assumed vertically propagating shear waves in a horizontally layered soil–rock system and simply ignored the effect of site response to vertical earthquake motion. In this paper, the dynamic response and instantaneous liquefaction of a porous seabed that is induced by vertical earthquake loading is studied using an analytical method. The seabed is treated as a two-layer poroelastic medium and characterized by the dynamic formulation of Biot theory. The analytical solutions for the response variables, such as induced displacement, pore pressure and vertical effective stress, are derived individually, and the mechanism of instantaneous liquefaction in liquefiable sediment is investigated based on the excess pore pressure criterion. A set of parametric analysis is performed to discuss the effects of seawater, the seabed and earthquake parameters on the seismic response and maximum liquefaction depth. It is worth noting that the properties of the surface seabed layer have a significant influence on the seismic response and, consequently, the potential stability of the seabed, which is important in the analysis of offshore structure foundations.

Dynamic response of a poro-elastic soil to the action of long water waves: Determination of the maximum liquefaction depth as an eigenvalue problem

In this work, a theoretical analysis of the dynamic response of a poro-elastic soil to the action of long water waves is conducted. For some combinations of the physical parameters of the soil and the water waves, the vertical stress tends towards zero at a certain unknown depth in the soil, as measured from the top of that medium. Under this condition, the liquefaction of the soil is imminent, at which time the excess pore pressure is essentially equal to the overburden soil pressure. Physical problems of this type have been widely studied in the specialized literature. However, most major studies have focused on solving the governing equations together with a liquefaction criterion. Here, the maximum momentary liquefaction depth induced by long water waves is considered as part of the problem, which is treated as an eigenvalue problem. To solve this problem, the governing equations are written in dimensionless form. The theoretical results show that for long waves, the horizontal displacements are smaller in magnitude than the vertical displacements, and when the wavelength or wave period increases, the maximum liquefaction also increases. Analytical solutions for the excess pore pressure and the horizontal and vertical displacements are obtained. The analytical results for the pore pressure are found to be very close to the analytical results reported in the specialized literature.

Numerical study on loosely deposited foundation behavior around a composite breakwater subject to ocean wave impact

In this study, an integrated model is developed to investigate the potential risk for failure of caisson-type breakwaters caused by liquefaction in its loosely deposited sand foundations. In the present model, the Volume-Averaged Reynolds Averaged Navier-Stokes (VARANS) equations are used for solving flow inside and outside the porous media, while Biot's consolidation equation is used for linking the soil skeleton-pore fluids interactions. A new developed poro-elastoplastic model is implemented to reproduce the behavior of loose sand foundation under cyclic shearing. Verification of the present numerical framework includes (i) comparison with the laboratory experiments in terms of water surface levels around the structure, and the fluctuating component of the pore water pressure inside the rubble mound and seabed foundation; and (ii) comparison with the geotechnical centrifugal wave tests for the wave-induced residual component of pore water pressures in a porous seabed. Based on the present model, the hydrodynamic process and the associated dynamic foundation behavior involved in the interactions between the ocean waves, a composite breakwater and its loose sand foundations was performed and analyzed. Particular focus is put on the residual pore pressure development and the resulting liquefaction around the structure under combined actions of both wave and structure rocking motions. Based on the numerical examples presented, under combined actions of both wave and caisson motions, liquefaction starts on both edges of the breakwater and spreads sideways until reaching an equilibrium state where the maximum liquefaction depth can be observed. The liquefied zone around the breakwater is asymmetric in nature, and the maximum depth of soil liquefaction appears at the seaward side of the structure. Furthermore, the parametric study indicates that the maximum liquefaction depth around the composite breakwater increases with increasing wave steepness (H/L0) and relative water depth (d/L0) and decreasing soil permeability (ks).

Parametric study of the wave-induced residual liquefaction around an embedded pipeline

Wave-induced liquefaction in a porous seabed around submarine pipeline may cause catastrophic consequences such as large horizontal displacements of pipelines on the seabed, sinking or floatation of buried pipelines. Most previous studies in relation to the wave and seabed interactions with embedded pipeline dealt with the wave-induced instaneous seabed response and possible resulting momentary liquefaction (where the soil is liquefied instantaneously during the passage of a wave trough), using theory of poro-elasticity. Studies for the interactions between a buried pipeline and a soil undergoing build-up of pore pressure and residual liquefaction have been comparatively rare. In this paper, this complicated process was investigated by using a new developed integrated numerical model with RANS (Reynolds averaged Navier–Stokes) equations used for governing the incompressible flow in the wave field and Biot consolidation equations used for linking the solid–pore fluid interactions in a porous seabed with embedded pipeline. Regarding the wave-induced residual soil response, a two-dimensional poro-elastoplastic solution with the new definition of the source term was developed, where the pre-consolidation analysis of seabed foundation under gravitational forces including the body forces of a pipeline was incorporated. The proposed numerical model was verified with laboratory experiment to demonstrate its accuracy and effectiveness. The numerical results indicate that residual liquefaction is more likely to occur in the vicinity of the pipeline compared to that in the far-field. The inclusion of body forces of a pipeline in the pre-consolidation analysis of seabed foundation significantly affects the potential for residual liquefaction in the vicinity of the pipeline, especially for a shallow-embedded case. Parametric studies reveal that the gradients of maximum liquefaction depth with various wave and soil characteristics become steeper as pipeline burial depth decreases.

Effects of cross-anisotropic soil behaviour on the wave-induced residual liquefaction in the vicinity of pipeline buried in elasto-plastic seabed foundations

In this paper, a two-dimensional integrated numerical model is developed to examine the influences of cross-anisotropic soil behaviour on the wave-induced residual liquefaction in the vicinity of a pipeline buried in a porous seabed. In the wave model, the RANS (Reynolds Averaged Navier–Stokes) equation is used to govern the wave motion. In the seabed model, the residual soil response in the vicinity of an embedded pipeline is considered with the 2-D elasto-plastic solution, where the phase-resolved shear stress is used as a source for the build-up of residual pore pressure. Classical Biot׳s consolidation equation is used for linking the solid-pore fluid interaction. The validation of the proposed integrated numerical model is conducted by the comparisons with the previous experimental data. Numerical examples show that the pore pressures can accumulate to a large value, thus resulting in a larger area of liquefaction potential in the given anisotropic soil compared to that with isotropic solution. The influences of anisotropic parameters on the wave-induced residual soil response in the vicinity of pipeline are significant. A high rate of pore pressure accumulation and dissipation is observed and the liquefaction potential develops faster as the anisotropic parameters increase. Finally, a simplified approximation based on a detailed parametric investigations is proposed for the evaluation of maximum liquefaction depth (zL) in engineering application.

Breaking wave-induced response of composite breakwater and liquefaction in seabed foundation

In the practice of engineering, breaking wave is much more dangerous for the stability of composite breakwater built on porous seabed than non-breaking wave in offshore area. In previous investigations or design codes, the empirical formulations generally were adopted to estimate the wave impact acting on the lateral side of caisson. The interaction between breaking wave, seabed foundation and composite breakwater is not taken into consideration. In this study, adopting the integrated numerical model PORO-WSSI 2D developed by (Ye, 2012a) and (Jeng et al., 2013), the interaction mechanism between breaking wave, seabed foundation and composite breakwater is investigated numerically. In PORO-WSSI 2D,the Volume-Averaged Reynolds Averaged Navier–Stokes (VARANS) equations govern the wave motion and the porous flow in seabed foundation and in rubble mound; and the dynamic Biot's equations (known as “u-p” approximation) govern the dynamic behaviors of seabed foundation and composite breakwater under breaking wave loading. Numerical analysis indicates that the turbulent energy of breaking wave is significant, and the wave impact on caisson applied by breaking wave is much greater than non-breaking wave. The composite breakwater and its seabed foundation respond to the breaking wave loading intensively. The maximum horizontal vibration magnitude of the composite breakwater is up to 5mm; the maximum liquefaction depth in the seabed in front of the composite breakwater reaches up to 1.2 to 1.6m. The parametric study shows that the permeability and saturation of seabed, wave height are three dominant factors for the wave-induced liquefaction in seabed foundation.

Dynamic Response in a Porous Seabed of Finite Depth to Combined Wave and Current Loadings

Liu, B.; Jeng, D.S., and Zhang, J.S., 2014. Dynamic response in a porous seabed of finite depth to combined wave and current loadings. In this study a u-p approximation for the dynamic response of a porous seabed to nature dynamic loadings is proposed. Unlike most previous research, the effects of currents are considered in the new analytical solution. Based on the numerical examples, the significant influence of combined wave and current loadings on seabed response in shallow water is concluded. This influence affects not only the amplitudes of the seabed response but also the distributions of the space region. The relative difference of the maximum pore pressure between different direction currents can reach 8% of the static water pressure. In addition, the relative difference of maximum liquefaction depth between the previous model (without currents) and the present model can reach 19% of the maximum liquefaction depth of the case without currents.

An Analytical Approximation for Dynamic Soil Response of a Porous Seabed due to Combined Wave and Current Loading

Liao, C.C.; Jeng, D.-S., and Zhang, L.L., 2015. An analytical approximation for dynamic soil response of a porous seabed due to combined wave and current loading.This paper presents a new analytical approximation for wave (current)–induced dynamic soil response. In this study, unlike in previous research projects, full dynamic soil behaviour was considered. The nonlinear waves propagating over an infinite seabed with uniform current were investigated, and the new analytical solution was validated with the previous field observations and laboratory experiments. The effects of currents and wave nonlinearity were examined based on the proposed analytical solution. Finally, a parametric study was carried out to examine the influence of the wave and seabed characteristics on the seabed response. As the numerical examples demonstrated, the effects of currents on the seabed response are significant only in the top region of the seabed (comprising approximately 10% of the wavelength). Based on parametric study, it is concluded that currents with third-order wave loading and full dynamic soil behaviour cannot always be ignored in the estimation of the wave-induced seabed responses, especially for almost-saturated soil, long-wave periods, and shallow water. A significant difference was also observed in the maximum liquefaction depth between the full dynamic and the consolidation models.

An analytical solution for response of a porous seabed to combined wave and current loading

In this paper, an analytical approximation for the evaluation of the pore pressure and effective stresses in marine sediments under combined wave and current loadings is derived. Unlike previous investigations, non-linear interactions between waves and currents are considered in this study. An analytical solution for the wave–current induced oscillatory soil response in marine sediment is presented first. Based on the proposed analytical solution, a parametric study for the liquefaction potential will be carried out. Parametric study results indicate that the influence of current and non-linear waves on the maximum liquefaction depth is significant.