Instantaneous Liquefaction Research Articles

Phase-lag effect on the instantaneously-liquefied seabed depth under progressive waves: Explicit approximations

Instantaneous liquefaction can be induced by the upward seepage force while waves propagating over a porous seabed. In this study, the instantaneous liquefaction within a non-cohesive seabed under progressive waves is analytically investigated and verified with the existing offshore observations. To characterize the instantaneous liquefaction potential, the vertical gradient of excess pore-pressure is employed, and the explicit solutions for the liquefied soil depth are then derived to reflect the phase-lag effect. Wave scale effect is further examined by comparative analysis of the liquefaction potential between laboratory and field conditions. It is indicated that, due to the phase-lag effect, the maximum liquefaction potential and the maximum liquefied soil depth no longer appear exactly under the wave trough; nevertheless, such phase difference relative to the wave trough wouldn't exceed π/4. Neglecting the phase-lag effects would considerably underestimate the liquefaction potential as well as the liquefaction depth. Moreover, both the liquefaction potential and the corresponding liquefied soil depth are predominantly related to the non-dimensional parameter Ic for characterizing the combined influence of wave and seabed properties.

Wave-Induced Instantaneous Liquefaction of a Non-Cohesive Seabed around Buried Pipelines: A Liquefaction-Associated Non-Darcy Flow Model Approach

In complex marine environments, the wave-induced instantaneous liquefaction of the seabed is a key issue for the long-term safety control of marine structures. Existing computational frameworks for instantaneous liquefaction result in unreasonable tensile stresses in a non-cohesive seabed. To address this issue, a liquefaction-associated non-Darcy flow model has been proposed, but it has only been applied to the scenario of a pure seabed without a structure. In this study, we applied the previously proposed non-Darcy flow model to investigate the mechanism of wave–seabed–structure interactions under extreme wave loading considering a pipeline fully buried in a non-cohesive seabed. By comparing the liquefaction depths in the presence and absence of structures, it was found that the existence of structures weakens the attenuation of the pore pressure amplitude and influences the overall pore pressure distribution. Parametric studies were conducted. It was found that the liquefaction depth from the non-Darcy model is approximately 0.73 times that from the traditional Darcy model, regardless of whether or not a pipeline is involved. A quantitative relationship between the wave loading and structural size was established. The liquefied zone above the buried pipeline was found to be smaller than that in a pure seabed without a structure. A tentative explanation is provided for this phenomenon.

Dynamic responses of a transversely isotropic poroelastic seabed subjected to nonlinear random waves with emphasis on liquefaction depth

Seabed instability is one of the important causes that lead to the failures of marine structures. Most previous works on seabed instability are limited to regular surface waves and linear random waves while nonlinear random waves are seldom touched. Hence, in this study, the hydrodynamic pressure of nonlinear random waves up to the second order is derived first. Then the analytical solutions of the dynamic responses of a transversely isotropic poroelastic seabed under the nonlinear hydrodynamic pressure are developed. The solutions are validated against analytical and experimental works in literature. The frequency response functions of pore water pressure, shear stress, vertical effective stress and horizontal effective stress are presented and discussed in the frequency domain. The influences of significant wave height, peak wave period and water depth on the dynamic responses and liquefaction depths of soil are analyzed in the time domain. The nonlinear random waves, linear random waves, linear regular waves and the second-order Stokes waves are compared in both time and frequency domains in terms of their influences on the dynamic responses and liquefaction depths of soil. The results reveal that the dynamic responses induced by second-order random waves are always greater than that induced by linear random waves, and much greater than that induced by equivalent linear waves and the second-order Stokes waves. The seabed may not liquefy under regular waves but does liquefy under random waves. Furthermore, the instantaneous liquefaction depths of soil caused by the second-order random waves are up to 23.5% larger than that induced by linear random waves. Therefore, the nonlinear random waves are recommended for the finite water depth use in engineering practice. In addition, the frequency-difference term plays an important role in soil liquefaction.

Analytical Calculation of Instantaneous Liquefaction of a Seabed around Buried Pipelines Induced by Cnoidal Waves

Cnoidal wave theory perfectly describes nearshore wave characteristics. However, cnoidal wave theory is not widely applied in practical engineering because the formula for the wave profile involves a complex Jacobian elliptic function. In this paper, the approximate cnoidal wave theory is presented. Based on the Biot consolidation theory and the approximate cnoidal wave theory, an analytical solution for the pore water pressure around buried pipelines caused by waves is derived. In addition, based on the principle of effective stress, a theory of soil liquefaction around pipelines is proposed. The theoretical results were virtually identical to the results obtained in a practical flume test. Thus, the analytical method proposed in this paper is feasible. Further, the theory is applied to analyze the instantaneous liquefaction of the seabed around buried pipelines and the stability of the pipeline in the Chengdao oilfield.

Evaluation of wave-induced instability of nearly saturated sandy slopes under partially undrained condition: A case study of landslide in Fraser River delta front

A significant amount of Methane gas in soil deposits at Fraser River Delta (FRD), Canada, was identified as it adversely impacted the stability of the sloping seabed in the area under waves and tides. In this study, an integrated FEM model is utilized to investigate the instability of FRD front due to 1985 storm waves. Despite earlier studies that focused only on the role of residual pore pressure reached at late wave cycles in inducing the slide of FRD front (using empirical correlations), the transient response of sediments at early wave cycles is considered herein. The effect of coupled-flow-and-deformation processes within the sediments on the extent of the sliding plane is considered. For wave-seabed interaction modeling, Biot’s poroelasticity and linear wave theory are employed to represent the fluid and seabed domains, respectively. The slide evaluation of the sloping seabed is conducted using Strength Reduction Technique with Mohr-Coulomb failure criterion. The results indicate that the storm waves cause a shallow slide within the slope, and the proximity of the unsaturated layer to mudline exacerbated the instability condition. Moreover, instantaneous liquefaction zones are found to emerge away from the slope; thus, they may not lead to an exacerbated sliding of the slope.

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.

NATURAL PROCESSES AS JUSTIFICATION FACTORS FOR DECISIONS ON PORT HYDRAULIC STRUCTURES

The effects of sea waves and currents on harbour hydraulic structures are analysed from published open source data and the characteristics of scour from waves, including tsunami waves, are considered. Local bottom scour threatening the general stability of gravity-type engineering structures can arise under the effect of storm waves and currents, jets from ship propulsion devices and tsunami waves near hydraulic engineering structures. The types of scour mechanisms from sea waves have been investigated, i.e., local, general, and overtopping scour. There is a lack of sufficient measurement data for general scour to verify the calculation methods. Generally, general scour does not damage a structure, although it can contribute to its destruction by other types of scour when they overlap. Therefore, existing studies mainly focus on the analysis of local scour. The relationship between local scour and ground liquefaction and their influence on the stability of marine hydraulic structures is established. Failure mechanisms of hydraulic structures due to erosion by tsunami waves are analyzed: leeward and seaward toe scour, crown armour failure, parapet wall failure, sliding failure. The tsunami wave scour enhancement parameter is given, which is the fraction by which the pore pressure gradient reduces the frictional forces resisting scour. Significant ground instability occurs when the scour amplification parameter Λ exceeds a value of 0.5 (Λ ≥ 0.5). The parameter Λ can be used to assess areas where instantaneous liquefaction may be responsible for scour and sediment movement and to further recalculate erosion depths obtained without considering liquefaction. Liquefaction from a tsunami wave may penetrate up to 28% of the maximum erosion depth due to shear forces. The liquefaction phenomenon may occur due to a sudden drop in the water level in the area of return flow concentration. Consequently, the liquefaction phenomenon must be considered in the stability and erosion analysis around the structure.

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.

Numerical analysis of the seabed liquefaction around a fixed gravity-based structure (GBS) of an offshore platform and protection

The fixed gravity-based structure (GBS) platform has been widely constructed offshore in support of exploring and drilling activities for oil and gas industry. The aim of the present study is to investigate the wave-induced instantaneous liquefaction of a poro-elastic seabed around a GBS offshore platform, including the consideration of the effect from the platform deck. Our approach is using an integrated three-dimensional numerical model that developed based on the Finite Volume method (FVM) in OpenFOAM. In addition, a protection system for the GBS platform has been proposed and its effect on the prevention of the wave-induced momentary liquefaction have been demonstrated. A series of simulations are performed, including a consolidation process, the fluid–structure–seabed interactions and the wave-induced liquefaction and shear failure near the GBS. Numerical results reveal that the proposed protection system can significantly reduce the wave forces and the liquefaction depth in front of the platform. The parametric study reveals that the wave height and current velocity have significant impact on the seabed liquefaction in the vicinity of the GBS offshore platform. The protecting effect of the protection piles decreases with increasing of the column spacing and the distance from the GBS.

Response and Instability of Sloping Seabed Supporting Small Marine Structures: Wave–Structure–Soil Interaction Analysis

Abstract Wave-induced liquefaction in seabed may adversely impact the stability and bearing capacity of the foundation elements of coastal structures. The interaction of wave, seabed, and structure has been studied mostly for only mildly sloping seabed (<5deg) using a decoupled approach. However, some of the marine hydrokinetic devices (MHKs) may be built on or anchored to the seabed with significant steepness. The wave-induced response and instantaneous liquefaction within sloping seabed supporting a small structure (representing a small MHK device) are evaluated herein by developing an almost fully coupled finite element model. The effects of coupling approach on the stress response and liquefaction of the seabed soils are investigated. Subsequently, post-liquefaction deformation of seabed soils around the structure is assessed. The poroelasticity equations governing the seabed response coupled with those for other domains are solved simultaneously. For post-liquefaction analysis, the soil is modeled as elastic-perfectly plastic material. The development of instantaneously liquefied zones near the foundation is studied in terms of seabed steepness and wave parameters. The changes in the effective stress paths due to the development of liquefied zones are evaluated in view of the soil's critical state. The results indicate that the decoupled solution yields significantly larger stresses and liquefaction zones around the structure. The seabed response and the liquefaction zones become smaller for steeper slopes. The presence of liquefied zones brings the stress state closer to the failure envelope, reduces the confining stresses, and induces larger plastic strains around the foundation element.

Modelling of dynamic response and instability of caisson-type quay wall–soil system under waves

In this study, the dynamic response and instability of a low-permeability deformable caisson-type quay wall (CQW) with backfill soil exposed to standing waves is evaluated. The focus is on the dynamic response and instantaneous liquefaction of seabed and backfill around the CQW. This study aims at closing the knowledge gap about the wave-induced CQW–seabed response without the presence of a breakwater, as the bulk of the prior research has been done on CQWs considering earthquakes as the primary loading source. Finite elements are used, and numerical results are obtained in terms of displacements, pore-pressure and shear stress variations in temporal and spatial domains. Wave-induced instantaneous liquefaction is analysed, and analyses are performed to determine the effect of soil/wave properties on dynamic response and liquefaction. Results indicate that there is considerable liquefaction potential in both seabed and backfill that may play a key role in the stability of the CQW. While such a response is dependent upon the induced wave energy and the CQW motion, seabed parameters alter the instantaneous liquefaction occurrence as well. A slight decrease in the seabed degree of saturation causes a contraction behaviour under the wave-induced motion of the CQW, which, in turn, affects the mechanism of response and the initiation of instability in the seabed.

A non-Darcy flow model for a non-cohesive seabed involving wave-induced instantaneous liquefaction

Prediction of wave-induced instantaneous (oscillatory or momentary) liquefaction is particularly important for the design of offshore foundations. Most previous studies applied the linear Darcy model to characterize the porous flow in a seabed. This treatment was found to cause fallacious tensile stresses in a non-cohesive seabed. In this study, to overcome such shortcomings of previous models, a non-Darcy flow model is proposed based on a Karush–Kuhn–Tucker (KKT) condition. In the KKT condition, the primal constraint arises from the fact that the tensile behavior does not exist in a non-cohesive seabed, while the dual condition arises from the physical evidences that the pore-fluid velocity increases during liquefaction. The non-linearity of the present model is handled by the Newton–Raphson method within the standard finite element framework, without coding constrained variational principle. This highlights the convenience for numerical implementation. The difficulties in treating the nonlinearity by previous dynamic permeability model are also eliminated by the non-Darcy flow model. The merits of the proposed model are validated by examining four numerical treatments and two liquefaction criteria. The liquefaction depth by the present model is found to be roughly 0.73 times of the value by the linear Darcy model.

Modelling the wave-induced instantaneous liquefaction in a non-cohesive seabed as a nonlinear complementarity problem

The estimation of the wave-induced instantaneous liquefaction is particularly important for the design of foundations of offshore structures. Regarding the occurrence of liquefaction in a non-cohesive seabed, most existing studies using constant permeability were found to cause fallacious tensile stresses in the liquefied zone and further pollute the overall pore pressure distribution. A dynamic permeability model was previously presented to mitigate the shortcoming but posed difficulties in the nonlinear convergence. To overcome the shortcoming of the previous studies, this study proposes the concept of modelling the liquefaction-involved wave-seabed interactions as a nonlinear complementarity problem, wherein a Karush–Kuhn–Tucker condition is constructed, based on revisiting the liquefaction criterion most widely applied in ocean engineering. The Lagrange multiplier method and the primal–dual active set strategy are employed to numerically deal with the nonlinear complementarity problem. The performance of the chosen multiplier space is investigated by theoretical analyzing and numerical modelling. Compared with the previous dynamic permeability model, the present model is totally free of extra parameters and precisely fulfills the no-tension requirement. Moreover, the difficulties of dynamic permeability in the nonlinear convergence are overcome and no divergence is observed in the numerical tests.

A new model for wave-induced instantaneous liquefaction in a non-cohesive seabed with dynamic permeability

Wave-induced instantaneous liquefaction is crucial to evaluating the stability of offshore foundations. For the instantaneous liquefaction, most previous studies treated the seabed as an invariant poro-elastic medium and hence led to nonphysical tensile stress in the non-cohesive liquefied zone. In this study, a penalty-like dynamic permeability model is proposed, based on the experimental evidences of permeability increase during soil liquefaction. The nonlinearity induced by the dynamic permeability is solved by an iterative procedure, based on the Newton-Raphson method. The numerical procedure is implemented in an in-house code and compared with analytical solutions under the constant permeability assumption. Numerical observations validate that the proposed dynamic permeability model can alleviate or even eliminate the nonphysical tensile stress in the instantaneously-liquefied zone. In contrast to the constant permeability model, the new model with a dynamic permeability obtains a better agreement with existing cylinder tests under one-dimensional wave loading conditions. For the numerical examples presented, the liquefaction depths predicted by constant permeability can be up to twice of those by the new dynamic permeability model. It is concluded that the conventional model with constant permeability overestimates the liquefaction potential.

Dynamic response and liquefaction analysis of seabed-rubble mound breakwater system under waves

Dynamic response and liquefaction potential of granular seabed around a rubble mound breakwater is investigated under waves. Dynamic response of the system is assumed to be governed by coupled Biot equations of poroelasticity. Mathematical formulations in terms of governing equations of partially-dynamic and quasi-static cases are considered. Dynamic response of seabed soil is analyzed using classical finite elements and a number of parametric studies are performed to draw a complete picture of the response of the system. Vertical displacement, shear stress and pore water pressure distributions are considered as the most representative variables defining the variations of response of the whole system and which are thus evaluated along some key cross sections around the breakwater. The results indicate that inertial terms associated with solid skeleton have almost no effect on the dynamic response and liquefaction potential. It was found that large amount of wave-induced shear stresses are taken by a relatively rigid core layer contributing to the breakwater stability where also the pore pressures dissipate significantly towards the seabed interface. Standing wave-induced instability of the system is also investigated in terms of instantaneous liquefaction based on the effective mean stress criterion. There is liquefaction observed at the seaward surface of the rubble whose depth increases significantly with decreasing saturation. While the core overall provides more stability, the adverse effect of this is more liquefaction in the outer layer.

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.

Wave induced instantaneously-liquefied soil depth in a non-cohesive seabed

Instantaneous liquefaction can be induced by the upward seepage force generated in a sandy seabed under wave troughs. The wave-induced pore-pressure distribution in the non-cohesive seabed with an instantaneously-liquefied layer is investigated analytically. Based on the analytical solution to Biot's consolidation equations for the response of a poro-elastic bed to water waves, the expressions of liquefied soil depth are derived with modifying the criterion for instantaneous liquefaction, which is verified with existing offshore field observations and multi-scale numerical simulations. Analytical investigation indicates that, in the instantaneously-liquefied soil layer, the buoyant weight of soil is essentially balanced by upward seepage force into a quasi-static state. Underneath the fully liquefied layer, the effective stress can be remarkably reduced. An excess pore-pressure ratio is then proposed to quantitatively evaluate the instantaneous liquefaction degree and its corresponding influential depth. Parametric studies indicate that, for a certain excess pore-pressure ratio, the influential depth decreases with increasing saturation degree, permeability of soil or water depth, but increases with increasing wave height. The influential depth of a non-cohesive seabed under waves increases significantly with reducing the threshold value of excess pore-pressure ratio, which may have much influence on the stability design for submarine structures.

Significance of seismites in the Late Cretaceous transgressive Nimar Sandstone succession, Son-Narmada rift valley, Central India

Detailed facies architecture study of the Late Cretaceous (Cenomanian) Nimar Sandstone (Bagh Group), from Son-Narmada rift valley, Central India, reveals deposition in a fluvial–marine environment. The lower part of the Nimar Sandstone succession depicts deposition in predominantly fluvial setting, whereas the middle–upper part of the succession manifests sedimentation under a tide-dominated estuarine to a tide–wave influenced shoreface environment. Retrogradational nature of the successions in the upper part and lateral facies change from west to east signifies an eastwardly decreasing marine influence. This attests to a sustained event of marine transgression from the west affecting the Son-Narmada rift valley during the Late Cretaceous time. Beds with various soft-sediment deformation structures (SSDS), viz., convolute laminae, load and flame structures, pseudonodules, contorted beddings, syn-sedimentary faults, and sand/silt dykes, occur in distinct stratigraphic levels within the middle part of the succession. These beds are separated by thick successions of undeformed beds. This paper reports these beds as seismites for the first time from the Son-Narmada rift valley. The seismites signify instantaneous liquefaction and fluidization of unconsolidated sediments triggered by passage of repetitive earthquake shock waves during sedimentation in fault-bound rift basin. These seismites are important as they mark a new phase of reactivation of the Son-Narmada South Fault within the Son-Narmada rift valley during the Cenomanian time. This reactivation of the Son-Narmada South Fault led to basinal subsidence under prevalent extensional tectonism, which controlled the sedimentation during the Late Cretaceous time. Copyright © 2016 John Wiley & Sons, Ltd.

Pore Pressure, Stress Distributions, and Instantaneous Liquefaction of Two-Layer Soil under Waves

AbstractIn this paper, shear, effective stress and pore pressure distributions of two-layer porous soils subjected to harmonic waves are presented. The instability of the porous soil because of wave loading is investigated in terms of instantaneous liquefaction. The governing equations are written in their fully dynamic form, and possible simplifications are introduced. Finite-element models are developed for each formulation, and numerical results are verified with their corresponding analytical solutions, which are also developed here. Then, the problem of a two-layer soil under waves both in an open domain and in front of a vertical wall is studied in terms of dynamic response variations and regions of instantaneous liquefaction. Both linear and nonlinear waves are considered. Finally, a number of parametric studies to investigate the effect of a surface clay layer, inertial terms in the equations, various soil and wave parameters, and wave nonlinearity on the dynamic behavior and instability are carri...

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

SUMMARYBreaking‐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.