Wave-induced Pressure Research Articles

Fracture connectivity can reduce the velocity anisotropy of seismic waves

Abstract The degree of connectivity of fracture networks is a key parameter that controls the hydraulic properties of fractured rock formations. The current understanding is that this parameter does not alter the effective elastic properties of the probed medium and, hence, cannot be inferred from seismic data. However, this reasoning is based on static elasticity, which neglects dynamic effects related to wave-induced fluid pressure diffusion (FPD). Using a numerical upscaling procedure based on the theory of quasi-static poroelasticity, we provide the first evidence to suggest that fracture connectivity can reduce significantly velocity anisotropy in the seismic frequency band. Analyses of fluid pressure fields in response to the propagation of seismic waves demonstrate that this reduction of velocity anisotropy is not due to changes of the geometrical characteristics of the probed fracture networks, but rather related to variations of the stiffening effect of the fracture fluid in response to FPD. These results suggest that accounting for FPD effects may not only allow for improving estimations of geometrical and mechanical properties of fracture networks, but may also provide information with regard to the effective hydraulic properties.

Investigation of nonlinear wave-induced seabed response around mono-pile foundation

Stability and safety of offshore wind turbines with mono-pile foundations, affected by nonlinear wave effect and dynamic seabed response, are the primary concerns in offshore foundation design. In order to address these problems, the effects of wave nonlinearity on dynamic seabed response in the vicinity of mono-pile foundation is investigated using an integrated model, developed using OpenFOAM, which incorporates both wave model (waves2Foam) and Biot's poro-elastic model. The present model was validated against several laboratory experiments and promising agreements were obtained. Special attention was paid to the systematic analysis of pore water pressure as well as the momentary liquefaction in the proximity of mono-pile induced by nonlinear wave effects. Various embedded depths of mono-pile relevant for practical engineering design were studied in order to attain the insights into nonlinear wave effect around and underneath the mono-pile foundation. By comparing time-series of water surface elevation, inline force, and wave-induced pore water pressure at the front, lateral, and lee side of mono-pile, the distinct nonlinear wave effect on pore water pressure was shown. Simulated results confirmed that the presence of mono-pile foundation in a porous seabed had evident blocking effect on the vertical and horizontal development of pore water pressure. Increasing embedded depth enhances the blockage of vertical pore pressure development and hence results in somewhat reduced momentary liquefaction depth of the soil around the mono-pile foundation.

Wave-Induced Pressure Distribution on Placed Perforated Revetment Block

In order to evaluate the stability of revetment block against wave attack, the information about hydrostatic pressure distribution induced by the wave is needed. In this paper, a simple mathematical model is developed to calculate the pressure distribution on revetment, which taking the effect of flow in filter layer and the perforated surface of revetment block into account. Physical test were done to observe the flow in filter and the coefficient discharge of perforated surface. The effect of filter and perforated surface latter on will called as filter-pore parameter. Model investigation were also performed on various filter under the loading condition which represent the wave loading. The result of this model investigation were compared to the mathematical model, and shows a great agreement between both of them. The result from both simulation shows that the filter-pore parameter has a great influence on the hydrostatic-pressure that act on the revetment block.

Breaking phase focused wave group loads on offshore wind turbine monopiles

The current method for calculating extreme wave loads on offshore wind turbine structures is based on engineering models for non-breaking regular waves. The present article has the aim of validating previously developed models at DTU, namely the OceanWave3D potential flow wave model and a coupled OceanWave3D-OpenFOAM solver, against measurements of focused wave group impacts on a monopile. The focused 2D and 3D wave groups are reproduced and the free surface elevation and the in-line forces are compared to the experimental results. In addition, the pressure distribution on the monopile is examined at the time of maximum force and discussed in terms of shape and magnitude. Relative pressure time series are also compared between the simulations and experiments and detailed pressure fields for a 2D and 3D impact are discussed in terms of impact type. In general a good match for free surface elevation, in-line force and wave-induced pressures is found.

Evaluation of storm wave-induced silty seabed instability and geo-hazards: A case study in the Yellow River delta

Models based on the theoretical framework of soil mechanics are presented to evaluate storm wave-induced silty seabed instability and geo-hazards through a case study in the Yellow River delta. First, the transient and residual mechanisms of wave-induced pore pressure are analyzed. Three typical models (i.e., elastic model, pore pressure development mode and elasto-plastic model) are proposed to calculate wave-induced stresses in the seabed. Next, mechanisms and calculation methods of wave-induced seabed instability modes such as scour, liquefaction, seepage instability and shear slide are proposed. Typical results of storm wave-induced excess pore pressure and seabed instability are given and relevant discussions are made. At last, the formation mechanism of geo-hazards in the Yellow River delta is analyzed based on the proposed mechanism and calculated results. Results and analysis indicate that both transient and residual mechanisms are important to storm wave-induced response of silty seabed and hence the elasto-plastic model is more appropriate. Complete liquefaction does not happen, while other types of instability occur mostly within 2–6m under the seabed surface. Wave-induced scour, seepage instability and shear slide are all possible instability modes under the 1-year storm waves, and scour is predominant for the 50-year storm waves. The formation mechanism of geo-hazards such as shallow slide and storm wave reactivation, pockmarks, silt flow and gully, disturbed stratum and hard crust in the Yellow River are well explained based on the proposed mechanisms and calculated results of storm wave-induced silty seabed instability.

Representative elementary volumes for evaluating effective seismic properties of heterogeneous poroelastic media

Understanding and quantifying seismic energy dissipation in fluid-saturated porous rocks is of considerable interest because it offers the perspective of extracting information with regard to the elastic and hydraulic rock properties. An important, if not dominant, attenuation mechanism prevailing in the seismic frequency band is wave-induced fluid pressure diffusion in response to the contrasts in elastic stiffness in the mesoscopic-scale range. An effective way to estimate seismic velocity dispersion and attenuation related to this phenomenon is through the application of numerical upscaling procedures to synthetic rock samples of interest. However, the estimated seismic properties are meaningful only if the underlying sample volume is at least of the size of a representative elementary volume (REV). In the given context, the definition of an REV and the corresponding implications for the estimation of the effective seismic properties remain largely unexplored. To alleviate this problem, we have studied the characteristics of REVs for a set of idealized rock samples sharing high levels of velocity dispersion and attenuation. For periodically heterogeneous poroelastic media, the REV size was driven by boundary condition effects. Our results determined that boundary condition effects were absent for layered media and negligible in the presence of patchy saturation. Conversely, strong boundary condition effects arose in the presence of a periodic distribution of finite-length fractures, thus leading to large REV sizes. The results thus point to the importance of carefully determining the REV sizes of heterogeneous porous rocks for computing effective seismic properties, especially in the presence of strong dry frame stiffness contrasts.

Wave-induced pressures in porous bonded revetments. Part I: Pressures on the revetment

Revetments made of polyurethane bonded aggregates (PBA) are a recent alternative to mitigate coastal erosion. Their advantages over conventional impermeable revetments are shown in previous studies, based on large-scale laboratory tests (Oumeraci et al., 2010) and CFD modelling (Foyer and Oumeraci, 2013). The latter were conducted to describe the hydrodynamic and hydro-geotechnical processes involved in the wave–structure interaction with PBA revetments. However, the data generated did not allow a full description of the wave-induced loading of the revetment and the response of the underlying soil; therefore, a comprehensive parameter study with a computational fluids dynamics–computational solid dynamics (CFD–CSD) model system was performed. This paper (Part I) focuses on the wave-induced pressures on the revetment, while a companion paper (Part II) describes the pore pressure development just beneath the revetment and in the embankment subsoil. In this first part, the following issues are addressed: (i) introduction to the numerical parameter study and the CFD–CSD model used for the modelling of the wave-induced pressures; (ii) brief review of the wave load classification and parameterization to define the elements and notations for the wave-induced pressure analysis; (iii) analysis of the peak pressure magnitude, its location on the revetment, and the spatial pressure distribution; and (iv) the development of prediction formulae, based on the results of the analysis in issue iii. Finally, a summary of the key results and concluding remarks are provided, including the implications and recommendations for engineering applications as well as for further research.

Wave-induced pressures in porous bonded revetments. Part II: Pore pressure just beneath the revetment and in the embankment subsoil

This paper considers pore pressure distribution in the embankment subsoil beneath PBA-revetments, based on the results of the parameter study using the new validated CFD–CSD model system wavePoreGeoFoam described in the companion paper (Part I), which focusses on wave-induced pressures on PBA-revetments (Alcérreca-Huerta and Oumeraci, 2016-in this issue). In this paper (Part II), a general overview is first provided on the numerical parameter study, especially on the model setup for the extraction of data related to the wave-induced pore pressures in the sand core beneath PBA-revetments. Secondly, wave-induced pore pressure just beneath the revetment is analysed considering: peak pressure magnitude, its location beneath the revetment and their spatial distribution. Afterwards, a process analysis of the results of the parameter study is performed for the wave-induced pore pressure distribution in the sand core. Formulae are developed for the prediction of the pore pressure distribution just beneath the revetment and of the damping of peak pore-pressures in the sand core. Subsequently, a comparative analysis of the proposed formulae and the approach of De Groot et al. (2006) for the assessment of pore pressure in a porous seabed is made, showing a very good agreement between both results. Finally, implications and recommendations for engineering applications and for further research are drawn from the results.

Poro-Elasto-Plastic Model for the Wave-Induced Liquefaction1

In this paper, we presented an integrated numerical model for the wave-induced pore pressures in marine sediments. Two mechanisms of the wave-induced pore pressures were considered. Both elastic components (for oscillatory) and the plastic components (for residual) were integrated to predict the wave-induced excess pore pressures and liquefaction in marine sediments. The proposed two-dimensional (2D) poro-elasto-plastic model can simulate the phenomenon of the pore pressure buildup and dissipation process in a sandy seabed. The proposed model overall agreed well with the previous wave experiments and geo-centrifuge tests. Based on the parametric study, first, we examined the effects of soil and wave characteristics on the pore pressure accumulations and residual liquefaction. Then, a set of analysis on liquefaction potential was presented to show the development of liquefaction zone. Numerical example shows that the pattern of progressive waves-induced liquefaction gradually changes from 2D to one-dimensional (1D), while the standing wave-induced liquefaction stays in a 2D pattern in the whole process.

A Divergence-Form Wave-Induced Pressure Inherent in the Extension of the Eliassen–Palm Theory to a Three-Dimensional Framework for All Waves at All Latitudes

Classical theory concerning the Eliassen–Palm relation is extended in this study to allow for a unified treatment of midlatitude inertia–gravity waves (MIGWs), midlatitude Rossby waves (MRWs), and equatorial waves (EQWs). A conservation equation for what the authors call the impulse-bolus (IB) pseudomomentum is useful, because it is applicable to ageostrophic waves, and the associated three-dimensional flux is parallel to the direction of the group velocity of MRWs. The equation has previously been derived in an isentropic coordinate system or a shallow-water model. The authors make an explicit comparison of prognostic equations for the IB pseudomomentum vector and the classical energy-based (CE) pseudomomentum vector, assuming inviscid linear waves in a sufficiently weak mean flow, to provide a basis for the former quantity to be used in an Eulerian time-mean (EM) framework. The authors investigate what makes the three-dimensional fluxes in the IB and CE pseudomomentum equations look in different directions. It is found that the two fluxes are linked by a gauge transformation, previously unmentioned, associated with a divergence-form wave-induced pressure [Formula: see text]. The quantity [Formula: see text] vanishes for MIGWs and becomes nonzero for MRWs and EQWs, and it may be estimated using the virial theorem. Concerning the effect of waves on the mean flow, [Formula: see text] represents an additional effect in the pressure gradient term of both (the three-dimensional versions of) the transformed EM momentum equations and the merged form of the EM momentum equations, the latter of which is associated with the nonacceleration theorem.

진행파동장하 해저지반내 잔류간극수압의 해석해

진행파동장하 해저지반내 잔류간극수압의 해석해

SOME EFFECTS OF INTRINSIC CYCLIC LOADING IN SATURATED SANDS

This paper presents original results of triaxial experiments performed at a cyclically changed pore pressure (intrinsic cyclic loading). The results display unusual behaviour of saturated sand subjected to such atypical loading. Some features of this behaviour are shown, including the following effects: static liquefaction of initially contractive sand, apparent creep of initially dilative sand, initial anisotropy, etc. Some differences between the classical geotechnical understanding of the effects of external cyclic loadings (such as earthquakes) and those caused by intrinsic cyclic loadings (such as wave-induced pressures) are discussed.

Effects of Cnoidal Wave-Induced Seepage on Vertical Breakwater Resting on Permeable Elastic Seabed

Theoretical investigations on cnoidal waves interacting with breakwater resting on permeable elastic seabed are presented in this paper. Based on the shallow water reflected wave theory and Biot consolidation theory on wave-induced seepage pressure, the analytical solutions to first order cnoidal wave reflection and wave-induced seepage pressure are obtained by the eigenfunction expansion approach. Numerical results are presented to show the effects of depth of water, breakwater geometry on cnoidal wave-induced seepage uplift force and overturning moment. Compared with Airy wave theory, in certain shallow water conditions, the shallow water wave theory can more effectively illustrate wave nonlinearity effect in wave load prediction.

Three-dimensional poro-elasto-plastic model for wave-induced seabed response around submarine pipeline

The evaluation of the wave-induced excess pore pressure around a buried pipeline is particularly important for pipeline engineers involved in the design of offshore pipelines. Existing models for the wave-induced seabed response around submarine pipeline have been limited to poro-elastic soil behavior and de-coupled oscillatory and residual mechanisms for the rise in excess pore water pressure. To overcome the shortcoming of the existing models, in this study a three-dimensional poro-elasto-plastic soil model with submarine pipeline is established, in which both oscillatory and residual mechanisms can be simulated simultaneously. With the proposed model, a parametric study is conducted to investigate the relative differences of the predictions of the wave-induced pore pressure with poro-elasto-plastic model. Based on numerical examples, it can be concluded that the poro-elasto-plastic behaviors of soil have more significant influence on wave-induced pore pressure of seabed around submarine pipeline. As the seabed depth increases, the normalized pore pressures decrease rapidly at the upper part of seabed, and then change slightly at the lower part of the seabed. Soil permeability and wave period have obvious influence on the wave-induced normalized pore pressure.

Performance of submerged nearshore sand-filled geosystems for coastal protection

Nearshore submerged structures made of sand-filled geosystems are an interesting use for this type of coastal protection technology. These systems have an advantage over more traditional materials such as concrete units or rock, which is the limited and non-permanent impact on natural coastal processes. On top of that are also some important research achievements and improvements at the level of the materials. However, at more exposed hydraulic conditions under high wave energy its application is still hampered by the lack of knowledge about their performance. This paper describes research results based on a series of laboratory measurements of the hydrodynamic and morphodynamic change produced in the vicinity of submerged nearshore structures. An analysis of the different model outputs produced, with respect to sediment transport, wave reflection and wave-induced pressures, has been made and is discussed throughout the paper. Such a comparative analysis provides insights into the efficiency of each defence scheme in maintaining a beach and in protecting the shoreline. The sand-filled geosystems as nearshore submerged structures proved to be efficient in retarding the offshore movement of sediments and in maintaining the shoreline, even if instabilities due to elements' displacement and local scour have been observed.

An experimental study on the wave-induced pore water pressure change and relative influencing factors in the silty seabed

In this study, a flume experiment was designed to investigate the characteristics of wave-induced pore water pressure in the soil of a silty seabed with different clay contents, soil layer buried depths and wave heights respectively. The study showed that water waves propagating over silty seabed can induce significant change of pore water pressure, and the amplitude of pore pressure depends on depth of buried soil layer, clay content and wave height, which are considered as the three influencing factors for pore water pressure change. The pressure will attenuate according to exponential law with increase of soil layer buried depth, and the attenuation being more rapid in those soil layers with higher clay content and greater wave height. The pore pressure in silty seabed increases rapidly in the initial stage of wave action, then decreases gradually to a stable value, depending on the depth of buried soil layer, clay content and wave height. The peak value of pore pressure will increase if clay content or depth of buried soil layer decreases, or wave height increases. The analysis indicated that these soils with 5% clay content and waves with higher wave height produce instability in bed easier, and that the wave energy is mostly dissipated near the surface of soils and 5% clay content in soils can prevent pore pressure from dissipating immediately.

Large-Eddy Simulation of Marine Atmospheric Boundary Layers above a Spectrum of Moving Waves

Abstract Momentum and scalar transport in the marine atmospheric boundary layer (MABL) is driven by a turbulent mix of winds, buoyancy, and surface gravity waves. To investigate the interaction between these processes, a large-eddy simulation (LES) model is developed with the capability to impose a broadband spectrum of time-varying finite-amplitude surface waves at its lower boundary. The LES model adopts a Boussinesq flow model and integrates the governing equations on a time-varying, surface-fitted, nonorthogonal mesh using cell-centered variables with special attention paid to the solution of the pressure Poisson equation near the wavy boundary. Weakly unstable MABLs are simulated with geostrophic winds increasing from 5 to 25 m s−1 and wave age varying from swell-dominated to wind-wave equilibrium. The simulations illustrate cross-scale coupling as wave-impacted near-surface turbulence transitions into shear-convective rolls with increasing distance from the water. In a regime with swell, low winds, and weak heating, wave-induced vertical velocity and pressure signals are readily observed well above the standard reference height ζa = 10 m. At wind-wave equilibrium, the small-scale wave-induced signals are detectable only near the water surface. Below ζa, a nearly-constant-flux layer is observed where the momentum flux carried by turbulence, form stress, and subgrid-scale motions shifts with varying wave age and distance above the water. The spectral content of the surface form stress is wave-age dependent, especially at low wavenumbers. The LES wind profiles deviate from Monin–Obukhov similarity theory in nonequilibrium wind-wave conditions, and entrainment is greatly enhanced by shear-induced engulfment events.

Seismic attenuation: effects of interfacial impedance on wave-induced pressure diffusion

AbstractSeismic attenuation and dispersion in layered sedimentary structures are often interpreted in terms of the classical White model for wave-induced pressure diffusion across the layers. However, this interlayer flow is severely dependent on the properties of the interface separating two layers. This interface behaviour can be described by a pressure jump boundary condition involving a non-vanishing interfacial impedance. In this paper, we incorporate the interfacial impedance into the White model by solving a boundary value problem in the framework of quasi-static poroelasticity. We show that the White model predictions for attenuation and dispersion substantially change. These changes can be attributed to petrophysically plausible scenarios such as imperfect hydraulic contacts or the presence of capillarity.

CFD-CSD NUMERICAL MODELLING OF WAVE-INDUCED PRESSURES IN OPEN- PORED PBA-REVETMENTS

The highly porous Polyurethane Bonded Aggregates (PBA) revetments represent a novel ecologically friendly solution for the protection of shorelines and vulnerable coastal areas against erosion. Advantages of the open-pored PBA-revetments over conventional smooth impermeable revetments are among others, the reduction of: wave run- up/run-down, wave reflection and wave-induced loads on the sand core beneath the revetment. However, the hydro- geotechnical processes involved in the interaction of waves with such PBA-revetments and their foundation are still not sufficiently understood. Therefore, a new 3-dimensional one-way coupled CFD-CSD model system "wavePoreGeoFoam" was developed at the Leichtweiß-Institute (LWI) within the OpenFOAM® framework for the analysis of the response of open-pored PBA-revetments due to wave-induced loads. In this way, this paper firstly describes the new CFD-CSD model system. Second, validation of the model "wavePoreGeoFoam" is shown considering large-scale laboratory tests performed in the Large Wave Flume (GWK) at the Coastal Research Center (FZK) in Hanover, Germany (Oumeraci et al. 2010). Third, the relevance of implementing the CFD-CSD coupling for modelling wave-induced pressures on and beneath PBA-revetments is discussed. Fourth, a sensitivity analysis related to the effect of the empirically defined parameters for the numerical model is described. Finally, recommendations and implications of the use of CFD-CSD model for further research will be addressed.

Stability and liquefaction analysis of porous seabed subjected to cnoidal wave

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