Wave-induced Pressure Research Articles

Two-dimensional one-way coupled modelling for fluid-structure-seabed interactions around a semicircular breakwater using OpenFOAM

Semicircular breakwaters, preferred for their lighter weight, wider base and superior resistance to overturning and sliding, have seen focused research on wave forces and hydrodynamic performance. Despite documented failures due to seabed instability, numerical examinations of the seabed response and stability around these structures are lacking in the literature. This study establishes an OpenFOAM model to numerically investigate hydrodynamic interactions, structural dynamics, seabed consolidation and liquefaction potential near a semicircular breakwater in two-dimensional, addressing complex fluid–structure-seabed interactions in a one-way coupling manner. A novel method for determining the compressibility of the pore fluid has been implemented, which integrates geostatic stress, atmospheric pressure and wave-induced excessive pore pressure within the seabed. The numerical results indicate that seabed responses are sensitive to the bulk modulus of pore air in partially saturated cases, where a decrease in pore pressure, an increase in the vertical effective stress and a decrease in the horizontal effective stress are observed. Further numerical analysis reveals that the most vulnerable part of the breakwater appears on the wave-facing side of the caisson, where reinforcement measurements are recommended during construction. A pronounced liquefaction zone is observed ahead of the breakwater, corresponding to the area with upward seepage, which is attributed to the combined effect of hydrodynamic interactions and direct stress action transferred from the semicircular breakwater.

Extreme Wave-Induced Pressure Distribution and Wave Forces on Tandem Pile Groups: An Experimental Study

As the foundation of marine infrastructure, pile groups are subjected to extreme wave loads. Existing research primarily focuses on regular waves and wave forces. There is limited research on the pressure distribution of pile bodies under extreme waves. This paper describes a wave flume experiment where waves of a self-proposed extreme wave type were generated. The experiment considers three water depths (25/35/45 cm), three wave-pushing velocities (20/30/40 cm/s), and two clear distances (D, 2D). A total of 216 measuring points equipped with digital pressure sensors captured the vertical and circumferential pressure distribution and wave positive force. The results show that (1) the vertical and circumferential pressure distribution patterns of each component pile and the single pile are similar in various loading scenarios and clear distances. (2) The measuring point pressure, pressure after circumferential integration, and wave positive force are positively correlated with wave-pushing velocity. (3) The wave pressure is positively correlated with the water depth, while the pressure after circumferential integration is negatively correlated with the water depth. (4) When the clear distance is D, the wave positive force coefficient of each component pile is less than 1.0.

Constraints on fracture connectivity from amplitude variations with incidence angle and azimuth analysis

The analysis of seismic reflection amplitude variations with incidence angle and azimuth (AVAz) is a powerful tool for studying and characterizing fractured formations. There is evidence to suggest that wave-induced fluid pressure diffusion (FPD) within connected fractures can significantly affect the AVAz response. This, in turn, indicates that this seismic attribute may contain information on the connectivity degree of the fracture network, which represents a key hydraulic property of fractured formations. The assessment of the sensitivity of seismic reflectivity with respect to fracture connectivity accounting for FPD effects to date is limited to 2D models, which is mainly due to the complexity and the associated computational cost of modeling the effective properties of the corresponding generically anisotropic 3D media. To overcome these issues, we use a numerical upscaling procedure based on Biot’s theory of poroelasticity that allows us to obtain effective anisotropic representations of 3D fractured formations accounting for the FPD effects. Using these effective properties, we then perform a plane-wave analysis to compute the reflection coefficients at the top of the corresponding fractured formation. The results of our numerical analyses extend the previous 2D studies and demonstrate that seismic reflection coefficients are highly sensitive to the degree of connectivity of the fracture networks. The reflectivity responses of formations comprising connected and unconnected fractures indicate pronounced differences not only with respect to incidence angle but also with respect to azimuth. Quite importantly, our results also demonstrate that crossplots of commonly used AVAz coefficients permit us to identify regions with higher or lower fracture connectivity.

Acoustic response of patchy-saturated porous media: Coupling Biot's poroelasticity equations for mono- and biphasic pore fluids.

Patchy saturation is a term used in the seismic prospecting literature to describe the state of a geological formation in which two immiscible pore fluids prevail in mesoscopic-scale clusters. If the pore fluids have contrasting compressibilities, wave-induced fluid pressure diffusion (FPD) processes may induce significant attenuation and velocity dispersion on seismic waves. Biot's monophasic poroelasticity theory is widely used to model the seismic response of rocks containing binary patches of two immiscible pore fluids. Even though effective fluid approximations may help to represent more realistic partially saturated patches using Biot's monophasic equations, the so inferred dissipation may not be representative of actual biphasic FPD phenomena. In this work, Biot's equations for mono- and biphasic fluids are combined to model FPD processes in porous media, comprising fully and partially saturated patches. An analytical solution for one-dimensional layered patchy-saturated media is presented which permits to explain some, as of yet enigmatic, experimentally observed characteristics such as increased seismic attenuation and stiffening effects occurring at low saturations. The results show that the existence of an additional diffusive wave mode within partially saturated patches may render conventional binary and effective fluid approaches incorrect and error prone.

Experimental study of dynamic pressure and wave load on variform vertical cylinders under extreme waves

Extreme waves pose a significant threat to the proliferating marine structures, however, the impact on the vertical cylinder with different cross-sectional shapes remains inadequately evaluated. Herein, we carried out a physical experiment, comprising 45 scenarios generated by three water depths, three wave paddle velocities, and five vertical cylinder models, to measure the extreme wave-induced pressure and load on this type of structure. The wave load and dynamic pressure distribution in time and spatial domains under the influence of cross-sectional shapes and wave conditions have been fully discussed. The experimental results indicate that: 1) As the position turns from front to back side, the circumferential pressure of five models initially decreases and then increases. 2) The maximum differential pressure between the front and back side decreases with increased water depth and decreased velocity, and occurs earlier than the peak pressure on the front side. 3) The chamfered cross-section (round and right triangle) can significantly reduce the wave load compared to the rectangular section, and the circular section suffers the lowest force logically. The dynamic pressure and wave load in this experiment can serve to establish a more sophisticated load model and provide valuable insights for marine structural design and disaster prevention.

Seismic wave modeling of fluid-saturated fractured porous rock: including fluid pressure diffusion effects of discretely distributed large-scale fractures

Abstract. The scattered seismic waves of fractured porous rock are strongly affected by the wave-induced fluid pressure diffusion effects between the compliant fractures and the stiffer embedding background. To include these poroelastic effects in seismic modeling, we develop a numerical scheme for discretely distributed large-scale fractures embedded in fluid-saturated porous rock. Using Coates and Schoenberg's local-effective-medium theory and Barbosa's dynamic linear slip model characterized by complex-valued and frequency-dependent fracture compliances, we derive the effective viscoelastic compliances in each spatial discretized cell by superimposing the compliances of the background and the fractures. The effective governing equations for fractured porous rocks are viscoelastic anisotropic and numerically solved by the mixed-grid-stencil frequency-domain finite-difference method. The main advantage of our proposed modeling scheme over poroelastic modeling schemes is that the fractured domain can be modeled using a viscoelastic solid, while the rest of the domain can be modeled using an elastic solid. We have tested the modeling scheme in a single fracture model, a fractured model, and a modified Marmousi model. The good consistency between the scattered waves off a single horizontal fracture calculated using our proposed scheme and the poroelastic modeling validates that our modeling scheme can properly capture the fluid pressure diffusion (FPD) effects. In the case of a set of aligned fractures, the scattered waves from the top and bottom of the fractured reservoir are strongly influenced by the FPD effects, and the reflected waves from the underlying formation can retain the relevant attenuation and dispersion information. The proposed numerical modeling scheme can also be used to improve migration quality and the estimation of fracture mechanical characteristics in inversion.

Laboratory investigation on pore pressures inside a rubble mound breakwater in depth-limited waters

The present paper reports the analysis of pore pressure measurements acquired inside a small-scale conventional breakwater during an experimental campaign performed at the EUMER laboratory of the University of Salento (Lecce, Italy). The new data are used to investigate the effects of depth-limited water conditions on the wave-induced pressures in a porous structure in front of a 1V:30H foreshore. Specifically, the paper addresses and discusses the impact of the relative depth on three aspects: the frequency response of pore water pressure in the structure, the energy dissipation through the cover layers and the pressure attenuation inside the breakwater core. Additionally, the paper includes a comparison between the experimental results and the empirical models actually available in literature, able to predict the reference pressure at the armour/filter layers interface and the pressure damping inside porous structures. Results firstly show that shallow water conditions amplified the influence of wave long components on breakwater response to wave action, inducing a pressure attenuation inside the structure of about 80%−90%, mostly between the armour and the filter layers and highly dependent on the wave period. Instead, the comparison with the empirical formulae shows that the predictive models considered in the present work generally underpredict the damping coefficient, especially in intermediate/shallow water conditions, demonstrating that the relative depth has a high influence on both the reference pressure and the damping coefficient.

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.

Azimuthal pore pressure response to teleseismic waves: effects of damage and stress anisotropy

SUMMARY Pore pressure oscillations induced by stress variations, including propagating seismic waves from remote earthquakes, have been widely observed in various groundwater systems. The monitored pressure change in wells shows significant water-level oscillations to volumetric strain as well as to S and Love waves. Recent observations demonstrated azimuthal dependence of the pore pressure oscillations with respect to stress indicators and fault zone orientation. Within the fault zone, damage-induced anisotropy is the result of the alignment and orientation of cracks and other internal flaws within the rock. In this work, we provide a complete quantitative description of the pore pressure changes induced by passing seismic waves associated with different orientations and values of principal stress and damage tensor components. The model quantifies the azimuthal dependence of the pore pressure response by a non-dimensional ratio defined as the amplitude of the pressure oscillations induced by a shear strain normalized to the volumetric strain. Three angles and two values are needed to calculate the azimuthal dependence of the pore pressure response: the angle between the directions of the maximum horizontal stress and the seismic event; fault zone orientation; microcrack orientation within the fault zone; and damage and stress values. The model predicts that maximum pore pressure response occurs when microcracks and maximum horizontal stress are in the same orientation, high damage and high stress anisotropy. By adjusting these quantities, we recalculate results of recent seismological studies in the Arbuckle disposal well, Osage County, Oklahoma. The presented model successfully predicts the observed azimuthal dependence in wave-induced fluid pressure response and relates the anisotropic response to tectonic indicators such as the orientations of the maximum horizontal stress, fault zone, and microfractures.

Vulnerability of the rip current phenomenon in marine environments using machine learning models

Hidden and perilous rip currents are one of the primary factors leading to drownings of beach swimmers. By identifying the coastal areas with the highest likelihood of generating rip currents, it becomes possible to prevent fatalities and mitigate economic losses associated with these hazardous currents. Rip currents are characterized as streams of water moving towards the open sea, forming within the area where waves break, due to variations in wave-induced radiation stresses and pressure along the coastline. This study utilized nine different Machine Learning (ML) models, including M5 Model Tree (MT), Multivariate Adaptive Regression Spline (MARS), Gene Expression Programming (GEP), Evolutionary Polynomial Regression (EPR), Random Forest (RF), Support Vector Machine (SVM), Extreme Gradient Boosting (XGBoost), Adaptive Boosting (AdaBoost), and Stacked ML models, to estimate the Relative Tide Range (RTR) values for 50 southern beaches in China. Through this approach, we gathered a reliable dataset from prior research conducted on the southern coast of China. In this study, two parameters, namely dimensionless fall velocity parameter (Ω) and tide range (TR) are used to predict the vulnerability of rip current event. The results of the AI models were assessed by various statistical analyses (Correlation of Coefficient [R], Root Mean Square Error [RMSE], violin diagram, heatmap, and taylor diagram) for training and testing stages. Accordingly, the MARS model exhibited superior performance compared to other AI models in accurately predicting the RTR value. The outcomes substantiated the significant effectiveness and capability in estimating the RTR with high accuracy. Southern China coasts have relative high risk level of rip current, necessitating the attention and strategic management of this dangerous current by the beach managers.

Design an Optimum Air Duct for Oscillating Water Column Wave Energy Device

Oscillating Water Column (OWC) is a technology that harvests wave energy to generate electricity. It works by harnessing the wave-induced pressure oscillation in the opening mouth of OWC. The oscillation of the pressurised air is extracted using a turbine placed at the top of the OWC structure. Although OWC has been studied for many years, designing an optimum air duct for such devices is still an open research area. The air duct plays a crucial role in the energy conversion process, as it is responsible for directing the airflow towards the turbine, and its design can greatly affect the performance and efficiency of the system. The article aims to study how the air duct design impacts the power output form. Moreover, the result will be compared with the conventional air duct design. The OWC performance is analysed using Computational Fluid Dynamic (CFD) software to identify which shape of the air duct has high efficiency. Autodesk Inventor is used to design the OWC devices modified from the basis design. Then these designs are imported into CFD software to simulate and obtain the energy extraction result. The CFD software is chosen to simulate the hydrodynamics problem. In this study, the oval design shows significant improvement in the energy extraction performance compared to the basis design. The oval design managed to produce 9.81, 10.02, and 11.66 J/kg of mechanical energy compared to 9.81, 9.82, and 10.04J/kg as prompted by the basis air duct design at the wave height of 0.2505, 0.75, and 2.25m, respectively. The result shows that the non-edge produces higher air pressure than the sharp edge of the air duct shape. Thus, the oval air duct design is more efficient, and it may increase the performance of the OWC wave energy converter device at a low wave height of 0.75 m.

Sensitivity of shear wave splitting to fracture connectivity

SUMMARY Shear wave splitting (SWS) is currently considered to be the most robust seismic attribute to characterize fractures in geological formations. Despite its importance, the influence of fluid pressure communication between connected fractures on SWS remains largely unexplored. Using a 3-D numerical upscaling procedure based on the theory of poroelasticity, we show that fracture connectivity has a significant impact on SWS magnitude and can produce a 90° rotation in the polarization of the fast quasi-shear wave. The simulations also indicate that SWS can become insensitive to the type of fluid located within connected fractures. These effects are due to changes of fracture compliance in response to wave-induced fluid pressure diffusion. Our results improve the understanding of SWS in fractured formations and have important implications for the detection and monitoring of fracture connectivity in hydrocarbon and geothermal reservoirs as well as for the use of SWS as a forecasting tool for earthquakes and volcanic eruptions.

Sensitivity limits for strain detection of hypothetical remote fluid-induced earthquakes (Mw ≥ 4): a case study in Taiwan

Capturing and quantifying the timing of remotely triggered earthquakes and understanding the physical processes responsible for this delay represent major challenges in earthquake forecasting. In this study, we propose a physical framework for the integration of borehole strainmeter observations for the investigation of remote triggering of moderate to large earthquakes (Mw ≥ 4) in Taiwan. Based on the time-delay computation between regional events and global earthquakes, we establish a selection of earthquakes showing fault zone properties (hydraulic diffusivity and nucleation length) that may be compatible with a magnitude-dependent fluid-induced nucleation process. Using theoretical fault zones parameters, we calculate the evolution of fluid pressure transiting along the nucleation region under the assumption of a one-dimensional, homogeneous poroelastic medium. Pore pressure levels reached before earthquake rupture are ranging from about 0.02 kPa to 3 kPa in the case of teleseismic wave-induced elastic pressure ranging from 0.15 kPa to 27.3 kPa. To compute the time-dependent evolution of deformation generated by a remote diffusing pressure front, we model the nucleation region using the analogue volcano source represented by a horizontal circular crack, and calculate synthetic dilatation at the strainmeter location from displacements using a finite-difference approach. In general, predictions are about two to four orders of magnitude smaller than observations (∼ 10–5 to 10–3 nϵ). Therefore, this suggests that detection of pore pressure-related deformation would have required change of volume in the nucleation region that is at least one order of magnitude larger than for the hypothetical cases considered here. The study represents the first attempt to analyze strain time-series for detecting pre-earthquake strain anomalies related to fluid-induced earthquakes and illustrates the challenge for detecting and characterizing intermediate-to far-field earthquake precursors caused by fluid flow in active regions.

Numerical study of regular wave-induced oscillatory soil response during the caisson installation

In this study, the PORO-FSSI-FOAM model is applied to investigate the wave-induced oscillatory soil response during the caisson installation, where the Reynolds averaged Navier-stokes equation is used to simulate the flow motions, and the poro-elastic equation is used to govern the soil dynamic response around the caisson. Unlike previous studies, the caisson installation process is considered when investigating the wave-induced oscillatory soil response in this paper. Firstly, the accuracy of the PORO-FSSI-FOAM model in simulating the wave-seabed interaction is validated. Then, the effects of the submerged depth, the geometrical dimensions and the installation sequence of the caisson on the wave-induced oscillatory pore pressure response are examined, and the momentary soil liquefaction during the caisson installation is explored. Finally, a simple formula that describes the relationship between the maximum soil liquefaction depth and the caisson submerged depth is proposed. Numerical results indicate that the caisson dimensions can greatly influence the wave-induced pore pressure response, and the relationship between the oscillatory pore pressure response and the caisson submerged depth is inconsistent at different locations surrounding the structure. Moreover, the installation sequence can significantly affect the momentary soil liquefaction and the simple formula proposed in this study can provide reference for engineers to assess the seabed stability during the caisson installation.

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.

Experimental investigations of wave interaction with semi-submerged horizontal rectangular cylinder of elastic bottom

Laboratory experiments were conducted to investigate the interaction of gravity waves with a semi-submerged rectangular cylinder of elastic bottom. Laboratory investigations were conducted for a wide range of wave parameters and a structure of different drafts. The analysis of results focuses on wave transmission at the structure, wave-induced pressures excreted on the plate, plate deflections, etc. The results shows that the nonlinear pressure and plate deflection components arising from the interaction of incoming waves with the structure are often significant. The results show that the nonlinear components often exceed their linear counterparts even for waves of low steepness. This is an original and surprising outcome of significant practical importance as the large nonlinear pressure and plate deflection components may spark a resonance. The problem is serious because plate natural vibration frequencies are often lower than the frequency of fundamental waves or their nonlinear components and the vibration of a plate may be amplified by incoming waves or their nonlinear products. The occurrence of a resonance amplified by incoming waves may lead to the failure of a structure. This outcome is of significant practical importance because it may occur for a wide range of wave parameters.

Efficient time-domain approach for hydroelastic-structural analysis including hydrodynamic pressure distribution on a moored SFT

This study investigates the hydroelastic analysis of a moored SFT (submerged floating tunnel) and the corresponding hydrodynamic pressure distribution under wave excitations. Time-domain discrete-module-beam (DMB) method, in which an elastic structure is modeled by multiple sub-bodies with beam elements, is employed to express the deformable tunnel with multiple mooring lines. Moreover, the top-down scheme is also adopted for detailed structure analyses with less computational cost, which applies the calculated hydrodynamic pressure distribution over SFT's surface to the three-dimensional finite element model. The hydrodynamic pressure includes both wave-induced diffraction pressure and motion-induced radiation pressure. For the validation of the developed numerical approach, comparisons are made with computationally intensive hydroelastic-structural direct-coupled method, two-dimensional wave flume experiment, and independently developed inhouse moored-SFT-simulation program. Furthermore, the influences of flexural motions with buoyancy-weight ratio (BWR) (or bending stiffness) and regular/irregular wave conditions on the dynamic pressure distribution and the resulting local stresses are investigated.

Theoretical Study on Wave-Induced Pressure and Drift Force on a Vertical Circular Column

Theoretical Study on Wave-Induced Pressure and Drift Force on a Vertical Circular Column

Elastic wave propagation characteristics in unsaturated double-porosity medium under capillary pressure

Rock pores often contain two-phase or multi-phase fluids, so it is important to understand how the wave-induced fluid pressure diffusion affects dispersion and attenuation of elastic waves for resource exploration. To describe the propagation of elastic wave in a double-porosity medium saturated by two-phase fluids, a wave propagation model, including both global and local flow mechanisms and considering the effect of capillary pressure, is derived. The dispersion and attenuation characteristics of three longitudinal waves (P1, P2, P3) and one transverse wave (S wave) are investigated by analyzing a plane wave, and the effects of physical parameters, such as inclusion radius, water saturation, permeability and porosity, on the propagation characteristics of P1 wave are investigated. Theoretical analysis shows that the model derived in this work can be degenerated into the Biot model under specific conditions. According to the numerical simulation results, due to the coupling of global flow and local flow, the P1 wave velocity may decrease below the Gassmann-Wood limit. The physical explanation of this phenomenon is as follows: when considering the effect of capillary pressure, the coupling effect of global flow and local flow will break the basic assumption that rock is undrained. The relationship between physical parameters of porous medium and the dispersion and attenuation characteristics of elastic wave is complicated and nonlinear. Compared with Santos model, elastic modulus predicted by Santos-Rayleigh model is in good agreement with the experimental data in the low frequency band, which proves that this model has good reliability in modeling the velocity field of seismic exploration.

Mechanism of wave-induced flow in reshaping breakwaters

The aim of this work was to investigate the reshaping mechanisms of a reshaping berm breakwater (BB) by assessing the results of a two-dimensional numerical model in OpenFoam. The flow inside and outside the breakwater was numerically simulated. The initial and reshaped form of the breakwater was modelled using the Darcy–Forchheimer equation and k–ϵ closure model. The numerical model was calibrated with and validated against experimental data of wave-induced pressure and water-level fluctuations inside and outside the breakwater. Both the initial and reshaped BB were evaluated for calibration and validation processes. The results show that the minimum run-down level on the breakwater slope is a critical area for armour instability due to outward driving forces caused by the critically synchronised outward flow and excess pressure gradient. Moreover, parallel downward flow occurs during a wave run-down, which can push the displaced armour down the slope. After reshaping, the breakwater profile has a milder slope than the initial profile, and the outward forces due to the excess pressure gradient are reduced to less than one-half of their initial amount, a result of the change in breaker type. Accordingly, the reshaped profile is modified to harmonise with the new flow field conditions.