The rapidly expanding fleet of offshore wind turbines (OWTs) faces seismic risks. Earthquakes can excite highfrequency structural modes that typically remain dormant under normal wind and wave loads. This study proposes a vibration control strategy (4-MTMD) using multiple tuned mass dampers targeted at the structure's first four bending modes. A 3D finite element model incorporating pile-soil interaction is presented for a 5 MW monopile-supported OWT. The effectiveness of the proposed 4-MTMD strategy is systematically evaluated and compared against conventional tuned mass dampers tuned to the first bending mode (1-TMD) and the first two bending modes (2-MTMD) under seismic excitations with different frequency characteristics. Key findings indicate that high-frequency excitations can activate the third and fourth bending modes, with peak horizontal accelerations occurring in the middle-upper tower section. The 4-MTMD strategy demonstrates superior overall performance, effectively controlling horizontal accelerations across all frequency ranges, particularly under highfrequency earthquakes. Although the 1-TMD strategy provides the best control for tower-top displacement under certain conditions, the 4-MTMD strategy offers more comprehensive displacement reduction along the entire tower height. Crucially, even for excitations containing frequencies beyond the fifth bending mode frequency, the OWT tower response remains dominated by the first four modes. Therefore, designing MTMD systems to control up to the fourth bending mode represents an effective and sufficient strategy for strengthening seismic resilience of OWTs.

The relative density of sand significantly influences the wave-induced excess pore water pressure (EPWP), which could further affect the instability of immersed tunnel in sandy seabed. However, the distribution of the relative density in sandy seabed is inherently inhomogeneous. This study investigates the effect of spatial variability in the seabed relative density on the dynamic response of wave-induced immersed tunnel. The covariance decomposition method, combined with the autocorrelation function, is used to simulate spatial variability in seabed relative density. This variability is then incorporated into a poro-elasto-plastic seabed model to analyze the dynamic behavior of wave-induced immersed tunnel. The results indicate that the uncertainty of the maximum EPWP ratio is significantly influenced by the spatial variability of the seabed relative density. The presence of the immersed tunnel increases the EPWP ratio at the structure-soil interface, enlarges the liquefaction zone, and amplifies soil displacement. The EPWP ratio beneath the immersed tunnel exhibits a saddleshaped distribution, with its peak value fluctuating as the wave propagates. Moreover, under wave loading, spatial variability in seabed relative density may induce differential settlement of the immersed tunnel, resulting from asymmetric generation of EPWP on either side of the structure.

This paper presents a series of centrifuge tests to investigate the uplift behavior of an immersed tunnel on liquefiable sand deposit under horizontal and bidirectional excitations. The centrifuge model was designed as a 1/100-scale model according to the similitude relationships. Fine sand and coarse sand were used to simulate the liquefiable sand deposit and backfill layer, respectively. An offshore earthquake was used as the input motion and was applied in sequence alternating between horizontal excitation and bidirectional excitations with increasing intensity. Test results indicate that the softening and damping effects induced by sand liquefaction hinder the upward transmission of shear waves from the fully liquefied middle part of the deposit to the immersed tunnel. The vertical component of bidirectional excitations aggravates the liquefaction process, which attenuates the upward transmission of horizontal acceleration while amplifying the transmission of vertical acceleration. The reduction in effective stress caused by excess pore water pressure in the liquefiable sand under horizontal excitation facilitates sliding of soil wedges, thereby increasing the upward soil reaction beneath the tunnel and inducing uplift of the immersed tunnel. Under bidirectional excitations, the amplified vertical accelerations exacerbate liquefaction and promote sliding of the soil wedges, enhancing the upward soil reaction and tunnel uplift, and the vertical inertial forces further increases the uplift. The uplift displacement of the immersed tunnel decreases with increasing intensity of horizontal excitations but increases with increasing intensity of bidirectional excitations.

The suffusion behavior of gap-graded soil can be significantly influenced by various factors, including hydraulic conditions, particle size distribution, and stress states. Among these factors, the effects of stress states are particularly complex, as they not only affect particle migration directly but also alter soil structure and particle-fluid interactions. Consequently, the meso-scale mechanisms underlying the effects of the stress state remain insufficiently understood. In this study, a series of CFD-DEM coupled simulations is conducted to examine the suffusion behavior of gap-graded sand under different initial stress conditions from both macroscopic and mesoscopic perspectives. An index N is introduced to quantify the alignment between the major principal stress and the seepage direction. It is revealed that when the major principal stress direction is more codirectional with the seepage direction (higher value of N), fine particle loss and hydraulic conductivity are significantly strengthened under higher confining pressures. A meso-scale analysis framework based on Voronoi tessellation was developed to identify preferential suffusion paths under anisotropic stress conditions. The results show that the suffusion paths tend to form along the major principal stress direction, explaining the aggravated loss of fines when the stress and seepage directions are aligned.

The seismic response of large-scale seabed sites is governed by complex coupling effects involving seawater-seabed interaction, seafloor micro-topography, soil heterogeneity, and marine soil nonlinearity. This study employs an acoustic-structure interaction approach to simulate seawater as an ideal fluid, establishing a refined finite element model of a large-scaled seabed at the Jintang Strait to investigate seabed seismic responses under multiple complex factors. Seismic responses under various scenarios demonstrate significant amplification effects at basin edges and local convex terrain. Comparison between horizontal-only and bidirectional bedrock motion reveals bidirectional seismic coupling effects: bidirectional motion significantly amplifies seabed seismic responses through superposition of horizontal and vertical seismic waves, enhancing ground motion amplification. Additionally, bidirectional coupling intensifies nonlinear seismic responses of the seabed site, causing horizontal acceleration transfer function peaks to shift toward intermediate-to-high frequencies (>0.3 Hz) while further amplifying low-frequency (<0.1 Hz) components. Seawater effect reduces both horizontal and vertical peak ground accelerations at the seafloor, with more pronounced attenuation in vertical components. The frequency-dependent behavior exhibits "intermediate-to-high frequency suppression and low-frequency amplification" characteristics, particularly suppressing the 0.05-0.3 Hz range, with fluid-solid coupling effects closely correlated to seafloor topography. The normalized response spectra of the seabed cross-section significantly exceed the design spectra specified in EUROCODE 8 and Chinese standards.

In recent years, immersed tunnels have been widely used in cross-river and cross-sea transportation projects due to their unique advantages. Unlike land-based tunnels, immersed tunnels are embedded in the shallow layers of nearshore seabeds, where the combined influence of seawater and seabed soil makes their seismic response more complex. Traditional seismic analysis methods for land tunnels are therefore less applicable. In this study, the DM04 model is adopted to simulate the mechanical behavior of marine sand, and the Coupled Acoustic-Structure (CAS) method is employed to model the dynamic interaction between seawater and the seabed, establishing a coupled system of seawater, seabed, and immersed tunnel. Using real seismic records from a marine region as input, this study investigates the effects of horizontal and vertical seismic intensities, overlying seawater, and sand compaction piles (SCPs) on the seismic stability of tunnel. The results indicate that under seismic loading, soil surrounding the tunnel liquefies earlier than soil in the far field, and significant seabed deformation may lead to buoyancy-induced instability. Stronger horizontal and vertical seismic motions increase the uplift and tilt of the tunnel. Seawater amplifies uplift displacement but reduces rotational motion during the uplift. SCPs effectively enhance seismic stability by suppressing soil liquefaction beneath the tunnel and limiting lateral soil flow, thereby mitigating uplift and rotation.

The immersed tunnels of Hong Kong-Zhuhai-Macao Bridge and the Shenzhen-Zhongshan Channel have lengths up to 6-7 km along the longitudinal direction and cross several soil regions. The traveling wave effect is observed in these long immersed tunnels when subjected to seismic waves. Based on the improved response displacement method, a theoretical model of a long immersed tunnel containing 33 tube elements and 32 flexible joints and considering the continuity conditions of flexible joints was developed in this study. The incorporation of the traveling wave effect was achieved by taking into account both the longitudinal propagation distance of the seismic wave within the immersed tunnel and the dynamic variations in seismic wave parameters as the wave traversed through diverse soil regions. An evaluation was developed to assess the traveling wave effect on the response of the long immersed tunnel, and the influences of incidence angles and initial apparent wave velocities of seismic wave were investigated. The results showed that ignoring traveling wave effect for the long immersed tunnel through various soil regions would result in significant underestimations of relative deformations of flexible joints by approximately one order of magnitude, leading to unsafe seismic design.

Understanding the seismic source mechanisms of offshore earthquakes in seismically active regions is essential for enhancing the resilience of marine and offshore structures. This study investigates the rupture process of the 2021 Fukushima Earthquake through waveform inversion using empirical Green's function (EGF). The analysis was based on strong ground motion data within the 0.2-2.0 Hz frequency range. Two primary slip areas, located southwest of the epicenter, were identified, with the maximum slip reaching 3.2 m at depths consistent with the hypocenter. The preferred seismic source model corresponds to a moment magnitude of M(W)7.3 and a rupture velocity of 2.4 km/s. Model validation was conducted by using various EGF combinations and simulating strong ground motion at additional observation stations not included in the initial inversion. The high correlation between synthesized and observed waveforms across a broad frequency spectrum validates the accuracy of the model in capturing the spatial and temporal characteristics of the rupture process. Moreover, the model exhibits minimal frequency dependence, consistent with existing source models despite differences in the frequency ranges used for inversion. These findings offer significant insights into improving the seismic safety and resilience of coastal and offshore infrastructure in response to earthquake-induced hazards.

The seabed is commonly covered with water and ice layers during winter in high-latitude regions. A novel dynamic model is presented to portray the seismic response of the seabed-water-ice system with imperfect interface under obliquely incident P/SV-wave. The seabed sediment is composed of a two-layer poroelastic material following Biot's dynamic poroelastic theory, while the ice layer is characterized as an ideally elastic medium. The imperfect interface connection between the seabed and underlying bedrock is simulated by a classical spring-type model. The rigorous solutions are derived using wave potential functions along with the boundary-value conditions of the layered system. The validity of proposed model is confirmed by comparing it with benchmark solutions under idealized conditions. The numerical results reveal that the existence of ice layer significantly amplifies the vertical displacement and pore pressure in the seabed with this effect being more pronounced as the ice thickness increases. The interface imperfection amplifies the horizontal displacement and shear stress in the seabed. The soft-bottom seabed layer amplifies vertical displacement and pore pressure while suppressing horizontal displacement and shear stress, whereas the stiff-bottom layer exhibits the opposite effect. The developed model provides valuable insights for assessing seismic response of the seabed in high-latitude environment.

The scarcity of strong-motion records in marine environments has constrained our current understanding of the seismic response of liquefiable seabed sites. In this study, the Dafalias-Manzari model served as the constitutive framework for sandy soils, while an acoustic-structure coupling approach is utilized to simulate seawater-seabed interaction. The effects of bidirectional seismic intensity, along with the thickness and depth of the liquefiable layer and seawater depth, on the seismic responses of marine sites are systematically analyzed. The findings reveal that the horizontal seismic motion triggers liquefaction within the sandy interlayer, and the liquefied soil layer impedes the transmission of shear waves. As the horizontal seismic intensity increases, the degree of liquefaction in the interlayer intensifies, and the damping effect becomes more pronounced. The vertical seismic motion exerts minimal impact on the liquefaction characteristics of the site. However, more intense vertical seismic motion induces dynamic water pressure from the overlying seawater, significantly suppressing vertical motion at the seabed. As the thickness of the liquefiable interlayer increases, its damping effect becomes more pronounced; however, a critical thickness exists beyond which the energy dissipation effect slightly diminishes. Compared to the deeper liquefiable interlayers, the shallower interlayers exhibit a more pronounced damping effect. During seismic events, seawater induces significant oscillations in the pore pressure response of the soil, yet it does not influence the overall development trend of pore pressure. Additionally, seawater exerts minimal impact on the horizontal motion response of the site but significantly suppresses vertical motion, simultaneously extending the period corresponding to the peak of the vertical response spectrum.

Studying the behavior of immersed tunnels through varying strata subjected to seismic loading is critically dependent on the flexibility of the joints. A theoretical model was established to study the dynamic response of flexible joint between tube elements crossing different strata under seismic waves. The flexible joint at the interface of adjacent tube elements was considered as a combination of flexible and shear springs, and the tubes on either side of the joint are considered as two semi-infinite elastic foundation beams. For the longitudinal seismic loading, the traveling wave effect has been simulated by the use of displacement phase angle. Finite element simulation results were used to verify the analytical solution. The findings revealed that the peak forces occurring at the interface of different soil regions can be significantly reduced by the flexible joint, and the relative deformation at the flexible joint could be accommodated by the joint itself and fall within allowable deformation range for normal operation. Results from a parametric study indicate that the joint flexural stiffness plays a more important role on the relative rotation angle between the tube elements, while the joint shear stiffness is more important for the vertical displacement difference between tube elements.

Many nearshore and offshore seabeds are classified as gently sloping seabeds, typically with an inclination angle of less than 10 degrees. This study employs a time-domain coupled dynamic analysis model to investigate a monopile foundation supporting a 5-MW offshore wind turbine (OWT) on a gently sloping sandy seabed, using the finite element software OpenSees. The feasibility of the numerical model for simulating the seismic response of a gently sloping sandy seabed was validated through Liquefaction Experiments and Analysis Projects (LEAP) centrifuge tests. The results indicate that the excess pore water pressure (EPWP) in the sloping seabed is influenced by the interaction between the initial shear stress and the lateral movement of the seabed. The maximum horizontal displacement of OWTs is significantly affected by the seabed slope angle, with the impact occurring through the rotation of the OWT monopile. As the EPWP increases, the dominant vibration frequency of the OWT system tends to approach the natural frequency of OWTs, resulting in a larger horizontal displacement. This process is affected by factors such as the peak of the seismic motion, seismic frequency, and the seabed slope. These findings provide key insights for improving OWT monopile stability under gently sloping seabed conditions.

The stability of rubble mound breakwaters is highly affected by extreme wave loading. While extensive research has been devoted to wave-induced scour and liquefaction around breakwaters, comprehensive stability evaluations of the rubble mound breakwater core remain limited. This study develops a numerical framework to investigate the stability of rubble mound breakwaters subjected to solitary wave loading. Wave motion is modeled using the Navier–Stokes equations, wave-induced pore pressure is computed based on Darcy’s law, and soil behavior is represented through the Mohr–Coulomb constitutive model. The numerical model is validated against experimental data. To assess structural stability, the strength reduction method is employed to calculate the Factor of Safety (FOS) during wave propagation, with the minimum FOS serving as the stability criterion. Furthermore, the influence of key parameters, including wave height, soil shear strength, wave–current interaction, berm dimensions, and slope gradient, on breakwater stability is systematically analyzed.

Understanding the nonlinear dynamic responses and damage mechanisms of subsea shield tunnel is essential for the seismic design, especially under near-field ground motions. However, conventional constitutive models often fail to capture the cyclic degradation of marine clays completely, leading to the underestimation of seawater-seabed-tunnel coupling effects. Thus, a modified Davidenkov model incorporating a damage evolution model and a critical shear modulus, is proposed and implemented in ABAQUS. Then, a three-dimensional (3D) seismic input method for marine sites is developed to simulate the obliquely incident P and SV waves. The proposed numerical method has been validated by comparing modelling results against both theoretical and numerical benchmarks in literature. Furthermore, a 3D finite element model for a segmental subsea shield tunnel has been developed to investigate the seismic responses under various incidence angles. Modelling results indicate that oblique waves intensify tunnel damage, with concentrations being found at the crown, invert, and haunch. The maximum damage occurs under 60 degrees incident P waves and 30 degrees SV waves. Oblique waves also exacerbate the residual vertically elliptical deformation and joint openings, particularly at the haunch. This study would pave a reliable numerical platform for the seismic design and safety assessment of subsea shield tunnels.

The influence of seawater on seafloor motions cannot be neglected in the seismic design of offshore structures. On the basis of a recently proposed generalized non-Masing hysteretic constitutive model, a nonlinear seismic response analysis of the seabed site crossing the Qiongzhou Strait is developed using the fluid-solid weak coupling method. In the proposed seabed site response analysis, the seafloor topographic characteristics and spatially inhomogeneous seabed soils of the Qiongzhou Strait are considered in detail. The seafloor motion characteristics are comprehensively affected by the fluid-solid coupling effect between seawater and seabed, the seabed topography effect, the nonlinearity of seabed soils, and the characteristics of seabed-bedrock input motions. Due to the fluid-solid coupling effect of the seawater-seabed system, the peak accelerations at the seafloor are reduced and the significant durations of seafloor motions from seabed bedrock are shortened, and the suppression effect of seawater on vertical seafloor motions is greater than that on horizontal seafloor motions. Seawater attenuates or amplifies the resonance-like phenomenon at the seabed surface in the high-frequency bands (similar to 2.0 Hz) or low-frequency bands (< 0.5 Hz) induced by the horizontal and vertical seismic components, and the attenuation or amplification effect increases with the intensity of the input seabed bedrock motions. The 5% damping normalized spectral accelerations beta at the seabed surface decrease and increase, respectively, near the fundamental period (0.25 similar to 1.1 s) of the seabed site or long period (> 1.1 s).

To adapt to complex underwater geological conditions, immersed tunnel projects have gone through the development from rigid and flexible to semirigid immersed tunnels. The stiffness of segment joints and the element joint could reflect the differences in structural characteristics of the three types of immersed tunnels. This paper presents a theoretical model using segment joints, the element joint, and 16 segments for the longitudinal seismic response analysis of the three types of immersed tunnels. Based on the matrix transfer principle, the end boundary conditions and the continuity conditions for the forces and deformations at the segment joints and element joint were considered. Analytical solutions were validated by verifying the established laws. Results indicate that the semirigid immersed tunnel, in contrast to the rigid immersed tunnel, can reduce shear forces and bending moments along the longitudinal direction by using segment joints and the element joint. In addition, compared with the flexible immersed tunnel, the semirigid immersed tunnel has higher overall stiffness and better continuity of deformation between the adjacent soil regions through the prestressed tendons inside the tube element. The semirigid immersed tunnel is a viable solution for complex geological conditions where the strata change every few tens of meters.

Offshore wind turbines (OWTs) are gaining prominence worldwide, and the hybrid pile-bucket foundation, which combines a monopole and a bucket, has emerged as a noteworthy development. In this study, a 3-D numerical model for the 5-MW OWT was constructed utilizing the OpenSees platform. The dynamic characteristics of the sand was modeled with the PDMY02 constitutive model and the soil was discretized using brick u-p elements. To investigate the dynamic behavior of the OWT in an actual marine environment, the coupled model was subjected to dynamic loadings, encompassing waves, wind, and earthquake. Two seismic motions with different frequency components were considered, respectively. The study focused on exploring the impacts of key influencing factors on the OWT rotation, tower-top acceleration development and spatiotemporal distribution of excess pore water pressure ratio (EPWPR). These factors include dynamic load combinations, earthquake intensity, soil relative density, wind speed, angle between load directions, and pile length. It is revealed that the inclination angle of offshore wind turbines (OWTs) may exceed the allowable threshold under specific conditions of load combinations, seismic motion inputs, and seabed conditions. Thus, it is suggested to appropriately consider the effects of wind and wave actions in the seismic analysis of OWTS.

Marine structures are commonly situated near the mildly sloping sandy seabed characterized by the slope angles (alpha) not exceeding 10 degrees. The seabed liquefaction can be triggered due to the generation of the excess pore water pressure (EPWP), posing a threat to the stability of marine structures. This study focuses on the analysis of waveinduced liquefaction in the mildly sloping (MS) sandy seabed. A dynamic poro-elasto-plastic seabed model is developed to simulate the behavior of the MS sandy seabed under wave loading. The results indicates that the loading cycle required to trigger the initial liquefaction decreased as the position moved from the toe towards the crest of the MS sandy seabed. The amplitude of shear stress increases with the loading cycle and tends to increase with growing alpha before liquefaction, resulting in a slower accumulation of EPWP with larger alpha. Both the horizontal and vertical displacements induced by wave action reach the maximum at the crest of the sloping seabed. Notably, the horizontal displacement is much greater than the vertical displacement in the seabed under wave action. The displacement of the MS sandy seabed depends on not only the shear stress amplitude developed in the soils but also the accumulation of EPWP required to trigger the liquefaction in the seabed.

In the marine environment, the seabed contains a certain amount of clay. Experimental studies show that the liquefaction susceptibility of the sandy seabed increases as clay content (CC) rises to a certain threshold, beyond which further increases in CC reduce liquefaction susceptibility. However, numerical models that describe the effect of CC on seabed liquefaction are very limited. This study proposed a dynamic poro-elasto-plastic finite element method model for analyzing liquefaction in the sandy seabed with CC below the threshold. Based on a series of undrained triaxial compression tests on sand-clay mixtures from existing literature, a unified constitutive framework was demonstrated to be effective for describing the liquefaction behavior of sand with low CC using one set of model parameters. Existing wave flume model tests validated the effectiveness of the proposed seabed model in describing the effect of low CC on excess pore water pressure (EPWP). Numerical results confirmed that adding a small amount of clay to the seabed increased the soil contraction and thus its liquefaction susceptibility. Wave-induced liquefaction was limited to a certain depth of the seabed, and the liquefaction depth was significantly affected by the CC. Adding a low content of clay the sandy seabed significantly increased both horizontal and vertical displacements under wave action, potentially leading to the instability of the seabed. This study provides a new method for accurately assessing the wave-induced stability of marine structures built on the sandy seabed containing certain amounts of clay.