Seabed Liquefaction Risk Assessment Based on Wave Spectrum Characteristics: A Case Study of the Yellow River Subaqueous Delta, China

Abstract

Seabed liquefaction induced by wave loading poses considerable risks to marine structures and requires careful consideration in marine engineering design and construction. Traditional methods relying on statistical wave parameters for analyzing random waves often underestimate the potential for seabed liquefaction. To address this underestimation, the present study employs field observations and numerical simulations to examine wave characteristics and liquefaction distribution across various wave return periods in the Chengdao Sea area of the Yellow River subaqueous delta. The research results indicated that the wave decay phase exhibited a higher liquefaction potential than the growth phase, primarily because of the prevalence of low-frequency swell waves. The China Hydrological Code Spectrum (CHC Spectrum) effectively captured the wave characteristics in the study area, with parameterization grounded in measured data. The poro-elastic wave–sediment interaction model further elucidated the liquefaction distribution under extreme wave conditions, revealing a maximum liquefaction depth exceeding 3 m and prominent liquefaction zones at water depths of 5–15 m. Notably, seabed properties emerged as a critical factor for liquefaction and overshadowed water depth, with non-liquefaction zones occurring at water depths of less than 15 m at high clay content, highlighting the general liquefaction risk of silty seabed. This study enhances understanding of the seabed liquefaction process and offers valuable insights into engineering safety.

1. Introduction

Seabed liquefaction is a geotechnical phenomenon characterized by a temporary loss of strength in seabed soil, particularly in sandy and silty sediments, and is induced by external forces such as seismic activity and intense wave action. This phenomenon is prevalent in coastal regions and poses substantial geological hazards that can undermine the structural integrity of marine infrastructure, including breakwaters, oil pipelines, subsea foundations, drilling platforms, and underwater tunnels [1]. In addition, as climate change drives sea level rise, the severity of liquefaction hazards is anticipated to increase [2]. Recent research has demonstrated that seabed liquefaction diminishes the soil-bearing capacity of the seabed and contributes to increased concentrations of suspended sediments within the water column, thus adversely affecting water quality and the ecological health of marine environments [3,4]. These challenges underscore the urgent need for effective seabed liquefaction management strategies in coastal zones.

Wave-induced seabed liquefaction is particularly pronounced in silty and muddy coastal areas and is widely distributed in estuaries and continental shelves around the world. The formation mechanism and evolution of seabed liquefaction have been previously elucidated through extensive field observations [5,6,7] and laboratory experiments involving wave flumes [8,9,10]. The dynamics of seabed liquefaction are inherently linked to reductions in effective stress within the soil, which correspondingly diminishes its shear strength. Bennet et al. [11] observed significant variations in pore water pressure in response to storm activity, based on field observations in the Mississippi Delta. Similarly, Klammler et al. [5], using field fan-scan sonar data from the northern Gulf of Mexico, demonstrated changes in the orientation of buried seabed targets, providing evidence of liquefaction. Xu et al. [6] conducted a detailed field monitoring study in the Chengdao Sea area of the Yellow River Delta, which revealed that liquefaction onset occurred at a water depth of 8 m when significant wave heights exceeded 0.5 m. An average liquefaction development rate of approximately 0.17 m per min was documented, with maximum liquefaction depths ranging from 3.3 to 3.8 m.

Unlike laboratory settings, natural wave environments are characterized by the superposition of waves across a spectrum of frequencies, with each contributing to the complex interplay of dynamic characteristics through nonlinear interactions. To facilitate quantitative assessments, researchers often rely on statistical wave parameters to represent the action of random waves, and frequently overlook the liquefaction potential associated with varying frequency components [8]. Recent studies have increasingly focused on the response of the seabed to distinct wave frequencies, leading to a growing consensus that low-frequency waves such as swells predominantly influence the development of liquefaction [5,8,9]. Therefore, employing a parametric function to characterize the wave spectrum through statistical analysis is essential to accurately depict the energy composition of these waves. Consequently, the wave spectrum described in the “Code for Sea Port Hydrology” [12], referred to as the China Hydrology Code Spectrum (CHC Spectrum), is derived from the actual wind wave conditions observed in China’s nearshore sea. An analysis of extensive wave observation data from the Yellow Sea, Bohai Sea, East China Sea, and South China Sea revealed that the CHC spectrum aligns more closely with the measured data compared to the internationally recognized JONSWAP spectrum [12]. As a result, the CHC spectrum has been widely adopted in coastal engineering applications.

In recent decades, several analytical solutions have been derived to estimate liquefaction depth [13,14]. Zhu et al. [4] integrated the analytical solution of liquefaction depth proposed by Jeng et al. [14] into the FVCOM, enabling predictions for the liquefaction distribution and associated sediment dynamics. Utilizing wave observation data coupled with sonar scans, Klammler et al. [15] employed a poro-elastic wave–sediment interaction model [16] to accurately predict the burial depths of pre-existing targets. However, the existing literature has not adequately addressed the risks associated with seabed liquefaction across random wave action, especially when predictions are based on measured wave spectra.

In the Yellow River subaqueous delta, wave characteristics are delineated through comprehensive wave observation data. The distribution of liquefaction under extreme wave events are assessed by integrating wave simulation data with sedimentological conditions and the poro-elastic wave–sediment interaction model, emphasizing the pivotal role of sediment properties in influencing liquefaction.

2. Materials and Methods

2.1. Study Area

The Yellow River is renowned globally for its significant amount of sediment transport, with an estimated annual delivery of approximately 1.08 × 10⁹ t of sediment to the sea, ranking second only to the Amazon River [17]. This remarkable sediment load has attracted substantial attention from researchers. Since 1855, the river has experienced 11 major channel shifts [18], each giving rise to new subdelta lobes.

Between 1970 and 1976, the river discharged into the sea via the Diaokou course, depositing a thick layer of silty soil several meters deep in the Diaokou lobe. However, by 1976, the river had shifted its course from Diaokou to Qingshuigou (Figure 1a). The cessation of sediment transport in the modern Yellow River has resulted in significant erosion of the Diaokou lobe, highlighting the profound influence of human activities on river and coastal dynamics.

The Bohai Sea, characterized as a semi-enclosed body of sea, is inherently influenced by its topography, which restricts the influx of waves from the open sea. Consequently, the wave characteristics within this region are predominantly shaped by prevailing winds, leading to rapid generation and dissipation phenomena. The Chengdao Sea area, situated in the northern part of the delta within the Diaokou lobe, exemplifies a wave-dominated environment. In this region, winter winds can generate waves exceeding 4 m in height, creating conditions that may induce seabed liquefaction and trigger sediment density flows [17,19]. These processes accelerate local topographic adjustments on the seabed. The area also encompasses the Chengdao oil field, part of the Shengli Oil Field—China’s second-largest oil reserve. Due to intensive oil extraction activities and frequent risks of liquefaction and erosion, the Chengdao Sea area has become a critical site for scientific investigation, serving as a natural laboratory for the study of wave dynamics.

2.2. Field Observations

From 17 December 2014 to 28 March 2015, a stainless-steel platform was deployed on the subaqueous seabed in the Chengdao Sea area (38.251° N, 118.845° E, the coordinate reference system is the World Geodetic System—1984). The platform was anchored into the seabed using piles to ensure a stable attitude of the instrument. The platform was equipped with an up-looking acoustic wave and current (AWAC, Nortek 600 kHz, Rud, Norway) at a height of 0.8 m to monitor currents (not used in this study) and surface waves in the upper water column. Wave measurements in burst mode were configured to sample every two hours for 1024 s per measurement.

In 2014, 435 surface sediment samples were collected from the seabed of Chengdao Sea (Figure 1). The samples were subjected to a particle size analysis in the laboratory using a laser particle size analyzer (Mastersizer 2000, Malvern Panalytical, Malvern, UK). The resulting data included key granulometric characteristics such as mean particle size, median particle size, sorting coefficient, skewness, kurtosis, and sediment classification. The sampling stations were distributed relatively uniformly throughout the study area with a sampling interval of 1000 m between adjacent stations.

2.3. Analysis Methods

2.3.1. Wave Parameter

Basic wave parameters such as wave height and period were calculated based on the AWAC observation results. The effect of the surface waves decays with depth. Recently, Kenneth et al. [20], based on field measurements, found that linear wave theory provides a more accurate prediction of bottom pressure changes caused by surface waves compared to the theory proposed by Longuet-Higgins [21], which is used to predict nonlinear interactions of surface waves. According to small amplitude theory, the underwater pressure ($p$) at $z$ varies with time ($t$) as follows:

$$p\left(x,z,t\right)=a{\displaystyle \frac{\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left[k\right(h+z\left)\right]}{\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left(kh\right)}}\mathrm{s}\mathrm{i}\mathrm{n}(kx-\omega t)$$

(1)

where the wave propagates along the $x$ axis, $z$ represents the observed depth, $a$ represents the amplitude on the surface, $k$ represents the wave number, $h$ represents the water depth, and $\omega$ represents the circular frequency. The fluctuation of the surface wave ($\eta$) with $t$ is as follows:

$$\eta \left(x,t\right)=a\mathrm{s}\mathrm{i}\mathrm{n}(kx-\omega t)$$

(2)

combining Equations (1) and (2), the following is obtained:

$$\eta \left(x,t\right)={\displaystyle \frac{p\left(x,z,t\right)}{K_p\left(z\right)}}$$

(3)

where $K_p\left(z\right)$ is the pressure correction factor of the surface wave.

$$K_p(z)={\displaystyle \frac{\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left[k\right(h+z\left)\right]}{\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left(kh\right)}}$$

(4)

The corresponding angular wave number $k$ was found from the dispersion relation.

$${\omega }^2=gk\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left(kh\right)$$

(5)

The zero-crossing wave analysis method was used to analyze the calibrated $\eta$, and the amplitude and period of each wave were obtained.

The zero-crossing wave analysis method in the time domain was used to analyze the calibrated $\eta$ to derive the wave height and wave period for individual waves [22]:

$$H={\displaystyle \frac{{\eta }_{max}-{\eta }_{min}}{2}}$$

(6)

where ${\eta }_{max}$ and ${\eta }_{min}$ are the maximum and minimum values, respectively, between two zero-up crossing points. For each burst, the significant wave height ($H_s$) and significant wave period ($T_s$) were expressed as the average wave height and period of the first third of a large wave, respectively.

The surface wave pressure spectrum $S_{\eta }\left(f\right)$ was obtained through a Fourier analysis of instantaneous wave pressure. The peak period ($T_p$) is defined as the period corresponding to the highest energy of $S_{\eta }\left(f\right)$.

2.3.2. Wave Spectrum

Wave spectra represent a crucial concept in ocean statistics because they characterize fundamental wave parameters, such as wave height and period, and facilitate the investigation of the energy distribution within ocean waves. This understanding is essential for calculating the wave load forces in coastal engineering applications. The spectral parameters of the CHC Spectrum were calculated according to the measured spectrum $S_{\eta }\left(f\right)$, and the obtained CHC spectrum was compared with the measured spectrum. When the zero-order moment $m_0$ of the wave spectrum and peak wave frequency $f_p$ are known, the general form of the CHC spectrum can be expressed as follows:

$$\left\{\begin{array}{c}s\left(f\right)=\alpha P\mathrm{e}\mathrm{x}\mathrm{p}\left[-95\ln \left(PQ\right){\left({\displaystyle \frac{f}{f_p}}-1\right)}^{12/5}\right] 0\le f\le 1.15f_p\\ s\left(f\right)={\displaystyle \frac{\alpha }{Q}}{\left({\displaystyle \frac{1.15f_p}{f}}\right)}^{\left(4-2H^{\mathrm{*}}\right)} f>1.15f_p\end{array}\right.$$

(7)

where

$$\alpha ={\displaystyle \frac{m_0}{f_p}}=A{H}_s^2{T}_s$$

(8)

$$P={\displaystyle \frac{f_{p}s\left(f_p\right)}{m_0}}={\displaystyle \frac{B{H}_s^{1.35}}{T_s^{2.7}}}, 1.27\le P<6.77$$

(9)

$$Q={\displaystyle \frac{5.813-5.137H^{*}}{\left(6.77-1.088P+0.013P^2\right)\left(1.307-1.426H^{*}\right)}}$$

(10)

$$H^{*}=0.626{\displaystyle \frac{H_s}{h}}$$

(11)

where $h$ is the water depth obtained by AWAC. $H^{\mathrm{*}}$ is close to 0 in deep water and 1/2 in shallow water, where waves break. $P$ is the spectral sharpness factor that satisfies the range requirements. The values of each parameter can be obtained by the measured spectrum $S_{\eta }\left(f\right)$.

2.3.3. Liquefaction Model

Based on the pressure observed near the seabed, Klammler et al. [15] used the poro-elastic wave–sediment interaction model [16] to accurately predict the buried depth of a pre-buried target through the vertical effective stress loss according to the criteria of sediment liquefaction. In this study, the liquefaction depth ($z_{liq}$) was calculated according to this liquefaction model. The key calculation processes and explanations are as follows.

The seabed was assumed to be fully saturated with an infinite thickness and isotropic. According to the linear wave theory, based on Equations (3)–(5), the pressure distribution $p_b$ on the seabed surface can be approximated as a truncated Fourier summation as follows:

$$P_b\left(x,t\right)=Re\{\sum _{m=1}^M{\displaystyle \frac{a_m}{\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left(k_m{d}_p\right)}}exp[i(k_{m}x-{\omega }_{m}t+{\epsilon }_m)]\}$$

(12)

where $d_p$ is a meter above seabed, $a_m$ and ${\epsilon }_m$ are the amplitudes and phase angles, respectively, ${\omega }_m$ is the angular frequency, $M$ is the number of summation terms used, $i$ is the imaginary unit, and $Re\left\{\right\}$ denotes the real part of a complex magnitude.

Respective solutions for the wave-induced sediment pore pressure ($P_p$), horizontal effective stress (${\sigma }_x^{\prime }$), vertical effective stress (${\sigma }_z^{\prime }$),’ and shear stress (${\tau }_{xz}$) as functions of $x$, $t$, and the vertical coordinate, z, are as follows [5]:

$$\left[\begin{array}{c}{P}_p\\ {\sigma }_x^{\prime }\\ \begin{array}{c}{\sigma }_z^{\prime }\\ {\tau }_{xz}\end{array}\end{array}\right]=Re\{\sum _{m=1}^M{\displaystyle \frac{a_m}{\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left(k_m{d}_p\right)}}\left[\begin{array}{c}P\\ -S_x\\ \begin{array}{c}{S}_z\\ iT\end{array}\end{array}\right]\mathrm{e}\mathrm{x}\mathrm{p}[i(k_{m}x-{\omega }_{m}t+{\epsilon }_m)]\}$$

(13)

$S_z$ is a complex variable that depends on seabed properties such as porosity ($n$), horizontal and vertical hydraulic conductivities ($K_x$ and $K_z$, respectively), degree of saturation ($S_r$), shear modulus ($G$), Poisson ratio ($\mu$), density and elastic modulus of sea water (${\rho }_w$ and $K_w$, respectively), and so on [5].

$$\begin{gathered} S_z=\left[C_1^m+C_2^m{k}_{m}z-{\displaystyle \frac{2{\lambda }_m\left(1-\mu \right)}{1-2\mu }}{C}_2^m\right]\exp \left(k_{m}z\right)+\left[C_3^m+C_4^m{k}_{m}z+{\displaystyle \frac{2{\lambda }_m\left(1-\mu \right)}{1-2\mu }}{C}_4^m\right]\exp \left(-k_{m}z\right) \\ +\left[{\displaystyle \frac{{\delta }_m^2\left(1-\mu \right)-k_m^2\mu }{1-2\mu }}\right][C_5^m\exp \left({\delta }_{m}z\right)+C_6^m\exp \left(-{\delta }_{m}z\right)] \end{gathered}$$

(14)

According to the effective stress criterion, the liquefaction degree $L$ is defined as follows:

$$L={\displaystyle \frac{{\gamma }_w{\sigma }_z^{\prime }}{({\gamma }_s-{\gamma }_w)z}}$$

(15)

where ${\gamma }_w$ and ${\gamma }_s$ represent the unit weights of the pore fluid and soil ($\mathrm{k}\mathrm{N}/{\mathrm{m}}^3$), respectively. In general, values of $L\ge 1$ are usually interpreted as the liquefaction state, and the corresponding liquefaction depth is expressed as $z_{liq}$.

As a further extension, when limiting the wave frequency band in Equation (13), the liquefaction degrees of the infra-gravity, swell, and wind wave bands can be evaluated and denoted as $L_{iw}$, $L_{sw}$, and $L_{ww}$, respectively.

2.3.4. FVCOM Simulation

This study analyzed wave conditions using simulation results from the Finite Volume Community Ocean Model (FVCOM) with an unstructured grid [23,24]. This model has been successfully applied to investigations of estuaries, coastal regions, and nearshore continental shelves [25]. The numerical model employed in this study encompassed the entire Bohai Sea area.

The wave module in FVCOM (FVCOM SWAVE) is based on the surface wave model SWAN, which simulate waves in nearshore environments [26]. The topographic data used in the model were extracted from the China Marine Atlas and ETOPO1 datasets [27]. Additionally, measured bathymetric data from nearshore estuarine areas were incorporated for further refinement. In the simulation, the model is driven by tidal forces and circulation from open boundary conditions, with input from eight tidal components (M2, S2, O1, Q1, K1, P1, K2, and N2). Initial temperature and salinity values were obtained from HYCOM data. Hourly-resolution sea surface forcing data, including wind, air pressure, air temperature, relative humidity, longwave and shortwave radiation, precipitation, and evaporation, were sourced from the ECMWF ERA Interim dataset.

The simulations were based on actual meteorological conditions from 2010 to 2021. The model was previously validated by Liu et al. [28]. This study primarily utilized the simulated significant wave height and peak wave period in conjunction with the spectral characteristics of the observed wave data to assess the liquefaction potential of the subaqueous delta of the Yellow River. For an additional introduction to the FVCOM numerical model, refer to Liu et al. [28].

3. Results and Discussion

3.1. Wave Conditions

The weather system is an important factor affecting wave conditions in the study area. During the observation period, with an increase in wind power, the study area experienced several large wave events with $H_s$ > 2 m (Figure 2). Previous work has shown that large waves in the study area mainly occur during northerly wind events, with the wave height and period rising rapidly under the influence of northeasterly winds and slowly decreasing during northwest winds [29,30,31]. In general, the trends of the wave height and period were mostly the same, and the two demonstrated a linear relationship. During wave growth, the wave height and period increased rapidly; however, during wave attenuation, the rate of decrease of $H_s$ was often faster than that of $T_p$, resulting in a relatively discrete relationship between $H_s$, $T_p$, and $T_s$ (Figure 2 and Figure 3). This relationship may have resulted from the gradual dominance of the imported long-period swells during wave decay. A similar phenomenon has been reported by Niu et al. [29], and 0.14 Hz (approximately 7 s) is considered the cut-off frequency of wind waves and swell waves.

3.2. Estimation of CHC Spectrum Parameter

The parameters of the CHC Spectrum were solved according to Equations (7)–(11). The significant wave height $H_s$ is the main characterization parameter of the wave intensity. In this study, appropriate models were used to fit the obtained spectral parameters to $H_s$ (Figure 4). To further evaluate the rationality of the fitted equation, the average value of each parameter within a certain wave height range was calculated (Figure 4). A strong correlation was observed between the parameters and $H_s$; most of the data points fell within the 95% confidence interval, and the average value was distributed along the fitting line (Figure 4).

The spectral sharpness factor $P$ was the premise for using the CHC Spectrum; although some $P$ values were less than 1.27, the group average values all met the range requirements, indicating that the CHC Spectrum could be used to represent the spectral characteristics of the study area. $H_s$ and $P$ exhibited a cubic polynomial relationship with a coefficient of determination $R^2$ of 0.21. $\alpha$ was jointly determined by wave height and period. Owing to the existence of a swell wave, the same wave height in the wave growth and decay stages often had different periods, which was the direct cause of errors in the fitting process. $H_s$ and $\alpha$ are quadratic polynomials, and the $R^2$ was 0.98. The value range of parameter $Q$ ranged between 0.8 and 1.2, and with the increase in wave height, $Q$ decreased slightly. However, as a variable dependent on the water depth, the fitting formula determined in this study may have had limitations. In practical applications, the $Q$ value can be jointly determined according to $P$ and $H^{\mathrm{*}}$ values. After $\alpha$, $P$ and $Q$ are determined, and the specific expression of the CHC Spectrum can be obtained.

The zero-moment and peak frequencies of the wave spectrum depend on the measured data and are often unknown in practical applications. When $H_s$ and $T_s$ are known, parameters $A$ and $B$ are required to determine the CHC Spectrum expression. $A$ and $B$ can be generally considered as fixed values for a particular sea area. For parameter $A$, because ${\displaystyle \frac{H_s}{\sqrt{m_0}}}\approx 4$, $A\propto {\displaystyle \frac{T_p}{T_s}}$ according to Equation (8). Although the data dispersion of $T_p$ and $T_s$ was relatively high, these variables were positively and linearly correlated (Figure 2d and Figure 4). Therefore, in this study, $A$ was set as 0.08 (Figure 4). The parameters $B$ and $H_s$ showed clear negative power correlation, and the $R^2$ was 0.81. According to the fitting equation, Equation (9) can be rewritten.

$$P={\displaystyle \frac{B{H}_s^{1.35}}{T_s^{2.7}}}=100.73{\displaystyle \frac{H_s^{0.111}}{T_s^{2.7}}}$$

(16)

This equation means that the expression of the CHC Spectrum may need to be further modified in this study area; however, this modification would require more measured data as support.

The CHC Spectrum was derived based on the values of each parameter and compared with the measured spectrum. Under varying wave conditions, the CHC Spectrum exhibits a strong correlation with the measured spectrum across all frequency wave bands (Figure 5). For all observed time series, the $R^2$ value between the two spectra exceeds 0.6, indicating that the CHC spectrum effectively captures the wave characteristics in the study area.

3.3. Wave Height Distribution in Different Return Periods

The annual maximum values at each grid point were calculated based on 11 years of continuously simulated wave data. The wave parameters in the return periods (2, 5, 10, 20, and 50 years) were then derived using the Pearson-III distribution (Figure 6). The distribution patterns of the wave heights in different return periods were generally consistent; hence, only the wave height distribution for the 50-year return period is presented in Figure 7. The wave height isopleths were nearly parallel to the depth contour lines, indicating larger wave heights in shallow coastal areas and smaller heights in deeper waters, with a rapid decrease in wave heights near the 10 and 5 m water depth contours.

3.4. Effect of Wave Frequency on Seabed Liquefaction

The liquefaction model was verified prior to its use to calculate the liquefaction depth. Zhu et al. [4] set the values of porosity $n$ and Poisson’s ratio $\mu$ as 0.51 and 0.35, respectively, ignored the frequency difference of waves, obtained the analytical solution of the liquefaction depth according to the statistical wave parameter ($H_s$), and calculated the maximum distribution of the liquefaction depth under a high wave event (22 February 2015). For comparison, this study accepted the Zhu et al. [4] parameter suggestion and calculated the liquefaction depth for the corresponding period (Figure 8). Similar results were obtained, with liquefaction in the present study mainly occurring in the water depth range of 5–10 m, and approximately the same location of the strong liquefaction zone. This result indicates that the liquefaction model used in this study was suitable for the study area. However, the calculated liquefaction depth was generally large, indicating that the use of statistical wave parameters may have underestimated the liquefaction potential, which is consistent with several previous experimental results [8,9].

The liquefaction depths at different wave development stages were evaluated based on the measured wave data. In the wave growth stage, $H_s$ was 3.3 m, the most obvious liquefaction event was dominated by wind waves, and the maximum liquefaction depth was close to 0.6 m (Figure 9a). After 4 h, the wave entered the decay stage, and because the peak frequency of the wave spectrum was not significantly reduced (Figure 3), the surging wave dominated the development of liquefaction. Although $H_s$ was reduced to 3 m, the liquefaction degree caused by the surging wave significantly increased, and the maximum depth of liquefaction was close to 0.8 m (Figure 9b). This result shows that it is necessary to consider the influence of wave frequency when calculating the liquefaction depth.

3.5. Liquefaction Depth in Different Return Periods

Based on the wave spectrum parameters determined in Section 3.2 and the FVCOM wave simulation data, random wave time series under different return periods were reconstructed to serve as the dynamic forcing of the liquefaction model.

This study primarily investigates the influence of seabed soil properties on seabed liquefaction through the parameter $S_z$, as shown in Equation (14). In practice, these parameters are not easily obtainable, especially when determining the corresponding seabed property values based on sediment sample grain size distributions. In the study area, Du [32] obtained a comprehensive set of geotechnical parameters based on 42 in situ-measured sediment core samples, predominantly silt, with an average porosity of 0.51. This value was later used in the work of Zhu et al. [4], who successfully reproduced the liquefaction zones in shallow sea. Poisson’s ratio describes the state of the soil; however, records of Poisson’s ratio are scarce. Both aforementioned studies adopted a value of 0.35 for this parameter. To account for the impact of grain size distribution in the liquefaction model, this study adopts a porosity value of 0.51, which represents the average in situ density state of the soil, thereby simplifying the model. Additionally, appropriate Poisson’s ratios are assigned to the sediment samples based on their grain size. For the other parameters required in the $S_z$, the recommendations of Zhu et al. [4] are followed.

Numerous relevant studies have been published on this topic. For instance, Porcino et al. [33] and Polito and Sibley [34], based on geotechnical testing, found that liquefaction is primarily associated with clean sand and silty sand, where the silt content is below a threshold limit. When the silt content exceeds this threshold, the liquefaction risk decreases accordingly. Bouferra and Shahrour [35], considering clay content, observed similar behavior. These studies have significantly enhanced the understanding of how sediment composition influences liquefaction behavior. However, in most of these reports, the silt content in the tested soils does not exceed 45%, with the poorest liquefaction resistance observed in soils with around 20–30% silt content. Therefore, for regions where the silt content generally exceeds 40% (Figure 1c and Figure 10), the liquefaction transition state remains uncertain.

Cao [36] conducted another valuable study based on field soil samples from the Chengdao Sea area, testing the critical shear stress of samples with varying clay content. The study found that when the clay content exceeded approximately 15%, the critical shear stress increased linearly, significantly enhancing the soil’s shear strength. Thus, clay content can be considered a key parameter for liquefaction resistance. In the current study, as clay content increases, silt content initially rises and then declines, with a critical inflection point at approximately 15% clay content (Figure 10). This suggests that the threshold is linked to a transition in soil properties. Higher clay content is typically associated with deeper marine environments (Figure 1c and Figure 10), where wave-induced seabed disturbances are minimal, indicating a sedimentary environment distinct from shallow waters. Consequently, in this study, when the clay content was <15%, Poisson’s ratio was set to 0.35, and when the clay content was >15%, Poisson’s ratio was reduced to 0.25. Notably, the relationship between $S_z$ and clay content is expressed through the adjusted Poisson’s ratio.

The distribution of the liquefaction depth under different wave return periods was further calculated (Figure 11), and the maximum liquefaction depth under 50-year wave conditions was more than 3 m. Generally, water depth is a key factor affecting the distribution of the liquefaction zone. With an increase in the wave return period, the overall seabed liquefaction depth increased within a certain depth range, the liquefaction zone expanded, and the position of the maximum liquefaction depth moved to the deep-water zone. The liquefaction zone was mainly concentrated at a water depth of 5–15 m, which was consistent with the results of Du [32].

Seabed properties are prerequisites for liquefaction. Being limited by the clay content, although the dynamic conditions were sufficiently strong in the present study, two non-liquefied centers appeared in the water depth range of 12–13 m. Under wave conditions of 10, 20, and 50 years, the liquefaction depth reached more than 2 m at a depth of 15 m. Therefore, in deeper sea areas, if the clay content of the silty seabed is low, the risk of seabed liquefaction cannot be ignored under sufficient wave conditions.

Seabed liquefaction is a particularly complex and challenging process to quantify. Soil properties and stress states dictate the type of soil movement, while ocean sediment dynamic processes—such as seabed erosion, sedimentation, and sediment re-suspension—serve as potential manifestations. Seabed liquefaction remains a working theory, and relevant observations have not yet been fully developed.

This study employs a series of theoretical formulas and models to calculate liquefaction depth by considering factors such as the wave spectrum (wave frequency), wave return period, and seabed characteristics. These calculations are based on several assumptions, including a fully saturated seabed and a relatively shallow liquefaction depth. However, the calculated liquefaction depth has not been validated against drilling or geophysical survey data. Consequently, the findings of this study require ongoing verification and refinement. Future research should prioritize the integration of seabed engineering properties—such as those obtained through cone penetration tests or dynamic triaxial tests—and bottom boundary layer sediment dynamics to advance understanding of seabed liquefaction processes.

4. Conclusions

This study was based on field observations of waves in the Yellow River subaqueous delta, and relevant wave characteristics were obtained. The seabed liquefaction distribution under extreme wave events was studied by considering the wave frequency and seabed conditions in a poro-elastic wave–sediment interaction model. The main conclusions are as follows:

(1)

The wave spectrum characteristics of different wave development stages were unique. Owing to the presence of a swell wave, the peak period decline was slower. Compared to similar wave height conditions in the wave growth stage, the wave decay stage had a greater liquefaction potential.

(2)

The CHC Spectrum can accurately reflect the wave characteristics of the study area, and this spectrum can be parameterized according to wave height and period.

(3)

The liquefaction zone was mainly distributed at water depths between 5 and 15 m. With an increase in the wave return periods, the seabed liquefaction depth increased, the liquefaction zone expanded, and the position of the maximum liquefaction depth moved to the deep-water zone. Under extreme wave conditions in 50-year return periods, the maximum depth of liquefaction exceeded 3 m. The clay content (seabed properties) was a prerequisite for liquefaction compared with water depth, and the risk of liquefaction is substantial for silty seabed with water depths greater than 15 m.