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Spatial and temporal variation process of seabed dynamic response induced by the internal solitary wave
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Zhuangcai Tian1, 2, *, Lei Jia1, Naili Hu3, Susheng Wang1, Mingwei Zhang1, *, Guoqing Zhou1
Acta Oceanologica Sinica | 2023, 42(2) : 142 - 149
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Acta Oceanologica Sinica | 2023, 42(2): 142-149
• Ocean Engineering •
Spatial and temporal variation process of seabed dynamic response induced by the internal solitary wave
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Zhuangcai Tian1, 2, *, Lei Jia1, Naili Hu3, Susheng Wang1, Mingwei Zhang1, *, Guoqing Zhou1
Affiliations
  • 1 State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China
  • 2 Key Laboratory of Coastal Science and Integrated Management, Ministry of Natural Resources, Qingdao 266061, China
  • 3 Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Ocean University of China, Qingdao 266100, China
Published: 2023-02-25 doi: 10.1007/s13131-022-2112-3
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Internal solitary wave (ISW) is often accompanied by huge energy transport, which will change the pore water pressure in the seabed. Based on the two-dimensional Biot consolidation theory, the excess pore water pressure in seabed was simulated, and the spatiotemporal distribution characteristics of excess pore water pressure was studied. As the parameters of both ISW and seabed can affect the excess pore water pressure, the distribution of pore water pressure showed both dissipation and phase lag. And parametric studies were done on these two phenomena. Due to influenced by the phase lag of excess pore water pressure, the penetration depth under the site of northern South China Sea with total water depth 327 m, induced by typical internal solitary wave increased by 26.19%, 53.27% and 149.86% from T 0 to T 0.5 in sand silt, clayey silt and fine sand seabed, respectively. That means the effect of ISW on seabed will be underestimated if we only take into accout the penetration depth under ISW trough, especially for fine sand seabed. In addition, the concept of “amplitude-depth ratio” had been introduced to describe the influence of ISW on seabed dynamic response in the actual marine environment. In present study, it is negatively correlated with the excess pore water pressure, and an ISW with smaller amplitude-depth ratio can wide the range of lateral impacts. Our study results help understand the seabed damage induced by the interaction between ISW and seabed.

internal solitary wave  /  pore water pressure  /  seabed  /  dynamic response  /  variation process
Zhuangcai Tian, Lei Jia, Naili Hu, Susheng Wang, Mingwei Zhang, Guoqing Zhou. Spatial and temporal variation process of seabed dynamic response induced by the internal solitary wave[J]. Acta Oceanologica Sinica, 2023 , 42 (2) : 142 -149 . DOI: 10.1007/s13131-022-2112-3
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1 Introduction
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Internal solitary wave (ISW), mainly generated by strong winds, tides, and currents, is a special nonlinear internal wave in the density stratified ocean. And it is widely distributed in the global ocean, such as the both sides of the Atlantic Ocean, the west bank of the Pacific Ocean, the coast of the Indian Ocean and the South China Sea (Jackson, 2007; Zhang et al., 2020; Lü et al., 2021). The observation of Huang et al. (2016) showed that the largest amplitude of ISW was up to 240 m. That means a strong water disturbance occuring when the ISW is passing. Also, sediment re-suspension, sand waves (a dynamic rhythmic bed form), sedimentary waves (a ripple topography formed by the resuspended sediment deposit), and scoured channels will be formed. In the areas with more obvious topographic fluctuations, such as submarine canyons, the effect of ISW is more obvious (Alford et al., 2015; Tian et al., 2019b, c, 2021a). Chen et al. (2012) suggested that ISW was also the important factors inducing submarine landslides. And in-situ observations had found that ISW can exert forces on the seabed and induces the dynamic response to the seabed, which in turn affects the stability of the seabed (Thomas et al., 2016).
Unlike surface waves, ISW usually has large amplitudes and wavelengths, which could cause significant bottom current and pressure backflow and interact with the seabed (Duda et al., 2004). Chen and Hsu (2005) is the first to conduct a simulation study on the change of seabed pore water pressure caused by ISW. They used an eigenvalue problem to solve the wave pressure on seabed surface caused by ISW and solved the pore water pressure in the seabed with infinite depths as well as the sediment displacement. Then, Williams and Jeng (2007) adopted the same method to calculate pore water pressure. In addition, their study paid attention to the attenuation of internal waves that induced by the interaction with seabed. Zhao et al. (2016) simulated seabed liquefaction caused by a solitary wave. Rivera-Rosario et al. (2017) established a two-layer water model and calculated the velocity and density fields by solving the Dubreil-Jacotin-Long equation. The results showed that poor conductive seabed was more likely to be damaged, and ISW was more likely to induce seabed damage when the seawater depth was within 100 m.
Based on the two-layer stratified fluid system and 2-D Biot theory, Qiao et al. (2016) conducted a parameter study on pore water pressure induced by ISW, including the permeability, shear modulus, porosity and saturation of seabed. Su et al. (2017) calculated three cases with common sediments on the northern continental slope of the South China Sea, and found that shear failure and residual liquefaction would not occur under the action of ISW, and transient liquefaction may only occur at shallow depths (z=−0.35 m). However, both Qiao et al. (2016) and Su et al. (2017) pay more attention to the macro impact, and lack investigation on the distribution of pore pressure. Tian et al. (2019a) analyzed the pore water pressure and penetration depth caused by ISW based on laboratory experiment and numerical simulation. In their study, the vertical distribution of pore water pressure in sandy silt and clayey silt was similar, and the penetration depth of sandy silt was greater than that of clayey silt. The vertical distribution of pore pressure also related to the phase of ISW (Rivera-Rosario et al., 2017; Tian et al., 2019a). However, these studies paid attention to the stability of seabed, and there is few study on the distribution of pore water pressure, especially the horizontal distribution. In present study, the distribution characteristcs of pore water pressure was studied, and the time effect was also considered, which is important for in-depth understanding and prediction of ISW-induced geological hazards.
Referring to the models of Chen and Hsu (2005), Qiao et al. (2016), and Tian et al. (2019a), this paper conducted a simulation using relevant parameters extracted from field observation. The study reveals the variation trend of pore water pressure in the seabed during the action of an ISW, as well as the spatial and temporal variation of pore water pressure in the vertical and horizontal directions. The results will provide a reference for theoretical analysis and in-situ observation of pore water pressure changes caused by ISW.
2 Numerical model
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The ISW-seabed numerical model established in this study is shown in Fig. 1. It is a two-layer fluid system structure for simulating the horizontal movement of the ISW. The ISW with wavelength L, the half of wavelength Lw, and amplitude A is also showen in Fig. 1. And the upper layer with thickness h 1 and density ρ 1 was lighter than the lower layer with thickness h 2 and density ρ 2.
The pressure associated with the free-surface displacement has little influence when the water depth is greater than 100 m (Rivera-Rosario et al., 2017). Thus the effect of surface waves was neglected in this study, as well as the viscosity and rotation of seawater (Chen and Hsu, 2005). The ISW moved forward only in one direction without considering its attenuation. The seabed was an isotropic and homogeneous porous structure. Pore water in the seabed could be compressed, and its seepage followed Darcy’s law. And the interface between the lower fluid and the seabed was regarded as a wall surface. Based on two-dimensional Biot consolidation theory, the excess pore water pressure in seabed caused by ISW is calculated.
2.1 Action of ISW
According to the equation sorted out by Qiao et al. (2016), the motion equation of the ISW surface at the interface of two layers of seawater was
$ \eta \left(x,t\right)=\left\{\begin{array}{ll}0,&t\in (0,T/4)\cup (3T/4,T)\\A{{\rm{e}}}^{{\rm{i}}\left(kx-\omega t\right)},& t\in [T/{4,3}T/4]\end{array},\right. $
where t is time, i is imaginary unit, k is the wavenumber ( $k= 2{\rm{\pi}}/L $), and ω is the angular frequency ( $\omega=2\rm{\pi}/T $).
The lower velocity potential of a fluid system is a function of horizontal and vertical coordinates x, y, and time t, defined as $\varphi({{x}}, {{z}}, {{t}})$. The velocity potential in the fluid layer follows the Laplace equation. The wave pressure resulting from an ISW at any point in the flow field of the lower seawater is P,
$ P=\rho \frac{{{\partial}} \varphi \left(x,z,t\right)}{{{\partial}} t}, $
where ρ is density of fluid.
According to initial conditions and boundary value such as velocity potential and wave motion equation, when $t\in [T/4, 3T/4] $, the hydrodynamic pressure generated by ISW at the seabed surface (namely, the vertical coordinate z=0) is expressed in Eq. (3) (Chen and Hsu, 2005; Qiao et al., 2016),
$ \begin{split}&{p}_{0}=-\dfrac{{\rm{i}}{\rho }_{w}A}{k{\rho }_{2}}\times\\&\left\{ \begin{array}{c}\dfrac{-gk{\rho }_{2}{\omega }^{2}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}k{h}_{1} + \left[{g}^{2}{k}^{2}\left({\rho }_{2} - {\rho }_{1}\right) + {\rho }_{1}{\omega }^{4}\right]\mathrm{sinh}k{h}_{1}}{gk\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}k{h}_{1}\;-\;{\omega }^{2}\mathrm{cosh}k{h}_{1}}\mathrm{cosh}k{h}_{2} \\+\dfrac{{\rho }_{2}{\omega }^{4}\mathrm{cosh}k{h}_{1}-gk{\rho }_{2}{\omega }^{2}\mathrm{sinh}k{h}_{1}}{gk\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}k{h}_{1}-{\omega }^{2}\mathrm{cosh}k{h}_{1}}\mathrm{sinh}k{h}_{2}\end{array} \right\}\times\\&{\rm{re}}\left\{{{\rm{e}}}^{{\rm{i}}\left(kx-\omega t\right)}\right\},\end{split} $
where ρ w is reference fluid density, A is the amplitude of ISW, k is wave number, $ \omega $ is angular frequency, ${\rm{re}} $ is the real part of the function, i is an imaginary unit, and g is the acceleration of gravity.
2.2 Seabed model
According to the two-dimensional Biot consolidation theory summarized by Chen and Hsu (2005) and Tian et al. (2019a), the general equation of pore water pressure in the seabed is
$ {K}_{x}\frac{{\partial }^{2}p}{\partial {x}^{2}}+{K}_{z}\frac{{\partial }^{2}p}{\partial {z}^{2}}-{\gamma}_{w }n\beta \frac{\partial p}{\partial t}={\gamma}_{w }\frac{\partial \varepsilon }{\partial t}, $
where p is the wave-induced excess pore water pressure, Kx is the permeability coefficient of sediment in the x direction, Kz is the permeability coefficient of sediment in the z direction, γ w is the bulk density of pore water, n is the porosity of sediment, β is the compression coefficient of pore fluid, and ε is volumetric strain. ε includes displacement in x and z directions,
$ \varepsilon =\frac{\partial u}{\partial x}+\frac{\partial w}{\partial z}, $
where u and w are the displacement of sediment in the x and z directions, respectively.
In the seabed sediment model, σ x and σ z represent the effective stress of sediment in x and z directions, respectively, and τ represents the shear stress. According to the two-dimensional Biot consolidation theory, the equilibrium equation of force in two dimensions is as follows:
$ \left\{\begin{split}&\frac{\partial {\sigma }_{x}}{\partial x}+\frac{\partial \tau }{\partial z}=\frac{\partial p}{\partial x},\\&\frac{\partial \tau }{\partial x}+\frac{\partial {\sigma }_{z}}{\partial z}=\frac{\partial p}{\partial z}.\end{split}\right. $
The specific derivation process can refer to the work of Chen and Hsu (2005) and Qiao et al. (2016). Here, the analytical equation similar to that established by Hsu et al. (1993) for solving the hydrodynamic pressure and displacement of the seabed is directly given as follows:
$ \begin{array}{c}\begin{array}{c}u={p}_{0}\left[-\left({C}_{0}+{C}_{1}z\right){\mathrm{e}}^{kz}+{C}_{2}{\mathrm{e}}^{\text{δ} z}\right]{\mathrm{e}}^{{\rm i}\left(kx-\omega t\right)}\end{array},\end{array} $
$ w={p}_{0}\left\{\left[-{\rm{i}}{C}_{0}-{\rm{i}}{C}_{1}z+\frac{\left(1+2\text{λ} \right)}{k}{\rm{i}}{C}_{1}\right]\left.{{\rm{e}}^{kz}}-\frac{\text{δ} }{k}{\rm{i}}{C}_{2}{\rm{e}}^{\text{δ} z}\right\}{{\rm{e}}}^{{\rm i}\left(kx-\omega t\right)}\right., $
$ \begin{split}p=&\left\{{p}_{0}-\frac{2G\left(1-2\mu -\text{λ} \right)}{\left(1-2\mu \right)}{\rm{i}}{C}_{1}{{\rm{e}}}^{kz}+\right.\\&\left.\frac{2G\left(1-2\mu \right)\left({k}^{2}-{\text{δ} }^{2}\right)}{\left(1-2\mu \right)k}{\rm{i}}{C}_{2}{{\rm{e}}}^{\text{δ} z}\right\}{{\rm{e}}}^{{\rm i}\left(kx-\omega t\right)},\end{split} $
where C 0, C 1, and C 2 are undetermined coefficients, δ and λ are correlation coefficients with sediment and wave.
2.3 ISW and seabed sediment parameters
The relevant parameters of ISW were selected from the observation in the Liuhua Sea of the South China Sea (Table 1; Duda et al., 2004). According to the study of Luan et al. (2012), the sediment types of the simulated seabed were fine sand, sandy silt, and clayey silt classified by Shepard method, which were widely distributed in the northern South China Sea. The strength parameters of surficial sediment should be important to the calculation results (Guo et al., 2022a, b), so the specific physical and mechanical property parameters of these sediments were collected from the research data of Sino-German SO(SONNE)95 voyage in 1994, SO72A voyage in 1990, HY4-20121 voyage of Guangzhou Marine Geological Survey in 2012 (Lu, 1996; Zhou et al., 2020). Mechanical parameters of similar sediments were used to supply some parameters that in-situ data could not be found. The sorted parameters were given in detail in Table 2.
3 Results
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ISW drives the movement of the upper and lower seawater to form a wave pressure on the top surface of seabed, which induces the seepage of pore water in seabed (Tian et al., 2022), and forms excess pore water pressure. Accordingly, the distribution of effective stress in the seabed will be changed. When the effective stress reached the threshold value, the seabed sediment will lose its original strength and be deformed and destroyed. Some studies focused on seabed damage induced by ISW had conducted (Su et al., 2017; Rivera-Rosario et al., 2017; Tian et al., 2021b). Then we paid more attention to the detailed variation of pore pressure in seabed, providing a reference to the observation of pore pressure in deep-sea.
3.1 Model validation
In order to verify the accuracy of the model, we adopted the same working conditions as Qiao et al. (2016), and simulated the excess pore water pressure curve. The comparation is shown in Fig. 2. Saturation had a significant influence on the vertical distribution of excess pore water pressure. At same depth, the greater was the saturation of the seabed, the greater was the excess pore water pressure. The present results were consistent with Qiao et al. (2016).
3.2 Vertical distribution of pore water pressure
In this section, the parameters of ISW1 in Table 1 had been used to calculate the pore water pressure in seabed. T 0 was defined as the time when the ISW trough located on the monitored section. T is the period of ISW. Then five moments had been selected, namely T −0.2=T 0−0.2T, T 0, T 0.1=T 0+0.1T, T 0.2=T 0+0.2T, T 0.5=T 0+0.5T. The results had been treated as dimensionless. The vertical coordinate y (y=10×z/Lw) is the relative depth, and the horizontal coordinate x (x=P/p 0) is the ratio of excess pore water pressure to maximum wave pressure, where P is the excess pore water pressure, and p 0 is the maximum wave pressure. It should be noted that the pore pressure caused by depression ISW is negative, and absolute values are used to compare sizes in this paper.
The vertical distribution of pore water pressure caused by ISW at position x=0, including five moments, is shown in Fig. 3. At the moments T −0.2, T 0, T 0.1, the ratio of the excess pore water pressure decreased rapidly to a stable value with depth in all three sediment (Figs 3a–c), but the corresponding depth is not same. For clayey silt seabed, the stable value occurs at 10z/Lw=−0.25. The result in sand silt seabed is similar with that of clayey silt. But it needs a deeper depth for pore pressure in fine sand to reach a stable vauel, and the relative depth (10z/Lw) is about −0.50. Then, at the moments T 0.2 and T 0.5 (Figs 3d, e), the ratio of the excess pore water pressure increases firstly at a shallow surface and then decreases rapidly with the depth. When t=T 0.2, the peak value occurs with the relative depth 0.02, 0.02, 0.09 for sand silt, clayey silt and fine sand seabed respectively. And when t=T 0.5, the peak value occurs with the relative depth 0.09, 0.16 and 0.38 for sand silt, clayey silt and fine sand seabed, respectively. There are also differences between the stable points. The stable values of P/p 0 in sand silt and clayey silt seabed are tending to 0, but it is tending to −0.10 in fine sand seabed.
3.3 Horizontal distribution of pore water pressure
Horizontally, the ratio of excess pore water pressure presented a similar distribution in three kinds sediment for all depth (Figs 4a–c). It is largest at the middle position and rapidly decreases to both sides. And it decreases with the depth. It is worth noting that the curve with a large depth generally falls to the left of that with a small depth, which indicated that there is a phase lag in dynamic response in seabed. In Fig. 4d, the peak values of each curve in Figs 4a–c are presented. Obviously, fine sand seabed has the largest peak (P/p 0=−0.49), sand silt seabed was second (P/p 0=−0.46), and clayey silt seabed was the smallest (P/p 0=−0.42). And we can evaluate the degree of phase lag by the horizontal distance between adjacent peak points. Then, it shows the phase lag in clayey silt seabed is most obvious, sand silt seabed is second, and fine sand seabed has a lower phase lag.
3.4 Seabed response under different ISWs
The vertical distribution of pore pressure induced by the two ISWs shows similar changes (Fig. 5). The ratio of the excess pore water pressure decreases with depth at the moment t=T −0.2, T 0, and T 0.1, and increases firstly and then decreases with depth at T 0.2 and T 0.5 . And the ratio of the excess pore water pressure caused by ISW1 in the seabed is slightly larger than that caused by ISW2 at the same depth.
As shown in Fig. 6, the excess pore water pressure induced by the two ISWs both present a U-shaped horizontal distribution with large in the middle and small on both sides. In the beginning, at z=−0.2 m (Fig. 6a), the ratios of the excess pore water pressure caused by the two ISWs are significantly different only in the range of −0.5< x/Lw< 0.5, and the maximum difference is about 0.02. When z=−0.4 m, it has a significant difference in the range of −0.7< x/Lw<0.8, and the maximum difference (about 0.04) is larger than z=−0.2 m. The difference continued to enlarge with depth until z=−0.1 m , where the obvious difference between two curves in the range of −1.2<x/Lw<1.8. And the maximum difference is about 0.07.
4 Discussion
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4.1 Dissipation and phase lag of pore water pressure
In the problem of wave-seabed intereaction, most studies consider the surface of seabed as a drainage boundary (Zhao et al., 2016; Rong et al., 2019), which means the wave pressure can change the pore pressure in the surface of seabed directly. Then the change will transfer vertically and horizontally, which is studied in this paper. In the present results, the vertical distribution of pore water pressure (Fig. 3) is similar to the study of Rivera-Rosario et al. (2017). And the horizontal distribution of pore water pressure (Fig. 4) shows a similar “U” shape to the results of Qiao et al. (2018) in the flume experiment. The impact on seabed induced by ISW is a dynamic process, and the transient variation of pore water pressure in seabed should be focused. And in present study, the distribution of pore water pressure in seabed shows both dissipation and phase lag. The dissipation is expressed the reduction of peak pore water pressure in the whole interaction. While the phase lag means that the peak value occurs a little later in a deeper position. Then the parametric studies are used to investigate the dissipation and phase lag in seabed (Fig. 7), including shear modulus, permeability, Poisson’s ratio and porosity.
In Fig. 7, the time history curves of pore water pressure in five depths were draw firstly, but only the peak values were kept in present graph. And these five points in one curve are located z=–0.2 m, z=–0.4 m, z=–0.6 m, z=–0.8 m and z=–1.0 m from left to right, respectively. For two adjacent points on the same curve, their vertical difference can reflect the dissipation of pore water pressure, and the horizontal difference can mirror the phase lag. In Fig. 7a, the values of P/p 0 are close in four cases with z=–0.2 m, but shows differences with the depth gradually. The greater is the porosity, the more is pore pressure dissipation, which indicated that poroisty has a positive effect on the dissipation of pore water pressure. But there is no obvious law of phase lag horizontally. Figure 7b shows that both dissipation and phase lag of pore water pressure reduce slightly with the increase of shear modulus. Permeability also shows a negative effect, and it has more obvious influence than shear modulus (Fig. 7c). However, there are just a little differences vertically between the four cases (Fig. 7d), and the rule of phase lag is not clear, which is not enough to estimate the effect of Poisson’s ratio on these two phenomena.
4.2 Amplitude-depth ratio
Wave parameters also play an important role in the response of pore water pressure in seabed. Chen and Hsu (2005) showed that pore pressure was related to the wave cycle. Rong et al. (2019) pointed out that wave amplitude would directly affect the wave pressure, and wave cycle would change the wave pressure on the seabed surface by affecting the wavelength. However, an actual ISW may have both the smaller amplitude and longer period, such as two ISWs in Table 1, it is difficult to compare the influence on the seabed response between two actual ISWs by controlling variables. Amplitude and lower water depth are two key parameters of ISW. Therefore, the concept of “amplitude-depth ratio” has been proposed in this paper, and is defined as the ratio of ISW amplitude to the lower water depth. According to this definition, the response of pore water pressure induced by ISW can be qualitatively described.
The amplitude-depth ratio of ISW1 was A/h 2=80.9/215=0.376, and the ratio of ISW2 was 0.550. By the results, ISW1 with a small amplitude-depth ratio has a larger ratio of excess pore water pressure at the same depth than ISW2. Also a smaller amplitude-depth ratio has a larger lateral range of influence, and the difference will enlarge with the depth.
However, only two groups of measured ISW data were used for comparison in this study. Therefore, these conclusions could not sufficiently reveal the generality of the effect of amplitude-depth ratio on seabed response. In the future, a large number of data comparisons are needed to determine the influence of this ratio on seabed response, which will be helpful to evaluate the impact induced by ISW on the seabed in the actual marine environment.
4.3 Penetration depth
Jeng and Cha (2003) numerically calculated the pore water pressure in the porous seabed induced by nonlinear waves. Their results showed that the ratio of the excess pore water pressure was larger in the seabed with higher saturation. Based on this result, it was speculated that excess pore water pressure induced by nonlinear waves would penetrate deeper in the seabed with high saturation. Olsthoorn et al. (2012) pointed out that the penetration depth of internal waves with long wavelengths was larger than that of surface waves. And it was positively correlated with wavelength.
In previous studies, the penetration depth was defined as the critical depth at which the change of excess pore water pressure at the trough was 10% of the minimum pressure induced by the ISW (Rivera-Rosario et al., 2017; Tian et al., 2019a). Because the seepage of pore water was not obvious in the sediment within the depth range of |P|/p 0< 0.1.
The distribution of pore water pressure both in present study and Rivera-Rosario et al. (2017) shows the characteristics of vertical distribution varies in the whole process. Further, because there is a phase lag when the pore pressure is transferred down, the excess pore water pressure can not reach the peak value immediately in a deeper position under the ISW trough. Therefore, the caculation with t=T 0 as the typical value of penetration depth is not enough. Thus more time nodes (T –0.2, T 0, T 0.1, T 0.2, T 0.5) had been selected to investigate the penetration depth in present study. Figure 8 shows the penetration depth in three kinds of seabed at five moments. The value of P/p 0 is close to but not the threshold value, so the penetration depth in fine sand seabed at t=T 0.2 is not given to the curve. The penetration depth in clayey silt, sand silt and fine sand seabed increases in turn, which partly consist with Tian et al. (2019a). However, the penetration depth under ISW trough (t=T 0) is not maximum, but increases gradually with time. Especially for fine sand seabed, the penetration depth under the site of northern South China Sea with total water depth 327 m, induced by typical internal solitary wave is about 10z/Lw=–0.36 at t=T 0, but increase significantly to –0.92 at t=T 0.5. Under the same water conditions, the penetration depth increased by 26.19%, 53.27% and 149.86% from T 0 to T 0.5 in sand silt, clayey silt and fine sand seabed, respectively.
Combining wave-current loading, Qi et al. (2019) showing that the wave-induced pore pressure was increased for the following-current case, but reduced for the opposing-current case. In the actual seabed environment, the penetration depth of the wave-induced pore pressure in the seabed was closely related to the wave’s parameters, motion, evolution, and seabed properties. Similarly, the evolution process of the ISW should also be considered when studying the penetration depth of ISW in the future.
5 Conclusions
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In present study, a two-layer and stratified fluid system and an seabed model based on Biot consolidation were established to investigate the spatial and temporal variation of excess pore water pressure in seabed induced by ISW. And some conslusions are summerized:
(1) Due to the dissipation and phase lag of pore water pressure in seabed, both vertical and horizontal distribution of excess pore water pressure are related to the phase of ISW. Porosity can promote the dissipation, while shear modulus and permeability have a negative impact on both the dissipation and phase lag.
(2) The ISW with smaller amplitude-depth ratio can cause a larger excess pore water pressure and wider horizontal distribution range. And the effect will be enlarged with depth.
(3) The three kinds of sediments simulated in this paper, the penetration depth in clayey silt, sand silt and fine sand seabed increases in turn. And the amplitude-depth ratio of ISW is negatively correlated with the penetration depth. Influenced by the phase lag of excess pore water pressure, the penetration depth under the site of northern South China Sea with total water depth 327 m, induced by typical internal solitary wave increased by 26.19%, 53.27% and 149.86% from T 0 to T 0.5 in sand silt, clayey silt and fine sand seabed, respectively. Clearly, the effect of ISW on seabed will be underestimate if we only take into accout the penetration depth at t=T 0, especially for fine sand seabed.
The paper is limited to discuss the horizontal seabed model, while the breaking phenomenon of ISW propagating over inclined seabed will result in a new distribution of pore pressure. Therefore, the distribution of pore pressure induced by ISW in inclined seabed should be studied in the future to compare their correlation and difference, providing more basis for the theoretical analysis of seabed dynamic response.
Funding
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  • The Natural Science Foundation of Jiangsu Province under contract No. BK20210527; the Open Research Fund of Key Laboratory of Coastal Science and Integrated Management, Ministry of Natural Resources under contract No. 2021COSIMQ002; the National Natural Science Foundation of China under contract No. 42107158.
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doi: 10.1007/s13131-022-2112-3
  • Receive Date：2022-01-01
  • Online Date：2025-11-21
  • Published：2023-02-25
Article Data
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History
  • Received：2022-01-01
  • Accepted：2022-07-18
Funding
The Natural Science Foundation of Jiangsu Province under contract No. BK20210527; the Open Research Fund of Key Laboratory of Coastal Science and Integrated Management, Ministry of Natural Resources under contract No. 2021COSIMQ002; the National Natural Science Foundation of China under contract No. 42107158.
Affiliations
    1 State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China
    2 Key Laboratory of Coastal Science and Integrated Management, Ministry of Natural Resources, Qingdao 266061, China
    3 Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Ocean University of China, Qingdao 266100, China

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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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