A method for predicting the amount of internal erosion and resuspension of seafloor sediments under wave action

Abstract

The present invention provides a method for evaluating and predicting the amount of internal erosion and resuspension of seabed sediments under wave action. Based on the mass conservation equation for sediment particles, the erosion constitutive equation, and the seepage continuity equation, this method considers the impact of the accumulation of seabed pore-water pressure under wave action on the internal erosion process of sediments. It also considers the impact of changes in the physical properties of seabed soil caused by internal erosion on the development of the cumulative pore-water pressure of the seabed. A coupled mathematical model of the cumulative response of the seabed under wave action and internal erosion is constructed. The model is solved using the finite element method to obtain the development and changes in the cumulative pore-water pressure, porosity, volume concentration of suspended fine particles, and the mass of eroded fine particles. The present invention quantitatively assesses the mass of fine particles within seabed sediments that migrate outward with seepage under wave action, as well as the spatiotemporal evolution characteristics and patterns of the internal erosion process of sediments. This allows for quantitative prediction and analysis of seabed stability and the internal erosion and resuspension characteristics of seabed sediments.

Description

Technical Field

[0001] The present invention relates to the technical field of seabed sediment erosion disaster assessment and prediction, and in particular to a method for assessing and predicting the amount of internal erosion and resuspension of seabed sediments under wave action. Background Art

[0002] With global climate change, extreme storm events are becoming more frequent in estuaries, deltas, and coastal areas. These storms significantly increase wave loads, triggering a series of marine geological disasters such as erosion and landslides in seabed sediments, seriously impacting coastal engineering and ecological safety. Under cyclic wave loads, excess pore water pressure can easily accumulate in sandy or silty seabeds with relatively low permeability, forming a significant seepage gradient within the seabed and generating upward seepage. Under certain seepage intensities, fine particles within the soil will break away from the soil skeleton, triggering internal erosion and resuspension of sediments. Internal erosion can lead to structural instability of the seabed, induce collapse and subsidence, and increase the risk of foundation failure for offshore structures such as submarine pipelines, breakwaters, and oil platforms. Internal erosion also has a significant impact on sediment transport and seabed topography evolution. Therefore, predicting the amount of internal erosion and resuspension of seabed sediments is of great engineering and theoretical significance.

[0003] Researchers typically use indoor flume tests and field observations to evaluate and analyze the internal erosion and resuspension of sediments under wave loads. These methods, such as deploying monitoring equipment on the seafloor to observe the sediment erosion and resuspension process and measuring the concentration of resuspended particles, are unable to quantitatively assess the spatiotemporal evolution of the internal erosion and resuspension of sediments. Other researchers have used the finite element method, based on mass conservation, the erosion constitutive equation, and Darcy's law, to simulate the temporal evolution of internal erosion characteristics of seafloor sediments under wave action. However, these methods do not consider the coupled interaction between wave-induced seabed response and internal sediment erosion, and cannot reflect the influence of fine particle content in sediments. Their calculation results are not conducive to the analysis and prediction of seabed stability and sediment resuspended particles in the marine environment. Summary of the Invention

[0004] In order to make up for the deficiencies of the prior art, the present invention provides a method for predicting the amount of internal erosion and resuspension of seabed sediments under wave action.

[0005] The present invention is achieved through the following technical solution: a method for predicting the amount of internal erosion and resuspension of seabed sediments under wave action, specifically comprising the following steps:

[0006] S1. Based on the mass conservation equation of sediment particles, the erosion constitutive equation, and the seepage continuity equation, the influence of the cumulative response of the seabed soil on internal erosion and the influence of internal erosion on the seepage field are considered. A coupled mathematical model of the seabed cumulative response and internal erosion under wave action, namely the partial differential governing equations, is constructed. Based on the actual wave conditions and seabed soil properties, the wave parameters, seabed soil parameters, and internal erosion model parameters are determined and input. The initial calculation time is t = 0.

[0007] S2. Based on the governing equations of the seabed cumulative response-internal erosion coupling model under wave action, the finite element method is used to solve the volume concentration c of suspended fine particles at each node at time t = t + Δt. fs , porosity φ fm and the cumulative pore water pressure p fm , and use the internal erosion constitutive equation to calculate the mass percentage F of fine particles eroded at each node from the initial moment to this moment er ;

[0008] S3, the cumulative pore water pressure p calculated based on time t fm , use the liquefaction judgment criteria to judge the liquefaction of the seabed. If the seabed liquefies, execute step S4; if not, return to step S2 and update the calculation of the suspended fine particle volume concentration c at the next time t = t + Δt fs , porosity φ fm , cumulative pore water pressure p fm and the mass percentage of fine particles eroded F er ;

[0009] S4. Based on the liquefaction identification results, the seabed is divided into a liquefied zone and a non-liquefied zone, the depth of the liquefied zone is updated, and the initial porosity φ0 of the liquefied zone is set as the maximum porosity of the sediment according to the characteristics of the liquefied soil mass;

[0010] S5. For the liquefied zone, the cumulative pore water pressure remains unchanged at the value when liquefaction occurs, and based on the internal erosion control equation, the suspended fine particle volume concentration c at time t = t + Δt is calculated and solved. fs , porosity φ fm and the mass percentage of fine particles eroded F er At the same time, the relevant variables of the unliquefied seabed area are updated, and the seabed cumulative response-internal erosion coupling control equation is used to solve the suspended fine particle volume concentration c in the unliquefied seabed area at time t = t + Δt. fs , porosity φ fm , cumulative pore water pressure p fm and the mass percentage of fine particles eroded F er ;

[0011] S6. Based on the results of cumulative pore water pressure calculation, liquefaction is identified and the liquefaction depth is determined; the cumulative mass M of fine particles per unit area (per square meter) of the seabed that migrates outward with seepage under the action of waves at different times is calculated. t , which is the prediction result of the amount of sediment eroded and resuspended under the action of waves, calculates the internal erosion rate of the soil at different depths of the seabed and the internal erosion rate of the soil at a certain depth of the seabed at different times, and comprehensively analyzes the spatiotemporal evolution characteristics of the internal erosion of the sediment;

[0012] S7. According to the wave action time, determine whether the calculation simulation time t has reached the calculation termination time. If not, return to step S4 to continue the calculation. If the calculation time has been reached, end the calculation.

[0013] As a preferred solution, the specific derivation process of the coupling control equation of internal erosion and seabed cumulative response in step S1 is as follows:

[0014] The porous medium with a microelement volume of dV is composed of a microelement with a volume of dV s The solid phase and volume dV fm The fluid mixture phase consists of a volume of dV fs The fluidized solid particles and volume dV f Fluid composition.

[0015] The governing equation for the coupling of internal erosion and seepage field considering the soil deformation effect is:

[0016]

[0017] Among them, φ fm and φ s represent the volume fractions of the liquefied and solid phases, respectively, φ fm =dV fm / dV,φ s =dV s / dV,φ fm is the porosity; c fs is the volume concentration of suspended fine particles, c fs =dV fs / dV fm ; v represents the displacement rate of the soil solid phase in the x and y directions; v r represents the true flow velocity of pore water; ρ s is the absolute density of soil particles; It is the erosion mass of unit volume of soil per unit time (i.e. internal erosion flux or internal erosion rate).

[0018] ρ fm is the fluid density, and the calculation expression is:

[0019] ρ fm=c fs ·ρ s +(1-c fs )·ρ fm (4)

[0020] q fm is the fluid flow rate, which is calculated according to Darcy's law:

[0021]

[0022] Among them, p fm To accumulate pore water pressure, during the internal erosion process, as fine particles continue to migrate, the porosity changes, and the permeability coefficient k also changes accordingly. The functional relationship between it and the porosity satisfies the classic Kozeny-Carmen relationship:

[0023]

[0024] The cumulative pore water pressure is calculated by introducing the pore pressure accumulation source term and the corresponding volume strain rate Introduce the control equation, that is Substituting it into the seepage continuity equation, the seabed cumulative response-internal erosion coupling control equation can be obtained as follows:

[0025]

[0026] Among them, m v is the soil volume compression coefficient; ψ is the pore pressure accumulation source term, and its expression is:

[0027]

[0028] Where T is the wave period, τ max is the maximum periodic shear stress of the seabed soil; σ′0 is the average effective deadweight stress of the seabed soil; α and β are experimental fitting parameters. When there is no experimental data, they can be calculated based on the relative density D of the seabed soil. r The calculation is as follows:

[0029] α=0.34D r +0.084, β=0.37D r -0.46 (11)

[0030] The internal erosion constitutive equation is used to solve the mass percentage of fine particle erosion. The specific internal erosion constitutive equation is as follows:

[0031]

[0032] Among them, v y is the vertical flow velocity of the pore fluid; ρ f is the real-time remaining fine particle density under internal erosion; ρf∞ is the final remaining fine particle density after internal erosion; β er is the erosion coefficient.

[0033] If 0≤hydraulic gradient i≤i*, then:

[0034]

[0035] If hydraulic gradient i≥i*, then:

[0036]

[0037] Where i* is the critical hydraulic gradient, which is 0.18; ρ t is the initial soil particle density; ρ f0 is the initial fine particle density; ρ f * is the density of fine particles remaining in the final stage of erosion when the hydraulic gradient i = i*; er is the erosion constitutive fitting parameter, which is taken as 4.76.

[0038] Furthermore, in step S2, based on the governing equations (7)-(9) of the seabed cumulative response-internal erosion coupling model under wave action, the volume concentration c of suspended fine particles at time t = t + Δt is solved using the finite element method. fs , porosity φ fm and the cumulative pore water pressure p fm , and use the internal erosion constitutive equation to solve the mass percentage of fine particles eroded F er , the calculation formula is as follows:

[0039]

[0040] As a preferred solution, in step S3, the seabed liquefaction is judged based on the cumulative pore water pressure at a certain depth of the seabed soil and the overlying vertical effective deadweight stress. The specific discriminant formula is as follows:

[0041] p fm =γ'|y| (16)

[0042] Among them, |y| is the distance from a point on the seabed to the seabed surface, that is, the depth; γ' is the effective weight of the soil.

[0043] When p fm When ≥γ'|y|, the seabed soil at this depth liquefies and enters S4; otherwise, it goes to S2 to continue the calculation of the cumulative pore water pressure and internal erosion process.

[0044] Furthermore, in step S5, the liquefied area and the unliquefied area are calculated separately, and the suspended fine particle volume concentration c is solved in the unliquefied area using the control equations (7)-(9).fs , porosity φ fm and the cumulative pore water pressure p fm At the same time, using equation (15), calculate the mass percentage of fine particles eroded from the initial time to time t: er The volume concentration of suspended fine particles c is calculated using the governing equations (7) and (8) in the liquefaction zone. fs and porosity φ fm At the same time, using equation (15), calculate the mass percentage of fine particles eroded from the initial time to time t: er .

[0045] Furthermore, in S6, based on the cumulative pore water pressure calculation results, liquefaction is discriminated using the liquefaction discriminant formula (16) and the liquefaction depth is determined. The cumulative mass of fine particles per unit area (per square meter) of the seabed that migrates outward with seepage under the action of waves at different times is calculated as follows:

[0046]

[0047] Where L is the wavelength, and the vertical velocity and volume concentration of fine particles are the values ​​on the seabed.

[0048] By calculating the cumulative mass of fine particles per unit area of ​​seabed that migrate outward with seepage under the action of waves, the amount of internal erosion and resuspension of seabed sediments under the action of waves can be predicted, providing a reference for the assessment and prediction of seabed geological disasters and marine ecological environment.

[0049] Due to the adoption of the above technical solution, the present invention has the following beneficial effects compared with the prior art:

[0050] 1. This method takes into account the effects of wave-induced seabed deformation and liquefaction on internal sediment erosion, and can more realistically reflect the internal sediment erosion process in the marine environment. The calculated internal eroded resuspension amount of seabed sediment is more referenceable.

[0051] 2. This method takes into account the impact of changes in the physical properties of seabed soil caused by internal sediment erosion on the seabed cumulative response process, making the simulation process more comprehensive and improving the reliability of the prediction of seabed cumulative response and liquefaction results.

[0052] 3. This method can quantitatively predict the changing characteristics and laws of the amount of eroded and resuspended sediments within the seabed as the wave action time progresses, which is beneficial to coastal engineering protection.

[0053] 4. This method can more intuitively and quantitatively reflect the changing characteristics and patterns of erosion at different depths within seabed sediments under wave action, providing new ideas for the quantitative study of seabed erosion and resuspension.

[0054] Additional aspects and advantages of the invention will become apparent from the description which follows, or may be learned by practice of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0056] Figure 1 It is a calculation flow chart of the present invention;

[0057] Figure 2 This is a table of soil and wave parameters for calculation examples of the present invention;

[0058] Figure 3 Schematic diagram of the geometric model of the present invention;

[0059] Figure 4 This is a graph showing the development of liquefaction depth over wave action time calculated by the present invention;

[0060] Figure 5 The volume concentration of suspended fine particles, porosity, and the mass percentage of eroded fine particles in the liquefied zone (y = -1 m) calculated by the present invention develop over time, wherein (a) the volume concentration changes over time, (b) the porosity changes over time, and (c) the percentage of eroded fine particles changes over time;

[0061] Figure 6 Figure 1 is a graph showing the temporal development of suspended fine particle volume concentration, porosity, mass percentage of eroded fine particles, and cumulative pore water pressure in the non-liquefied zone (y = -6 m) calculated by the present invention, where (a) is the temporal development of volume concentration, (b) is the temporal development of porosity, (c) is the temporal development of percentage of eroded fine particles, and (d) is the temporal development of cumulative pore water pressure.

[0062] Figure 7 The internal erosion rate distribution along the depth at 3000 wave action cycles (3000T) calculated by the present invention is shown in the figure.

[0063] Figure 8 The internal erosion rate of the liquefied area (y = -1m) and the non-liquefied area (y = -6m) calculated by the present invention develops over time, wherein (a) is the internal erosion rate change over time (y = -1m), and (b) is the internal erosion rate change over time (y = -6m);

[0064] Figure 9 The distribution diagram of the mass percentage of eroded fine particles along the depth calculated by the present invention at different wave action times;

[0065] Figure 10This is a graph showing the time evolution of the cumulative mass of fine particles transported to the seabed surface per unit area, calculated by the present invention. Specific implementation plan

[0066] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present application and the features therein can be combined with each other.

[0067] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0068] The following combination Figures 1 to 10 The method for predicting the amount of internal erosion and resuspension of seabed sediments under the action of waves according to an embodiment of the present invention is described in detail.

[0069] The present invention provides a method for predicting the amount of internal erosion and resuspension of seabed sediments under the action of waves. It considers the influence of the accumulation of seabed pore water pressure under the action of waves on the calculation of the internal erosion process of sediments, and also considers the influence of internal erosion of sediments and the changes in the physical properties of the seabed caused by it on the calculation of the cumulative response of the seabed. On this basis, a coupled mathematical model of the cumulative response of the seabed under the action of waves and internal erosion is established, and the coupled mathematical model is solved using the finite element method, thereby realizing the numerical simulation study of the coupled process of the cumulative response of the seabed under the action of waves and internal erosion. In the numerical calculation process, the influence of the seabed liquefaction effect is considered. The geometric area of ​​the calculation is discretized using quadratic Lagrangian rectangular units, and the size of the unit is refined to not affect the calculation results. Its basic flow chart is as follows. Figure 1 As shown, the specific steps include:

[0070] S1. Based on the mass conservation equation of sediment particles, the erosion constitutive equation, and the seepage continuity equation, and considering the influence of the cumulative response of the seabed soil on internal erosion and the influence of internal erosion on the seepage field, a coupled mathematical model of the seabed cumulative response and internal erosion under wave action (i.e., the partial differential governing equation) is constructed. The specific derivation process of the governing equation of the coupled seabed cumulative response and internal erosion model is as follows:

[0071] The porous medium with a microelement volume of dV is composed of a microelement with a volume of dV s The solid phase and volume dV fm The fluid mixture phase consists of a volume of dV fs The fluidized solid particles and volume dV f Fluid composition.

[0072] The governing equation for the coupling of internal erosion and seepage field considering the soil deformation effect is:

[0073]

[0074] Among them, φ fm and φ s represent the volume fractions of the liquefied and solid phases, respectively, φ fm =dV fm / dV,φ s =dV s / dV,φ fm is the porosity; c fs is the volume concentration of suspended fine particles, c fs =dV fs / dV fm ; v represents the displacement rate of the soil solid phase in the x and y directions; v r represents the true flow velocity of pore water; ρ s is the absolute density of soil particles, which is 2650 kg / m 3 ; It is the erosion mass of unit volume of soil per unit time (i.e. internal erosion flux or internal erosion rate).

[0075] ρ fm is the fluid density, calculated as:

[0076] ρ fm =c fs ·ρ s +(1-c fs )·ρ fm (4)

[0077] q fm is the fluid flow rate, which is calculated according to Darcy's law:

[0078]

[0079] Among them, p fm To accumulate pore water pressure, during the internal erosion process, as fine particles continue to migrate, the porosity changes, and the permeability coefficient k also changes accordingly. The functional relationship between it and the porosity satisfies the classic Kozeny-Carmen relationship:

[0080]

[0081] The cumulative pore water pressure is calculated by introducing the pore pressure accumulation source term and the corresponding volume strain rate Introduce the control equation, that is Substituting it into the seepage continuity equation, the seabed cumulative response-internal erosion coupling control equation can be obtained as follows:

[0082]

[0083] Among them, m v is the soil volume compression coefficient; ψ is the pore pressure accumulation source term, and its expression is:

[0084]

[0085] Where T is the wave period, τ max is the maximum periodic shear stress of the seabed soil; σ′0 is the average effective deadweight stress of the seabed soil; α and β are experimental fitting parameters. When there is no experimental data, they can be calculated based on the relative density D of the seabed soil. r The calculation is as follows:

[0086] α=0.34D r +0.084, β=0.37D r -0.46(11)

[0087] The internal erosion constitutive equation is used to solve the mass percentage of fine particles. The specific internal erosion constitutive equation is as follows:

[0088]

[0089] Among them, v y is the vertical flow velocity of the pore fluid; ρ f is the real-time remaining fine particle density under internal erosion; ρ f∞ is the final remaining fine particle density; β er is the erosion coefficient, which is 1.95×10 -3 m -1 .

[0090] If 0≤hydraulic gradient i≤i*, then:

[0091]

[0092] If hydraulic gradient i≥i*, then:

[0093]

[0094] Where i* is the critical hydraulic gradient, which is 0.18; ρ t is the initial soil particle density, which is 1700 kg / m 3 ρ f0 is the initial fine particle density, ρ f0 / ρ t Take 20%; ρ f * is the residual fine particle density at the final stage of erosion when the hydraulic gradient i = 0.18; er is the erosion constitutive fitting parameter, which is taken as 4.76.

[0095] According to the actual wave conditions and seabed soil properties, wave parameters, seabed soil parameters and internal erosion model parameters are determined and input. Specific parameters are as follows: Figure 2 As shown, the volume concentration of the initial suspended fine particles c fs =0, porosity φ fm =φ0, initial calculation time t=0;

[0096] S2. Combination Figure 3 , the boundary conditions of the coupled model of sediment internal erosion and seabed response under wave action are set as follows:

[0097] (1) At the seabed surface (y = 0), it is assumed that fine particles escape from the seabed surface with seepage and are diluted by seawater, and the concentration is approximately 0. The cumulative pore water pressure at the seabed surface is also 0, that is,

[0098] c fs (x,0,t)=0,p fm =0 (15)

[0099] (2) At the bottom of the seabed (y = -h), an impermeable boundary is set.

[0100]

[0101] (3) At x = 0 and x = L, i.e., the two sides of the seabed are periodic boundaries,

[0102] p fm | x＝0 =p fm | x＝L ,φ fm | x＝0 =φ fm | x＝L ,c fs | x＝0 =c fs | x＝L (17)

[0103] Based on the governing equations (7)-(9) of the coupled model of seabed cumulative response and internal erosion under wave action, the volume concentration c of suspended fine particles at time t = t + Δt is solved by the finite element method. fs , porosity φ fm and the cumulative pore water pressure p fm , and use the internal erosion constitutive equation to calculate the mass percentage F of fine particles eroded at each node from the initial moment to this moment er , the calculation formula is as follows:

[0104]

[0105] S3, the cumulative pore water pressure p calculated based on time t fm , using the liquefaction judgment criterion, the seabed liquefaction is judged based on the cumulative pore water pressure at a certain depth of the seabed soil and the overlying vertical effective deadweight stress. The specific judgment formula is as follows:

[0106] p fm =γ'|y| (19)

[0107] Among them, |y| is the distance from a point on the seabed to the seabed surface, that is, the depth; γ' is the effective weight of the soil.

[0108] When p fm ≥γ'|y|, the seabed soil at this depth has liquefied, and step S4 is executed; if it has not liquefied, the process returns to step S2 and updates the calculation of the volume concentration c of suspended fine particles at the next time t=t+Δt. fs , porosity φ fm , cumulative pore water pressure p fm and the percentage of fine particles eroded F er ;

[0109] S4. Based on the liquefaction identification results, the seabed is divided into liquefied areas and non-liquefied areas. The depth of the liquefied area and related variables are updated in real time. The depth of the liquefied area changes over time. Figure 4 According to the characteristics of liquefied soil, the initial porosity φ0 of the liquefied zone is set to 0.5 of the maximum porosity of the sediment. As erosion progresses, the porosity is continuously updated.

[0110] S5. For the liquefied zone, the cumulative pore water pressure remains unchanged at the value when liquefaction occurs. Using the governing equations (7) and (8), the volume concentration of suspended fine particles c at time t = t + Δt is calculated. fs and porosity φ fm , using equation (18), calculate the mass percentage of fine particles eroded from the initial time to time t, F er , the solution is as follows Figure 5 As shown; update the relevant variables of the unliquefied area of ​​the seabed, and continue to use the coupled control equations (7)-(9) to solve the volume concentration c of suspended fine particles in the unliquefied area at time t = t + Δt fs , porosity φ fm and the cumulative pore water pressure p fm , using equation (18), calculate the mass percentage of fine particles eroded from the initial time to time t, F er , the solution is as follows Figure 6 As shown; at the same time, the evolution characteristics of the internal erosion rate of fine particles with time and space can be quantitatively analyzed. The simulation results are shown in Figure 7 and Figure 8 shown.

[0111] It should be noted that in the specific implementation process, as the liquefied area is updated, the boundary conditions between the liquefied area and the non-liquefied area need to be updated accordingly. The specific boundary conditions are as follows:

[0112] S5-1. For the updated liquefaction zone, at the upper surface of the liquefaction zone (y = 0), it is assumed that fine particles escape from the seabed with seepage and are diluted by seawater. At the same time, there is no need to calculate the cumulative response of the seabed. Therefore, the upper boundary condition of the liquefaction zone is:

[0113] c fs,2 (x,0,t)=0 (20)

[0114] At the bottom of the liquefaction zone (y=-z L ,z L is the liquefaction depth), considering the continuity of concentration, the boundary condition at the bottom of the liquefaction zone is:

[0115] c fs,2 =c fs,1 (twenty one)

[0116] The subscript 1 of the fine particle volume concentration represents the non-liquefied area, and the subscript 2 represents the liquefied area.

[0117] The seabed has periodic boundaries on both sides:

[0118] φ fm | x＝0 =φ fm | x＝L ,c fs | x＝0 =c fs | x＝L (twenty two)

[0119] S5-2. For the unliquefied zone of the seabed, considering the continuity of particle concentration, the particle volume concentration at the upper boundary of the unliquefied zone is equal to the volume concentration at the lower boundary of the liquefied zone. At the same time, the cumulative pore water pressure varies with the depth of the top of the unliquefied zone. At this time, the upper boundary condition of the unliquefied zone is:

[0120] c fs,1 =c fs,2 ,p fm =γ'z L (twenty three)

[0121] The bottom of the unliquefied area is the bottom of the seabed (y = -h), which is still set as an impermeable boundary:

[0122]

[0123] S6. Based on the results of the cumulative pore water pressure calculation, use the liquefaction discriminant formula (19) to perform liquefaction discrimination and determine the liquefaction depth. Calculate the cumulative mass M of fine particles per unit area (per square meter) of the seabed that migrates outward with seepage under the action of waves at different times. t , the calculation formula is as follows:

[0124]

[0125] Where L is the wavelength, and the vertical velocity and volume concentration of fine particles are the values ​​on the seabed.

[0126] S7. According to the wave action time, determine whether the calculation simulation time t reaches the calculation termination time. If not, return to step S4 to continue the calculation. If the calculation time is reached, end the calculation.

[0127] After the calculation is completed, the cumulative mass of fine particles per unit area of ​​seabed that migrate outward with seepage under the action of waves is obtained according to formula (25), as follows: Figure 10 As shown in the figure, the results are the prediction results of the internal erosion and resuspension amount of seabed sediments under the action of waves. At the same time, the temporal and spatial evolution characteristics of the internal erosion rate of the seabed soil under the action of waves are quantitatively evaluated, and the internal erosion of the soil under the time of wave action is comprehensively analyzed, providing a reference for the assessment and prediction of submarine geological disasters and marine ecological environment.

[0128] Throughout this specification, terms such as "one embodiment," "some embodiments," and "specific embodiments" mean that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, schematic representations of these terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0129] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for predicting the amount of internal erosion and resuspension of seabed sediments under wave action, characterized in that: The specific steps include: S1. Based on the mass conservation equation of sediment particles, the erosion constitutive equation, and the seepage continuity equation, a coupled mathematical model of the seabed cumulative response under wave action and internal erosion, i.e., a set of partial differential governing equations, is constructed. Based on the actual wave conditions and seabed soil properties, wave parameters, seabed soil parameters, and erosion model parameters are determined and input. The initial calculation time is t = 0. S2. Based on the governing equations of the seabed cumulative response-internal erosion coupling model under wave action, the finite element method is used to solve the volume concentration c of suspended fine particles at each node at time t = t + Δt. fs , porosity φ fm and the cumulative pore water pressure p fm , and use the internal erosion constitutive equation to calculate the mass percentage F of fine particles eroded at each node from the initial time to time t er ; S3, the cumulative pore water pressure p calculated based on time t fm , use the liquefaction judgment criteria to judge the liquefaction of the seabed. If the seabed liquefies, execute step S4; if not, return to step S2 and calculate the suspended fine particle volume concentration c at the next time t = t + Δt fs , porosity φ fm , cumulative pore water pressure p fm and the mass percentage of eroded fine particles F er ; S4. Based on the liquefaction identification results, the seabed is divided into a liquefied zone and a non-liquefied zone, the depth of the liquefied zone is updated, and the initial porosity φ0 of the liquefied zone is set as the maximum porosity of the sediment according to the characteristics of the liquefied soil mass; S5. For the liquefied zone, the cumulative pore water pressure remains unchanged at the value when liquefaction occurs. Based on the internal erosion control equation, the suspended fine particle volume concentration c at time t = t + Δt is calculated. fs , porosity φ fm and the mass percentage of eroded fine particles F er At the same time, the relevant variables of the unliquefied seabed area are updated, and the seabed cumulative response-internal erosion coupling control equation is continued to be used to solve the suspended fine particle volume concentration c in the unliquefied seabed area at time t = t + Δt. fs , porosity φ fm , cumulative pore water pressure p fm and the mass percentage of eroded fine particles F er ; S6. Based on the results of cumulative pore water pressure calculations, perform liquefaction identification and determine the liquefaction depth; calculate the cumulative mass M of fine particles that migrate outward with seepage under the action of waves per unit area, i.e., per square meter, at different times. t , which is the prediction result of the amount of sediment eroded and resuspended under the action of waves, and calculates the internal erosion rate of the soil at different depths of the seabed and the internal erosion rate of the soil at a certain depth of the seabed at different times, and comprehensively analyzes the spatiotemporal evolution characteristics of the internal erosion of the sediment; S7. According to the wave action time, determine whether the calculation simulation time t has reached the calculation termination time. If not, return to step S4 to continue the calculation. If the calculation time has been reached, end the calculation.

2. The method for predicting the amount of internal erosion and resuspension of seabed sediments under wave action according to claim 1, characterized in that: The specific derivation process of the seabed cumulative response-internal erosion coupling mathematical model in step S1, i.e., the partial differential control equations, is as follows: The porous medium with a microelement volume of dV is composed of a microelement with a volume of dV s The solid phase and volume dV fm The fluid mixture phase consists of a volume of dV fs The fluidized solid particles and volume dV f Fluid composition; The governing equation for the coupling of internal erosion and seepage field considering the soil deformation effect is: Among them, φ fm and φ s represent the volume fractions of the liquefied and solid phases, respectively, φ fm =dV fm / dV,φ s =dV s / dV,φ fm is the porosity; c fs is the volume concentration of suspended fine particles, c fs =dV fs / dV fm ; v represents the displacement rate of the soil solid phase in the x and y directions; v r represents the true flow velocity of pore water; ρ s is the absolute density of soil particles; is the erosion mass per unit volume of soil per unit time (i.e., internal erosion flux or internal erosion rate); ρ fm is the fluid density, calculated as: r fm =c fs ·r s +(1-c fs )·r fm (4) q fm is the fluid flow rate, which is calculated according to Darcy's law: Among them, p fm The cumulative pore water pressure is expressed as follows. During the internal erosion process, as fine particles continue to migrate, the porosity changes, and the permeability coefficient k also changes accordingly. The functional relationship between the permeability coefficient k and the porosity satisfies the classic Kozeny-Carmen relationship: The cumulative pore water pressure is calculated by introducing the pore pressure accumulation source term and the corresponding volume strain rate Introduce the control equation, that is Substituting it into the seepage continuity equation, the seabed cumulative response-internal erosion coupling control equation can be obtained as follows: Among them, m v is the soil volume compression coefficient; ψ is the pore pressure accumulation source term, and its expression is: Where T is the wave period, τ max is the maximum periodic shear stress of the seabed soil; σ′0 is the average effective deadweight stress of the seabed soil; α and β are experimental fitting parameters. When there is no experimental data, they can be calculated based on the relative density D of the seabed soil. r The calculation is as follows: α=0.34D r +0.084, β=0.37D r -0.46 (11) The internal erosion constitutive equation is used to solve the mass percentage of fine particle erosion. The specific internal erosion constitutive equation is as follows: Among them, v y is the vertical flow velocity of the pore fluid; ρ f is the real-time remaining fine particle density under internal erosion; ρ f∞ is the final remaining fine particle density after internal erosion; β er is the erosion coefficient; If 0≤hydraulic gradient i≤i*, then: If hydraulic gradient i≥i*, then: Where i* is the critical hydraulic gradient, which is 0.18; ρ t is the initial soil particle density; ρ f0 is the initial fine particle density; ρ f * is the residual fine particle density at the final stage of erosion when the hydraulic gradient i = i*; er is the erosion constitutive fitting parameter, which is taken as 4.

76.

3. The method for predicting the amount of internal erosion and resuspension of seabed sediments under wave action according to claim 2, characterized in that: In step S2, based on the control equations (7)-(9) of the seabed cumulative response-internal erosion coupling model under wave action, the volume concentration c of suspended fine particles at time t=t+Δt is solved by the finite element method. fs , porosity φ fm and the cumulative pore water pressure p fm , and use the internal erosion constitutive equation to calculate the mass percentage F of fine particles eroded at each node from the initial moment to this moment er , the calculation formula is as follows:

4. The method for predicting the amount of internal erosion and resuspension of seabed sediments under wave action according to claim 1, characterized in that: The cumulative pore water pressure p calculated based on time t in step S3 fm The liquefaction judgment criteria are used to judge the liquefaction of the seabed. The liquefaction of the seabed is judged based on the cumulative pore water pressure at a certain depth of the seabed soil and the overlying vertical effective deadweight stress. The specific judgment formula is as follows: p fm =γ'|y|(16) Where |y| is the distance from a point on the seabed to the seabed surface, i.e., the depth; γ' is the effective weight of the soil; When p fm When ≥γ'|y|, the seabed soil at this depth liquefies and enters S4; otherwise, it goes to S2 to continue the calculation of the cumulative pore water pressure and internal erosion process.

5. The method for predicting the amount of internal erosion and resuspension of seabed sediments under wave action according to claim 3, characterized in that: In step S5, the liquefied area and the unliquefied area are calculated separately. The suspended fine particle volume concentration c is solved in the unliquefied area using the control equations (7)-(9) fs , porosity φ fm and the cumulative pore water pressure p fm At the same time, using equation (15), calculate the percentage of fine particles eroded from the initial time to time t: er ; The suspended fine particle concentration c is calculated using the governing equations (7) and (8) in the liquefaction zone. fs and porosity φ fm At the same time, using equation (15), calculate the percentage of fine particles eroded from the initial moment to this moment F er .

6. The method for predicting the amount of internal erosion and resuspension of seabed sediments under wave action according to claim 4, characterized in that: In step S6, liquefaction is discriminated based on the result of cumulative pore water pressure calculation using liquefaction discriminant formula (16) to determine the liquefaction depth; the cumulative mass of fine particles that migrate to the outside of the seabed due to seepage under the action of waves per unit area, i.e., per square meter, at different times is calculated, and the calculation formula is as follows: Where L is the wavelength, and the vertical velocity and volume concentration of fine particles are the values ​​on the seabed.

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