Prediction method for internal erosion resuspension amount of submarine sediment under wave action

Abstract

The invention provides a method for evaluating and predicting the internal erosion resuspension amount of submarine sediments under the action of waves, which is based on a mass conservation equation, an erosion constitutive equation and a seepage continuity equation of sediment particles and considers the influence of accumulation of seabed pore water pressure on the internal erosion process of the sediments under the action of the waves. Meanwhile, the influence of seabed soil physical property change caused by internal erosion on the seabed accumulated pore water pressure development process is considered, a seabed accumulated response-internal erosion coupling mathematical model under the wave action is constructed, and a finite element method is used for solving; and the development change of the accumulated pore water pressure, the porosity, the suspended fine particle volume concentration and the eroded fine particle mass of the seabed is obtained. According to the method, the mass of fine particles in the seabed sediment moving outwards along with seepage under the action of waves and the spatio-temporal evolution characteristics and rules of the erosion process in the sediment are quantitatively evaluated, and therefore quantitative prediction analysis can be conducted on the seabed stability and the erosion resuspension characteristics in the seabed sediment.

Description

Technical Field

[0001] The 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 the change of global climate, extreme storm events frequently occur in estuary deltas and coastal areas. Extreme storms significantly increase wave loads, induce a series of marine geological disasters such as erosion and landslides of seabed sediments, and seriously affect coastal engineering and ecological environmental safety. Under the action of cyclic wave loads, excess pore water pressure is easily accumulated in sandy or silty soil seabeds with relatively low permeability, forming a significant seepage gradient inside the seabed, generating upward seepage. Under a certain seepage intensity, fine particles inside the soil will break away from the soil skeleton, thereby causing internal erosion and resuspension of sediments. Internal erosion can lead to instability of the seabed soil structure, induce collapse and subsidence, and increase the risk of foundation failure of offshore structures such as submarine pipelines, breakwaters and oil platforms; at the same time, internal erosion also has an important impact on sediment transport and seabed topography evolution. Therefore, predicting the amount of internal erosion and resuspension of seabed sediments has important engineering and theoretical significance.

[0003] Researchers usually use indoor water tank tests and field observations to evaluate and analyze the internal erosion and resuspension of sediments under wave loads. They observe the sediment erosion and resuspension process by placing monitoring equipment on the seabed and measure the concentration of resuspended particles. Such methods cannot quantitatively evaluate the spatiotemporal evolution characteristics of the internal erosion and resuspension of sediments. Other scholars use the finite element method to simulate the evolution of internal erosion characteristics of seabed sediments under wave action over time based on mass conservation, erosion constitutive equations, and Darcy's law. However, they do not consider the coupling process of wave-induced seabed response and internal sediment erosion, and cannot reflect the influence of fine particle content in sediments. The 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 the action of waves.

[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 the internal erosion and the influence of the internal erosion on the seepage field are considered, and a coupled mathematical model of the seabed cumulative response-internal erosion under the action of waves, i.e., a group of partial differential control equations, is constructed; according to the actual wave conditions and the properties of the seabed soil, the wave parameters, seabed soil parameters and internal erosion model parameters are determined and input, and the initial calculation time is t=0;

[0007] S2. Based on the control equation 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 from the initial moment to this moment at each node 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 it does not liquefy, 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. According to the liquefaction identification results, the seabed is divided into liquefied area and non-liquefied area, the depth of the liquefied area is updated, and the initial porosity of the liquefied area is φ according to the characteristics of the liquefied soil. 0 Set to the maximum porosity of the sediment;

[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 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. According to the calculation results of cumulative pore water pressure, 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 migrate outward with seepage under the action of waves at different times is calculated. t , which is the prediction result of the internal erosion and resuspension amount of sediment under wave action time, calculates the internal erosion rate of soil at different depths of the seabed and the internal erosion rate of soil at a certain depth of the seabed at different times, and comprehensively analyzes the spatiotemporal evolution characteristics of the internal erosion amount of 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 volume of dV s The solid phase and volume of 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, and 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 soil per unit volume 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 periodic maximum 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 fis 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.

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

[0034]

[0035] If the 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 and is taken as 4.76.

[0038] Furthermore, 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 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 according to 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 certain 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 for the unliquefied area using 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, according to the calculation results of the cumulative pore water pressure, the liquefaction discriminant formula (16) is used to perform liquefaction discrimination and determine the liquefaction depth. The cumulative mass of fine particles per unit area (per square meter) of the seabed that migrate to the outside of the seabed under the action of waves with seepage 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 erosion and resuspension amount of seabed sediments 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 cumulative response process of the seabed. The simulation process is more comprehensive, which improves 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 internal erosion and resuspension amount of seabed sediments with the time of wave action, which is beneficial to coastal engineering protection.

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

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

[0055] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following 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 It is a schematic diagram of the geometric model of the present invention;

[0059] Figure 4 The liquefaction depth calculated by the present invention develops over the wave action time;

[0060] Figure 5 The volume concentration of suspended fine particles, porosity and the mass percentage of eroded fine particles in the liquefied zone (y = -1m) calculated by the present invention are developed 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 The volume concentration of suspended fine particles, porosity, mass percentage of eroded fine particles and cumulative pore water pressure of the non-liquefied zone (y=-6m) calculated by the present invention are developed over time, wherein (a) is the volume concentration changing over time, (b) is the porosity changing over time, (c) is the percentage of eroded fine particles changing over time, and (d) is the cumulative pore water pressure changing over time;

[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 FIG.

[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 changes with time, wherein (a) is the change of the internal erosion rate with time (y = -1m), and (b) is the change of the internal erosion rate with time (y = -6m);

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

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

[0066] In order to more clearly understand the above-mentioned purpose, 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 the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[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 protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0068] Combine the following 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 specifically described.

[0069] The present invention provides a method for predicting the amount of internal erosion and resuspension of seabed sediments under the action of waves, taking into account 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 taking into account 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 a numerical simulation study of the coupled process of the cumulative response of the seabed under the action of waves and internal erosion. In the process of numerical calculation, the influence of the liquefaction effect of the seabed 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, the influence of the cumulative response of the seabed soil on the internal erosion and the influence of the internal erosion on the seepage field are considered, and a mathematical model of the seabed cumulative response-internal erosion coupling under wave action (i.e., the partial differential control equation) is constructed. The specific derivation process of the control equation of the seabed cumulative response-internal erosion coupling model is as follows:

[0071] The porous medium with a microelement volume of dV is composed of a volume of dV s The solid phase and volume of dV fm The fluid mixture phase consists of a volume of dVfs 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, and 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 soil per unit volume 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 periodic maximum 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 the 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 1700kg / m 3 ρ f0 is the initial fine particle density, ρ f0 / ρ t Take 20%;f * is the residual fine particle density at the final stage of erosion when the hydraulic gradient i = 0.18; α er is the erosion constitutive fitting parameter and 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 =φ 0 , 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 bed surface with seepage and are diluted by seawater, and the concentration is approximately 0, and the cumulative pore water pressure at the seabed surface is 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, that is, 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 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 from the initial moment to this moment at each node 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 liquefaction of the seabed is judged according to 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 certain 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 liquefies, and step S4 is executed; if it does not liquefy, the process returns to step S2 and updates 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 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 development and change of the depth of the liquefied area over time are as follows: Figure 4 According to the characteristics of liquefied soil, the initial porosity of the liquefied zone is 0 The maximum porosity of the sediment is set to 0.5, and the porosity is continuously updated as erosion progresses;

[0110] S5. For the liquefied zone, the cumulative pore water pressure remains unchanged at the value when liquefaction occurs. Using the control equations (7) and (8), the volume concentration c of suspended fine particles 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: er , the solution result is 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: er , the solution result is 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 liquefied zone, on the upper surface of the liquefied zone (y=0), it is considered that the fine particles are diluted by seawater as they escape from the seabed surface with the seepage. At the same time, there is no need to calculate the cumulative response of the seabed. Therefore, the upper boundary condition of the liquefied 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 unliquefied 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 area of ​​the seabed, considering the continuity of particle concentration, the particle volume concentration at the upper boundary of the unliquefied area is equal to the volume concentration at the lower boundary of the liquefied area. At the same time, the cumulative pore water pressure changes with the depth of the top of the unliquefied area. At this time, the upper boundary condition of the unliquefied area is:

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

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

[0122]

[0123] S6. According to the calculation results of the cumulative pore water pressure, the liquefaction discriminant formula (19) is used to discriminate the liquefaction and determine the liquefaction depth. Calculate the cumulative mass M of fine particles that migrate outward with the seepage under the action of waves per unit area (per square meter) of the seabed 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 the calculation time has not been reached, return to step S4 to continue the calculation. If the calculation time has been 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: Fig.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 action of waves is comprehensively analyzed, which provides a reference for the assessment and prediction of submarine geological disasters and marine ecological environment.

[0128] In the description of this specification, the description of the terms "one embodiment", "some embodiments", "specific embodiments", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0129] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the amount of internal erosion and resuspension of seafloor 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 mathematical model of the seabed cumulative response-internal erosion coupling under wave action, i.e., a group of partial differential control equations, is constructed; according to the actual wave conditions and seabed soil properties, wave parameters, seabed soil parameters and erosion model parameters are determined and input, and the initial calculation time is t=0; S2. Based on the control equation 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 criterion to judge the liquefaction of the seabed. If the seabed liquefies, execute step S4; if it does not liquefy, 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. According to the liquefaction identification result, 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 body; 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 and solved. 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. According to the calculation results of cumulative pore water pressure, liquefaction is identified and the liquefaction depth is determined; 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 is calculated. t , which is the prediction result of the internal erosion and resuspension amount of sediment under wave action time, and calculates the internal erosion rate of soil at different depths of the seabed and the internal erosion rate of soil at a certain depth of the seabed at different times, and comprehensively analyzes the spatiotemporal evolution characteristics of the internal erosion amount of 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 seafloor 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, i.e., the partial differential control equation group in step S1 is as follows: The porous medium with a microelement volume of dV is composed of a volume of dV s The solid phase and volume of 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, and 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 it 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 the 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*; α er is the erosion constitutive fitting parameter and is taken as 4.

76.

3. The method for predicting the amount of internal erosion and resuspension of seafloor 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 from the initial moment to this moment at each node er , the calculation formula is as follows:

4. The method for predicting the amount of internal erosion and resuspension of seafloor 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) Among them, |y| is the distance from a certain point on the seabed to the seabed surface, that is, 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 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 seafloor 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 under the action of waves per unit area, i.e., per square meter, is calculated at different times. 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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