Calculation method for seabed liquefaction caused by elliptic cosine wave load

Abstract

The invention discloses a calculation method for seabed liquefaction caused by an elliptic cosine wave load. According to the technical scheme, the calculation method comprises the following steps that 1, an elliptic cosine wave model and a porous elastic seabed model are constructed; 2, the model is solved through a (u-p) form potential function and a dual variation and position method, and the seabed displacement, the pore water pressure and the total stress under the action of the elliptic cosine wave load can be rapidly calculated by applying MATLAB software; and step 3, judging according to a three-dimensional liquefaction judgment criterion that the seabed soil body is liquefied when the excess pore water pressure is greater than the gravity of the soil body, and effectively predicting the possibility of seabed liquefaction by the calculation method so as to take effective measures to protect the offshore structure.

Description

Technical Field

[0001] The present invention relates to the field of ocean engineering, and more particularly to a method for calculating seabed liquefaction caused by elliptical cosine wave loads. Background Art

[0002] Affected by the monsoon climate, marine structures are susceptible to large wave loads. The huge pressure caused by the waves acts on the seabed soil. Clayey soil with low consolidation degree or sandy soil with low density is prone to liquefaction under the action of wave pressure, losing strength, and then causing other disasters such as submarine landslides, seawall collapses, and submarine pipeline sinking.

[0003] Current research rarely takes into account both the transverse isotropy of the seabed and the seabed liquefaction phenomenon caused by elliptical cosine wave loads. Therefore, it is necessary to propose a reliable and efficient calculation method to predict the possibility of seabed liquefaction so that effective measures can be taken to protect marine structures. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a calculation method for seabed liquefaction caused by elliptical cosine wave loads, which can effectively predict the possibility of seabed liquefaction so that effective measures can be taken to protect offshore structures.

[0005] To achieve the above object, the present invention provides the following technical solution: a method for calculating seabed liquefaction caused by elliptical cosine wave loads, comprising the following steps:

[0006] Step 1, constructing an elliptical cosine wave model and a poroelastic seabed model;

[0007] Step 2: Solve the model using the (up) form potential function and the DVP method (DVP). MATLAB software can be used to quickly calculate the seabed displacement, pore water pressure, and total stress under elliptical cosine wave loads.

[0008] Step 3: judge by using the three-dimensional liquefaction judgment criterion that the seabed soil liquefies when the excess pore water pressure is greater than the soil's own gravity.

[0009] In summary, the present invention has the following beneficial effects: Based on the above technical solutions and concepts, various corresponding changes and variations can be implemented. The calculation results can be used to predict whether seabed soil liquefaction is occurring, pre-diagnose the potential for instability of marine structures, and implement targeted monitoring and preventive measures. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 Schematic diagram of the Cartesian coordinate system for a transversely isotropic multilayer poroelastic seabed of finite thickness under elliptical cosine wave loading;

[0011] Figure 2 This is a schematic diagram of the liquefaction results of the case;

[0012] Figure 3 Diagram showing the steps of the calculation method for seabed liquefaction caused by elliptical cosine wave loads. DETAILED DESCRIPTION

[0013] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0014] Reference Figures 1 to 3 As shown, to achieve the above purpose, the present invention provides the following technical solution: a calculation method for seabed liquefaction caused by elliptical cosine wave load, comprising the following steps:

[0015] Step 1, constructing an elliptical cosine wave model and a poroelastic seabed model;

[0016] According to the model, the wave type is determined to be an elliptical cosine wave, the seabed type is a transversely isotropic multi-layer poroelastic seabed of finite thickness, the interfaces between adjacent layers of the seabed are continuous, the bottom surface of the seabed is assumed to be a rigid, impermeable bedrock, and Biot's dynamic consolidation theory is adopted.

[0017] Step 2: Solve the model using the (up) form potential function and the DVP method (DVP). MATLAB software can be used to quickly calculate the seabed displacement, pore water pressure, and total stress under elliptical cosine wave loads.

[0018] Step 3: Calculate the liquefaction of the seabed soil using the three-dimensional liquefaction criterion, which indicates when the excess pore water pressure exceeds the soil's own weight. This calculation can predict whether the seabed soil is liquefied, pre-diagnose the potential for instability of marine structures, and implement targeted monitoring and preventive measures.

[0019] like Figure 1 The origin of the coordinates shown is located at the interface between seawater and seabed, H is the wave height, L is the wavelength, the period is T, the angular velocity is ω, and k is the wave number. d is the water depth, h j is the thickness of the jth layer of seabed, h is the total thickness of the seabed. The upper interface of the jth layer is z j-1 , the lower interface is z i , the corresponding sublayers are S1 and S2, the bottom of the seabed is rigid, impermeable bedrock, M is the Biot modulus, C ij is the elastic constant of the transversely isotropic medium, E h 、Ev are Young's modulus in the horizontal and vertical directions, G h , G v are the shear modulus in the horizontal and vertical directions respectively. h 、υ v are the Poisson's ratios in the horizontal and vertical directions, k h 、k v are the horizontal and vertical permeability coefficients, α1 and α3 are the horizontal and vertical effective stress coefficients, K s , K f are the bulk modulus of soil and pore fluid respectively. φ is the porosity of the seabed, S r is the saturation, ρ is the seabed density, ρ f is the pore fluid density, ρ s is the soil density, u i (i=x,z) is the displacement of the seabed soil in the i direction, ω i (i=x,z) is the displacement of pore fluid relative to seabed soil in direction i, σ xx ,σ zz is the total stress, τ xz is the shear stress, and p is the pore water pressure. and and The amplitude of the seabed dynamic response, which represents the displacement, total stress, shear stress, and pore water pressure caused by wave loads.

[0020] Step 1:

[0021] Based on the elliptical cosine wave theory, the pressure on the seabed surface (p b ) can be expressed as

[0022]

[0023] in

[0024]

[0025] Where m is the nonlinear order of the elliptic cosine wave, a positive integer m = 1-30; g is the acceleration of gravity; K(κ) is the complete elliptic integral of the first kind; κ is the elliptic parameter.

[0026] For the solution of arbitrary seabed layer, based on Biot's two-phase material dynamic consolidation theory equation, the constitutive relationship of transversely isotropic poroelastic medium and pore fluid pressure, the relative displacement is eliminated. and The following equation (3) can be obtained.

[0027]

[0028] in

[0029]

[0030]

[0031] Introducing the potential function of the (up) form As shown in the following formula (6)

[0032]

[0033] Substituting equation (6) into equation (3), we finally obtain the following differential equation.

[0034]

[0035] The parameters See Appendix A for details, and the solution is as follows

[0036]

[0037] The parameter λ i (i=1-3) See Appendix B, a i 、b i (i=1-3) is the unknown coefficient determined by the boundary conditions.

[0038] Substituting the solution given in equation (8) into equation (6) and Biot's two-phase material dynamic consolidation theory equation, the following result (9) can be obtained.

[0039]

[0040] The coefficient χ 1i , χ 2i , χ 3i ,ξ i , ψ 1i , ψ 2i , ψ 3i (i=1-3) See Appendix C for details. Substituting the boundary conditions into Equation (9), we can obtain the analytical solution of the dynamic response of the transversely isotropic multi-layered poroelastic seabed under cosine wave loads.

[0041] Step 2:

[0042] For multi-layer seabed, in order to facilitate the calculation of e im(kx-ωt) is ignored, the general solution for any layer of the seabed can be rewritten in matrix form as shown below (10)

[0043]

[0044] Among them U (m) (z), T (m) (z), and for

[0045]

[0046]

[0047] in is a 3×3 matrix, is the unknown coefficient, see Appendix D for details.

[0048] Step 2

[0049] like Figure 1 The upper interface of the jth layer is z i-1 , the lower interface is z i , introducing the decoupled variable position method (DVP) and eliminating the unknown coefficients, we can get the field values of the upper and lower bounds of the jth layer, which can be connected through the layer-matrix relationship (13).

[0050]

[0051] in

[0052]

[0053] Similarly, we can obtain the field values of the upper and lower bounds of the j+1th layer, the layer-matrix relationship, and further derive the recursive relationship from the jth layer interface to the j+1th layer interface.

[0054]

[0055] in

[0056]

[0057] Where S (m,j:j+1) The superscript j:(j+1) denotes the transfer matrix from the jth layer to the j+1th layer; I is the 3×3 identity matrix.

[0058] The boundary conditions of the multi-layer seabed can be written as

[0059]

[0060] Where z = z0 is the interface between seawater and seabed; z = z n is the seabed bottom interface; α 31 It represents the vertical effective stress coefficient α3 of the first layer of seabed.

[0061] Substituting the boundary condition (17) into equation (15), we can obtain that at any depth of the jth layer z = z s The dynamic response of the seabed at is

[0062]

[0063] Where S1 and S2 are the upper and lower sublayers of layer j respectively, S (m,1:S1) The superscript 1:S1 represents the transfer matrix from the first layer to the S1 layer, S (m,S2:n) The superscript S2:n represents the transfer matrix from the S2th layer to the nth layer. According to the elliptic cosine wave theory, the positive integer m is 1-30, and the arbitrary depth z determined by formula (19) is s The field quantity of each m is summed up to obtain the final solution of the multi-layer seabed under the action of cosine wave:

[0064]

[0065] Step 3:

[0066] When the excess pore water pressure is greater than or equal to the soil gravity, the seabed soil at a depth of z will liquefy.

[0067]

[0068] Where K0 = υ h / (1-v h ) is the static earth pressure coefficient at depth z, γ s is the soil weight, γ w is the density of pore water, p b is the seabed surface pressure due to the elliptical cosine wave, and p(z) is the pore water pressure at the seabed depth z caused by the wave.

[0069] In summary, those skilled in the art can devise various modifications and variations based on the above technical solutions and concepts, all of which are intended to be within the scope of protection of the present invention. The calculation results can be used to predict whether seabed soil is liquefied, anticipate the potential for instability of marine structures, and implement targeted monitoring and preventive measures.

[0070] Case Implementation

[0071] In a water depth of 20m, the wave height of the elliptical cosine wave is 8m, the wavelength is 200m, the water depth is 20m, the ellipse parameter is 0.9464, and the complete integral of the first kind of ellipse is 2.8151.

[0072] The seabed information is two layers of seabed with a total seabed thickness of 24m. The thickness of each layer of seabed is 1m and 23m respectively.

[0073] First layer of porous elastic seabed information: Young's modulus in the horizontal direction is 1.4×10 7 Pa, and the Young's modulus in the vertical direction is 1.4×10 7Pa, the horizontal Poisson's ratio is 0.4, the vertical Poisson's ratio is 0.4, and the vertical shear modulus is 5×10 6 Pa, horizontal permeability coefficient 1×10 -4 m / s, vertical permeability coefficient 1×10 -4 m / s, seabed porosity 0.35, pore fluid density 1000 kg / m 3 , soil density 2650kg / m 3 , soil bulk modulus 3.6×10 10 Pa, pore fluid bulk modulus 2×10 9 Pa.

[0074] Second layer of porous elastic seabed information: Young's modulus in the horizontal direction is 1.4×10 7 Pa, and the Young's modulus in the vertical direction is 1.8×10 7 Pa, the horizontal Poisson's ratio is 0.35, the vertical Poisson's ratio is 0.35, and the vertical shear modulus is 5×10 6 Pa, horizontal permeability coefficient 1×10 -4 m / s, vertical permeability coefficient 1.5×10 -4 m / s, seabed porosity 0.35, pore fluid density 1000 kg / m 3 , soil density 2650kg / m 3 , soil bulk modulus 3.6×10 10 Pa, pore fluid bulk modulus 2×10 9 Pa.

[0075] like Figure 2 The figure below shows the liquefaction results for this case. The maximum liquefaction depth under elliptical cosine wave load is 1.29m. This could cause the offshore structure to fail due to insufficient support provided by the liquefied seabed, leading to instability and failure.

[0076] Appendix A:

[0077]

[0078]

[0079]

[0080]

[0081] Appendix B: Lambda i (i=1-3)

[0082]

[0083]

[0084] in

[0085]

[0086]

[0087] Appendix C: χ 1i , χ 2i , χ 3i ,ξ i , ψ 1i , ψ 2i , ψ 3i (i=1-3)

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] Appendix D:B j (j=1-4)

[0096]

[0097]

[0098] The above description is only a preferred embodiment of the present invention. The protection scope of the present invention is not limited to the above embodiment. All technical solutions under the concept of the present invention belong to the protection scope of the present invention.

Claims

1. A method for calculating seabed liquefaction caused by elliptical cosine wave loads, characterized by: The following steps are involved: Step 1, constructing an elliptical cosine wave model and a poroelastic seabed model; Step 2: Solve the model using the (up) form potential function and the DVP method (DVP). MATLAB software can be used to quickly calculate the seabed displacement, pore water pressure, and total stress under elliptical cosine wave loads. Step 3: liquefaction judgment is performed based on the three-dimensional liquefaction judgment criterion that the seabed soil liquefies when the excess pore water pressure is greater than the soil's own gravity.

2. The method for calculating seabed liquefaction caused by elliptical cosine wave loads according to claim 1 is characterized by: Based on the elliptical cosine wave theory, the pressure on the seabed surface (p b ) can be expressed as: in Where m is the nonlinear order of the elliptical cosine wave, a positive integer m=1-30, g is the acceleration of gravity; K(κ) is the complete elliptic integral of the first kind, and k is the ellipse parameter.

3. The method for calculating seabed liquefaction caused by elliptical cosine wave loads according to claim 2 is characterized by: For the solution of arbitrary seabed layer, based on Biot's two-phase material dynamic consolidation theory equation, the constitutive relationship of transversely isotropic poroelastic medium and pore fluid pressure, the relative displacement is eliminated. and The following equation can be obtained: in Introducing the potential function of the (up) form As shown in the following formula (6): Substituting equation (6) into equation (3), we finally get the following differential equation: The parameters The solution is as follows: The parameter λ i (i=1-3), a i 、b i (i=1-3) is the coefficient determined by the boundary conditions; Substituting the solution given in equation (8) into equation (6) and Biot's two-phase material dynamic consolidation theory equation, the following results can be obtained: The coefficient χ 1i , χ 2i , χ 3i ,ξ i , ψ 1i , ψ 2i , ψ 3i (i=1-3) Substituting the boundary conditions into Equation (9), we can obtain the analytical solution of the dynamic response of the transversely isotropic multi-layered poroelastic seabed under cosine wave loads.

4. The method for calculating seabed liquefaction caused by elliptical cosine wave loads according to claim 3 is characterized by: For a multi-layer seabed, the general solution for any layer of the seabed can be rewritten in matrix form as follows: Among them U (m) (z), T (m) (z), and for: in is a 3×3 matrix, is the coefficient.

5. The method for calculating seabed liquefaction caused by elliptical cosine wave loads according to claim 4 is characterized by: Assume that the upper interface of the jth layer of the seabed is z i-1 , the lower interface is z i , by introducing the dynamic variable position method (DVP) and eliminating the coefficients, we can get the field values of the upper and lower interfaces of the jth layer.

6. The method for calculating seabed liquefaction caused by elliptical cosine wave loads according to claim 5 is characterized by: Through layer-matrix relationship: in The layer-matrix relationship between the field values of the upper and lower interfaces of the jth layer can be obtained. Similarly, the recursive relationship from the jth layer interface to the j+1th layer interface can be obtained: in Where S (m,j:j+1) The superscript j:(j+1) denotes the transfer matrix from the jth layer to the j+1th layer; I is the 3×3 identity matrix; The boundary conditions of the multi-layer seabed can be written as: Where z = z0 is the interface between seawater and seabed; z = z n is the seabed bottom interface; α 31 represents the vertical effective stress coefficient α3 of the first layer of seabed; Substituting the boundary condition (17) into equation (15), we can obtain that at any depth of the jth layer z = z s The solution of the seabed dynamic response at is: Where S1 and S2 are the upper and lower sublayers of layer j respectively, S (m,1:S1) The superscript 1:S1 represents the transfer matrix from the first layer to the S1 layer, S (m,S2:n) The superscript S2:n represents the transfer matrix from the S2th layer to the nth layer; According to the elliptical cosine wave theory, the positive integer m is 1-30, and the arbitrary depth z is determined s The field quantity at each m is summed up to obtain the final solution of the multi-layer seabed under the action of cosine wave:

7. The method for calculating seabed liquefaction caused by elliptical cosine wave loads according to claim 6 is characterized by: When the excess pore water pressure is greater than or equal to the soil gravity, the seabed soil at depth z will liquefy: Where K0 = υ h / (1-v h ) is the static earth pressure coefficient at depth z, γ s is the soil weight, γ w is the density of pore water, p b is the seabed surface pressure due to the elliptical cosine wave, and p(z) is the pore water pressure at the seabed depth z caused by the wave.

8. The method for calculating seabed liquefaction caused by elliptical cosine wave loads according to claim 1 is characterized by: The seabed is rigid, impermeable bedrock.

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