Double-pile foundation seabed dynamic response simulation method under wave action based on multi-physics field coupling model

Abstract

The invention relates to a double-pile foundation seabed dynamic response simulation method under the wave action based on a multi-physics field coupling model. According to the method, a Wave-Stratum-Seabed Interference (WSSI) model integrating wave-seabed-structure interaction is constructed, the interaction between waves and a double-pile foundation under different pile spacing ratios and incoming flow deflection angles is simulated on an OpenFOAM platform through a finite volume method (FVM), and then the dynamic response of a seabed is analyzed. The model comprises a wave sub-model and a seabed sub-model based on the Biot three-phase consolidation theory, and key parameters such as free surface rise, dynamic wave pressure, vertical pore water pressure, vertical effective normal stress and liquefaction depth can be accurately calculated. An effective simulation tool and method are provided for pile foundation design and safety evaluation in ocean engineering, optimization of the pile foundation layout is facilitated, and the stability of an ocean structure is improved.

Description

Technical Field

[0001] This invention relates to the field of marine engineering technology, and in particular to a method for simulating the dynamic response of a double-pile foundation seabed under wave action based on a multiphysics coupling model. This method accurately simulates the dynamic response of a double-pile foundation seabed under wave action by integrating the interactions between waves, the seabed, and the structure, providing technical support for the safety design and assessment of marine engineering structures. Background Technology

[0002] In the field of marine engineering, pile foundations, as a key element supporting offshore structures, have always been a focus of research regarding their stability and safety. During service, pile foundations are inevitably subjected to wave erosion and dynamic loads, which not only directly affect the stability of the pile foundation but also generate significant dynamic responses to the surrounding seabed. In particular, for twin-pile foundations, their arrangement (such as the pile spacing ratio and the incoming current angle) has a significant impact on wave propagation characteristics, wave pressure distribution, and the dynamic response of the seabed.

[0003] Traditional research methods largely focus on wave-structure-seabed interactions under single piles, with less systematic exploration of how variations in pile arrangement affect wave-induced seabed dynamic responses. This limitation leads to insufficient understanding of pile foundation design and optimization in practical engineering. In particular, when waves impact double-pile foundations at different inflow angles, the interactions between piles, wave diffraction, and reflection become more complex, significantly impacting the seabed's dynamic response. To more accurately simulate and predict the dynamic response of double-pile foundations under wave action, a multiphysics coupled model that fully considers the interactions between waves, seabed, and structure is needed. This model should capture wave propagation, diffraction, and reflection between the piles, as well as the resulting changes in seabed pore water pressure, soil skeleton displacement, and potential liquefaction. However, existing simulation methods often simplify these physical processes, neglecting their coupling relationships, thus limiting the accuracy of simulation results. Furthermore, experimental methods also face numerous challenges in studying the dynamic response of pile foundations to the seabed under wave action. For example, limitations in experimental conditions, high costs, and the difficulty in acquiring and analyzing experimental data all restrict the breadth and depth of experimental research. Therefore, developing a numerical simulation-based method that can accurately simulate the dynamic response of a double-pile foundation on the seabed under wave action is particularly important.

[0004] In summary, this invention aims to propose a simulation method for the dynamic response of seabed under wave action using a multiphysics coupling model. This method, by constructing an integrated coupled model of wave, seabed, and structural interactions and employing advanced numerical simulation techniques, can accurately simulate the wave-induced dynamic response of the seabed under different pile spacing ratios and current deflection angles. This not only contributes to a deeper understanding of the dynamic response mechanism of seabed under wave action but also provides a scientific basis and technical guidance for the design, construction, and subsequent maintenance of pile foundations in marine engineering. Summary of the Invention

[0005] Objective: This invention aims to provide a simulation method for the dynamic response of seabed on twin-pile foundations under wave action based on a multiphysics coupling model. This addresses the lack of systematic exploration of the dynamic response of twin-pile foundations in wave-structure-seabed interaction (WSSI) studies in existing technologies. By integrating wave, structure, and seabed models, a multiphysics coupling model is constructed within the OpenFOAM framework using the finite volume method (FVM). This method can accurately simulate the changes in key parameters such as seabed free surface rise, dynamic wave pressure, vertical pore water pressure, vertical effective normal stress, and liquefaction depth caused by wave-pile foundation interaction under different pile spacing ratios and incoming / outgoing current angles. The purpose of this invention is to provide a reliable numerical simulation tool for the design, optimization, and safety assessment of marine engineering structures, thereby reducing the risk of seabed liquefaction under wave action and improving the stability and durability of marine engineering structures.

[0006] Technical Solution: To achieve the above-mentioned objectives, the technical solution adopted by this invention is: a method for simulating the dynamic response of a double-pile foundation on the seabed under wave action based on a multi-physics coupling model, characterized by comprising the following steps:

[0007] Step 1) Model Construction: Construct an integrated wave-structure-seabed interaction (WSSI) model.

[0008] Step 2) Define boundary conditions and computational domain: Clarify the model boundary conditions, including the setting of wave generation zone, absorption zone, computational zone, and the definition of the geometric dimensions of the seabed model;

[0009] Step 3) Mesh generation and verification: Mesh the wave sub-model and the seabed sub-model respectively, and verify the mesh convergence to ensure the accuracy of the simulation results and the computational efficiency;

[0010] Step 4) Parameter setting and working condition simulation: By setting different pile spacing ratios (G / D, ranging from 1 to 3) and inflow deflection angles (α, ranging from 0° to 90°), the interaction between waves and double pile foundations under different working conditions is simulated.

[0011] Step 5) Simulation Results Output and Analysis: Output simulation results, including time series data and spatial distribution maps of free surface rise, dynamic wave pressure, vertical pore water pressure, vertical effective normal stress, and liquefaction depth, and perform detailed analysis on these key parameters;

[0012] Furthermore, in step 1), the wave sub-model is built based on the wave2Foam toolbox of the open-source OpenFOAM platform, and the Navier-Stokes equations and fluid volume equations are solved using the finite volume method (FVM). Therefore, it simulates wave propagation and dynamic wave pressure p. d The two-phase flow equation is:

[0013]

[0014] In the formula, • Represents the divergence operator; Gradient operator; u represents fluid velocity; t represents time; dynamic wave pressure p d =p w -ρg·x, where p w The hydrostatic pressure is given by g; g is the acceleration due to gravity; x is the Cartesian coordinate vector. μ represents the dynamic fluid viscosity; the relative velocity field is u. r =u w -u a (u w It is the water velocity, u a (This refers to air velocity). α represents the volume fraction function, defined as the volume ratio of water to the total volume in each computational grid. Therefore, α = 1 indicates that water completely occupies the computational grid, while α = 0 indicates that the computational grid is filled with air. 0 < α < 1 represents a computational grid containing a water-air mixture.

[0015] The density ρ and dynamic viscosity μ of the fluid mixture are obtained by the following equations:

[0016] ρ=αρ w +ρ a (1-α)

[0017] μ=αμ w +μ a (1-α)

[0018] In the formula, ρ w , ρ a μ w μ aThe same indicates the density and corresponding viscosity of water and air.

[0019] It is worth noting that the wave sub-model employs a relaxation zone approach in terms of wave generation and absorption. This solution is formulated as a weighted merging of simulation results within a specific domain, and a linear solution based on defined boundary conditions (or objectives). In the relaxation zone, φ can be used to represent the weighting coefficients of eigenvalues ​​in the fluid. water φ represents the weighting coefficient of the characteristic values ​​in the water body. air The weighting coefficients representing characteristic values ​​in the air, such as ρ and μ, are determined by the following formula:

[0020] φ=α R φ water +(1-α R )φ air

[0021] In the formula, α R It is a weighting factor, which can be calculated using the following formula:

[0022]

[0023] Where χ R The definition is a scaling coordinate perpendicular to the boundary. When χ... R =0, α R When χ = 0, it indicates that the position remains at the boundary. Furthermore, when χ... R When α = 1, R It remains at 1 at the interface between the non-relaxed part and the relaxed region of the computational domain.

[0024] Furthermore, in step 1), the seabed sub-model is based on Biot's three-phase consolidation theory and uses the Up approximation equations to describe the pore water pressure and soil skeleton displacement of the seabed soil. The dynamic response of the seabed is calculated by solving these equations. The expressions for the continuity and momentum control equations of the seabed sub-model are as follows:

[0025]

[0026] In the formula, Let represent the Laplacian operator, be the divergence of the gradient; p represents the pore water pressure caused by waves; γ w The unit of measurement is water weight; n s For soil porosity; k s This refers to Darcy permeability. The compressibility β of pore fluids... s and volumetric strain ε s It can be described as follows:

[0027]

[0028] In the formula, S rIndicates soil saturation; K f It is the bulk modulus of pore water; P w0 Absolute static pressure; u s v s w s These represent soil displacements in the x, y, and z directions, respectively. The force balance equations for a porous elastic seabed can be calculated using the following formula:

[0029]

[0030] Where v represents Poisson's ratio; G s The shear modulus of soil can be described by Young's modulus E:

[0031]

[0032] In the formula, the effective normal stress σ′ i and shear stress τ ij Hooke's Law should be followed, which can be determined as follows:

[0033]

[0034] The subscripts i, j = x, y, z represent the directions of the Cartesian coordinates.

[0035] Furthermore, the specific boundary conditions and computational domain definitions in step 2) include:

[0036] Set a length of L at the starting end of the wave propagation direction. w Wave generation zone, L w This indicates the wave length, ensuring that the wave can be stably generated before entering the computational domain. The target wave is generated within this domain using specific wave generators or numerical wave generation methods.

[0037] A 1.5-meter long section is placed at the end of the wave propagation direction. xw A wave absorption zone is defined to eliminate the influence of wave reflection on the calculation results. This zone employs damping layers or numerical absorption techniques to gradually attenuate the waves to zero. The computational region, located between the wave generation zone and the absorption zone, has a length of 2L. w This is the main region for simulating the interaction between waves and structures / seabed. The mesh generation and calculation settings within this region must meet accuracy requirements.

[0038] At the interface between waves and structures / seabed, appropriate boundary conditions are set to simulate the dynamic pressure transmission of waves and the displacement response of the soil skeleton. For example, at the interface between waves and structures, the dynamic wave pressure equals the dynamic stress of the structure;

[0039] At the interface between the waves and the seabed, the pore water pressure equals the dynamic wave pressure. The geometry of the seabed model is consistent with the computational domain of the wave model, with a width designed to be 20D (D being the pile diameter) to eliminate the influence of lateral boundary effects on the simulation results. The thickness h of the seabed model is determined based on actual working conditions and soil conditions, typically ranging from several meters to tens of meters.

[0040] Furthermore, step 3) of mesh generation and verification includes:

[0041] The wave sub-model uses a structured mesh, with the mesh size adjusted in the x, y, and z directions according to wave propagation characteristics and computational accuracy requirements. Furthermore, multiple mesh schemes are set up, and mesh convergence is evaluated by gradually increasing the number of meshes.

[0042] The seabed sub-model also employs structured mesh generation, with mesh sizes typically larger than those in the wave sub-model, to accommodate the nonlinear response characteristics of the seabed soil. Similarly, multiple mesh schemes are implemented, with the number of meshes gradually increasing, to verify mesh convergence and ensure computational efficiency.

[0043] Furthermore, in step 4), 12 different working condition combinations were designed, covering the main pile spacing ratios and incoming flow deflection angles. Under each working condition, the interaction process between waves and the double-pile foundation was simulated, including wave propagation, generation of dynamic wave pressure, changes in seabed pore water pressure, and seabed liquefaction.

[0044] Furthermore, the analysis results in step 5) include:

[0045] As the incoming flow deflection angle increases, the free surface elevation in front of the twin-pile foundation gradually increases, while the free surface elevation in the central region decreases. This reflects the influence of the incoming flow deflection angle on the wave propagation path and wave height.

[0046] The dynamic wave pressure differs significantly between the front and rear of the twin-pile foundation. Furthermore, the dynamic wave pressure of the front pile increases with increasing flow angle, while the dynamic wave pressure of the rear pile changes less. Additionally, increasing the pile spacing ratio reduces the interference effect between the twin piles.

[0047] In wave-current coupling, a stronger forward current enhances the phase superposition effect of wave loads on the upstream pile foundation through wave-current synergy, resulting in a significant increase in free surface elevation and dynamic wave pressure. Conversely, a stronger reverse current reduces the hydrodynamic impact in this area through a wave-current energy cancellation mechanism.

[0048] Vertical pore water pressure is concentrated in shallow seabed and decreases rapidly with increasing depth. As the inflow angle increases, the vertical pore water pressure at the front pile gradually increases, while that at the rear pile decreases. Increasing the pile spacing ratio also reduces the impact of the two piles on pore water pressure.

[0049] The effective vertical normal stress and the vertical pore water pressure exhibit opposite trends to ensure dynamic stress balance. At the crest of the wave, the effective vertical normal stress around the forward pile is negative, reflecting the liquefaction tendency of the seabed soil.

[0050] Furthermore, regarding the key inventive points and effects of each of the above claims, as well as the beneficial effects in solving the technical problems, the following is a summary:

[0051] 1. Numerical simulation was performed using an integrated WSSI model based on the finite volume method (FVM).

[0052] • Function: This model can more accurately simulate the dynamic response of the seabed caused by waves around the twin piles, including changes in key parameters such as free surface elevation, dynamic wave pressure, and seabed pore water pressure.

[0053] • Effect: Through high-precision numerical simulation, the dynamic behavior of the seabed around the double piles under different pile spacing and flow direction angles can be predicted, providing a scientific basis for pile foundation design.

[0054] • Technical problems solved: It solved the problem that previous studies lacked exploration of the systematic influence of pile group arrangement on the dynamic response of the seabed caused by waves, and improved the accuracy and reliability of numerical simulation.

[0055] 2. Couple wave and seabed models at a common boundary using data interpolation.

[0056] • Function: To ensure data consistency and computational efficiency between wave models and seabed models on common boundaries, avoiding mismatches and computational errors between models.

[0057] • Effects: Improved the stability and computational efficiency of numerical simulations, reduced computational costs, and made large-scale numerical simulations possible.

[0058] • Technical problem solved: Resolved the difficulty in coupling wave models and seabed models in traditional numerical simulations.

[0059] This improved the accuracy and efficiency of the simulation.

[0060] 3. Define detailed boundary conditions, including boundary conditions for the wave model, structure model, and seabed model.

[0061] • Function: To accurately simulate the interaction between waves and pile foundations under actual working conditions, including wave generation, propagation, reflection, and the blocking effect of pile foundations on waves.

[0062] • Effects: Makes numerical simulation results closer to actual conditions, providing a more accurate reference for pile foundation design. • Technical problems solved: Solves the problem of simple boundary condition settings in traditional numerical simulations that do not match actual working conditions, improving the accuracy and practicality of the simulation.

[0063] 4. Systematically explore the influence of different pile spacing and flow direction deflection angle on the dynamic response of the seabed around the twin piles.

[0064] • Function: To provide comprehensive scientific basis for pile foundation design and guide engineers to select appropriate pile spacing and flow direction angle according to actual working conditions.

[0065] •Results: By comparing and analyzing simulation results under different pile spacings and flow direction angles, pile foundation design can be optimized.

[0066] Improve the safety and stability of marine engineering structures.

[0067] • Technical problems solved: It solved the problem that previous studies lacked a systematic exploration of the impact of pile group arrangement on the dynamic response of the seabed, and provided a more comprehensive scientific basis for pile foundation design.

[0068] 5. The proposed integrated WSSI model improves the accuracy and efficiency of numerical simulation.

[0069] • Function: This model combines the wave2Foam tool and Biot consolidation theory, enabling a more comprehensive consideration of the interaction between waves and the seabed.

[0070] • Effects: Improved the accuracy and efficiency of numerical simulation, reduced computational costs, and made large-scale numerical simulation possible.

[0071] • Technical problems solved: It solved the problems of simple models and low computational efficiency in traditional numerical simulation, and improved the accuracy and efficiency of simulation.

[0072] 6. A detailed analysis was conducted on key parameters such as free surface elevation, dynamic wave pressure, seabed pore water pressure, effective vertical normal stress, and liquefaction depth.

[0073] • Function: To provide comprehensive data support for seabed stability assessment and guide engineers in evaluating the stability and safety of the seabed based on actual working conditions.

[0074] • Effects: By analyzing the variation patterns of these key parameters in detail, we can predict the liquefaction depth and stress distribution of the seabed, providing a scientific basis for the design and construction of marine engineering structures.

[0075] • Technical problems solved: It addresses the lack of detailed analysis of key parameters in previous studies, providing more comprehensive data support for seabed stability assessment. Attached Figure Description

[0076] Figure 1 This is a schematic diagram of the simulation method for dynamic response of a double-pile foundation on the seabed under wave action using a multiphysics coupling model implemented in this invention.

[0077] Figure 2 This is a planar schematic diagram of the wave-shaped model according to the present invention;

[0078] Figure 3 This is a diagram showing the distribution of different inflow deflection angles of the double-pile foundation in this invention.

[0079] Figure 4 This invention analyzes the change in the free surface elevation at point 1 on the upstream side of the pile under different inflow deflection angles when the pile spacing ratio G / D = 3.

[0080] Figure 5 This invention describes the change in the free surface elevation at the center point 0 of a double-pile foundation over time under different inflow deflection angles when the pile spacing ratio G / D = 3.

[0081] Figure 6 This invention describes the dynamic wave pressure variation over time around a double-pile foundation under different incoming flow deflection angles when the pile spacing ratio G / D = 1.

[0082] Figure 7 This invention relates to the influence of different wave-current combinations on the elevation of the free surface in front of the upstream pile foundation when the incoming flow deflection angle α = 90° and the pile spacing ratio G / D = 1.

[0083] Figure 8 This invention relates to the influence of different wave-current combinations on the dynamic wave pressure in front of the upstream pile foundation when the incoming flow deflection angle α = 90° and the pile spacing ratio G / D = 1.

[0084] Figure 9 This invention analyzes the distribution of the effective vertical normal stress at analysis points 0, 1, 2, and 3 under the condition of fixed pile spacing G / D = 1 and different incoming flow deflection angles.

[0085] Figure 10 This invention illustrates the distribution of the maximum liquefaction depth around the upstream pile foundation and different incoming flow deflection angles under the condition of a fixed pile spacing ratio G / D = 1.

[0086] Figure 11 This invention illustrates the distribution of maximum liquefaction depth with different pile spacing ratios under a fixed inflow deflection angle α = 0°. Detailed Implementation

[0087] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0088] Figure 1 This is a schematic diagram of the simulation method for the dynamic response of a double-pile foundation on the seabed under wave action using a multiphysics coupling model, as shown below. Figure 1 As shown, the process includes the following steps:

[0089] Step 1: Construct an integrated wave-structure-seabed interaction (WSSI) model, which consists of two sub-models: a wave sub-model and a seabed sub-model based on Biot's three-phase consolidation theory.

[0090] The wave model is built based on the wave2Foam toolbox of the open-source OpenFOAM platform, and uses the finite volume method (FVM) to solve the Navier-Stokes and Volume of Fluid (VOF) equations. Therefore, it simulates wave propagation and dynamic wave pressure p. d The two-phase flow equation is:

[0091]

[0092] In the formula, • Represents the divergence operator; Gradient operator; u represents fluid velocity; t represents time; dynamic wave pressure p d =p w -ρg·x, where p w The hydrostatic pressure is given by g; g is the acceleration due to gravity; x is the Cartesian coordinate vector. μ represents the dynamic fluid viscosity; the relative velocity field is u. r =u w -u a (u w It is the water velocity, u a (This refers to air velocity). α represents the volume fraction function, defined as the volume ratio of water to the total volume in each computational grid. Therefore, α = 1 indicates that water completely occupies the computational grid, while α = 0 indicates that the computational grid is filled with air. 0 < α < 1 represents a computational grid containing a water-air mixture.

[0093] The density ρ and dynamic viscosity μ of the fluid mixture are obtained by the following equations:

[0094] ρ=αρw +ρ a (1-α)

[0095] μ=αμ w +μ a (1-α)

[0096] In the formula, ρ w , ρ a μ w μ a The same indicates the density and corresponding viscosity of water and air.

[0097] It is worth noting that the wave sub-model employs a relaxation zone approach in terms of wave generation and absorption. This solution is formulated as a weighted merging of simulation results within a specific domain, and a linear solution based on defined boundary conditions (or objectives). In the relaxation zone, φ can be used to represent the weighting coefficients of eigenvalues ​​in the fluid. water φ represents the weighting coefficient of the characteristic values ​​in the water body. air The weighting coefficients representing characteristic values ​​in the air, such as ρ and μ, are determined by the following formula:

[0098] φ=α R φ water +(1-α R )φ air

[0099] In the formula, α R It is a weighting factor, which can be calculated using the following formula:

[0100]

[0101] Where χ R The definition is a scaling coordinate perpendicular to the boundary. When χ... R =0, α R When χ = 0, it indicates that the position remains at the boundary. Furthermore, when χ... R When α = 1, R It remains at 1 at the interface between the non-relaxed part and the relaxed region of the computational domain.

[0102] The seabed sub-model is based on Biot's three-phase consolidation theory and uses the Up approximation equations to describe the pore water pressure and soil skeleton displacement of the seabed soil. The dynamic response of the seabed is calculated by solving these equations. The continuity and momentum governing equations of the seabed sub-model are expressed as follows:

[0103]

[0104] In the formula, Let represent the Laplacian operator, be the divergence of the gradient; p represents the pore water pressure caused by waves; γ w The unit of measurement is water weight; ns For soil porosity; k s This refers to Darcy permeability. The compressibility β of pore fluids... s and volumetric strain ε s It can be described as follows:

[0105]

[0106] In the formula, S r Indicates soil saturation; K f It is the bulk modulus of pore water; P w0 Absolute static pressure; u s v s w s These represent soil displacements in the x, y, and z directions, respectively. The force balance equations for a porous elastic seabed can be calculated using the following formula:

[0107]

[0108] Where v represents Poisson's ratio; G s The shear modulus of soil can be described by Young's modulus E:

[0109]

[0110] In the formula, the effective normal stress σ′ i and shear stress τ ij Hooke's Law should be followed, which can be determined as follows:

[0111]

[0112] The subscripts i, j = x, y, z represent the directions of the Cartesian coordinates.

[0113] Step 2, Define boundary conditions and computational domain: Define the model boundary conditions, including the settings of the wave generation zone, absorption zone, and computational domain, as well as the geometric dimensions of the seabed model:

[0114] Set a length of L at the starting end of the wave propagation direction. w A wave generation zone is defined to ensure that waves can be generated stably before entering the calculation area. See details. Figure 2 The target wave is generated within this area using specific wave-generating plates or numerical wave generation methods;

[0115] A 1.5L length is set at the end of the wave propagation direction. w The wave absorption zone is used to eliminate the influence of wave reflection on the calculation results. See details. Figure 2 Within this region, damping layers or numerical absorption techniques are employed to gradually attenuate waves to zero; the computational domain, located between the wave generation and absorption zones, has a length of 2L. wThis is the main region for simulating the interaction between waves and structures / seabed. The mesh generation and calculation settings within this region must meet accuracy requirements.

[0116] At the interface between waves and structures / seabed, appropriate boundary conditions are set to simulate the dynamic pressure transmission of waves and the displacement response of the soil skeleton. For example, at the interface between waves and structures, the dynamic wave pressure equals the dynamic stress of the structure;

[0117] At the interface between the wave and the seabed, the pore water pressure equals the dynamic wave pressure. The geometry of the seabed model is consistent with the computational domain of the wave model, with a width designed to be 20D (D being the pile diameter) to eliminate the influence of lateral boundary effects on the simulation results. See details... Figure 2 The thickness h of the seabed model is determined based on actual working conditions and soil conditions, and usually ranges from a few meters to tens of meters.

[0118] Step 3: Mesh the wave sub-model and the seabed sub-model separately, and verify the mesh convergence to ensure the accuracy of the simulation results and computational efficiency.

[0119] The wave sub-model uses a structured mesh, with the mesh size adjusted in the x, y, and z directions according to wave propagation characteristics and computational accuracy requirements. Furthermore, multiple mesh schemes are set up, and mesh convergence is evaluated by gradually increasing the number of meshes.

[0120] The seabed sub-model also employs structured mesh generation, with mesh sizes typically larger than those in the wave sub-model, to accommodate the nonlinear response characteristics of the seabed soil. Similarly, multiple mesh schemes are implemented, with the number of meshes gradually increasing, to verify mesh convergence and ensure computational efficiency.

[0121] Step 4: By setting different pile spacing ratios (G / D, with values ​​ranging from 1, 2, to 3) and inflow deflection angles (α, with values ​​ranging from 0°, 30°, 60°, to 90°), the interaction between waves and the double pile foundation under different working conditions is simulated.

[0122] In this embodiment of the invention, 12 different working condition combinations were designed, covering the main pile spacing ratios and inflow deflection angle values. The distribution of dual pile foundations is shown in [reference needed]. Figure 3 For each working condition, the interaction between waves and the twin-pile foundation was simulated, including wave propagation, generation of dynamic wave pressure, changes in seabed pore water pressure, and seabed liquefaction. In the wave model, the wave height was 1.2m, the wave period was 4s, the water depth was 4m, and the wave number was 0.3m. 1 The wavelength is 20.86 m, and detailed parameters are shown in Table 3. In the seabed model, the Young's modulus of seabed soil particles in the x, y, and z directions are 2 × 10⁻⁶ m. 7 2×10 7 2.6×107 Pa; Poisson's ratio is 0.4, 0.4, and 0.4 in the x, y, and z directions, respectively; permeability coefficient is 5 × 10⁻⁶ in the x, y, and z directions, respectively. -4 5×10 -4 1×10 -4 m / s; shear modulus in the x, y, and z directions is 8 × 10 m / s; 6 8×10 6 1×10 7 Pa; soil particle saturation is 0.98; soil porosity is 0.3.

[0123] Step 5: Output the simulation results, including time series data and spatial distribution maps of free surface rise, dynamic wave pressure, vertical pore water pressure, vertical effective normal stress, and liquefaction depth. Perform a detailed analysis of these key parameters and draw the following conclusions:

[0124] (1) Time-series data on free surface rise show the dynamic changes in seabed surface height during wave propagation under different combinations of pile spacing ratio (G / D) and incoming flow deflection angle (α). Comparative analysis reveals that as the incoming flow deflection angle increases, the free surface rise in front of the upstream pile gradually increases. (See details...) Figure 4 The free surface elevation in the central region of the twin piles shows a decreasing trend, see details. Figure 5 This phenomenon indicates that changes in the incoming flow angle significantly affect the wave propagation path and energy distribution.

[0125] (2) Figure 6 Time-series data on dynamic wave pressure reveal the dynamic changes in wave pressure at various points on the piles during the interaction between waves and the twin-pile foundation. Analysis shows that as the inflow angle increases, the dynamic wave pressure increases at the front and bottom of the upstream pile, while decreasing at the top. The dynamic wave pressure in the central region of the twin piles decreases with increasing inflow angle, reflecting a weakening of the upstream pile's blocking effect on wave propagation.

[0126] (3) The WSSI model can also be used to explore the working conditions of wave-current interaction. Figure 7 The distribution of free surface elevation in the xy-plane under different wave-current combinations is shown. Analysis reveals that the combination of waves and stronger forward current generates a greater free surface elevation in front of the upstream pile foundation; conversely, stronger reverse current hinders the development of free surface elevation in front of the upstream pile foundation. Furthermore, under wave-current coupling, the direction and magnitude of the current have a significant impact on the dynamic wave pressure. Stronger forward current enhances the phase superposition effect of wave loads in front of the upstream pile foundation through wave-current synergy, leading to a significant increase in dynamic wave pressure. Stronger reverse current, on the other hand, weakens the hydrodynamic impact in this area through a wave-current energy cancellation mechanism (see details). Figure 8 .

[0127] (4) The spatial distribution diagram of vertical pore water pressure shows the variation of pore water pressure at different depths inside the seabed under wave action. Analysis revealed that as the pile spacing ratio increases, the vertical pore water pressure around the double-pile foundation gradually decreases, indicating that the increase in the pile spacing ratio weakens the mutual interference effect between the two piles. At the same time, the increase in the inflow deflection angle increases the vertical pore water pressure on the front side of the upstream pile, while decreasing it on the rear and upper sides, as detailed in Table 1.

[0128] Table 1. Distribution of maximum pore water pressure in double pile foundations under different pile spacing ratios and inflow deflection angles.

[0129]

[0130]

[0131]

[0132] (5) The spatial distribution diagram of the vertical effective normal stress reflects the changes in the effective stress borne by the seabed soil skeleton under wave action. Analysis shows that when the wave crest propagates to the upstream pile, the vertical effective normal stress on the front side of the upstream pile is negative and increases with the increase of the incoming flow angle; while the stress on the rear and upper sides is positive. (See details...) Figure 9 This change, contrary to the trend of vertical pore water pressure, together maintains the stress balance of the seabed soil.

[0133] (6) The spatial distribution map of liquefaction depth shows the areas and depths of seabed liquefaction under wave action. Analysis revealed that as the inflow angle increases, the liquefaction depth in front of the upstream pile gradually increases, and the location of the maximum liquefaction depth shifts forward. This indicates that changes in the inflow angle have a significant impact on seabed liquefaction. (See details...) Figure 10 Meanwhile, increasing the pile spacing ratio helps reduce the liquefaction depth and improve seabed stability; see details below. Figure 11 .

[0134] In summary, this study, through the construction of an integrated wave-seabed-structure interaction (WSSI) model, explored the dynamic response of the seabed during the interaction between waves and a twin-pile foundation under different combinations of pile spacing ratio (G / D) and incoming flow deflection angle (α). This model, based on the open-source computational fluid dynamics platform OpenFOAM, employs the finite volume method (FVM) as the core numerical algorithm to achieve accurate simulations of wave propagation, seabed deformation, and pile-soil interaction. Firstly, through numerical simulation, this study outputs time-series data and spatial distribution maps of key parameters such as free surface rise, dynamic wave pressure, vertical pore water pressure, vertical effective normal stress, and liquefaction depth. The acquisition of these data provides important evidence for in-depth analysis of the seabed's dynamic response mechanism. Regarding free surface rise, the study found that with the increase of the incoming flow deflection angle, the free surface rise in front of the upstream pile gradually increases, while the free surface rise in the central region of the twin piles shows a decreasing trend. This phenomenon indicates that the change in the incoming flow deflection angle significantly affects the wave propagation path and energy distribution. The analysis of dynamic wave pressure reveals the dynamic changes in wave pressure at various points on the pile body during the interaction between waves and the twin-pile foundation. As the inflow deflection angle increases, the dynamic wave pressure at the front and bottom of the upstream piles increases, while it decreases at the top. The dynamic wave pressure in the central region of the twin piles also decreases with increasing inflow deflection angle, reflecting a weakening of the upstream piles' blocking effect on wave propagation. Furthermore, the WSSI model's study of different wave-current combinations revealed that a stronger forward current enhances the phase superposition effect of wave loads at the front of the upstream pile foundation through wave-current synergy, leading to a significant increase in dynamic wave pressure. Conversely, a stronger reverse current weakens the hydrodynamic impact in this region through a wave-current energy cancellation mechanism. Spatial distribution maps of vertical pore water pressure and effective vertical normal stress illustrate the variations in pore water pressure and effective stress at different depths within the seabed under wave action. Analysis shows that changes in the pile spacing ratio and inflow deflection angle jointly affect the stress state and pore water pressure distribution of the seabed soil. As the pile spacing ratio increases, the vertical pore water pressure around the twin pile foundation gradually decreases, indicating that increasing the pile spacing ratio weakens the mutual interference effect between the twin piles. Meanwhile, the increase in the inflow deflection angle increases the vertical pore water pressure in front of the upstream pile, while decreasing it behind and above. The trend of the vertical effective normal stress is opposite to that of the vertical pore water pressure, together maintaining the stress balance of the seabed soil. The spatial distribution map of liquefaction depth directly reflects the liquefaction risk of the seabed under wave action. The study found that with the increase of the inflow deflection angle, the liquefaction depth in front of the upstream pile gradually increases, and the location of the maximum liquefaction depth shifts forward. This indicates that the change in the inflow deflection angle has a significant impact on seabed liquefaction. At the same time, increasing the pile spacing ratio helps to reduce the liquefaction depth and improve seabed stability. This study not only reveals the dynamic response mechanism of the seabed during the interaction between waves and twin-pile foundations, but also provides a scientific basis for the design and construction of marine engineering structures.By optimizing parameters such as the pile spacing ratio and the inflow deflection angle, the risk of seabed liquefaction can be effectively reduced, improving the stability and safety of the structure. Furthermore, the WSSI model constructed in this study provides a powerful tool and reference for future related research, possessing significant theoretical and practical value.

[0135] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A method for simulating seabed dynamic response of a double-pile foundation under wave action based on a multi-physical field coupling model, characterized in that, Comprising the following steps: Step 1) Model construction: Construct the integrated wave-seabed-structure interaction Wave-Structure-Seabed Interaction (WSSI) model, namely the WSSI model; the model consists of two sub-models: a wave sub-model and a seabed sub-model based on Biot's three-phase consolidation theory; Step 2) Define boundary conditions and calculation domain: Define the model boundary conditions, including the setting of the wave generation zone, absorption zone, calculation zone, and the definition of the geometric size of the seabed model; Step 3) Mesh division and verification: Mesh division is performed for the wave sub-model and the seabed sub-model respectively, and mesh convergence verification is performed to ensure the accuracy and computational efficiency of the simulation results; Step 4) Parameter setting and working condition simulation: By setting different pile spacing ratios G / D and incoming flow angle α, the interaction between waves and double pile foundations under different working conditions is simulated, the pile spacing ratio G / D is in the range of 1 to 3, and the incoming flow angle α is in the range of 0° to 90°; Step 5) Simulation result output and analysis: Output the simulation results, including the time series data and spatial distribution graph of the free surface elevation, dynamic wave pressure, vertical pore water pressure, vertical effective normal stress and liquefaction depth, and analyze these key parameters in detail.

2. The method of claim 1, wherein, In the step 1), the wave model is constructed based on the wave2Foam toolbox of the open source OpenFOAM platform, and the Navier-Stokes equation and the fluid volume equation are solved by using the finite volume method (FVM), so as to simulate the propagation of the wave and the dynamic wave pressure p d The two-phase flow equation of the wave pressure p is: wherein denotes the divergence operator; denotes the gradient operator; u denotes the fluid velocity; t represents time; Dynamic wave pressure p d = p w - pg-x, where p w is the hydrostatic pressure; g is the gravitational acceleration, x is the Cartesian coordinate vector, p is the dynamic fluid viscosity; the relative velocity field u r = u w - u a , where u w is the water velocity, u a is the air velocity; a denotes the volume fraction function defined as the volume ratio of water to the total volume in each computational grid, thus, a = 1 indicates that the computational grid is completely occupied by water, a = 0 indicates that the computational grid is filled with air, and 0 < a < 1 indicates the computational grid of water-air mixture; The fluid mixture density ρ and dynamic viscosity μ are obtained from the following equations: p = a p w + p a (1 - a) μ = αμ w + μ a (1 - α) wherein p w , p a , m w , m a are the densities of water, air and their respective viscosities. It is worth noting that the wave child model adopts the strategy of setting the relaxation zone method in terms of wave generation and wave absorption; this solution is expressed as a weighted combination of simulation results within a specific domain, as well as a linear solution based on defined boundary conditions or objectives; in the relaxation zone, φ can be used to represent the weight coefficient of the eigenvalue in the fluid, φ water represents the weight coefficient of the eigenvalue in the water body, φ air represents the weight coefficient of the eigenvalue in the air, such as ρ and μ, which is determined by the following formula: φ = a R φ water + (1 - a R )φ air wherein α R is a weighting factor that can be calculated by the following equation: where χ R The definition of χ R = 0, a R = 0 indicates that the position stays at the boundary. Furthermore, when χ R = 1, a R is always maintained to be 1 at the interface between the non-relaxed part of the domain and the relaxation zone.

3. The method of claim 1, wherein, In the step 1), the seabed sub-model is based on Biot's three-phase consolidation theory, which uses soil skeleton displacement and pore water pressure (hereinafter referred to as: u-p) approximation equations to describe the pore water pressure and soil skeleton displacement of the seabed soil, and solves these equations to calculate the dynamic response of the seabed; the continuity and momentum control equation expressions of the seabed sub-model are: where represents the Laplacian, the divergence of the gradient; p represents the wave-induced pore water pressure; γ w represents the unit water weight; n s is the soil porosity; k s is the Darcy permeability; the compressibility of the pore fluid β s and the volumetric strain ε s can be described as follows: where S r represents the soil saturation; K f is the bulk modulus of the pore water; P w0 is the absolute static pressure; u s , v s , w s are the soil displacements in the x, y, and z directions, respectively; and the force balance equation for the poroelastic seabed can be calculated by the following equation: where v represents the Poisson's ratio; G s The shear modulus of the soil can be described by the Young's modulus E: where the effective normal stress σ' i and shear stress τ ij Hooke's law should be followed, which can be determined as follows: Where subscript i, j = x, y, z represents the direction of Cartesian coordinates.

4. The method of claim 1, wherein, In the step 2), the specific boundary conditions and calculation domain definition include: A wave generation area with length L w is set at the beginning of the wave propagation direction to ensure that the wave can be generated stably before entering the calculation area; the target wave is generated in this area by a specific wave maker or numerical wave generation method; A wave absorbing zone with length of 1.5L w is set at the end of the wave propagation direction to eliminate the influence of wave reflection on the calculation results; a damping layer or numerical absorption technique is used in the zone to gradually attenuate the wave to zero; the calculation zone is located between the wave generation zone and the absorbing zone with a length of 2L w , which is the main area for simulating the interaction between the wave and the structure and the seabed; the grid division and calculation settings in the area need to meet the accuracy requirements; On the interface between the wave and the structure, seabed, appropriate boundary conditions are set to simulate the dynamic pressure transmission of the wave and the displacement response of the soil skeleton; for example, on the interface between the wave and the structure, the dynamic wave pressure is equal to the dynamic stress of the structure; On the interface between the wave and the seabed, the pore water pressure is equal to the dynamic wave pressure; the geometric size of the seabed model is consistent with the calculation domain of the wave model, and the width is designed to be 20D, where D is the pile diameter, to eliminate the influence of lateral boundary effects on the simulation results; the thickness h of the seabed model is determined according to the actual working conditions and soil conditions, which is usually several meters to several tens of meters.

5. The method of claim 1, wherein, In the step 3), mesh division and verification include: The wave sub-model is divided by structured mesh, and the mesh size in x, y, z directions is adjusted according to the wave propagation characteristics and calculation accuracy requirements; and multiple mesh schemes are set, and the mesh convergence is evaluated by gradually increasing the number of meshes; The seabed sub-model is also divided by structured mesh, and the mesh size is usually larger than that of the wave sub-model to adapt to the nonlinear response characteristics of the seabed soil; similarly, multiple mesh schemes are set, and the number of meshes is gradually increased to verify the mesh convergence and ensure the computational efficiency.

6. The method of claim 1, wherein, In step 4), 12 different combinations of main pile spacing ratio and incident flow angle were designed to cover the interaction between waves and double pile foundations, including wave propagation, dynamic wave pressure generation, seabed pore water pressure change and seabed liquefaction.

7. The method of claim 1, wherein, It can be further extended to the dynamic wave pressure changes caused by the combined action of wave current and wave.

8. The method of claim 1, wherein, The analysis results in step 5) include: With the increase of incident flow angle, the free surface elevation in front of the double pile foundation gradually increases, while the free surface elevation in the central region decreases; this reflects the influence of incident flow angle on wave propagation path and wave height; Dynamic wave pressure exists significant differences in front and back of the double pile foundation, and with the increase of incident flow angle, the dynamic wave pressure of the front pile increases, while the dynamic wave pressure of the back pile changes little. In addition, the increase of pile spacing ratio will weaken the interference effect between the double piles; In wave current coupling, the stronger positive flow enhances the phase superposition effect of wave load in front of the upstream pile through wave current synergistic effect, resulting in significant increase of free surface elevation and dynamic wave pressure, while the stronger reverse flow weakens the hydrodynamic effect in this area through wave current energy offset mechanism; The vertical pore water pressure is concentrated in the shallow seabed layer and decreases rapidly with depth. With the increase of incident flow angle, the vertical pore water pressure of the front pile gradually increases, while that of the back pile decreases, and the increase of pile spacing ratio also weakens the influence of double piles on pore water pressure; The vertical effective normal stress and the vertical pore water pressure have opposite trends to ensure dynamic stress balance. At the wave peak moment, the vertical effective normal stress around the front pile presents negative value, reflecting the liquefaction trend of seabed soil.

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