An overlying water area site modeling method combining static analysis and dynamic analysis

Abstract

This invention provides a method for modeling overlying water bodies in a site that combines static and dynamic analysis. The method includes establishing a soil geometric model, inputting soil material parameters, adding water components to the soil geometric model, defining boundary conditions and loads, inputting water material parameters, extracting support reactions from the side and bottom boundaries and adding them to the corresponding boundary nodes, adding viscoelastic boundaries, inputting seismic loads as equivalent nodal forces, and using the site's stress equilibrium result as the initial field for dynamic calculations to obtain the overlying water body site model. This method, combining static and dynamic analysis, first achieves stress equilibrium, using this as the starting state for dynamic calculations. It effectively simulates and represents the actual state of the overlying water body site, providing a theoretical basis for pre-construction surveys.

Description

Technical Field

[0001] This invention relates to the field of dynamic analysis of riverbed or seabed sites, and more particularly to a method for modeling overlying water areas that combines static and dynamic analysis. Background Technology

[0002] In the early stages of constructing large-scale equipment projects such as bridges, wind turbine generators, river-crossing tunnels, and submarine pipelines, geological exploration and safety and risk assessment of the construction site are crucial steps. These include safety assessments of underwater explosions, dynamic characteristic analysis of steel water tanks, and analysis of soil-structure dynamic interactions under seismic loading. These studies provide theoretical basis for research on structural seismic performance and vibration reduction measures.

[0003] Existing methods for modeling complex water areas are not yet mature, and the simulated water environment is relatively simple. Traditional water area analysis can generally only consider hydrostatic pressure and apply hydrostatic pressure loads to the model. For deep water-covered sections, the influence of dynamic water pressure is not considered.

[0004] However, actual natural water body environments are far more complex. The combined effects of factors such as dynamic water pressure, water depth, and P-waves are significant, and existing site models struggle to capture the characteristics of such sites. Therefore, there is an urgent need for a computational method for overlying water bodies that can accurately represent the state of natural water body sites and has high computational efficiency. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a site modeling method for overlying water bodies that combines static and dynamic analysis. First, the ground stress balance is achieved, which serves as the starting state for dynamic calculations. This method can effectively simulate and represent the actual state of the overlying water body site, providing a theoretical basis for preliminary surveying in engineering construction.

[0006] The technical solution adopted by this invention to solve its technical problem is: to provide a method for modeling overlying water areas that combines static and dynamic analysis, including the following steps:

[0007] S1. Establish a soil geometric model and divide it into meshes, wherein the mesh size meets the convergence requirements of the dynamic calculation;

[0008] S2. Input the material parameters of the soil: Select the constitutive model according to the type of soil;

[0009] S3. Add water components to the soil geometry model, divide it into elements, use acoustic elements as the element type, and ensure that the element size meets the convergence criterion.

[0010] S4. Define boundary conditions and loads: Define bottom bidirectional constraints and side boundary normal constraints. Apply hydrostatic pressure to the top of the soil in the soil geometry model and apply body forces to the soil to obtain the stress field of the soil under gravity and overlying water. Use this stress field as the initial predefined field to perform site stress equilibrium, thereby completing the static analysis.

[0011] S5. Input water material parameters: Add water material properties, including fluid density ρ. f and bulk modulus K f This forms the initial site model;

[0012] S6. Extract the support reactions of the side and bottom boundaries in the static analysis of step S4, add them back to the nodes of the corresponding boundaries in the form of concentrated forces, add viscoelastic boundaries, and input the seismic load in the form of equivalent nodal forces to realize the input of seismic motion.

[0013] S7. Set a predefined field and use the results of the site after the ground stress balance as the initial field for dynamic calculation, thus obtaining the site model of the overlying water area.

[0014] The convergence requirement for the dynamic calculation in step S1 is: ΔL ≤ 1 / 8λ ~ 1 / 10λ, where ΔL represents the element size and λ represents the wavelength.

[0015] The medium described by the acoustic unit in step S3 is assumed to be a compressible, non-viscous fluid material, and the governing equation for the fluid passing through the resistance material is:

[0016]

[0017] Where x is the spatial position of the fluid particle, and p is the hydrostatic pressure in the fluid. and These are the velocity and acceleration of a fluid particle, p, respectively. and ρ is the unknown quantity to be solved in the governing equations. f Let ρ be the density of the fluid, and γ be the volumetric resistance caused by the fluid flowing through the resistance material.

[0018] The convergence criterion mentioned in step S3 refers to the maximum length L of the acoustic unit. max The following conditions must be met:

[0019]

[0020] Where c is the wave velocity in the acoustic medium, and n min f represents the number of intervals between acoustic grid nodes corresponding to the shortest wavelength. max This is the cutoff frequency.

[0021] The addition of viscoelastic boundaries in step S6 includes setting the boundaries of the fluid and solid units as Tie constraints, while constraining the p-degree of freedom represented by the acoustic pressure field.

[0022] The equivalent nodal force described in step S6 is derived using the following formula:

[0023] F equi (t)=L grid [K BN u inc (t)+C BN v inc (t)+ρV P v inc (t)]

[0024] Where F equi L is the equivalent nodal force corresponding to the incident wave. grid K is the control length of the node. BN and C BN These represent the spring stiffness and damping coefficient, u, along the normal to the two-dimensional transmission boundary. inc and v inc For the time history of the synthesized input stimulus, V P The velocity is the longitudinal wave velocity.

[0025] The beneficial effects of this invention based on its technical solution are as follows:

[0026] This invention provides a site modeling method for overlying water bodies that combines static and dynamic analysis. First, a soil geometric model is established, and pressure is applied to the soil to simulate the unit weight of natural soil. Then, acoustic elements are added to the soil model as water components, effectively simulating the hydrodynamic pressure caused by longitudinal waves propagating from the site surface to the overlying water body. Step S1 utilizes a mesh generation tool to create a complex engineering site mesh, achieving complex site modeling. In step S2, appropriate constitutive models can be selected based on different soil layers, and secondary constitutive modeling is also supported. Through steps S1 to S4, the equilibrium process of ground stress can be achieved, resulting in a more realistic gravity field. In step S5, acoustic elements are used to simulate the hydrodynamic pressure of an ideal fluid, offering higher computational efficiency compared to other fluid simulation methods such as CEL and SPH. Step S6 ensures the correct input of seismic loads; equivalent nodal forces at the side boundaries are used to simulate soil pressure; and transmission or viscoelastic boundaries are set to absorb reflected waves and reduce the influence at the boundaries. Through steps S5 to S7, the dynamic response of complex overlying water sites considering ground stress conditions can be realized. Through the above steps, compared with traditional site analysis methods, this method can model real complex sites, while taking into account the hydrodynamic pressure and ground stress during earthquakes with overlying water, achieving accurate input of ground motion, and having high computational efficiency. It is a highly efficient and rigorous method for analyzing complex sites with overlying water. Attached Figure Description

[0027] Figure 1 These are schematic diagrams of two one-dimensional hypothetical site models.

[0028] Figure 2 This is a schematic diagram of the synthesized incident wave based on the Ricker function, where... Figure 2 (a) is the time history of the composite incident wave. Figure 2 (b) is the Fourier spectrum of the synthesized incident wave.

[0029] Figure 3 This is a diagram comparing analytical and numerical solutions, where... Figure 3 (a) is a time-history comparison diagram. Figure 3 (b) is a schematic diagram comparing the W / L spectral ratio. Figure 3 (c) is the ratio of surface displacement amplitude (W / L) between the water-bearing site and the waterless site. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] This invention provides a site modeling method for overlying water bodies that combines static and dynamic analysis, comprising the following steps:

[0032] S1. Establish a soil geometric model and divide it into meshes. The mesh size should meet the convergence requirements of the dynamic calculation.

[0033] The meshing process for the soil geometry model can be optimized by selecting appropriate tools based on the simulated site object. If the simulated site object is a simple layered diagram, ABAQUS can be used directly to complete the meshing and soil layering. If the simulated site object is an engineering site with complex soil layer distribution, tools such as ANSA and Hypermesh can be combined to complete the soil layering.

[0034] The convergence requirement for the dynamic calculation is: ΔL≤1 / 8λ~1 / 10λ, where ΔL represents the element size and λ represents the wavelength.

[0035] S2. Input the material parameters of the soil: Select the constitutive model according to the type of soil, including Mohr-Coulomb, Duncan-Zhang, modified Cambridge, and secondary developed constitutive models.

[0036] S3. Add water components to the soil geometric model, divide it into elements, using acoustic elements as the element type, and ensure the element size meets the convergence criterion. The medium described by the acoustic elements is assumed to be a compressible, non-viscous fluid material, and the governing equation for the fluid passing through the resistance material is:

[0037]

[0038] Where x is the spatial position of the fluid particle, and p is the hydrostatic pressure in the fluid. and These are the velocity and acceleration of a fluid particle, p, respectively. and ρ is the unknown quantity to be solved in the governing equations. f ρ is the density of the fluid, γ is the volumetric drag caused by the fluid flowing through the dragging material, and ρ is the density of the fluid. f Both γ and γ are known quantities.

[0039] In acoustic-solid analysis, since the node spacing of the acoustic mesh should match the wavelength in the acoustic medium, the allowable size for mesh refinement should be estimated for reasonable accuracy. Given the acoustic wave velocity, the wavelength increases as the frequency decreases, indicating that the cutoff frequency in the analysis process determines the maximum length L of the acoustic element. max The main factors. The maximum length of the acoustic unit can be estimated by the following formula:

[0040]

[0041] In the formula: c is the wave velocity in the acoustic medium; n min This represents the number of intervals between acoustic grid nodes corresponding to the shortest wavelength; n is generally recommended. min ≥10; fmax The cutoff frequency is used, and unlike underwater explosion analysis, the cutoff frequency for seismic waves is generally much lower than the explosion cutoff frequency. In this embodiment, the acoustic unit size is set to about 1m, which is sufficient to capture the frequency band included in the seismic motion.

[0042] S4. Define boundary conditions and loads: Define bottom bidirectional constraints and side boundary normal constraints. Apply hydrostatic pressure to the top of the soil in the soil geometry model and apply body forces to the soil to obtain the stress field of the soil under gravity and overlying water. Use this stress field as the initial predefined field to perform site stress equilibrium, thereby completing the static analysis.

[0043] S5. Input water material parameters: Add water material properties, including fluid density ρ. f and bulk modulus K f This forms the initial site model.

[0044] S6. Extract the support reactions of the side and bottom boundaries from the static analysis in step S3, and re-add them to the corresponding boundary nodes as concentrated forces. This extraction can be done directly using a predefined set of nodes on the boundary in ABAQUS, or by writing an extraction result file in Python.

[0045] Add viscoelastic boundaries, including setting the boundaries of fluid and solid elements as Tie constraints, while constraining the p-degree of freedom represented by the acoustic pressure field.

[0046] Then, the seismic load is input in the form of equivalent nodal forces to realize the input of seismic motion. The equivalent nodal forces are derived by the following formula:

[0047] F equi (t)=L grid [K BN u inc (t)+C BN v inc (t)+ρV P v inc (t)]

[0048] Where F equi L is the equivalent nodal force corresponding to the incident wave. grid The control length of the model boundary nodes, K BN and C BN These represent the spring stiffness and damping coefficient, u, along the normal to the two-dimensional transmission boundary. inc and v inc These are the time histories of displacement and velocity of the synthetic input excitation, V. P K represents the longitudinal wave velocity. BN and C BN It can be obtained through calculation using viscoelastic boundary theory.

[0049] S7. Set a predefined field and use the results of the site after the ground stress balance as the initial field for dynamic calculation, thus obtaining the site model of the overlying water area.

[0050] To evaluate the feasibility of using acoustic units to simulate the response of a site with overlying water, a theoretical model was established to characterize the impact of overlying water on the site response.

[0051] The presence of overlying water has a certain suppressive effect on the vertical component of ground motion because P-waves can propagate through the water layer and reflect to the bottom, causing the P-waves to resonate at the natural frequency of the water layer. This model can obtain the Fourier spectral ratio of ground motions in sites with and without an overlying water layer, denoted as the W / L ratio, which can be expressed as:

[0052]

[0053] In the formula, f is the frequency, α = (ρ1c1) / (ρ2c2) is the impedance ratio of the soil-water interface, c1 and c2 are the longitudinal wave velocities in the fluid and solid media, respectively, and H1 is the water depth. This formula shows that |F(f,α)| ≤ 1 and This indicates that the suppression of longitudinal waves occurs at the resonant frequency of the water layer.

[0054] Two one-dimensional hypothetical site models were derived from the design. One site model consists of an aquifer and a homogeneous soil layer, while the other site model consists only of a homogeneous soil layer, such as... Figure 1 As shown. The soil depth in both models was set to 100m. For the model with a water layer, the water depth was set to 50m. To ensure the accuracy of the calculation results, the water layer and soil layer were discretized using AC2D4 and CPE4R elements in ABAQUS, respectively, with a uniform element size of 1m. To simulate the vertical propagation process of P-waves, the boundary conditions were set as follows: the sound pressure at the top boundary of the water layer was set to 0, the horizontal boundary of the soil part was set with horizontal constraints, and the vertical constraints were relaxed. In addition, a transmission boundary was formed by springs and dampers connected in parallel to simulate the process of P-waves penetrating the bedrock. At the same time, equivalent nodal forces were set at the boundaries to simulate the transmission boundary conditions in the assumed site model.

[0055] Since the Ricker function can be adjusted by its center frequency f s The frequency range to be analyzed is used as the synthetic input excitation applied to the bottom nodes of the site model, and its expression is:

[0056] R(f s ,t s )=(1-2α 2 )exp(-α 2 ), α=πf s (tt s )

[0057] Where f s and t s The center frequency and peak time are set to 12.5 Hz and 0.4 s, respectively. The time period is 5.115 s, and the time increment is 0.005 s. The time history and Fourier spectrum of the Ricker function are as follows: Figure 2 As shown.

[0058] Input the equivalent nodal forces corresponding to the Ricker function time histories at the bottom nodes of the site models, and then perform explicit dynamic analysis calculations on both site models in ABAQUS. Extract the acceleration time histories at the top nodes of the two site models and obtain their Fourier spectra through Fast Fourier Transform (FFT). The W / L spectral ratio of the analytical solution and the numerical solution can be compared, such as... Figure 3 As shown.

[0059] Therefore, the presence of overlying water can significantly alter vertical ground motion at the site surface, specifically suppressing the surface amplification effect of overlying water. From a frequency domain perspective, the suppression effect of overlying water on vertical ground motion exhibits a certain periodicity, consistent with the resonant frequency of the P-waves in the water layer. (Resonant frequency) n is an odd number. Generally, the propagation speed of P-waves in water can be considered constant; therefore, the degree of suppression of the vertical component of ground motion depends primarily on the depth of the overlying water. For riverbed sites, the water depth is typically between tens and hundreds of meters. In this case, compared to seabed sites, the fundamental frequency of P-waves in the water layer may be significantly higher, which could suppress the range of ground motion frequencies that need to be analyzed in the overlying site. As shown in the assumed site model, the maximum frequency suppression of vertical ground motion by the overlying water is 7.14 Hz, 21.42 Hz, and 35.70 Hz. Therefore, the site response characteristics of overlying sites are a matter of concern.

[0060] This invention provides a site modeling method for overlying water bodies that combines static and dynamic analysis. First, the ground stress balance is achieved, which serves as the starting state for dynamic calculations. This method can effectively simulate and represent the actual state of the overlying water body site, providing a theoretical basis for preliminary surveying in engineering construction.

Claims

1. An overlying water body site modeling method combining static and dynamic analysis, characterized by Includes the following steps: S1. Establish a soil geometric model and divide it into meshes, wherein the mesh size meets the convergence requirements of the dynamic calculation; S2. Input the material parameters of the soil: Select the constitutive model according to the type of soil; S3. Add water components to the soil geometric model, divide it into elements, using acoustic elements as the element type, and ensure the element size meets the convergence criterion; the medium described by the acoustic elements is assumed to be a compressible, inviscid fluid material, and the governing equation for the fluid passing through the resistance material is: ， Where x is the spatial position of the fluid particle, and p is the hydrostatic pressure in the fluid. and These are the velocity and acceleration of a fluid particle, p, respectively. and It is the unknown quantity to be solved in the governing equation. ρ f For the density of the fluid, γ The volumetric resistance caused by fluid flowing through a resistance material; S4. Define boundary conditions and loads: Define bottom bidirectional constraints and side boundary normal constraints. Apply hydrostatic pressure to the top of the soil in the soil geometry model and apply body forces to the soil to obtain the stress field of the soil under gravity and overlying water. Use this stress field as the initial predefined field to perform site stress equilibrium, thereby completing the static analysis. S5. Input water material parameters: Add water material properties, including fluid density. ρ f and bulk modulus K f This forms the initial site model; S6. Extract the support reactions of the side and bottom boundaries from the static analysis in step S4, and re-add them to the nodes of the corresponding boundaries in the form of concentrated forces. Add viscoelastic boundaries, and input the seismic load in the form of equivalent nodal forces to realize the input of seismic motion. The equivalent nodal forces are derived by the following formula: ， in F equi The equivalent nodal force corresponding to the incident wave. L grid The control length of the node, K BN and C BN These represent the spring stiffness and damping coefficient along the normal to the two-dimensional transmission boundary, respectively. u inc and v inc The time history of the synthesized input stimulus. V P For longitudinal wave velocity; S7. Set a predefined field and use the results of the site after the ground stress balance as the initial field for dynamic calculation, thus obtaining the site model of the overlying water area.

2. The method of modeling a site with an overlying water body combining static and dynamic analysis of claim 1, wherein: The convergence requirement for the dynamics calculation described in step S1 is that where denotes the cell size, denotes the wavelength.

3. The method of modeling a site with an overlying water body combining static and dynamic analysis of claim 1, wherein: The convergence criterion of step S3 refers to the maximum length of the acoustic cell L max satisfies the following condition: ， where c is the wave speed in the acoustic medium, n min represents the number of acoustic grid node intervals corresponding to the shortest wavelength, f max is the cutoff frequency.

4. The method for modeling a site with an overlying water body combining static and dynamic analysis of claim 1, wherein: The addition of viscoelastic boundaries in step S6 includes setting the boundaries of the fluid and solid units as Tie constraints, while constraining the p-degree of freedom represented by the acoustic pressure field.

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