Dynamic similarity design method for soil-structure-water centrifugal model
By adjusting the geometric similarity constant of the structure in the centrifuge vibration table test, the complex problem of model production in the existing technology is solved, and the high-precision similarity design of the soil-structure-water model is realized, which simplifies model production and improves response accuracy.
Patent Information
- Application Number
- CN202510248017.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-04
- Publication Date
- 2025-07-04
AI Technical Summary
In the physical model test of centrifuge vibration table, when aluminum alloy simulates reinforced concrete materials, the prior art needs to change the cross-sectional internal structure of the structure to meet the similarity of stiffness, resulting in complex model production and affecting the similarity of mass, making it difficult to achieve an effective similar design of soil-structure-water.
By determining the gravity similarity constant Sg and the geometric similarity constant Sl, using aluminum alloy to simulate structural materials, and keeping the physical properties of soil and water unchanged, the geometric similarity constants Slx and Sly in the horizontal seismic action direction are adjusted by using the structural dynamic equilibrium equation to achieve the dynamic similarity of the model.
The model production process is simplified and the accuracy and accuracy of the test model are improved, especially the structural response errors of the bridge pier and pile foundation are between 1.1% and 4.9%, which meets the dynamic similar design requirements of the soil-structure-water centrifugal model.
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Figure CN120257701A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of civil engineering, and particularly relates to a dynamic similarity design method for soil-structure-water centrifuge models. Background Art
[0002] In the field of civil engineering, offshore reinforced concrete structures such as cross-sea bridges and offshore wind farms are widely used, and their seismic analysis is an important part of the seismic design of such structures. Offshore reinforced concrete structures involve soil-structure interaction and water-structure interaction, so the dynamic response of the structure under seismic action is complex, and physical model tests on a centrifuge shaking table are usually required for seismic performance analysis. Due to the large size of offshore structures, the test models need to be scaled according to the prototype structure parameters. Therefore, reasonable similarity design is the premise to ensure the scientific and reasonable physical model test.
[0003] In physical model tests on a centrifuge shaking table, aluminum alloy materials are often selected to simulate the reinforced concrete materials in the prototype structure, while the same materials as the prototype are used for soil and water. However, there are differences in the physical parameters of aluminum alloy materials, including density and elastic modulus, compared with reinforced concrete, which makes the similarity design of centrifuge models involving three media of soil, structure, and water complex. The current common practice is to change the internal structure of the cross-section of structural members, such as changing the solid cross-section to a hollow cross-section, to make the stiffness of the cross-section similar. However, changing the internal structure of the cross-section makes the model manufacturing and processing complex, and will change the mass similarity of the structure, making the water-structure similarity design challenging. Summary of the Invention
[0004] In order to solve the above problems, the purpose of the present invention is to provide a dynamic similarity design method for soil-structure-water centrifuge models, which is applicable to the similarity design of soil-structure-water models in physical model tests on a centrifuge shaking table, and has high accuracy in simulating the reinforced concrete prototype structure and is simple and convenient for model manufacturing.
[0005] In order to achieve the above purpose, the dynamic similarity design method for soil-structure-water centrifuge models provided by the present invention includes the following steps carried out in sequence:
[0006] Step 1: Determine the gravity similarity constant S g and the geometric similarity constant S l ;
[0007] Step 2: Select aluminum alloy as the structural material of the test model to simulate the reinforced concrete material of the prototype structure, so as to determine the density similarity constant S ρ and the elastic modulus similarity constant S ESelect materials with the same physical properties of soil and water as those in the prototype as the test model materials, so as to determine the density similarity constant S of the soil in the test model ρs and the elastic modulus similarity constant S Es , as well as the density similarity constant S of the water body in the test model ρw ;
[0008] Step 3: Use the geometric similarity constant S determined in Step 1 above l to determine the vertical geometric similarity constant S lz ;
[0009] Step 4: Using the structural dynamic equilibrium equation, with the constraint that the structural inertia force similarity constant is equal to the soil-structure interaction force similarity constant and the water-structure interaction force similarity constant, and based on the results of Steps 2 and 3 above, determine the geometric similarity constant S in the direction of the horizontal seismic action lx and the geometric similarity constant S orthogonal to it horizontally ly ;
[0010] Step 5: Based on the results of Steps 1 to 4 above, use the principle of dimensional coordination to determine the similarity constants of other physical parameters of the test model
[0011] In Step 1, the method for determining the gravity similarity constant S g and the geometric similarity constant S l is as follows:
[0012] The gravity similarity constant S g should not exceed 2 / 3 of the maximum designed gravity similarity constant that the centrifuge shaking table test equipment can withstand; the geometric similarity constant S l has the following relationship with the gravity similarity constant S g :
[0013]
[0014] In Step 2, the density similarity constant S of the test model structure ρ = density of the test model structure / density of the prototype structure, and the elastic modulus similarity constant S of the test model structure E = elastic modulus of the test model structure / elastic modulus of the prototype structure; since the density and elastic modulus of the soil in the test model are the same as those of the soil in the prototype, and the density of the water body in the test model is the same as that of the water body in the prototype, the density similarity constant S of the soil in the test model ρs = 1, the elastic modulus similarity constant S Es = 1, and the density similarity constant S of the water body in the test model ρw = 1
[0015] In Step 3, the vertical geometric similarity constant Slz The expression is:
[0016] S lz = S l
[0017] In Step 4, assuming that the structural inertia force similarity constant is equal to the soil-structure interaction force similarity constant and the water-structure interaction force similarity constant, then the geometric similarity constant S lx in the horizontal earthquake action direction and the geometric similarity constant S ly orthogonal to it horizontally have the following expressions respectively:
[0018]
[0019] S ly = S ρ S lx
[0020] In Step 5, the similarity constants of other physical parameters of the test model are:
[0021] The mass similarity constant S m = S ρ S lx S ly S lz of the structural mass of the test model, the acceleration similarity constant S a = S g in the earthquake action direction, the concentrated force similarity constant S F = S m S a and the bending moment similarity constant S M = S F S lz .
[0022] The advantages and positive effects of the present invention are as follows: In the physical model test of the centrifuge shaking table, aluminum alloy is commonly used to simulate the elastic dynamic response of the prototype reinforced concrete structure, and the soil and water bodies are simulated with the same materials as the prototype. The traditional method needs to change the internal structure of the cross-section of the structure to meet the structural stiffness similarity, and the model manufacturing and processing are complex; by using the structural model designed in the present invention, only the geometric similarity constants in two horizontal directions of the structure need to be changed to meet the dynamic similarity of the model. This similarity method is simple and practical, and the model manufacturing is simple and convenient, providing a new method for the centrifuge shaking table test design of the soil-structure-water model under earthquake action. BRIEF DESCRIPTION OF THE DRAWINGS
[0023] Figure 1 Schematic diagram of the deep-water pile foundation pier adopted in the present invention;
[0024] Figure 2Comparison diagram of the top displacement of the test model designed by the method of the present invention and the prototype pier
[0025] Figure 3 Comparison diagram of the bottom bending moment of the test model designed by the method of the present invention and the prototype pier
[0026] Figure 4 Comparison diagram of the top bending moment of the test model designed by the method of the present invention and the prototype pile
[0027] Figure 5 Comparison diagram of the hydrodynamic pressure of the test model designed by the method of the present invention and the prototype pier
[0028] Figure 6 Comparison diagram of the dynamic earth pressure in the middle of the test model designed by the method of the present invention and the prototype pile Detailed implementation mode
[0029] In order to further understand the content, characteristics and effects of the present invention, the following examples are given and described in detail with the accompanying drawings and tables as follows:
[0030] The soil-structure-water centrifugal model dynamic similarity design method provided by the present invention includes the following steps carried out in sequence:
[0031] Step 1: Determine the gravity similarity constant S g and the geometric similarity constant S l ;
[0032] The gravity similarity constant S g shall not exceed 2 / 3 of the maximum designed gravity similarity constant that the centrifuge shaking table test equipment can bear; the geometric similarity constant S l and the gravity similarity constant S g are related as follows:
[0033]
[0034] Step 2: Select aluminum alloy as the structural material of the test model to simulate the reinforced concrete material of the prototype structure, so as to determine the density similarity constant S ρ and the elastic modulus similarity constant S E ; Select materials with the same physical properties as the soil and water in the prototype as the test model materials, so as to determine the density similarity constant S ρs and the elastic modulus similarity constant S Es of the test model soil body, as well as the density similarity constant S ρw of the test model water body.
[0035] The density similarity constant S of the test model structureρ = Test model structure density / Prototype structure density, Elastic modulus similarity constant S of the test model structure E = Elastic modulus of the test model structure / Elastic modulus of the prototype structure; Since the soil density and elastic modulus of the test model are the same as those of the prototype soil, and the water density of the test model is the same as that of the prototype water, the soil density similarity constant S of the test model ρs = 1, Elastic modulus similarity constant S Es = 1, Water density similarity constant S of the test model ρw = 1.
[0036] Step 3: Use the geometric similarity constant S determined in the above Step 1 l To determine the vertical geometric similarity constant S lz ;
[0037] The vertical geometric similarity constant S lz The expression is:
[0038] S lz = S l
[0039] Step 4: Use the structural dynamic equilibrium equation, with the condition that the structural inertia force similarity constant is equal to the soil-structure interaction force similarity constant and the water-structure interaction force similarity constant, and according to the results of Step 2 and Step 3, determine the geometric similarity constant S in the direction of the horizontal seismic action lx And the geometric similarity constant S orthogonal to it horizontally ly ;
[0040] The geometric similarity constant S in the direction of the horizontal seismic action lx And the geometric similarity constant S orthogonal to it horizontally ly The expressions are respectively:
[0041]
[0042] S ly = S ρ S lx
[0043] Step 5: Based on the results of the above Steps 1 to 4, use the principle of dimensional consistency to determine the similarity constants of other physical parameters of the test model.
[0044] The similarity constants of other physical parameters of the test model are:
[0045] Mass similarity constant S of the test model structure m = S ρ S lx S ly S lz, Acceleration similarity constant \(S\) in the direction of seismic action a = \(S\) g , Concentrated force similarity constant \(S\) in the direction of seismic action F = \(S\) m \(S\) a and bending moment similarity constant \(S\) M = \(S\) F \(S\) lz .
[0046] By changing the geometric similarity constants in different directions, the present invention realizes the similarity of dynamic characteristics among soil, structure and water, so as to achieve the purpose that the soil-structure-water centrifuge model can accurately simulate the dynamic response of the prototype.
[0047] The superiority of the present invention will be illustrated by an application example below.
[0048] In this embodiment, the maximum designed gravity similarity constant of the centrifuge shaking table test equipment selected is 100g, and the gravity similarity constant \(S\) of the selected test model g = 50, so the geometric similarity constant \(S\) l = 1 / 50.
[0049] Please refer to Figure 1 . In this embodiment, the pier 1 in the prototype has a rectangular cross-section, with a length of 4.0m, a width of 1.6m, and a height of 17.0m. The cuboid-shaped bearing platform 2 has a height of 2.0m and a width of 2.2m. Under the bearing platform 2 is a row of four pile foundations 3, and the length of the pile foundations 3 to the bearing stratum is 10.0m. The load transferred by the main beam to the top of the pier 1 is equivalent to a mass of 100t. The pier 1, the bearing platform 2 and the pile foundations 3 are all reinforced concrete structures, and their concrete strength grade is C40 and the steel bars are HRB400. The density of the reinforced concrete structure is 2500 kg / m 3 , and the elastic modulus is 35.0 GPa. The soil body 4 where the pile foundations 3 are located is divided into three layers, and the soil layer distribution parameters are shown in Table 1. The depth of the water 5 is 10m.
[0050] Table 1 Soil layer parameters
[0051]
[0052] In this embodiment, the density of the aluminum alloy of the test model is 2600 kg / m 3 , and the elastic modulus is 70.0 GPa. Therefore, the structural density similarity constant \(S\) of the test model ρ = 1.0, and the elastic modulus similarity constant \(S\) E = 2. The same materials as the prototype are selected for the soil and water. Therefore, the density similarity constant \(S\) of the soil body of the test model ρs = 1, and the elastic modulus similarity constant \(S\) Es = 1. The density similarity constant \(S\) of the water body of the test model ρw= 1. From this, the geometric similarity constant \(S\) in the horizontal seismic action direction lx and the geometric similarity constant \(S\) orthogonal to it horizontally ly are 1 / 63 and 1 / 63 respectively. Finally, the mass similarity constant \(S\) of the test model structure is determined m = 1 / 198425, the acceleration similarity constant \(S\) in the seismic action direction a = 50, the concentrated force similarity constant \(S\) in the seismic action direction F = 1 / 3969, and the bending moment similarity constant \(S\) M = 1 / 198425.
[0053] The test models of the above pier 1, cap 2, pile foundation 3, soil layer 4 and water 5 are designed by the method of the present invention. The dynamic time-history response numerical calculations of the prototypes of the pier 1, cap 2, pile foundation 3, soil layer 4 and water 5 and the test models designed by the method of the present invention under the action of the Loma Prieta ground motion are carried out by the finite element - fluid mechanics coupling calculation software respectively. The numerical calculation results of the displacement at the top of the pier, the bending moment at the bottom of the pier, the bending moment in the middle of the pile, the hydrodynamic pressure of the pier and the dynamic earth pressure in the middle of the pile are extracted. Then, the prototype seismic response results are obtained by back-calculating the response numerical calculation results of the test models designed by the method of the present invention according to the corresponding similarity constants respectively, and are compared with the prototype seismic response results obtained by direct numerical calculation.
[0054] Please refer to Figure 2 , under the action of the Loma Prieta earthquake, the maximum value of the displacement at the top of the prototype pier is 44.7 mm, and the maximum value of the displacement at the top of the test model pier designed by the method of the present invention is 43.9 mm, with a relative error of 1.7%.
[0055] Please refer to Figure 3 , under the action of the Loma Prieta earthquake, the maximum value of the bending moment at the bottom of the prototype pier is 4.69 MN·m, and the maximum value of the bending moment at the bottom of the test model pier designed by the method of the present invention is 4.92 MN·m, with a relative error of 4.9%.
[0056] Please refer to Figure 4 , under the action of the Loma Prieta earthquake, the maximum value of the bending moment in the middle of the prototype pile is 0.90 MN·m, and the maximum value of the bending moment in the middle of the test model pile designed by the method of the present invention is 0.71 MN·m, with a relative error of 1.1%.
[0057] Please refer to Figure 5 , under the action of the Loma Prieta earthquake, the maximum value of the hydrodynamic pressure of the prototype pier is 3.18 kPa, and the maximum value of the hydrodynamic pressure of the test model pier designed by the method of the present invention is 2.76 kPa, with a relative error of 13.2%.
[0058] Please refer to Figure 6 , under the action of the Loma Prieta earthquake, the maximum dynamic earth pressure in the middle of the prototype pile is 5.92 kPa, and the maximum dynamic earth pressure in the middle of the test model pile designed by the method of the present invention is 5.48 kPa, with a relative error of 7.4%.
[0059] In summary, under the action of the Loma Prieta earthquake, the relative errors of the seismic responses of each part of the test model designed by the method of the present invention are between 1.1% and 13.2%. In particular, the relative errors of the structural responses of the bridge pier and the pile foundation (including the displacement, moment of the bridge pier and the moment of the pile) are between 1.1% and 4.9%, indicating the accuracy of the present invention in the design of the soil-structure-water centrifuge model.
[0060] Although the preferred embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit and scope of the present invention as protected by the claims. All of these fall within the protection scope of the present invention.
Claims
1. A dynamic similarity design method for soil-structure-water centrifuge models, characterized in that: The soil-structure-water centrifugal model dynamic similarity design method includes the following steps carried out in sequence: Step 1: Determine the gravitational similarity constant \(S_{g}\) and the geometric similarity constant \(S_{l}\) based on the maximum effective load of the centrifuge shaking table test equipment and the weight of the prototype g and the geometric similarity constant \(S_{l}\) l ; Step 2: Select aluminum alloy as the structural material of the test model to simulate the reinforced concrete material of the prototype structure, so as to determine the density similarity constant S of the test model structure ρ and the elastic modulus similarity constant S E ; Select materials with the same physical properties as the soil and water in the prototype as the test model materials, so as to determine the density similarity constant S of the test model soil mass ρs and the elastic modulus similarity constant S Es , as well as the density similarity constant S of the test model water body ρw ; Step 3: Use the geometric similarity constant S determined in the above Step 1 l to determine the vertical geometric similarity constant S lz ; Step 4: Using the structural dynamic equilibrium equation, with the constraint that the structural inertia force similarity constant is equal to the soil-structure interaction force similarity constant and the water-structure interaction force similarity constant, determine the geometric similarity constant S in the direction of the horizontal seismic action according to the results of Steps 2 and 3 above lx and the geometric similarity constant S that is horizontally orthogonal to it ly ; Step Five: Based on the results of the above Steps One to Four, use the principle of dimensional harmony to determine the similarity constants of other physical parameters of the test model.
2. The soil-structure-water centrifugal model dynamic similarity design method according to claim 1, characterized in that: In Step 1, the method for determining the gravity similarity constant S g and the geometric similarity constant S l is as follows: The gravity similarity constant S g shall not exceed 2 / 3 of the maximum designed gravity similarity constant that the centrifuge shaking table test equipment can withstand; the geometric similarity constant S l and the gravity similarity constant S g are related as follows:
3. The soil-structure-water centrifugal model dynamic similarity design method according to claim 1, wherein: In Step 2, the density similarity constant S of the test model structure ρ = density of the test model structure / density of the prototype structure, and the elastic modulus similarity constant S of the test model structure E = elastic modulus of the test model structure / elastic modulus of the prototype structure; since the density and elastic modulus of the soil in the test model are the same as those of the soil in the prototype, and the density of the water in the test model is the same as that of the water in the prototype, the density similarity constant S of the soil in the test model ρs = 1, the elastic modulus similarity constant S Es = 1, and the density similarity constant S of the water in the test model ρw = 1.
4. The soil-structure-water centrifugal model dynamic similarity design method according to claim 1, characterized in that: In step three, the vertical geometric similarity constant S lz has the following expression: S lz = S l .
5. The soil-structure-water centrifugal model dynamic similarity design method according to claim 1, wherein: In Step 4, assume that the structural inertia force similarity constant is equal to the soil-structure interaction force similarity constant and the water-structure interaction force similarity constant. Then, the geometric similarity constant S lx in the horizontal seismic action direction and the geometric similarity constant S ly orthogonal to it horizontally are expressed as follows: S ly = S ρ S lx .
6. The soil-structure-water centrifugal model dynamic similarity design method according to claim 1, wherein: In Step Five, the similarity constants of other physical parameters of the test model are: Mass similarity constant \(S\) of the test model structure m = \(S\) ρ \(S\) lx \(S\) ly \(S\) lz and acceleration similarity constant \(S\) in the direction of seismic action a = \(S\) g and concentrated force similarity constant \(S\) in the direction of seismic action F = \(S\) m \(S\) a as well as bending moment similarity constant \(S\) M = \(S\) F \(S\) lz .