Method for predicting seismic hydrodynamic pressure effect of pier with rectangular section

Abstract

The invention discloses a seismic hydrodynamic pressure effect prediction method for a rectangular-section pier. The method comprises the steps of generating artificial seismic waves; drawing up the size and material parameters of the bridge pier; carrying out pier dynamic response simulation; determining a dynamic response increase rate; fitting a relation equation of the ratio of the water depth to the pier height, the section length-width ratio, the ratio of the upper structure mass to the pier mass and the dynamic response increase rate of the pier; determining a relation equation of a ratio of water depth to pier height, a section length-width ratio, a ratio of upper structure mass to pier mass and a dynamic response increase rate of the pier under different pier height-width ratios; and establishing a prediction equation of the dynamic response increase rate of the pier with any parameter. During anti-seismic design of wading piers such as sea-crossing and river-crossing, complex numerical simulation is not needed for the hydrodynamic pressure effect caused by an earthquake, the earthquake hydrodynamic effect can be considered only by multiplying the structural response by a corresponding amplification coefficient through a traditional non-wading pier anti-seismic design method, calculation is simple, efficiency is high, and the method is suitable for large-scale popularization and application. And the bridge aseismic design application is facilitated.

Description

Technical Field

[0001] The present invention belongs to the technical field of civil engineering, and in particular relates to a method for predicting earthquake water pressure effects on rectangular cross-section bridge piers. Background Art

[0002] In the field of civil engineering, sea- and river-spanning bridges are now widely constructed. To meet stiffness requirements in both longitudinal and transverse directions, pier cross-sections are often designed with rectangular cross-sections. The movement of piers during earthquakes can stimulate hydrodynamic pressure in the surrounding water, which acts on the piers. my country's current "Seismic Code for Highway Bridges" explicitly stipulates that the seismic design of piers in water depths exceeding 5 meters must consider the effects of earthquake-induced hydrodynamic pressure.

[0003] Current simulations of seismic water pressure on rectangular-section bridge piers primarily include two methods: refined fluid-structure coupling numerical simulation and simplified added mass simulation. The refined fluid-structure coupling numerical simulation method models the structure and water body separately for fluid-structure coupling calculations, offering high accuracy but low efficiency. The simplified added mass simulation method simplifies the water body into a mass point and attaches it to the pier for seismic analysis. However, the added mass calculation formula is generally based on the Morison equation and radiation wave theory and is applicable to circular cross-sections. While there are correction coefficients for rectangular cross-sections, the difficulty in determining the values ​​of the multiple parameters in the formula limits its application in engineering. Furthermore, the simplified added mass simulation method requires finite element modeling of the pier for seismic analysis, which can be inconvenient for engineering applications. Summary of the Invention

[0004] In order to solve the above problems, the purpose of the present invention is to provide a method for predicting the seismic water pressure effect of rectangular cross-section bridge piers, which converts the influence of seismic water pressure on the dynamic response of the bridge piers into an amplification coefficient, which is convenient for engineering designers to use.

[0005] To achieve the above-mentioned object, the present invention provides a method for predicting the seismic water pressure effect of rectangular cross-section bridge piers, comprising the following steps performed in sequence:

[0006] Step 1: Generate artificial seismic waves representing the five types of sites specified in the "Highway Bridge Seismic Code";

[0007] Step 2: Develop the dimensional parameters and material parameters of conventional rectangular cross-section piers with different height-to-width ratios (HWR) specified in the Highway Bridge Seismic Code;

[0008] Step 3: Based on the dimensional parameters and material parameters of the rectangular cross-section bridge pier determined in Step 2, the water depth to pier height ratio (DHR), the cross-sectional aspect ratio (SAR), and the superstructure mass to pier mass ratio (MMR) are used as parameter variables. A fluid-structure interaction numerical simulation method is used to establish a numerical analysis model of the bridge pier and water body under different parameters. The artificial seismic waves obtained in Step 1 are used as seismic excitation to carry out numerical simulations of the dynamic response of bridge piers with different parameters under seismic action.

[0009] Step 4: Extract the peak value of the pier dynamic response obtained in step 3 above, and determine the increase rate IR of the pier dynamic response under water conditions compared to the water-free conditions based on the peak value;

[0010] Step 5: Linear fitting method is used to fit the relationship equations of the water depth to pier height ratio DHR, cross-sectional aspect ratio SAR, superstructure mass to pier mass ratio MMR and pier dynamic response increase rate IR respectively;

[0011] Step 6: Use linear interpolation to determine the relationship equations between the water depth and pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR, and the pier dynamic response increase rate IR for different pier height-to-width ratios HWR;

[0012] Step 7: Based on the relationship equations in steps 5 and 6 above, a prediction equation for the dynamic response increase rate IR of the bridge pier with arbitrary parameters is established to represent the earthquake water pressure effect.

[0013] In step 1, the method for generating artificial seismic waves for five types of sites is based on constructing corresponding design acceleration response spectra corresponding to the dominant periods Ι0, Ι1, II, III, and IV of the five types of sites specified in the "Highway Bridge Seismic Code".

[0014] In step 2, at least three different pier height-to-width ratios are selected; the dimensional parameters of the rectangular cross-section pier are length, width, and height; and the material parameters are material type, material density, and elastic modulus.

[0015] In step three, the fluid-solid coupling simulation equation is performed using general software including ANSYS and ABAQUS to perform fluid-solid coupling simulation, and numerical analysis models of the pier and water body are established respectively; the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, and the superstructure mass to pier mass ratio MMR are in the ranges of 0-1.0, 0-3.0, and 0-1.0, respectively.

[0016] In step 4, the dynamic response of the pier includes parameters such as the relative displacement response between the pier top and the pier bottom, the bending moment response at the pier bottom, and the shear response at the pier bottom. The increase rate IR of the dynamic response of the pier under water conditions compared to the water-free conditions is defined as follows:

[0017]

[0018] Where R w is the peak value of the pier dynamic response under water conditions, R nw It is the peak value of the dynamic response of the pier under the water-free condition.

[0019] In step 5, when the linear fitting method is used, the regression determination coefficient R in the relationship equation between the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR and the pier dynamic response increase rate IR is 2 It should be at least 0.5 to ensure higher accuracy.

[0020] In step 6, the relationship equations between the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR, and the pier dynamic response increase rate IR for different pier height-to-width ratios HWR are as follows:

[0021]

[0022] Where: is the relationship equation between the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR, and the pier dynamic response increase rate IR. The variable x in HWR-x is the value of the pier height-to-width ratio HWR, m represents the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, and the superstructure mass to pier mass ratio MMR, and n is the value of the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, and the superstructure mass to pier mass ratio MMR.

[0023] In step seven, the prediction equation for the dynamic response increase rate IR of the bridge pier with arbitrary parameters is:

[0024]

[0025] Where,

[0026]

[0027] The advantages and positive effects of the present invention are as follows: in the seismic design of water-related bridge piers such as those across seas and rivers, there is no need to perform complex numerical simulations on the dynamic water pressure caused by earthquakes. The seismic hydrodynamic effects can be considered by simply multiplying the structural response by the corresponding amplification factor using the method adopted in the seismic design of traditional non-water-related bridge piers. This method is simple to calculate, highly efficient, and convenient for application in bridge seismic design. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Artificial seismic waves for five types of sites generated using the method of the present invention;

[0029] Figure 2 This is the DHR-IR diagram of the dynamic response of the pier bending moment calculated using the method of the present invention;

[0030] Figure 3 SAR-IR diagram of the dynamic response of the pier bending moment calculated using the method of the present invention;

[0031] Figure 4 This is the MMR-IR diagram of the dynamic response of the pier bending moment calculated using the method of the present invention. DETAILED DESCRIPTION

[0032] In order to further understand the content, features and effects of the present invention, the following embodiments are given as examples and described in detail with reference to the accompanying drawings and tables:

[0033] The method for predicting the earthquake water pressure effect of rectangular cross-section bridge piers provided by the present invention comprises the following steps performed in sequence:

[0034] Step 1: Generate artificial seismic waves representing the five types of sites specified in the "Highway Bridge Seismic Code";

[0035] The method for generating artificial seismic waves for five types of sites is based on constructing corresponding design acceleration response spectra corresponding to the dominant periods Ι0, Ι1, II, III, and IV of the five types of sites specified in the "Highway Bridge Seismic Code".

[0036] Step 2: Develop the dimensional parameters and material parameters of conventional rectangular cross-section piers with different height-to-width ratios (HWR) specified in the Highway Bridge Seismic Code;

[0037] The different height-to-width ratios of the bridge piers are at least 3; the size parameters of the rectangular cross-section bridge pier are length, width, and height; and the material parameters are material type, material density, and elastic modulus.

[0038] Step 3: Based on the dimensional parameters and material parameters of the rectangular cross-section bridge pier determined in Step 2, the water depth to pier height ratio (DHR), the cross-sectional aspect ratio (SAR), and the superstructure mass to pier mass ratio (MMR) are used as parameter variables. A fluid-structure interaction numerical simulation method is used to establish a numerical analysis model of the bridge pier and water body under different parameters. The artificial seismic waves obtained in Step 1 are used as seismic excitation to carry out numerical simulations of the dynamic response of bridge piers with different parameters under seismic action.

[0039] The fluid-solid coupling simulation equation is performed using general software including ANSYS and ABAQUS to establish numerical analysis models of the pier and water body respectively; the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, and the superstructure mass to pier mass ratio MMR are in the ranges of 0-1.0, 0-3.0, and 0-1.0, respectively.

[0040] Step 4: Extract the peak value of the pier dynamic response obtained in step 3 above, and determine the increase rate IR of the pier dynamic response under water conditions compared to the water-free conditions based on the peak value;

[0041] The dynamic response of the pier includes parameters such as the relative displacement response between the pier top and the pier bottom, the bending moment response at the pier bottom, and the shear force response at the pier bottom. The increase rate IR of the dynamic response of the pier under water-related conditions is defined as follows:

[0042]

[0043] Where R w is the peak value of the pier dynamic response under water conditions, R nw It is the peak value of the dynamic response of the pier under the water-free condition.

[0044] Step 5: Linear fitting method is used to fit the relationship equations of the water depth to pier height ratio DHR, cross-sectional aspect ratio SAR, superstructure mass to pier mass ratio MMR and pier dynamic response increase rate IR respectively;

[0045] When the linear fitting method is used, the regression determination coefficient R in the relationship equation between the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR and the pier dynamic response increase rate IR is 2 It should be at least 0.5 to ensure higher accuracy.

[0046] Step 6: Use linear interpolation to determine the relationship equations between the water depth and pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR, and the pier dynamic response increase rate IR for different pier height-to-width ratios HWR;

[0047] The relationship equations between the water depth and pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass and pier mass ratio MMR, and the pier dynamic response increase rate IR for different pier height-to-width ratios HWR are as follows:

[0048]

[0049] Where: is the relationship equation between the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR, and the pier dynamic response increase rate IR. The variable x in HWR-x is the value of the pier height-to-width ratio HWR, m represents the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, and the superstructure mass to pier mass ratio MMR, and n is the value of the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, and the superstructure mass to pier mass ratio MMR.

[0050] Step 7: Based on the relationship equations in steps 5 and 6 above, a prediction equation for the dynamic response increase rate IR of the bridge pier with arbitrary parameters is established to represent the earthquake water pressure effect.

[0051] The prediction equation for the dynamic response increase rate IR of the bridge pier with arbitrary parameters is:

[0052]

[0053] Where,

[0054]

[0055] The present invention simulates the dynamic response of rectangular cross-section bridge piers through a fluid-solid coupling numerical simulation method, obtains the increase rate of the peak dynamic response of the piers under water conditions compared with those under water-free conditions under different parameters, and fits and establishes the increase rate of the dynamic response of the piers with arbitrary parameters due to seismic water pressure, thereby achieving the purpose of quickly predicting the dynamic water pressure effect of rectangular cross-section bridge piers under earthquake action.

[0056] The advantages of the present invention are described below through an application example.

[0057] See also Figure 1 In this embodiment, the five types of sites Ι0, Ι1, II, III, and IV specified in the "Highway Bridge Seismic Code" are used as benchmarks, corresponding to the dominant periods of 0.2s, 0.35s, 0.45s, 0.65s, and 0.90s, respectively, to construct the corresponding design acceleration response spectrum, and then generate 5 artificial seismic waves for the corresponding sites.

[0058] In this example, the rectangular cross-section of the bridge piers analyzed is 9.0m x 3.0m in length x width, and 6m, 18m, and 30m in height, respectively. The corresponding height-to-width ratios (HWR) of the bridge piers are 2, 6, and 10. The bridge piers are made of reinforced concrete, with a material density of 2500kg / m 3 , the elastic modulus is 30 GPa. ANSYS LS-DYNA general software is used to establish a numerical analysis model of the bridge pier and water body. Then, using the five generated artificial seismic waves as seismic excitations, numerical simulations are performed on the dynamic response of the pier under the working conditions of DHR = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0, SAR = 3.0, and MMR = 0.0; the dynamic response of the pier under the working conditions of DHR = 1.0, SAR = 1.0, 1.5, 2.0, 2.5, 3.0, and MMR = 0.0; and the dynamic response of the pier under the working conditions of DHR = 1.0, SAR = 3.0, and MMR = 0.0, 0.25, 0.50, 0.5, and 1.0. Finally, the peak values ​​of the pier bottom bending moment response under different working conditions are extracted in this embodiment, and the pier bottom bending moment response increase rate IR is determined accordingly.

[0059] Please refer to Figure 2 , linearly fit DHR = 0.2, 0.4, 0.6, 0.8, 1.0 with the corresponding pier bottom bending moment response increase rate IR, and the relationship equation of DHR-IR is obtained as follows:

[0060] Please refer to Figure 3 SAR = 1.0, 1.5, 2.0, 2.5, 3.0 are linearly fitted with the corresponding pier bottom bending moment response increase rate IR, and the relationship equation between SAR and IR is obtained as follows:

[0061] Please refer to Figure 4 , linearly fit MMR = 0.0, 0.25, 0.5, 0.75, 1.0 with the corresponding pier bottom bending moment response increase rate IR, and the relationship equation of MMR-IR is obtained as follows:

[0062] Combining the above DHR-IR, SAR-IR, and MMR-IR relationship equations, the prediction equation for the dynamic response increase rate IR of piers with arbitrary parameters can be established as follows:

[0063]

[0064] Where,

[0065]

[0066] in,

[0067] Where:

[0068] Two bridge piers, No. 1 and No. 2, were randomly selected, and their parameters are shown in Table 1. Using the method provided by the present invention to predict the earthquake hydraulic pressure effect on rectangular-section bridge piers, the IR values ​​for the bottom bending moment response of Piers 1 and 2 were calculated to be 16% and 18%, respectively. Using the fluid-structure coupling simulation method, the IR values ​​for the bottom bending moment response of Piers 1 and 2 were calculated to be 12% and 13%, respectively. Therefore, the predicted values ​​of the IR values ​​for Piers 1 and 2 differed from the numerical simulation results by 4% and 5%, respectively, demonstrating the high accuracy of the method provided by the present invention to predict the earthquake hydraulic pressure effect on rectangular-section bridge piers.

[0069] Table 1 Pier parameters

[0070]

[0071] 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-mentioned specific embodiments. The above-mentioned specific embodiments are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, which all fall within the scope of protection of the present invention.

Claims

1. A method for predicting the earthquake hydraulic pressure effect on rectangular cross-section bridge piers, characterized by: The method for predicting the seismic water pressure effect of rectangular cross-section bridge piers comprises the following steps performed in sequence: Step 1: Generate artificial seismic waves representing the five types of sites specified in the "Highway Bridge Seismic Code"; Step 2: Develop the dimensional parameters and material parameters of conventional rectangular cross-section piers with different height-to-width ratios (HWR) specified in the Highway Bridge Seismic Code; Step 3: Based on the dimensional parameters and material parameters of the rectangular cross-section bridge pier determined in Step 2, the water depth to pier height ratio (DHR), the cross-sectional aspect ratio (SAR), and the superstructure mass to pier mass ratio (MMR) are used as parameter variables. A fluid-structure interaction numerical simulation method is used to establish a numerical analysis model of the bridge pier and water body under different parameters. The artificial seismic waves obtained in Step 1 are used as seismic excitation to carry out numerical simulations of the dynamic response of bridge piers with different parameters under seismic action. Step 4: Extract the peak value of the pier dynamic response obtained in step 3 above, and determine the increase rate IR of the pier dynamic response under water conditions compared to the water-free conditions based on the peak value; Step 5: Linear fitting method is used to fit the relationship equations of the water depth to pier height ratio DHR, cross-sectional aspect ratio SAR, superstructure mass to pier mass ratio MMR and pier dynamic response increase rate IR respectively; Step 6: Use linear interpolation to determine the relationship equations between the water depth and pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR, and the pier dynamic response increase rate IR for different pier height-to-width ratios HWR; Step 7: Based on the relationship equations in steps 5 and 6 above, a prediction equation for the dynamic response increase rate IR of the bridge pier with arbitrary parameters is established to represent the earthquake water pressure effect.

2. The method for predicting earthquake water pressure effects on rectangular cross-section bridge piers according to claim 1, characterized in that: In step 1, the method for generating artificial seismic waves for five types of sites is based on constructing corresponding design acceleration response spectra corresponding to the dominant periods Ι0, Ι1, II, III, and IV of the five types of sites specified in the "Highway Bridge Seismic Code".

3. The method for predicting earthquake water pressure effects on rectangular cross-section bridge piers according to claim 1, characterized in that: In step 2, at least three different pier height-to-width ratios are selected; the dimensional parameters of the rectangular cross-section pier are length, width, and height; and the material parameters are material type, material density, and elastic modulus.

4. The method for predicting earthquake water pressure effects on rectangular cross-section bridge piers according to claim 1, characterized in that: In step three, the fluid-solid coupling simulation equation is performed using general software including ANSYS and ABAQUS to perform fluid-solid coupling simulation, and numerical analysis models of the pier and water body are established respectively; the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, and the superstructure mass to pier mass ratio MMR are in the ranges of 0-1.0, 0-3.0, and 0-1.0, respectively.

5. The method for predicting earthquake water pressure effects on rectangular cross-section bridge piers according to claim 1 is characterized by: In step 4, the dynamic response of the pier includes parameters such as the relative displacement response between the pier top and the pier bottom, the bending moment response at the pier bottom, and the shear response at the pier bottom. The increase rate IR of the dynamic response of the pier under water conditions compared to the water-free conditions is defined as follows: Where R w is the peak value of the pier dynamic response under water conditions, R nw It is the peak value of the dynamic response of the pier under the water-free condition.

6. The method for predicting earthquake water pressure effects on rectangular cross-section bridge piers according to claim 1, characterized in that: In step 5, when the linear fitting method is used, the regression determination coefficient R in the relationship equation between the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR and the pier dynamic response increase rate IR is 2 It should be at least 0.5 to ensure higher accuracy.

7. The method for predicting earthquake water pressure effects on rectangular cross-section bridge piers according to claim 1, characterized in that: In step 6, the relationship equations between the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR, and the pier dynamic response increase rate IR for different pier height-to-width ratios HWR are as follows: Where: is the relationship equation between the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, the superstructure mass to pier mass ratio MMR, and the pier dynamic response increase rate IR. The variable x in HWR-x is the value of the pier height-to-width ratio HWR, m represents the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, and the superstructure mass to pier mass ratio MMR, and n is the value of the water depth to pier height ratio DHR, the cross-sectional aspect ratio SAR, and the superstructure mass to pier mass ratio MMR.

8. The method for predicting earthquake water pressure effects on rectangular cross-section bridge piers according to claim 1 is characterized by: In step seven, the prediction equation for the dynamic response increase rate IR of the bridge pier with arbitrary parameters is: Where,

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