Estimation method for seismic hydrodynamic effect of reinforced concrete circular pier

Abstract

A method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers is disclosed. The method includes: determining parameter values; constructing five types of artificial seismic waves; building a water-pier fluid-structure interaction numerical model; obtaining parameter sets corresponding to different pier height-to-width ratios (HWRs); calculating the amplification rate of the seismic hydrodynamic effects of the piers; establishing the relational equation for the amplification rate of the seismic hydrodynamic effects of the piers; and establishing an estimation equation for the amplification rate of the comprehensive seismic hydrodynamic effects of the piers with arbitrary parameters. This invention overcomes the problems of parameter uncertainty, high computational cost, and lack of universality in traditional methods for calculating hydrodynamic pressure. By introducing the amplification rate of the seismic hydrodynamic effects of the piers, a method for converting the hydrodynamic pressure response between traditional non-water-borne piers and water-borne piers can be constructed. This method is computationally efficient and simple, facilitating its application in bridge seismic design. This method avoids complex fluid dynamics simulations, estimating the fluid-structure interaction simulation results within a very small error range using only simple algebraic operations.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering technology, and in particular relates to a method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers. Background Technology

[0002] In the field of civil engineering, with the large-scale construction of cross-sea and cross-river bridges, circular cross-section bridge piers are widely used due to their excellent streamlined shape, which can effectively reduce the impact of fluid loads such as waves and water flow. However, under seismic action, the vibration of bridge piers can induce hydrodynamic pressure, which has a significant impact on the structural stress.

[0003] Currently, there are three main methods for quantifying the impact of hydrodynamic pressure on circular cross-section bridge piers: First, the fluid-structure interaction numerical simulation method, which achieves high-precision analysis by directly solving the fluid and structure control equations, but it has high computational costs and complex modeling, making it difficult to use in daily design; second, the added mass method, which treats hydrodynamic pressure as an additional inertial force attached to the structure, is the mainstream simplification method in current engineering practice, but its formula depends on multiple parameters such as excitation frequency and amplitude, and the uncertainty of the values ​​affects the reliability of the results; third, the model test method (such as underwater shaking table test), which can directly measure the dynamic response, but it has a long cycle, high cost, and is difficult to carry out large-scale parametric research, thus having limited universality. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide a method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers.

[0005] To achieve the above objectives, the method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers provided by the present invention includes the following steps performed in sequence:

[0006] Step 1: Based on the "Code for Seismic Design of Highway Bridges in China", a reinforced concrete circular pier is selected as the research object. Under the specified three pier height-to-width ratio (HWR) values, the following parameters are determined under the reference working conditions: water depth-to-pier height ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), superstructure mass to pier mass ratio (MMR), material physical and mechanical properties, and damping ratio.

[0007] Step 2: Based on the characteristic periods corresponding to different types of sites in the "Code for Seismic Design of Highway Bridges in China", construct five types of artificial seismic waves as seismic inputs;

[0008] Step 3: Based on the parameter values ​​determined in Step 1, a water-bridge pier fluid-structure interaction numerical model is constructed using simulation software. Then, the artificial seismic wave constructed in Step 2 is input into the model to apply seismic motion. After that, the existing underwater shaking table test data is compared with the parameter values ​​output by the water-bridge pier fluid-structure interaction numerical model to verify the model and confirm whether it can reasonably simulate the seismic response of bridge piers in water.

[0009] Step 4: Under the condition that the pier height-to-width ratio HWR is a certain value, change the water depth-to-pier height ratio DHR, cross section diameter SD, cross section void ratio SHR, and the ratio of superstructure mass to pier mass MMR by one value in turn within their respective ranges to obtain a total of multiple parameter sets corresponding to different pier height-to-width ratios HWR.

[0010] Step 5: Set up the working conditions of the five types of artificial seismic waves constructed in Step 2 and the parameter groups corresponding to different pier height-to-width ratios HWR obtained in Step 4. At the same time, set up water-containing and waterless working conditions respectively under the same working conditions. Then, using the water-pier fluid-structure interaction numerical model that has been verified in Step 3, extract the peak values ​​of the relative displacement response of the pier top to the pier bottom, the peak value of the bending moment response of the pier bottom, and the peak value of the shear force response of the pier bottom under the above working conditions. Carry out the dynamic response numerical simulation of piers with different parameters under the action of the five types of artificial seismic waves. By comparing the three corresponding peak values ​​under the above water-containing and waterless working conditions, calculate the corresponding pier seismic hydrodynamic effect amplification rate IR.

[0011] Step Six: Using linear fitting methods, construct the relationship equations between the pier height-to-depth ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), and the ratio of superstructure mass to pier mass (MMR) with the corresponding increase rate (IR) of the seismic hydrodynamic effect of the pier under different pier height-to-width ratios (HWR). ;

[0012] Step 7: Based on the relational equations constructed above Establish the amplification rate of the comprehensive seismic hydrodynamic effect of bridge piers with arbitrary parameters. The estimation equation is used to represent the seismic hydrodynamic effect.

[0013] In step one, according to the "Code for Seismic Design of Highway Bridges in China", the pier height-to-width ratio (HWR) is typically taken as three values: 2, 6, and 10. Under the reference working conditions, the cross-sectional diameter (SD) of the reinforced concrete circular pier is 3m, corresponding to pier heights of 6m, 18m, and 30m. The water depth-to-pier height ratio (DHR) is 1.0, the cross-sectional void ratio (SHR) is 0.64, and the superstructure mass to pier mass ratio (MMR) is 0.0. The material is reinforced concrete with a density of 2500 kg / m³. 3 The elastic modulus is 30 GPa and the damping ratio is 5%.

[0014] In step two, the five types of artificial seismic waves are generated based on the dominant periods corresponding to the five types of sites I0, I1, II, III, and IV specified in the "Code for Seismic Design of Highway Bridges in China".

[0015] In step three, the water-pier fluid-structure interaction numerical model is constructed using simulation software including LS-DYNA, and includes a pier structure and a water body model. Seismic motion is applied via a unidirectional horizontal input method at the bottom of the pier. The water-pier fluid-structure interaction numerical model outputs parameters such as relative displacement, nodal acceleration, and hydrodynamic pressure at a certain part of the pier. These parameters are then compared with underwater shaking table test data. Figure 1 As shown, if the two values ​​are close, it proves that the water-bridge pier fluid-structure interaction numerical model is reasonable and can be used to simulate the seismic response of bridge piers in water; otherwise, the parameter values ​​under the reference working condition are re-determined according to the method in step one.

[0016] In step four, the water depth to pier height ratio (DHR) is 0.2, 0.4, 0.6, 0.8, and 1.0; the cross-sectional diameter (SD) is 1.0m, 1.5m, 2.0m, 2.5m, and 3.0m; the cross-sectional void ratio (SHR) is 0.0, 0.04, 0.16, 0.32, and 0.64; and the superstructure mass to pier mass ratio (MMR) is 0.0, 0.25, 0.50, 0.75, and 1.0.

[0017] Under the condition that the pier height-to-width ratio HWR takes a certain value, a total of four corresponding parameter sets are obtained:

[0018] The first group involves sequentially changing the water depth to pier height ratio (DHR):

[0019] ①DHR=0.2, SD=3.0, SHR=0.64, MMR=0.0;

[0020] ②DHR=0.4, SD=3.0, SHR=0.64, MMR=0.0;

[0021] ③DHR=0.6, SD=3.0, SHR=0.64, MMR=0.0;

[0022] ④DHR=0.8, SD=3.0, SHR=0.64, MMR=0.0;

[0023] ⑤DHR=1.0, SD=3.0, SHR=0.64, MMR=0.0;

[0024] The second group involves sequentially changing the cross-sectional diameter SD:

[0025] ①DHR=1.0, SD=1.0, SHR=0.64, MMR=0.0;

[0026] ②DHR=1.0, SD=1.5, SHR=0.64, MMR=0.0;

[0027] ③DHR=1.0, SD=2.0, SHR=0.64, MMR=0.0;

[0028] ④DHR=1.0, SD=2.5, SHR=0.64, MMR=0.0;

[0029] ⑤DHR=1.0, SD=3.0, SHR=0.64, MMR=0.0;

[0030] The third group involves sequentially changing the cross-sectional void ratio (SHR):

[0031] ①DHR=1.0, SD=3.0, SHR=0.00, MMR=0.0;

[0032] ②DHR=1.0, SD=3.0, SHR=0.04, MMR=0.0;

[0033] ③DHR=1.0, SD=3.0, SHR=0.16, MMR=0.0;

[0034] ④DHR=1.0, SD=3.0, SHR=0.32, MMR=0.0;

[0035] ⑤DHR=1.0, SD=3.0, SHR=0.64, MMR=0.0;

[0036] The fourth group involves sequentially changing the mass ratio (MMR) of the superstructure to the piers:

[0037] ①DHR=1.0, SD=3.0, SHR=0.64, MMR=0.00;

[0038] ②DHR=1.0, SD=3.0, SHR=0.64, MMR=0.25;

[0039] ③DHR=1.0, SD=3.0, SHR=0.64, MMR=0.50;

[0040] ④DHR=1.0, SD=3.0, SHR=0.64, MMR=0.75;

[0041] ⑤DHR=1.0, SD=3.0, SHR=0.64, MMR=1.00;

[0042] In step five, the formula for calculating the seismic hydrodynamic effect amplification rate IR of the bridge pier is as follows:

[0043] ;

[0044] In the formula, These represent the peak relative displacement between the pier top and pier bottom, the peak bending moment at the pier bottom, or the peak shear force at the pier bottom under water conditions. The peak values ​​of the relative displacement between the pier top and pier bottom, the peak value of the bending moment at the pier bottom, or the peak value of the shear force at the pier bottom are all under waterless conditions.

[0045] In step six, the relationship equations between the pier height-to-depth ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), and the ratio of superstructure mass to pier mass (MMR) under different pier height-to-width ratios (HWR) and the aforementioned pier seismic hydrodynamic effect amplification rate (IR) are as follows:

[0046] ;

[0047] In the formula. The equation relating the water depth to pier height ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), or the ratio of superstructure mass to pier mass (MMR) to the pier seismic hydrodynamic effect amplification rate (IR) is given. In HWR-x, x is the value of the pier height-to-width ratio (HWR), m is the value of the water depth to pier height ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), or the ratio of superstructure mass to pier mass (MMR), and n is the value of the water depth to pier height ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), or the ratio of superstructure mass to pier mass (MMR).

[0048] In step seven, the increase rate of the comprehensive seismic hydrodynamic effect of the bridge piers for the arbitrary parameters is... The estimation equation is:

[0049]

[0050] In the formula, ; ;

[0051] ;

[0052] .

[0053] This invention overcomes the difficulties of traditional methods in calculating hydrodynamic pressure, such as parameter uncertainty, high computational cost, and lack of universality. By introducing the amplification rate of seismic hydrodynamic effects on bridge piers, a method for converting the hydrodynamic pressure response between traditional non-water-bound bridge piers and water-bound bridge piers can be constructed. This method is computationally efficient and simple, making it convenient for application in bridge seismic design. Furthermore, this invention avoids complex fluid dynamics simulations, estimating fluid-structure interaction simulation results within a very small error range using only simple algebraic operations. Attached Figure Description

[0054] Figure 1 (a) to (c) are comparisons of numerical simulation results of relative displacement, nodal acceleration, and hydrodynamic pressure obtained using the method of this invention;

[0055] Figure 2 (a) to (e) are the five types of artificial seismic spectrum maps corresponding to the five types of sites I0, I1, II, III and IV generated by the method of the present invention, respectively;

[0056] Figure 3 The image shows the DHR-IR diagram of the dynamic response of the bending moment at the bottom of the bridge pier calculated using the method of this invention.

[0057] Figure 4 The image shows the SD-IR plot of the dynamic response of the bending moment at the bottom of the bridge pier calculated using the method of this invention.

[0058] Figure 5 The image shows the SHR-IR diagram of the dynamic response of the bending moment at the bottom of the bridge pier calculated using the method of this invention.

[0059] Figure 6 The image shows the MMR-IR diagram of the dynamic response of the bending moment at the bottom of the bridge pier calculated using the method of this invention. Detailed Implementation

[0060] The method of this invention simulates the dynamic response of reinforced concrete circular bridge piers using fluid-structure interaction numerical simulation, obtains the increase rate of seismic hydrodynamic effect of bridge piers under different parameters with and without water, and fits and establishes the increase rate of dynamic response of bridge piers caused by ground motion water pressure under arbitrary parameters, so as to achieve the purpose of rapid estimation of the hydrodynamic effect of circular bridge piers under seismic action.

[0061] The method of the present invention will be described in detail below with reference to an embodiment and accompanying drawings.

[0062] In this embodiment, based on the "Code for Seismic Design of Highway Bridges in China", the cross-sectional diameter SD of the reinforced concrete circular pier is selected as 3m, corresponding to pier heights of 6m, 18m, and 30m. The water depth to pier height ratio DHR=1.0, the cross-sectional void ratio SHR=0.64, and the superstructure mass to pier mass ratio MMR=0.0. The material is reinforced concrete with a density of 2500kg / m³. 3 The elastic modulus is 30 GPa and the damping ratio is 5%.

[0063] Based on the dominant periods of 0.2s, 0.35s, 0.45s, 0.65s, and 0.90s corresponding to the five site types I0, I1, II, III, and IV specified in the "Code for Seismic Design of Highway Bridges in China," corresponding design response spectra are constructed, and five types of artificial seismic waves for the corresponding sites are generated, such as... Figure 2 As shown.

[0064] A water-pier fluid-structure interaction numerical model, including the pier structure and water body model, was constructed using the ANSYS LS-DYNA general-purpose software. The five types of artificial seismic waves mentioned above were input into the model in a unidirectional horizontal manner at the bottom of the pier to apply seismic motion. The water-pier fluid-structure interaction numerical model outputs parameters such as relative displacement, nodal acceleration, and hydrodynamic pressure at a certain part of the pier. These parameters were then compared with underwater shaking table test data, proving that the water-pier fluid-structure interaction numerical model is reasonable and can be used to simulate the seismic response of bridge piers in water.

[0065] With the pier height-to-width ratio HWR set to 2, 6, and 10 respectively, the water depth-to-pier height ratio DHR, cross-section diameter SD, cross-section void ratio SHR, and the ratio of superstructure mass to pier mass MMR were changed by one value in turn within their respective ranges, resulting in a total of multiple parameter sets corresponding to different pier height-to-width ratios HWR.

[0066] Five types of artificial seismic waves and parameter groups corresponding to different pier height-to-width ratios (HWR) were set up. Under the same working conditions, water-containing and waterless working conditions were set up respectively. Then, the peak value of the pier bottom bending moment response under each working condition was extracted using a verified and reasonable water-pier fluid-structure interaction numerical model. By comparing the peak value of the pier bottom bending moment response under the water-containing and waterless working conditions, the corresponding pier seismic hydrodynamic effect amplification rate (IR) was calculated.

[0067] Linear fitting was performed between the water depth-to-pier height ratios (DHR) of 0.2, 0.4, 0.6, 0.8, and 1.0 and the corresponding seismic hydrodynamic effect amplification rate (IR) of the piers, yielding the following DHR-IR relationship equation: , , ,like Figure 3 As shown;

[0068] Linear fitting was performed between the cross-sectional diameters SD = 1.0, 1.5, 2.0, 2.5, and 3.0 and the corresponding seismic hydrodynamic effect amplification rate IR of the bridge piers, yielding the following relationship equation: , , ,like Figure 4 As shown;

[0069] The cross-sectional void ratios SHR = 0.0, 0.04, 0.16, 0.32, and 0.64 were linearly fitted with the corresponding seismic hydrodynamic effect amplification rate IR of the bridge piers, and the SHR-IR relationship equation was obtained as follows: , , ,like Figure 5 As shown;

[0070] The ratios of superstructure mass to pier mass (MMR) of 0.0, 0.25, 0.5, 0.75, and 1.0 were linearly fitted with the corresponding seismic hydrodynamic effect amplification rate (IR) of the piers, yielding the following MMR-IR relationship equation: , , .like Figure 6 As shown.

[0071] By combining the above-mentioned relationship equations of DHR-IR, SD-IR, SHR-IR and MMR-IR, the amplification rate of the comprehensive seismic hydrodynamic effect of bridge piers with arbitrary parameters can be established. The estimation equation is:

[0072]

[0073] In the formula, , ,

[0074] ,

[0075] .

[0076] in,

[0077] In the formula, , , , , , , , , , ,

[0078] , .

[0079] As shown in Table 1, three bridge pier sections were randomly selected, and the peak bending moment response of the pier base sections was obtained by inputting five types of artificial seismic waves under both dry (DHR=0.0) and wet (DHR=0.7 / 0.9) conditions. The seismic hydrodynamic effect amplification rates (IR) of the pier base bending moment corresponding to the three piers, calculated using the method of this invention, were 12.9%, 26.5%, and 17.7%, respectively. The seismic hydrodynamic effect amplification rates (IR) of the pier base bending moment corresponding to the pier base bending moment calculated using the fluid-structure interaction simulation method were 10.5%, 21.8%, and 16.9%, respectively. That is, the estimated values ​​differed from the numerical simulation values ​​by 2.4%, 4.7%, and 0.8%, respectively. This result indicates that the estimation accuracy of the method of this invention is high.

[0080] .

Claims

1. A method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers, characterized in that: The method includes the following steps performed in sequence: Step 1: Based on the "Code for Seismic Design of Highway Bridges in China", a reinforced concrete circular pier is selected as the research object. Under the specified three pier height-to-width ratio (HWR) values, the following parameters are determined under the reference working conditions: water depth-to-pier height ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), superstructure mass to pier mass ratio (MMR), material physical and mechanical properties, and damping ratio. Step 2: Based on the characteristic periods corresponding to different types of sites in the "Code for Seismic Design of Highway Bridges in China", construct five types of artificial seismic waves as seismic inputs; Step 3: Based on the parameter values ​​determined in Step 1, a water-bridge pier fluid-structure interaction numerical model is constructed using simulation software. Then, the artificial seismic wave constructed in Step 2 is input into the model to apply seismic motion. After that, the existing underwater shaking table test data is compared with the parameter values ​​output by the water-bridge pier fluid-structure interaction numerical model to verify the model and confirm whether it can reasonably simulate the seismic response of bridge piers in water. Step 4: Under the condition that the pier height-to-width ratio HWR is a certain value, change the water depth-to-pier height ratio DHR, cross section diameter SD, cross section void ratio SHR, and the ratio of superstructure mass to pier mass MMR by one value in turn within their respective ranges to obtain a total of multiple parameter sets corresponding to different pier height-to-width ratios HWR. Step 5: Set up the working conditions of the five types of artificial seismic waves constructed in Step 2 and the parameter groups corresponding to different pier height-to-width ratios HWR obtained in Step 4. At the same time, set up water-containing and waterless working conditions respectively under the same working conditions. Then, using the water-pier fluid-structure interaction numerical model that has been verified in Step 3, extract the peak values ​​of the relative displacement response of the pier top to the pier bottom, the peak value of the bending moment response of the pier bottom, and the peak value of the shear force response of the pier bottom under the above working conditions. Carry out the dynamic response numerical simulation of piers with different parameters under the action of the five types of artificial seismic waves. By comparing the three corresponding peak values ​​under the above water-containing and waterless working conditions, calculate the corresponding pier seismic hydrodynamic effect amplification rate IR. Step Six: Using linear fitting methods, construct the relationship equations between the pier height-to-depth ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), and the ratio of superstructure mass to pier mass (MMR) with the corresponding increase rate (IR) of the seismic hydrodynamic effect of the pier under different pier height-to-width ratios (HWR). ; Step 7: Based on the relational equations constructed above Establish the amplification rate of the comprehensive seismic hydrodynamic effect of bridge piers with arbitrary parameters. The estimation equation is used to represent the seismic hydrodynamic effect.

2. The method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers according to claim 1, characterized in that: In step one, according to the "Code for Seismic Design of Highway Bridges in China", the pier height-to-width ratio (HWR) is typically taken as three values: 2, 6, and 10. Under the reference working conditions, the cross-sectional diameter (SD) of the reinforced concrete circular pier is 3m, corresponding to pier heights of 6m, 18m, and 30m. The water depth-to-pier height ratio (DHR) is 1.0, the cross-sectional void ratio (SHR) is 0.64, and the superstructure mass to pier mass ratio (MMR) is 0.

0. The material is reinforced concrete with a density of 2500 kg / m³. 3 The elastic modulus is 30 GPa and the damping ratio is 5%.

3. The method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers according to claim 1, characterized in that: In step two, the five types of artificial seismic waves are generated based on the dominant periods corresponding to the five types of sites I0, I1, II, III, and IV specified in the "Code for Seismic Design of Highway Bridges in China".

4. The method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers according to claim 1, characterized in that: In step three, the water-pier fluid-structure interaction numerical model is constructed using simulation software including LS-DYNA, and includes the pier structure and water body model. The seismic action is applied by unidirectional horizontal input at the bottom of the pier. The water-pier fluid-structure interaction numerical model outputs parameters such as relative displacement, nodal acceleration, and hydrodynamic pressure at a certain part of the pier. These parameter values ​​are then compared with the underwater shaking table test data, as shown in Figure 1. If the values ​​are close, it proves that the water-pier fluid-structure interaction numerical model is reasonable and can be used to simulate the seismic response of bridge piers in water; otherwise, the parameter values ​​under the reference working condition are re-determined according to the method in step one.

5. The method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers according to claim 1, characterized in that: In step four, the water depth to pier height ratio (DHR) is 0.2, 0.4, 0.6, 0.8, and 1.0; the cross-sectional diameter (SD) is 1.0m, 1.5m, 2.0m, 2.5m, and 3.0m; the cross-sectional void ratio (SHR) is 0.0, 0.04, 0.16, 0.32, and 0.64; and the superstructure mass to pier mass ratio (MMR) is 0.0, 0.25, 0.50, 0.75, and 1.

0. Under the condition that the pier height-to-width ratio HWR takes a certain value, a total of four corresponding parameter sets are obtained: The first group involves sequentially changing the water depth to pier height ratio (DHR): ①DHR=0.2, SD=3.0, SHR=0.64, MMR=0.0; ②DHR=0.4, SD=3.0, SHR=0.64, MMR=0.0; ③DHR=0.6, SD=3.0, SHR=0.64, MMR=0.0; ④DHR=0.8, SD=3.0, SHR=0.64, MMR=0.0; ⑤DHR=1.0, SD=3.0, SHR=0.64, MMR=0.0; The second group involves sequentially changing the cross-sectional diameter SD: ①DHR=1.0, SD=1.0, SHR=0.64, MMR=0.0; ②DHR=1.0, SD=1.5, SHR=0.64, MMR=0.0; ③DHR=1.0, SD=2.0, SHR=0.64, MMR=0.0; ④DHR=1.0, SD=2.5, SHR=0.64, MMR=0.0; ⑤DHR=1.0, SD=3.0, SHR=0.64, MMR=0.0; The third group involves sequentially changing the cross-sectional void ratio (SHR): ①DHR=1.0, SD=3.0, SHR=0.00, MMR=0.0; ②DHR=1.0, SD=3.0, SHR=0.04, MMR=0.0; ③DHR=1.0, SD=3.0, SHR=0.16, MMR=0.0; ④DHR=1.0, SD=3.0, SHR=0.32, MMR=0.0; ⑤DHR=1.0, SD=3.0, SHR=0.64, MMR=0.0; The fourth group involves sequentially changing the mass ratio (MMR) of the superstructure to the piers: ①DHR=1.0, SD=3.0, SHR=0.64, MMR=0.00; ②DHR=1.0, SD=3.0, SHR=0.64, MMR=0.25; ③DHR=1.0, SD=3.0, SHR=0.64, MMR=0.50; ④DHR=1.0, SD=3.0, SHR=0.64, MMR=0.75; ⑤DHR=1.0, SD=3.0, SHR=0.64, MMR=1.

00.

6. The method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers according to claim 1, characterized in that: In step five, the formula for calculating the seismic hydrodynamic effect amplification rate IR of the bridge pier is as follows: ； In the formula, These represent the peak relative displacement between the pier top and pier bottom, the peak bending moment at the pier bottom, or the peak shear force at the pier bottom under water conditions. The peak values ​​of the relative displacement between the pier top and pier bottom, the peak value of the bending moment at the pier bottom, or the peak value of the shear force at the pier bottom are all under waterless conditions.

7. The method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers according to claim 1, characterized in that: In step six, the relationship equations between the pier height-to-depth ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), and the ratio of superstructure mass to pier mass (MMR) under different pier height-to-width ratios (HWR) and the aforementioned pier seismic hydrodynamic effect amplification rate (IR) are as follows: ； In the formula, The equation relating the water depth to pier height ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), or the ratio of superstructure mass to pier mass (MMR) to the pier seismic hydrodynamic effect amplification rate (IR) is given. In HWR-x, x is the value of the pier height-to-width ratio (HWR), m is the value of the water depth to pier height ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), or the ratio of superstructure mass to pier mass (MMR), and n is the value of the water depth to pier height ratio (DHR), cross-sectional diameter (SD), cross-sectional void ratio (SHR), or the ratio of superstructure mass to pier mass (MMR).

8. The method for estimating the seismic hydrodynamic effects of reinforced concrete circular bridge piers according to claim 1, characterized in that: In step seven, the increase rate of the comprehensive seismic hydrodynamic effect of the bridge piers for the arbitrary parameters is... The estimation equation is: In the formula, ; ; ； 。

Images