Similar design method for underwater vibration table test model of rectangular reinforced concrete pier

Abstract

The invention discloses a similar design method for an underwater vibration table test model of a reinforced concrete rectangular pier. The method comprises the steps of determining geometric similarity constants; determining an elastic modulus similarity constant, a longitudinal bar strength similarity constant, a stirrup strength similarity constant and a water density similarity constant of the reduced-scale pier; determining an acceleration similarity constant of the reduced-scale pier; determining a structural density similarity constant; determining a flexural rigidity similarity constant of the rectangular section of the reinforced concrete pier; determining the wall thickness of the reduced-scale pier with the hollow structure; determining the weight of the bridge pier in unit height and converting the weight into a mass block of an iron block or a lead block with the same weight; determining a longitudinal bar area similarity constant and a stirrup area similarity constant of the reduced-scale pier; and correcting the stirrup area similarity constant and the like. The method provided by the invention can provide a feasible method for similar design of the reinforced concrete rectangular pier model in an underwater vibration table test.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering technology, and in particular relates to a similar design method for an underwater shaking table test model of a reinforced concrete rectangular bridge pier. Background Technology

[0002] In bridge structural design, reinforced concrete is widely used, and to meet the longitudinal and transverse stiffness requirements of the bridge, the pier cross-section is often designed as rectangular. The seismic design of large deep-water bridges often requires specialized analysis and research through underwater shaking table scaled-down model tests to ensure the safety of the bridge's seismic design. Among these, the model similarity design for scaled-down model tests is crucial. Test results from a scientifically and rationally designed scaled-down model can accurately reproduce the seismic response of the prototype structure, thus providing strong support for the seismic design of the prototype structure.

[0003] Currently, scaled-down model similarity design methods for underwater shaking table tests aim at structural elastic similarity. However, for reinforced concrete rectangular bridge pier structures, underwater shaking table tests often lead to plastic deformation of the piers, making elastic similarity-based model design unsuitable. The plastic behavior of reinforced concrete must be considered in model similarity design. In underwater shaking table tests, the density similarity constants of water and structure must remain consistent to ensure the similarity of water-structure interactions. This results in high complexity for model similarity design. Furthermore, considering the similarity of the structure's plastic behavior under seismic loading further increases the difficulty of model similarity design for reinforced concrete rectangular bridge piers. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide a similar design method for an underwater shaking table test model of a reinforced concrete rectangular bridge pier. The scaled-down model produced by this method can accurately reproduce the seismic response of the prototype structure exhibiting plastic behavior.

[0005] To achieve the above objectives, the underwater shaking table test model similarity design method for reinforced concrete rectangular bridge piers provided by this invention includes the following steps performed in sequence:

[0006] Step 1: Determine the geometric similarity constant S based on the maximum effective load of the underwater shaking table test equipment, the maximum water depth of the pool, and the dimensions and weight of the prototype bridge pier. l ;

[0007] Step Two: Select the same reinforced concrete material as the prototype pier as the structural material of the scaled-down pier, and select a material with the same water physical properties as the prototype as the water material for the scaled-down model test, thereby determining the elastic modulus similarity constant S of the scaled-down pier. E longitudinal reinforcement strength similarity constant S fy Stirrup strength similarity constant S fyvand the water density similarity constant S ρw ;

[0008] Step 3: Determine the acceleration similarity constant S of the scaled-down bridge pier according to Froude's criterion. a ;

[0009] Step 4: Using the equality of the structural inertial force similarity constant and the seismic hydraulic similarity constant as a constraint, determine the structural density similarity constant S. ρ ;

[0010] Step 5: Using the equality of the structural inertial force similarity constant and the elastic force similarity constant as a constraint, based on the geometric similarity constant S obtained in Step 1... l The acceleration similarity constant S obtained in step three a The structural density similarity constant S obtained in step four ρ The similarity constant S for the flexural stiffness of the rectangular section of the reinforced concrete bridge pier was determined. EI ;

[0011] Step Six: Based on the similarity constant S of the flexural stiffness of the rectangular section of the reinforced concrete bridge pier obtained in Step Five. EI The geometric similarity constant S obtained in step one l In addition to the rectangular cross-sectional dimensions of the prototype bridge pier, the rectangular cross-section was hollowed out to form a hollow cross-section, and the wall thickness t of the scaled-down bridge pier with the hollow structure was determined. m ;

[0012] Step 7: Determine the wall thickness t of the scaled-down pier with a hollow structure based on the information obtained in Step 6. m The geometric similarity constant S obtained in step one l Based on the rectangular cross-sectional dimensions of the prototype bridge pier and the density ρ of the concrete, the weight M per unit height of the pier is determined and converted into a mass block of the same weight, either iron or lead. These mass blocks are then evenly distributed along the scaled-down pier height to ensure that the structural density similarity constant S obtained in step four is consistent with this. ρ Remain unchanged;

[0013] Step 8: Using the principle of dimensional consistency, based on the geometric similarity constant S obtained in Step 1... l Step 2 obtains the longitudinal reinforcement strength similarity constant S. fy Similarity constant S to the strength of stirrups fyv Step 3 obtains the acceleration similarity constant S a and the structural density similarity constant S obtained in step four ρ The similarity constant of the longitudinal reinforcement area of ​​the scaled-down bridge pier was determined. Similarity constant of stirrup area ;

[0014] Step Nine: Based on the shear strength of the reinforced concrete section and the shear strength of the stirrups, the stirrup section is increased to compensate for the decrease in shear strength caused by hollowing out the concrete section, and a stirrup area similarity constant is established. The correction factor β is finally used to adjust the stirrup area similarity constant obtained in step eight. Make corrections to obtain the corrected stirrup area similarity constants. And the similarity constant of the longitudinal reinforcement area of ​​the scaled-down pier obtained in step eight. Together they form the final design result.

[0015] In step one, the geometric similarity constant S l =Scaled-down bridge pier structural dimensions / Prototype bridge pier structural dimensions, determined by the following method:

[0016] According to the geometric similarity constant S l The weight of the scaled-down bridge pier must not exceed the maximum effective load that the underwater shaking table test equipment can withstand, and must be determined according to the geometric similarity constant S. l The water depth after scaling down must not exceed the maximum water depth of the pool.

[0017] In step two, the elastic modulus similarity constant S E = Elastic modulus of scaled-down pier / Elastic modulus of prototype pier, water density similarity constant S ρw =Water density in the scaled-down test / Water density in the prototype; Since the scaled-down bridge pier uses the same material as the prototype bridge pier and water, the elastic modulus similarity constant S E =1, longitudinal reinforcement strength similarity constant S fy =1, Stirrup strength similarity constant S fyv =1, water density similarity constant S ρw =1.

[0018] In step three, the acceleration similarity constant S of the scaled-down bridge pier is determined according to Froude's criterion. a The method is:

[0019] According to Froude's criterion, the acceleration similarity constant S of the scaled-down bridge pier is... a The expression is:

[0020] ;

[0021] In the formula, S g is the gravitational acceleration similarity constant, with a value of 1.0.

[0022] In step four, the structural density similarity constant S is determined by using the equality of the structural inertial force similarity constant and the seismic hydraulic similarity constant as a constraint. ρ The method is:

[0023] Assuming the structural inertial force similarity constant is equal to the seismic hydraulic similarity constant, then the structural density similarity constant S ρ =1.0.

[0024] In step five, the constraint condition is that the structural inertial force similarity constant and the elastic force similarity constant are equal, based on the geometric similarity constant S obtained in step one. l The acceleration similarity constant S obtained in step three a The structural density similarity constant S obtained in step four ρ The similarity constant S for the flexural stiffness of the rectangular section of the reinforced concrete bridge pier was determined. EI The method is:

[0025] Assuming the similarity constants for structural inertial forces and elastic forces are equal, then the similarity constant S for the flexural stiffness of the rectangular section of a reinforced concrete bridge pier is... EI The expression is:

[0026] .

[0027] In step six, the wall thickness t of the scaled-down pier with the hollow structure m Solve using the following equation:

[0028] ;

[0029] In the formula, B is the side length of the rectangular section of the prototype pier that is aligned with the direction of the seismic action, and H is the side length of the rectangular section of the prototype pier that is orthogonal to side length B.

[0030] In step seven, the wall thickness t of the scaled-down pier with a hollow structure obtained in step six is... m The geometric similarity constant S obtained in step one l Based on the rectangular cross-sectional dimensions of the prototype bridge pier and the density ρ of the concrete, the weight M per unit height of the pier is determined and converted into a mass block of the same weight, either iron or lead. These mass blocks are then evenly distributed along the scaled-down pier height to ensure that the structural density similarity constant S obtained in step four is consistent with this. ρ The method to keep it unchanged is:

[0031] The formula for calculating the weight of the bridge pier per unit height is as follows:

[0032] ;

[0033] Then, the weight M of the pier per unit height is converted into mass blocks of the same weight, including iron or lead blocks, and these mass blocks are evenly distributed along the scaled-down pier height to ensure that the structural density similarity constant S obtained in step four is consistent with the structural density similarity constant S. ρ It remains unchanged.

[0034] In step eight, the formula for calculating the similarity constant of the longitudinal reinforcement area of ​​the scaled-down pier is as follows: The formula for calculating the similarity constant of the stirrup area is: .

[0035] In step nine, based on the concrete shear strength and stirrup shear strength of the reinforced concrete section, the shear strength reduction caused by hollowing out the concrete section is compensated by increasing the stirrup cross-section, and a stirrup area similarity constant is established. The correction factor β is finally used to adjust the stirrup area similarity constant obtained in step eight. Make corrections to obtain the corrected stirrup area similarity constants. And the similarity constant of the longitudinal reinforcement area of ​​the scaled-down pier obtained in step eight. The method of combining them as the final design result is:

[0036] The similarity constant of the stirrup area The formula for calculating the correction factor β is:

[0037] ;

[0038] In the formula, f t s is the tensile strength of concrete, s is the spacing of the reduced-size pier stirrups, and A is the tensile strength of concrete. c The cross-sectional area of ​​the hollow section is expressed as follows: f yv For the stirrup yield strength, h = HS l A sv The area of ​​the pier stirrups is the scaled-down cross-sectional area calculated before correction; then the similarity constant of the stirrup area after correction is... The calculation formula is:

[0039] ;

[0040] Based on the modified stirrup area similarity constant Similarity constant of longitudinal reinforcement area to the scaled-down pier obtained in step eight Together they form the final design result.

[0041] The advantages and positive effects of this invention are as follows: In underwater shaking table tests, the density similarity constants of water and structure must be kept consistent to ensure the similarity of water-structure interaction, which leads to high complexity in model similarity design. Considering the plastic behavior of the structure under seismic loading further increases the difficulty of similarity design of reinforced concrete rectangular bridge pier models. By using the scaled-down model in the test design of this invention, and by changing the rectangular cross-section to a hollow cross-section and modifying the cross-sectional area of ​​the stirrups, similarity design of the plastic behavior of the reinforced concrete rectangular bridge pier under seismic loading is achieved. Moreover, the scaled-down model has high accuracy in restoring the seismic response of the prototype structure. This method can provide a feasible approach for similarity design of reinforced concrete rectangular bridge pier models in underwater shaking table tests. Attached Figure Description

[0042] Figure 1 (a) is a front view of the reinforced concrete prototype bridge pier used in this invention; Figure 1 (b) is Figure 1 (a) Sectional view along line 1-1;

[0043] Figure 2 A comparison diagram of the displacement of the top of the bridge pier under seismic loading between the scaled-down model designed using the method of this invention and the prototype bridge pier.

[0044] Figure 3 A comparison diagram of the bending moment at the bottom of the bridge pier under seismic loading between the scaled-down model and the prototype bridge pier designed using the method of this invention.

[0045] Figure 4 This is a comparison diagram of the scaled-down model and the prototype bridge pier under seismic loading, designed using the method of this invention.

[0046] Figure 5 A comparison diagram of the dynamic water pressure at the center of the bridge pier under seismic loading between the scaled-down model designed using the method of this invention and the prototype bridge pier. Detailed Implementation

[0047] To further understand the invention's content, features, and effects, the following embodiments are provided, and detailed descriptions are given below in conjunction with the accompanying drawings:

[0048] The underwater shaking table test model similarity design method for reinforced concrete rectangular bridge piers provided by this invention includes the following steps performed in sequence:

[0049] Step 1: Determine the geometric similarity constant S based on the maximum effective load of the underwater shaking table test equipment, the maximum water depth of the pool, and the dimensions and weight of the prototype bridge pier. l ;

[0050] The geometric similarity constant S l =Scaled-down bridge pier structural dimensions / Prototype bridge pier structural dimensions, determined by the following method:

[0051] According to the geometric similarity constant S l The weight of the scaled-down bridge pier must not exceed the maximum effective load that the underwater shaking table test equipment can withstand, and must be determined according to the geometric similarity constant S. l The water depth after scaling down must not exceed the maximum water depth of the pool.

[0052] Step Two: Select the same reinforced concrete material as the prototype pier as the structural material of the scaled-down pier, and select a material with the same water physical properties as the prototype as the water material for the scaled-down model test, thereby determining the elastic modulus similarity constant S of the scaled-down pier. E longitudinal reinforcement strength similarity constant S fy Stirrup strength similarity constant S fyv and the water density similarity constant S ρw ;

[0053] The elastic modulus similarity constant S E = Elastic modulus of scaled-down pier / Elastic modulus of prototype pier, water density similarity constant S ρw =Water density in the scaled-down test / Water density in the prototype; Since the scaled-down bridge pier uses the same material as the prototype bridge pier and water, the elastic modulus similarity constant S E =1, longitudinal reinforcement strength similarity constant S fy =1, Stirrup strength similarity constant S fyv =1, water density similarity constant S ρw =1.

[0054] Step 3: Determine the acceleration similarity constant S of the scaled-down bridge pier according to Froude's criterion. a ;

[0055] According to Froude's criterion, the acceleration similarity constant S of the scaled-down bridge pier is... a The expression is:

[0056] ;

[0057] In the formula, S g is the gravitational acceleration similarity constant, with a value of 1.0.

[0058] Step 4: Using the equality of the structural inertial force similarity constant and the seismic hydraulic similarity constant as a constraint, determine the structural density similarity constant S. ρ ;

[0059] Assuming the structural inertial force similarity constant is equal to the seismic hydraulic similarity constant, then the structural density similarity constant S ρ =1.0.

[0060] Step 5: Using the equality of the structural inertial force similarity constant and the elastic force similarity constant as a constraint, based on the geometric similarity constant S obtained in Step 1... l The acceleration similarity constant S obtained in step three a The structural density similarity constant S obtained in step four ρ The similarity constant S for the flexural stiffness of the rectangular section of the reinforced concrete bridge pier was determined. EI ;

[0061] Assuming the similarity constants for structural inertial forces and elastic forces are equal, then the similarity constant S for the flexural stiffness of the rectangular section of a reinforced concrete bridge pier is... EI The expression is:

[0062] ;

[0063] Step Six: Based on the similarity constant S of the flexural stiffness of the rectangular section of the reinforced concrete bridge pier obtained in Step Five. EI The geometric similarity constant S obtained in step one l In addition to the rectangular cross-sectional dimensions of the prototype bridge pier, the rectangular cross-section was hollowed out to form a hollow cross-section, and the wall thickness t of the scaled-down bridge pier with the hollow structure was determined. m ;

[0064] The wall thickness t of the scaled-down bridge pier with a hollow structure m Solve using the following equation:

[0065] ;

[0066] In the formula, B is the side length of the rectangular section of the prototype pier that is aligned with the direction of the seismic action, and H is the side length of the rectangular section of the prototype pier that is orthogonal to side length B.

[0067] Step 7: Determine the wall thickness t of the scaled-down pier with a hollow structure based on the information obtained in Step 6. m The geometric similarity constant S obtained in step one l Based on the rectangular cross-sectional dimensions of the prototype bridge pier and the density ρ of the concrete, the weight M per unit height of the pier is determined and converted into a mass block of the same weight, either iron or lead. These mass blocks are then evenly distributed along the scaled-down pier height to ensure that the structural density similarity constant S obtained in step four is consistent with this. ρ Remain unchanged;

[0068] The formula for calculating the weight of the bridge pier per unit height is as follows:

[0069] ;

[0070] Then, the weight M of the pier per unit height is converted into mass blocks of the same weight, including iron or lead blocks. These mass blocks are then evenly distributed along the scaled-down pier height. During distribution, the mass blocks and the scaled-down pier must be reliably and completely fixed to ensure that the structural density similarity constant S obtained in step four is maintained. ρ It remains unchanged.

[0071] Step 8: Using the principle of dimensional consistency, based on the geometric similarity constant S obtained in Step 1... l Step 2 obtains the longitudinal reinforcement strength similarity constant S. fy Similarity constant S to the strength of stirrups fyv Step 3 obtains the acceleration similarity constant S a and the structural density similarity constant S obtained in step four ρ The similarity constant of the longitudinal reinforcement area of ​​the scaled-down bridge pier was determined. Similarity constant of stirrup area ;

[0072] The formula for calculating the similarity constant of the longitudinal reinforcement area of ​​the scaled-down pier is as follows: The formula for calculating the similarity constant of the stirrup area is: .

[0073] Step Nine: Based on the shear strength of the reinforced concrete section and the shear strength of the stirrups, the stirrup section is increased to compensate for the decrease in shear strength caused by hollowing out the concrete section, and a stirrup area similarity constant is established. The correction factor β is finally used to adjust the stirrup area similarity constant obtained in step eight. Make corrections to obtain the corrected stirrup area similarity constants. And the similarity constant of the longitudinal reinforcement area of ​​the scaled-down pier obtained in step eight. Together they form the final design result.

[0074] The similarity constant of the stirrup area The formula for calculating the correction factor β is:

[0075] ;

[0076] In the formula, f t s is the tensile strength of concrete, s is the spacing of the reduced-size pier stirrups, and A is the tensile strength of concrete. c The cross-sectional area of ​​the hollow section is expressed as follows: f yv For the stirrup yield strength, h = HS l A sv The area of ​​the pier stirrups is the scaled-down cross-sectional area calculated before correction; then the similarity constant of the stirrup area after correction is... The calculation formula is:

[0077] ;

[0078] Based on the modified stirrup area similarity constant Similarity constant of longitudinal reinforcement area to the scaled-down pier obtained in step eight Together they form the final design result.

[0079] This invention achieves a similar design for the plastic behavior of reinforced concrete rectangular bridge piers under seismic loading by changing the rectangular cross-section of the reinforced concrete rectangular bridge pier to a hollow cross-section and modifying the cross-sectional area of ​​the stirrups. This enables the accurate reproduction of the dynamic response of the prototype reinforced concrete rectangular bridge pier structure under seismic loading.

[0080] The advantages of this invention will be illustrated below through an application example.

[0081] In this embodiment, the maximum water depth of the selected pool is 2.0m, and the maximum load capacity of the underwater vibration table test equipment is 26t. Please refer to [link / reference]. Figure 1 The prototype bridge pier 1 is made of reinforced concrete with a density of 2500 kg / m³. 3 The elastic modulus is 26.3 GPa, the concrete strength grade is C30, the longitudinal reinforcement is HRB400, and the stirrups are HPB300. The prototype pier 1 has a height of 4000 mm, a rectangular cross-section with a length of 1000 mm and a width of 400 mm, and 18 longitudinal reinforcement bars with a diameter of 20 mm are arranged within the cross-section. Stirrups 3 are arranged along the height of prototype pier 1 at 100 mm intervals and have a diameter of 6 mm. The load transmitted from the main beam to the top of prototype pier 1 is equivalent to a mass of 175 t. The water depth where the prototype pier is located is 3.6 m, and the direction of the seismic action is the same as the 400 mm width direction of the rectangular cross-section.

[0082] In this embodiment, the geometric similarity constant S of the scaled-down pier is... l =1 / 2, and its material selection is the same as that of the prototype pier 1. Therefore, the elastic modulus similarity constant S of the scaled-down pier is... E =1, longitudinal reinforcement strength similarity constant S fy =1, Stirrup strength similarity constant S fyv =1, water density similarity constant S ρw =1; Determine the acceleration similarity constant S according to the Froude criterion. a =1; using the equality of the structural inertial force similarity constant and the seismic hydraulic similarity constant as a constraint, the structural density similarity constant S is determined. ρ =1; therefore, the similarity constant S for the flexural stiffness of the rectangular section of the reinforced concrete bridge pier can be obtained. EI =1 / 32, wall thickness t of the hollow section m=19mm. Therefore, the weight per unit height (M) of the longitudinal reinforcement pier is determined to be 188.5kg. Using the principle of dimensional compatibility, the similarity constant of the longitudinal reinforcement area is determined. =1 / 8, similarity constant for stirrup area =1 / 8. Finally, the similarity constant of the stirrup area is obtained. The correction factor β = 11.8 was used to determine the similarity constant of the stirrup area after correction. =1.478.

[0083] A scaled-down pier of the prototype pier 1 was designed using the method of this invention. The dynamic time-history response of both the prototype pier 1 and the scaled-down pier designed using this invention under an El-Centro earthquake with a peak acceleration of 0.6g was numerically calculated using finite element analysis software. The numerical calculation results of the top displacement, bottom bending moment, bottom shear force, and mid-section hydrodynamic pressure of the scaled-down pier were extracted. Then, the seismic response results of the scaled-down pier designed using this invention were back-calculated using the corresponding similarity constants to obtain the seismic response results of the prototype pier 1, which were then compared with the seismic response results of the prototype pier 1 obtained through direct numerical calculation.

[0084] Please see Figure 2 Under the El-Centro earthquake, the maximum displacement of the top of the prototype pier 1 was 0.260m, while the maximum displacement of the top of the scaled-down pier designed using the method of this invention was 0.276m, with a relative error of 6.2%.

[0085] Please see Figure 3 Under the El-Centro earthquake, the maximum bending moment at the bottom of the prototype pier 1 was 0.850 MN·m, while the maximum bending moment at the bottom of the scaled-down pier designed using the method of this invention was 0.821 MN·m, with a relative error of 3.4%.

[0086] Please see Figure 4 Under the El-Centro earthquake, the maximum shear force at the bottom of the prototype pier 1 was 0.162MN, while the maximum shear force at the bottom of the scaled-down pier designed using the method of this invention was 0.157MN, with a relative error of 2.9%.

[0087] Please see Figure 5 Under the El-Centro earthquake, the maximum dynamic water pressure in the middle of the prototype pier 1 was 3.320 kPa, while the maximum dynamic water pressure in the middle of the scaled-down pier designed using the method of this invention was 3.248 kPa, with a relative error of 2.2%.

[0088] In summary, the relative errors of the responses of the scaled-down bridge piers designed using the method of this invention under El-Centro earthquake loading are between 2.2% and 6.2%, indicating that the underwater shaking table test of the scaled-down reinforced concrete bridge piers designed using the method of this invention accurately reproduces the dynamic response of the prototype bridge piers.

[0089] Although preferred embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other modifications under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these modifications are within the scope of protection of the present invention.

Claims

1. A similarity design method for an underwater shaking table test model of a reinforced concrete rectangular bridge pier, characterized in that: The similarity design method for the underwater shaking table test model of the reinforced concrete rectangular bridge pier includes the following steps performed in sequence: Step 1: Determine the geometric similarity constant S based on the maximum effective load of the underwater shaking table test equipment, the maximum water depth of the pool, and the dimensions and weight of the prototype bridge pier. l ; Step Two: Select the same reinforced concrete material as the prototype pier as the structural material of the scaled-down pier, and select a material with the same water physical properties as the prototype as the water material for the scaled-down model test, thereby determining the elastic modulus similarity constant S of the scaled-down pier. E longitudinal reinforcement strength similarity constant S fy Stirrup strength similarity constant S fyv and the water density similarity constant S ρw ; Step 3: Determine the acceleration similarity constant S of the scaled-down bridge pier according to Froude's criterion. a ; Step 4: Using the equality of the structural inertial force similarity constant and the seismic hydraulic similarity constant as a constraint, determine the structural density similarity constant S. ρ ; Step 5: Using the equality of the structural inertial force similarity constant and the elastic force similarity constant as a constraint, based on the geometric similarity constant S obtained in Step 1... l The acceleration similarity constant S obtained in step three a The structural density similarity constant S obtained in step four ρ The similarity constant S for the flexural stiffness of the rectangular section of the reinforced concrete bridge pier was determined. EI ; Step Six: Based on the similarity constant S of the flexural stiffness of the rectangular section of the reinforced concrete bridge pier obtained in Step Five. EI The geometric similarity constant S obtained in step one l In addition to the rectangular cross-sectional dimensions of the prototype bridge pier, the rectangular cross-section was hollowed out to form a hollow cross-section, and the wall thickness t of the scaled-down bridge pier with the hollow structure was determined. m ; Step 7: Determine the wall thickness t of the scaled-down pier with a hollow structure based on the information obtained in Step 6. m The geometric similarity constant S obtained in step one l Based on the rectangular cross-sectional dimensions of the prototype bridge pier and the density ρ of the concrete, the weight M per unit height of the pier is determined and converted into a mass block of the same weight, either iron or lead. These mass blocks are then evenly distributed along the scaled-down pier height to ensure that the structural density similarity constant S obtained in step four is consistent with this. ρ Remain unchanged; Step 8: Using the principle of dimensional consistency, based on the geometric similarity constant S obtained in Step 1... l Step 2 obtains the longitudinal reinforcement strength similarity constant S. fy Similarity constant S to the strength of stirrups fyv Step 3 obtains the acceleration similarity constant S a and the structural density similarity constant S obtained in step four ρ The similarity constant of the longitudinal reinforcement area of ​​the scaled-down bridge pier was determined. Similarity constant of stirrup area ; Step Nine: Based on the shear strength of the reinforced concrete section and the shear strength of the stirrups, the stirrup section is increased to compensate for the decrease in shear strength caused by hollowing out the concrete section, and a stirrup area similarity constant is established. The correction factor β is finally used to adjust the stirrup area similarity constant obtained in step eight. Make corrections to obtain the corrected stirrup area similarity constants. And the similarity constant of the longitudinal reinforcement area of ​​the scaled-down pier obtained in step eight. Together they form the final design result.

2. The similarity design method for underwater shaking table test model of reinforced concrete rectangular bridge piers according to claim 1, characterized in that: In step one, the geometric similarity constant S l =Scaled-down bridge pier structural dimensions / Prototype bridge pier structural dimensions, determined by the following method: According to the geometric similarity constant S l The weight of the scaled-down bridge pier must not exceed the maximum effective load that the underwater shaking table test equipment can withstand, and must be determined according to the geometric similarity constant S. l The water depth after scaling down must not exceed the maximum water depth of the pool.

3. The similarity design method for underwater shaking table test model of reinforced concrete rectangular bridge piers according to claim 1, characterized in that: In step two, the elastic modulus similarity constant S E = Elastic modulus of scaled-down pier / Elastic modulus of prototype pier, water density similarity constant S ρw =Water density in the scaled-down test / Water density in the prototype; Since the scaled-down bridge pier uses the same material as the prototype bridge pier and water, the elastic modulus similarity constant S E =1, longitudinal reinforcement strength similarity constant S fy =1, Stirrup strength similarity constant S fyv =1, water density similarity constant S ρw =1.

4. The similarity design method for underwater shaking table test model of reinforced concrete rectangular bridge piers according to claim 1, characterized in that: In step three, the acceleration similarity constant S of the scaled-down bridge pier is determined according to Froude's criterion. a The method is: According to Froude's criterion, the acceleration similarity constant S of the scaled-down bridge pier is... a The expression is: ； In the formula, S g is the gravitational acceleration similarity constant, with a value of 1.

0.

5. The similarity design method for underwater shaking table test model of reinforced concrete rectangular bridge piers according to claim 1, characterized in that: In step four, the structural density similarity constant S is determined by using the equality of the structural inertial force similarity constant and the seismic hydraulic similarity constant as a constraint. ρ The method is: Assuming the structural inertial force similarity constant is equal to the seismic hydraulic similarity constant, then the structural density similarity constant S ρ =1.

0.

6. The similarity design method for underwater shaking table test model of reinforced concrete rectangular bridge piers according to claim 1, characterized in that: In step five, the constraint condition is that the structural inertial force similarity constant and the elastic force similarity constant are equal, based on the geometric similarity constant S obtained in step one. l The acceleration similarity constant S obtained in step three a The structural density similarity constant S obtained in step four ρ The similarity constant S for the flexural stiffness of the rectangular section of the reinforced concrete bridge pier was determined. EI The method is: Assuming the similarity constants for structural inertial forces and elastic forces are equal, then the similarity constant S for the flexural stiffness of the rectangular section of a reinforced concrete bridge pier is... EI The expression is: 。 7. The similarity design method for underwater shaking table test model of reinforced concrete rectangular bridge piers according to claim 1, characterized in that: In step six, the wall thickness t of the scaled-down pier with the hollow structure m Solve using the following equation: ； In the formula, B is the side length of the rectangular section of the prototype pier that is aligned with the direction of the seismic action, and H is the side length of the rectangular section of the prototype pier that is orthogonal to side length B.

8. The similarity design method for underwater shaking table test model of reinforced concrete rectangular bridge piers according to claim 1, characterized in that: In step seven, the wall thickness t of the scaled-down pier with a hollow structure obtained in step six is... m The geometric similarity constant S obtained in step one l Based on the rectangular cross-sectional dimensions of the prototype bridge pier and the density ρ of the concrete, the weight M per unit height of the pier is determined and converted into a mass block of the same weight, either iron or lead. These mass blocks are then evenly distributed along the scaled-down pier height to ensure that the structural density similarity constant S obtained in step four is consistent with this. ρ The method to keep it unchanged is: The formula for calculating the weight of the bridge pier per unit height is as follows: ； Then, the weight M of the pier per unit height is converted into mass blocks of the same weight, including iron or lead blocks, and these mass blocks are evenly distributed along the scaled-down pier height to ensure that the structural density similarity constant S obtained in step four is consistent with the structural density similarity constant S. ρ It remains unchanged.

9. The similarity design method for underwater shaking table test model of reinforced concrete rectangular bridge piers according to claim 1, characterized in that: In step eight, the formula for calculating the similarity constant of the longitudinal reinforcement area of ​​the scaled-down pier is as follows: The formula for calculating the similarity constant of the stirrup area is: .

10. The similarity design method for underwater shaking table test model of reinforced concrete rectangular bridge piers according to claim 1, characterized in that: In step nine, based on the concrete shear strength and stirrup shear strength of the reinforced concrete section, the shear strength reduction caused by hollowing out the concrete section is compensated by increasing the stirrup cross-section, and a stirrup area similarity constant is established. The correction factor β is finally used to adjust the stirrup area similarity constant obtained in step eight. Make corrections to obtain the corrected stirrup area similarity constants. And the similarity constant of the longitudinal reinforcement area of ​​the scaled-down pier obtained in step eight. The method of combining them as the final design result is: The similarity constant of the stirrup area The formula for calculating the correction factor β is: ； In the formula, f t s is the tensile strength of concrete, s is the spacing of the reduced-size pier stirrups, and A is the tensile strength of concrete. c The cross-sectional area of ​​the hollow section is expressed as follows: f yv For the stirrup yield strength, h = HS l A sv The area of ​​the pier stirrups is the scaled-down cross-sectional area calculated before correction; then the similarity constant of the stirrup area after correction is... The calculation formula is: ； Based on the modified stirrup area similarity constant Similarity constant of longitudinal reinforcement area to the scaled-down pier obtained in step eight Together they form the final design result.

Images