Evaluation method of residual drift ratio of unbonded prestressed reinforced concrete bridge piers

Abstract

The present invention relates to the technical field of pier deformation, and specifically to a method for evaluating the residual drift ratio of an unbonded prestressed reinforced concrete pier, comprising the following evaluation steps: firstly, a finite element model of the pier is established based on various parameters of the pier; then, the residual drift ratio of the pier is obtained by simulating the finite element model; then, a corresponding functional relationship between various parameters of the pier and the residual drift ratio is constructed; finally, a residual drift ratio prediction model is established according to various functional relationships, and the residual drift ratio generated by the pier in an earthquake is calculated by the residual drift ratio prediction model; the present invention can accurately calculate the residual drift ratio of the pier.

Description

Technical Field

[0001] The invention relates to the technical field of bridge pier deformation, and in particular to a residual drift ratio evaluation method for unbonded prestressed reinforced concrete bridge piers. Background Art

[0002] Bridge piers located in areas of high seismic activity are generally required to have greater ductility, allowing the piers to undergo larger displacements during earthquakes to extend the structural period and dissipate seismic energy to prevent the bridge from collapsing during an earthquake; however, bridge piers with high ductility requirements often retain larger permanent displacements; due to the existence of excessively large residual drift ratios, although some bridges do not collapse during an earthquake, they lose their normal performance after the earthquake and have to be demolished.

[0003] Unbonded Prestressed Reinforced Concrete (UBRC) piers are self-centering piers. Since they are equipped with vertical unbonded prestressed steel bars as self-resetting components, they can effectively reduce the residual drift ratio of the piers. In the seismic resistance of bridge structures, unbonded prestressed concrete piers have gradually received more and more attention. However, the residual drift ratio of UBPRC piers after an earthquake still requires a fast quantitative calculation method, which needs to be solved urgently. Summary of the invention

[0004] In order to avoid and overcome the technical problems existing in the prior art, the present invention provides a method for evaluating the residual drift ratio of unbonded prestressed reinforced concrete bridge piers. The present invention can accurately calculate the residual drift ratio of the bridge piers.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The residual drift ratio evaluation method of unbonded prestressed reinforced concrete bridge piers includes the following evaluation steps:

[0007] S1. Establish a finite element model of the pier based on various parameters of the pier;

[0008] S2. Obtaining the residual drift ratio of the bridge pier by simulating the finite element model;

[0009] S3, constructing the corresponding functional relationship between various parameters of the bridge pier and the residual drift ratio;

[0010] S4. A residual drift ratio prediction model is established based on various functional relationships, and the residual drift ratio generated by the bridge pier during an earthquake is calculated using the residual drift ratio prediction model.

[0011] As a further technical solution: the residual drift ratio prediction model is expressed as follows:

[0012] RDr =e W

[0013] W=β 0 +β 1 ln(A r )+β 2 ln(α c )+β 3 ln(ρ l )

[0014] +β 4 ln(ρ s )+β 5 ln(f c )+β 6 ln(f y )

[0015] +β 7 ln(ρ p )+β 8 ln(α ps )+β 9 ln(D r )

[0016] Among them, RD r represents the residual drift ratio; e represents the Napier constant; W represents the exponent of e; β 0 , β 1 , …, β 9 Respectively represent the unknown coefficients corresponding to each parameter; ln represents the logarithmic function; A r Indicates the slenderness ratio of the pier; α c represents the axial compression ratio of the pier; ρ l represents the longitudinal reinforcement ratio of the pier; ρ s Indicates the stirrup reinforcement ratio of the pier; f c Indicates the compressive strength of the pier concrete; f y represents the yield strength of the longitudinal reinforcement of the pier; ρ p represents the reinforcement ratio of prestressed steel bars in bridge piers; α ps Indicates the prestress of the pier; D r Represents the drift ratio of the bridge pier.

[0017] As a further technical solution: the specific steps of step S1 are as follows:

[0018] S11. Setting the values ​​of various parameters of the bridge pier, including the height of the bridge pier, slenderness ratio, axial compression ratio, longitudinal reinforcement ratio, stirrup reinforcement ratio, compressive strength of concrete, yield strength of longitudinal reinforcement, prestressed reinforcement ratio, and prestressing strength of the bridge pier;

[0019] S12, according to the set height, slenderness ratio and axial compression ratio of the bridge pier, the nonlinear beam-column unit in the OpenSees finite element analysis software is used to simulate the main body of the bridge pier;

[0020] S13, according to the set longitudinal reinforcement ratio of the bridge pier, stirrup reinforcement ratio, compressive strength of concrete, yield strength of the longitudinal reinforcement and prestressed reinforcement ratio, the truss unit in the OpenSees finite element analysis software is used to simulate the unbonded prestressed steel bars in the bridge pier;

[0021] S14. According to the set prestress of the bridge pier, the zero-length unit in the OpenSees finite element analysis software is used to simulate the bond slip of the steel bars in the bridge pier, thereby forming a complete finite element model of the bridge pier.

[0022] 4. The residual drift ratio evaluation method of unbonded prestressed reinforced concrete bridge pier according to claim 3 is characterized in that the specific contents of step S2 are as follows:

[0023] S21, inputting the values ​​of the set parameters and the prestress representing the earthquake intensity applied along the axial direction of the bridge pier into the finite element model, and obtaining the quasi-static residual drift ratio corresponding to the bridge pier through simulation;

[0024] S22. Using the quasi-static residual drift ratio as the residual drift ratio.

[0025] As a further technical solution: the functional relationship between each parameter and the residual drift ratio is expressed as follows:

[0026] Residual drift ratio RD r Slenderness ratio A to the pier r The functional relationship between them is:

[0027]

[0028] Among them, μ 1 Indicates A r The exponent of 1 represents the exponent of e;

[0029] Residual drift ratio RD r Axial compression ratio α to the pier c The functional relationship between them is:

[0030]

[0031] Among them, μ 2 Represents α c The exponent of 2 represents the exponent of e;

[0032] Residual drift ratio RD rThe longitudinal reinforcement ratio of the pier is ρ r The functional relationship between them is:

[0033]

[0034] Among them, μ 3 Represents ρ r The exponent of 3 represents the exponent of e;

[0035] Residual drift ratio RD r Stirrup reinforcement ratio ρ s The functional relationship between them is:

[0036]

[0037] Among them, μ 4 Represents ρ s The exponent of 4 represents the exponent of e;

[0038] Residual drift ratio RD r The compressive strength of the pier concrete c The functional relationship between them is:

[0039]

[0040] Among them, μ 5 represents f c The exponent of 5 represents the exponent of e;

[0041] Residual drift ratio RD r The yield strength f of the longitudinal reinforcement of the pier y The functional relationship between them is:

[0042]

[0043] Among them, μ 6 represents f y The exponent of 6 represents the exponent of e;

[0044] Residual drift ratio RD r The reinforcement ratio of the prestressed steel bars of the piers p The functional relationship between them is:

[0045]

[0046] Among them, μ 7 Represents ρ p The exponent of 7 represents the exponent of e;

[0047] Residual drift ratio RDr The prestress of the bridge pier α ps The functional relationship between them is:

[0048]

[0049] Among them, μ 8 Represents α ps The exponent of 8 represents the exponent of e;

[0050] Residual drift ratio RD r Drift ratio to bridge pier D r The functional relationship between them is:

[0051]

[0052] Among them, μ 9 Indicates D r The exponent of 9 Represents the exponent of e; e in all the above calculation formulas is Napier's constant.

[0053] As a further technical solution: the specific content of step S4 is as follows:

[0054] First, according to the residual drift ratio RD r The functional relationship between the various parameters of the bridge pier is constructed by logarithmic transformation to obtain the residual drift ratio RD. r The joint function relationship between the various parameters of the bridge pier is expressed as follows:

[0055] ln(RD r )=β 0 +β 1 ln(A r )+β 2 ln(α c )+β 3 ln(ρ l )

[0056] +β 4 ln(ρ s )+β 5 ln(f c )+β 6 ln(f y )

[0057] +β 7 ln(ρ p )+β 8 ln(α ps )+β 9 ln(D r )

[0058] Then the corresponding residual drift ratio prediction model is obtained through secondary logarithmic transformation.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] 1. The present invention quantifies the drift ratio and residual drift ratio of the UBPRC pier from the hysteresis curve, takes the drift ratio as a parameter to construct a residual drift ratio prediction model, and constructs a residual drift ratio prediction model, which can quickly and accurately evaluate the residual drift ratio of unbonded prestressed reinforced concrete piers under different parameters such as height, cross-sectional size, reinforcement ratio, and steel and concrete strength. At the same time, the corresponding residual drift ratio target can be achieved by changing the parameter value, which can be applied to the preliminary design of unbonded prestressed reinforced concrete piers. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a diagram of the main evaluation steps of the present invention.

[0062] Figure 2 It is the finite element model of the bridge pier in the present invention.

[0063] Figure 3 It is the maximum displacement diagram in the present invention.

[0064] Figure 4 It is the displacement map in the present invention.

[0065] Figure 5 This is a comparison chart between the predicted value and the true value in the present invention.

[0066] Figure 6 This is a distribution diagram of predicted values ​​in the present invention.

[0067] Figure 7 This is a distribution diagram of predicted values ​​of an embodiment of the present invention. DETAILED DESCRIPTION

[0068] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0069] See also Figure 1 to Figure 7 In an embodiment of the present invention, a residual drift ratio evaluation method for unbonded prestressed reinforced concrete bridge piers includes the following contents:

[0070] 1. Establishment of the finite element model of UBPRC bridge pier

[0071] like Figure 2As shown in the figure, the finite element model of the UBPRC bridge pier is established in the OpenSees finite element analysis software. The main body of the bridge pier is modeled by nonlinear beam-column elements; the unbonded prestressed steel bars are simulated by truss elements; and zero-length elements are used to simulate the bond-slip of the steel bars.

[0072] The height of the pier is H, the cross section is a square with a side length of D, and the slenderness ratio of the pier is A. r =H / D. The axial pressure ratio is α c The bridge piers are simulated using nonlinear beam-column elements, and the length of the element is 6 times the length of the plastic hinge. In the discretized section, both the cover concrete and the core concrete are modeled using the Kent-Scott-Park model, and the compressive strength of the concrete is f c The reinforcement ratio of the longitudinal reinforcement is ρ l and the yield strength of the longitudinal reinforcement is f y , Steel02 constitutive model is used for modeling. The stirrup reinforcement ratio is ρ s The prestressed steel truss unit in the pier is modeled, which connects the bottom and top nodes and runs through the entire UBPRC pier. The prestressed steel reinforcement ratio is ρ p , the Steel02 constitutive model is also used for modeling, and the magnitude of the prestress is determined by the prestress ratio α ps The zero-length element in the finite element model simulates the bond-slip effect of the longitudinal reinforcement, and the longitudinal reinforcement uses the Bond_SP01 constitutive model. The prestressed reinforcement ratio (p) and prestress (αps) are two parameters related to the prestressed reinforcement. The specific values ​​of the parameters in the UBPRC pier model are shown in Table 1.

[0073] Table 1 Value ranges of UBPRC pier structure and material parameters

[0074]

[0075] 2. Extraction of residual drift ratio

[0076] Since the hysteresis curve of the UBPRC pier is flag-shaped and shows an obvious pinching effect, this application uses the quasi-static residual drift ratio as the residual drift ratio of the UBPRC pier. r is the ratio of displacement to pier height. Figure 3 As shown, Figure 3 The abscissa represents the displacement of the top of the pier. Figure 3 The ordinate in represents the lateral force applied to the top of the pier. The hysteresis curve of the UBPRC pier is plotted to the maximum displacement, and the corresponding residual drift ratio is called the maximum residual drift ratio MRD. rThe maximum displacement is assumed to occur when the core concrete of the specimen reaches its maximum strain. In each hysteresis curve, there is a maximum drift ratio MD r and its corresponding maximum residual drift ratio MRD r ,like Figure 4 For each pier, starting from the first hysteresis until the maximum displacement is reached, 5 drift ratios D are selected with uniform steps. r , and get 5 corresponding residual drift ratios RD r .

[0077] 3. Relationship between various parameters and residual drift ratio

[0078] The finite element model of the UBPRC pier was established according to the parameter range specified in Table 1, and the drift ratio D r and the corresponding residual drift ratio RD r Each parameter has a significant impact on RD r The influence is expressed as the following formula, where the index is shown in Table 2:

[0079] Table 2 Index values

[0080]

[0081] Residual drift ratio RD r Slenderness ratio A to the pier r The functional relationship between them is:

[0082] RD r =A r 0.64 / e 6.92

[0083] Residual drift ratio RD r Axial compression ratio α to the pier c The functional relationship between them is:

[0084] RD r =α r -0.51 / e 6.8

[0085] Residual drift ratio RD r The longitudinal reinforcement ratio of the pier is ρ r The functional relationship between them is:

[0086] RD r =ρ r 1.49 ·e 0.47

[0087] Residual drift ratio RD r Stirrup reinforcement ratio ρ sThe functional relationship between them is:

[0088] RD r =ρ s 0.78 / e 2.54

[0089] Residual drift ratio RD r The compressive strength of the pier concrete c The functional relationship between them is:

[0090] RD r =f c -1.70 ·e 0.39

[0091] Residual drift ratio RD r The yield strength f of the longitudinal reinforcement of the pier y The functional relationship between them is:

[0092] RD r =f y 0.3 / e 7.49

[0093] Residual drift ratio RD r The reinforcement ratio of the prestressed steel bars of the piers p The functional relationship between them is:

[0094] RD r =ρ p -0.09 / e 6.13

[0095] Residual drift ratio RD r The prestress of the bridge pier α ps The functional relationship between them is:

[0096] RD r =α ps -0.29 / e 6.59

[0097] Residual drift ratio RD r Drift ratio to bridge pier D r The functional relationship between them is:

[0098] RD r =D r 1.95 ·e 1.49

[0099] 4. Establishment of residual drift ratio prediction model

[0100] In logarithmic space, the residual drift ratio RD can be expressed using the following formula: rJoint functional relationship with various parameters of bridge piers.

[0101] ln(RD r )=β 0 +β 1 ln(A r )+β 2 ln(α c )+β 3 ln(ρ l )

[0102] +β 4 ln(ρ s )+β 5 ln(f c )+β 6 ln(f y )

[0103] +β 7 ln(ρ p )+β 8 ln(α ps )+β 9 ln(D r )

[0104] When establishing the residual drift ratio model, the logarithmic linear relationship between these parameters and the residual drift ratio is considered, and the residual drift ratio is predicted using the following formula.

[0105] RD r =e W

[0106] W=β 0 +β 1 ln(A r )+β 2 ln(α c )+β 3 ln(ρ l )

[0107] +β 4 ln(ρ s )+β 5 ln(f c )+β 6 ln(f y )

[0108] +β 7 ln(ρ p )+β 8 ln(α ps )+β 9 ln(D r )

[0109] The above formula is used to fit the residual drift ratio of the UBPRC pier, and the values ​​of the various unknown coefficients are shown in Table 3.

[0110] Table 3 Undetermined coefficient values

[0111]

[0112]

[0113] Substituting the data in Table 3 into the residual drift ratio prediction model, the residual drift ratio of the UBPRC pier calculated by the residual drift ratio prediction model is compared with the residual drift ratio quantified by the hysteresis curve. The comparison results are shown in Figure 5 The prediction effect of the residual drift ratio prediction model is shown in Figure 2. 2 To express, Figure 5 The goodness of fit in is 0.90, indicating that the residual drift ratio prediction model works well. In addition, the standard deviation between the predicted results and the actual results is 1.45.

[0114] exist Figure 6 In the figure, the residual drift ratios are arranged in ascending order according to the values ​​calculated by the residual drift ratio prediction model. The residual drift ratios quantified by the hysteresis curves are also shown in Figure 6 The average value represents the residual drift ratio of the UBPRC pier calculated using the average value of the undetermined parameters. It can be seen that most of the quasi-static residual drift ratios fall within one standard deviation centered on the predicted value, and all fall within two standard deviations, indicating that the residual drift ratio prediction model has a high accuracy.

[0115] choose Figure 6 Taking a UBPRC pier in as an example, the values ​​of its parameters are shown in Table 4.

[0116] Table 4 Example of bridge pier parameter values

[0117]

[0118] The residual drift ratio prediction model is used to calculate the residual drift ratio according to the values ​​of each parameter. The calculated residual drift ratio is compared with the residual drift ratio obtained from the hysteresis curve. Figure 7 As shown. Figure 7 It can be seen that the quasi-static residual drift ratio falls within a standard deviation range centered on the predicted value, indicating that the residual drift ratio prediction model has better results.

[0119] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. The residual drift ratio evaluation method of unbonded prestressed reinforced concrete bridge piers is characterized by: The assessment steps include: S1. Establish a finite element model of the pier based on various parameters of the pier; S2. Obtaining the residual drift ratio of the bridge pier by simulating the finite element model; S3, constructing the corresponding functional relationship between various parameters of the bridge pier and the residual drift ratio; S4. establishing a residual drift ratio prediction model according to various functional relationships, and calculating the residual drift ratio of the bridge pier generated in an earthquake through the residual drift ratio prediction model; The specific content of step S2 is as follows: S21, inputting the values ​​of the set parameters and the prestress representing the earthquake intensity applied along the axial direction of the bridge pier into the finite element model, and obtaining the quasi-static residual drift ratio corresponding to the bridge pier through simulation; S22, using the quasi-static residual drift ratio as the residual drift ratio; The functional relationship between each parameter and the residual drift ratio is expressed as follows: Residual drift ratio RD r Slenderness ratio A to the pier r The functional relationship between them is: Where μ1 represents A r The exponent of , θ1 represents the exponent of e; Residual drift ratio RD r Axial compression ratio to the pier α c The functional relationship between them is: Among them, μ2 represents α c The exponent of , θ2 represents the exponent of e; Residual drift ratio RD r The longitudinal reinforcement ratio of the pier is ρ r The functional relationship between them is: Where μ3 represents ρ r The exponent of , θ3 represents the exponent of e; Residual drift ratio RD r Stirrup reinforcement ratio of piers s The functional relationship between them is: Where μ4 represents ρ s The exponent of , θ4 represents the exponent of e; Residual drift ratio RD r The compressive strength of the pier concrete c The functional relationship between them is: Where μ5 represents f c The exponent of , θ5 represents the exponent of e; Residual drift ratio RD r The yield strength f of the longitudinal reinforcement of the pier y The functional relationship between them is: Where μ6 represents f y The exponent of θ6 represents the exponent of e; Residual drift ratio RD r The reinforcement ratio of the prestressed steel bars of the piers p The functional relationship between them is: Where μ7 represents ρ p The exponent of θ7 represents the exponent of e; Residual drift ratio RD r The prestress of the bridge pier α ps The functional relationship between them is: Among them, μ8 represents α ps The exponent of θ8 represents the exponent of e; Residual drift ratio RD r Drift ratio to bridge pier D r The functional relationship between them is: Where μ9 represents D r The exponent of θ9 represents the exponent of e; the e in all the above calculation formulas is the Napier constant; The specific content of step S4 is as follows: First, according to the residual drift ratio RD r The functional relationship between the various parameters of the bridge pier is constructed by logarithmic transformation to obtain the residual drift ratio RD. r The joint function relationship between the various parameters of the bridge pier is expressed as follows: ln(RD r )=β0+β1ln(A r )+β2ln(α c )+β3ln(ρ l )+β4ln(ρ s )+β5ln(f c )+β6ln(f y )+β7ln(ρ p )+β8ln(α ps )+β9ln(D r ) Then the corresponding residual drift ratio prediction model is obtained through secondary logarithmic transformation; The residual drift ratio prediction model is expressed as follows: RD r =e W W=β0+β1ln(A r )+β2ln(α c )+β3ln(ρ l )+β4ln(ρ s )+β5ln(f c )+β6ln(f y )+β7ln(ρ p )+β8ln(α ps )+β9ln(D r ) Among them, RD r represents the residual drift ratio; e represents the Napier constant; W represents the exponent of e; β0, β1, …, β9 represent the unknown coefficients corresponding to each parameter; ln represents the logarithmic function; A r Indicates the slenderness ratio of the pier; α c represents the axial compression ratio of the pier; ρ l represents the longitudinal reinforcement ratio of the pier; ρ s Indicates the stirrup reinforcement ratio of the pier; f c Indicates the compressive strength of the pier concrete; f y represents the yield strength of the longitudinal reinforcement of the pier; ρ p represents the reinforcement ratio of prestressed steel bars in bridge piers; α ps Indicates the prestress of the pier; D r Represents the drift ratio of the bridge pier.

2. The residual drift ratio evaluation method of unbonded prestressed reinforced concrete bridge pier according to claim 1 is characterized in that: The specific steps of step S1 are as follows: S11. Setting the values ​​of various parameters of the bridge pier, including the height of the bridge pier, slenderness ratio, axial compression ratio, longitudinal reinforcement ratio, stirrup reinforcement ratio, compressive strength of concrete, yield strength of longitudinal reinforcement, prestressed reinforcement ratio, and prestressing strength of the bridge pier; S12, according to the set height, slenderness ratio and axial compression ratio of the bridge pier, the nonlinear beam-column unit in the OpenSees finite element analysis software is used to simulate the main body of the bridge pier; S13, according to the set longitudinal reinforcement ratio of the bridge pier, stirrup reinforcement ratio, compressive strength of concrete, yield strength of the longitudinal reinforcement and prestressed reinforcement ratio, the truss unit in the OpenSees finite element analysis software is used to simulate the unbonded prestressed steel bars in the bridge pier; S14. According to the set prestress of the bridge pier, the zero-length unit in the OpenSees finite element analysis software is used to simulate the bond slip of the steel bars in the bridge pier, thereby forming a complete finite element model of the bridge pier.

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