Performance-based seismic design method for prefabricated bridge piers with hybrid connections

Abstract

The present invention provides a performance-based seismic design method for hybrid-connected prefabricated piers, relating to the technical field of seismic design for prefabricated piers. The method comprises: determining the initial design parameters, expected structural performance indicators (including target maximum displacement and target residual displacement), and structural design parameters of the pier; establishing a lateral deformation analysis model; calculating target equivalent single-degree-of-freedom restoring force model parameters based on the lateral deformation analysis model; using a preset machine learning prediction model to predict the maximum displacement and residual displacement of the pier under actual earthquake action; adjusting the structural design parameters of the hybrid-connected prefabricated pier based on the prediction results until the relevant requirements are met; and then calculating the design force and design bending moment of the pier. By implementing the method of the present invention, a hybrid-connected prefabricated pier suitable for medium- and high-intensity zones is obtained, and the pier has the advantages of stable structural performance and easy post-earthquake recovery and repair.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic design of prefabricated bridge piers, and in particular to a performance-based seismic design method for hybrid-connected prefabricated bridge piers. Background Art

[0002] With the rapid advancement of industrialization and urbanization in my country, traditional extensive production methods are unable to cope with urban land resource constraints, traffic congestion, and severe noise pollution. Transportation infrastructure construction is rapidly developing towards industrialization, assembly, and intelligentization. Prefabrication technology has been widely used in highway, municipal, railway, and rail transit bridges in non-seismic and low-intensity areas. However, the main obstacle to its application in medium- and high-intensity areas is that prefabricated piers currently using a single connection method have weak lateral constraints at the segment joints, resulting in the piers' seismic performance failing to meet design requirements under strong earthquakes. Therefore, a prefabricated pier structure using a combination of connection methods is the most practical measure to improve the seismic resistance and shock absorption capabilities of such bridges.

[0003] Currently, seismic design methods for prefabricated bridge piers primarily include direct displacement-based seismic design and the ductile seismic design method based on conventional reinforced concrete piers. However, the direct displacement-based seismic design method is only applicable to prefabricated piers with a single connection method and is difficult to apply directly to prefabricated piers with mixed connections. Furthermore, this method makes several oversimplified assumptions, resulting in inaccurate design results. Furthermore, by only considering the influence of maximum displacement, it fails to effectively control the residual displacement of the bridge after an earthquake. Even if the piers do not collapse during severe earthquake damage, large residual displacements may still necessitate demolition and reconstruction. The ductile seismic design method based on conventional reinforced concrete piers allows for plastic deformation of the piers to prevent collapse under strong earthquakes. However, this method presents challenges in post-earthquake repair and is unsuitable for prefabricated piers designed to incorporate self-centering features.

[0004] Therefore, how to propose a seismic design method for hybrid-connected prefabricated and assembled bridge piers suitable for medium and high intensity areas, and taking into account the requirements of stable structural performance of the piers and easy recovery and repair after earthquakes, has become a technical problem that needs to be solved urgently. Summary of the Invention

[0005] In view of this, in order to solve the above technical problems, the present invention provides a performance-based seismic design method for hybrid-connected prefabricated and assembled bridge piers.

[0006] The present invention adopts the following technical solutions:

[0007] The present invention provides a performance-based seismic design method for a hybrid-connected prefabricated pier, comprising:

[0008] Determining initial design parameters and expected structural performance indicators of the hybrid connection prefabricated and assembled bridge piers, wherein the expected structural performance indicators include a target maximum displacement and a target residual displacement;

[0009] Determining the structural design parameters of the hybrid connection prefabricated assembled bridge pier;

[0010] establishing a lateral deformation analysis model based on the initial design parameters and the structural design parameters, and calculating the yield displacement of the hybrid-connected prefabricated pier based on the lateral deformation analysis model;

[0011] Calculating a displacement ductility coefficient and an equivalent period of the hybrid-connected prefabricated pier based on the initial design parameters, the target maximum displacement, and the yield displacement;

[0012] Based on the lateral deformation analysis model, and in accordance with the initial design parameters, the expected structural performance indicators, and the structural design parameters, target equivalent single-degree-of-freedom restoring force model parameters corresponding to the hybrid-connected prefabricated pier are calculated;

[0013] Inputting the target seismic site type and the target equivalent single-degree-of-freedom restoring force model parameters at the hybrid-connected prefabricated bridge pier into a preset machine learning prediction model to obtain a prediction result output by the preset machine learning prediction model, the prediction result including a maximum displacement and a residual displacement;

[0014] Analyzing the prediction results to obtain analysis results;

[0015] If the analysis result shows that a first relative deviation between the maximum displacement and the target maximum displacement meets a first deviation requirement, and a second relative deviation between the residual displacement and the target residual displacement meets a second deviation requirement, then calculating a design force and a design bending moment of the hybrid-connected prefabricated and assembled bridge pier based on the displacement ductility coefficient and the equivalent period;

[0016] If the analysis result shows that the first relative deviation between the maximum displacement and the target maximum displacement does not meet the first deviation requirement, or the second relative deviation between the residual displacement and the target residual displacement does not meet the second deviation requirement, the step of determining the structural design parameters of the hybrid-connected prefabricated and assembled bridge pier is performed.

[0017] Optionally, the initial design parameters include: pier top superstructure quality, pier height, concrete material parameters, ordinary steel bar material parameters, and prestressed steel bar material parameters;

[0018] The concrete material parameters include the compressive strength and elastic modulus of the concrete;

[0019] The material parameters of ordinary steel bars include the yield strength and elastic modulus of ordinary steel bars;

[0020] The material parameters of the prestressed tendons include the yield strength and elastic modulus of the prestressed tendons.

[0021] Optionally, the structural design parameters include: pier cross-sectional dimensions, ordinary steel bar design parameters, and prestressed steel bar design parameters;

[0022] The common steel bar design parameters include longitudinal bar diameter, longitudinal bar reinforcement ratio and longitudinal bar spacing;

[0023] The prestressed tendon design parameters include prestressed tendon specifications, prestressed tendon reinforcement ratio, layout position and initial stress level.

[0024] Optionally, the lateral deformation analysis model is expressed as follows:

[0025] Δ=Δ y +Δ p

[0026] Where, Δ is the displacement of the top of the hybrid connection prefabricated pier; Δ y is the yield displacement of the hybrid connection prefabricated assembled bridge pier; Δ p is the plastic displacement of the hybrid connection prefabricated assembled bridge pier.

[0027] Optionally, the process of establishing the preset machine learning prediction model includes:

[0028] Establishing an equivalent single-degree-of-freedom restoring force model of the hybrid-connected prefabricated pier;

[0029] Strong earthquake records matching the code response spectra of different seismic site types are selected as seismic inputs, and nonlinear time history analysis is performed on the equivalent single-degree-of-freedom restoring force model to obtain the maximum displacement and residual displacement of the dynamic response of the pier structure under different combinations of model input parameters; the model input parameter combinations include the seismic site type and the equivalent single-degree-of-freedom restoring force model parameters;

[0030] Determining the different model input parameter combinations and corresponding maximum displacements and residual displacements as training data sets for the preset machine learning prediction model;

[0031] Use the training data set to construct the preset machine learning prediction model; the artificial neural network model architecture adopted by the preset machine learning prediction model is a convolutional neural network, a recurrent neural network, a multi-layer perceptron, a linear regression, a support vector machine, a decision tree, a random forest or a gradient boosting.

[0032] Optionally, establishing an equivalent single-degree-of-freedom restoring force model of the hybrid-connected prefabricated pier specifically includes:

[0033] Establishing a bilinear elastic model of the hybrid connection prefabricated assembled bridge pier, wherein the bilinear elastic model is used to characterize the self-resetting ability of the unbonded prestressed system;

[0034] Establishing a fulcrum hysteresis model of the hybrid connection prefabricated and assembled bridge pier, wherein the fulcrum hysteresis model is used to characterize the hysteretic energy dissipation capacity of the hybrid connection prefabricated and assembled bridge pier;

[0035] The bilinear elastic model and the support hysteresis model are connected in parallel to obtain the equivalent single-degree-of-freedom restoring force model.

[0036] Optionally, calculating the design force and design bending moment of the hybrid-connected prefabricated pier based on the displacement ductility coefficient and the equivalent period specifically includes:

[0037] Calculating the equivalent stiffness of the hybrid-connected prefabricated pier according to the equivalent period;

[0038] Calculating the ultimate horizontal force of the hybrid connection prefabricated and assembled bridge pier based on the equivalent stiffness;

[0039] Calculating the ultimate bending moment of the hybrid-connected prefabricated pier based on the ultimate horizontal force;

[0040] Calculating the design force according to the ultimate horizontal force and the displacement ductility coefficient;

[0041] The design bending moment is calculated based on the design force.

[0042] The present invention adopts the above technical solution by establishing a lateral deformation analysis model. Based on the lateral deformation analysis model, the target equivalent single-degree-of-freedom restoring force model parameters are calculated. A preset machine learning prediction model is used to predict the corresponding maximum and residual displacements. The structural design parameters of the hybrid-connected prefabricated bridge piers are adjusted based on the prediction results until the relevant requirements are met. The design force and design bending moment of the piers are then calculated. In this way, the performance-based seismic design method of the present invention can be conveniently, efficiently, and intelligently applied to the seismic design of hybrid-connected prefabricated bridge piers in moderate-to-high-seismic intensity zones. Furthermore, the impact of horizontal maximum and residual displacements on the seismic performance of the piers can be comprehensively considered, meeting the seismic requirements of post-earthquake recoverability and easy repair. Furthermore, the machine learning-based maximum and residual displacement prediction model fully considers the impact of different structural design parameters, eliminating errors caused by assumptions and simplifications in traditional methods. Thus, by implementing the method of the present invention, a hybrid-connected prefabricated bridge pier suitable for moderate-to-high-seismic intensity zones can be obtained, which exhibits the advantages of stable structural performance and post-earthquake recoverability and easy repair. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0044] Figure 1 1 is a flow chart of a performance-based seismic design method for a hybrid-connected prefabricated bridge pier provided by an embodiment of the present invention;

[0045] Figure 2 Schematic diagram of a lateral deformation analysis model of an equivalent single-degree-of-freedom system provided by an embodiment of the present invention;

[0046] Figure 3 This is a schematic diagram of an equivalent single-degree-of-freedom restoring force model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0047] To make the objectives, technical solutions, and advantages of the present invention more apparent, the technical solutions of the present invention will be described in detail below. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other implementations obtained by those of ordinary skill in the art without inventive effort are within the scope of protection of the present invention.

[0048] With the rapid advancement of industrialization and urbanization in my country, traditional extensive production methods are unable to cope with problems such as limited urban land resources, traffic congestion, and severe noise pollution. Transportation infrastructure construction is rapidly developing towards industrialization, assembly, and intelligentization. Prefabrication and assembly technology has been widely used in highway, municipal, railway, and rail transit bridges. Prefabricated bridge piers are already widely used in non-seismic and low-intensity areas. However, the main obstacle to their further application in medium- and high-intensity areas is that current prefabricated bridge piers mostly use a single connection method, which is difficult to meet the seismic requirements of medium- and high-intensity areas. Therefore, the use of prefabricated bridge pier structures with mixed connection methods is the most practical measure to improve the seismic resistance and shock absorption capabilities of such bridges.

[0049] The current performance-based seismic design schemes for prefabricated and assembled bridge piers include a direct displacement-based seismic design method and a ductile seismic design method that follows the conventional reinforced concrete bridge design method.

[0050] Among them, the direct displacement-based seismic design method can refer to the literature: Bu Zhanyu, Ye Hanhui, Ge Shengliang, Zhang Xu. Direct displacement-based seismic design of precast assembled pier columns [J]. China Journal of Highway and Transport, 2018, 31(12): 205-257. This method is aimed at precast assembled single-column concrete bridge piers. The direct displacement-based seismic design steps are as follows:

[0051] (1) Select target displacement Δ u , determine the initial parameters.

[0052] (2) Calculate the yield displacement and ductility coefficient according to the following formula, and read the equivalent period T from the inelastic displacement response spectrum. eq .

[0053]

[0054] μ=Δ u / Δ y ...... (2)

[0055] Where, φ y is the equivalent yield curvature of the section, which is obtained based on the section bending moment-curvature analysis; H is the height of the pier; L p is the equivalent plastic hinge length.

[0056] (3) Determine the equivalent stiffness.

[0057]

[0058] Where m is the concentrated mass at the pier top.

[0059] (4) Determine the design force and design bending moment.

[0060]

[0061] M d =F d H...... (5)

[0062] Where r is the ratio of the post-yield stiffness to the elastic stiffness.

[0063] (5) Design the pier diameter and reinforcement.

[0064] (6) Calculate the yield displacement and compare it with the yield displacement estimated in step 2. If the error is less than 5%, it is considered to meet the requirements. Otherwise, substitute the yield displacement calculated in step 6 into step 2, update the displacement ductility and damping, and re-execute the calculations from steps 2 to 6 until convergence.

[0065] (7) Capacity protection design, including transverse reinforcement design and shear strength verification.

[0066] In addition, the ductile seismic design method used for ordinary reinforced concrete bridges can be referred to the document: "Technical Code for Prefabricated Assembled Bridge Piers" DG / TJ08-2160-2015.

[0067] Specifically, under an E1 earthquake, prefabricated assembled columns operate within the elastic range and are essentially undamaged. Under an E2 earthquake, prefabricated assembled columns may be damaged, undergoing elastic-plastic deformation to dissipate earthquake energy. However, the plastic hinge area of ​​the column should have sufficient plastic deformation capacity. The plastic rotation capacity and column top displacement of the potential plastic hinge area should satisfy the following equations:

[0068] θ p ≤θ u ......(6)

[0069] Δ d ≤Δ u ......(7)

[0070] Where θ p , Δ d are the plastic rotation angle and column top displacement of the potential plastic hinge area under E2 earthquake, and the maximum allowable rotation angle θ u and allowable displacement Δ u Calculate as follows:

[0071] θ u =L p (φ u -φ y ) / K......(8)

[0072]

[0073] Where, φ y 、φ u are the equivalent yield curvature of the section and the curvature capacity of the ultimate failure state, respectively; K is the ductility safety factor, which is 2.2 when the connecting sleeve is located in the plastic hinge area of ​​the column, and 2.0 when the connecting sleeve or metal bellows is located in the pedestal or cap beam; H is the pier height; L p is the equivalent plastic hinge length.

[0074] However, the direct displacement-based seismic design method is only applicable to prefabricated and assembled bridge piers with a single connection method and is difficult to directly apply to prefabricated and assembled bridge piers with mixed connections. In addition, the method's multiple assumptions are overly simplified, resulting in low accuracy of the design results. It also only considers the influence of the maximum displacement and cannot effectively control the residual displacement of the bridge after the earthquake. If the earthquake damage is severe, even if the piers do not collapse, the large residual displacement may still cause the bridge to need to be demolished and rebuilt. The ductile seismic design method used for ordinary reinforced concrete piers allows plastic deformation of the piers at the cost of avoiding collapse under strong earthquakes, but there are problems such as difficulty in post-earthquake repair. It is not suitable for prefabricated assembled bridge piers that take into account the self-resetting function.

[0075] Based on this, the present invention provides a performance-based seismic design method for hybrid-connected prefabricated bridge piers. By implementing this method, a hybrid-connected prefabricated bridge pier suitable for moderate-to-high-seismicity zones can be obtained, offering stable structural performance and easy post-earthquake recovery and repair.

[0076] The technical solution of the present invention is described in detail below with reference to the accompanying drawings.

[0077] Figure 1 This is a flow chart of a performance-based seismic design method for a hybrid-connected prefabricated pier provided by an embodiment of the present invention. Figure 1 As shown, this process includes:

[0078] Step 101: Determine initial design parameters and expected structural performance indicators of the hybrid-connected prefabricated bridge pier, wherein the expected structural performance indicators include a target maximum displacement and a target residual displacement.

[0079] Specifically, the relevant designers can determine the values ​​of the initial design parameters of the hybrid connection prefabricated assembled bridge pier based on the actual bridge parameters and input them into the relevant computer program. The initial design parameters may include: the mass m of the pier top superstructure, the pier height L, the concrete material parameters, the ordinary steel bar material parameters and the prestressed bar material parameters; the concrete material parameters may include the compressive strength f of the concrete. c ′ and elastic modulus E c ; Ordinary steel bar material parameters may include the yield strength f of ordinary steel bars sy and elastic modulus E s ; Prestressed tendon material parameters may include the yield strength f of the prestressed tendon pty and elastic modulus E pt .

[0080] Relevant designers can determine the expected structural performance indicators of hybrid prefabricated piers based on the importance of the bridge, site conditions, seismic protection level, post-earthquake recovery capacity and owner needs, and input them into relevant computer programs. The expected structural performance indicators can include the target maximum displacement Δu,t and target residual displacement Δ r,t .

[0081] Step 102: Determine the structural design parameters of the hybrid connection prefabricated assembled bridge pier.

[0082] Specifically, relevant designers can determine the values ​​of the design parameters of the hybrid connection prefabricated and assembled pier structure based on the normal use limit state of the bridge, design experience and construction requirements, and input them into the relevant computer program.

[0083] Structural design parameters may include: pier cross-sectional dimensions, common steel bar design parameters, and prestressed bar design parameters; common steel bar design parameters may include longitudinal bar diameter, longitudinal bar reinforcement ratio ρ s and longitudinal reinforcement spacing; prestressed reinforcement design parameters may include prestressed reinforcement specifications, prestressed reinforcement ratio ρ pt , layout location and initial stress level.

[0084] Step 103: Based on the initial design parameters and the structural design parameters, a lateral deformation analysis model is established, and based on the lateral deformation analysis model, the yield displacement of the hybrid connection prefabricated and assembled bridge pier is calculated.

[0085] Specifically, the lateral deformation analysis model is an equivalent single-degree-of-freedom system lateral deformation analysis model. Figure 2 Schematic diagram of an equivalent single degree of freedom system lateral deformation analysis model provided by an embodiment of the present invention. Figure 2 As shown in the figure, (a) is the deformation diagram of the hybrid connection prefabricated and assembled bridge pier, (b) is the equivalent single degree of freedom system of the hybrid connection prefabricated and assembled bridge pier, (c) is the bending moment distribution diagram of the hybrid connection prefabricated and assembled bridge pier, and (d) is the curvature distribution diagram of the hybrid connection prefabricated and assembled bridge pier.

[0086] Where, L is the total height of the pier (from the critical section B to the horizontal load application point); L G is the length of the grouting sleeve; L0 is the effective height of the pier (from the key section A to the horizontal load loading point); L p M is the length of the equivalent plastic hinge area at the top of the pier top grouting sleeve; A is the bending moment of the key interface A; M B Bending moment at key interface B; φ A The bending moment of the critical section A is M A The corresponding curvature when φ B The bending moment of the critical section B is M B The corresponding curvature is ; F is the horizontal load on the pier top.

[0087] Under horizontal loads, for hybrid-connected prefabricated bridge piers that experience bending failure, the lateral deformation analysis model is expressed as follows:

[0088] Δ=Δ y +Δ p ......(1)

[0089] Where, Δ is the displacement of the pier top of the hybrid connection prefabricated pier; Δ y is the yield displacement of the hybrid connection prefabricated pier; Δ p Plastic displacement of prefabricated piers with hybrid connections.

[0090] Δ y The calculation formula is as follows:

[0091] Δ y =Δ yb +Δ yr +Δ yo ......(2)

[0092] Where, Δ yb is the contribution of elastic bending of the ordinary reinforcement area of ​​the pier body to the horizontal displacement of the pier top under the yield state of the pier; Δ yr is the contribution of the rigid rotation of the grouting sleeve area at the bottom of the pier to the horizontal displacement of the pier top under the yield state of the pier; Δ yo is the contribution of the opening of the pier bottom joint to the horizontal displacement of the pier top under the pier yielding condition.

[0093] Δ p The calculation formula is as follows:

[0094] Δ p =Δ pb +Δ pr +Δ po ......(3)

[0095] Where, Δ pb is the contribution of plastic bending of the ordinary reinforcement area of ​​the pier body to the plastic displacement of the pier top under the ultimate state of the pier; Δ pr is the contribution of the rigid rotation of the grouting sleeve area at the bottom of the pier to the plastic displacement of the pier top under the ultimate state of the pier; Δ po is the contribution of the opening of the pier bottom joint to the plastic displacement of the pier top under the ultimate limit state of the pier.

[0096] (a) Yield displacement of prefabricated piers with hybrid connections

[0097] Before the longitudinal reinforcement of the key section B at the pier bottom joint yields, the pier as a whole is basically in the elastic range, and the bending moment and curvature are linearly distributed along the pier body (except for the grouting sleeve area). yb The curvature of the key section A at the top of the pier bottom grouting sleeve can beyA Integral calculation along the effective height L0, the calculation formula is as follows:

[0098]

[0099] Where, φ yA is the curvature of the key section A at the top of the pier bottom grouting sleeve when the longitudinal reinforcement of the key section B yields, φ yA =M yA / E0I0,M yA The yield moment M of the critical section B yB Linear interpolation is used to obtain M yB The moment-curvature analysis of the key section B can be carried out based on the initial design parameters, expected structural performance indicators and structural design parameters determined above, and E0I0 is the flexural stiffness of the section in the ordinary steel bar area of ​​the pier body.

[0100] Since the grouting sleeve area at the bottom of the pier is still in an elastic state when the longitudinal reinforcement at the joint of the pier bottom yields, the curvature is small. To simplify the calculation, it is assumed that the curvature of the grouting sleeve area is uniform along the height distribution. yr The calculation formula is as follows:

[0101] Δ yr =φ yBm L G (L-0.5L G )......(5)

[0102] Where, φ yBm is the curvature of the middle section of the grouting sleeve area at the bottom of the pier when the longitudinal reinforcement of the key section B yields, φ yBm =M yBm / EI,M yBm The yield moment M of the critical section B yB Linear interpolation results in that EI is the bending stiffness of the cross section in the grouting sleeve area.

[0103] Since the cracks at the joints develop less when the longitudinal reinforcement at the bottom of the pier yields, Δ yo =0.

[0104] (b) Plastic displacement of prefabricated piers with hybrid connections

[0105] For plastic deformation, based on the concentrated plastic hinge theory, the curvature within a certain height range of the top of the pier bottom grouting sleeve is assumed to be uniformly distributed, Δ pb The calculation formula is as follows:

[0106] Δ pb =(φ uA -φ yA )L p (L0-0.5L p)......(6)

[0107] Where, φ uA is the limiting curvature of the critical section A, L p Calculated based on 0.08L.

[0108] Δ pr The calculation formula is as follows:

[0109] Δ pr =φ pBm L G (L0-0.5L G )......(7)

[0110] Where, φ pBm is the curvature of the middle section of the grouting sleeve area at the bottom of the pier when the key section A reaches the limit state, φ pBm =M pBm / EI,M pBm The plastic bending moment M of the critical section A pA Linear interpolation calculation, M pA The result can be obtained by conducting moment-curvature analysis of the key section A based on the initial design parameters, expected structural performance indicators and structural design parameters determined above.

[0111] For the pier bottom joints with shallow socket connections, when the horizontal load increases to a certain extent, the joint opening deformation is limited by the constraints of the side walls and bottom of the pier cap. Based on the elastic foundation beam theory, the interaction between the pier cap and the bridge pier is simplified to a rotation spring at the connection section. po The calculation formula is as follows:

[0112] Δ po =θL......(8)

[0113] θ=θ1+θ2+θ3......(9)

[0114] Where the total rotation angle θ of the connection area is caused by the combined effect of the horizontal load F (θ1) on the pier top, the moment M1 (θ2) generated by the horizontal load, and the bearing pile resisting bending moment M2 (θ3), and can be calculated according to the elastic foundation beam theory.

[0115] Step 104: Based on the initial design parameters and the target maximum displacement Δ u,t and yield displacement Δ y , calculate the displacement ductility coefficient μ and equivalent period T of the hybrid connection prefabricated assembled bridge pier eq .

[0116] Specifically, the calculation formula for the displacement ductility coefficient μ of the hybrid connection prefabricated pier is as follows:

[0117] μ=Δu,t / Δ y ......(10)

[0118] Equivalent period T of hybrid connection prefabricated pier eq The calculation formula is as follows:

[0119]

[0120] Step 105: Based on the lateral deformation analysis model, according to the initial design parameters, the expected structural performance indicators and the structural design parameters, the target equivalent single-degree-of-freedom restoring force model parameters corresponding to the hybrid-connected prefabricated and assembled bridge pier are calculated.

[0121] Specifically, the target equivalent single-degree-of-freedom restoring force model parameters include period, displacement ductility ratio, initial stiffness ratio η, first post-bend stiffness ratio γ PT , stiffness ratio after the second bending γ EC , yield strength ratio λ.

[0122] Step 106: Input the target seismic site type and the target equivalent single-degree-of-freedom restoring force model parameters at the hybrid connection prefabricated pier into the preset machine learning prediction model to obtain the prediction results output by the preset machine learning prediction model, including the maximum displacement Δ u and residual displacement Δ r .

[0123] Step 107: Analyze the prediction results to obtain an analysis result. If the analysis result shows that the first relative deviation between the maximum displacement and the target maximum displacement meets the first deviation requirement, and the second relative deviation between the residual displacement and the target residual displacement meets the second deviation requirement, then execute step 108. If the analysis result shows that the first relative deviation between the maximum displacement and the target maximum displacement does not meet the first deviation requirement, or the second relative deviation between the residual displacement and the target residual displacement does not meet the second deviation requirement, then execute step 102.

[0124] Specifically, during the process of analyzing the prediction results, a first relative deviation of the maximum displacement relative to the target maximum displacement is calculated, and it is determined whether the first relative deviation is greater than a first preset deviation threshold. If the first relative deviation is greater than the first preset deviation threshold, it is determined that the first relative deviation does not meet the first deviation requirement, and step 102 is executed. If the first relative deviation is not greater than the first preset deviation threshold, it is determined that the first relative deviation meets the first deviation requirement. A second relative deviation of the residual displacement relative to the target residual displacement is calculated, and it is determined whether the second relative deviation is greater than a second preset deviation threshold. If the second relative deviation is greater than the second preset deviation threshold, it is determined that the second relative deviation does not meet the second deviation requirement, and step 102 is executed. If the second relative deviation is not greater than the second preset deviation threshold, it is determined that the second relative deviation meets the second deviation requirement, and step 108 is executed. Here, the first relative deviation = (maximum displacement - target maximum displacement) / target maximum displacement * 100%; the second relative deviation = (residual displacement - target residual displacement) / target residual displacement * 100%.

[0125] Here, the first preset deviation threshold and the second preset deviation threshold may be the same, for example, the first preset deviation threshold and the second preset deviation threshold are both 5%. In addition, the first preset deviation threshold and the second preset deviation threshold may also be different, which is not specifically limited in the present invention.

[0126] Step 108: Calculate the design force and design bending moment of the hybrid-connected prefabricated bridge pier based on the displacement ductility coefficient and the equivalent period.

[0127] Specifically, the design force and design bending moment of the hybrid connection prefabricated pier are calculated based on the displacement ductility coefficient and the equivalent period, which may include:

[0128] (1) Based on the equivalent period, the equivalent stiffness of the hybrid connection prefabricated assembled bridge pier is calculated.

[0129] Specifically, the equivalent stiffness K eq The calculation formula is as follows:

[0130]

[0131] (2) Based on the equivalent stiffness, calculate the ultimate horizontal force and ultimate bending moment.

[0132] Specifically, the limit horizontal force F u The calculation formula is as follows:

[0133] F u =K eq Δ u ......(13)

[0134] Ultimate bending moment M u The calculation formula is as follows:

[0135] M u =F u L......(14)

[0136] (3) Calculate the design force and design bending moment based on the displacement ductility coefficient.

[0137] Specifically, the design force F d The calculation formula is as follows:

[0138]

[0139] Where γ is the post-buckling stiffness ratio.

[0140] Design bending moment M d The calculation formula is as follows:

[0141] M d =F d L...... (16)

[0142] Subsequently, relevant designers can refer to the relevant parameters calculated using the method of the present invention, design the transverse reinforcement and pier neck joint concrete shear keys according to relevant specifications and construction requirements, and perform shear strength verification. In addition, they can use the finite element method to calculate the bearing capacity of the hybrid-connected prefabricated and assembled bridge piers under the target maximum displacement, and compare and verify it with the base shear force of the above-mentioned performance-based seismic design method.

[0143] In an embodiment of the present invention, the process of establishing a preset machine learning prediction model may include:

[0144] (1) Establish an equivalent single-degree-of-freedom restoring force model for hybrid-connected prefabricated bridge piers.

[0145] Figure 3 Schematic diagram of an equivalent single-degree-of-freedom restoring force model provided by an embodiment of the present invention. Figure 3 As shown in Figure 2, (a) is the bilinear elastic model, (b) is the pivot hysteresis model, and (c) is the generalized flag-type hysteresis model (i.e., the equivalent single-degree-of-freedom restoring force model). Specifically, the bilinear elastic model is used to characterize the self-restoring capacity of the unbonded prestressed system, while the pivot hysteresis model is used to characterize the hysteretic energy dissipation capacity of the "equivalent cast-in-place" bridge pier (grouting sleeve, socket-and-spigot hybrid connection system). The two models are then connected in parallel to form the generalized flag-type hysteresis model, which is the equivalent single-degree-of-freedom restoring force model.

[0146] Among them, F PT is the horizontal load of the unbonded prestressed system; k PT is the initial stiffness of the unbonded prestressed system; γ PT is the post-buckling stiffness ratio of the unbonded prestressed system; F ECis the horizontal load of the “equal to cast-in-place” pier; k EC is the horizontal load of the “equal to cast-in-place” pier; γ EC is the post-buckling stiffness ratio of the “equivalent cast-in-place” pier; F is the horizontal load of the hybrid connection prefabricated and assembled pier; k is the initial stiffness of the hybrid connection prefabricated and assembled pier.

[0147] (2) Strong earthquake records that match the standard response spectra of different seismic site types are selected as seismic inputs, and nonlinear time-history analysis is performed on the equivalent single-degree-of-freedom restoring force model to obtain the maximum displacement and residual displacement of the dynamic response of the pier structure under different combinations of model input parameters; the model input parameter combination includes the seismic site type and the equivalent single-degree-of-freedom restoring force model parameters.

[0148] Specifically, strong earthquake records that match the standard response spectra of different seismic site types are selected as seismic inputs, and nonlinear time history analysis is carried out on the equivalent single-degree-of-freedom restoring force model. During the analysis, the values ​​of the equivalent single-degree-of-freedom restoring force model parameters are changed. The equivalent single-degree-of-freedom restoring force model parameters include period, displacement ductility ratio, initial stiffness ratio η=k EC / k, stiffness ratio after first bending γ PT , stiffness ratio after the second bending γ EC and yield strength ratio λ=F yPT / F yEC , where the period can range from 0.05s to 6s, the displacement ductility ratio can range from 1 to 6, the initial stiffness ratio can range from 0 to 1, and the first post-bend stiffness ratio γ PT , stiffness ratio after the second bending γ EC The value range of can be 0 to 0.2, and the value range of yield strength ratio can be 0 to 2. Finally, the maximum displacement and residual displacement of the dynamic response of the pier structure under different model input parameter combinations are obtained. It should be noted that under each model input parameter combination, the maximum displacement and residual displacement corresponding to multiple strong earthquake records are obtained. The average of these maximum displacements and residual displacements is calculated to obtain the maximum displacement and residual displacement for the current model input parameter combination.

[0149] (3) Determine the different model input parameter combinations and the corresponding maximum displacement and residual displacement as the training data set of the preset machine learning prediction model.

[0150] (4) Use the training data set to build a preset machine learning prediction model.

[0151] Specifically, first, the training data set is standardized so that each value is distributed between 0 and 1, which can significantly improve the network prediction accuracy and accelerate the network convergence speed.

[0152] Then, the standardized training data set is divided into a training set, a validation set, and a test set, which account for 60%, 20%, and 20% of the total data, respectively.

[0153] Next, according to the characteristics and type of the data, an appropriate artificial neural network model architecture is selected for this application from the artificial neural network model architectures such as Convolutional Neural Network (CNN), Recurrent Neural Network (RNN), Multilayer Perceptron (MLP), Linear Regression, Support Vector Machine, Decision Tree, Random Forest and Gradient Boosting.

[0154] This article uses the MLP as an example to illustrate its use in this application. An MLP typically consists of an input layer, hidden layers, an activation function, and an output layer. The number of nodes in the input layer is determined by the number of input features; the hidden layer is initially configured with three layers, and the number of hidden layers can be increased based on prediction needs; the activation function is the ReLU function, commonly used in machine learning.

[0155] When training the model, a combination of model input parameters and the corresponding maximum and residual displacements are fed into the MLP. The MLP then predicts the predicted maximum and residual displacements based on the current model input parameter combination. The predicted maximum displacement and its actual value (the current input maximum displacement) and the predicted residual displacement and its actual value (the current input residual displacement) are then fed into the loss function to obtain the predicted loss. With the goal of minimizing the loss function, the model parameters are adjusted based on the current predicted loss. This iterative process is repeated until the preset maximum number of iterations is reached. A learning rate scheduler is used during training to dynamically adjust the learning rate to ensure model convergence stability.

[0156] Next, the loss function is evaluated using the training set and validation set to check whether the model is overfitting or underfitting; the key evaluation indicators are then calculated using the validation set to evaluate the generalization ability of the model; and finally, the test set is used for a final evaluation to ensure the accuracy and stability of the model on unseen data.

[0157] The embodiments of the present invention employ the above technical solutions. By establishing a lateral deformation analysis model, the equivalent single-degree-of-freedom restoring force model parameters are calculated based on the lateral deformation analysis model. A preset machine learning prediction model is used to predict the corresponding maximum and residual displacements. The structural design parameters of the hybrid-connected prefabricated bridge piers are adjusted based on the prediction results until the relevant requirements are met. The design force and design bending moment of the piers are then calculated. Thus, the performance-based seismic design method of the present invention can be conveniently, efficiently, and intelligently applied to the seismic design of hybrid-connected prefabricated bridge piers in moderate-to-high-seismic intensity zones. Furthermore, the impact of horizontal maximum and residual displacements on the seismic performance of the piers can be comprehensively considered, meeting the seismic requirements of post-earthquake recoverability and easy repair. Furthermore, the machine learning-based maximum and residual displacement prediction model fully considers the impact of different structural design parameters, eliminating errors caused by assumptions and simplifications in traditional methods. Thus, by implementing the method of the present invention, a hybrid-connected prefabricated bridge pier suitable for moderate-to-high-seismic intensity zones can be obtained, which exhibits the advantages of stable structural performance and post-earthquake recoverability and easy repair.

[0158] It can be understood that the same or similar parts of the above embodiments can be referenced to each other, and the contents not described in detail in some embodiments can refer to the same or similar contents in other embodiments.

[0159] It should be noted that, in the description of the present invention, the terms "first", "second", etc. are used for descriptive purposes only and should not be understood as indicating or implying relative importance. In addition, in the description of the present invention, unless otherwise specified, the meaning of "plurality" is at least two.

[0160] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present invention pertain.

[0161] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0162] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0163] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing module, or each unit may exist physically separately, or two or more units may be integrated into a single module. The aforementioned integrated modules may be implemented in the form of hardware or in the form of software functional modules. If the integrated modules are implemented in the form of software functional modules and sold or used as independent products, they may also be stored in a computer-readable storage medium.

[0164] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc.

[0165] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0166] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A performance-based seismic design method for hybrid-connected prefabricated bridge piers, characterized in that: include: Determining initial design parameters and expected structural performance indicators of the hybrid connection prefabricated and assembled bridge piers, wherein the expected structural performance indicators include a target maximum displacement and a target residual displacement; Determining the structural design parameters of the hybrid connection prefabricated assembled bridge pier; establishing a lateral deformation analysis model based on the initial design parameters and the structural design parameters, and calculating the yield displacement of the hybrid-connected prefabricated pier based on the lateral deformation analysis model; Calculating a displacement ductility coefficient and an equivalent period of the hybrid-connected prefabricated pier based on the initial design parameters, the target maximum displacement, and the yield displacement; Based on the lateral deformation analysis model, and in accordance with the initial design parameters, the expected structural performance indicators, and the structural design parameters, target equivalent single-degree-of-freedom restoring force model parameters corresponding to the hybrid-connected prefabricated pier are calculated; Inputting the target seismic site type and the target equivalent single-degree-of-freedom restoring force model parameters at the hybrid-connected prefabricated bridge pier into a preset machine learning prediction model to obtain a prediction result output by the preset machine learning prediction model, the prediction result including a maximum displacement and a residual displacement; Analyzing the prediction results to obtain analysis results; If the analysis result shows that a first relative deviation between the maximum displacement and the target maximum displacement meets a first deviation requirement, and a second relative deviation between the residual displacement and the target residual displacement meets a second deviation requirement, then calculating a design force and a design bending moment of the hybrid-connected prefabricated and assembled bridge pier based on the displacement ductility coefficient and the equivalent period; If the analysis result shows that a first relative deviation between the maximum displacement and the target maximum displacement does not meet a first deviation requirement, or a second relative deviation between the residual displacement and the target residual displacement does not meet a second deviation requirement, then performing a step of determining structural design parameters of the hybrid-connected prefabricated and assembled bridge pier; The process of establishing the preset machine learning prediction model includes: Establishing an equivalent single-degree-of-freedom restoring force model for the hybrid connection prefabricated and assembled bridge pier, specifically comprising: establishing a bilinear elastic model for the hybrid connection prefabricated and assembled bridge pier, the bilinear elastic model being used to characterize the self-resetting ability of the unbonded prestressed system; establishing a fulcrum hysteresis model for the hybrid connection prefabricated and assembled bridge pier, the fulcrum hysteresis model being used to characterize the hysteretic energy dissipation capacity of the hybrid connection prefabricated and assembled bridge pier; and connecting the bilinear elastic model and the fulcrum hysteresis model in parallel to obtain the equivalent single-degree-of-freedom restoring force model; Strong earthquake records matching the code response spectra of different seismic site types are selected as seismic inputs, and nonlinear time history analysis is performed on the equivalent single-degree-of-freedom restoring force model to obtain the maximum displacement and residual displacement of the dynamic response of the pier structure under different combinations of model input parameters; the model input parameter combinations include the seismic site type and the equivalent single-degree-of-freedom restoring force model parameters; Determining the different model input parameter combinations and corresponding maximum displacements and residual displacements as training data sets for the preset machine learning prediction model; Use the training data set to construct the preset machine learning prediction model; the artificial neural network model architecture adopted by the preset machine learning prediction model is a convolutional neural network, a recurrent neural network, a multi-layer perceptron, a linear regression, a support vector machine, a decision tree, a random forest or a gradient boosting.

2. The performance-based seismic design method for hybrid-connected prefabricated piers according to claim 1 is characterized in that: The initial design parameters include: pier top superstructure quality, pier height, concrete material parameters, ordinary steel bar material parameters and prestressed steel bar material parameters; The concrete material parameters include the compressive strength and elastic modulus of the concrete; The material parameters of ordinary steel bars include the yield strength and elastic modulus of ordinary steel bars; The material parameters of the prestressed tendons include the yield strength and elastic modulus of the prestressed tendons.

3. The performance-based seismic design method for hybrid-connected prefabricated piers according to claim 1 is characterized in that: The structural design parameters include: pier cross-sectional dimensions, common steel bar design parameters, and prestressed steel bar design parameters; The common steel bar design parameters include longitudinal bar diameter, longitudinal bar reinforcement ratio and longitudinal bar spacing; The prestressed tendon design parameters include prestressed tendon specifications, prestressed tendon reinforcement ratio, layout position and initial stress level.

4. The performance-based seismic design method for hybrid-connected prefabricated piers according to claim 1 is characterized in that: The expression formula of the lateral deformation analysis model is as follows: Where, is the pier top displacement of the hybrid connection prefabricated assembled pier; is the yield displacement of the hybrid connection prefabricated assembled bridge pier; is the plastic displacement of the hybrid connection prefabricated assembled bridge pier.

5. The performance-based seismic design method for hybrid-connected prefabricated piers according to claim 1 is characterized in that: Calculating the design force and design bending moment of the hybrid-connected prefabricated pier based on the displacement ductility coefficient and the equivalent period specifically includes: Calculating the equivalent stiffness of the hybrid-connected prefabricated pier according to the equivalent period; Calculating the ultimate horizontal force of the hybrid-connected prefabricated pier based on the equivalent stiffness; Calculating the ultimate bending moment of the hybrid-connected prefabricated pier based on the ultimate horizontal force; Calculating the design force according to the ultimate horizontal force and the displacement ductility coefficient; The design bending moment is calculated based on the design force.

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