Fast analysis method and system for multi-level damage constitutive model of HSC-HSSB structure

Abstract

The present invention proposes a multi-level damage constitutive rapid analysis method and system for HSC-HSSB structures, which is applicable to the seismic multi-level damage constitutive analysis of high-strength reinforced concrete piers. After pre-defining the damage state index in the present invention, only by inputting the key parameters, i.e., the state characterization variables, the pier bottom shear force F and the pier top displacement Δ corresponding to each damage state can be obtained. By connecting the origin with the points corresponding to the damage states (the abscissa is the pier top displacement Δ, and the ordinate is the pier bottom shear force F) in sequence, the F-Δ curve (F-Δ: force-displacement) can be obtained. Through the present invention, the F-Δ hysteretic curve and the displacement time history of the pier can be obtained efficiently and conveniently, realizing the rapid assessment of the seismic performance of the pier and the quantitative description of the seismic displacement performance.

Description

Technical Field

[0001] The present invention relates to the field of construction, and in particular to a method and system for rapid analysis of multi-level damage constitutive of HSC-HSSB structures. Background Art

[0002] Considering that large-scale experimental projects require more time, research funds and are difficult to implement compared with numerical simulations, numerical simulations can become an important supplementary tool for evaluating the seismic performance of HSC-HSSB (High-Strength Concrete-High-Strength Steel Bar; HSC: High-Strength Concrete, high-strength concrete; HSSB: High-Strength Steel Bar, high-strength steel bar) piers.

[0003] Some numerical simulation software such as OpenSees can be used to generate the F-Δ curves of predefined HSC-HSSB piers. However, existing simulation software is mainly developed for foreign codes, and there are certain differences between the analysis control parameters, material properties, etc. and domestic regulations. If used blindly, large errors will occur and even wrong results will be obtained.

[0004] Furthermore, numerical simulation software such as OpenSees is not user-friendly for beginners. A large amount of time is required to learn programming languages and complex material properties, etc. Moreover, even if a model has been built in OpenSees, it takes a certain amount of time to extract useful information from the calculation results and draw the F-Δ curve.

[0005] After inputting relevant data during daily operations of tools such as OpenSees, the output data needs to be statistically analyzed and classified one by one. It is impossible to conduct large-scale analysis, summarize the influence of each variable on the displacement limit state of components, and even less possible to optimize actual projects.

[0006] In addition, software such as OpenSees needs to modify the corresponding values when analyzing different parameters. Changing the concrete compressive strength and volumetric stirrup ratio requires redefining the material information. If the change amplitude is small each time, such mechanical operations are inefficient and consume a large amount of time and energy. Summary of the Invention

[0007] In order to solve the defects of constructing the F-Δ curve of piers based on software in the above-mentioned existing technologies, the present invention proposes a method for rapid analysis of multi-level damage constitutive of HSC-HSSB structures. Based on the fitting analytical formula of the approximate limit state proposed by big data, a simple and reliable method is provided for obtaining the F-Δ curve.

[0008] A multi - level damage constitutive fast analysis method of HSC - HSSB structure proposed by the present invention is applicable to constructing the F - Δ curve of a columnar reinforced concrete structure. The columnar reinforced concrete structure includes a steel bar mesh, a protective layer concrete wrapped around the outer periphery of the steel bar mesh, and a core layer concrete filled in the inner periphery of the steel bar mesh; the steel bar mesh is composed of longitudinal bars and stirrups; when the columnar reinforced concrete structure is vertically arranged, the longitudinal bars are in the vertical direction;

[0009] The analysis method includes the following steps:

[0010] S1. Define the damage state and the set of state characterization variables θ, where θ includes parameter items for characterizing the state of the columnar reinforced concrete structure; construct the curvature fitting formula (1') and the moment fitting formula (2').

[0011]

[0012] M = f(θ, τ c ) (2')[[]END]]

[0013] Wherein, and M respectively represent the curvature and moment of the columnar reinforced concrete structure; τ a , τ c represent the corresponding calculation parameter sets;

[0014] S2. Obtain the set of state characterization variables θ of the analysis object under different working conditions as data samples, and classify the data samples into data sample classes corresponding one - to - one with the damage states; the analysis object is the columnar reinforced concrete structure;

[0015] S3. For each damage state, fit the curvature fitting formula (1') and the moment fitting formula (2') through the data samples in the corresponding data sample class to obtain the curvature analytical formula (1 - 1') and the moment analytical formula (2 - 1') corresponding to each damage state of the analysis object, denoted as

[0016]

[0017] M i = f(θ, τ ci ) (2 - 1')[[]END]]

[0018] Wherein, and M i respectively represent the curvature and moment of the analysis object in the damage state i; τ ai and τ ci respectively represent the fitting parameter sets of τ a and τ c corresponding to the damage state i;

[0019] S4. Calculate the curvature under each damage state according to the corresponding curvature analytical formula (1-1') and bending moment analytical formula (2-1'). and the bending moment M i ;

[0020] S5. Combine the curvature and the bending moment M i to calculate the top displacement Δ i and the bottom shear force F i of the analysis object under each damage state, and draw a broken line graph connecting the origin of coordinates and multiple two-dimensional coordinate points (Δ i , F i ) in the two-dimensional coordinate system of shear force-displacement as the F-Δ curve.

[0021] Preferably, the set of state characterization variables θ defined in S1 = {L, R ac , ρ l , ρ s , f co , f y}, where L, R ac and f co are respectively the cross-sectional dimension, axial compression ratio and concrete compressive strength of the columnar reinforced concrete structure; ρ l , ρ s and f y are respectively the longitudinal reinforcement ratio, volumetric stirrup ratio and longitudinal yield strength in the columnar reinforced concrete structure; the curvature fitting formula is:

[0022] The bending moment fitting formula is: M = c0 × L c1 R ac c2 ρ l c3 ρ s c4 f co c5 f y c6 (2)

[0023] a0, a1, a2, a3, a4, a5, a6, c0, c1, c2, c3, c4, c5 and c6 are all calculation parameters;

[0024] The curvature analytical formula in S3 is:

[0025] The bending moment analytical formula is:

[0026] a0 i 、a1 i, a2 i , a3 i , a4 i , a5 i , a6 i , c0 i , c1 i , c2 i , c3 i , c4 i , c5 i and c6 i respectively represent the fitting parameters corresponding to a0, a1, a2, a3, a4, a5, a6, c0, c1, c2, c3, c4, c5 and c6 in the damage state i.

[0027] Preferably, the damage states are divided into a slight damage state, a moderate damage state, a severe damage state, and a collapse damage state with increasing damage degrees in sequence.

[0028] Preferably, in S5, the top displacement of the analysis object in the slight damage state is denoted as Δ y , the top displacement of the analysis object in the moderate damage state is denoted as Δ m , the top displacement of the analysis object in the severe damage state is denoted as Δ e , the top displacement of the analysis object in the collapse damage state is denoted as Δ u ;

[0029]

[0030]

[0031]

[0032]

[0033] Among them, and respectively represent the curvatures of the analysis object in the slight damage state, moderate damage state, severe damage state, and collapse damage state, L p represents the plastic hinge length of the analysis object, and H represents the height of the analysis object.

[0034] Preferably, the calculation formula for the plastic hinge length L p is:

[0035]

[0036] Among them, f y represents the yield strength of the longitudinal reinforcement of the analysis object, d b represents the diameter of the longitudinal reinforcement of the analysis object, f c ' represents the compressive strength of the core concrete of the analysis object.

[0037] Preferably, the base shear force F of the analysis object in each damage state in S5 i is calculated as follows:

[0038] F i = (M i - R ac f co L 2 Δ i ) / H, i ∈ {y, m, e, u}. (8)

[0039] Among them, M i represents the bending moment of the analysis object in the damage state i, and Δ i represents the top displacement of the analysis object in the damage state i; L is the cross-sectional dimension of the columnar reinforced concrete structure, that is, the side length of the equivalent square cross-section; R ac and f co are respectively the axial compression ratio and the concrete compressive strength of the columnar reinforced concrete structure, H represents the height of the analysis object; y, m, e, and u respectively represent the slight damage state, moderate damage state, severe damage state, and collapse damage state.

[0040] Preferably, in S5, a broken line graph connecting the origin, (Δ y , F y ), (Δ m , F m ), and (Δ u , F u ) in sequence in the shear force - displacement two-dimensional coordinate system is drawn as the F - Δ curve of the analysis object; Δ y and F y respectively represent the top displacement and the base shear force corresponding to the slight damage state; Δ m , F m respectively represent the top displacement and the base shear force corresponding to the moderate damage state; Δ u , F u respectively represent the top displacement and the base shear force corresponding to the collapse damage state.

[0041] Preferably, in S2, the damage state is divided according to the curve.

[0042] The present invention also proposes a multi-level damage constitutive rapid analysis system for the HSC - HSSB structure, which provides a carrier for the above-mentioned multi-level damage constitutive rapid analysis method of the HSC - HSSB structure and facilitates the popularization of the method.

[0043] A multi-level damage constitutive rapid analysis system with an HSC-HSSB structure proposed by the present invention includes a memory that stores a computer program, and when the computer program is executed, it is used to implement the multi-level damage constitutive rapid analysis method of the HSC-HSSB structure.

[0044] Preferably, it further includes a processor connected to the memory, and the processor is used to execute the computer program to implement the multi-level damage constitutive rapid analysis method of the HSC-HSSB structure.

[0045] The advantages of the present invention are as follows:

[0046] (1) A multi-level damage constitutive rapid analysis method with an HSC-HSSB structure proposed by the present invention is applicable to the multi-level damage constitutive analysis of high-strength reinforced concrete (HSC: High-Strength Concrete; HSSB: High-Strength Steel Bar; HSC-HSSB) piers. After pre-defining the damage state index in the present invention, only by inputting the key parameters, that is, the state characterization variables, the pier bottom shear force F and the pier top displacement Δ corresponding to each damage state can be obtained. Connecting the origin with the points corresponding to the damage states (the abscissa is the pier top displacement Δ, and the ordinate is the pier bottom shear force F) in sequence, the F-Δ curve (F-Δ: force-displacement) can be obtained. In this way, only by inputting the F-Δ curve, that is, the three-fold line model constructed by the present invention, into OpenSees, OpenSees can quickly output the F-Δ hysteretic curve and the displacement time history; compared with the prior art that requires constructing a single-pier model in OpenSees, the present invention saves the model construction time, is conducive to quickly obtaining the F-Δ hysteretic curve and the displacement time history, quickly evaluating the seismic performance of the pier, and quantitatively describing the seismic displacement performance of the pier.

[0047] (2) Based on the proposed parametric moment-curvature method, the present invention calculates the curves corresponding to a large number of sample working conditions, fits the analytical expressions for each damage state, formulates the curvature formula for each damage state, and is more rapid and efficient to use. In the usual pier analysis process, piers with different concrete compressive strengths and volumetric stirrup ratios often need to modify the material properties again, while using the present invention, only by changing the value of the state characterization variable can the analytical expression be fitted, saving a large amount of time for modifying the material properties and improving the analysis efficiency of reinforced concrete structures.

[0048] (3) After dividing the damage states based on the curve, for the curvature under different damage states ​The analytical formula fitting is carried out for the curvature φ and bending moment M, and the displacement at the top of the pier and the shear force at the bottom of the pier are calculated through the plastic hinge length formula combined with the theoretical method. This method makes the formulas for the displacement at the top of the pier and the shear force at the bottom of the pier, and the calculation is more rapid and efficient.

[0049] (4) The fitting analytical formula of the approximate limit state proposed by the present invention based on big data realizes the rapid evaluation of the seismic performance of the pier. During the implementation process, only 6 key parameters need to be determined to obtain the three-line F-Δ curve, shortening the process of obtaining the F-Δ curve, and it can be directly used by researchers.

[0050] (5) From the analytical formula of the present invention, it can be intuitively seen how much each key parameter affects the curvature and bending moment under each damage state, and whether it is a positive or negative influence, providing a reference for the design of reinforced concrete structures.

[0051] (6) The present invention has good calculation accuracy, high efficiency, simple operation, considers multiple states, and has a wide application range.

[0052] (7) The present invention also proposes a multi-level damage constitutive rapid analysis system for HSC-HSSB structures, which is used to carry the above-mentioned multi-level damage constitutive rapid analysis method for HSC-HSSB structures, facilitating the popularization of this method. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is the flow chart of the multi-level damage constitutive rapid analysis method for HSC-HSSB structures proposed by the present invention

[0054] Figure 2 is the three-line model proposed by the present invention;

[0055] Figure 3 is the comparison diagram of the three-line model and the single pier model in Scenario 0 of Embodiment 1;

[0056] Figure 4(a) is the comparison diagram of the three-line model and the single pier model in Scenario 1 of Embodiment 1;

[0057] Figure 4(b) is the comparison diagram of the three-line model and the single pier model in Scenario 2 of Embodiment 1;

[0058] Figure 4(c) is the comparison diagram of the three-line model and the single pier model in Scenario 3 of Embodiment 1;

[0059] Figure 4(d) is the comparison diagram of the three-line model and the single pier model in Scenario 4 of Embodiment 1;

[0060] Figure 4(e) is the comparison diagram of the three-line model and the single pier model in Scenario 5 of Embodiment 1;

[0061] Figure 4(f) is the comparison diagram of the three-line model and the single pier model in Scenario 6 of Embodiment 1;

[0062] Figure 5 Comparison of the force-displacement hysteretic curve corresponding to the three-line model and the force-displacement hysteretic curve corresponding to the single-pier model in scenario 0 of Example 1;

[0063] Figure 6 Comparison of the force-displacement hysteretic curve corresponding to the three-line model and the force-displacement hysteretic curve constructed from experimental data in Example 2;

[0064] Figure 7(a) shows the comparison of the displacement time histories of the three-line model and the single-pier model of analysis object 1 in the seismic wave in Example 3;

[0065] Figure 7(b) shows the comparison of the displacement time histories of the three-line model and the single-pier model of analysis object 2 in the seismic wave in Example 3;

[0066] Figure 8(a) shows the curvature errors of 5 samples in the slightly damaged state in Example 4;

[0067] Figure 8(b) shows the curvature errors of 5 samples in the moderately damaged state in Example 4;

[0068] Figure 8(c) shows the curvature errors of 5 samples in the severely damaged state in Example 4;

[0069] Figure 8(d) shows the curvature errors of 5 samples in the collapsed damaged state in Example 4. Detailed implementation manners

[0070] To prove the reliability of the multi-level damage constitutive rapid analysis method for the HSC-HSSB structure proposed by the present invention, the method is verified in combination with multiple embodiments below.

[0071] In the following embodiments, the parameters calculated by the multi-level damage constitutive rapid analysis method for the HSC-HSSB structure proposed by the present invention are verified by comparison with the simulation data of OpenSees. For the sake of convenience of description, in the following text, the three-line F-Δ curve obtained by the multi-level damage constitutive rapid analysis method for the HSC-HSSB structure provided by the present invention is denoted as the three-line model, and the F-Δ curve obtained by the OpenSees simulation is denoted as the single-pier model.

[0072] Example 1

[0073] In this embodiment, the F-Δ curve of a certain pier is constructed by using the multi-level damage constitutive rapid analysis method for the HSC-HSSB structure provided by the present invention.

[0074] In this embodiment, the damage states are divided into a slightly damaged state, a moderately damaged state, a severely damaged state, and a collapsed damaged state in ascending order of damage degree.

[0075] In this embodiment, first, a sample space containing 6 6 working conditions is established, that is, 6 key parameters are studied - the cross-sectional dimension L, the axial compression ratio R ac , the concrete compressive strength f co , the longitudinal reinforcement ratio ρ l , the volumetric stirrup ratio ρ s , and the yield strength of steel bars f y . Each parameter is studied for 6 working conditions, totaling 46,656 working conditions, that is, data samples. The value ranges of the working conditions are shown in Table 1:

[0076] Table 1 Value ranges of working conditions

[0077]

[0078] Adopt the method of Chinese patent document CN113378399A to construct the curves of 46,656 working conditions. Calibrate the damage states of 46,656 working conditions through four predefined damage state indicators, complete the classification of data samples, and obtain data sample classes corresponding one-to-one to the damage states. It should be noted that the severe damage state defined in the present invention is equivalent to the ultimate damage state defined in Chinese patent document CN113378399A.

[0079] Substitute the working conditions in each data sample class into formula (1) and formula (2) respectively, and fit to obtain the curvature analytical formula and moment analytical formula under each damage state. In this embodiment, the two-dimensional coordinate points (Δ y , F y ), (Δ m , F m ), and (Δ u , F u ) corresponding to the slight damage state, moderate damage state, and collapse damage state are used to construct a three-line model. y, m, and u represent the slight damage state, moderate damage state, and collapse damage state respectively. The three-line model is as Figure 2 shown.

[0080] In this embodiment, the curvature analytical formulas of the bridge pier under each damage state are shown in Table 2 below:

[0081] Table 2 Curvature analytical formulas under each damage state

[0082]

[0083] R 2 represents the goodness of fit. In Table 2, R 2 are all greater than 0.9. It can be seen that the curvature analytical formulas corresponding to each damage state have good fitting effects.

[0084] In this embodiment, the moment analytical expressions for each damage state of the bridge pier are shown in Table 3 below:

[0085] Table 3 Moment Analytical Expressions for Each Damage State of the Pier Bottom Section

[0086]

[0087] Table 4 Calculation Formulas for the Key Points of the Three - fold Line of the Bridge Pier

[0088]

[0089] Among them, Δ y is the top displacement of the bridge pier in the slight damage state, Δ m is the top displacement of the bridge pier in the moderate damage state, Δ u is the top displacement of the bridge pier in the collapse damage state; F y is the bottom shear force of the bridge pier in the slight damage state, F m is the bottom shear force of the bridge pier in the moderate damage state, F u is the bottom shear force of the bridge pier in the collapse damage state; L p represents the plastic hinge length of the bridge pier, and H represents the height of the analysis object.

[0090]

[0091] f y represents the yield strength of the longitudinal bars in the steel bar mesh of the analysis object, d b represents the diameter of the longitudinal bars, and fc’ represents the compressive strength of the core - layer concrete of the analysis object.

[0092] In this embodiment, the parameters of the bridge pier are a rectangular reinforced concrete with a cross - section of 1.2m×1.2m. C60 concrete and HRB400 steel bars are selected. The thickness c0 of the protective layer concrete is 30mm, the stirrup spacing is 100mm, the longitudinal bar reinforcement ratio is 2.0%, the volumetric stirrup ratio is 1.0%, and the axial compression ratio is set to 0.1. This set of data is denoted as Scenario 0, and its corresponding three - fold line model is as Figure 3 shown. In this embodiment, in order to further study the influence of parameters on the accuracy of the three - fold line model, any one parameter in Scenario 0 is modified to derive Scenarios 1 - 6, as shown in the following table specifically.

[0093] Table 6: Working Conditions of the Embodiment

[0094] Scenario 0 Scenario 1 Scenario 2 Scenario 3 Cross-sectional dimension L 1.2m 1m 1.2m 1.2m <![CDATA[Axial compression ratio R ac > 0.1 0.1 0.15 0.1 <![CDATA[Longitudinal reinforcement ratio ρ l > 0.02 0.02 0.02 0.015 <![CDATA[Volume stirrup ratio ρ s > 0.01 0.01 0.01 0.01 <![CDATA[Concrete compressive strength f co > 60 60 60 60 <![CDATA[Yield strength of steel bar f y > 600 600 600 600 <![CDATA[Slight damage (Δ y , F y )]]> 0.0383,1579 0.0459,891 0.0403,1789 0.0377,1330 <![CDATA[Moderate injury (Δ m , F m )]]> 0.0515,1997 0.0619,1129 0.0543,2249 0.0509,1670 <![CDATA[Collapse damage (Δ u , F u )]]> 0.2409,1930 0.2826,1019 0.2003,2114 0.2597,1537 Scenario 4 Scenario 5 Scenario 6 Cross-sectional dimension L 1.2m 1.2m 1.2m <![CDATA[Axial compression ratio R ac > 0.1 0.1 0.1 <![CDATA[Longitudinal reinforcement ratio ρ l > 0.02 0.02 0.02 <![CDATA[Volume stirrup ratio ρ s > 0.013 0.01 0.01 <![CDATA[Concrete compressive strength f co > 60 70 60 <![CDATA[Yield strength of steel bar f y > 600 600 700 <![CDATA[Slight damage (Δ y , F y )]]> 0.0383,1578 0.0383,1665 0.0439,1752 <![CDATA[Moderate injury (Δ m , F m )]]> 0.0515,1997 0.0514,2105 0.0594,2213 <![CDATA[Collapse damage (Δ u , F u )]]> 0.2608,1932 0.1949,2067 0.2416,2166

[0095] In this embodiment, the three - fold line models corresponding to Scenarios 0 - 6 are respectively as Figure 3 , Figures 4(a) - (f) shown, Figure 3In Figures 4(a)-(f), the three-line model and the single pier model are further compared in each scenario. It can be seen that the fitting effect of the three-line model and the single pier model is good in any scenario. It can be seen that the six state characterization variables selected in the present invention, combined with the constitutive rapid analysis method provided by the present invention, result in a three-line F-Δ curve with high accuracy and a wide application range.

[0096] In this embodiment, the three-line model obtained in Scenario 0 is further input into OpenSees to obtain the force-displacement hysteretic curve corresponding to the three-line model, that is, the F-Δ hysteretic curve, as Figure 5 shown. And this curve is compared with the force-displacement hysteretic curve obtained by directly inputting the limited data of Scenario 0 into OpenSees (that is, the force-displacement hysteretic curve corresponding to the single pier model). Combining Figure 5 it can be known that the force-displacement hysteretic curve corresponding to the three-line model fits well with the force-displacement hysteretic curve corresponding to the single pier model, and the maximum displacements are almost completely coincident, indicating that the three-line model proposed by the present invention is a quantitative model that can well describe the seismic performance of bridge piers and can be used to quickly obtain the F-Δ curve under the damaged state of bridge piers.

[0097] Example 2

[0098] In this embodiment, an experimental measurement is carried out on an analysis object to verify the accuracy of the three-line model proposed by the present invention.

[0099] In this embodiment, the analysis object is a bridge pier, and its parameters are shown in the following table:

[0100] Table 7: Example working conditions

[0101] Cross-sectional dimension L 0.6 <![CDATA[Axial compression ratio R ac > 0.3 <![CDATA[Longitudinal reinforcement ratio ρ l > 0.013 <![CDATA[Volume stirrup ratio ρ s > 0.01 <![CDATA[Concrete compressive strength f co > 68.7 <![CDATA[Yield strength f of steel bars y > 667 <![CDATA[Minor damage (Δ y , F y )]]> 0.0132，835 <![CDATA[Moderate injury (Δ m , F m )]]> 0.0333，986 <![CDATA[Collapse damage (Δ u , F u )]]> 0.0783，723

[0102] In this embodiment, first, a three-line model is obtained according to the multi-level damage constitutive rapid analysis method of the HSC-HSSB structure proposed by the present invention, and then the three-line model is used as input data to build a model in OpenSees to obtain the corresponding force-displacement hysteretic curve as Figure 6 shown by the dotted line in Figure 6 and the solid line in

[0103] is the test data obtained by in-situ measurement of the analysis object. It can be seen that the fitting degree between the two is good, proving that the three-line model proposed by the present invention can meet the scientific research needs.

[0104] In this embodiment, two analysis objects, namely Analysis Object 1 and Analysis Object 2, are selected to verify the reliability of the three-line model in the displacement time history of different seismic waves with the same magnitude. The key parameters of Analysis Object 1 and Analysis Object 2 are the same, as shown in the following table:

[0105] Table 8: Example working conditions

[0106] Analysis object 1 Analysis object 2 Product Bridge pier Bridge pier Cross-sectional dimension L 1.2 1.2 <![CDATA[Axial compression ratio R ac > 0.1 0.1 <![CDATA[Longitudinal reinforcement ratio ρ l > 0.02 0.02 <![CDATA[Volume stirrup ratio ρ s > 0.01 0.01 <![CDATA[Concrete compressive strength f co > 60 60 <![CDATA[Yield strength f of steel bars y > 600 600 Seismic wave parameters 0.5g 0.5g

[0107] In this embodiment, first, a three-line model is obtained according to the multi-level damage constitutive rapid analysis method of the HSC-HSSB structure proposed by the present invention. Then, with the three-line model as the input data, a model is built in OpenSees, and the variation of the pier top displacement with time, i.e., the displacement time history, of analysis object 1 and analysis object 2 in the seismic wave is obtained respectively, as shown by the solid lines in FIGS. 7(a) and 7(b). The dashed lines in FIGS. 7(a) and 7(b) show the variation of the pier top displacement with time, i.e., the displacement time history, of the analysis object obtained by building a single pier model in OpenSees. It can be seen that the curves in FIGS. 7(a) and 7(b) are well-fitted, further proving the reliability of the three-line model proposed by the present invention.

[0108] Embodiment 4

[0109] When analyzing the analysis object through the three-line model proposed by the present invention, the calculation of curvature and bending moment is very important. In this embodiment, multiple samples are selected to verify the accuracy of the curvature analytical formula shown in Table 2 obtained by parameter fitting in the present invention.

[0110] The parameters of each sample obtained in this embodiment are shown in the following table:

[0111] Table 9: Sampling conditions

[0112]

[0113] In this embodiment, the curvature of each sample is calculated by combining the curvature analytical formula in Table 2 and the method in Chinese Patent Document CN113378399A, i.e., the empirical capacity model. The results are shown in the following table:

[0114] Table 10: Verification results

[0115]

[0116] Where and respectively represent the ultimate curvatures of each sample in each damage state obtained from the curvature analytical formula in Table 2; and respectively represent the ultimate curvatures of each sample in each damage state obtained from the empirical capacity model; The comparison of the ultimate curvatures of each sample obtained by the two methods in different damage states is shown in FIGS. 8(a)-(d). It can be seen that in various damage states, the error between the ultimate curvature obtained from the curvature analytical formula and the ultimate curvature obtained from the empirical capacity model is less than 5%, proving that the curvature analytical formula derived in Embodiment 1 has high accuracy, meets the requirements of scientific research, and can be used for further academic research.

[0117] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A rapid analysis method for multi-level damage constitutive model of HSC-HSSB structure, applicable to constructing the F-Δ curve of columnar reinforced concrete structure, where the columnar reinforced concrete structure is a high-strength steel bar and high-strength concrete structure, including a steel bar mesh, a protective layer concrete wrapped around the outer periphery of the steel bar mesh, and a core layer concrete filled in the inner periphery of the steel bar mesh; the steel bar mesh is composed of longitudinal bars and stirrups; when the columnar reinforced concrete structure is vertically arranged, the longitudinal bars are in the vertical direction; It is characterized in that The analysis method includes the following steps: S1. Define the damage state and the set of state characterization variables θ, where θ contains parameter items for characterizing the state of the columnar reinforced concrete structure; construct the curvature fitting formula (1’) and the moment fitting formula (2’); M = f(θ, τ c ) (2’) Among them, and M respectively represent the curvature and bending moment of the columnar reinforced concrete structure; τ a , τ c represent the corresponding calculation parameter sets; S2. Obtain the set of state characterization variables θ of the analysis object under different working conditions as data samples, and classify the data samples into data sample classes corresponding one-to-one to the damage states; the analysis object is the columnar reinforced concrete structure; S3. For each damage state, fit the curvature fitting formula (1’) and the moment fitting formula (2’) through the data samples in the corresponding data sample class to obtain the curvature analytical formula (1-1’) and the moment analytical formula (2-1’) corresponding to each damage state of the analysis object, denoted as M i = f(θ, τ ci ) (2-1’) Among them, and M i represent the curvature and bending moment of the analysis object in the damage state i, respectively; τ ai and τ ci represent the sets of fitting parameters corresponding to τ a and τ c in the damage state i, respectively; S4. Calculate the curvature at each damage state according to the corresponding curvature analytical formula (1-1') and bending moment analytical formula (2-1'). and the bending moment M i ; S5. Combined curvature and bending moment M i Calculate the top displacement Δ of the analysis object in each damage state i and the bottom shear force F i , and plot a broken line graph connecting the origin of coordinates and multiple two-dimensional coordinate points (Δ i , F i ) in the two-dimensional coordinate system of shear force-displacement as the F-Δ curve.

2. The rapid analysis method for multi-level damage constitutive of the HSC-HSSB structure according to claim 1, characterized in that The set of state characterization variables θ defined in S1 = {L, R ac , ρ l , ρ s , f co , f y}}, where L, R ac and f co are the cross-sectional dimension, axial compression ratio, and concrete compressive strength of the columnar reinforced concrete structure respectively; ρ l , ρ s and f y are the longitudinal reinforcement ratio, volumetric stirrup ratio, and longitudinal yield strength in the columnar reinforced concrete structure respectively; the curvature fitting formula is: The bending moment fitting formula is: M = c0 × L c1 R ac c2 ρ l c3 ρ s c4 f co c5 f y c6 (2) a0, a1, a2, a3, a4, a5, a6, c0, c1, c2, c3, c4, c5 and c6 are all calculation parameters; The curvature analytical formula in S3 is as follows: The bending moment analytical formula is as follows: a0 i 、a1 i 、a2 i 、a3 i 、a4 i 、a5 i 、a6 i 、c0 i 、c1 i 、c2 i 、c3 i 、c4 i 、c5 i and c6 i respectively represent the fitting parameters corresponding to a0, a1, a2, a3, a4, a5, a6, c0, c1, c2, c3, c4, c5 and c6 in the damage state i.

3. The rapid constitutive analysis method for multi-level damage of the HSC-HSSB structure according to claim 2, wherein The damage states are divided into a slight damage state, a moderate damage state, a severe damage state, and a collapse damage state with gradually increasing damage degree.

4. The rapid analysis method for multi-level damage constitutive of the HSC-HSSB structure according to claim 3, wherein In S5, the top displacement of the object under analysis in the slightly damaged state is denoted as Δ y , the top displacement of the object under analysis in the moderately damaged state is denoted as Δ m , the top displacement of the object under analysis in the severely damaged state is denoted as Δ e , the top displacement of the object under analysis in the collapsed damaged state is denoted as Δ u ; Among them, and respectively represent the curvatures of the analysis object in the slightly damaged state, moderately damaged state, severely damaged state, and collapsed damaged state. L p represents the plastic hinge length of the analysis object, and H represents the height of the analysis object.

5. The rapid analysis method for multi-level damage constitutive of the HSC-HSSB structure according to claim 4, characterized in that, Plastic hinge length L p The calculation formula is as follows: Among them, f y represents the yield strength of the longitudinal reinforcement of the analysis object, d b represents the diameter of the longitudinal reinforcement of the analysis object, and f c ' represents the compressive strength of the core layer concrete of the analysis object.

6. The rapid constitutive analysis method for multi-level damage of the HSC-HSSB structure according to claim 3, characterized in that, The base shear force F of the analysis object in each damage state in S5 i The calculation formula is as follows: F i = (M i - R ac f co L 2 Δ i ) / H, i ∈ {y, m, e, u} (8) Among them, M i represents the bending moment of the analysis object in the damage state i, and Δ i represents the top displacement of the analysis object in the damage state i; L is the cross-sectional dimension of the columnar reinforced concrete structure, that is, the side length of the equivalent square cross-section; R ac and f co are respectively the axial compression ratio and the concrete compressive strength of the columnar reinforced concrete structure, and H represents the height of the analysis object; y, m, e, and u respectively represent the slight damage state, moderate damage state, severe damage state, and collapse damage state.

7. The multi-level damage constitutive fast analysis method of the HSC-HSSB structure according to claim 3, characterized in that, In S5, a broken line graph connecting the origin, (Δ y , F y ), (Δ m , F m ), and (Δ u , F u ) in sequence in the two-dimensional coordinate system of shear force - displacement is drawn as the F - Δ curve of the analysis object; Δ y and F y respectively represent the top displacement and bottom shear force corresponding to the slight damage state; Δ m , F m respectively represent the top displacement and bottom shear force corresponding to the moderate damage state; Δ u , F u respectively represent the top displacement and bottom shear force corresponding to the collapse damage state.

8. The multi-level damage constitutive fast analysis method for the HSC-HSSB structure according to claim 3, characterized in that, In S2, divide the damage state according to the curve.

9. A multi-level damage constitutive rapid analysis system with an HSC-HSSB structure, characterized in that, It includes a memory that stores a computer program, and the computer program is used to implement the rapid analysis method for multi-level damage constitutive model of HSC-HSSB structure according to any one of claims 1-8 when executed.

10. The multi-level damage constitutive rapid analysis system of the HSC-HSSB structure according to claim 9, characterized in that, It further includes a processor, the processor is connected to the memory, and the processor is used to execute the computer program to implement the rapid analysis method for multi-level damage constitutive model of HSC-HSSB structure according to any one of claims 1-8.

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