CN112883463A - Reinforced concrete column earthquake failure mode probability model and probability prediction method thereof - Google Patents
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Abstract
The invention discloses a reinforced concrete column earthquake failure mode probability model and a probability prediction method thereof, wherein the reinforced concrete column earthquake failure mode probability model is expressed as follows:
Description
Technical Field
The invention belongs to the technical field of reinforced concrete structure earthquake resistance research, and particularly relates to a method for predicting earthquake failure mode probability of a reinforced concrete column.
Background
Under the action of earthquake load, the Reinforced Concrete (RC) column (pier) usually generates bending, shearing or bending-shearing damage, and the properties of the 3 kinds of damage modes are different, and the earthquake resistance of the structure is different. Particularly, direct shear failure, the longitudinal bars cannot yield to present complete brittleness characteristics, while for bending shear failure with limited ductility, the shear strength is reduced along with the increase of deformation after the longitudinal bars yield, and finally shear failure also occurs, and the two failure modes are both insufficient in energy consumption and are strived to avoid in earthquake-proof design, but existing RC column shear or bending shear failure in the past earthquake occupies a considerable proportion, and may be related to the limited understanding of early shear problems and the incomplete anti-seismic specifications. The earthquake-resistant performance of the existing structure or member can be known by accurately predicting the failure mode of the RC column under the action of an earthquake, so that the earthquake-resistant safety of the structure is reasonably evaluated, and proper preparation is made for earthquake-resistant reinforcement. At present, the bending damage to the RC column can be simulated by adopting a classical fiber beam column unit model; for shear failure and bending shear failure, because the shear action mechanism is complex, a completely reasonable theoretical calculation model does not describe the two failure characteristics. Thus, there remains difficulty in predicting the seismic failure mode of the RC column from a direct computational perspective.
Scholars at home and abroad put forward corresponding RC column earthquake damage mode discrimination methods from different angles. Theoretically, the shearing resistance requirement and the shearing strength (V) of the section of the plastic hinge area can be adoptedp/V0) The relationship between them is used for structural member seismic failure mode discrimination (Priestley et al, 1994; barghi and Youssefi, 2009; Liu-Rong, etc., 2011). Furthermore, ASCE/SEI 41-17 adopts Vp/V00.6 is used as the criterion for breaking bending and generalized shearing (including bending shearing). The method needs to firstly determine the shear strength of the section of the RC column plastic hinge area, but at present, theoretical models for shear strength calculation are different at home and abroad, a unified calculation method is not available, and the calculation accuracy is limited. Ang et al (1985) used a displacement ductility coefficient to determine the failure mode of the pier column after shear oblique cracks appear in the RC column pseudo-static test process,this method is only applicable to test pieces. QI et al (2013) analyzed the RC pier column destruction pattern influencing factors by FDA (Fisher statistical analysis), which indicates Vp/V0The influence is the largest, the ratio of the shearing-span ratio, the stirrup spacing and the section depth is the second, and then 3 parameters with larger influence are used for statistical analysis so as to judge the earthquake damage mode. Sun Zhi Guo et al (2015) etc. are aware of Vp/V0The calculation precision is limited, the shearing and bending deformation of the RC column during ultimate load are calculated based on a modified pressure field theory (MCFT) and a fiber beam column unit model respectively, and the judgment criterion of column bending, bending shearing and shearing failure modes is provided from a deformation angle according to the ratio relation of the shearing and bending deformation. Ning and Feng (2019) by calculating the bending strength MfAnd shear strength V0The ratio relation of the two is provided with a probability index Mf/L×1/V0(i.e. V)p/V0And L is the height of the pier stud), and a likelihood uncertainty estimation method is adopted to determine unknown parameters so as to judge the damage mode of the pier stud. Mangalathu and Jeon (2019) adopt six different machine learning methods, predict the earthquake damage mode of the circular RC column and show that the artificial neural network algorithm has good effect.
The above methods do not consider the influence of uncertainty, and have no probability significance. And has a limited application range.
Disclosure of Invention
The factors influencing the earthquake failure mode of the column are numerous, various influencing factors are mutually crossed, and various uncertain influences existing in engineering, such as material parameters, geometric dimensions, load intensity, calculation models, measurement errors and the like, are considered, so that the earthquake failure mode of the column can be predicted by adopting a probability method, and the Bayesian theory is an important probability statistical method. The Bayesian method is to synthesize prior information and sample information to deduce posterior information. Therefore, the invention provides a reinforced concrete column earthquake damage probability prediction method, which provides a new reinforced concrete column member bending, bending shearing or shearing damage probability prediction method based on Bayesian theory to overcome the defects of the existing prediction model, so that the method can identify the main influence factors of the earthquake damage mode of the reinforced concrete column and realize the probability prediction of the damage mode of the reinforced concrete column under the earthquake action; and various uncertainties existing in engineering practice are considered.
The purpose of the invention is realized by the following technical scheme:
a reinforced concrete column seismic failure mode probability model represented as:
FM(x,Θ)＝fmd(x)+γ(x,θ)+σε (1)
in the formula, FM represents a random variable earthquake damage mode; x represents variables affecting the earthquake damage mode of the RC column, namely variables measured in the test, such as material characteristics, geometric dimension, reinforcing bars, axial pressure and the like; θ ═ θ, (σ), θ ═ θ1,θ2,..) unknown parameters that correct existing calculations for fitting to the test data; fmd(x) Representing the existing calculation formula for judging the earthquake damage mode of the RC column; gamma (x, theta) represents the deviation between the calculated value and the measured value of the existing formula; ε is the standard normal distribution variable with mean 0 and variance as unit 1; σ represents the standard deviation of the deviation-corrected probabilistic model.
The earthquake damage mode probability model of the reinforced concrete column is shown in the formula (1)
hi(x) Where i 1.
The above reinforced concrete column earthquake failure mode probability model is the existing deterministic model fm for distinguishing the earthquake failure mode of the reinforced concrete column in the formula (1)d(x) 0; meanwhile, the probability model formula (1) for judging the earthquake damage mode of the reinforced concrete column needs to satisfy the following two assumptions: model variance σ2Independent of variable x, homovariance assumption; epsilon is in accordance with normal distribution, and the assumption of normal distribution is made; to meet the hypothesis requirements, the model usually needs to be transformed reasonably; taking the natural logarithm form to satisfy the "covariance assumption", the probability model equations (1) and (2) can be expressed as:
in the earthquake damage mode probability model of the reinforced concrete column, the correction constant term h is selected from the formula (2)1(x) The deviation of the reaction model and the longitudinal rib reinforcement ratio h are represented by ln22(x)＝ln(ρl) Characteristic value h of longitudinal bar3(x)＝ln(ρlfy/fc'), volume coupling ratio h4(x)＝ln(ρsv) Characteristic value h of stirrup5(x)＝ln(ρsvfyv/fc') and axial pressure ratio h6(x)＝ln(P/Agfc'), shear-span ratio h7(x) Ln (a/d), ratio h of stirrup spacing to cross-sectional depth8(x) Where ln (s/d) is the "interpretation" function hi(x) (ii) a The mode of taking the natural logarithm of each function item is more favorable for the establishment and deviation of the model, so the 'explanation' function adopts the natural logarithm mode; the "interpretation" functions chosen for the correction are all dimensionless functions, with ln [ FM (x, Θ)]The dimensions of the components are consistent; these "interpretation" functions hi(x) Factors which may influence the earthquake damage mode of the RC column can be captured more comprehensively and are obtained by substituting the formula (3):
in the formula, ρlIs the longitudinal reinforcement ratio, fyIs the yield strength of the longitudinal bar, fc' is the compressive strength, rho, of the concrete cylindersvIs the volume coupling ratio of the stirrup, fyvIs the yield strength of the stirrup, P is the axial pressure, AgIs the total area of the section of the pier, a is the shear span, i.e. the high speed of the pier, d is the height of the section of the pier, and s is the stirrup spacing.
A method for predicting the earthquake damage mode probability of a reinforced concrete column comprises the following steps:
a. predicting whether the reinforced concrete column is subjected to bending damage, bending shear damage or shearing damage according to the earthquake damage mode probability model value of the reinforced concrete column;
b. the prediction criteria are as follows: for a rectangular stirrup column test piece, when FM is more than 0 and less than or equal to 4.3, the column is subjected to bending damage, when FM is more than 4.3 and less than or equal to 8, the column is subjected to bending shear damage, and when FM is more than 8, the column is subjected to shear damage; for a round or spiral stirrup column test piece, when FM is more than 0 and less than or equal to 5, the column is subjected to bending damage, when FM is more than 5 and less than or equal to 8.7, the column is subjected to bending shear damage, and when FM is more than 8.7, the column is subjected to shear damage.
By adopting the technical scheme, the invention has the beneficial effects that:
(1) based on Bayesian theory and method, a general method for establishing a probability statistical model through experimental data is provided under the condition that prior information or the existing model is lack and influence factors are ambiguous. The probability discrimination of the damage modes of the bending, shearing and bending shearing of the RC column is realized.
(2) The probability model for judging the earthquake damage mode of the reinforced concrete column considers the uncertainty of chance and cognition, and the model comprises the posterior statistics of the mean value and the standard deviation and has probability significance. Also, rather than performing regression analysis on all parameter combinations, any potentially important influencing factors are considered and their importance can be identified. Finally determining the volume banding rate rho as the factor which significantly influences the earthquake damage mode of the RC columnsvLongitudinal bar characteristic value rholfy/fc' and the shear-span ratio a/d.
(3) The method for predicting the earthquake damage mode probability of the reinforced concrete column is simple and convenient to apply, and the damage mode which is possible to happen can be judged only by inputting the design parameters of the reinforced concrete column. And the method has wide application range and is suitable for judging earthquake damage modes of rectangular, circular and spiral stirrup reinforced concrete columns.
Drawings
FIG. 1 is a diagram of a frequency distribution of a predicted earthquake bending failure of a 195 rectangular stirrup column test piece according to the invention.
FIG. 2 is a diagram of a frequency distribution of the predicted earthquake bending shear failure of a 195 rectangular stirrup column test piece according to the invention.
FIG. 3 is a diagram of a frequency distribution of the predicted earthquake shear failure of a 195 rectangular stirrup column test piece according to the invention.
FIG. 4 is a diagram of a frequency distribution of the 141 spiral stirrup column specimens for predicting earthquake bending failure according to the invention.
FIG. 5 is a diagram of a frequency distribution of the 141 spiral stirrup column samples in the invention for predicting earthquake bending shear failure.
FIG. 6 is a diagram of a frequency distribution of the 141 spiral stirrup column test pieces in the invention for predicting earthquake shear failure.
FIG. 7 is a comparison graph of the actual measurement seismic failure mode and the prediction result of the 195 rectangular stirrup column test pieces.
FIG. 8 is a diagram comparing the actual measurement seismic failure mode and the prediction result of the 141 spiral stirrup column test pieces.
FIG. 9 is a graph comparing the actual measurement seismic failure mode and the predicted result of 102 circular stirrup column test pieces and 209 spiral stirrup column test pieces of the invention.
Detailed Description
The model and method of the present invention will be described in detail below with reference to fig. 1, 2, 3, 4, 5, 6, 7, 8 and 9.
A reinforced concrete column seismic failure mode probability model represented as:
FM(x,Θ)＝fmd(x)+γ(x,θ)+σε (1)
in the formula, FM represents a random variable earthquake damage mode; x represents variables affecting the earthquake damage mode of the RC column, namely variables measured in the test, such as material characteristics, geometric dimension, reinforcing bars, axial pressure and the like; θ ═ θ, (σ), θ ═ θ1,θ2,..) unknown parameters that correct existing calculations for fitting to the test data; fmd(x) Representing the existing calculation formula for judging the earthquake damage mode of the RC column; gamma (x, theta) represents the deviation between the calculated value and the measured value of the existing formula; ε is the standard normal distribution variable with mean 0 and variance as unit 1; σ represents the standard deviation of the deviation-corrected probabilistic model.
In the reinforced concrete column earthquake failure mode probability model, because the real form of the existing model deviation correction term gamma (x, theta) is unknown, the model deviation correction term gamma (x, theta) is based on mechanism analysisAnd engineering experience, using some combination of influencing factors as 'interpretation' function hi(x) 1.. p, which is linearly expressed herein as:
that is, in the formula (1)
hi(x) Where i 1.
In the reinforced concrete column earthquake damage mode probability model, because the shearing action mechanism is complex, the damage mode model of the reinforced concrete column cannot be established from the theoretical and calculation angles at present for bending shear and shearing damage, and the existing deterministic model fm for judging the earthquake damage mode of the reinforced concrete column in the formula (1)d(x) 0; meanwhile, the probability model formula (1) for judging the earthquake damage mode of the reinforced concrete column needs to satisfy the following two assumptions: model variance σ2Independent of variable x, homovariance assumption; epsilon is in accordance with normal distribution, and the assumption of normal distribution is made; to meet the hypothesis requirements, the model usually needs to be transformed reasonably; taking the natural logarithm form to satisfy the "covariance assumption", the probability model equations (1) and (2) can be expressed as:
this probabilistic model can reasonably account for both incidental and cognitive uncertainty. Accidental uncertainties are inherent in nature and are unavoidable and not affected by the observer and the observation mode. The uncertainty of cognition mainly comes from the limit of object cognition, the selection of a simplified model, the error of test measurement and the range of effective sample data, and can be reduced by improving the model, precisely measuring and collecting a large number of samples. Occasional uncertainties are present in the variable x, and cognitive uncertainties are present in the unknown model parameters θ. The error term σ ε contains both incidental and cognitive uncertainty.
According to the analysis of factors influencing the earthquake damage mode of the RC columnMainly comprises the following steps: shear span ratio, axial compression ratio, longitudinal bar configuration, stirrup configuration, concrete and steel bar strength and the like. According to the research, the logarithm form of each function term (namely, influencing factor) is more favorable for establishing a model and correcting deviation, so that a correction constant term h is selected from the formula (2) of the reinforced concrete column earthquake failure mode probability model1(x) The deviation of the reaction model and the longitudinal rib reinforcement ratio h are represented by ln22(x)＝ln(ρl) Characteristic value h of longitudinal bar3(x)＝ln(ρlfy/fc'), volume coupling ratio h4(x)＝ln(ρsv) Characteristic value h of stirrup5(x)＝ln(ρsvfyv/fc') and axial pressure ratio h6(x)＝ln(P/Agfc'), shear-span ratio h7(x) Ln (a/d), ratio h of stirrup spacing to cross-sectional depth8(x) Where ln (s/d) is the "interpretation" function hi(x) (ii) a The mode of taking the natural logarithm of each function item is more favorable for the establishment and deviation of the model, so the 'explanation' function adopts the natural logarithm mode; the "interpretation" functions chosen for the correction are all dimensionless functions, with ln [ FM (x, Θ)]The dimensions of the components are consistent; these "interpretation" functions hi(x) Factors which may influence the earthquake damage mode of the RC column can be captured more comprehensively and are obtained by substituting the formula (3):
in the formula, ρlIs the longitudinal reinforcement ratio, fyIs the yield strength of the longitudinal bar, fc' is the compressive strength, rho, of the concrete cylindersvIs the volume coupling ratio of the stirrup, fyvIs the yield strength of the stirrup, P is the axial pressure, AgIs the total area of the section of the pier, a is the shear span, i.e. the high speed of the pier, d is the height of the section of the pier, and s is the stirrup spacing.
A reinforced concrete column earthquake failure mode probability model prediction method comprises the following steps:
a. predicting whether the reinforced concrete column is subjected to bending damage, bending shear damage or shearing damage according to the earthquake damage mode probability model value of the reinforced concrete column;
b. the prediction criteria are as follows: for a rectangular stirrup column test piece, when FM is more than 0 and less than or equal to 4.3, the column is subjected to bending damage, when FM is more than 4.3 and less than or equal to 8, the column is subjected to bending shear damage, and when FM is more than 8, the column is subjected to shear damage; for a round or spiral stirrup column test piece, when FM is more than 0 and less than or equal to 5, the column is subjected to bending damage, when FM is more than 5 and less than or equal to 8.7, the column is subjected to bending shear damage, and when FM is more than 8.7, the column is subjected to shear damage.
Assuming that the RC column earthquake damage mode FM respectively represents bending, bending shear and shearing damage by using a small value, a middle value and a large value, the invention takes ln (FM) 1, 2 and 3 (namely FM) e and e2、e3) Respectively, which represent measured values of bending, bending and shearing failures, which values can be adjusted by means of a control error term.
According to the experimental example, by means of a pacific earthquake research center RC column earthquake resistance test Database (PEER-Structural Performance Database) in America, pseudo-static test data of 336 pier columns with the axial-pressure ratio larger than 0 are arranged for analysis, wherein 195 rectangular stirrup columns are arranged, and 141 spiral stirrup columns (circular, octagonal and square sections) are arranged. The unknown parameter Θ (θ, σ) of equation (4) is estimated by a bayesian parameter estimation method. Take theta ═ theta1,...,θ8σ) to obtain a mean model for discriminating the seismic destruction mode of the RC column (assuming that e meets the standard normal distribution, take e to be 0):
the posterior mean of σ of equation (5) was 0.532. Some of the 8 factors may have insignificant influence on the establishment of the probability model, and the insignificant factors can be eliminated to simplify the formula (5).
When theta is equal to (theta)1,...,θ8Sigma) based on posterior distribution statistics, using Bayesian methodsSecondary "interpretation" function terms that are less influential can be progressively eliminated, simplifying the formula and improving the accuracy of the model (reducing the posterior mean of σ). According to theta ═ theta1,θ2,...,θ8]TThe posterior distribution of (A) can calculate the parameter thetaiCoefficient of variation (CV (theta))i)＝σi/μi,σiAnd muiRespectively represent thetaiStandard deviation and mean of a posterior distribution) for the maximum | CV (θ)i) To describe this thetaiCorresponding "interpretation" function hi(x) The influence on the judgment of the earthquake damage mode of the RC column is least remarkable, and the term can be eliminated. Rejection parameter thetaiAnd (4) after the corresponding function item is explained, estimating the posterior statistics of the model parameters by reapplying a Bayesian method to the rest model parameters. If the posterior mean value of sigma in the probability model formula (5) is continuously reduced, repeating the above process to remove the next item. Culling stops until the a posteriori mean of σ increases, indicating that the accuracy of the model is degraded, and this culling should be preserved. The simplified probability model obtained by the bayesian method is as follows:
the parameter Θ in the probabilistic model calculation formula (6) is (θ)1,θ3,θ7σ) are shown in Table 1. The parameter Θ in the formula (6) is expressed by a mean value (assuming that epsilon meets the standard normal distribution, and epsilon is 0), and an exponential function with e as the base is taken at both sides, and after arrangement, a simplified probability model for distinguishing the earthquake damage mode of the RC column can be obtained:
TABLE 1A posteriori statistics of simplified probabilistic model parameters
And (4.3) and 8 are respectively selected for the judgment boundaries a and b of the rectangular stirrup column test piece through optimization analysis calculation. When FM is more than 0 and less than or equal to 4.3, the probability of bending, bending shearing and shearing damage of the test piece is respectively 96 percent, 4 percent and 0; when FM is more than 4.3 and less than or equal to 8, the probability of bending damage, bending shear and shearing damage of the test piece is respectively 15%, 72% and 13%; when FM >8, the probability of the test piece undergoing bend failure, bend shear, and shear failure was 0, 13%, and 87%, respectively, as shown in fig. 1, 2, and 3.
For the spiral stirrup column test piece, 5 and 8.7 are respectively selected for the distinguishing boundaries a and b. When FM is more than 0 and less than or equal to 5, the probability of bending, bending shearing and shearing damage of the test piece is 93 percent, 7 percent and 0 respectively; when FM is more than 5 and less than or equal to 8.7, the probability of bending damage, bending shear and shearing damage of the test piece is respectively 13 percent, 75 percent and 12 percent; when FM >8.7, the probability of the test piece undergoing bend failure, bend shear and shear failure was 0, 16% and 84%, respectively, as shown in fig. 4, 5 and 6.
The validity of the experimental example of the invention is verified.
Fig. 7 and 8 show a comparison of the measured failure mode and the predicted (identified) failure mode for a 195 rectangular-stirrup reinforced concrete column test piece and a 141 spiral-stirrup reinforced concrete column test piece, respectively. The diagonal line represents the number of specimens predicted correctly and the off-diagonal line represents the number of specimens predicted incorrectly. The brackets are used to indicate the correct rate and error rate of the failure mode prediction. As can be seen from fig. 7, for the rectangular stirrup reinforced concrete column, the number of correctly predicted bending failures is 123, the number of correctly predicted bending shear failures is 27, and the number of correctly predicted shearing failures is 11; the prediction accuracy of bending, bend shearing and shearing failures is 63%, 14% and 6% respectively; the failure mode prediction accuracy is 83% (+ 63% + 14% + 6%). It can also be seen from fig. 8 that for the spiral stirrup reinforced concrete column, the bending failure prediction is correct 76, the bending shear failure prediction is correct 20, and the shear failure prediction is correct 22; the failure mode prediction accuracy is 84% (+ 54% + 14% + 16%).
In addition, 311 round or spiral stirrup column specimens (102 round stirrup column specimens, 209 spiral stirrup column specimens) from the document Mangalathu and Jeon [2019] were used as test sets, with 28 column specimens having an axial compression ratio equal to 0. Fig. 9 shows a comparison of the measured failure mode and the predicted (identified) failure mode for this 311-column test piece. It can be seen that for a circular or spiral stirrup RC column, the correct prediction of bending damage is 186, the correct prediction of bending shear damage is 40, and the correct prediction of shearing damage is 30; the failure mode prediction accuracy is 82% (+ 60% + 13% + 9%). Therefore, the probability discrimination method based on the Bayesian theory can reasonably reflect the failure mode of the reinforced concrete column under the earthquake action, has a wide application range, and is suitable for discriminating the earthquake failure modes of rectangular, round and spiral stirrup RC columns.
From the engineering application angle, the column is subjected to bending damage when FM is more than 0 and less than or equal to 4.3, bending shear damage when FM is more than 4.3 and less than or equal to 8 and shearing damage when FM is more than 8 for a rectangular stirrup column test piece; for a round or spiral stirrup column test piece, when FM is more than 0 and less than or equal to 5, the column is subjected to bending damage, when FM is more than 5 and less than or equal to 8.7, the column is subjected to bending shear damage, and when FM is more than 8.7, the column is subjected to shear damage.
By adopting the technical scheme, the invention has the following technical effects
(1) Based on Bayesian theory and method, a general method for establishing a probability statistical model through experimental data is provided under the condition that prior information or the existing model is lack and influence factors are ambiguous. The probability discrimination of the failure modes of bending, shearing and bending-shearing of the reinforced concrete column is realized.
(2) The probability model for judging the earthquake damage mode of the reinforced concrete column considers the uncertainty of chance and cognition, and the model comprises the posterior statistics of the mean value and the standard deviation and has probability significance. Also, rather than performing regression analysis on all parameter combinations, any potentially important influencing factors are considered and their importance can be identified. Finally determining the volume banding rate rho as the factor which significantly influences the earthquake damage mode of the RC columnsvLongitudinal bar characteristic value rholfy/fc' and the shear-span ratio a/d.
(3) The method for predicting the earthquake damage mode probability of the reinforced concrete column is simple and convenient to apply, and the damage mode which is possible to happen can be judged only by inputting the design parameters of the reinforced concrete column. And the method has wide application range and is suitable for judging earthquake damage modes of rectangular, circular and spiral stirrup reinforced concrete columns.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the overall concept of the invention, and these should be considered as the protection scope of the present invention, which will not affect the effect of the implementation of the present invention and the practicability of the patent.
Claims (5)
1. The utility model provides a reinforced concrete column earthquake failure mode probability model which characterized in that: the probability model of the earthquake damage mode of the reinforced concrete column is expressed as follows:
FM(x,Θ)＝fmd(x)+γ(x,θ)+σε (1)
in the formula, FM represents a random variable earthquake damage mode; x represents variables affecting the earthquake damage mode of the RC column, namely variables measured in the test, such as material characteristics, geometric dimension, reinforcing bars, axial pressure and the like; θ ═ θ, (σ), θ ═ θ1,θ2,..) unknown parameters that correct existing calculations for fitting to the test data; fmd(x) Representing the existing calculation formula for judging the earthquake damage mode of the RC column; gamma (x, theta) represents the deviation between the calculated value and the measured value of the existing formula; ε is the standard normal distribution variable with mean 0 and variance as unit 1; σ represents the standard deviation of the deviation-corrected probabilistic model.
2. A reinforced concrete column seismic failure mode probability model as claimed in claim 1 wherein: in the formula (1)
hi(x) Where i 1.
3. A reinforced concrete column seismic failure mode probability model as claimed in claim 1 wherein: the existing deterministic model fm for distinguishing the earthquake damage mode of the reinforced concrete column in the formula (1)d(x) 0; meanwhile, the probability model formula (1) for judging the earthquake damage mode of the reinforced concrete column needs to satisfy the following two assumptions: model variance σ2Independent of variable x, homovariance assumption; epsilon is in accordance with normal distribution, and the assumption of normal distribution is made; to meet the hypothesis requirements, the model usually needs to be transformed reasonably; taking the natural logarithm form to satisfy the "covariance assumption", the probability model equations (1) and (2) can be expressed as:
4. a reinforced concrete column seismic failure mode probability model according to claim 2, characterized in that: selecting a correction constant term h in the formula (2)1(x) The deviation of the reaction model and the longitudinal rib reinforcement ratio h are represented by ln22(x)＝ln(ρl) Characteristic value h of longitudinal bar3(x)＝ln(ρlfy/fc'), volume coupling ratio h4(x)＝ln(ρsv) Characteristic value h of stirrup5(x)＝ln(ρsvfyv/fc') and axial pressure ratio h6(x)＝ln(P/Agfc'), shear-span ratio h7(x) Ln (a/d), ratio h of stirrup spacing to cross-sectional depth8(x) Where ln (s/d) is the "interpretation" function hi(x) (ii) a The "interpretation" functions chosen are all dimensionless functions, with ln [ FM (x, Θ)]The dimensions of the components are consistent; it is substituted by the formula (3) to obtain:
in the formula, ρlIs the longitudinal reinforcement ratio, fyIs the yield strength of the longitudinal bar, fc' is the compressive strength, rho, of the concrete cylindersvIs the volume coupling ratio of the stirrup, fyvIs the yield strength of the stirrup, P is the axial pressure, AgIs the total area of the section of the pier, a is the shear span, i.e. the high speed of the pier, d is the height of the section of the pier, and s is the stirrup spacing.
5. A reinforced concrete column earthquake failure mode probability prediction method is characterized by comprising the following steps: the method comprises the following steps:
a. predicting whether the reinforced concrete column is subjected to bending damage, bending shear damage or shearing damage according to the reinforced concrete column earthquake damage mode probability model value in the claims 1-3;
b. the prediction criteria are as follows: for a rectangular stirrup column test piece, when FM is more than 0 and less than or equal to 4.3, the column is subjected to bending damage, when FM is more than 4.3 and less than or equal to 8, the column is subjected to bending shear damage, and when FM is more than 8, the column is subjected to shear damage; for a round or spiral stirrup column test piece, when FM is more than 0 and less than or equal to 5, the column is subjected to bending damage, when FM is more than 5 and less than or equal to 8.7, the column is subjected to bending shear damage, and when FM is more than 8.7, the column is subjected to shear damage.
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