CN111339497A - Probability prediction model for evaluating strength index of recycled concrete - Google Patents

Probability prediction model for evaluating strength index of recycled concrete Download PDF

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CN111339497A
CN111339497A CN202010145622.9A CN202010145622A CN111339497A CN 111339497 A CN111339497 A CN 111339497A CN 202010145622 A CN202010145622 A CN 202010145622A CN 111339497 A CN111339497 A CN 111339497A
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recycled concrete
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徐金俊
陈文广
鲁骏
陈杰
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Nanjing Fuyuan Resource Utilization Co ltd
Nanjing Tech University
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Abstract

The invention discloses a probability prediction model for evaluating a strength index of recycled concrete, which not only takes various factors influencing the strength index of the recycled concrete into consideration, but also can know the following factors through comparative analysis among a prior model calculated value, a posterior model calculated value and a test value: the Bayesian model has certain deviation from the existing model, so that Bayesian inference can better utilize the advantage of good accuracy of natural information, prior information and the model can be utilized and updated, and the calculated value of the posterior model can be closer to the test result. The invention fully embodies the application of data mining and big data analysis in civil engineering.

Description

Probability prediction model for evaluating strength index of recycled concrete
Technical Field
The invention relates to an evaluation method of a recycled concrete strength index, in particular to a probability prediction model for evaluating the recycled concrete strength index.
Background
The recycled concrete is prepared by crushing, cleaning and grading waste concrete blocks, mixing the crushed, cleaned and graded waste concrete blocks with grading according to a certain proportion, and partially or completely replacing natural aggregates. However, due to the essential characteristic of the recycled concrete material that it has great discreteness, its strength index is different from that of natural aggregate concrete. Therefore, before the recycled concrete is widely used in the construction industry, an accurate relationship between the strength index and the mix ratio needs to be established. Compressive strength, flexural strength, tensile strength at cleavage and modulus of elasticity are key material properties for concrete structure analysis and design. However, since existing models are mostly limited to a specific subset of samples, it is difficult to develop reliable and accurate expressions to predict the recycled concrete strength index. In order to further improve the prediction accuracy of the model, the invention provides a probability prediction model for evaluating the strength index of the recycled concrete by mining and analyzing the existing test data, estimating unknown parameters, correcting a prior model and establishing a posterior model, thereby more accurately predicting the strength index of the recycled concrete.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a probability prediction model for evaluating the strength index of recycled concrete.
The technical scheme of the invention is as follows: a probability prediction model for evaluating strength indexes of recycled concrete comprises the following steps:
(1) bayesian multivariate statistical probabilistic inference uses prior information and sample information. The prior information is a calculation method of the existing recycled concrete strength index, wherein the calculation method comprises the cubic uniaxial compressive strength (f) of the recycled concretecu) Uniaxial compressive strength (f) of cylindercy) Flexural strength (f)r) Tensile strength at cleavage (f)st) Triaxial compressive strength (f)cc) Uniaxial elastic modulus (E)cu) And triaxial elastic modulus (E)cc) And 7 recycled concrete strength indexes are calculated, and sample information is a database which is completed with experimental research. And the Bayesian method is applied to synthesize the two types of information for inference, so that the posterior distribution of the strength index of the recycled concrete is obtained.
(2) And (3) establishing a prediction model of the strength index of the recycled concrete according to the Bayesian theory provided in the step (1) and the calculation method of the strength index of the recycled concrete. On a certain basis, the method corrects the deviation in the existing deterministic model, so that the predicted result is closer to the test result.
(3) According to the recycled concrete strength index prediction model established in the step (2), a series of functions g influencing the recycled concrete strength index parameters are adoptedi(y) as a correction term.
(4) Based on conjugate prior distribution and variance σ2Posterior edge distribution to eliminate g with insignificant influence on the whole in step (3)iAnd (y) so as to achieve the purpose of eliminating the parameters.
(5) And (4) obtaining a posterior calculation formula of the strength index of the recycled concrete according to the elimination parameters in the step (4) and by combining model verification and comparative analysis.
Preferably, the step (1) of a priori knowledge of the uniaxial compressive strength (f) of the existing recycled concrete cubecu) The calculation formula is as follows:
Figure BDA0002400609580000021
uniaxial compressive strength (f) of recycled concrete cylindercy)：
Figure BDA0002400609580000022
Breaking strength (f) of recycled concreter)：
fr[MPa]＝0.022·(1.2-0.002R％)·(2.3-0.3weff/c)6.9
Cleavage tensile strength (f) of recycled concretest)：
fst[MPa]＝0.012·(0.9-0.002R％)·(2.1-0.3weff/c)9.1
Recycled concrete triaxial compressive strength (f)cc)：
fcc[MPa]＝fcy+5.009·σ3
Uniaxial modulus of elasticity (E) of recycled concretecu)：
Ecu[MPa]＝0.016·(6.1-0.015R％)·(5.3-1.7weff/c)3.9
Recycled concrete triaxial modulus of elasticity (E)cc)：
Ecc[GPa]＝5.243+0.058fcc
The 328 groups of regenerated concrete cubic uniaxial compression test piece test database comprises:
Figure BDA0002400609580000023
Figure BDA0002400609580000031
in the table, S1 and S2 represent 150mm cube specimens each having a 100mm edge length.
303 group recycled concrete cylinder unipolar compression test piece test database do:
Figure BDA0002400609580000032
Figure BDA0002400609580000041
in the table, C1 and C2 represent 150mm diameter cylindrical test pieces having a diameter of 100mm, respectively.
The 145 groups of recycled concrete bending test piece test databases are as follows:
Figure BDA0002400609580000042
in the table, B1 and B2 represent 100 × 100 × 500mm prism test pieces and 150 × 150 × 750mm prism test pieces, respectively.
324 recycled concrete splitting tensile test piece test databases are:
Figure BDA0002400609580000043
Figure BDA0002400609580000051
the 113 groups of recycled concrete triaxial test piece test databases are as follows:
Figure BDA0002400609580000052
the 415 groups of recycled concrete uniaxial elastic modulus test database comprises:
Figure BDA0002400609580000053
Figure BDA0002400609580000061
given the data y, bayesian centers on computing the posterior distribution f (θ | y) of the parameter θ. The general pattern of bayesian inference is:
Figure BDA0002400609580000071
in the formula, f (theta) is prior information of the strength index of the recycled concrete; f (y | theta) is a likelihood function of the recycled concrete strength index; f (theta | y) is the posterior distribution of the recycled concrete strength index.
Preferably, the prediction model of the recycled concrete strength index in step (2) is:
ln[T(Y,φ)]＝ln[Td(Y)]+γ(Y,θ)+σε
in the formula, Y represents a vector form of factors influencing the strength index of the recycled concrete; Φ (θ, σ) represents a posterior estimate of the trial parameters corrected by fitting the trial data; t isdRepresenting an existing calculation formula of the strength index of the recycled concrete; theta is ═ theta1,θ2,……θp]TRepresents a correction coefficient for Y; γ (Y, θ) represents the deviation between the already existing formula and the exact value; ε is a random variable; sigma2Is the variance of the error produced by the a posteriori distribution. To fit the model to the test results, the variance σ2Independent of the strength index factor Y of the recycled concrete. The variable of T (Y, phi) is the variance sigma2And ε follows a standard normal distribution.
To find the deviation γ (Y, θ), it can be linearly expressed by p functions as:
Figure BDA0002400609580000072
in the formula, gi(y) is a function of parameters affecting the recycled concrete strength index, and on the basis of two preconditions, can obtain:
Figure BDA0002400609580000073
preferably, the function g influencing the strength index parameter of the recycled concrete in the step (3)i(y) is:
g1(y)＝1，g2(y)＝R％，g3(y)＝ln(weff/c)，g4(y)＝ln(a/c)，g5(y)＝ln(Dmax,r/Dmax,n)
wherein R% is the substitution rate of recycled aggregate, weffC is the effective water cement ratio, a/c is the aggregate-cement ratio, Dmax,r/Dmax,nIs the ratio of the maximum recycled concrete size to the maximum natural coarse aggregate size.
Preferably, σ in the step (4)2When the change is small, it indicates the removed gi(y) and θ corresponding theretoiThe influence on the whole is not obvious, the steps are eliminated, and the steps are repeated when the sigma is less than the threshold value2With large variation, i.e. sigma2When significantly increased, the removed g is indicatedi(y) and θ corresponding theretoiIf the influence on the whole is obvious, the elimination is stopped.
The cubic uniaxial compressive strength (f) of the recycled concretecu) Middle elimination of g with insignificant overall effectiThe process and method are as follows:
Figure BDA0002400609580000081
in table, g5(y) maximum coefficient of variation, g1The coefficient of variation of (y) is minimal. By analysis of giAnd (y) carrying out Bayesian parameter elimination according to the variation coefficient of the (y) in descending order.
With proposed uniaxial compressive strength (f) of the cube of recycled concretecu) The formula is used as a prior model to carry out Bayesian correction, and the parameter elimination process is as follows:
Figure BDA0002400609580000082
in the table, "X" represents a culled function item, "O" represents an uncapped function item, and "1-5" represent a step process of a culling parameter.
Figure BDA0002400609580000083
The uniaxial compressive strength (f) of the recycled concrete cylindercy) Middle elimination of g with insignificant overall effectiThe process and method are as follows:
Figure BDA0002400609580000084
in table, g5(y) maximum coefficient of variation, g1(y) minimum coefficient of variation。
With the proposed uniaxial compressive strength (f) of the recycled concrete cylindercy) The formula is used as a prior model to carry out Bayesian correction, and the parameter elimination process is as follows:
Figure BDA0002400609580000085
Figure BDA0002400609580000091
Figure BDA0002400609580000092
the recycled concrete has flexural strength (f)r) Middle elimination of g with insignificant overall effectiThe process and method are as follows:
Figure BDA0002400609580000093
in table, g5(y) maximum coefficient of variation, g1The coefficient of variation of (y) is minimal.
With the proposed breaking strength (f) of the recycled concreter) The formula is used as a prior model to carry out Bayesian correction, and the parameter elimination process is as follows:
Figure BDA0002400609580000094
Figure BDA0002400609580000095
the recycled concrete has cleavage tensile strength (f)st) Middle elimination of g with insignificant overall effectiThe process and method are as follows:
Figure BDA0002400609580000096
Figure BDA0002400609580000101
in table, g5(y) maximum coefficient of variation, g1The coefficient of variation of (y) is minimal.
With the proposed cleavage tensile strength (f) of the recycled concretest) The formula is used as a prior model to carry out Bayesian correction, and the parameter elimination process is as follows:
Figure BDA0002400609580000102
Figure BDA0002400609580000103
the recycled concrete has three-axis compressive strength (f)cc) Middle elimination of g with insignificant overall effectiThe process and method are as follows:
Figure BDA0002400609580000104
in table, g2(y) maximum coefficient of variation, g1The coefficient of variation of (y) is minimal.
With proposed triaxial compressive strength (f) of recycled concretecc) The formula is used as a prior model to carry out Bayesian correction, and the parameter elimination process is as follows:
Figure BDA0002400609580000105
Figure BDA0002400609580000106
Figure BDA0002400609580000111
the uniaxial elastic modulus (E) of the recycled concretecu) Middle elimination of g with insignificant overall effecti(y) Process and methodComprises the following steps:
Figure BDA0002400609580000112
in table, g5(y) maximum coefficient of variation, g1The coefficient of variation of (y) is minimal.
With the proposed uniaxial modulus of elasticity (E) of the recycled concretecu) The formula is used as a prior model to carry out Bayesian correction, and the parameter elimination process is as follows:
Figure BDA0002400609580000113
Figure BDA0002400609580000114
the recycled concrete has three-axis elastic modulus (E)cc) Middle elimination of g with insignificant overall effectiThe process and method are as follows:
Figure BDA0002400609580000115
in table, g2(y) maximum coefficient of variation, g1The coefficient of variation of (y) is minimal.
With the proposed triaxial elastic modulus (E) of the recycled concretecc) The formula is used as a prior model to carry out Bayesian correction, and the parameter elimination process is as follows:
Figure BDA0002400609580000116
Figure BDA0002400609580000128
Figure BDA0002400609580000121
preferably, the recycled concrete of the step (5)Cubic uniaxial compressive strength (f)cu) The posterior calculation formula:
Figure BDA0002400609580000122
uniaxial compressive strength (f) of recycled concrete cylindercy) The posterior calculation formula:
Figure BDA0002400609580000123
breaking strength (f) of recycled concreter) The posterior calculation formula:
Figure BDA0002400609580000124
cleavage tensile strength (f) of recycled concretest) The posterior calculation formula:
Figure BDA0002400609580000125
recycled concrete triaxial compressive strength (f)cc) The posterior calculation formula:
fcc[MPa]＝(fcy+5.009σ3)·e0.041
uniaxial modulus of elasticity (E) of recycled concretecu) The posterior calculation formula:
Figure BDA0002400609580000126
recycled concrete triaxial modulus of elasticity (E)cc) The posterior calculation formula:
Figure BDA0002400609580000127
the invention has the beneficial effects that:
provides a probability prediction model for evaluating the strength index of the recycled concrete, which not only considers the influence on the strength index of the recycled concreteSuch as the substitution rate of recycled aggregate (R%), the effective water-cement ratio (w)effAnd/c), aggregate-cement ratio (a/c), etc., and is known from comparative analysis of prior model calculation, posterior model calculation, and test values with each other: the Bayesian model has certain deviation from the existing model, so that Bayesian inference can better utilize the advantage of good accuracy of natural information, prior information and the model can be utilized and updated, and the calculated value of the posterior model can be closer to the test result.
The invention fully embodies the application of data mining and big data analysis in civil engineering. The data mining and big data analysis architecture comprises four major stages of engineering problem definition and architecture, test database preparation, probability prediction model establishment and result verification and evaluation.
Drawings
FIG. 1 is a Bayesian inference probabilistic predictive model for civil engineering that can be modeled as a rule and pattern.
FIG. 2 is a graph of the three-axis compressive strength (f) of recycled concrete based on its databasecc) And establishing a prior model.
FIG. 3 is a three-axis modulus of elasticity (E) of recycled concrete based on its databasecc) And establishing a prior model.
FIG. 4 is a graph of the cubic uniaxial compressive strength (f) of recycled concrete based on its databasecu) And (5) testing and verifying.
FIG. 5 is a graph of the uniaxial compressive strength (f) of recycled concrete cylinders based on its databasecy) And (5) testing and verifying.
FIG. 6 shows the flexural strength (f) of recycled concrete based on its databaser) And (5) testing and verifying.
FIG. 7 is a graph of recycled concrete split tensile strength (f) based on its databasest) And (5) testing and verifying.
FIG. 8 is a graph of the three-axis compressive strength (f) of recycled concrete based on its databasecc) And (5) testing and verifying.
FIG. 9 is the uniaxial modulus of elasticity (E) of recycled concrete based on its databasecu) And (5) testing and verifying.
FIG. 10 is a graph based on the numbers thereofDatabase recycled concrete triaxial modulus of elasticity (E)cc) And (5) testing and verifying.
Detailed Description
The following will build a prediction model of the recycled concrete strength index in the technical scheme of the invention and g with insignificant influence on the wholeiThe removal method of (y) will be further described.
Establishing a strength index prediction model of the recycled concrete:
the core of bayesian is to calculate the posterior distribution of the parameter θ, so the prior information f (θ) and the likelihood function f (y | θ) should be determined first. The Bayesian assumption can be used to obtain that the non-information prior distribution f (theta, sigma) of the parameters (theta, sigma) is uniformly distributed in the value range of (theta, sigma), and the mathematical expression is as follows:
f(θ)∝1,θ∈φ
f(σ)＝σ-1,σ＞0
Figure BDA0002400609580000131
the likelihood function f (y | θ) can be expressed as:
Figure BDA0002400609580000141
in the formula, α represents a normal distribution probability density function, β represents a normal distribution function
Through experimental study recycled concrete destruction test piece, proposed under unipolar or triaxial compression load, recycled concrete test piece's the critical expression form of destruction:
the failure test shows that: ln [ T (Y, phi)]＝ln[Td(Y)]+γ(Y,θ)+σε
The upper bound represents: ln [ T (Y, phi)]＞ln[Td(Y)]+γ(Y,θ)+σε
The lower bound represents: ln [ T (Y, phi)]＜ln[Td(Y)]+γ(Y,θ)+σε
Removing g with insignificant effect on the wholei(y) method:
based on Bayesian theorem, the Bayesian theorem is known to have a relationship between a Bayesian prediction value and a test valueSmaller errors, g that have insignificant overall effect should be rejectedi(y) then:
ln[Ti/Tdi]＝θ1g1i(y)+θ2g2i(y)+…+θpgpi+σiεi
let ln [ Ti/Tdi]＝WiIt can be expressed in matrix form as:
W＝g(y)θ+σε
wherein W is (W)1…Wn)T，
Figure BDA0002400609580000142
θ＝(θ1…θp)T
According to the least square method, the following steps are obtained: θ' ═ g (y)Tg(y))-1g(y)TW, shape parameter v ═ n-p, error Sn 2＝(W-W’)T(W-W'), the likelihood function is:
Figure BDA0002400609580000143
known from bayesian assumptions: the a posteriori distribution density function f (θ, σ | W, g (y)) of the parameters (θ, σ) is proportional to the product of the likelihood function f (y | θ) and the a priori distribution density f (θ, σ), and then:
Figure BDA0002400609580000144
integrating theta from both sides of the above equation, the posterior edge distribution of the standard deviation sigma is easily obtained:
Figure BDA0002400609580000145
from the posterior edge distribution of the standard deviation sigma, the variance sigma can be found2Posterior edge distribution density function of (1):
Figure BDA0002400609580000146
from bayesian probability statistics, the standard definition of inverse Gamma distribution is:
Figure BDA0002400609580000151
Figure BDA0002400609580000152
can know sigma2The posterior edge distribution being an inverse Gamma distribution, i.e. sigma2～IG(v/2,Sn 2/2), obtainable from the standard definition of the inverse Gamma distribution:
Figure BDA0002400609580000153
thus the variance σ2The Bayesian posterior estimated value is Sn 2/v-2＝Sn 2N-p-2. By analysing the variance σ2The degree of change of the correction term is used for judging the degree of decision of the correction term on the strength index of the recycled concrete, and g with insignificant influence on the whole is further removediAnd (y) so as to achieve the purpose of eliminating the parameters.
It should be noted that, for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be construed as the protection scope of the present invention. Components not explicitly described in this example can be implemented using existing techniques.

Claims (6)

1. A probability prediction model for evaluating strength indexes of recycled concrete is characterized in that: the method comprises the following steps:
(1) bayesian multivariate statistical probability inference, prior information and sample information are used; the prior information is a calculation method of the existing recycled concrete strength index, wherein the calculation method comprises the cubic uniaxial compressive strength f of the recycled concretecuCompressive strength f of single axis of cylindercyBending strength frTensile strength at cleavage fstTriaxial compressive strength fccUniaxial elastic modulus EcuAnd triaxial modulus of elasticity EccThe method comprises the following steps of (1) calculating 7 recycled concrete strength indexes, wherein sample information is a database which is completed with experimental research; the Bayesian method is applied to synthesize the two types of information for inference, so that the posterior distribution of the strength index of the recycled concrete is obtained;
(2) establishing a prediction model of the strength index of the recycled concrete according to the Bayesian theory provided in the step (1) and the calculation method of the strength index of the recycled concrete; the method corrects the deviation in the existing deterministic model, so that the predicted result is closer to the test result;
(3) according to the recycled concrete strength index prediction model established in the step (2), a function g influencing the recycled concrete strength index parameter is adoptedi(y) as a correction term;
(4) based on conjugate prior distribution and variance σ2Posterior edge distribution to eliminate g with insignificant influence on the whole in step (3)i(y), thereby achieving the purpose of eliminating parameters;
(5) and (4) obtaining a posterior calculation formula of the strength index of the recycled concrete according to the elimination parameters in the step (4) and by combining model verification and comparative analysis.
2. The probabilistic predictive model for evaluating a strength index of recycled concrete according to claim 1, wherein: the existing uniaxial compressive strength f of the recycled concrete cube of the prior information in the step (1)cuThe calculation formula is as follows:
Figure FDA0002400609570000011
uniaxial compressive strength f of recycled concrete cylindercy：
Figure FDA0002400609570000012
Breaking strength f of recycled concreter：
fr[MPa]＝0.022·(1.2-0.002R％)·(2.3-0.3weff/c)6.9
Cleavage tensile strength f of recycled concretest：
fst[MPa]＝0.012·(0.9-0.002R％)·(2.1-0.3weff/c)9.1
Recycled concrete triaxial compressive strength fcc：
fcc[MPa]＝fcy+5.009·σ3
Uniaxial elastic modulus E of recycled concretecu：
Ecu[MPa]＝0.016·(6.1-0.015R％)·(5.3-1.7weff/c)3.9
Regenerated concrete triaxial elastic modulus Ecc：
Ecc[GPa]＝5.243+0.058fcc
The database of the sample information comprises a plurality of groups of cubic single-axis compression test pieces of the recycled concrete, cylindrical single-axis compression test pieces, bending test pieces, splitting tensile test pieces, three-axis compression test pieces, single-axis elastic modulus test pieces and three-axis elastic modulus test pieces;
given the data y, bayesian centers on computing the posterior distribution f (θ | y) of the parameter θ. The general pattern of bayesian inference is:
Figure FDA0002400609570000021
in the formula, f (theta) is prior information of the strength index of the recycled concrete; f (y | theta) is a likelihood function of the recycled concrete strength index; f (theta | y) is the posterior distribution of the recycled concrete strength index.
3. The probabilistic predictive model for evaluating a strength index of recycled concrete according to claim 1, wherein: the prediction model of the strength index of the recycled concrete in the step (2) is as follows:
ln[T(Y,φ)]＝ln[Td(Y)]+γ(Y,θ)+σε
in the formula, Y represents a vector form of factors influencing the strength index of the recycled concrete; Φ (θ, σ) represents a posterior estimate of the trial parameters corrected by fitting the trial data; t isdRepresenting an existing calculation formula of the strength index of the recycled concrete; theta is ═ theta1,θ2,……θp]TRepresents a correction coefficient for Y; γ (Y, θ) represents the deviation between the already existing formula and the exact value; ε is a random variable; sigma2Is the variance of the error produced by the posterior distribution; to fit the model to the test results, the variance σ2Independent of the strength index factor Y of the recycled concrete; the variable of T (Y, phi) is the variance sigma2And ε follows a standard normal distribution;
to solve the deviation γ (Y, θ), it is linearly expressed by p functions:
Figure FDA0002400609570000022
in the formula, gi(y) is a function influencing the index parameters of the recycled concrete strength, and on the basis of two preconditions, the following parameters are obtained:
Figure FDA0002400609570000023
4. the probabilistic predictive model for evaluating a strength index of recycled concrete according to claim 1, wherein: the function g influencing the index parameter of the strength of the recycled concrete in the step (3)i(y) is:
g1(y)＝1，g2(y)＝R％，g3(y)＝ln(weff/c)，g4(y)＝ln(a/c)，g5(y)＝ln(Dmax,r/Dmax,n)
wherein R% is the substitution rate of recycled aggregate, weffC is the effective water cement ratio, a/c is the aggregate-cement ratio, Dmax,r/Dmax,nIs the ratio of the maximum recycled concrete size to the maximum natural coarse aggregate size。
5. The probabilistic predictive model for evaluating a strength index of recycled concrete according to claim 1, wherein: in the step (4), g is analyzedi(y) carrying out Bayesian parameter elimination according to the variation coefficient of the (y) in the descending order; when sigma is2When the change is small, it indicates the removed gi(y) and θ corresponding theretoiThe influence on the whole is not obvious, the steps are eliminated, and the steps are repeated when the sigma is less than the threshold value2With large variation, i.e. sigma2When significantly increased, the removed g is indicatedi(y) and θ corresponding theretoiIf the influence on the whole is obvious, the elimination is stopped.
6. The probabilistic predictive model for evaluating a strength index of recycled concrete according to claim 1, wherein: the cubic uniaxial compressive strength f of the recycled concrete in the step (5)cuThe posterior calculation formula:
Figure FDA0002400609570000031
uniaxial compressive strength f of recycled concrete cylindercyThe posterior calculation formula:
Figure FDA0002400609570000032
breaking strength f of recycled concreterThe posterior calculation formula:
Figure FDA0002400609570000033
cleavage tensile strength f of recycled concretestThe posterior calculation formula:
Figure FDA0002400609570000034
recycled concrete triaxial compressive strength fccThe posterior calculation formula:
fcc[MPa]＝(fcy+5.009σ3)·e0.041
uniaxial elastic modulus E of recycled concretecuThe posterior calculation formula:
Figure FDA0002400609570000035
regenerated concrete triaxial elastic modulus EccThe posterior calculation formula:
Figure FDA0002400609570000041
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112883463A (en) * 2021-01-18 2021-06-01 华北水利水电大学 Reinforced concrete column earthquake failure mode probability model and probability prediction method thereof

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107122547A (en) * 2017-04-27 2017-09-01 上海理工大学 Sophisticated testing uncertainty evaluation method based on Bayes principle
CN107871038A (en) * 2017-10-31 2018-04-03 南京林业大学 A kind of method of prediction FRP- steel compound constant concrete cylindrical compression full curve
CN110826199A (en) * 2019-10-21 2020-02-21 清华大学 Method for updating concrete structure durability prediction model based on incomplete information

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107122547A (en) * 2017-04-27 2017-09-01 上海理工大学 Sophisticated testing uncertainty evaluation method based on Bayes principle
CN107871038A (en) * 2017-10-31 2018-04-03 南京林业大学 A kind of method of prediction FRP- steel compound constant concrete cylindrical compression full curve
CN110826199A (en) * 2019-10-21 2020-02-21 清华大学 Method for updating concrete structure durability prediction model based on incomplete information

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
党伟;申世飞;刘喜;: "贝叶斯概率模型计算钢筋混凝土柱受剪承载力" *
吴涛;刘喜;邢国华;: "基于贝叶斯理论的钢筋混凝土柱受剪承载力计算" *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112883463A (en) * 2021-01-18 2021-06-01 华北水利水电大学 Reinforced concrete column earthquake failure mode probability model and probability prediction method thereof

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