JP2007113967A - Method of evaluating reliability of structure deteriorated due to aging - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To evaluate reliability of a structure, while taking deterioration due to aging of the structure into consideration, even when information about the load and the strength has not been obtained completely. <P>SOLUTION: In this method, a probability density function is deduced for each characteristic variable, based on investigation data an actual condition of the deteriorated structure due to aging and a questionnaire investigation data to an expert, relative occurrence of ease for each combination of values in the characteristic variables is calculated, based on the probability density in each characteristic variables, finite element analysis is carried out for each combination, probability density function of a generation stress is deduced, based on the generation stress for each combination, obtained as a result of the finite element analysis and the relative occurrence of ease for each combination, and a breakage probability and a safety index are calculated, based on the probability density function of the generation stress and the probability density function of the strength that has been set, based on the existing data. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method for evaluating the reliability of a structure that has deteriorated over time. More specifically, the present invention relates to a method for evaluating the reliability of a structure in which member corrosion or the like has occurred due to aging.

  In the present invention, a variable related to aging of a structure is expressed as a characteristic variable.

  In order to formulate a rational maintenance plan for an aged civil engineering structure, as in the design stage, it is necessary to include external events such as earthquakes, winds, and waves, as well as loads caused by deterioration and operation. Risk assessment that takes into account typical events is necessary. In the risk assessment, first, it is necessary to quantitatively grasp the current and future reliability of the target structure. The application of structural reliability theory in the civil engineering field is summarized in Non-Patent Document 1, for example.

Japan Society of Civil Engineers Structural Engineering Committee: Structural Engineering Series 2 Evaluation of Lifetime Risk of Structures, 1988.

  However, some actual structures include a plurality of members and the load-displacement relationship exhibits nonlinear behavior. In addition, particularly for outdoor structures, it is rare that complete information on load and strength is obtained. For this reason, it is practically difficult to grasp the characteristics of all random variables and to strictly calculate the fracture probability based on the bond probability density function. Therefore, it is difficult to say that the reliability evaluation of Non-Patent Document 1 is a general-purpose method that can be widely applied to any structure.

  Therefore, an object of the present invention is to provide a method capable of evaluating the reliability of a structure while taking into account the aging of the structure even when information on the load and strength is not completely obtained. .

  In order to achieve such an object, the reliability evaluation method for an aged structure according to the present invention is a probability density function for each characteristic variable based on survey data on the actual condition of an aged structure and questionnaire survey data for experts. Is calculated from the probability density for each characteristic variable, and the relative likelihood of each characteristic variable value combination is calculated, and the frequency distribution of the generated stress obtained by the finite element analysis performed for each combination is calculated for each combination. The probability density function is estimated from the frequency distribution of the generated stress converted using the relative likelihood of occurrence, and the fracture probability and the probability density function based on the probability density function of the generated stress and the strength probability density function set from existing data are calculated. Calculate safety indicators.

  Therefore, according to the reliability evaluation method for this structure, a questionnaire survey is performed on experts, and the probability density function of the value of the characteristic variable is estimated based on the questionnaire survey data. Further, the relative probability of occurrence for each combination of characteristic variable values is calculated, and the probability density function of the value of the generated stress in consideration of the relative probability of occurrence is estimated. Further, the fracture probability and the safety index are calculated based on the probability density function of the generated stress and the probability density function of the strength, and the reliability of the structure is evaluated.

  As described above, according to the structure reliability evaluation method of the present invention, information on the load of the structure is obtained by estimating the probability density function of the value of the characteristic variable based on questionnaire survey data to experts. Even if it is not given completely, the reliability of the structure can be evaluated without performing a huge number of calculations, so it is possible to evaluate various structures and improve versatility. Is possible. In addition, by estimating the probability density function of the value of the generated stress considering the relative likelihood of each combination of characteristic variable values, the generated stress corresponding to the actual state can be assumed, It is possible to improve the accuracy of the reliability evaluation of structures.

  Hereinafter, the configuration of the present invention will be described in detail based on the best mode shown in the drawings.

  1 to 6 show an example of an embodiment of a structure reliability evaluation method of the present invention. In the present embodiment, a dam spillway radial gate (hereinafter simply referred to as a radial gate) 1 shown in FIG. 2 is taken as an example of a structure for which reliability evaluation is performed (hereinafter referred to as an evaluation target structure). ing. In addition, since the radial gate of this embodiment is left-right symmetric, only the right half of the radial gate when facing the surface to the skin plate 4 is an object of reliability evaluation.

  In this structure reliability evaluation method, as shown in the flow of FIG. 1, a step (S1) of creating a three-dimensional finite element analysis model for performing finite element analysis and a frequency distribution for each characteristic variable are created. Step (S2), step (S3) for estimating a probability density function for each characteristic variable, step (S4) for performing finite element analysis for each combination of characteristic variable values, and occurrence for each combination of characteristic variable values A step of calculating easiness (S5), a step of creating a frequency distribution of minimum principal stress by finite element analysis (S6), a step of estimating a probability density function of minimum principal stress (S7), and a probability density of strength It comprises a function setting step (S8) and a step of evaluating the reliability of the structure (S9).

(1) Creation of 3D finite element analysis model (S1)
First, a three-dimensional finite element analysis model for performing finite element analysis is created. Finite element analysis itself and creation of an analysis model for performing finite element analysis are well-known techniques, and finite element analysis and creation of an analysis model according to the present invention are the same as in the conventional method, and therefore details are omitted here. .

  There are no particular restrictions on the number of elements and the number of nodes in the 3D finite element analysis model, and the work takes into account the size of the structure to be evaluated, the amount of work required for finite element analysis, and the accuracy of the required analysis results The person sets an appropriate number of elements and number of nodes. Specifically, for example, it is conceivable to create a three-dimensional finite element analysis model in the order of thousands of elements and nodes. However, the present invention is not limited to this, and a smaller number of elements / nodes can be used. The number of elements / nodes may be good or larger. Furthermore, when the structure to be evaluated is symmetrical, the entire structure may be converted into an analysis model, or only one of the left and right halves of the structure is analyzed as in this embodiment. You may make it model.

  In the present embodiment, as shown in FIG. 2, some of the auxiliary members such as the main girder 2, the leg column 3, the skin plate 4, the inter-leg column connecting member 5, and the stringer 6 of the radial gate 1 are three-dimensional thin-walled. The other auxiliary member 7 is modeled by a three-dimensional beam element. The three-dimensional finite element analysis model of this embodiment has 6184 elements and 5882 nodes.

(2) Creation of frequency distribution for each characteristic variable (S2)
Next, a frequency distribution of characteristic variables is created. The characteristic variable is set according to the members constituting the structure to be evaluated. Specifically, for example, the amount of corrosion of the member and the friction coefficient of the movable member can be considered, but this is not a limitation, and factors that may affect the reliability of the structure due to aging are considered as characteristic variables. Set.

  Then, survey data on the actual condition of each factor set as a characteristic variable, case data shown in the literature, and the like are collected, and a frequency distribution is created for each of the characteristic variables using the actual survey data and the like.

  In addition, if the actual survey data for the factors set as characteristic variables are not sufficient to create a frequency distribution, research on the structure to be evaluated is necessary to reflect the so-called expert opinion. A questionnaire survey is conducted on experts such as engineers and engineers, and a frequency distribution of characteristic variables is created based on the questionnaire survey results. In this case, the frequency distribution may be created using only the questionnaire survey data, or the frequency distribution may be created by combining the questionnaire survey data and the above-described actual survey data. good.

  Further, the range of possible values for each characteristic variable is set in consideration of the frequency distribution created as described above. The setting method of the range of possible values is not particularly limited, and is set as appropriate by the operator. Specifically, for example, it is conceivable to set from the minimum value and the maximum value of values whose characteristic variable values are greater than 0, but as described above, the method is not limited to this method.

  In this embodiment, the corrosion of the members constituting the radial gate 1 and the change in the sliding frictional resistance of the trunnion pin 9 of the radial gate support are considered as factors that affect the structural reliability of the radial gate 1 due to aging. Then, a frequency distribution of the average corrosion amount (hereinafter simply referred to as the average corrosion amount) of the members constituting the radial gate 1 and the friction coefficient of the trunnion pin (hereinafter simply referred to as the friction coefficient) is created.

  Regarding the average corrosion amount, the corrosion of the four members of the skin plate 4 of the radial gate 1, the main girder 2, the pedestal 3 and the main girder stiffener 8 is considered. Since the frequency distribution of the average corrosion amount of these members reflects the actual corrosion of the hydraulic structure, we collect the survey data of the actual condition of the hydraulic structure and the case data shown in the literature. The frequency distribution of the average corrosion amount is created using the survey data.

  In this embodiment, the investigation data of 62 locations of hydraulic iron pipes (Koji Numazaki: Investigation on corrosion and strength of existing hydraulic iron pipes, Electric Power Engineering, No. 151, pp. 37-40, 54, 1977.) and gate 71 Data of 37 locations and hydraulic iron pipes (Taguchi Yasuaki et al .: Hydraulic steel pipe soundness investigation method research report-Corrosion survey of hydraulic iron pipe small abutment by special ultrasonic wave-, Shimon iron pipe, No. 211, pp.54 -59, June 2002.) to create a frequency distribution of the average corrosion amount.

  The range of values that the average corrosion amount can take is set to 0.0 mm to 2.0 mm in consideration of the frequency distribution.

  In addition, since the frequency distribution of the friction coefficient reflects the so-called expert opinion, a questionnaire survey was conducted to ask experts about the range of pin friction coefficient values in actual hydraulic structures, and the questionnaire survey data was used. To create a frequency distribution of the coefficient of friction.

  In the present embodiment, a questionnaire survey is conducted on a total of 30 power company engineers, manufacturer engineers, consultant company engineers, and laboratory researchers who are experts in hydraulic structures, and the questionnaire survey data is used. A frequency distribution of the friction coefficient is created (FIG. 3).

  The range of values that the friction coefficient can take is set to 0.0 to 1.0 in consideration of the frequency distribution.

(3) Estimation of probability density function for each characteristic variable (S3)
Next, a probability density function is estimated using the nonlinear least square method for the frequency distribution created in S2. The distribution form of the probability density function of the characteristic variable is not particularly limited, and any distribution form may be used. Specifically, for example, a lognormal distribution, an exponential distribution, a Rayleigh distribution, a Frechet distribution, a Weibull distribution, and the like can be considered, but as described above, the distribution form is not limited thereto.

  In the present embodiment, the average corrosion amount and the friction coefficient are modeled with a lognormal distribution (FIGS. 4 and 5).

(4) Finite element analysis for each combination of characteristic variable values (S4)
Next, using the three-dimensional finite element analysis model created in S1, the finite element analysis is performed using the characteristic variables set in S2 as parameters, and the minimum principal stress (compressive stress) at the stress evaluation location of the structure to be evaluated is calculated. To do. Then, the value of the minimum principal stress having the maximum absolute value among the calculated values of the minimum principal stress is extracted. As described above, since the finite element analysis itself is a well-known technique, the details are omitted here.

  Here, regarding the setting of the stress evaluation location, in this embodiment, the location where the fracture mode and the stress are maximized is specified by performing the nonlinear structural analysis of the radial gate 1, and the failure cases of the radial gate that have occurred in the past are specified. (Koji Kawamura and Shunji Nakano: Summary of the cause investigation report of the Wachi Dam Gate, Civil Engineering Data, Vol. 10, No. 9, pp. 26-32, September 1968, US Department of the Interior, Bureau of Reclamation, Mid Pacific Region: Forensic Report Excerpt Spillway Tainter Gate3 Failure, Folsom Dam, CA, USA, 1996. and Fosker. H. et al .: Improved Diagnostics for Detecting Friction on Dam Gates, Water Power & Dam Construction, pp. 39-41, August 2001.). Based on the results of nonlinear structural analysis and past accidents, in the case of a radial gate, considering that the buckling of the pedestal base of the radial gate that occurs during winding is the most problematic, the base of the pedestal 3 of the radial gate 1 is The stress evaluation location O was set. In the three-dimensional finite element analysis model, a plurality of elements are designated as stress evaluation points O.

  Subsequently, a finite element analysis using the average corrosion amount and the friction coefficient as parameters is performed using the three-dimensional finite element analysis model created in S1, and the minimum principal stress at the stress evaluation point O of the radial gate 1 is calculated. Then, the value of the minimum principal stress having the maximum absolute value among the calculated values of the minimum principal stress is extracted.

The finite element analysis for the radial gate 1 of the present embodiment was performed according to the following procedure.
(Step 1) Self-weight analysis: The self-weight acting on each part is obtained from the volume and unit weight of the steel material of the radial gate 1, and a stress analysis is performed on this.

  (Step 2) Analysis at design flood level load: Stress is analyzed by applying the design flood level to the radial gate 1 statically.

  (Step 3) Analysis with a hoisting load applied: The hoisting load caused by the friction of the trunnion pin 9 is applied statically to the hoisting wire attachment portion 10 to perform stress analysis.

  The boundary conditions of the finite element analysis of the present embodiment are that, in Step 1 and Step 2, the roller is supported in the horizontal direction by the radial gate ground surface 11 or the winding wire attaching portion 10 and only the rotation by the trunnion pin 9 is free. . In step 3, the boundary condition is changed and rigidly connected by the trunnion pin 9, the winding wire attachment portion 10 is made free, and the winding load accompanying the trunnion pin friction is applied to the winding wire attachment portion 10.

  Here, the purpose of S4 is to perform a finite element analysis for each state in which the value of the characteristic variable is changed, and to calculate the minimum principal stress at the stress evaluation location for each state. At this time, the characteristic variable is changed within the range of the value set in S2. Specifically, the value range set in S2 is divided into several values, and finite element analysis is performed for each value at both ends of the value range and the boundary value of the division. Here, the number of divisions in the value range of the characteristic variable is not particularly limited, and is set as appropriate by the operator in consideration of the amount of work required for the analysis and the required analysis accuracy. Specifically, for example, it can be considered to be about 10 categories (in this case, the number of cases in which the value of the characteristic variable is changed is 11 cases), but is not limited to this as described above. Further, when dividing the range of the value of the characteristic variable, the entire range may be equally divided or unequal.

  The finite element analysis is performed for each combination of cases in which the value of each characteristic variable is changed. Therefore, the total number of cases for which the finite element analysis is performed is a number obtained by multiplying the number of cases of each characteristic variable. In the following, the characteristic variables set in S2 are characteristic variable A and characteristic variable B, the case of the value of characteristic variable A is case i (i = 1, 2,...), And the case of the value of characteristic variable B is case. j (j = 1, 2,...), and a combination of these cases is referred to as case (i, j). Then, finite element analysis is performed for each case (i, j) to calculate the minimum principal stress (compressive stress) at the stress evaluation location of the structure to be evaluated, and the absolute value is the largest among the calculated minimum principal stress values. Extract the minimum principal stress value.

  In this embodiment, a finite element analysis is performed for each combination of the average corrosion amount value and the friction coefficient value. In this embodiment, the case of the average corrosion amount is case i (i = 1, 2,...), The case of the coefficient of friction is case j (j = 1, 2,...), And combinations thereof. This case is referred to as case (i, j). Then, the finite element analysis is performed for each case (i, j) to calculate the minimum principal stress at the stress evaluation point O of the radial gate 1, and the minimum principal stress having the maximum absolute value among the calculated minimum principal stress values. Extract the value.

  In this embodiment, as set in S2, the range of the value of the average corrosion amount is 0.0 mm to 2.0 mm, and the range of this value is equally divided into 10 to perform finite element analysis for 11 cases. Moreover, the range of the value of the friction coefficient is 0.0 to 1.0, and the range of this value is equally divided into five to perform finite element analysis on six cases. Therefore, in this embodiment, a finite element analysis is performed for a total of 66 cases (= 11 × 6), and the absolute value is the largest among the values of the minimum principal stress at the stress evaluation point O of the radial gate 1 for each case. Extract the minimum principal stress value.

(5) Calculation of the likelihood of occurrence for each combination of characteristic variable values (S5)
Next, the relative likelihood of occurrence for each combination of characteristic variable values is calculated. The relative likelihood of occurrence for each combination of characteristic variable values is calculated using a probability density based on the probability density function for each characteristic variable estimated in S3. Specifically, the relative likelihood between cases (i, j) of the combination of the value of the characteristic variable A and the value of the characteristic variable B is expressed by (Equation 1).

(Equation 1) w _{i, j} = f _A (a _i ) × f _B (b _j )
Where w _{i, j is} the relative likelihood of case (i, j), and f _A (a _i ) is the probability density when the value of characteristic variable A is a _i (case i of characteristic variable A) , F _B (b _j ): probability density when the value of the characteristic variable B is b _j (case j of the characteristic variable B).

(6) Creation of frequency distribution of minimum principal stress (S6)
Next, the combination of the absolute value maximum of the minimum principal stress at the stress evaluation point of the structure to be evaluated and the value of the characteristic variable calculated in S5 for each case (i, j) of the combination of the characteristic variable values calculated in S4. The frequency distribution of the minimum principal stress is created using the relative likelihood w _{i, j} for each case (i, j). Specifically, the value of the relative likelihood w _{i, j} of case (i, j) is accumulated as the frequency of the minimum principal stress of case (i, j) calculated as a result of finite element analysis. By doing in this way, this frequency distribution becomes a more realistic frequency distribution in consideration of the relative ease of occurrence between cases (i, j).

(7) Estimating probability density function of minimum principal stress (S7)
Next, the shape of the probability distribution is estimated using the nonlinear least square method for the frequency distribution of the minimum principal stress created in S6. The distribution form of the probability density function of the minimum principal stress is not particularly limited, and any distribution form may be used. Specifically, for example, a lognormal distribution, an exponential distribution, a Rayleigh distribution, a Frechet distribution, a Weibull distribution, and the like can be considered, but as described above, the distribution form is not limited thereto.

  In this embodiment, the probability density function of the minimum principal stress is estimated using a lognormal distribution.

(8) Setting of probability density function of intensity (S8)
When yield strength is treated as a random variable, the distribution form is set based on the survey data of the actual yield strength of the structure to be evaluated, case data shown in the literature, etc. It is possible.

  In this embodiment, in order to reflect the actual state of an aged hydraulic steel structure and impose severe material conditions for the maintenance of an aged hydraulic steel structure, survey data and literature on the actual yield strength of the hydraulic steel structure Is collected, and the probability density function of intensity is set using the survey data of the actual situation. Specifically, the actual value of the yield strength of the hydraulic iron pipes installed in the Showa 20s (Yoshi Numasaki: About the strength of welded pipes in the Showa 20s, Electric Power Engineering, No. 167, pp. 76-79, 1980 )), The probability density function of intensity is set with the distribution form of the probability density function as a normal distribution.

  The stress probability density function (S7) and strength probability density function (S8) of the present embodiment calculated as described above are as shown in FIG.

(9) Evaluation of structure reliability (S9)
In this method, the failure probability of the structure and the safety index β are calculated using a first-order Gaussian second-moment method. Since the first-order Gaussian approximation itself is a well-known technique, details are omitted here (for example, Hasofer, AM and NC Lind: Exact Invariant Second-Moment Code Format, J. Eng. Mech. Div., ASCE, Vol. 100, No. EM1, pp. 111-121, 1974.).

Specifically, first, as shown in (Expression 2), the performance function Z _i = g (X ₁ ,..., X _n ) is changed to a point on the limit state surface g (X ₁ ,..., X _n ) = 0. Taylor expansion is performed around x ⁰ = (x ⁰ ₁ ,..., x ⁰ _n ).

  If the series on the right side of (Equation 2) is truncated at the first-order term, (Equation 3) is obtained.

Assuming that all the random variables in (Equation 3) are approximated by normal random variables, (Equation 3) is a linear linear function of the normal random variables, and Z _i is also a normal random variable. That is, if the average value μ _Zi and standard deviation σ _Zi of Z _i can be obtained, the failure probability P _f can be calculated by (Equation 4) without using (Equation 3).

In the present invention, variables that cannot be regarded as normal random variables are treated as non-normal random variables, and the safety index is calculated. Here, when (Equation 3) is rewritten with the average value μ _xj of each random variable, ( _Equation 5) is obtained.

Here, if an arbitrary point x ^* is a point on the performance function Z _i = 0, (Expression 6) is established.

The average value μ _z of Z _i is obtained from (Equation 7), and the variance σ _z of Z _i is obtained from (Equation 8).

However, α _j in ( _Equation 8) is as (Equation 9).

  Then, the safety index β is calculated by (Equation 10).

(Equation 10) β = μ _z / σ _z

Smaller failure probability P _f is calculated by the above, also structural reliability of the radial gate 1 larger the safety index β is evaluated as high.

  In addition, although the above-mentioned form is an example of the suitable form of this invention, it is not limited to this, A various deformation | transformation implementation is possible in the range which does not deviate from the summary of this invention. In the present embodiment, the number of characteristic variables is two. However, the number is not limited to this, and three or more characteristic variables may be set. In this case, the relative likelihood for each combination of characteristic variable values is calculated from the multidimensional probability distribution.

  In the present embodiment, the load at the design flood level is applied as the hydrostatic pressure load of the dam. However, the hydrostatic pressure load of the dam is not limited to this and is adapted to the purpose of the structural reliability evaluation. The structural reliability should be evaluated by setting the water level of the dam. Furthermore, a load due to seismic motion may be considered. In this case, a load due to seismic motion is applied based on the seismic intensity. In this case as well, the seismic intensity may be set in accordance with the purpose of the structural reliability evaluation, a load due to the earthquake motion may be applied, and the structural reliability may be evaluated.

  Furthermore, in the present embodiment, changes due to aging of the intensity are not taken into consideration, but the present invention is not limited to this, and a probability density function for each elapsed period in which the intensity decreases depending on the elapsed years may be estimated.

It is a flowchart which shows an example of embodiment of the reliability evaluation method of the structure of this invention. It is a perspective view which shows a three-dimensional finite element analysis model (element division figure) with the whole radial gate outline | summary of this embodiment. It is a frequency distribution figure of the trunnion pin friction coefficient of this embodiment. It is a figure which shows the probability density function of the average corrosion amount of the radial gate of this embodiment. It is a figure which shows the probability density function of the trunnion pin friction coefficient of this embodiment. It is a figure which shows the probability density function of the stress and intensity | strength in the stress evaluation location O of this embodiment.

Explanation of symbols

1 radial gate 2 main girder 3 pedestal 9 trunnion pin

Claims (1)

  Estimating the probability density function for each characteristic variable based on the survey data on the actual condition of the structure deteriorated over time and the questionnaire survey data to experts, and the relative value for each combination of the characteristic variables from the probability density for each characteristic variable From the frequency distribution of the generated stress obtained by converting the frequency distribution of the generated stress obtained by the finite element analysis performed for each combination using the relative likelihood of the combination for each combination. A reliability evaluation method for an aged structure that estimates a probability density function and calculates a fracture probability and a safety index based on a probability density function of the generated stress and a probability density function of strength set from existing data.

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