外文翻译不确定性和灵敏性在混凝土时间中所受影响的分析

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1、 外文原文一Uncertainty and sensitivity analysis of time-dependent effects inconcrete structuresIn Hwan YangDaelim Industrial Co., Ltd, Technical Research Institute, 146-12, Susong-dong, Jongro-ku, Seoul 110-732, Republic of KoreaReceived 21 March 2006; received in revised form 18 July 2006; accepted 18 J

2、uly 2006Available online 10 October 2006Abstract: The purpose of this paper is to propose the method of uncertainty and sensitivity analysis of time-dependent effects due to creep and shrink age of concrete in concrete structures. The uncertainty and sensitivity analyses are performed using the Lati

3、n Hypercube sampling method. For each sample, a time-dependent structural analysis is performed to produce response data, which are then analyzed statistically. Two measures are examined to quantify the sensitivity of the outputs to each of the input variables. These are partial rank correlation coe

4、fficient (PRCC) and standardized rank regression coefficient (SRRC) computed from the ranks of the observations. Three possible sources of the uncertainties of the structural response have been taken into account creep and shrinkage model uncertainty, variation of material properties and environment

5、al conditions. The proposed theory is applied to the uncertainty and sensitivity of time-dependent axial shortening and time-dependent prestress forces in an actual concrete girder bridge. The numerical results indicate that the creep model uncertainty factor and relative humidity appear to be the m

6、ost dominant factors with regard to the model output uncertainty. The method provides a realistic method of determining the uncertainty analysis of concrete structures and identifies the most important factors in the long-term prediction of time-dependent effects in those structures. Keywords： Uncer

7、tainty; Sensitivity; Concrete structures; Creep; Shrinkage 1.IntroductionTime-dependent effects of concrete structures result from creep and shrinkage of concrete. Creep and shrinkage are important factors in the design of concrete structures. For example, they affect the setting of bearings of conc

8、rete bridges including the size of sliding plates or laminated bearing pads. They also affect the sizing and setting of expansion joints due to time-dependent axial shortening arising from creep and shrinkage effects of prestress force and thereby also affect the secondary moments in prestressed con

9、crete bridges. The creep and shrinkage models which are capable of predicting long-term structural response are specified in design codes such as ACI 209-92, CEB-FIP Model Code 90, etc.However, the application of current code formulations may result in considerable prediction errors stemming from se

10、veral sources of uncertainty. They predict only mean values and cannot predict the statistical variation. Therefore, a method to deal with the uncertainty involved in the prediction of creep and shrinkage effects of concrete is necessary.Creep and shrinkage in concrete structures are very complex ph

11、enomena in which various uncertainties exist with regard to inherent material variations as well as modelling uncertainties. The study on the uncertainties in creep and shrinkage effects has been continuously an area of significant efforts. Particular attention has given to the problem of creep and

12、shrinkage with uncertainty modelling and with the variability in external loads. The variation of creep and shrinkage properties is caused by various factors commonly classified as internal and external factors. The change of environmental conditions, such as humidity, may be considered as an extern

13、al factor. The internal factors include the variation of the quality and the mix composition of the materials used in concrete and the variation due to internal mechanism of creep and shrinkage.In the prediction formulas of creep and shrinkage of concrete, various kinds of parameters are involved to

14、 express the characteristics of concrete under consideration, i.e. the mix proportion of concrete, the shape of the structure, relative humidity, etc. Since it is not possible to remove the statistical variation involved in the parameters, it may be necessary to estimate how much the variation of ea

15、ch parameter influences the predicted values. Several different approaches of sensitivity analysis have been developed as numerical tools for reliability assessment of structures. Also, a review of different methods for this sensitivity analysis has been provided by Novak et al. Another example for

16、sensitivity analysis is shown by Tsubaki.The aim of the present study is to propose an analytical approach for the uncertainty and sensitivity analyses of creep and shrinkage effects in concrete structures utilizing the models in the design codes. The present study deals with the uncertainties in th

17、e long-term prediction of creep and shrinkage effects, taking into account the statistical variation of both internal and external factors as well as the uncertainty of the model itself. The sensitivity analysis is performed to show the relative importance of individual random variables employed in

18、the creep and shrinkage models. The time-dependent axial shortening of a prestressed concrete girder bridge is analyzed to show the application of proposed method.2. Method of uncertainty analysisSimulation is the process of replicating the real world based on a set of assumptions and conceived mode

19、ls of reality. It may be performed theoretically or experimentally. For engineering purposes simulation may be applied to predict or study the performance and/or response of a system or structure. With a prescribed set of values for the system parameter (or design variable), the simulation process y

20、ields a specific measure of performance or response. A conventional approach to this process is the Monte Carlo simulation technique. However, in practice, Monte Carlo simulations may be limited by constraints, computer capability and the significant expense of computer runs in time-dependent struct

21、ural analysis of concrete bridges. An alternative approach is to use a constrained sampling scheme. One such scheme, developed by Iman and co-workers, is Latin Hypercube sampling (LHS) method. By sampling from the assumed probability density function of the _ and evaluating Y for each sample, the di

22、stribution of Y , its mean, standard deviation and percentiles etc., can be estimated. The representative value in each interval is used just once during the simulation procedure and so there are N observations on each of the K input variables. They are ordered in the table of random permutations of

23、 rank numbers which have N rows and K columns. Each row of a table is used on the ith computer run. For such a sample one can evaluate the corresponding value Yn of the output variable. From N simulations one can obtain a set of statistical data Y = Y1, Y2, . . . , YN T. This set is statistically as

24、sessed and thus the estimations of some statistical parameters, such as the mean value and the variance of the response, are obtained. Interested readers are referred to Novak et al. for a more detailed discussion of this sampling method.3. Method of sensitivity analysisThe results of the Latin Hype

25、rcube simulations can be used to determine which of the model parameters are most significant in affecting the uncertainty of the design. Two closely related, but different, measures will be examined in this study. These are partial rank correlation coefficient (PRCC) and standardized rank regressio

26、n coefficient (SRRC) computed on the ranks of the observations. This method is particularly useful when there are a large number of inputs and several outputs having an associated time history.Sensitivity analysis in conjunction with sampling is closely related to the construction of regression mode

27、ls which approximate the behaviour calculated by the computer runs. The constant b0 and the ordinary regression coefficient bj are obtained by the usual methods of least squares. The ordinary regression coefficients are the partial derivatives of the regression model with respect to the input variab

28、les. However, these ordinary regression coefficients are easily influenced by the units in which the variables are measured.The coefficient of b_j in standardized models is called the standardized regression coefficient. It is a unit free measurement; such coefficients are useful since they can prov

29、ide a direct measure of the relative importance of the input variables. After making N runs of the model with varying input, a correlation matrix between the input and output is computed for a given step in the output time history. Let the correlation matrix be represented as follows: The PCC and SR

30、C measure the linear association between variables. When nonlinear relationships are involved, it is often more revealing to calculate the SRCs and PCCs on variable integer ranks than on the actual values for the variables. Such coefficients are the SRRCs and PRCCs.4. Application to long-term predic

31、tion of axial shorteningand prestress force in concrete bridges4.1. Description of structure and finite element modelingThe bridge deck consists of seven continuous spans and each span is 50 m long. The 50 m interior span of the 7-continuous span bridge system is shown in Fig. 2. It is a precast seg

32、mental prestressed concrete girder bridge whose typical cross section is also shown in Fig. 2. The interior span of the box girder has nine segments per cantilever (i.e. per half span). The segments are placed symmetrically on both sides of the span. The cantilevers are joined at midspan. The cantil

33、ever tendons (top slab tendons) anchored in each segment are stressed at the time of erection of that segment, while the continuity tendons (bottom slab tendons) are stressed after midspan joining as shown in Fig. 2.The finite element analysis method in this study is based on the procedure developed

34、 originally by Kang and improved by Oh and Yang for the analysis of segmentally erected prestressed concrete bridges. This procedure involves the timedependent prediction of deformations and an assessment of prestress losses in such structures under construction stage, and after completion of struct

35、ures. A box girder of arbitrary plane geometry and variable cross section can be modelled as an assembly of finite elements interconnected at nodal points. Each element is divided into a discrete number of concrete and reinforcing steel layers.The analytical model for structural analysis consists of

36、 20 nodes, 19 frame elements and 22 prestressing tendons. The cross section is subdivided into 9 layers (Fig. 2). The twenty nodes are located at segment joints along the centroidal axis of the box girder. Nineteen frame elements are used to model the box girder. The elements are prismatic with the

37、cross-section of a point at the mid length of the element. Each cantilever segment and midspan closure segment (key segment) is modelled with one frame element. Twenty-twoprestressing tendons are used to model the cantilever and continuity prestressing tendons. Dead load consists of self weight and

38、the design dead load. The design dead load of 29.4 kN/m, is assumed to be applied permanently, which contributes to creep.4.2. Statistical properties of input variablesShrinkage and creep model uncertainty factors (1, 2), compressive strength of concrete ( f 0 c ), relative humidity (h), sandaggrega

39、te ratio (s/a), slump (S), and cement contents (c) are assumed to be random variables. All random variables are assumed to be normally distributed. It is also assumed that these variables are independent, which is a simplification. Each random variable is represented by its mean value and coefficien

40、t of variation. The numerical values for the mean and the coefficient of variation of input variables are listed in Table 1 for ACI 209-92 model and in Table 2 for CEBFIP MC 90 model. Model uncertainty factors for prediction models of creep and shrinkage were already examined in Eqs. (7) and (11) in

41、 the previous section. The numerical values for relative humidity and compressive strength of concrete were determined using the observed data in the sites. The values for remaining variables were selected on the basis of nominal values of mix design of concrete.The site for the bridge has four seas

42、ons a year. The relative humidity is high in summer and low in winter. The variation of relative humidity is significant over a year. To investigate the distribution of relative humidity, the records from the Meteorological Observatory (about 3 km north of the present bridge) were analyzed statistic

43、ally and the probability distribution function was ascertained. Also, to investigate the distribution of compressive strength of concrete in 28 days, the results from strength test of concrete cylinders which had been used in construction were analyzed statistically and the probability distribution

44、function was obtained.4.3. Uncertainty analysis results of the axial shortening of concrete girderIf the values of input variables _1, _2, . . . , _K are specified, the creep and shrinkage effects or response Y (_i , t) at time t, such as the axial shortening of concrete girder, can be calculated by

45、 running a computer program through the deterministic analysis of the structure. The statistical prediction of axial shortening of concrete girder after continuity tendons are all stressed at midspan has been calculated for 20 samples of parameter _i , which represent the number of computer runs.Eac

46、h comparison of shrinkage and creep compliance predictions using ACI 209-92 model and those using CEBFIP MC 90 model is shown in Fig. 3 and Fig. 4. Each curve represents mean value and mean (2 standard deviation). Shrinkage prediction using the ACI 209-92 model is larger than that using CEB-FIP MC 9

47、0 model but creep compliance prediction using ACI 209-92 model is smaller than that using CEB-FIP MC 90 model.The prediction of axial shortening versus time obtained using ACI 209-92 model is plotted in Fig. 5. The dashed lines in these figures represent Y 2s(t), in which Y = mean response at age t,

48、 and s(t) = standard deviation of the response at age t. As might be expected, the probability band width of structural response widens with time, indicating an increase of prediction uncertainty with time. To assure long-term serviceability it seems reasonable to require that the design of concrete

49、 girder bridges should be based on these limits.4.4. Sensitivity analysis results of axial shortening and prestress forceThe sensitivity analysis results of axial shortening of girder using ACI 209-92 model are shown in Fig. 6. For the present problem, the most highly correlated parameters measured

50、by the SRRC and PRCC is the creep model uncertainty factor. The two most important variables are creep model uncertainty factor and relative humidity. The creep model uncertainty factor has positive SRRCs and PRCCs, which indicates that an increase of this variable tends to increase the axial shorte

51、ning. The relative humidity has negative SRRCs and PRCCs, which indicates that increase of this variable tends to decrease the axial shortening. This effect may occur because increase of relative humidity tends to reduce the humidity correction factor in ACI 209-92 model and thus decrease the creep

52、coefficient and shrinkage value. The variables of creep model uncertainty factor and relative humidity consistently appear as important variables in the analyses presented in these figures. The variable with the next largest SRRCs and PRCCs is shrinkage model uncertainty factor. It is also seen that

53、 the positive correlation is shown for shrinkage model uncertainty factor, which indicates that increasing this variable tends to increase the amount of shrinkage strains. The sensitivity analysis results indicate that axial shortening was inversely correlated with concrete strength and weakly posit

54、ively correlated with slump, sandaggregate ratio and cement content.The sensitivity analysis results of axial shortening of girder using CEB-FIP MC 90 model are shown in Fig. 7. The most highly correlated parameters measured by the SRRC and PRCC is relative humidity. The most important variable at e

55、arly ages is creep model uncertainty factor. The value of the SRRCs and PRCCs of creep model uncertainty factor decreases gradually with time. The value of the SRRCs and PRCCs of shrinkage model uncertainty factor increases gradually with time. Relative humidity and shrinkage model uncertainty facto

56、r are two most important variables at 10,000 days. Creep model uncertainty factor and shrinkage model uncertainty factor have positive SRRCs and PRCCs for axial shortening, while relative humidity and compressive strength of concrete have negative SRRCs and PRCCs for axial shortening.The sensitivity

57、 analysis results of prestress force using the ACI 209-92 model are shown in Fig. 8. For the present problem, the most highly correlated parameters measured by the SRRC and PRCC are the creep model uncertainty factor. The two most important variables are creep model uncertainty factor and relative h

58、umidity. The creep model uncertainty factor has negative SRRCs and PRCCs, which indicates that an increase of this variable tends to decrease the prestress forces. The relative humidity has positive SRRCs and PRCCs, which indicates that increase of this variable tends to increase the prestress force

59、. This effect may occur because increase of relative humidity tends to reduce the humidity correction factor in ACI 209-92 model and thus decrease the creep coefficient and shrinkage value. The prestress force has an inverse relation with the creep coefficient and shrinkage value. The variables of c

60、reep model uncertainty factor and relative humidity consistently appear as important variables in the analyses presented in these figures. The variable with the next largest SRRCs and PRCCs is shrinkage model uncertainty factor. It is also seen that the negative correlation is shown for shrinkage mo

61、del uncertainty factor, which indicates that increasing this variable tends to lower the prestress forces. The sensitivity analysis results indicate that prestress force is positively correlated with concrete strength and weakly negatively correlated with slump, sandaggregate ratio and cement conten

62、t.The sensitivity analysis results obtained for the CEB-FIP MC 90 model are shown in Fig. 9. The most highly correlated variable measured by the SRRC and PRCC is relative humidity.The most important variable at early ages is the creep model uncertainty factor. The value of the SRRCs and PRCCs of the

63、 creep model uncertainty factor decreases gradually with time. The value of the SRRCs and PRCCs of the shrinkage model uncertainty factor increases gradually with time. Relative humidity and the shrinkage model uncertainty factor are the two most important variables at 10,000 days. The creep model u

64、ncertainty factor and shrinkage model uncertainty factor have negative SRRCs and PRCCs whereas relative humidity and compressive strength of concrete have positive SRRCs and PRCCs.5. ConclusionsA method of uncertainty and sensitivity analysis to assess the creep and shrinkage effects of concrete str

65、uctures such as prestressed concrete bridges is proposed. Latin Hypercube simulation technique was used to study the uncertainty of model parameters. The samples are obtained according to underlying probabilistic distributions, and then the outputs from the numerical simulations are translated into

66、probabilistic distributions. The statistical method developed in this study predicts the variability of the long term prediction of time dependent effects of concrete structures. It provides measures of the expected uncertainty and the distribution of timedependent effects. The time-dependent effects versus time curves obtained from the numerica