1、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 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 1
2、8 July 2006; accepted 18 July 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 ar
3、e performed using the Latin 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 pa
4、rtial rank correlation coefficient (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
5、properties and environmental 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 h
6、umidity appear to be the most 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 s
7、tructures. Keywords： Uncertainty; 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 s
8、etting of bearings of concrete 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
9、moments in prestressed concrete 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 predicti
10、on errors stemming from several 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 stru
11、ctures are very complex phenomena 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
12、 the problem of creep and 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
13、be considered as an external 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
14、parameters are involved to 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 ho
15、w much the variation of each 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 e
16、t al. Another example for 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 wi
17、th the uncertainties in the 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 ran
18、dom variables employed in 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 assu
19、mptions and conceived models 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)
20、, the simulation process yields 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 run
21、s in time-dependent structural 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
22、 Y for each sample, the distribution 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
23、 of random permutations of 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. Th
24、is set is statistically assessed 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
25、 results of the Latin Hypercube 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 s
26、tandardized rank regression 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 const
27、ruction of regression models 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 r
28、espect to the input variables. 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
29、useful since they can provide 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
30、as follows: The PCC and SRC 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. Appli
31、cation to long-term prediction 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 F
32、ig. 2. It is a precast segmental 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 joi
33、ned at midspan. The cantilever 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 original
