عدم اطمینان و آنالیز حساسیت اثرات وابسته به زمان در سازه های بتنی

The purpose of this paper is to propose the method of uncertainty and sensitivity analysis of time-dependent effects due to creep and shrinkage of concrete in concrete structures. The uncertainty and sensitivity analyses are 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 partial 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 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 humidity 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 structures.

Time-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 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 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 [1], CEB-FIP Model Code 90 [2], etc. However, the application of current code formulations may result in considerable prediction 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 structures 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 the problem of creep and shrinkage with uncertainty modelling [3], [4], [5], [6] and [7] and with the variability in external loads [8] and [9]. The variation of creep and shrinkage properties is caused by various factors commonly classified as internal and external factors [10]. The change of environmental conditions, such as humidity, may 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 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 how 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 [11], [12], [13], [14] and [15]. Also, a review of different methods for this sensitivity analysis has been provided by Novák et al. [16]. Another example for sensitivity analysis is shown by Tsubaki [17]. 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 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 random 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.

A method of uncertainty and sensitivity analysis to assess the creep and shrinkage effects of concrete structures 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 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 time-dependent effects. The time-dependent effects versus time curves obtained from the numerical example indicate a significant statistical scatter in the predicted long-term axial shortening. The probability band widens with time, which indicates an increase of prediction uncertainty with time. Also, the proposed method can identify the most influential factors in the long-term prediction of structural response in concrete structures. The coefficients of the regression equations, or response surface equation, are related to the coefficient of determination and can be used to identify the most important model parameters. Numerical results indicate that the creep modelling uncertainty factor and the variability of relative humidity are two most significant factors on time-dependent effects such as axial shortening of girder and prestress force in prestressed concrete bridge. The proposed method can be efficiently used to perform a sensitivity analysis of time-dependent effects of concrete structures.