Unbiased Statistical Comparison of Creep and Shrinkage Prediction Models

2008 ACI Materials Journal  
The paper addresses the problem of selecting the most realistic creep and shrinkage prediction model, important for designing durable and safe concrete structures. Statistical methods of standard and several nonstandard types and a very large experimental database have recently been used to compare and rank the existing prediction models, but conflicting results have been obtained by various investigators. This paper attempts to overcome this confusion. It introduces data weighting required to
more » ... ghting required to eliminate the bias due to improper data sampling in the database, and then examines Bažant and Baweja's model B3, ACI model, CEB model, and two Gardner's models. The statistics of prediction errors are based strictly on the method of least squares, which is the standard and the only statistically correct method, dictated by the maximum likelihood criterion and the central limit theorem of the theory of probability. Several nonstandard statistical methods that have recently been invented to deal with creep and shrinkage data are also examined and their deficiencies are pointed out. The ranking of the models that ensues is quite different from the rankings obtained by the nonstandard methods. 3) Model of Comité européen de béton, labelled CEB, which is based on the work of Müller and Hilsdorf [14] (it was adopted in 1990 by CEB [3], updated in 1999 [15], and co-opted in 2002 for Eurocode 2). 4) Gardner and Lockman's model, labelled GL [9]. 5) Gardner's earlier model, labelled GZ [6]. Sakata's model [5, 8] , whose scope is somewhat limited, as well as the crude old models of Dischinger, Illston, Nielsen, Rüsch and Jungwirth, Maslov, Arutyunyan, Aleksandrovskii, Ulickii, Gvozdev, Prokopovich and others [16, 17, 18] , will be left out of consideration. Although there exist certain fundamental theoretical requirements [19] , which are essential for choosing the right model, necessitate rejecting some models even before their comparison to test data, and happen to favor model B3, most engineers place emphasis on statistical comparisons with the existing experimental database. Therefore, this paper will deal exclusively with statistics. The first comprehensive database, comprising about 400 creep tests and about 300 shrinkage tests, was compiled at Northwestern University in 1978 [2], mostly from American and European tests. In collaboration with CEB, begun at the 1980 Rüsch Workshop [20], this database was slightly expanded by an ACI-209 subcommittee chaired by L. Panula. A further slight expansion was undertaken in a subcommittee of RILEM TC-107, chaired by H. Müller. It led to what became known as the RILEM database [21, 14, 22], which contained 518 creep tests and 426 shrinkage tests. Recently, a significantly enlarged database, named NU-ITI database [23] and consisting of 621 creep tests and 490 shrinkage tests, has been assembled in the Infrastructure Technology Institute of Northwestern University by adding many recent Japanese and Czech data. A reduced database, consisting of 166 creep tests and 106 shrinkage tests extracted from the RILEM database, has recently been used in Gardner's studies [24, 9, 25] . Among concrete researchers, a popular way to verify and calibrate a model has been to plot the measured values y k (k = 1, 2, ...n) from an experimental database against the corresponding model predictions Y k , or to plot the errors (or residuals) k = y k − Y k versus time (Fig. 1 ) [26, 27, 28 ]. If the model were perfect and the tests scatter-free, the former plot would give a straight line of slope 1, and the latter a horizontal line of ordinate 0. Fig. 1 shows examples of such plots for some of the aforementioned models and the NU-ITI database. One immediately notes that, in this kind of comparison, there is very little difference among the models, even those which are known to give very different long-time predictions. The same is true for another popular comparison where the ratio r k = y k /Y k is plotted versus time, for which, if the model were perfect and the tests scatter-free, one would get a horizontal plot r k = 1 (for problems of such kind of statistics, see comments on Eqs. 15 and 16 which follow). Therefore, such comparisons are ineffectual for our purpose. The causes are four: 1) The statistical trends are not reflected in such plots. 2) The statistics are dominated by the data for short times t − t , low ages t at loading and small specimen sizes D, while predictions for long times are of main interest for practice. This is due to highly nonuniform data distributions evident from the histograms in Fig. 2 . 3) Because of their longer test durations and high creep and shrinkage, the statistics are also dominated by the data for old low-strength concretes not in use any more. Long-duration tests of modern high strength concretes, which creep little, are still rare, as documented by Fig. 2. 4) The variability of concrete composition and other parameters in the database causes enormous scatter masking the scatter of creep and shrinkage evolution. If the worldwide testing in the past could have been planned centrally, so as to follow the
doi:10.14359/20203 fatcat:42fee7x5srhu5cl66zk6ilbc5i