Statistical Evaluation of Shrinkage and Creep Models

The objective of this study is to evaluate four shrinkage and creep prediction models, namely the ACI 209 model, the CEB 90 model, the B3 model, and the GL 2000 model. The shrinkage and creep values determined by the models are compared against the RILEM experimental data bank. Five statistical methods are used to determine the order of performance of each model. The study finds that the B3 and the GL 2000 are best performing models for shrinkage strain prediction while the CEB 90, B3, and GL 2000 models perform best for creep prediction.

Keywords: creep; shrinkage; test.

(ProQuest Information and Learning: ... denotes formulae omitted.)

INTRODUCTION

Shrinkage and creep have a significant impact on the performance of concrete structures. They cause deflections and affect the stress distribution in reinforced concrete structures and within concrete elements.1-3 Effects of shrinkage and creep are related to safety against failure and economic factors such as durability, serviceability, and long-term reliability. Therefore, it is important to find an appropriate prediction model for shrinkage and creep.

Four shrinkage and creep prediction models are presented in this paper. These four models are the ACI 209 model,4 the CEB 90 model,5 the B3 model,6 and the GL 2000 model.7 The discussion is concentrated on evaluating the accuracy of the four models by comparing the theoretical results with the RILEM experimental data bank.8

The current ACI 209 model is based on the works by Branson and Christiason.9 This model is the current model recommended by the American Concrete Institute. It has been incorporated in most building codes in the U.S. and serves as the basis for comparable codes in Canada, New Zealand, Australia, and parts of Latin America. The model is purely empirical, based on creep and shrinkage testing data obtained, prior to 1968 in the U.S., from standard 150 x 300 mm (6 x 12 in.) cylinders. The creep and shrinkage formulas given in the model represent the mean behavior for hundreds of tested specimens.

The CEB 90 model is recommended by CEB-FIP Model Code 1990 (Euro-International Concrete Committee and International Federation for Prestressing).10 Earlier models include the CEB-FIP-197011 and CEB-FIP-1978 models.12

The B3 model is the latest version in a number of shrinkage and creep prediction methods. It was developed by Bazant and Baweja in 1997.6 An earlier version of this model was proposed in 1978 and was called the BP model.13 It was then modified in 1991 and was named the BP-KX model.14-18 The latest B3 model is a simpler version of the expanded BP-KX model.

The GL 2000 model is a modified version of the GZ model proposed by Gardner and Zhao in 1993 and 1997.19,20 The GL 2000 model itself was influenced by the CEB 90 model, and was developed to correct the negative relaxation3 at early ages of loading and the unrealistic creep recovery of the GZ model.

Input factors for predicting shrinkage and creep of the four models are presented in Table 1. It can be observed from the table that the only model that includes water-cement ratio (w/c), aggregate-cement ratio (a/c), and specimen shape is the B3 model.

In this study, all shrinkage strain and creep compliance values are calculated by the four different models for each data set in the RILEM Data Bank.8 The calculated values are grouped together and sorted in different time ranges. The different time ranges consist of the following intervals: 0 to 10 days, 11 to 99 days, 100 to 365 days, 366 to 730 days, 731 to 1095 days, and above 1095 days are used. These time ranges refer to the duration the concrete member experienced shrinkage or creep. The models are compared with the RILEM Data Bank and graphs are plotted to reflect the accuracy of each model. Five methods for assessments of the model accuracy were used: the residual method, the B3 coefficient of variation method, the CEB coefficient of variation method, the CEB mean square error method, and the CEB mean deviation method.

For each statistical method, the two best-performing models are identified and ranked as first and second. The model that ranks the first or second most frequently is considered to be the best-performing model for shrinkage or creep.

RESEARCH SIGNIFICANCE

The significance of this study is to evaluate the accuracy of four shrinkage and creep prediction models, namely the ACI 209 model, the CEB 90 model, the B3 model, and the GL 2000 model. The shrinkage and creep values determined by the models are compared against the RILEM experimental data. The work is conducted as a part of a study for ACI Committee 209.

MODELS LIMITATIONS AND DATA SELECTION CRITERIA

The RILEM Data Bank consists of 7053 shrinkage data points (426 shrinkage data sets) and 8790 creep data points (518 data sets). Some of the data points are excluded in this study because their experimental conditions are beyond the application of an individual prediction model. Table 2 lists the individual model's applicable range for different input categories. In addition to the limitations listed in Table 2, some other criteria are imposed in the data selection process. Data points with swelling phenomena (a positive value) instead of a shrinkage trend (a negative value) are excluded from the shrinkage analysis.