Prediction of modulus of elasticity of UHPC using maximum likelihood estimation method

Abstract

Modulus of elasticity (MOE) is a significant design parameter representative of the stiffness of concrete materials. In the current design practice, the determination of MOE primarily relies on empirical equations. Previous studies have recommended different equations to predict the MOE of ultra-high performance concrete (UHPC) based on a correlation with concrete compressive strength. The coefficients of these equations are dependent on the chosen empirical fits, in which the least-squares estimation (LSE) is one of the most popular fits. This study proposes a new approach by using a probabilistic method called the maximum likelihood estimation (MLE). A data set consisting of 364 data points of concrete compressive strength and MOE was developed for the MLE analysis. The negative log-likelihood is used as an indicator for the analysis. Two MOE equations are proposed. The proposed equations achieved negative log-likelihoods of 3,725 and 3,720, respectively, in comparison to 3,737 and 3,999 as the smallest and greatest negative log-likelihoods of the equations of the literature. These equations reveal that the MOE of UHPC is not proportional to the square root of concrete compressive strength as the current code equations specify for conventional concrete. The difference in the microstructure between UHPC and conventional concrete is a key factor attributing to the observation.