Development of satisfaction curves to evaluate concrete mix design performance using a Bayesian probabilistic method

Due to the restrictions of the current prescriptive design methods and standards, structural and material engineers sought to find an innovative design method to implement creative and novel approaches in designing. One type of design method receiving a keen interest in civil engineering field is performance based design (PBD) method. Presently, PBD is used in seismic design of structures and is specified in the code standards of earthquake resistant design. One specific approach in structural seismic design and damage evaluation is called fragility method developed by Shinozuka. Fragility method is developed based on Bayesian method, which is presented as the conditional probability of exceeding some limit state (minor, moderate, major, and collapse) for a given ground motion. In this study, the focus is to apply the Bayesian approach for the evaluation of concrete mixture design in assessing concrete material performance based on selected conditional parameters (i.e., safety, durability, etc.). The performance based evaluation of concrete mix proportion is presented as a satisfaction probability percentage (e.g., 0-100%) as a function of specified material parameter (i.e., water, water-to-cement ratio, cement content, etc.) for a specified performance criterion value (i.e., compressive strength, slump, elastic modulus, etc.). This relationship curve is titled satisfaction curve (SC). The paper presents a detailed explanation of developing and drawing SC based on Bayesian method, an example of application of SC, and result comparisons between the results obtained using our SC method with ACI 214R-02 normal distribution probability method. The result verification shows that concrete mix proportion performance evaluation using SC is reliable and the difference is within an acceptable range of accuracy of 5% difference.