Reliability Based Single and Multi-Objective Optimization of Concrete Mix Design Parameters

Abstract

Concrete is a composite construction material made by water; Portland cement; and fine and coarse aggregates in desired proportions. Additional components such as chemical and mineral admixtures may be added to the basic mix constituents to enhance certain properties of fresh or hardened concrete. The process of selecting suitable ingredients for concrete and their relative amount with the objective of producing concrete of required strength, durability and workability as economically as possible is termed as mix design. However, concrete mix design is always under the effect of random environment, and the sources of randomness are variations in quality of materials, mixing and transporting procedures, major methods of placing concrete; and methods of curing and testing procedures. As such actual compressive strength of concrete in a structure is always different from the specimen obtained under controlled laboratory conditions. This gap between the expected performance and obtained performance is even larger when the mix design is deterministically optimized since Deterministic Design Optimization (DDO) typically yields optimal designs that are pushed to the limits of design constraint boundaries; leaving no room for uncertainties in manufacturing imperfections, modeling and design variables. In the present work, a reliability based design optimization strategy has been developed for finding reliable optimal concrete mix proportions under single and multi-objective environments. The steps considered in this strategy are: statistical analysis of the data; developing models for concrete mix parameters; and reliability based single and multi-objective optimization of concrete mix proportions. In statistical analysis step, experimental data generated by Kumar (2002) has been explored to identify the input parameters for developing models for compressive strength of concrete. Selected parameters have been analyzed to study inter-dependency among them. In the second step, Ordinary Least Square Regression (OLSR), Principal Component Regression (PCR), Traditional Ridge Regression (TRR) and Generalized Ridge Regression (GRR) techniques have been employed to develop models for prediction of compressive strength of concrete for different curing ages. The models are then incorporated into the Reliability Based Design Optimization (RBDO) model. In the third step, the efficient and well-known RBDO method, namely, Sequential Optimization and Reliability Assessment (SORA) method is employed to determine reliable optimal concrete mix proportions in single objective environment. Safety factor based DDO designs have also been obtained using Sequential Quadratic Programming (SQP) technique. Reliabilities of DDO designs have been computed using Advanced Mean Value (AMV) algorithm. It is seen that reliability of RBDO designs are more than that of DDO designs. Elitist Non-Dominated Sorting Algorithm (NSGA-II) developed by Deb et al. (2002) has been used to study the tradeoff between cost of concrete and reliability of compressive strength constraint satisfaction in multi-objective environment. The optimal concrete mix proportions obtained in this work satisfy compressive strength requirement constraint with desired reliability. Results from this research suggest that the RBDO methodology could be a valuable tool for minimizing the number of trial batches required to identify the optimal concrete mix proportions having desired properties and reliability.