Optimizing compressive strength of plinth concrete mix using quad-axial weighted simplex centroid designs and second order kronecker model

Abstract

In the construction industry, Engineers, Quantity surveyors and other stakeholders work towards obtaining civil structures with desired compressive strength at minimum costs. In Kenya and many parts of the world, many cases of collapsing buildings causing fatal damage are reported from time to time. A study by the National Construction Authority of Kenya () attributed the causes of these collapses, among others to the compromised concrete mixes. Researches done on optimizing concrete mixes have dealt with three variables, Cement, Sand (fine aggregate) and Ballast (coarse aggregate), while keeping water constant. This study was geared to find a procedure for the optimal strength of M25 class of concrete to mitigate the collapsing of buildings. This included water a major contribution of strength as one of the variables for finding the optimal mix for the said class. To actualize the study, an experiment was conducted in the concrete laboratory at the Jomo Kenyatta University of Agriculture and Technology (JKUAT). The main objective was to obtain a statistical model using second order Kronecker model and a quad-axial weighted simplex centroid designs, satisfying the D- G- and I- optimality tests performed in order to locate the optimum values of the design. The specific objectives for the study were to construct an optimal inscribed tetrahedral weighted simplex centroid design. To evaluate its D-, G- and I- optimality conditions using the H-Invariant matrices with two weighted designs namely; equally and unequally weighted simplex centroid axial design (EWSCAD) and (UWSCAD). To perform a concrete mixture experiment using the design and to fit a second-degree Kronecker model for the experiment. Finally, to obtain the optimal mix for the experiment and to evaluate its optimality conditions. The study applied Response Surface Methodology (RSM). The results revealed that the centroid obtained the best D- and G-optimal values. The UWSCAD was D-efficient while EWSCAD was G- efficient. I-optimality of the two designs occurred at similar design points. The concrete model obtained the same optimality conditions as the adopted design. The second- degree Kronecker model fitted showed that the adjusted R-squared was 0.9951. The variance inflation factors (V.I.F) for the squared portions and the interactions were 3.3344 and 5.0891 respectively, hence no serious multi-collinearity problem. The descriptive statistics showed the distribution of the experiment outcomes while the contours and the response surfaces showed the effect on compressive strength due to interactions of two components. The response trace plot revealed the optimal point for the ratio water: cement: sand: ballast as 0.52:1:1.4:2.8 for the optimal compressive strength of 27.63N/mm 2 for the M25 class. In conclusion, the model obtained was appropriate in estimating the optimal ratios since it occurred in the class of interest. The study therefore recommends that the procedure used for this study be applied in search of the concrete mixing ratio for the construction of the plinth of M25 class, for the four components which may differ due to the source of variables.