# Multivariate Analysis for Prediction of Splitting Tensile Strength in Concrete Paving Blocks
## 1 Introduction
### Related Work  
Predicting concrete tensile splitting strength from related properties has been an important research focus. Simple linear regression models provide initial correlations but limited analysis. Several studies used linear and nonlinear regression models to predict splitting strength. The research by [5] used simple linear regression to correlate tensile splitting strength with compressive strength, water/binder ratio, and age. While simple, this limited analysis of related variables. Nonlinear equations proposed increasing tensile strength slower than compression. The investigation in [6] related abrasion and splitting strength to bulk density and ultrasonic pulse velocity, finding that the logarithmic transform of dry bulk specific better predicted splitting strength than the linear model. The study that was carried out by [4] indicated that the compression test described in Standard NS 6717:1986, which is carried out in the laboratory, does not represent the real behavior in the paving blocks in real conditions of use and is caused by splitting stresses, which generates a fracture by dividing the paving block into two parts. Compressive and tensile strengths were related through regression. Compressive strength is also related to density. The study carried out by [7] elaborated mixes with recycled aggregates, establishing compressive strength's dependence on density. Ref. [8] related density and compression to rubber content through linear and logarithmic regression, with increased rubber reducing both. High compressive strengths occurred alongside high densities. The prediction by multiple linear regression of the compressive strength can be seen in the study carried out by [9], where it is indicated that the compressive and traction strength decreases by incorporating rubber from vehicular transport tires in the paving block mixture. The relationship of different physical and mechanical properties of concrete paving blocks was investigated by [10], where it is described in terms of physical variables--water absorption, porosity, and specific gravity--and mechanical variables--compressive strength and tensile splitting strength. The regressions of the variables were carried out, where it was found that the most robust correlation coefficients are (a) correlation between the water absorption and the tensile splitting strength, (b) the compressive strength and the water absorption, (c) porosity and compressive strength, (d) porosity and tensile splitting strength. Additionally, it is indicated that water absorption is a physical property that can be easily determined, has a high correlation with performance parameters, and can also be used as a rapid quality control parameter. The research led by [11] used 200 \(\times\) 100 \(\times\) 100 paving blocks manufactured by vibrop compaction; the objective was to determine the changes in density using the DIN12390-7 standard, absorption, freezing-thawing resistance, and tensile splitting strength of paving blocks on the pallet. It is indicated that the changes at the ends of the tray were attributable to the uneven distribution of the compaction and filling of the mixture in the vibro-compacting machine, making the density higher in the center and lower at the ends. Likewise, when the density is lower at the ends, the product's resistance is lower. In the investigation carried out by [12], several concrete mixtures with different densities and water/cement ratios were elaborated to relate them with the resistance at 28 days of age. The increase in the density of the concrete increased the compressive strength with an exponential behavior. The study described by [13] incorporates tea waste ash with different proportions to replace cement, giving us a lower density and compression with a higher proportion of ash. It can be seen in the graphs that the first two mixtures with the minor cement replacement give us the highest compressive strength, and these same samples are the ones with the highest density.