# Multivariate Analysis for Prediction of Splitting Tensile Strength in Concrete Paving Blocks
## 2 Materials and Methods  
The paving blocks of the present investigation were obtained from a factory that produces 30,000 units per day in Quito-Ecuador; the paving block model is rectangular with nominal dimensions of 200 mm in length, 100 mm in width, and 60 mm in thickness. The research has a quantitative approach, since all the variables to be analyzed are continuous quantitative. As a first point, the sample size is estimated using the G* Power software for multiple linear regression of 5 predictors, using a medium range effect size of 0.0363, which allowed us to estimate a sample size of 300 paving stones, with which an estimated power of the test of 0.9502764 was obtained. On production day, the paving blocks for the population of 30,000 units are sampled as the pieces come out of the vibro-compacting machine, the measurements of the length, width, thickness, and mass of the fresh paving block are taken, the paving blocks are marked to guarantee traceability, and the absorption and resistance tests are carried out according to the [1] The database consists of rows representing the analysis individuals of the sampled and numbered paving blocks; the columns represent the analysis variables. The variables that enter the models of multivariate techniques, also called input, predictor, or independent, are length in mm, width in mm, height in mm, the mass of the fresh paving blocks (each piece fresh from the vibro-compacting process) expressed in grams, and the percentage of absorption based on the NTE INEN 3040 standard. Additionally, since the dimensional variables of the paving blocks and the mass of the fresh product can be reformulated into a new variable called the density of the fresh product expressed in units of (kg/m\({}^{3}\)), this was taken into account together with the percentage of water absorption to make the prediction and compare the multivariate methods. The response variable, also called dependent or output, is the indirect tensile strength in megapascals (MPa), which will depend on the predictor variables, which are grouped into the first group of predictor variables (5): length, width, thickness, mass of the fresh product, and water absorption percentage. The second group of predictor variables were (2) density of the fresh paving block and percentage of water absorption. **Water absorption. ** The water absorption test is carried out by reference to the NTE INEN 3040 (2016) standard, which indicates that to determine the absorption rate, the paving block must be submerged in potable water at 20 \(\pm\) 5 \({}^{\circ}\)C minimum for three days, and then the surface must be cleaned of excess water with a moistened cloth, and the moistened paving block must be weighed to a constant mass. In the same way, an oven is used to find the mass of the dry paving block, and it is placed for a minimum period of 3 days at 105 \(\pm\) 5 \({}^{\circ}\)C until constant mass. The calculation is made by the difference between the saturated and dry mass divided by the dry mass. This would correspond to the percentage of the maximum mass of water that the paving block has absorbed from the dry state to the saturated state. The calculation formula is as follows:  
\[W_{a}=\frac{M_{1}-M_{2}}{M_{2}} \tag{1}\]  
\(M_{1}\) is the mass of the specimen saturated with water, expressed in grams. \(M_{2}\) is the final mass of the dry specimen, expressed in grams. **Fresh paving block weight (mass). ** It is the mass of the paving block expressed in grams taken just after it leaves the mold in the vibro-compaction process. **Thickness (height), length, and width of the paving block. ** The height of the paving block, or thickness, is the distance between the lower and upper face. In practice, the height variation is given by the vertical mobility of the mechanical parts in the vibro-compactor, where the plate of tamping compresses the mixture into the mold. The width and length of the paving blocks are taken from one end to the other. **Tensile splitting strength.