2.2.7. Rapid Chloride (Im-)Permeability (RCP)

Another indicator of the durability of concrete is its ability to resist chloride ion penetration. This can be performed by testing the concrete material samples using a rapid chloride ion rapid test (RCPT) with an applied electrical voltage. This test method can be performed in accordance with ASTM C1202 [35].

## 2.2.8. Electrical Resistivity on Surface (ERoS)

To evaluate concrete compactness and the durability of cement composites in an HPC sample, the ERoS can be measured. The higher the electrical resistance, the more compact the substrate, which increases durability. This study considers ERoS to be a durability variable (see Section 2.1.2), which can be tested using ASTM C876 [36].

#### *2.3. The Methods: A Brief Review*

#### 2.3.1. Correlation Analysis

This study uses the Pearson correlation coefficient (*P-Co-Co*) method as the basis of the analysis to identify the correlation between each pair of experimental parameters (variables). The computation of a *P-Co-Co* is typically defined as the following:

$$PCoCo(X, Y) = \frac{n \sum\_{i}^{n} (X\_i Y\_i) - \left(\sum\_{i}^{n} X\_i\right) \left(\sum\_{i}^{n} Y\_i\right)}{\sqrt{n \sum\_{i}^{n} \left(X\_i^2\right) - \left(\sum\_{i}^{n} X\_i\right)^2} \sqrt{n \sum\_{i}^{n} \left(Y\_i^2\right) - \left(\sum\_{i}^{n} Y\_i\right)^2}}\tag{2}$$

where *X* and *Y* are variables between which the *P-Co-Co* is to be calculated; *n* is the data size (length) of each variable; and *i* is the identifier for a specific data entry.

There are two primary reasons for using the *P-Co-Co* method:


2.3.2. Cosine Similarity Analysis

The cosine similarity (*Cos-Sim*) analysis diverges from the traditional thinking in statistics, treating experimental parameters as 'vectors', rather than 'variables'; in so doing the similarity between two series of parametric values from the tests can be justified by the *Cos-Sim* index in the dimensional space. The standard computational process for this index can be written as:

$$\text{CostSim}(X, Y) = \frac{\sum\_{i}^{n} X\_{i} Y\_{i}}{\sqrt{\sum\_{i}^{n} X\_{i}^{2}} \sqrt{\sum\_{i}^{n} Y\_{i}^{2}}} \tag{3}$$

where *X* and *Y* are variables being treated as vectors between which the index is to be calculated (so *Xi* or *Yi* is the *i*-th element of vector *X* or vector *Y*); the other symbols are as defined previously.

The reasons to apply *Cos-Sim* in this context are as follows:

