*4.2. Theory-Linking*

In this section, from three theoretical perspectives, the importance of several theoryreflexive finding and insights are discussed.

Through the numerical analysis, the relationship between FS and CS identified in this study (in its mathematical form) is found to concur with their relationship as defined in ACI 318-19 [40–42] and in [43] (except for the coefficients). Therefore, this result is reflexive to the existing theories; in turn, this outcome further validates the results obtained in this study.

Next to this, the measures, data variables, and tests established for the durability of concrete are critical, as durability is an important category of parameters for HPC, particularly when it is to be used in humid areas or marine environments which are prone to acid attacks [44–46]. However, due to the time required to obtain results, true tests for durability are difficult to perform, so other indirect tools such as ASC, RCP, and ERoS should be applied. For this, a conventional theory is that, if a correlation between a hardened mechanical (i.e., strength) property and another durability property can be identified (or if their causal relationship can be established), durability can thus be anticipated by strength properties. In this research, other than very strong or strong relationships identified for the HPC parameters in the same variable category, some significant relationships (from strong to median intensities) between variables across the two categories (see Sections 3 and 4.1) are also found. In other words, these positive outcomes have confirmed the core theoretical logic.

Following these, another theoretical perspective relates to destructive and non-destructive tests (NDTs) [23,47]. Referring to Table 8, which is a simplified version of Table 2 with colour levels added (full red for 1, gradient red (lighter and lighter) for (less) positive values, gradient blue (heavier and heavier) for (more) negative values, dark blue for −1), the upper left cells containing the hardened mechanical properties show that, other than the very strong or near very strong correlations identified among the three destructive 'strength' measures, {CS, TS, FS}, USPV and HbRH are NDTs. Two interesting and important observations about these NDTs can be made.

The first observation is that USPV is an NDT that is more correlated with all destructive tests than HbRH, as evidenced by the magnitude of the *P-Co-Co*s, |0.43176| > |−0.39808|, |0.62297| > |−0.40234|, and |0.31071| > |−0.30525|. Thus, USPV has a medium correlation with TS, a medium correlation with CS, and a weak correlation with FS, while HbRH has a weak negative correlation with TS, a weak negative correlation with CS, and a weak negative correlation with FS. Therefore, the test results for USPV may be more associated with the results obtained from the destructive tests than that of HbRH. This supports the recommendation to keep only one NDT (i.e., USPV, because it provides links

to destructive tests more effectively), which is similar to the previous finding supporting the recommendation to keep only one destructive test (i.e., either CS, or TS, or FS, because they are interchangeable; see Section 4.1).

**Table 8.** Simplified and visualised information for Table 2.


The second observation is that there is no significant correlation between the two NDTs for hardened mechanical properties, despite the fact that the test results for USPV may have a weak negative correlation with those of HbRH (−0.23428). This means that, for two similar HPC samples (with the same admixture) tested on the same day, these two NDTs would typically produce diversified results. An evidence-based argument can be presented that the mechanisms behind these two NDTs should be intrinsically different.

Similar observations to the destructive tests and NDTs can also be made by examining the lower right cells with respect to the durability properties. Other theory-reflexive insights of interest based on these results could be gained through future studies.
