## 3 Damage Characteristics  
### Expansion and Shrinkage Properties  
The volumetric changes exhibited by specimens subjected to dry-wet cycling have been a central focus of research. As depicted in Figure 3a, there is some dispersion in the change in volume from one specimen to another. There are no exceptions that the specimen's volume undergoes continuous alteration throughout the wet-dry cycles, wherein the expansion after wetting results in volumetric increments and the contraction after drying lead to volumetric decrement. The volumetric change in the specimen is pronounced during the initial wet-dry cycle, whereas the observed volumetric change becomes negligible after the third cycle. In previous studies, the volume change during wet-dry cycling has typically been expressed using axial strain [30,31]. However, a notable disadvantage of this approach is that axial strain solely describes the height change in the specimen. Figure 3b clearly demonstrates the presence of a significant annular gap between the specimen and the ring knife, indicating lateral expansion and contraction of the specimen during wet-dry cycling. Consequently, \(\delta_{a}\) and \(\eta_{a}\) emerge as more suitable metrics to describe the specimen's volume change behavior. They are used to represent the cumulative rate of change in sample volume relative to the initial, untreated sample volume (\(V_{0}\)) during the testing process. The calculation formula is as follows:  
\[\delta_{a}=\frac{V_{W(i)}-V_{0}}{V_{0}}\times 100\% \tag{1}\]  
\[\eta_{a}=\frac{V_{0}-V_{d(i)}}{V_{0}}\times 100\% \tag{2}\]  
In the aforementioned formulae, \(\delta_{a}\) represents the absolute expansion rate (%); \(\eta_{a}\) the absolute shrinkage rate (%); \(V_{0}\) the volume of the initial state specimen (mm\({}^{3}\)); \(V_{w(i)}\) the volume of the specimen after wetting in the ith cycle (mm\({}^{3}\)); \(V_{d(i)}\) the volume of the specimen after drying in the ith cycle (mm\({}^{3}\)). During the data calculation and processing, the following considerations were accounted for: 1 The tool used in this study to measure the volumetric parameters was a vernier caliper with an accuracy of 0.02 mm. 2 For the  
Figure 2: **(a)** Water content of sample in wet–dry cycles; **(b)** time of wet-dry cycles. specimen after wetting, we assumed the diameter of the sample is consistent with the diameter of the ring cutter, which was 61.8 mm, and the height of the specimen was measured accurately using vernier calipers. 3 For the specimen after drying, their diameter and height are measured accurately with vernier calipers. 4 The accurate determination of the height and diameter of each sample necessitates performing at least three parallel measurements across diverse locations. Subsequently, the arithmetic mean of these measurements is utilized to count the volume of the sample. 5 The volume of the sample is taken as the average of all sample volumes, but those that deviate significantly from the others need to be excluded. \(\delta_{a}\) and \(\eta_{a}\) quantify the extent of cumulative expansion and cumulative contraction, as well as their patterns of change, across the wet-dry cycles. These indices serve as indicators of the volume change in the specimen throughout the wet-dry cycles. Figure 3c illustrates the variation trend of \(\delta_{a}\) and \(\eta_{a}\) with respect to \(N\). It is evident that during the wetting process, as \(N\) increases, \(\delta_{a}\) gradually rises, with the rate of increase diminishing progressively, ultimately stabilizing after the third wet-dry cycle. During the drying process, as \(N\) increases, \(\eta_{a}\) gradually declines, with the rate of decrease diminishing progressively, ultimately reaching stabilization after the third wet-dry cycle. It is notable that the specimen undergoes significant expansion during the wetting phase, leading to a volume of the specimen after wetting (\(V_{w}\)) that consistently surpasses \(V_{0}\). The gradual increase in \(\delta_{a}\) signifies a corresponding gradual increase in \(V_{w}\).