# Meso-Scale Failure of Freezing-Thawing Damage of Concrete under Uniaxial Compression
## 2 Experimental Materials and Methods
### Damaged Layer of Frozen-Thawed Concrete  
Concrete specimens subjected to the various numbers of freeze-thaw cycles are shown in Figure 1. As concrete is categorized as a multiphase heterogeneous material, different degrees of micro-cracks appeared. As the freezing-thawing test proceeded, the number of micro-cracks on the surface of concrete increased after 25 freezing-thawing cycles, and the surface of the specimens began to be rough, with a small amount of cement mortar falling off. After 50 freezing-thawing cycles, cracks were visible on the surface of the specimens, which had become obviously rough; after 75 cycles, the micro-cracks on the surface of concrete gradually expanded, part of the surface began to peel off, and some aggregate was exposed. After 100 freezing-thawing cycles, the concrete surface seriously peeled off with some coming off in scales or layers, and aggregate was more exposed; after 125 freezing-thawing cycles, more concrete peeled off in scales or layers with some corners even peeling off. After 150 freezing-thawing cycles, aggregate was exposed in large areas and more areas in the corner peeled off.  
Concrete freezing-thawing is a gradual process. The outermost layer of concrete is seriously damaged, but the deeper in the concrete, the less the damage. Therefore, concrete is considered in three parts: freezing-thawing damage layer, freezing-thawing damage transition layer, and undamaged layer [18]. The freezing-thawing damage transition layer is a dense and thin area. To simplify the analysis of such behavior, this part of the concrete is considered the undamaged layer of concrete. The degradation of mechanical properties of freezing-thawing concrete is mainly caused by the degradation of mechanical properties of the damaged layer of concrete [19]. A simplified sketch of a  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Specimen** & **Water/Binder** & **Sand** & \multicolumn{4}{c}{**1 m\({}^{3}\) Material Content of Concrete/kg**} \\ \cline{4-9}
**Strength** & **Ratio** & **Ratio** & **Water** & **Cement** & **Sand** & **Stone** & **Fly Ash** & **Admixture** \\ \hline C30 & 0.53 & 0.4 & 170 & 256 & 765 & 1150 & 64 & 9.6 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mix of C30 concrete.  
Figure 1: Concrete specimens with the different number of freezing-thawing cycles.  
concrete section is shown in Figure 2a. This paper assumed that the damaged layer of concrete was uniformly spread around the section.  
The thicknesses of the damaged layer of the six groups of concrete specimens under the different numbers of freezing-thawing cycles were measured using ultrasonic nondestructive testing technology [20]. HC-U81 concrete strength defect detector was used to measure the thickness of concrete freeze-thaw damage layer, and the measurement accuracy was 0.01 mm. A concrete specimen was divided into three regions, in which the thicknesses of the damaged layer of concrete was detected by ultrasonic nondestructive testing, and the average value of the results was used. Using Origin software (OriginLab, USA), the polynomial fitting of the thickness \(d\) of freezing-thawing damage layer with the number of freezing-thawing cycles \(N\) was conducted, and the fitting curve is shown in Figure 2b.  
Figure 2b shows that the thickness of the damaged layer of concrete increased with increasing number of freezing-thawing cycles, the growth rate of concrete damage layer thickness from 25 to 125 freeze-thaw cycles was basically unchanged, and the growth rate of the layer of damaged concrete thickness with more than 125 freeze-thaw cycles obviously accelerated. In the process of repeated freezing-thawing of free capillary water in concrete, the damage stress caused by volume expansion increased gradually, causing new micro-cracks to continue developing and damage to accumulate continuously. When the damage value exceeds a certain range, the damage will increase sharply.