## 4 Conclusions  
In this study, X-ray CT in situ compressive loading in combination with DVC was used to analyze the localized damage behavior of cement mortar. Some valuable observations or findings can be summarized as follows:  
1. The unhydrated cement in the cement matrix had a significant effect on localized fracture, and cracks expanded along the boundary of the unhydrated cement under compressive loading. Hence, during the use of cement mortar, special attention should be paid to sufficient cement hydration.
2. No obvious cracks were observed on the surface of the cement mortar, but the damage inside the specimen was very apparent, and the large damage localization area was also distributed in the material during the compression process, which fully indicated that the internal failure in the material occurred earlier than the surface. However, the damage develops from the inside out, which may be caused by the phenomenon of compression load or bias pressure. Further tests are needed to obtain an accurate conclusion. Cracks inside the cement mortar did not always expand with the increase in the load, and new cracks compressed the original cracks and reduced the width of individual cracks.  
Figure 18: Localization factor under different stress stages.  
3. The 3D strain field showed that the cement mortar specimen did not have a uniform distribution of the strain. It is due to the heterogeneity of cement-based materials and the eccentric compression that occurred during loading that this occurred. It should be noted that further testing is needed on samples with parallel planes (without an eccentric effect), which can be referred to as the overall behavior of the material. The maximum principal strain of the specimen was entirely tensile strain, which led to tensile deformation. The increased tensile deformation finally resulted in macrofractures as well. The site of the macroscopic fracture matches the localization of the maximum principal strain. With the increase in stress, the localized region in the specimen expanded and was distributed randomly.
4. The gray value of the CT image and the damage index defined by the maximum principal strain could reflect the damage inside the specimen. The damage in the center position was obviously higher than that at the edge of the specimen, indicating that the failure of the specimen was caused by internal damage. The localization factor could effectively reflect the dispersion of the high-magnitude strain element, and the results were consistent with the damage law. The analysis of the gray value, damage index, and localization factor all showed that the failure of the specimen was caused by the internal localized damage. It shows that the study of the internal damage is of great significance to the engineering application of concrete.
5. Through X-ray CT in situ loading scanning and DVC calculation, the damage distribution inside the material can be defined, and the direction of damage development can be determined, which can provide a reference for the study of the macroscopic mechanical behavior of cement mortar materials. During the use of cement mortar, we should not only take surface damage as the criterion of failure but also pay attention to the damage inside the material.  
Conceptualization, Y.Z. and Y.X.; formal analysis, N.L.; funding acquisition, Y.Z.; project administration, Y.X. and X.H.; supervision, X.H.; writing--original draft, N.L.; writing--review and editing, N.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (12162025, 11762015), Natural Science Foundation of Inner Mongolia (2021 LHMS05010, 2020 LH05008), and Scientific Research Project of Universities in Inner Mongolia (NJZY21365).  
Not applicable.  
The authors would like to acknowledge [PERSON] (Beihang University) for his help of DVC calculation and constructive comments.  
The authors declare no conflict of interest.