## 4 Conclusions  
In this study, two different sizes of silica are added based on the added self-healing agent. Compared with the previous study results of adding single-size silica, this work optimizes particle gradation at the microscopic level and reveals the positive effects of the varying silica sizes on the mechanical and self-healing properties of cement mortar at different curing ages. We draw the following conclusions based on the experimental data and mechanism analysis:  
1. Expanded perlite as a bacterial carrier can effectively protect the survival of bacteria. When expanded perlite adsorbing bacterial liquid is added to cement mortar as a self-healing agent, it can not only fill pores, compact the structure, and improve the strength through metabolic reactions in the early stage of curing, but also realize the self-healing of microcracks after cracking of cement mortar.
2. When silica of a certain particle size is added to cement mortar alone, there is an optimal dosage related to the particle size. Adding silica at the optimal dosage can effectively improve the strength of cement mortar. Mixing silica of different particle sizes can optimize the particle size distribution of silica. Silica of nanometer particle size is beneficial to improving the early compressive strength of cement mortar, and silica of micrometer particle size is beneficial to improving the final compressive strength of cement mortar. The mechanical properties of cement mortar can be further improved through the mutual influence between silica of different particle sizes.
3. XRD analysis tests have shown that the self-healing product at the cracks of cement mortar is calcium carbonate. Adding silica can improve the density of the cement matrix, provide more crystal nuclei, and promote the precipitation of calcium carbonate. The synergistic effect of silica of different particle sizes improves the self-healing effect, resulting in more calcium carbonate in the healing product and a more significant filling effect.
4. Through SEM observation results, it can be determined that the main components of the self-healing product are irregularly shaped calcium carbonate and fibrous C-S-H gel. Under the combined action of calcium carbonate and C-S-H, the cracks can be effectively filled and repaired.  
X.L.: Conceptualization, Methodology, Investigation, Writing--original draft preparation. W.Y.: Methodology, Data curation, Investigation, Writing--review and editing. S.W.: Methodology, Investigation. S.L.: Writing--review, Funding acquisition. Z.S.: Methodology, Supervision, Writing--review. H.W.: Conceptualization, Supervision, Project administration, Writing--review, Funding acquisition. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Fundamental Research Funds for the Central Universities (No. 2572022 DX07), and the National Natural Science Foundation of China (No. 52108193).  
Data Availability Statement: The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
Author [PERSON] was employed by the company Longjian Road and Bridge Co. Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.