## 3 Results and Discussion
### Compressive Strength
This enhances the hydration reaction of cement, promotes a more complete reaction with calcium hydroxide in the early stages, and results in a higher generation of calcium silicate hydrate (C-S-H) gel. Micron-sized silica is less efficient in promoting the cement hydration reaction, but it can also complete the full reaction with calcium hydroxide as the curing age increases, and the compressive strength increases rapidly in the later stage as C-S-H is continuously generated. Figure 4 shows that, for cement mortar containing the same self-healing agent, the compressive strength varies with the amount and particle size of the added silica. At different curing ages, the compressive strengths of cement mortar specimens in groups N1.125-M6.75, N2.25-M13.5, N3.375-M20.25, and N4.5-M27 all showed a trend of first increasing and then decreasing. When cured for 28 days, the compressive strengths of cement mortar specimens in groups N1.125-M6.75, N2.25-M13.5, and N3.375-M20.25 were all higher than that of the Control-2 specimens, and only the compressive strength of cement mortar specimens in group N4.5-M27 was lower than that of the Control-2 specimens. This is also related to the amount of silica added, and the reason is the same as the compressive strength results of cement mortar [48]. In addition, by comparing the compressive strength of cement mortar specimens of group 4.5, group M27, group N2.25-M13.5, and group N3.375-M20.25, it can be seen that when two orders of magnitude of silica particle size are added at 50% of the optimal addition amount, the compressive strength of the cement mortar specimen is lower than the compressive strength of the cement mortar specimen with a single order of magnitude of silica particle size added at the optimal addition amount, and when two orders of magnitude of silica particle size are added at 75% of the optimal addition amount, the compressive strength of the cement mortar specimen is higher than the compressive strength of the cement mortar specimen with a single order of magnitude of silica particle size added at the optimal addition amount. This shows that the simultaneous addition of silica of different orders of magnitude can optimize the particle grading, and there is a mutual influence between the two orders of magnitude of silica particle size, and the simple average distribution principle cannot play the role of silica of a single order of magnitude. Increasing the dosage within an appropriate range can couple the synergistic effect of silica particles of different sizes. This is because nano- and micro-sized particles can synergistically fill, and silica particles of different sizes can better fill the gaps between cement particles. Nano-sized particles fill the tiny gaps between micro-sized particles, while micro-sized particles fill larger gaps. This multi-scale filling effect significantly improves the density of cement paste, reduces porosity, and thus enhances compressive strength. In addition, there is the active synergistic effect of multi-size particles. Nano-sized silica particles can promote cement hydration reactions and generate more C-S-H gel due to their high specific surface area and high activity. Micro-sized particles can provide additional silicon sources and further participate in secondary reactions. This synergistic effect can generate more C-S-H gel and enhance the strength of the paste. Therefore, adding silica particles of different sizes within an appropriate range and their synergistic effect can further improve the compressive strength of cement mortar specimens.