## 2 Materials and Methods
### Mixing Ratio and Standard Preparation  
Based on the existing research results, adding silica of different particle sizes to cement mortar can improve the performance of cement mortar to different degrees [41]. This study, based on the addition of a self-healing agent (expanded perlite with adsorbed bacteria) to cement mortar, considered the simultaneous addition of two silica particles with different particle sizes, analyzed the performance of modified cement mortar, and determined the optimal dosage of different materials. The experiment first selected two silica particles with particle sizes of 60 microns and 20 nanometers, respectively, and determined the optimal dosage. A total of seven groups of different cement mortar samples were designed. The specimens mainly included ordinary Portland cement, standard sand, a self-healing agent, tap water, silica, and calcium lactate. The seven groups of specimens were all added with a 10% volume fraction of expanded perlite with adsorbed bacteria as a self-healing agent and were marked as M1, M3, M5, M10, N0.5, N1, and N2 according to the differences in particle size and dosage of added silica. Among them, M1, M3, M5, and M10 represent the addition of 1%, 3%, 5%, and 10% of micron-sized silica, respectively, and N0.5, N1, and N2 represent the addition of 0.5%, 1%, and 2% of nano-sized silica, respectively. In addition, 1% by mass of cement calcium lactate was added to the specimen as an organic precursor. Existing research results show that the addition of 1% cement calcium lactate can maximize the strength and pore densification of microbial mortar [42]. The formulation of internally mixed single-particle-size silica cement mortar is shown in Table 3.  
Based on the discussion results of the effects of adding only micron-sized silica or nano-sized silica, their optimal dosages were used as the benchmark dosages. In addition, the test was based on the benchmark dosage. In the environment of cement mortar containing an internal self-healing agent, the optimal mixed dosage of the two was further determined by selecting different mixing ratios. Therefore, eight groups of cement mortar samples were designed with 25%, 50%, 75%, and 100% of the benchmark parameters mixed and added, and they were marked as Control-1, Control-2, N4.5, M27, N4.5-M27, N2.25-M13.5, N1.125-M6.75, and N3.375-M20.25. Among them, the Control-1 group was used as the control group, and 10% expanded perlite without adsorbed bacteria was added. The Control-2 group was added with 10% expanded perlite adsorbed with bacteria as a self-healing agent. The N4.5 group was based on the Control-2 group with 4.5 g of nano-silicon dioxide added. The M27 group was based on the Control-2 group with 27 g of micro-silicon dioxide added. The N4.5-M27 group was based on the Control-2 group with 4.5 g of nano-silicon dioxide and 27 g of micro-silicon dioxide added at the same time. The remaining groups were the same, and will not be repeated here. Similarly, 1% cement lactate calcium was added to the specimen as a calcium source. The eight groups of cement mortar proportions  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Group**} & **Standard** & \multirow{2}{*}{**Cement**} & **Water** & **Self-Healing** & \multirow{2}{*}{**Silica**} & **Silica** & **Calcium** \\  & **Sand** & **(g)** & **(g)** & **Agent** & **(g)** & **(g)** & **Percentage** & **Latate** \\ \hline M1 & 1620 & 891 & 450 & 12 & 9 & 1\% & 9 \\ M3 & 1620 & 873 & 450 & 12 & 27 & 3\% & 9 \\ M5 & 1620 & 865 & 450 & 12 & 45 & 5\% & 9 \\ M10 & 1620 & 810 & 450 & 12 & 90 & 10\% & 9 \\ N0.5 & 1620 & 895.5 & 450 & 12 & 4.5 & 0.5\% & 9 \\ N1 & 1620 & 891 & 450 & 12 & 9 & 1\% & 9 \\ N2 & 1620 & 882 & 450 & 12 & 18 & 2\% & 9 \\ \hline \end{tabular}
\end{table}
Table 3: Mixing ratios of internally mixed single-particle-size silica cement mortar.  
with self-healing agents added and mixed with silica of different particle sizes are shown in Table 4.