# Effect of Particle Size on Mechanical Property of Bio-Treated Sand Foundation
## 3 Results and Discussion
### Direct Analysis of Orthogonal Experiment
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Index** & & \(d\) **(mm)** & \(C_{\rm b}\) **OD\({}_{\rm 600}\)** & \(C_{\rm c}\) **(mol**:L\({}^{-1}\))** \\ \hline \multirow{6}{*}{\(\lambda\)/times} & \(k_{j1}\) & 5.25 & 6.83 & 7.83 \\  & \(k_{j2}\) & 6.00 & 5.33 & 4.33 \\  & \(k_{j3}\) & 7.00 & - & - \\  & \(R_{j}\) & 1.75 & 1.50 & 3.5 \\  & Primary and secondary order & & \(C_{\rm c}>d>C_{\rm b}\) & \\  & Preferred embodiment & & \(C_{\rm c1}d_{3}C_{\rm b1}\) & \\ \hline \multirow{6}{*}{\(q_{\rm u}\)/kPa} & \(k_{j1}\) & 380 & 540 & 676 \\  & \(k_{j2}\) & 500 & 498 & 362 \\ \cline{1-1}  & \(k_{j3}\) & 675 & - & - \\ \cline{1-1}  & \(R_{j}\) & 295 & 42 & 314 \\ \cline{1-1}  & Primary and secondary order & & \(C_{\rm c}>d>C_{\rm b}\) & \\ \cline{1-1}  & Preferred embodiment & & \(C_{\rm c1}d_{3}C_{\rm b1}\) & \\ \hline \multirow{6}{*}{\(\overline{\delta}\)/\%} & \(k_{j1}\) & 11.63 & 12.78 & 13.73 \\  & \(k_{j2}\) & 12.39 & 12.02 & 11.82 \\ \cline{1-1}  & \(k_{j3}\) & 13.18 & - & - \\ \cline{1-1}  & \(R_{j}\) & 1.55 & 0.76 & 1.91 \\ \cline{1-1}  & Primary and secondary order & & \(C_{\rm c}>d>C_{\rm b}\) & \\ \cline{1-1}  & Preferred embodiment & & \(C_{\rm c1}d_{3}C_{\rm b1}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The values of \(K_{jm}\), \(k_{jm}\), and \(R_{j}\) at each factor level. reaction time, and the fuller the pores between sand particles are filled with calcium carbonate, which eventually leads to the rising unconfined compressive strength of bio-treated column samples. The \(k_{jm}\) values of \(\lambda\), \(q_{\mathrm{u}}\) and \(\overline{\delta}\) decreased with the increase of concentration of cementation reagent \(C_{\mathrm{c}}\) within the test range, as shown in Figure 6b. In the process of grouting and curing, the higher concentration of cement solution can provide sufficient mineralization raw materials for the formation of thehoate calcium carbonate, so the gap of sand particles was filled quickly by the generated calcium carbonate from the mineralization reaction. Due to the limitation of the vertical injection operation, the pores in the upper part of the sand column were filled rapidly. The number of total fluid injection was reduced on account of pore plugging in the upper part of sand column [33]. Not only that, a high concentration of cementation reagent may obstruct the formation of calcium carbonate. A large amount of Ca\({}^{2+}\) will be adsorbed on the surface of bacterial cells, which will affect the hydrolysis of urea by bacterial urease [23]. This also means that the adoption of solutions with lower concentration of cementation reagent may require more fluid injection times and thus more time cost in the actual operation. The \(k_{jm}\) values of \(\lambda\), \(q_{\mathrm{u}}\) and \(\overline{\delta}\) also decreased with the increase of concentration of bacterial suspension \(C_{\mathrm{c}}\) within the test range, as shown in Figure 6c. This indicates that the high concentration of bacterial suspension is not conducive to the increase of calcium carbonate content in the overall column and the improvement of unconfined compressive strength of the sand column. Figure 6: The variation pattern of \(k_{jm}\) value of each test factor with level: (**a**) effects of sand particle size on test index; (**b**) effects of concentration of bacterial suspension on test index; (**c**) effects of concentration of cementation reagent on test index.