# Experimental Study on the Permeability of Microbial-Solidified Calcareous Sand Based on MICP
## 3 Results and Discussion
### The Effect of Gradation on the Permeability Coefficient
In this study, the total particle size interval (0.01-5 mm) and the effective particle size (\(d_{10}=0.25\) mm) were limited, and when the uniformity coefficient is larger (e.g., \(C_{u}=6\), 8), it can be seen from Equation (7) that \(d_{60}\) corresponds to a larger particle size (see Figure 1), i.e., more  
Figure 8: Porosity difference (n) vs. the content of induced CaCO3 (M) of MICP-treated sand at different gradations and compactness (\(D_{r}\)): (**a**) \(D_{r}=30\%\) for samples A1, B1 and E1; (**b**) \(D_{r}=60\%\) for samples A2, B2 and E2; (**c**) \(D_{r}=85\%\) for samples A3, B3 and E3; (**d**) \(D_{r}=30\%\) for samples B1, C1 and D1; (**e**) \(D_{r}=60\%\) for samples B2, C2 and D2; (**f**) \(D_{r}=85\%\) for samples B3, C3 and D3; (**g**) samples B and Y.  
coarse particles and less fine particles (see Figure 2). During the sample preparation process, larger pores can be formed between the coarse particles, while the fine particles cannot completely fill these pores. Therefore, the initial pore space of the sand sample is larger when \(C_{u}\) increases, which is conducive to the penetration of the cementation solution and increases the filling effect of the cementation products, resulting in a larger decrease in the permeability coefficient:  
\[Cu=\frac{d_{60}}{d_{10}} \tag{7}\]  
However, for samples with different \(C_{c}\) (i.e., samples B, C and D), as the total particle size interval (0.01-5 mm), the effective particle size (\(d_{10}\) = 0.25 mm) and uniformity coefficient (\(C_{u}\) = 8) are fixed, it can be calculated from Equation (7) that the \(d_{60}\) is also fixed (\(d_{60}\) =2 mm, see Figure 1). Therefore, different \(C_{c}\) leads to different particle content in the three particle size ranges of 0.25-0.5 mm, 0.5-1 mm and 1-2 mm (see Figure 2). As can be seen from Figure 1, when \(C_{c}\) is smaller (e.g., \(C_{c}\) = 0.5 for sample D), the gradation curve appears as an upper convex segment, indicating that there are more particles with particle size \(\leq\) 1 mm and less particles with particle sizes of 1-2 mm. Thus the relatively finer particles can properly fill the pores between the coarse particles exhibiting the smaller initial pore space. As \(C_{c}\) increases (i.e., \(C_{c}\) = 1.5 for sample B and \(C_{c}\) = 2.0 for sample C), the gradation curve exhibits a downward concave segment, which indicates an increase in the content of the relatively coarser particles and a decrease in the content of the relatively finer particles, resulting in a decrease in the filling effect by the finer particles, i.e., a larger initial pore space. Therefore, the larger initial pore space facilitates the penetration of the cementation solution and the filling effect of the cementation products, causing the obvious reduction in the permeability coefficient. In addition, taking the sample B and the original gradation sample Y as examples (see Figure 6g), it can be found that for samples with the same \(D_{r}\), the \(\Delta k\) increased with the rise in \(C_{c}\) and \(C_{u}\). This can be also attributed to the more coarse particles and less fine particles in sample B (see Figure 2). Therefore, the larger the initial pore space when both \(C_{c}\) and \(C_{u}\) increase, the more conducive they are to cementation solution penetration and more favorable to the filling effect of the cementation products, resulting in a significant reduction in the permeability coefficient. In conclusion, the above experimental results confirm the differences in the application of the MICP technique for calcareous sands with different gradations and that soils with larger \(C_{c}\) and \(C_{u}\) are better improved in terms of permeability by applying MICP. Moreover, with the same gradation, the \(\Delta k\) decreased with the rise in \(D_{r}\). This is because the increase in compactness further compresses the size of the penetrating pore channels inside the sample and reduces the permeability of the sample.