# Experimental Study on the Permeability of Microbial-Solidified Calcareous Sand Based on MICP
## 3 Results and Discussion
### Porosity and Mass Variation  
Figure 8 shows the porosity difference (\(\Delta n\)) vs. the content of induced CaCO\({}_{3}\) (\(M\)) for MICP-treated sands at different relative densities (\(D_{r}\)) and grain gradations. \(\Delta n\) refers to the difference in porosity before and after each MICP treatment cycle. Overall, all sand samples showed a certain increase in \(M\) and decrease in \(n\) after the MICP treatments. Specifically, with the increase in MT, the \(\Delta n\) first increases, then decreases and finally, tends to a dynamic equilibrium (MT = 5-7); the variation pattern of \(\Delta n\) corresponds to the changes in permeability (Figure 7). This can be attributed to the fact that pore structure characteristics are the key factors affecting permeability [4]; that is, the induced CaCO\({}_{3}\) filled the pores leading to the reduction in porosity, which inevitably reduces permeability. Therefore, the porosity and the permeability exhibit the same trend with the change in MT  
(the explanation of this trend can be found in Section 3.1). Meanwhile, during the MICP treatment, the increase in \(M\) was smaller in the late stage (MT = 5-7). Such a change trend is shown in Figure 8, with dense data points at the end of the curve and discrete data points in the front section of the curve. The decrease in porosity and the increase in mass suggested that the induced CaCO\({}_{3}\) filled the pores between the sand particles, but with the increase in MT (MT = 5-7), cementation products filled most of the pores, resulting in small changes in \(\Delta n\) and \(M\).  
It is of interest to note that, from Figure 8a-c, it can be seen that for sand samples with the same \(D_{r}\) and \(C_{c}\) (e.g., groups A1, B1 and E1 or A2, B2 and E2 or A3, B3 and E3), the \(\Delta n\) and \(M\) increased with the rise in \(C_{u}\). Similarly, from Figure 8d-f, for the sand samples with the same \(D_{r}\) and \(C_{u}\) (e.g., groups B1, C1 and D1 or B2, C2 and D2 or B3, C3 and D3), the \(\Delta n\) and \(M\) increased with the rise in \(C_{c}\). In addition, taking sample B and the original gradation sample Y as examples (see Figure 8g), it can be found that for samples with the same \(D_{r}\), \(\Delta n\) and \(M\) are larger when both \(C_{c}\) and \(C_{u}\) increase.  
In sum, the test results once again confirm the differences in the application of the MICP technique for calcareous sands of different gradations; specifically, soils with larger \(C_{c}\) and \(C_{u}\) have a greater decrease in porosity and more CaCO\({}_{3}\) generated within the soil after MICP treatment, thus the decrease in the permeability coefficient is also more significant.  
Moreover, with the same gradation, \(\Delta n\) and \(M\) decreased with the rise in \(D_{r}\). This is because the increase in compactness further reduces the initial pore space, and the limited pore space can only be filled by a small amount of cementation product, causing a lower \(\Delta n\) and \(M\). Thus, a lower \(D_{r}\) can obtain more induced CaCO\({}_{3}\) to fill pore places [50], leading to an obvious reduction in porosity.