# 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  
Figure 7 shows the permeability coefficient difference (\(\Delta k\)) vs. the cycles of MICP treatment (MT) curves for calcareous sands with different gradations and relative densities (\(D_{r}\)). \(\Delta k\) refers to the difference in the permeability coefficients before and after each MICP treatment cycle. Note that the initial permeability coefficients of all of the sand samples are between \(10^{-2}\) and \(10^{-4}\) cm/s, which is close to the data of relevant studies [43], proving the credibility of the data provided by the permeability test device. Overall, with the increase in MT, the \(\Delta k\) first sharply increases, then rapidly decreases and finally, tends to a relatively stable equilibrium state (MT = 5-7). Such a trend is the process of calcium carbonate (CaCO\({}_{3}\)) gradually filling the intergrain pore places. That is, in the early grouting  
Figure 6: X-ray computed tomography (CT) scan: 2D images of the sample at different sections. stage (MT = 1-2), the pore places between sand particles are continuously filled, so the permeability sharply decreases (i.e., the \(\Delta k\) rapidly increases). With continuous grouting (MT = 3-4), the partial pore places are filled, so the permeability slowly decreases (i.e., the \(\Delta k\) rapidly decreases). At the final grouting stage (MT = 5-7), a large number of pore places are basically filled, and the permeability changes little (i.e., the \(\Delta k\) finally tends to a relatively stable equilibrium state). In fact, the cementation product filling or coating on the particle surfaces changes the specific surface area of the pores. The pore surface is the interface for the fluid flow in sand particles, and its dimensions affect the flow of fluid. As the number of MICP treatments increased, the pore-specific surface area increased, although the porosity of the samples decreased (Figure 8). As an example, the specific surface area was 24 mm\({}^{-1}\) without the MICP treatment and 29 mm\({}^{-1}\) after seven MICP treatments for sample Y2. Usually, the permeability of the soil decreases with the increase in the pore-specific surface area, so the permeability coefficient decreased with the increase in MT. This relationship between permeability and MT was also confirmed by [PERSON] et al. [50]. Moreover, the small change in permeability (MT = 5-7) can be attributed to the ineffective filling of some cementation products [51]. That is, some CaCO\({}_{3}\) crystals fill the particle surfaces rather than the interparticle pore spaces and cannot lead to a reduction in permeability. Figure 7: Permeability coefficient difference (\(\Delta k\)) vs. cycles of MICP treatment (MT) of 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. From Figure 7a-c, it can be seen that for the sand samples with the same \(D_{r}\) and \(C_{c}\) (e.g., groups A1, E1 and B1 or A2, E2 and B2 or A3, E3 and B3), the \(\Delta k\) increased with the rise in \(C_{u}\). Similarly, in the case of the same \(D_{r}\) and \(C_{u}\) in Figure 7d-f (e.g., groups B1, C1 and D1 or B2, C2 and D2 or B3, C3 and D3), the \(\Delta k\) increased with the rise in \(C_{c}\). These results show that the CaCO\({}_{3}\) crystals produced by the MICP treatment filled the pores and cemented the grain particles, resulting in a decrease in \(k\) in the sand samples, but the decreasing amplitude of \(k\) in the samples with various \(C_{u}\) and \(C_{c}\) is different.