# Water Retention Curve of Biocemented Sands Using MIP Results
## 4 Results and Discussion
### Mercury Intrusion Porosimetry Tests and Water Retention Curve  
The pore size distribution curves from the MIP tests are presented in Figure 5 for the biocemented soil (Bact) and the untreated soil (Soil). For the untreated soil, a marked peak is found at 100 \(\upmu\)m, and a second one, much smaller and less narrow, is found around 800 nm. The treated soil presents a bimodal pore distribution, with dominant pores sizes of 75 \(\upmu\)m and 60 \(\upmu\)m. A very small quantity of pores with a diameter of 4 \(\upmu\)m were also detected for this material that are not representative, and eventually there were also some pores around 800 nm that were detected. This result is consistent with the reduction of permeability observed after the treatment. The experimental points measured with WP4-C and after vapor equilibrium are presented in Figure 6 for the drying branch of the WRC. They are all above 1 MPa due to the limitation of these methods. The WRCs computed from the pore size distribution measured in MIP tests, using the model proposed (Equations (4)-(6), (9) and (10); the values of \(\kappa\) used are those for the unsaturated cases in Table 1) are also in Figure 6 (bacteria MIP--biocemented soil: \(\kappa\) = 0.031, \(e_{MIP,max}\) = 0.308, \(e\) = 0.582; water MIP--untreated soil: \(\kappa\) = 0.033, \(e_{MIP,max}\) = 0.314, \(e\) = 0.588). It can be seen that there is a good adjustment of the curve to the measured points. Figure 4: SEM images of the soil: (**a**) before treatment; (**b**) after treatment, showing calcite crystals. As expected, the curves computed from pore size distribution data have very low air entry value, followed by an almost-horizontal part. The air entry values are very similar for both the treated and untreated soils, being slightly larger for the biocemented soil. This result was expected because the largest pores of the two soils have similar diameters (same peaks in Figure 5); however, the biocemented soil has a double peak, and, therefore, the smallest pores are contributing to increase the value air entry value. The transition to the largest suctions is not very sharp, probably due to the existence of some small pores detected in the MIP tests, as well (around 800 nm and 4 \(\upmu\)m for the treated soil). The differences on the water-retention behavior observed before and after the treatment are expected because the pores' geometry (size, volume, and tortuosity) has changed. The curves from pore size distribution obtained in MIP tests were adjusted by using the expression proposed by [PERSON] (Equation (12)). They are all presented in Figure 7 (bacteria VG--biocemented soil; water VG--untreated soil). Figure 5: Pore size distributions of the samples tested (bacteria—biocemented soil; water—untreated soil in natural state). Figure 6: Water retention curve and its adjustment from using the equations proposed in this paper in which the material behaves elastically under isotropic compression. (Bacteria—biocemented soil; water—untreated soil in natural state). In Figure 7a (P = 0.02 MPa and y = 0.38 for the untreated soil, and P = 0.03 MPa and y = 0.33 for the biochemical soil), the curve computed by using Equation (12) was fitted for the experimental points. In Figure 7b (P = 0.005 MPa and y = 0.30 for the untreated soil, and P = 0.003 MPa and y = 0.30 for the biochemical soil), the curve computed by using Equation (12) was fitted considering the curve computed using pore size distribution data. The adjustment in Figure 7b appears to be worse than in Figure 7a because it does not fit the experimental points or the computed curve well; however, it fits the air entry value better and reduces the overall error computed by using mean square method. The adjustment using data from pore size distribution obtained in MIP tests is considered acceptable below the air entry value [16], where the pressures applied for mercury intrusion are very small. The same is valid here, as insignificant changes in the void ratio are experienced for this range of pressures.