# Experimental Study on Microstructure of Unsaturated Expansive Soil Improved by MICP Method
## 3 Results and Analysis of SWCC Test  
### Selection of the SWCC Fitting Model  
To facilitate the analysis of the test data, empirical models of SWCC were used to fit the test results. Commonly used SWCC models include the Van Genuchten model (VG model) [31,32], the Gardner model [33] and the Fredlund & Xing model [34]. Among them, the VG model is in two- and three-parameter forms, and the commonly used empirical model equations are as follows.  
\[\theta=\theta_{r}+\frac{\theta_{s}-\theta_{r}}{\left[1+(\alpha\varphi)^{n} \right]^{(1-\frac{1}{n})}} \tag{2}\]  
\[\theta=\theta_{r}+\frac{\theta_{s}-\theta_{r}}{\left[1+(\alpha\varphi)^{n} \right]^{(m)}} \tag{3}\]  
\[\theta=\theta_{r}+\frac{\theta_{s}-\theta_{r}}{1+\left(\frac{\varphi}{\alpha }\right)^{n}} \tag{4}\]  
\[\theta=\theta_{r}+\frac{\theta_{s}-\theta_{r}}{\left\{ln\left[e+\left(\frac{ \varphi}{\alpha}\right)^{n}\right]\right\}^{m}} \tag{5}\]  
where \(\theta\) represents the soil volumetric moisture content, \(\theta_{s}\) represents the saturated volumetric moisture content, \(\theta_{r}\) represents the residual volumetric moisture content, \(e\) represents the base of the natural logarithm and \(e\approx 2.71\), \(\varphi\) represents the matric suction, \(\alpha\), \(n\), \(m\) all represents the fitted parameters.  
Figure 2: Measurement for matrix suction: (**a**) sealed storage; (**b**) dried filter paper.  
The four models mentioned above were used to fit the test results of the expansive soils after improvement with different cementation liquid contents. The SWCC was obtained for the improved expansive soils with different fitting models, as shown in Figure 3.  
Figure 3 shows that the SWCC of the expansive soils is anti-\"S\" shaped after the different solutions. The transition section of SWCC in unimproved expansive soils is relatively steep, the rate of desorption in expansive soils is greater, matrix suction has a greater effect on the volumetric moisture content of the soil and the capacity to hold water is weaker. The transition section of the SWCC of the improved expansive soil tends to flatten out as the admixture of cementation liquid increases, the rate of desorption gradually decreases and the capacity to hold water gradually increases.  
The saturated volumetric moisture content and residual volumetric moisture content of the improved expansive soils, and the fitting parameters of the different empirical models, as shown in Table 4.  
Figure 3: Soil-water characteristic curves obtained by model fitting: (**a**) fitted curve for unimproved expansive soil; (**b**) A1 fitted curve; (**c**) A2 fitted curve; (**d**) A3 fitted curve.  
From Table 4, the correlation coefficients of the four empirical models fitted above are all more than 0.99 when fitted by the models to the SWCCs of unsaturated expansive soils, indicating that the fitted results are reliable. The fitting of the various models, in descending order, is the Fredlund & Xing model, the three-parameter [PERSON] model, the Gardner model and the two-parameter Van Genuchten model. The saturated volumetric moisture content of the expansive soil increased from 50.87% to 51.18% with an increase in the admixture of the cementation liquid at the same admixture of the bacterial liquid. Similarly, its residual volumetric moisture content increased from 5.53% to 6.47%. Furthermore, the increasing trend of both saturated and residual volumetric moisture content is non-linear. The Fredlund & Xing model with the optimum fit was selected to investigate the variation of the SWCC parameters of the improved expansive soils, to analyze the SWCC of the expansive soils under different cementation liquid content. It shows that the water-holding capacity of the improved expansive soil is gradually increasing, and the water stability of the soil, which is positively correlated with the water-holding capacity also tends to increase.