# Strength Characteristics and Slope Stability Analysis of Expansive Soil with Filled Fissures
## 5 Stability Analysis of Expansive Soil Slope Considering Filled Fissures
### Slope Generalization and its Stability Analysis  
The stability analysis of slope was carried out by using the platform Slide, which is the two-dimensional limit equilibrium process for the evaluation of the rock and soil slope safety coefficient and failure probability. Three limit equilibrium methods, namely Janbu correction, Spencer and Morgenstern, which could meet inter slice force and moment equilibrium and were suitable for a broken line slide surface, were chosen for slope stability calculation. According to the actual slope, the 2D geometry model of the slope was established. The vertical fissures at the top of the slope and the controlled fissures in the slope body were converted into thin layers in the model, and the mechanical strength parameters of the thin layers were considered to reflect the influence of the fissures on the slope stability. The thickness of the thin layer was selected as the average thickness of the measured fissure. According to the measured statistics, the thickness of the fissure was generally 3 to 8 cm. Therefore, the following methods were used to generalize the spatial distribution of fractures  
Firstly, the slope surface equation was established in the plane coordinate system. \[y=ax+b,\ x\in\ (m,\ n) \tag{3}\]  
For the fissure distributed in the elevation \(h\), with the inclination angle of \(\theta\), the length of \(l\), and the thickness of \(t\), the coordinate at the endpoint in the slope surface was \([(h-b)/a,h]\). In the model, the fissure was simplified to a linear form, and the equation could be expressed as follows. \[y=\tan\theta\bigg{(}x-\frac{h-b}{a}\bigg{)}+h,\ x\in\bigg{(}\frac{l}{\sqrt{1+ \tan^{2}\theta}}\bigg{)}+\frac{h-b}{a},\frac{h-b}{a} \tag{4}\]  
In the actual modeling, through the preparation of the program, the fissure Equation (4) was translated upward by the fissure thickness \(t\), and the intersection point with the slope Equation (3) is obtained to obtain the coordinates of the four vertices of the parallelogram fissure. The geometric model of slope fissure surface distribution is basically consistent. These coordinates were importedinto the slope model to establish the geometric model of the slope with filled fissures. The calculation model is shown in Figure 10.  
In situ direct shear tests were carried out on the slope soil, and indoor triaxial tests were carried out on the filled fissure. Strength parameters were confirmed in a comprehensive consideration of the test data of the undisturbed expansive soil and the expansive soil with filled fissures (Table 4). The first layer of reddish brown clay was hard plastic, with a free expansion rate of 42%, low permeability, and the lowest shear strength. The second layer of brown-yellow clay was hard plastic, with a free expansion rate of 56%, low permeability, relatively developed fissures, and high shear strength. The third layer of brown clay and gray-green clay was hard plastic, with a free expansion rate of 93% and strong swelling characteristics, and shear strength equivalent to that of the previous layer. The fissures were very developed, and most of them were long-large fissures. Incorporating typical filled fissures into the model and calculating under the conditions closest to the real working conditions, it could be found that the safety factor of the slope was about 0.9. The slope was in an unstable state. At the same time, under the same geometric model, soil parameters and groundwater conditions, the stability analysis of the homogeneous expansive soil slope without fissures was carried out. It was found that the safety factor of the slope was about 1.2, and the slope was not unstable. As shown in Figure 11, in a homogeneous expansive soil slope without fissures, the sliding surface is arc-shaped, extending from the top of the slope to the foot of the slope (Figure 11a).