# Strength Characteristics and Slope Stability Analysis of Expansive Soil with Filled Fissures
## 4 Analysis of Strength Characteristics of Expansive Soil with Filled Fissures
### Strength Fitting Method and Strength Characteristic Analysis  
According to the stress-strain relationship curve of the triaxial test results, the peak stress (\(\sigma_{1f}\)-\(\sigma_{3f}\)) of the specimen at failure was obtained. According to the static equilibrium conditions, Equations (1) and (2) were used to calculate the normal stress \(\sigma_{n}\) and shear stress \(\tau\) in the filled fissure when the specimen failed [38].  
\[\sigma_{n}=\frac{\left(\sigma_{1f}+\ \sigma_{3f}\right)}{2}+\frac{\left(\sigma_{1 f}-\ \sigma_{3f}\right)}{2}\cos 2\alpha \tag{1}\]  
Figure 6: Stress–strain curve of the triaxial test. (a) Without a filled fissure; (b) filled fissure with an inclination angle of \(15^{\circ}\); (c) filled fissure with an inclination angle of \(30^{\circ}\); (d) filled fissure with an inclination angle of \(45^{\circ}\).  
Figure 7: The shear failure characteristics of the sample along the diagonal of the filled fissure.  
\[\tau=\frac{\left(\sigma_{1f}-\sigma_{3f}\right)}{2}\sin 2\alpha \tag{2}\]  
where \(\sigma_{n}\) is the normal stress on the shear plane, \(\tau\) is the shear stress on the shear plane, \(\sigma_{1f}\) is the large peak principal stress, \(\sigma_{3f}\) is the small peak principal stress, and \(\alpha\) is the angle between the shear plane and the horizontal plane.  
According to the Mohr-Coulomb theory, the relationship curve between normal stress \(\sigma_{n}\) and shear stress \(\tau\) could be obtained, and the shear strength parameters \(c\) and \(\varphi\) of the filled fissure can be obtained. The fitting results are shown in Figure 8 and Table 3, respectively.  
It can be seen that the homogeneous medium expansive soil matrix was used for the triaxial test, and the strength parameter \(c=17.81\) kPa and \(\varphi=8.07^{\circ}\). After setting the filled fissures of gray-green strong expansive soil in the medium expansive soil matrix, it had a greater impact on the mechanical properties of the expansive soil, resulting in different degrees of strength attenuation at various load levels in the triaxial tests. The strength attenuation was positively correlated with the inclination of the filled fissure. The strength parameters of expansive soils with filled fissures were basically stable, in which the cohesive force \(c\) was about 12 to 15 kPa and the internal friction angle \(\varphi\) was about 3\({}^{\circ}\) to  
Figure 8: Shear strength fitting results of the triaxial test. (**a**) Without a filled fissure; (**b**) filled fissure with an inclination angle of 15\({}^{\circ}\); (**c**) filled fissure with an inclination angle of 30\({}^{\circ}\); (**d**) filled fissure with an inclination angle of 45\({}^{\circ}\).  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Shear Strength**} & \multicolumn{4}{c}{**Inclination Angle of the Filled Fissure (\({}^{\circ}\))**} \\ \cline{2-5}  & **No Filled Fissure** & **15** & **30** & **45** \\ \hline \(c\) (kPa) & 17.81 & 14.63 & 14.22 & 12.04 \\ \(\varphi\) (\({}^{\circ}\)) & 8.07 & 5.84 & 4.01 & 2.97 \\ \hline \end{tabular}
\end{table}
Table 3: Shear strength results of the triaxial test.  
\(6^{\circ}\). The deformation characteristics of the samples had a tendency to develop from strain hardening to strain softening after setting the filled fissures, and this was most significant when the fissure was filled with a \(45^{\circ}\) inclination angle.