# Eigendegradation Algorithm Applied to Visco-Plastic Weak Layers
## 4 Applications
### Shear Test  
In the first example, the behavior of a weak layer under a shear test is analyzed. In Figure 5, an embankment of 10 m of depth is presented. A weak layer in the bottom of the domain of 0.5 m appears. The proposed shear test is similar to the one proposed by [PERSON] et al. [54]. Although different constitutive laws are employed (local and non-local), it is expected to obtain comparable results since both laws are based on similar degradation processes.  
The original embankment's length is 700 m. Since the softened zone only extends 90 m and considering infinite conditions at both sides of this softened zone, only this 90 m is modeled in order to save computational effort. Unlike the original example, gravity conditions are neglected, considering the failure of the embankment at the final of the residual strength. Thus, the parameters needed in this example are shown in Table 2. It is important to point out that in this research, the proposed non-local degradation model has been employed with a neighborhood parameter, \(C_{e}\), of 1.5. This is an important difference with respect to the model proposed for the original example, which evaluates the degradation locally in an Arbitrary Eulerian-Lagrangian (ALE) configuration.  
In addition, the geometry and boundary conditions can be seen in Figure 5. Regarding the latest, two boundary conditions have been considered. In the first one, \(\Gamma_{1}\) in Figure 5, both vertical and horizontal displacements are constrained. In \(\Gamma_{2}\), a horizontal displacement of 10 m is imposed gradually from 0 to 1000 s.  
The stress behavior is analyzed in Figure 6. In order to assess the performance of the proposed algorithm, similar to the figure proposed by [PERSON] et al. [54], in Figure 6, a dimensionless measurement of the shear stress is plotted. It is calculated as a relative increment from the residual shear strength \(\tau_{95}\) and divided by the maximum increment, which is measured from the initial (or peak) strength to the residual one, \(\tau_{p}-\tau_{95}\). On the other hand, in the abscissa, the dimensionless distance from the beginning of the degradation is plotted. Thus, the degradation starts from 0 until reaching the \(\tau_{95}\) at distance 1.  
\begin{table}
\begin{tabular}{l l} \hline Softened/modeled length \(L=l_{0}\) & 90 m \\ Overall height, \(H\) & 10 m \\ Height of sliding material, \(h\) & 7.2 m \\ Shear band thickness, \(s\) & 0.5 m \\ Submerged density of the soil, \(\rho\) & 600 kg/m\({}^{3}\) \\ Poisson’s ratio, \(\
u\) & 0.495 \\ Young’s modulus, \(E\) & 1.98 MPa \\ Peak shear strength, \(\tau_{p}=\tau_{i}\) & 10 kPa \\ Residual (95\%) shear strength, \(\tau_{95}=\tau_{r}\) & 1.25 kPa \\ Plastic shear strain to 95\% reduction in strength, \(\gamma_{p}\) & 0.6 \\ Neighborhood parameter, \(C_{e}\) & 1.5 \\ \hline \end{tabular}
\end{table}
Table 2: Parameters for the shear degradation analysis.  
Figure 5: Geometry and loading conditions of the shear degradation problem.  
Results obtained in this research and the ones obtained by [PERSON] et al. [54] are not coincident, since they are different approaches; however, the overall trend, mainly after the beginning of the degradation, is similar to the reference research. This application allows us to assess the performance of a degraded layer of soft clay, which has been proved to perform similar to other validated studies.