# Eigendegradation Algorithm Applied to Visco-Plastic Weak Layers
## 5 Conclusions  
A new visco-plastic degradation model has been proposed in order to simulate the behavior of layers of soft clays. The main aim of this model is to eliminate the mesh dependence shown by other methodologies available in the literature. Taking benefits of the concept of eigendeformation, this model can reproduce both non-local and localized (shear bands) failures. The non-local performance of the proposed algorithm has been considered following concepts of non-local meshfree models capable of reproducing both brittle (eigenerosion) and quasi-brittle (eigensoftening) behaviors. Thus, the proposed algorithm takes the name of _eigendegradation_. Two main properties define the proposed constitutive model: softening due to degradation and visco-plastic behavior. Thus, two different examples are provided in order to validate both properties. Figure 14: Distribution of the equivalent plastic strain in the deformed model obtained with the eigendegradation model at 4 different times. Figure 15: Distribution of the equivalent plastic strain in the deformed model obtained with the standard softening model (FEM) at 3 different times. The first example reproduces a shear test of a soil with a thin soft layer. This test shows the performance of the degradation behavior from the beginning of the reduction of the shear strength to the final of this reduction, obtaining a residual strength. This result has been compared to other similar work of degradation of clays, obtaining very close curves, which let us think the behavior of the proposed algorithm when modeling this material is correct. The second example studies the behavior of a soil loaded by a strip footing. In this case, the visco-plastic concept is the one to be assessed. Since the von Mises yield surface is employed, the traditional Prandtl mechanism is obtained. Moreover, a hardening behavior is observed either when the viscosity becomes higher or when the load is applied quicker. This example allows us to validate the viscous behavior, as well as to verify that the degradation acts as a softening of the material that helps to define clearer the shear bands formed in the plastic mechanism. Finally, a vertical cut of soil is modeled. This soil contains a 45\({}^{\circ}\) soft layer. A compound load is applied, the first part being the one that causes the beginning of the degradation of the material and the last part being the one that causes the whole degradation of the shear strength and the final failure of the slope. In comparison with a traditional softening law, the proposed one is capable of producing degradation with elastic accumulated strain, with the accumulation under both loading or unloading conditions. This behavior is seen in many failures of this type of soft layer, where a load is much lower than the critical one, but it is held in time, causing the fatigue of the material and the final failure of the soil structure. The present algorithm has performed successfully with the proposed applications. The algorithm is robust, and its conjunction with any particle-based numerical technique (OTM in this research) presents an interesting feasibility. The proposed methodology is able to reproduce previous results with degradation models (example 1) and visco-plastic materials (example 2). Moreover, as it is observed in example 3, once the mechanism is activated, the model is capable of capturing the degradation of the material even in small elastic cycles, which allows reproducing the triggering of a landslide from a very low loading range. Further research can be made in order to be able to reproduce a wide range of problems. First of all, this model should be calibrated against experimental tests such as the shear test. Moreover, only the von Mises yield surface has been validated in this manuscript. Although it is able to reproduce the undrained conditions of the soil, more sophisticated yield surfaces, such as the Cam-Clay one, would improve the type of problems to be modeled.