Slope Stability and Mesh Fineness

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Hello,

I want to run slope stability analysis for a slope using COMSOL. The slope dimensions and the soil properties are obtained from an example discussed in the Griffiths and Lane’s paper. The FS in the mentioned paper and from the limit equilibrium method are obtained as 1.40 and 1.38, respectively. The issue is that the FS based on COMSOL results is highly dependent on mesh resolution. For direct solver, Constant Newton method, and quadratic triangle mesh with maximum element size of 4m and 0.2m, the FS is computed as 1.4, and 1.0 (finer mesh results in wrong FS). Could you please let me know why by using the finer mesh incorrect results are obtained? What solving method should be used for finer mesh? When the FS parameter is gradually increasing in this method, do the results (deformation, stress) of new FS depend on the results of previous FS? (i.e. is there any searching procedure with respect to strength reduction factor?)

The model is attached.

Thanks a lot in advance. Amin



3 Replies Last Post Mar 15, 2019, 8:08 PM EDT
Henrik Sönnerlind COMSOL Employee

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Posted: 1 month ago Mar 7, 2019, 2:13 PM EST

Hi Amin,

What you see is a 'numerical' formation of artificial shear bands.

There are some remedies:

  • You can change the discretization to use linear shape functions (which of course allows you to use even more elements). Since linear shape functions imply constant stress within the element, the possibility to form this kind of pattern is reduced.
  • Use a less regular mesh. Change the method to Delauney in the Free Triangular node. It will be more difficult to form this kind of patterns in an unstructured mesh.
  • More advanced: Add some kind of stabilization equation which penalizes either gradients within elements or gradients over a certain distance. This is the same kind of techniques as is used in the Damage feature (new in version 5.4).

Regards,
Henrik

Hi Amin, What you see is a 'numerical' formation of artificial shear bands. There are some remedies: * You can change the discretization to use linear shape functions (which of course allows you to use even more elements). Since linear shape functions imply constant stress within the element, the possibility to form this kind of pattern is reduced. * Use a less regular mesh. Change the method to Delauney in the Free Triangular node. It will be more difficult to form this kind of patterns in an unstructured mesh. * More advanced: Add some kind of stabilization equation which penalizes either gradients within elements or gradients over a certain distance. This is the same kind of techniques as is used in the Damage feature (new in version 5.4). Regards, Henrik

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Posted: 1 month ago Mar 14, 2019, 11:20 PM EDT

Thanks a lot Henrik for the percise response! It resolved the issue.

Amin

Thanks a lot Henrik for the percise response! It resolved the issue. Amin

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Posted: 1 month ago Mar 15, 2019, 8:08 PM EDT

Hello,

Similar to the previous question, I want to run slope stability analysis but for an infinite slope. In order to simulate infinite slope condition, periodic boundary conditions are implemented on the lateral sides of the domain. The FS from the analytical limit state equilibrium method is computed as 2.15, and COMSOL results in the same value, as well (c’=0 Pa, phi’=30 deg, slope=15 deg). However, the issue is that under the geostatic condition prior to slope stability analysis, by evaluating the elastic stress state, most of the soil elements have exceeded Mohr-Coulomb failure envelope (implying element failure). In this regard, why the FS is obtained more than unity indicating a stable slope while soil elements have already failed?

The model has been attached.

Thank you very much for the assistance.

Hello, Similar to the previous question, I want to run slope stability analysis but for an infinite slope. In order to simulate infinite slope condition, periodic boundary conditions are implemented on the lateral sides of the domain. The FS from the analytical limit state equilibrium method is computed as 2.15, and COMSOL results in the same value, as well (c’=0 Pa, phi’=30 deg, slope=15 deg). However, the issue is that under the geostatic condition prior to slope stability analysis, by evaluating the elastic stress state, most of the soil elements have exceeded Mohr-Coulomb failure envelope (implying element failure). In this regard, why the FS is obtained more than unity indicating a stable slope while soil elements have already failed? The model has been attached. Thank you very much for the assistance.

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