1. Reference problem

1.1. Geometry and meshing

We consider an embankment (with a slope of 1:2) made of homogeneous material with a height of 4.5m. The model is 18m wide and 6.5m high.

We define the right side as the upstream surface in contact with water (river or water reservoir), and the slope as well as the downstream surface.

The mesh is shown in fig1-geom-mail. This is the same model used in the ssnop006 test case (V6.03.006) but with a rough mesh to speed up the calculation.

1.2. Material properties

The same material properties as the SSNP006 test case are adopted, i.e.:

• Unit mass of soil: \({\gamma }_{\mathit{sol}}=16\mathit{kN}\)

• Ground friction angle: \(\varphi =20\mathit{deg}\)

• Soil cohesion: \(c=5\mathit{kN}/{m}^{2}\)

• Soil permeability: \(k=1e-7m/s\)

• Biot coefficient: \(b=1.0\)

For the Mohr_Coulomb law, we hypothesize the associated plastic flow law.

The parameters of the Drucker-Prager law were obtained by the following formulas:

\(A=\dfrac{2\mathrm{sin}(\varphi )}{3-\mathrm{sin}(\varphi )},{\sigma }_{y}=\dfrac{6c\mathrm{cos}(\varphi )}{3-\mathrm{sin}(\varphi )}\)

• The angle of expansion is equal to the angle of friction in the Drucker-Prager law.

  In order to simplify the calculation, the cumulative plastic deformation ultimate \({p}_{\mathit{ultm}}\) is considered void (= 0).

• The porosity is uniform in the model and is equal to 0.62.

1.3. Boundary conditions

The hydraulic boundary conditions applied to the model are as follows:

• The bottom of the model is waterproof.

• Hydraulic pressure from the 4 m upstream coast (peak elevation = 6.5 m).

• Hydraulic pressure defined from the level of the groundwater downstream, which is equal to 2m.