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Muskat problem

Development of geometry model and groups

Creating a geometry is the first step to run a problem in numgeo with GiD. The shape can be made by using the straight line Icon toggle and entering exact coordinates into the command line. Following are the cordinates for the muskat problem:

0,0
0,3.22
0,4
1.62,4
1.62,0.48
1.62,0

After entering all coordinates, close the shape by clicking on the first point to join it. Then, define the NURBS surface by selecting all the lines and press ‘Esc’ to finish.

Initial loads
Figure 2: Geometry of the model

Add all relevant groups using the tab on the right side. For the groups nleft, nleft_sat, nright, nright_sat, ntop, and nbottom, select the corresponding lines. For the group eall, select the entire surface.

Initial loads
Figure 3: Creating groups of the numerical model

Next, the mesh was generated. The element type can be triangular or quadrilateral; in this simulation, a triangular mesh element was used. The mesh was created with an element size of 0.1 m. For improved visualization, the mesh view was toggled using the button Icon toggle on the left toolbar.

Initial loads Initial loads
Figure 4: Generating mesh

To define the model properties, first load the numgeo problem type in GiD by navigating to Data → Problem type → numgeo. A data tree will appear on the left hand side of the screen.

Initialloads
Figure 5: Loading numgeo problemtype

Set the problem dimension to 2D (Plane strain), and assign element 3-phase u-p stabilized formulation with full integration to soil_all, which enables the simultaneous consideration of soil, water, and air phases.

Initialloads
Figure 6 Assigning dimension and element type

Materials properties

Next, we define the material properties. Under Material Definition, create a material named “mat_subsoil” and specify its parameters, including the number of phases, stress–strain model, density, permeability, saturation–suction relationship, permeability–saturation relationship, Bishop’s effective stress, bulk modulus, and dynamic viscosity, as shown in Figure 8.

Materialsubsoil parameters 1 Materialsubsoil parameters 2
Figure 8: Material parameters of soil

Assign materials

Next, we assign the materials. This step involves specifying the defined material properties to the corresponding section.

Material subsoil parameters 1
Figure 11: Assign material

Initial conditions

The next step is to define the initial conditions for the numerical model.

Material subsoil parameters 1
Figure 11: Assign material