Data part, generate mesh with Tochnog

control_mesh_macro 10 -rectangle soil1_group 7 25
control_mesh_macro_parameters 10 1.5 3.0 3.0 6.0
control_mesh_macro_element 10 -quad4

control_mesh_macro 20 -rectangle soil0_group 7 9
control_mesh_macro_parameters 20 1.5 7.0 3.0 2.0
control_mesh_macro_element 20 -quad4

control_mesh_merge 30 -yes
control_mesh_merge_macro_generate 30 10 20

Tochnog has some build in mesh generation possibilities which are convenient for relatively easy meshes. If the mesh is complex, Gid works better.

With control_mesh_macro 10, control_mesh_macro_parameters 10 and control_mesh_macro_element we specify that a rectangular mesh should be generated, with quad4 elements and the elements should be assigned to group 1. The rectangle has middle point ($x=1.5$,$y=3.0$), width $3.0$ and height $6.0$; the number of nodes in width direction, so $x$-direction, is 7 and the number of nodes in height direction, so $y$-direction, is 25. Similar, the records with index 20 generate a second rectangular mesh. These 10 and 20 records together generate the left part of the mesh, that is all quad4 elements to the left of the sheet pile.

The two rectangular meshes each have nodes at a common line $y=6.0$, so in fact there are duplicate nodes at this line. The control_mesh_merge 20 takes care that these duplicate nodes are merged, so that at the common line the meshes connect to the same nodes, and solution field like velocities, displacement and water pressure are continuous. With control_mesh_merge_macro_generate 20 we ensure that the meshes as specified with the macro's with index 10 and 20 are merged.

control_mesh_macro 40 -rectangle soil1_group 28 25
control_mesh_macro_parameters 40 7.5 3.0 9.0 6.0
control_mesh_macro_element 40 -quad4

control_mesh_macro 50 -rectangle soil0_group 28 9
control_mesh_macro_parameters 50 7.5 7.0 9.0 2.0
control_mesh_macro_element 50 -quad4

control_mesh_merge 60 -yes
control_mesh_merge_macro_generate 60 40 50

With the macro's with indices 40 and 50 rectangular meshes are generated to the right of the sheet pile. Again we merge the top and bottom mesh at the common line at $y=6.0$.

control_mesh_merge 70 -yes
control_mesh_merge_macro_generate 70 10 40
control_mesh_merge_not 70 -beam_short_line

Up to now we only merged rectangular meshes along $y=6.0$, so at their common horizontal line. Here we merge the left and right meshes at their common line along $x=3.0$. However, to allow for slip along the sheet pile, we do not want to merge nodes along the location of the sheet pile, so that slip and different displacements at the sheet pile remains possible. Thus the merging with index 70, is not done at the sheet pile, by including control_mesh_merge_not 70. In fact we use a geometrical line a bit shorter than the actual length of the sheet pile. The reason for this is that the nodes at the end of the sheet-pile can either be considered to be part of the sheet-pile, or part of the soil underneath the sheet-pile. We prefer to consider these nodes the be part of the soil underneath the sheet-pile, and so prefer to merge these nodes.

control_mesh_generate_truss_beam 80 sheet_pile_group -beam_line
control_mesh_generate_truss_beam_loose 80 -yes
control_mesh_generate_truss_beam_macro 80 10 20

control_mesh_generate_contact_spring 90 contact_spring_group -beam_line
control_mesh_generate_contact_spring_element 90 -quad4 -truss_beam

With the previous macro and merge records we have generated quad4 elements for the soil. Here with the control_mesh_generate_truss_beam 80 record we generate the truss-beam elements for the sheet-pile line, and should be assigned to the group sheet_pile_group.. The control_mesh_generate_truss_beam_loose 80 record tells Tochnog that the generated truss-beam elements should not be fixed to the existing nodes of the quad4 elements, but should get their own new nodes; this will allow for slip between the sheet-pile truss_beam nodes and the quad4 soil element nodes. The control_mesh_generate_truss_beam_macro 80 record tells Tochnog that only truss elements should be placed near nodes which have been generated from a macro with index 10 or 20 (if we would not do this, then twice too much truss-beam elements).

Contact springs between truss_beam nodes and quad4 nodes are generated with the control_mesh_generate_contact_spring 90 records.

Figures 14 shows the generated mesh, and 15 gives a schematic drawing how the truss_beam elements are connected to the quad4 elements. The detail drawing with the springs in figure 15 is really only for clarity; in reality the nodes of the truss_beam elements and the quad4 elements have the same position in space, but that would not give a very clear drawing.

Figure 14: Mesh with quadrilateral elements, truss_beam and contact springs

Figure 15: Model of slip at beam with springs