Fixities and deformation boundary conditions

In PLAXIS 3D, default boundary conditions are automatically applied: see PLAXIS 3D Reference Manual in the section about Standard Boundary Conditions. For e.g. soil volumes this means:

• Vertical model boundaries with their normal in x-direction (i.e. parallel to the yz-plane) are fixed in x-direction (u_x = 0) and free in y- and z-direction.
• Vertical model boundaries with their normal in y-direction (i.e. parallel to the xz-plane) are fixed in y-direction (u_y = 0) and free in x- and z-direction.
• Vertical model boundaries with their normal neither in x- nor in y-direction are fixed in x- and y-direction (u_x = u_y = 0) and free in z-direction.
• The model bottom boundary is fixed in all directions (u_x = u_y = u_z = 0).
• The 'top surface' is free in all directions.

It is also possible to define user defined fixities and/or prescribed displacements on points, lines and surfaces. A user defined fixity can be defined by introducing a prescribed displacement and then set the displacements in a certain direction to “Fixed” or set the value to zero.

When these default boundaries and the user defined boundaries conflict the user-defined prescribed displacements/fixities always 'win' from automatically defined fixities. This means that if a prescribed surface displacement is placed on the top surface and this surface displacement shares an edge with the side surface of the model (e.g. in the modelling of a symmetrical smooth footing), there will be no horizontal fixity on the shared edge. In this case, add a line prescribed displacement along this edge and assign the proper fixity conditions to it.

When there are multiple restrictions defined for a direction for a single location/node:

• a non-free prescribed displacement will take preference over a load
• a user defined prescribed displacement will take preference over a standard boundary condition
• a user defined prescribed displacement set to Fixed will take preference over other user defined prescribed displacements
• a prescribed displacement value will take preference over a prescribed displacement set to free
• a higher user defined prescribed displacement (absolute) value will will take preference over a lower user defined prescribed displacement (absolute) value. E.g. for two connected plates: plate 1 will have a prescribed displacement of u_z = +0.05 m and plate 2 will be subjected to a prescribed displacement of u_z = -0.07 m, the connected line will be subjected to a prescribed displacement of the highest absolute value: u_z = -0.07 m.
  

Combination of standard boundary conditions and prescribed displacements: Footing

In this example, we model a quarter of a geometry of a square footing: there is a symmetry axis in the x-axis, and also in the y-axis:

The footing will be modelled by a prescribed displacement, with u_z = - 0.01 m for this case.

Case A: rigid

First we model the footing as a prescribed displacement rigidly connected to the soil, meaning all horizontal displacements directly beneath the footing are prevented (=fixed). At intersection of the boundary and the footing, the displacements are defined twice: e.g. at the x-axis / footing intersection, the default boundary conditions are:

• u_y is fixed
• u_x and u_z are free

However, the footing defines this at the x-axis:

• u_z = -0.01 m
• u_x and u_y are fixed

According to the rules above this will be used for the calculation:
User defined boundary conditions overrule the default boundary conditions, so at the intersection of the x-axis and the footing:

• u_z = -0.01 m
• u_x and u_y are fixed

This is exactly what was intended

Case B: smooth

Secondly we model the footing (=prescribed displacement) as being completely smooth, meaning all horizontal displacements directly beneath the footing are possible: u_x and u_y are free. At intersection of the boundary and the footing, the displacements are defined twice: e.g. at the x-axis / footing intersection, the default boundary conditions are:

• u_y is fixed
• u_x and u_z are free

However, the footing defines this at the x-axis:

• u_z = -0.01 m
• u_x and u_y are free

According to the rules above this will be used for the calculation: User defined boundary conditions overrule the default boundary conditions, so at the intersection of the x-axis and the footing:

• u_z = -0.01 m
• u_x and u_y are free

This is not what is intended for the calculation: in the axis of symmetry, it is not correct to have displacements perpendicular to the axis of symmetry.

In order to overcome this problem, some specific boundary conditions must be applied on the intersection of the footing and the model’s boundary. This can be done by adding a line with a prescribed displacement and setting the correct prescribed displacement conditions:

At the x-axis, a line was added that has the same conditions as the default boundary conditions at that side: u_y is fixed, while u_x and u_z are free.
Now, at intersection of the x-axis and the footing, the displacements are defined three times. The default boundary conditions are:

• u_y is fixed
• u_x and u_z are free

The footing defines this at the x-axis:

• u_z = -0.01 m
• u_x and u_y are free

And the line defines:

• u_y is fixed
• u_x and u_z are free

According to the rules above this will be used for the calculation:

• u_x is free since all three conditions set u_x to free
• u_y is fixed. This is defined by the line. It overrules the setting of the surface/footing, which is set to free.
• u_z is set to -0.01 m, as defined by the surface/footing. The line does not take preference here, since u_z is set to free for the line prescribed displacement.