1. Reference problem#
1.1. Geometry#
Software MISS3D uses the frequency coupling method to take into account soil-structure interaction. This method, based on dynamic substructuring, consists in dividing the field of study into three sub-areas:
the ground (which is discretized into border elements),
the foundation (which is meshed in EF),
the structure (which is meshed in EF and represents the building and/or an area bounded by ground).
The floor
The soil corresponds to a homogeneous semi-infinite layer of medium.
The foundation
The rectangular foundation is shown on [Figure 1.1-a] below. Its dimensions are \(24m\) in the \(X\) direction, a width of \(12m\) in the \(Y\) direction, and an indentation height of \(8m\). It is then modelled by 108 surface elements. To speed up the calculations, we deliberately de-refined the height: in practice, it would be necessary to use square-shaped meshes and therefore twice as many meshes in height.
0
z
Figure 1.1-a: Foundation surface mesh
The structure
The structure consists of massive elements representing a homogeneous volume of soil surrounding the foundation. Its dimensions are \(72m\) in the \(X\) direction, a width of \(72m\) in the \(Y\) direction, and an indentation height of \(36m\). It is then modelled by 11520 massive elements. The structure is shown in [Figure 1.1-b] below.
Z
Figure 1.1-b: Volume mesh of the structure
The floor
The mechanical characteristics of the elastic ground model that were used are those indicated below. They make it possible to obtain a shear wave speed of \(800m/s\) for homogeneous soil.
\(E\) (\(N/{m}^{2}\)) |
4.13 E9 |
\(\nu\) |
0.333 |
\(\rho\) (\(\mathrm{kg}/{m}^{3}\)) |
2420 |
\(\text{AMOR\_HYST}\) |
0.1 |
The foundation and the structure
The mechanical characteristics of the foundation and the structure that were used are the same as those of the soil described above.
1.2. Boundary conditions and mechanical loads#
To calculate the 6 static rigid body modes of the foundation and the natural modes, we block the 6 degrees of freedom of translation and rotation of the central node at the base of the foundation by imposing a solid connection relationship. In this central node, 6 nodal force loads of module 1.E6 are also applied to each of the 6 translation and rotation components.
As responses to these 6 requests, the inverse transfer functions of the impedances are then obtained by two harmonic calculation paths: either a modal calculation based on static foundation modes by directly inverting the impedances obtained by the chaining between Code_Aster and MISS3D on a model reduced to the foundation, or a calculation on a physical basis by another method using an exclusive modeling by Code_Aster of a large volume of soil. homogeneous surrounding the foundation: with this modeling, we represents the condition of an infinite medium by absorbent surface elements assigned to the borders of this volume.