Reference problem
=====================


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, which are soil, foundation and structure. Here we treat the case of a superficial foundation alone (without structure). It is a circular foundation with radius :math:`>`. The geometry is that of the foundation treated in reference [:ref:`bib1 <bib1>`] and represented in paragraph 3.


Material properties
----------------------

The soil corresponds to a homogeneous semi-infinite medium whose characteristics are summarized in the table below:


.. csv-table::

    "**Layer**", "**Thickness**
    :math:`>` "," :math:`>` "," :math:`>` "," :math:`>` "," :math:`>`"
    "Layer 1", "40. ", "1875", "0.33", "0.33", "1800", "0.10"
    "Layer 2", "Substratum", "1875", "1875", "0.33", "1800", "0.10"


**Table 1.2-1: Mechanical characteristics of homogeneous soil**

The foundation is considered rigid and weightless.


Boundary conditions and loads
-------------------------------------



Seismic loading consists of a unit excitation in the frequency domain. This makes it possible to directly determine the transfer functions (between seismic excitation and structural response). The foundation is considered rigid. This results in a solid bond of the GROUP_NO radier.