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


Geometry
---------

We consider a floor column resulting from the sdnx100 test case, whose main characteristics are described below:

**The floor**


.. image:: images/10000000000002D2000001D634DA637CBB3A5AC5.png
    :width: 4.1472in
    :height: 2.5646in


.. _RefImage_10000000000002D2000001D634DA637CBB3A5AC5.png:

Laminate flooring configuration


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


Elastic properties of the material
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The mechanical characteristics of the soil model layers that were used are summarized in the table below:


.. csv-table::

    "**Layer**", "**Sub-layer**", ":math:`\mathrm{vs}(m/s)` "," "," :math:`E(\mathit{Pa})` "," :math:`\rho (\mathrm{kg}/{m}^{\mathrm{²}})` "," :math:`\nu` "," :math:`\xi (\text{\%})` "," :math:`h(m)` "," :math:`b(\text{\%})` "," "," :math:`{N}_{1}`"
    "1", "1", "184", "2.67 108", "2.67 108", "2650", "0.49", "2.5", "7.6", "5.0", "0"
    "1", "2", "206", "3.35 108", "3.35 108", "2650", "0.49", "2.5", "7.6", "5.0", "0"
    "2", "3", "340", "9.21 108", "9.21 108", "2710", "0.47", "2.5", "33.0", "5.0", "0"
    "2", "4", "417", "1.39 109", "1.39 109", "2.5", "34.0", "5.0", "5.0", "0", "0"
    "2", "5", "496", "1.96 109", "1.96 109", "2.5", "34.0", "5.0", "5.0", "0", "0"
    "3", "6", "620", "3.02 109", "3.02 109", "2710", "2710", "0.45", "2.5", "5.50", "5.0", "0"
    "3", "7", "870", "5.95 109", "5.95 109", "2710", "2710", "0.45", "2.5", "5.50", "5.0", "0"
    "4", "8", "2500", "4.23 1010", "4.23 1010", "2710", "0.25", "1.0", "-", "2.0", "2.0", "0"


The values of SPT (:math:`{N}_{1}`) are provided equal to zero in order to test the computer operation of the macrocontrol only for modeling E with the Byrne model.


Shear modulus degradation and damping increase curves
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The three materials (alluvium and two types of marl) have curves of degradation of the elastic modulus G and of hysteretic damping given by the following curves:


+-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+
|                                                                                                                             |                                                                                                                             |
+ .. image:: images/1000020100000320000002586167299479DA7395.png                                                              + .. image:: images/10000201000003200000025880C244D4D41F880F.png                                                              +
|    :width: 3.3681in                                                                                                         |    :width: 3.3681in                                                                                                         |
+    :height: 2.5256in                                                                                                        +    :height: 2.5256in                                                                                                        +
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+                                                                                                                             +                                                                                                                             +
|                                                                                                                             |                                                                                                                             |
+-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+



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


Boundary condition
~~~~~~~~~~~~~~~~~~~~~~~

The boundary conditions applied to the column during the dynamic calculation phase are as follows:


* *Bottom of the column*: Assignment of an absorbent border element.

If 1D calculation — 1 component:


* *Right and left edges of the column*: Periodicity condition. This means that the movements of the nodes on the left and right faces facing each other are made equal.

If 1D calculation — 3 components:


* *Side edges*: Penalty rate encircling the column, so as to ensure a unique response in horizontal directions (stratified half-space hypothesis)


Loading
~~~~~~~~~~

Transient acceleration in the ground given by functions LBNS. If free-field → outcropping rock deconvolution calculation, a coefficient of :math:`1.5` is applied. If flush rock → free field convolution calculation, a coefficient of :math:`0.3` is applied.


.. image:: images/100000000000038600000298FD295AE75E99B8D8.png
    :width: 2.9638in
    :height: 2.7618in


.. _refImage_100000000000038600000298 FD295AE75E99B8D8 .png: