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


Geometry
---------


.. image:: images/10000201000008CA0000062F2D355399BB224B6A.png
    :width: 4.5299in
    :height: 3.1862in


.. _RefImage_10000201000008CA0000062F2D355399BB224B6A.png:

**Figure** 1.1-a **: Geometry** of the dam **** (not to scale) **
We consider a 2D dam with a geometry presented in.

In the one presented the geometric dimensions of the dam, as well as in the one specified the coordinates of the post-treatment points.

**Table** 1.1-1 **:**: **Geometric dimensions** of the dam**

.. csv-table::

    "", "**H** s", "**H** f", "**H** f", "**H** b", "**L** s", "**L** f", "**L** bi", "**L** bi", "**L** bs"
    "Measure [m]", "50", "80", "80", "20", "20", "290", "100", "90", "10"


**Table** 1.1-2 **: Coordinates of post-processing points**

.. csv-table::

    "", "**A**", "**B**", "**C**", "**D**"
    "Coordinate X [m]", "0", "0", "0", "90"
    "Coordinate Y [m]", "0", "0", "80", "100", "0"



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

Material properties are summarized in the.

**Table** 1.2-1 **:** **Properties**of materials**

.. csv-table::

    "", "**E** [GPa]", ":math:`\nu` "," "," :math:`\rho` [:ref:`kg/m3 <kg/m3>`]", ":math:`\alpha` "," :math:`\beta` ", "**c** e [m/s]"
    "Concrete", "22.41", "0.2", "0.2", "2483", "0.0005", "0.75", "-"
    "Sol", "22.41", "0.2", "0.2", "2483", "-", "-"
    "Water", "-", "-", "-", "1000", "-", "-", "1440"


Where:


* **E** is Young's modulus;


* :math:`\nu` is Poisson's ratio;


* :math:`\rho` is the volume density;


* :math:`\alpha` and :math:`\beta` are the coefficients that define Rayleigh damping;


* **this** is the speed of waves in water.


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

There are two types of boundary conditions (see):


* At the lateral edges of the ground absorbent borders are assigned;


* A fluid absorbent border is assigned to the left edge of the fluid part.

There are also two fluid-structure interfaces defined between the ground and the fluid part as well as between the dam and the fluid part. In addition, for 3D models (C and E), a periodicity condition is added in the direction in which the plane deformation is imposed.

The imposed dynamic load is a Ricker wavelet that is shown in. Charging is required for a total time of **1s**. This wavelet has a direction of propagation inclined by 20° with respect to the vertical. This wavelet is injected as both a P wave and an S wave.


.. image:: images/10000201000007D00000051430EAE85B93017BC1.png
    :width: 5.5118in
    :height: 3.5665in


.. _RefImage_10000201000007D00000051430EAE85B93017BC1.png:

**Figure** 1.3-a **: Ricker wavelet**