C modeling
==============


Characteristics of modeling
-----------------------------------

**C** modeling is*bidimensional* and*quasistatic*. We use *modeling with classical integration* (MODELISATION = 'HM'). The first difference with **A** modeling is linked to the transition from 3D_HM modeling to DPLAN_HM modeling. The second difference is due to the use of a secant stiffness matrix to resolve the overall balance of the structure between the internal forces and the external forces applied.


Characteristics of the mesh
----------------------------

Each layer is represented by a QUAD8 element. The complete mesh is therefore made up of 11 QUAD8 elements.


Tested sizes and results
------------------------------

The settlement is calculated at the top of each layer and compared to given solutions GEFDYN:

*Settlement (in millimeters) of layer no. 1*

.. csv-table::

    "Step number", "GEFDYN ", "Tolerance (%)"
    "2", "-4.648", "4.00"
    "3", "-8.391", "3.00"
    "4", "-11.940", "2.00"
    "5", "-15.440", "2.00"
    "6", "-18.980", "2.00"
    "7", "-22.650", "2.00"
    "8", "-26.470", "2.00"
    "9", "-30.490", "2.00"
    "10", "-34.730", "2.00"


*Settlement (in millimeters) of layer no. 2*

.. csv-table::

    "Step number", "GEFDYN ", "Tolerance (%)"
    "3", "-8.409", "3.00"
    "4", "-15.720", "2.00"
    "5", "-22.780", "2.00"
    "6", "-29.830", "2.00"
    "7", "-37.030", "2.00"
    "8", "-44.510", "2.00"
    "9", "-52.360", "2.00"
    "10", "-60.610", "2.00"


*Settlement (in millimeters) of layer no. 3*

.. csv-table::

    "Step number", "GEFDYN ", "Tolerance (%)"
    "4", "-11.980", "2.00"
    "5", "-22.800", "2.00"
    "6", "-33.410", "2.00"
    "7", "-44.120", "2.00"
    "8", "-55.150", "2.00"
    "9", "-66.650", "2.00"
    "10", "-78.730", "2.00"


*Settlement (in millimeters) of layer no. 4*

.. csv-table::

    "Step number", "GEFDYN ", "Tolerance (%)"
    "5", "-15.470", "2.00"
    "6", "-29.840", "2.00"
    "7", "-44.110", "2.00"
    "8", "-58.650", "2.00"
    "9", "-73.690", "2.00"
    "10", "-89.430", "2.00"


*Settlement (in millimeters) of layer no. 5*

.. csv-table::

    "Step number", "GEFDYN ", "Tolerance (%)"
    "6", "-19.020", "2.00"
    "7", "-37.050", "2.00"
    "8", "-55.150", "2.00"
    "9", "-73.700", "2.00"
    "10", "-92.980", "2.00"


*Settlement (in millimeters) of layer No. 6*

.. csv-table::

    "Step number", "GEFDYN ", "Tolerance (%)"
    "7", "-22.680", "2.00"
    "8", "-44.540", "2.00"
    "9", "-66.650", "2.00"
    "10", "-89.440", "2.00"


*Settlement (in millimeters) of layer No. 7*

.. csv-table::

    "Step number", "GEFDYN ", "Tolerance (%)"
    "8", "-26.500", "2.00"
    "9", "-52.380", "2.00"
    "10", "-78.720", "2.00"


*Settlement (in millimeters) of layer No. 8*

.. csv-table::

    "Step number", "GEFDYN ", "Tolerance (%)"
    "9", "-30.520", "2.00"
    "10", "-60.630", "2.00"


*Settlement (in millimeters) of layer No. 9*

.. csv-table::

    "Step number", "GEFDYN ", "Tolerance (%)"
    "10", "-34.750", "2.00"


The elementary calculation option INDL_ELGA is also tested in non-regression to validate its development in modeling DPLAN_HM. All components are tested on mesh :math:`\mathrm{M2}`, located at the base of the column, just above the elastic rock.


.. csv-table::

    "Step number", "Component INDL_ELGA ", "Reference type", "Reference", "Tolerance (absolute)"
    "10"," INDICE "," NON_REGRESSION ", "0.0", "0.001"
    "10"," DIR1 "," NON_REGRESSION ", "0.0", "0.001"
    "10"," DIR2 "," NON_REGRESSION ", "0.0", "0.001"
    "10"," DIR3 "," NON_REGRESSION ", "0.0", "0.001"
    "10"," DIR4 "," NON_REGRESSION ", "0.0", "0.001"


The elementary calculation option PDIL_ELGA is tested in non-regression to validate its development in modeling DPLAN_HM. The A1_ LC2 component is tested on mesh :math:`\mathrm{M2}`, located at the base of the column, just above the elastic rock.


.. csv-table::

    "Step number", "Component INDL_ELGA ", "Reference type", "Reference", "Tolerance (absolute)"
    "10", "A1_ LC2 "," NON_REGRESSION "," ", "0.0", "0.001"



Comments
------------

The relative error is at most :math:`\text{4\%}`, which is relatively satisfactory. The results are generally closer to the results from the reference, compared to the **A** and **B** models. It can be added that the algorithm used in this modeling to solve the balance of the structure is identical to that of the reference, which may explain these results.