Benchmark solution
=====================


Reference quantities and results
------------------------

The reference values are the mass loss readings during the drying test from benchmark CONCRACK.

To calculate the loss of water from the numerical test piece at a given moment, one must calculate in succession:


1. for each finite element, the integral of the water concentration over the volume of the element: :math:`\underset{V}{\mathrm{\int }}C\mathit{dV}` which is equivalent to the volume of water remaining (in l).


2. Sum of quantities of water remaining :math:`\mathrm{\sum }_{\mathit{éléments}}\underset{V}{\mathrm{\int }}C\mathit{dV}`: this is the total volume of water remaining in the sample (in l).


3. Average water concentration (in l/m³) divided by volume: :math:`{C}_{\mathit{moy}}\mathrm{=}\frac{\mathrm{\sum }_{\mathit{éléments}}\underset{V}{\mathrm{\int }}C\mathit{dV}}{{V}_{\mathit{tot}}}`


4. The volume lost (in l) is: :math:`{C}_{0}{V}_{\mathit{tot}}-\sum _{\mathit{éléments}}\underset{V}{\int }C\mathit{dV}` and the mass lost (in kg) is: :math:`{\mathrm{\rho }}_{\mathit{eau}}({C}_{0}{V}_{\mathit{tot}}-\sum _{\mathit{éléments}}\underset{V}{\int }C\mathit{dV})` with :math:`{\mathrm{\rho }}_{\mathit{eau}}=1\mathit{kg}/l`.


5. Mass loss (%) is: :math:`100\times \frac{{\mathrm{\rho }}_{\mathit{eau}}({C}_{0}{V}_{\mathit{tot}}-\sum _{\mathit{éléments}}\underset{V}{\int }C\mathit{dV})}{{\mathrm{\rho }}_{\mathit{beton}}{V}_{\mathit{tot}}}=100\times \frac{{\mathrm{\rho }}_{\mathit{eau}}({C}_{0}-{C}_{\mathit{moy}})}{{\mathrm{\rho }}_{\mathit{beton}}}` with :math:`{\mathrm{\rho }}_{\mathit{beton}}=2410\mathit{kg}/{m}^{3}`.

Steps 2 and 3 are results of the POST_ELEM option INTEGRALE command in Code_Aster.

We compare all the experimental points and the numerical points except the first one, which is not relevant.


.. image:: images/100000000000053C0000032C2D841ADBAD1E9853.jpg
    :width: 5.1728in
    :height: 2.9984in


.. _RefImage_100000000000053C0000032C2D841ADBAD1E9853.jpg:


Bibliographical references
---------------------------


1. J. HAELEWYN, "Benchmark CONCRACK: Modeling concrete at an early age", note H-T64-2011-03057-FR.