2. Benchmark solution#

2.1. 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:

for each finite element, the integral of the water concentration over the volume of the element: \(\underset{V}{\mathrm{\int }}C\mathit{dV}\) which is equivalent to the volume of water remaining (in l).
Sum of quantities of water remaining \(\mathrm{\sum }_{\mathit{éléments}}\underset{V}{\mathrm{\int }}C\mathit{dV}\): this is the total volume of water remaining in the sample (in l).
Average water concentration (in l/m³) divided by volume: \({C}_{\mathit{moy}}\mathrm{=}\frac{\mathrm{\sum }_{\mathit{éléments}}\underset{V}{\mathrm{\int }}C\mathit{dV}}{{V}_{\mathit{tot}}}\)
The volume lost (in l) is: \({C}_{0}{V}_{\mathit{tot}}-\sum _{\mathit{éléments}}\underset{V}{\int }C\mathit{dV}\) and the mass lost (in kg) is: \({\mathrm{\rho }}_{\mathit{eau}}({C}_{0}{V}_{\mathit{tot}}-\sum _{\mathit{éléments}}\underset{V}{\int }C\mathit{dV})\) with \({\mathrm{\rho }}_{\mathit{eau}}=1\mathit{kg}/l\).
Mass loss (%) is: \(100\times \frac{{\mathrm{\rho }}_{\mathit{eau}}({C}_{0}{V}_{\mathit{tot}}-\sum _{\mathit{éléments}}\underset{V}{\int }C\mathit{dV})}{{\mathrm{\rho }}_{\mathit{beton}}{V}_{\mathit{tot}}}=100\times \frac{{\mathrm{\rho }}_{\mathit{eau}}({C}_{0}-{C}_{\mathit{moy}})}{{\mathrm{\rho }}_{\mathit{beton}}}\) with \({\mathrm{\rho }}_{\mathit{beton}}=2410\mathit{kg}/{m}^{3}\).

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.

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