2. Reference solution

2.1. Calculation method

The analytical solution for this hydro-mechanical load has not been developed. Also, the reference solution is obtained numerically using the Scilab 2.7.2 software for BETON_UMLV or python for BETON_BURGER. Each deformation component is calculated separately:

• endogenous shrinkage deformities are determined from the relationship:

• 

where

refers to the degree of hydration of the material

• the desiccation shrinkage deformations are determined from the relationship:

• 

where

refers to the water content of the material

• thermal expansion deformations are determined from the relationship:

• 

where

and

designate respectively the temperature at the current moment and the reference temperature of the material

the natural creep deformations are calculated numerically using a discretization identical to that implemented in the*Code_Aster for BETON_UMLV and an layout according to an explicit diagram for BETON_BURGER. The time discretization is then necessarily finer for the explicit schema.

• the desiccation creep deformations are calculated analytically from the relationship:

• 

where

refers to the humidity of the material

The results of the calculation with Scilab are shown in the figure below.

2.2. Reference quantities and results

The test is homogeneous. The deformation is tested at any node.

2.3. Uncertainty about the solution

Numerical result obtained with Scilab 2.7.2 or python (SSNV180B .44)

2.4. Bibliographical references

1. THE PAPE Y.: UMLV behavioral relationship for the clean creep of concrete, Code_Aster Reference Documentation, [R7.01.06] 16 p (2002).

2. FOUCAULT A.: BETON_BURGER behavioral relationship for the clean creep of concrete, Code-Aster Reference Documentation, [R7.01.35], 2011.