2. Benchmark solution

2.1. Calculation method

The analytical solution is based on the resolution of the two differential equations that govern the deviatory part of the behavior (cf. [R7.01.06] and [R7.01.35]). Choosing the \(\kappa\) parameter to a very large value ensures equivalence between the two models for the load applied.

Deviatory stresses are at the origin of a sliding mechanism (or mechanism of virtual dislocation) of sheets of CSH in nano-porosity. Under deviatoric stress, creep takes place at constant volume. Moreover, creep law UMLV assumes the isotropy of deviatoric creep. Phenomenologically, the sliding mechanism includes a reversible viscoelastic contribution of water strongly adsorbed to the sheets of CSH and an irreversible viscous contribution of free water:

eq 2.1-1

The \({j}^{\mathrm{ème}}\) main component of total deviatoric deformation is governed by equations [éq2.1‑2] and [éq 2.1-3]:

Eq 2.1-2

where

refers to the stiffness associated with the capacity of adsorbed water to transmit charges (load bearing water);

and

the viscosity associated with the water adsorbed by the hydrate sheets.

Eq 2.1-3

where

refers to the viscosity of free water.

In the case of a constraint step

, the corresponding deviatoric creep deformation is immediately deduced:

Eq 2.1-4

When the elastic part is added, it follows that the total shear deformation is equal to:

Eq 2.1-5

2.2. Reference quantities and results

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

2.3. Uncertainties about the solution

Analytical solution.

2.4. Bibliographical references

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

• FOUCAULT, A.: Behavioral Relationship BETON_BURGER, Code-Aster Reference Documentation [R7.01.35], 2011.