Reference problem ===================== Geometry --------- .. image:: images/Object_1.svg :width: 321 :height: 276 .. _RefImage_Object_1.svg: +--------------------------------+--------------------------+ | .. code:: |:math:`h=\mathrm{1,00}[m]`| + + + | Hauteur: | | +--------------------------------+--------------------------+ |Width: |:math:`l=\mathrm{1,00}[m]`| +--------------------------------+--------------------------+ |Thickness: |:math:`e=\mathrm{1,00}[m]`| +--------------------------------+--------------------------+ Material properties ---------------------- +---------------------------------------------------------------------------------------------------------------------------------+---------------------------------+ | |Modulus of elasticity | + .. image:: images/Object_2.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{GPa}]` + + | | | +---------------------------------------------------------------------------------------------------------------------------------+---------------------------------+ | |Poisson's ratio | + .. image:: images/Object_3.svg + + | :width: 321 | | + :height: 276 + + | | | + + + | | | +---------------------------------------------------------------------------------------------------------------------------------+---------------------------------+ | |endogenous shrinkage coefficient | + .. image:: images/Object_4.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{\mu m}/m]` + + | | | +---------------------------------------------------------------------------------------------------------------------------------+---------------------------------+ | |desiccation shrinkage coefficient| + .. image:: images/Object_5.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{\mu m}/{\mathrm{m.m}}^{3}/l]` + + | | | +---------------------------------------------------------------------------------------------------------------------------------+---------------------------------+ | |coefficient of thermal expansion | + .. image:: images/Object_6.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{\mu m}/m/°C]` + + | | | +---------------------------------------------------------------------------------------------------------------------------------+---------------------------------+ Here we also enter the sorption-desorption curve that relates the water content .. image:: images/Object_7.svg :width: 321 :height: 276 .. _RefImage_Object_7.svg: To hygrometry .. image:: images/Object_8.svg :width: 321 :height: 276 .. _RefImage_Object_8.svg: . In this case it was assumed that the two quantities were linked by the following linear relationship: .. image:: images/Object_9.svg :width: 321 :height: 276 .. _RefImage_Object_9.svg: [:ref:`l/m3 `] = .. image:: images/Object_10.svg :width: 321 :height: 276 .. _RefImage_Object_10.svg: [%]. Parameters specific to desiccation creep: .. image:: images/Object_18.svg :width: 321 :height: 276 .. _RefImage_Object_18.svg: :math:`[\mathrm{MPa.s}]` Settings specific to BETON_UMLV: +-------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | |spherical part: apparent stiffness associated with the skeleton formed by hydrate blocks at the mesoscopic scale | + .. image:: images/Object_11.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa}]` + + | | | +-------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | |spherical part: apparent stiffness intrinsically associated with hydrates at the microscopic scale | + .. image:: images/Object_13.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa}]` + + | | | +-------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | |deviatoric part: stiffness associated with the capacity of adsorbed water to transmit charges (*load bearing water*)| + .. image:: images/Object_15.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa}]` + + | | | +-------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | |spherical part: apparent viscosity associated with the diffusion mechanism within the capillary porosity | + .. image:: images/Object_17.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa.s}]` + + | | | +-------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | |spherical part: apparent viscosity associated with the mechanism of interlamellar diffusion | + .. image:: images/Object_80.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa.s}]` + + | | | +-------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | |deviatory part: viscosity associated with water adsorbed by hydrate sheets | + .. image:: images/Object_82.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa.s}]` + + | | | +-------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | |deviatoric part: viscosity of free water. | + .. image:: images/Object_84.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa.s}]` + + | | | +-------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------+ Settings specific to BETON_BURGER: +--------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+ | |spherical part: apparent stiffness associated with the reversible domain of delayed deformations | + .. image:: images/Object_93.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa}]` + + | | | +--------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+ | |deviatoric part: associated stiffness associated with the reversible domain of delayed deformations | + .. image:: images/Object_97.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa}]` + + | | | +--------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+ | |spherical part: apparent viscosity associated with the reversible range of delayed deformations | + .. image:: images/Object_99.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa.s}]` + + | | | +--------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+ | |spherical part: apparent viscosity associated with the irreversible diffusion mechanism | + .. image:: images/Object_101.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa.s}]` + + | | | +--------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+ | |deviatory part: viscosity associated with the reversible domain of delayed deformations | + .. image:: images/Object_103.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa.s}]` + + | | | +--------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+ | |deviatoric part: apparent viscosity associated with the irreversible diffusion mechanism | + .. image:: images/Object_105.svg + + | :width: 321 | | + :height: 276 + + | | | + :math:`[\mathrm{MPa.s}]` + + | | | +--------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+ |:math:`\kappa =3.0\times {10}^{-3}` |Irreversible deformation standard controlling the nonlinearity applied to the long-term deformation module| +--------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+ Boundary conditions and loads ------------------------------------- In this test, a homogeneous drying field is created in the structure varying linearly over a period of 750 days, the initial humidity is :math:`100\text{\%}` (condition of a sealed test piece) and decreases progressively to :math:`50\text{\%}` on the 750th day. The degree of hydration varies linearly from 0 to 1 between the initial moment and the 28th day. The reference temperature is :math:`20°C`. Thermal loading corresponds to a rise in temperature varying from :math:`20°C` and :math:`40°C` between the initial instant and the final instant. Mechanical loading corresponds to unidirectional compression in the vertical direction (:math:`z` in :math:`\mathrm{3D}`); its intensity is :math:`12[\mathrm{MPa}]`. The load is applied in :math:`\mathrm{1s}` and is kept constant for 100 days. Initial conditions -------------------- The start of the calculation is assumed at time :math:`–1`. At this moment there is no drying field or mechanical stress. At instant 0, a drying field corresponding to :math:`100\text{\%}` humidity is applied, a hydration field corresponding to zero progress and a thermal field at the reference temperature are applied.