1. Reference problem#

1.1. Geometry#

Consider an infinite tube with an inner radius of \(\mathrm{20m}\) and an outer radius of \(\mathrm{21m}\). The length of the tube is not involved in the evaluation of the reference solution, but this length is set to \(\mathrm{10m}\) for the physical modeling of the problem (illustration).

_images/10000000000001D30000027336934B21081ADB55.png

Illustration 1.1.1: Geometry of the concrete tube with a thickness of 1 m and an internal radius of 20 m

1.2. Material properties#

The concrete material is isotropic elastic whose properties are:

  • \(E=31000\mathrm{MPa}\)

  • \(\nu =0.2\)

The properties of clean creep concrete (model ULMV_FP) are given below:

  • K_RS = \(2.0e11\mathrm{Pa}\),

  • ETA_RS = \(4.0e16\mathrm{Pa.s}\),

  • K_IS = \(5.0e10\mathrm{Pa}\),

  • ETA_IS = \(1.0e17\mathrm{Pa.s}\),

  • K_RD = \(5.0e11\mathrm{Pa}\),

  • ETA_RD = \(1.0e16\),

  • ETA_ID = \(1.0e17\).

1.3. Boundary conditions and loads#

On edge \(\mathrm{AB}\), vertical movements along the \(Y\) axis are blocked.

On edge \(\mathrm{AD}\), a confinement pressure of \(\mathrm{1MPa}\) is imposed.

On edge \(\mathrm{BC}\), a uniform connection is imposed for all the nodes in the \(X\) direction.

On edge \(\mathrm{CD}\), a uniform connection is imposed for all the nodes in the \(Y\) direction.

Uniform bond boundary conditions ensure that an infinite cylinder is modelled and not a finite dimensional cylinder.

1.4. Initial conditions#

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