1. Reference problem#
1.1. Presentation#
In this test case, we study the hydraulic behavior of a saturated porous medium constituted by a single fluid: water in its liquid phase. The associated law of fluid behavior is of type LIQU_SATU. The modeling is hydromechanical (HM). The fluid is incompressible and the medium is infinitely rigid. It is therefore a stationary problem involving an analytical solution. The objective of this test is to validate the correct consideration of a hydraulic flow boundary condition in the case of axisymmetric modeling.
1.2. Geometry#
A bar of length \(L=\mathrm{1m}\) is represented. Its width l is not involved in the analytical solution because the problem is purely 1D. Here we take \(l=\mathrm{0,2}m\). Point N1 corresponds to the coordinate point \((\mathrm{0,0})\mathrm{.}\)
Illustration 1: vertical bar in vertical positioning
1.3. Material properties#
Liquid water |
Density \({\rho }_{l}({\mathit{kg.m}}^{-3})\) Dynamic viscosity of liquid water \({\mu }_{l}(\mathit{Pa.s})\) Compressibility \({K}_{w}({\mathit{Pa}}^{-1})\) |
\(0.001\) \(0\) |
Solid |
Drained Young’s Module \(E(\mathrm{Pa})\) Poisson’s Ratio \(\nu\) |
\(0.3\) |
Reference state |
Porosity \(\phi\) Temperature \({T}^{\text{ref}}(K)\) Liquid pressure \({P}^{\text{ref}}(\mathit{Pa})\) Vapor pressure \({\mathit{Pv}}^{\text{ref}}(\mathit{Pa})\) |
\(293\) \(0\) \(0.1\) |
Constants |
Ideal gas constant R |
\(8.32\) |
Homogenized coefficients |
Homogenized density \({r}_{0}({\mathit{kg.m}}^{-3})\) Biot coefficient b Intrinsic permeability \({K}_{\text{int}}({m}^{2})\) |
\(0.6\) \({K}_{\text{int}}={10}^{-12}\) |
Table 1.3-1 : Material data
The gravity of water is overlooked.
1.4. Boundary conditions and loads#
On all sides
blocked trips \({u}_{x}={u}_{y}={u}_{z}=0\)
Upper edge:
water flow: \(q=1{\mathit{kg.s}}^{-1}\mathrm{.}{m}^{-2}\)
Lower edge:
Liquid pressure: \({P}_{\mathit{lq}}={P}_{0}=1\mathit{atm}\)
Side edges:
zero flow
1.5. Initial conditions#
The initial pressure is \(1\mathit{atm}\). All other fields are null.