1. Reference problem#
1.1. Geometry of the problem#
It is a block with height \(\mathit{LZ}=10m\), length \(\mathit{LX}=10m\), and width \(\mathit{LY}=2m\). This block has a cohesive interface-type discontinuity (a non-meshed interface that is introduced into the model through level-sets using the DEFI_FISS_XFEM operator). It is identified by the normal level-set of equation \(\mathit{lsn}=Z-5\) and crosses the block entirely in the horizontal direction by dividing it into two identical sub-blocks. Points \(A(\mathrm{0,}\mathrm{0,}5)\), \(A\text{'}(\mathrm{0,}\mathrm{2,}5)\), \(B(\mathrm{3,}\mathrm{0,}5)\), and \(B\text{'}(\mathrm{3,}\mathrm{2,}5)\) will be used for the imposition of boundary conditions and the evaluation of the quantities tested.
The geometry of the block is represented in the figure.
Figure 1.1-a : Problem geometry
1.2. Material properties#
The parameters given in the Table correspond to the parameters used for modeling in the hydro-mechanical coupled case. The coupling law used is” LIQU_SATU “. The cohesive model type is” STANDARD “and the cohesive law used is” CZM_OUV_MIX “.
Liquid (water) |
Viscosity \({\mu }_{w}(\mathit{en}\mathit{Pa.s})\) Compressibility module \(\frac{1}{{K}_{w}}(\mathit{en}{\mathit{Pa}}^{\text{-1}})\) Liquid density \({\rho }_{w}(\mathit{en}\mathit{kg}\mathrm{/}{m}^{3})\) |
\({5.10}^{\text{-10}}\) \(1\) |
Elastic parameters |
Young’s modulus \(E(\mathit{en}\mathit{MPa})\) Poisson’s Ratio \(\nu\) Thermal expansion coefficient \(\alpha (\mathit{en}{K}^{\text{-1}})\) |
\(0.2\) \(0\) |
Coupling parameters |
Biot coefficient \(b\) Initial homogenized density \({r}_{0}(\mathit{en}\mathit{kg}\mathrm{/}{m}^{3})\) Intrinsic permeability \({K}^{\text{int}}(\mathit{en}{m}^{2})\) |
\(\mathrm{2,5}\) \({10}^{\text{-18}}\) |
Parameters of the cohesive law |
Critical constraint \({\mathrm{\sigma }}_{c}(\mathit{en}\mathit{MPa})\) Cohesive energy \({G}_{c}(\mathit{en}\mathit{Pa}\mathrm{.}m)\) Increase coefficient \(r\) |
\(9000\) \(100\) |
Table 1.2-1 : Material Properties
On the other hand, the forces related to gravity (in the equation for the conservation of momentum) are neglected. The reference pore pressure is taken to be zero \({p}_{1}^{\text{ref}}=0\mathit{MPa}\) and the porosity of the material is \(\mathrm{\varphi }\phantom{\rule{0.5em}{0ex}}=\phantom{\rule{0.5em}{0ex}}\mathrm{0,1}\).
1.3. Boundary conditions and loads#
The Dirichlet conditions that are applied are:
the following moves \(x\) are stuck in on the left edge of the domain,
the movements following \(y\) and \(z\) are blocked on the lower and upper edges of the domain.
Also, a punctual flow of fluid \(Q=0.025\mathit{kg}\mathrm{.}{m}^{-1}\mathrm{.}{s}^{-1}\) is injected into the cohesive interface on the left edge of the domain for a period of time \(t=10s\).