laws:wavat
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laws:wavat [2019/09/19 12:00] helene created |
laws:wavat [2023/12/12 16:47] (current) gilles [WAVAT/WAVAT2/WAVAT3] |
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| ====== WAVAT/WAVAT3 ====== | ====== WAVAT/WAVAT3 ====== | ||
| ===== Description ===== | ===== Description ===== | ||
| - | Water-air seepage- thermal coupled – vapour diffusion 2D/3D constitutive law for solid elements | + | Water - air seepage - thermal coupled – vapour diffusion 2D/3D constitutive law for solid elements |
| ==== The model ==== | ==== The model ==== | ||
| This law is only used for water seepage - air seepage-thermal coupled and vapour diffusion for non linear analysis in 2D/3D porous media. | This law is only used for water seepage - air seepage-thermal coupled and vapour diffusion for non linear analysis in 2D/3D porous media. | ||
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| === Ecoulement du liquide et de la vapeur === | === Ecoulement du liquide et de la vapeur === | ||
| - | En partant de l’équation de Darcy, la vitesse du liquide ( Volume de fluide par unité de surface de sol ) est donnée par : | + | En partant de l’équation de Darcy, la vitesse du liquide (Volume de fluide par unité de surface de sol) est donnée par : |
| \[ | \[ | ||
| \vec{q_l} = - \frac{k_w}{\mu_w}\left[ \vec{grad}(p_w) + g \rho_w \vec{grad}(y)\right]\ \text{où}\ k_w = K_w \frac{\mu_w}{\rho_w g}\left[ m^2\right] | \vec{q_l} = - \frac{k_w}{\mu_w}\left[ \vec{grad}(p_w) + g \rho_w \vec{grad}(y)\right]\ \text{où}\ k_w = K_w \frac{\mu_w}{\rho_w g}\left[ m^2\right] | ||
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| ^ Line 1 (2I5, 60A1)^^ | ^ Line 1 (2I5, 60A1)^^ | ||
| |IL|Law number| | |IL|Law number| | ||
| - | |ITYPE| 171 (Rem : =174 in LOI2 for 3D state) | | + | |ITYPE| 171 (= 174 in LOI2 for 3D state) | |
| |COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing| | |COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing| | ||
| ==== Integer parameters ==== | ==== Integer parameters ==== | ||
| ^ Line 1 (18I5) ^^ | ^ Line 1 (18I5) ^^ | ||
| |IANI|= 0, isotropic permeability case| | |IANI|= 0, isotropic permeability case| | ||
| - | |:::| $\neq$ 0, anisotropic permeability case| | + | |:::| ≠ 0, anisotropic permeability case| |
| |IKW|formulation index for $k_w$| | |IKW|formulation index for $k_w$| | ||
| |IKA|formulation index for $k_a$| | |IKA|formulation index for $k_a$| | ||
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| |:::|= 1, $\chi_w = \chi_w + \frac{H}{p_a}$ ( $p_a$ is partial pressure of air and H is Henry coefficient)| | |:::|= 1, $\chi_w = \chi_w + \frac{H}{p_a}$ ( $p_a$ is partial pressure of air and H is Henry coefficient)| | ||
| |IDIFF|= 0, with diffusion of dissolved air| | |IDIFF|= 0, with diffusion of dissolved air| | ||
| - | |:::|$\neq$ 0, divisor (integer becomes real) of diffusion coefficient of dissolved air| | + | |:::|≠ 0, divisor (integer becomes real) of diffusion coefficient of dissolved air| |
| |ISTRUCT|= 0, constant permeability| | |ISTRUCT|= 0, constant permeability| | ||
| |:::|= 1, permeability depends on microstructure evolution| | |:::|= 1, permeability depends on microstructure evolution| | ||
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| ==== Real parameters: permeabilities definition ==== | ==== Real parameters: permeabilities definition ==== | ||
| The permeability $k_f$ is an \underline{intrinsic} permeability ($\left[L^2\right]$) $\boxed{ \begin{array}{l} k_{f, intrinsic} = K_f \frac{\mu_f}{\rho_f g}\\ \left[ L^2 \right] = \left[ LT^{-1} \right] \frac{ \left[ ML^{-1}T^{-1}\right]}{\left[ML^{-3}\right]\left[LT^{-2}\right]} \end{array}}$\\ | The permeability $k_f$ is an \underline{intrinsic} permeability ($\left[L^2\right]$) $\boxed{ \begin{array}{l} k_{f, intrinsic} = K_f \frac{\mu_f}{\rho_f g}\\ \left[ L^2 \right] = \left[ LT^{-1} \right] \frac{ \left[ ML^{-1}T^{-1}\right]}{\left[ML^{-3}\right]\left[LT^{-2}\right]} \end{array}}$\\ | ||
| - | ^If IANI$\neq$0 (4G10.0) - Repeated IANI times^^ | + | ^If IANI ≠ 0 (4G10.0) - Repeated IANI times^^ |
| |PERME(I)|soil anisotropic int. permeability ($k_f$) in the direction I| | |PERME(I)|soil anisotropic int. permeability ($k_f$) in the direction I| | ||
| |COSX(I)|director cosinus of the direction I \\ (in 3d state)| | |COSX(I)|director cosinus of the direction I \\ (in 3d state)| | ||
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| ^If IANI = 0 (1G10.0)^^ | ^If IANI = 0 (1G10.0)^^ | ||
| |PERME|soil isotropic intrinsic permeability ($k_f$)| | |PERME|soil isotropic intrinsic permeability ($k_f$)| | ||
| - | EndIf | ||
| ==== Real parameters ==== | ==== Real parameters ==== | ||
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| ^If IANITH = 0: nothing^^ | ^If IANITH = 0: nothing^^ | ||
| |Isotropic thermal conductivity is already defined by preceding coefficients ITHERM, CLT1, CLT2, CLT3, CT4, CONS0, CONW0, CONA0 …|| | |Isotropic thermal conductivity is already defined by preceding coefficients ITHERM, CLT1, CLT2, CLT3, CT4, CONS0, CONW0, CONA0 …|| | ||
| - | |||
| - | ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– | ||
| Following empirical formulations for describing the evolution of the relative permeability, the thermal conductivity and saturation with the suction are possible: see [[appendices:a8|Appendix 8]]. | Following empirical formulations for describing the evolution of the relative permeability, the thermal conductivity and saturation with the suction are possible: see [[appendices:a8|Appendix 8]]. | ||
| For any suction lower than air entry value (AIREV), the saturation is equal to SRFIELD value. \\ | For any suction lower than air entry value (AIREV), the saturation is equal to SRFIELD value. \\ | ||
| - | __Kozeny Karman formulation :__ | + | __Kozeny Karman formulation:__ |
| \[K = C_0 \frac{n^{EXPN}}{(1-n)^{EXPM}}\] | \[K = C_0 \frac{n^{EXPN}}{(1-n)^{EXPM}}\] | ||
| $C_0$ is computed automatically from $C_0 = K_0 \frac{(1-n_0)^{EXPM}}{(n_0)^{EXPn}}$ \\ | $C_0$ is computed automatically from $C_0 = K_0 \frac{(1-n_0)^{EXPM}}{(n_0)^{EXPn}}$ \\ | ||
| - | __GDR Momas formulation :__ | + | __GDR Momas formulation:__ |
| \[ | \[ | ||
| \frac{k}{k_0} = 1+EXPM\left[ \phi - \phi_0\right]^{EXPN}\ \text{où}\ EXPM = 2.10^{12}\ \text{et}\ EXPN = 3 | \frac{k}{k_0} = 1+EXPM\left[ \phi - \phi_0\right]^{EXPN}\ \text{où}\ EXPM = 2.10^{12}\ \text{et}\ EXPN = 3 | ||
| \] | \] | ||
| - | __Coupling permeability-deformation formulation :__ (only in 2D) | + | __Coupling permeability-deformation formulation:__ (only in 2D) |
| \[ | \[ | ||
| K_{ij} = \sum_n K_n^0 (1+A\varepsilon_n^T)^3\beta_{ij} (\alpha_n) | K_{ij} = \sum_n K_n^0 (1+A\varepsilon_n^T)^3\beta_{ij} (\alpha_n) | ||
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| |Q(24)|$\varepsilon_1$ | | |Q(24)|$\varepsilon_1$ | | ||
| |Q(25)|$\varepsilon_2$ | | |Q(25)|$\varepsilon_2$ | | ||
| - | |Q(26)|$\alpha$ (=angle between principal stress and horizontal) | | + | |Q(26)|$\alpha$ (= angle between principal stress and horizontal) | |
laws/wavat.1568887221.txt.gz · Last modified: 2020/08/25 15:35 (external edit)
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