laws:ecous
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laws:ecous [2019/08/23 14:17] helene created |
laws:ecous [2025/11/28 20:44] (current) frederic [Number of state variables] |
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| This law is used for non linear analysis of seepage in porous media. The case of free surface seepage is also treated. This law is used in two or three dimensional flow. \\ | This law is used for non linear analysis of seepage in porous media. The case of free surface seepage is also treated. This law is used in two or three dimensional flow. \\ | ||
| - | The mathematical model is : | + | The mathematical model is: |
| - | 1) Conservation of the mass of the fluid : \[\frac{\partial}{\partial t}(\rho_f.\theta)+div(\rho_f.\underline{q})=0\] | + | - Conservation of the mass of the fluid: \[\frac{\partial}{\partial t}(\rho_f.\theta)+div(\rho_f.\underline{q})=0\] |
| - | 2) Motion of the fluid : \[\underline{q} = \frac{-k}{\mu}\left(\underline{grad}(p)+\rho_f.g.\underline{grad}(z)\right)\] | + | - Motion of the fluid: \[\underline{q} = \frac{-k}{\mu}\left(\underline{grad}(p)+\rho_f.g.\underline{grad}(z)\right)\] |
| ==== Files ==== | ==== Files ==== | ||
| - | |||
| - | |||
| Prepro: LECOUS.F \\ | Prepro: LECOUS.F \\ | ||
| + | Lagamine: ECOU2.F, ECOU22.F, ECOU3.F | ||
| ===== Availability ===== | ===== Availability ===== | ||
| - | |||
| |Plane stress state| YES| | |Plane stress state| YES| | ||
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| ===== Input file ===== | ===== Input file ===== | ||
| - | |||
| ==== Parameters defining the type of constitutive law ==== | ==== Parameters defining the type of constitutive law ==== | ||
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| ^ Line 1 (6I5) ^^ | ^ Line 1 (6I5) ^^ | ||
| - | |ISEMI| = 0 : flow analysis | | + | |ISEMI| = 0 → flow analysis | |
| - | |:::| = 1 : if semi-coupled mechanical-flow analysis | | + | |:::| = 1 → if semi-coupled mechanical-flow analysis | |
| - | |:::| = 2 : if full coupled mechanical-flow analysis | | + | |:::| = 2 → if full coupled mechanical-flow analysis | |
| - | |IANI| = 0 : isotropic case | | + | |IANI| = 0 → isotropic case | |
| - | |:::| $\neq 0$ : anisotropic case | | + | |:::| ≠ 0 → anisotropic case | |
| |IKRN| = 0 | | |IKRN| = 0 | | ||
| - | |:::| = 1 : Kozeny Karman relation $K=f(n)$ | | + | |:::| = 1 → Kozeny Karman relation $K=f(n)$ | |
| - | |:::| = 2 : GDR Momas relation $K=f(n)$ | | + | |:::| = 2 → GDR Momas relation $K=f(n)$ | |
| |ISRW| Formulation index for $S_w$ (see [[appendices:a8|Appendix 8]]) | | |ISRW| Formulation index for $S_w$ (see [[appendices:a8|Appendix 8]]) | | ||
| - | |:::| $\neq 0$ : in case of seepage with free surface | | + | |:::|≠ 0 → in case of seepage with free surface | |
| - | |:::| = 0 : in absence of free surface | | + | |:::| = 0 → in absence of free surface | |
| |IKW| Formulation index for $k_w$ (see [[appendices:a8|Appendix 8]]) | | |IKW| Formulation index for $k_w$ (see [[appendices:a8|Appendix 8]]) | | ||
| - | |ISTRUCT| Formulation index for istruct | | + | |ISTRUCT| Formulation index for ISTRUCT | |
| - | ==== Real parameters : permeability definition ==== | + | ==== Real parameters: permeability definition ==== |
| The permeability $k$ is an intrinsic permeability ([$L^2$]) and $K$ is the permeability coefficient ([$LT^{-1}$]) : \[k_{intrinsic} = K\frac{\mu_f}{\rho_f g}\]\[[L^2]=[LT^{-1}]\frac{[ML^{-1}T^{-1}]}{[ML^{-3}][LT^{-2}]}\] | The permeability $k$ is an intrinsic permeability ([$L^2$]) and $K$ is the permeability coefficient ([$LT^{-1}$]) : \[k_{intrinsic} = K\frac{\mu_f}{\rho_f g}\]\[[L^2]=[LT^{-1}]\frac{[ML^{-1}T^{-1}]}{[ML^{-3}][LT^{-2}]}\] | ||
| - | If IANI$\neq$ 0, then for I=1 : | + | __If IANI ≠ 0__ |
| - | ^ Line 1 (4G10.0) ^^ | + | ^ Line 1 (4G10.0) - Repeat IANI times (I=1,IANI) ^^ |
| |PERMEA(I)| Soil anisotropic intrinsic permeability (k) in the direction I | | |PERMEA(I)| Soil anisotropic intrinsic permeability (k) in the direction I | | ||
| |COSX(I)| Director cosinus of the direction I | | |COSX(I)| Director cosinus of the direction I | | ||
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| |COSZ(I)| Director cosinus of the direction I | | |COSZ(I)| Director cosinus of the direction I | | ||
| - | Else, if IANI = 0 : | + | __Else, if IANI = 0__ |
| ^ Line 1 (1G10.0) ^^ | ^ Line 1 (1G10.0) ^^ | ||
| |PERME| Soil isotropic intrinsic permeability (k) | | |PERME| Soil isotropic intrinsic permeability (k) | | ||
| Line 98: | Line 93: | ||
| |CKW3| 3rd coefficient of the function $k_{rw}$ | | |CKW3| 3rd coefficient of the function $k_{rw}$ | | ||
| |CSR5| 5th coefficient of the function $S_w$ (if ISRW=26) | | |CSR5| 5th coefficient of the function $S_w$ (if ISRW=26) | | ||
| - | ^ Line 4 (3G10.0) ^^ | + | ^ Line 4 (8G10.0) ^^ |
| |EXPM| km exponent for the Kozeny Karman formulation | | |EXPM| km exponent for the Kozeny Karman formulation | | ||
| |EXPN| kn exponent for the Kozeny Karman formulation | | |EXPN| kn exponent for the Kozeny Karman formulation | | ||
| |HENRY| Henry's coefficient : solubility coefficient of air into water | | |HENRY| Henry's coefficient : solubility coefficient of air into water | | ||
| - | ^ Line 5 (3G10.0) ^^ | + | |EPSEQ0| | |
| + | |EQ1| | | ||
| + | |EQ2| | | ||
| + | |EQ3| | | ||
| + | |EPSEQMAX| | | ||
| + | ^ If ISTRUCT$\neq$0 OR ISRW=26 Line 5 (3G10.0) ^^ | ||
| |SOIL MICROPOROSITY| Microstructural void ratio for dry material (if ISTRUCT$\neq$0) | | |SOIL MICROPOROSITY| Microstructural void ratio for dry material (if ISTRUCT$\neq$0) | | ||
| - | |COEF.BETA0| For microporosity evolution (if ISTRUCT$\neq$0) | | + | |BETA0| First coefficient for microporosity evolution (if ISTRUCT$\neq$0) | |
| - | |COEF.BETA1| For microporosity evolution (if ISTRUCT$\neq$0) | | + | |BETA1| Second coefficient for microporosity evolution (if ISTRUCT$\neq$0) | |
| Following empirical formulations for describing the evolution of the relative permeability, and saturation with the suction are possible : see [[appendices:a8|Appendix 8]].\\ | Following empirical formulations for describing the evolution of the relative permeability, and saturation with the suction are possible : see [[appendices:a8|Appendix 8]].\\ | ||
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| ===== Stresses ===== | ===== Stresses ===== | ||
| - | |||
| ==== Number of stresses ==== | ==== Number of stresses ==== | ||
| - | |||
| 5 for 3D state \\ 4 for the other cases | 5 for 3D state \\ 4 for the other cases | ||
| - | |||
| ==== Meaning ==== | ==== Meaning ==== | ||
| - | |||
| For the 3-D state: | For the 3-D state: | ||
| Line 140: | Line 136: | ||
| |SIG(4)| fluid mass stored as a consequence of the evolution of soil porosity ($=\rho_e=\frac{\partial}{\partial t}(\rho_f\theta)$) | | |SIG(4)| fluid mass stored as a consequence of the evolution of soil porosity ($=\rho_e=\frac{\partial}{\partial t}(\rho_f\theta)$) | | ||
| |SIG(5)| none | | |SIG(5)| none | | ||
| - | |||
| For the other cases: | For the other cases: | ||
| Line 148: | Line 143: | ||
| |SIG(3)| fluid mass stored as a consequence of the evolution of soil porosity ($=\rho_e=\frac{\partial}{\partial t}(\rho_f\theta)$) | | |SIG(3)| fluid mass stored as a consequence of the evolution of soil porosity ($=\rho_e=\frac{\partial}{\partial t}(\rho_f\theta)$) | | ||
| |SIG(4)| none | | |SIG(4)| none | | ||
| - | |||
| ===== State variables ===== | ===== State variables ===== | ||
| Line 154: | Line 148: | ||
| ==== Number of state variables ==== | ==== Number of state variables ==== | ||
| - | 5 | + | 16 |
| ==== List of state variables ==== | ==== List of state variables ==== | ||
| - | |Q(1)| 0 (meaningless) | | + | |Q(1)| POROB*ONE*RHOWB/(RHOS*(ONE-POROB)) | |
| |Q(2)| Soil isotropic permeability ($=k$) | | |Q(2)| Soil isotropic permeability ($=k$) | | ||
| |Q(3)| Soil porosity ($=n_0$) | | |Q(3)| Soil porosity ($=n_0$) | | ||
| Line 166: | Line 160: | ||
| |:::| $S_r=\frac{\theta}{n_0}$ if $p<0$ | | |:::| $S_r=\frac{\theta}{n_0}$ if $p<0$ | | ||
| |Q(5)| Actualised fluid specific mass | | |Q(5)| Actualised fluid specific mass | | ||
| - | + | |Q(6)| Permeability $K_{xx}$ | | |
| - | + | |Q(7)| Permeability $K_{yy}$ | | |
| - | + | |Q(8)| Permeability $K_{xy}$ | | |
| - | + | |Q(10)| DLOG10($\frac{K_{xx}}{K_{xx_0}}$) | | |
| - | + | |Q(11)| DLOG10($\frac{K_{yy}}{K_{yy_0}}$) | | |
| - | + | |Q(13)| Microporosity | | |
| - | + | |Q(14)| Dry density $\rho_d$ | | |
| - | + | |Q(15)| Void ratio $e$ | | |
| - | + | |Q(16)| VOIDMICB (mothymar law) | | |
| - | + | ||
| - | + | ||
laws/ecous.1566562645.txt.gz · Last modified: 2020/08/25 15:34 (external edit)
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