appendices:a7
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appendices:a7 [2024/06/20 16:22] frederic |
appendices:a7 [2024/06/20 16:25] (current) frederic |
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| ^ISOL = 9 : Only for CSOL2 element and ORTHOPLA mechanical law^^ | ^ISOL = 9 : Only for CSOL2 element and ORTHOPLA mechanical law^^ | ||
| - | $\sigma_{ij} = \sigma'_{ij} - b_{ij}\theta(S_r)p , \forall p$ with ISEM = 1 or 2 \\ | + | $\sigma_{ij} = \sigma'_{ij} - b_{ij} S_r p_w , \forall p_w$ \\ |
| with $b_{ij}$ the anisotropic Biot’s coefficient. In the orthotropic axes: \[b_{ij}=\delta_{ij}-\frac{C^e_{ijkk}}{3K_s}\] | with $b_{ij}$ the anisotropic Biot’s coefficient. In the orthotropic axes: \[b_{ij}=\delta_{ij}-\frac{C^e_{ijkk}}{3K_s}\] | ||
| In case of orthotropic axes rotation, it is transposed in the global axes as follows: \[b_{ij}=R_{ik}R_{jl}b'_{kl}\] | In case of orthotropic axes rotation, it is transposed in the global axes as follows: \[b_{ij}=R_{ik}R_{jl}b'_{kl}\] | ||
| where $R_{ij}$ is the rotation matrix. More details about this anisotropy are available in the definition of element CSOL2 and orthotropic law ORTHOPLA. \\ \\ | where $R_{ij}$ is the rotation matrix. More details about this anisotropy are available in the definition of element CSOL2 and orthotropic law ORTHOPLA. \\ \\ | ||
| - | $\theta(S_r)$ is the Bishop's coefficient, depending on the material saturation, and included between 0 and 1: | ||
| - | \[ \theta(S_r) = \begin{cases} S_r = 1 & \quad \text{if } p \geq 0 \\ | ||
| - | S_r = \frac{n}{n_0}=\frac{S}{S_0} & \quad \text{if } p < 0 | ||
| - | \end{cases} | ||
| - | \] | ||
| - | with: | ||
| - | * $p$ the pore pressure in CSOL2 | ||
| - | * $n$ the soil porosity | ||
| - | * $S$ the accumulated fluid volume | ||
| - | * $S_0$: $S$ in $p = 0$ | ||
appendices/a7.1718893321.txt.gz · Last modified: 2024/06/20 16:22 by frederic
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