appendices:a7
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| ====== Appendix 7: Notion of effective stress and signification of parameter ISOL in elements CSOL2 and MWAT2 ====== | ====== Appendix 7: Notion of effective stress and signification of parameter ISOL in elements CSOL2 and MWAT2 ====== | ||
| - | The definition of effective stress is mandatory when using CSOL2, MWAT2, CSOL3, MWAT3, FAIL2, FAIL3, FAIF2, FAIF3, FAIN2, FAIN3, SGRC2, SGRT2: | + | The definition of effective stress is mandatory when using CSOL2, MWAT2, CSOL3, MWAT3, FAIL2, FAIL3, FAIF2, FAIF3, FAIN2, FAIN3, SGRC2, SGRT2. |
| + | |||
| + | __Remark:__ \\ | ||
| + | For other elements than CSOL2 or MWAT2, the parameter ISOL can only be equal to 0 or 1. \\ | ||
| + | For PLXLS : ISOL < 0 => for non saturated soil (suction effect and considered in the mechanic law) (for the Alonso's law). | ||
| + | |||
| The total stress σ is split into an effective stress σ' in the matrix and a pressure p_f in the fluid. | The total stress σ is split into an effective stress σ' in the matrix and a pressure p_f in the fluid. | ||
| Line 49: | Line 54: | ||
| * $b$ is the Biot coefficient | * $b$ is the Biot coefficient | ||
| * $\pi$ is the generalized pore pressure (Coussy-Danglat) | * $\pi$ is the generalized pore pressure (Coussy-Danglat) | ||
| - | __Remark:__ \\ | ||
| - | For other elements than CSOL2 or MWAT2, the parameter ISOL can only be equal to 0 or 1. \\ | ||
| - | For PLXLS : ISOL < 0 => for non saturated soil (suction effect and considered in the mechanic law) (for the Alonso's law). | ||
| ^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/a7.1718893248.txt.gz · Last modified: 2024/06/20 16:20 by frederic
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