laws:bbm
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laws:bbm [2026/03/17 08:44] gilles |
laws:bbm [2026/03/17 08:48] (current) gilles |
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| |IELAS| Expression | Parameters | | |IELAS| Expression | Parameters | | ||
| - | | | \[\kappa_{s0}=\kappa_{s0,ref}\left(\frac{\rho_d}{\rho_{d,ref}}\right)^{N_{\kappa_{s}}}\] | $\kappa_{s0,ref}$ = KAPPAS0 \\ $N_{\kappa_{s}}$ = KAPPAS3 \\ IF $N_{\kappa_{s}}$=0: Reference case without effect of density | | + | | | \[\kappa_{s0}=\kappa_{s0,ref}\left(\frac{\rho_d}{\rho_{d,ref}}\right)^{N_{\kappa_{s}}}\] | $\kappa_{s0,ref}$ = KAPPAS0 \\ $N_{\kappa_{s}}$ = KAPPAS3 (Default value $N_{\kappa_{s}}$=0:\\ Reference case without density effects) | |
| |0| \[\kappa_s=\kappa_{s0}\] | $\kappa_{s0}$ = KAPPAS0 | | |0| \[\kappa_s=\kappa_{s0}\] | $\kappa_{s0}$ = KAPPAS0 | | ||
| |1| \[\kappa_s = \kappa_{s0}\left[1+\alpha_p.\ln\left(\frac{p}{u_{atm}}\right)\right].\exp(\alpha_s.s)\] | $\kappa_{s0}$ = KAPPAS0 \\ $\alpha_p$ = KAPPAS1 \\ $\alpha_s$ = KAPPAS2 \\ $u_{atm}$ = PATM | | |1| \[\kappa_s = \kappa_{s0}\left[1+\alpha_p.\ln\left(\frac{p}{u_{atm}}\right)\right].\exp(\alpha_s.s)\] | $\kappa_{s0}$ = KAPPAS0 \\ $\alpha_p$ = KAPPAS1 \\ $\alpha_s$ = KAPPAS2 \\ $u_{atm}$ = PATM | | ||
| |2| Not defined || | |2| Not defined || | ||
| |3| \[\kappa_s = \kappa_{s0}.(1-\alpha_s.s)\] | $\kappa_{s0}$ = KAPPAS0 \\ $\alpha_s$ = KAPPAS2 | | |3| \[\kappa_s = \kappa_{s0}.(1-\alpha_s.s)\] | $\kappa_{s0}$ = KAPPAS0 \\ $\alpha_s$ = KAPPAS2 | | ||
| - | |4| \[\kappa_s = \kappa_{s0}.\exp(-\alpha_p.p)\] \\ \[\alpha_p = \alpha_{p,ref} \exp(-M_{\alpha_{p}} \left(\rho_d-\rho_{d,ref}\right))\] | $\kappa_{s0}$ = KAPPAS0 \\ $\alpha_{p,ref}$ = KAPPAS1 \\ $M_{\alpha_{p}}$ = KAPPAS4 | | + | |4| \[\kappa_s = \kappa_{s0}.\exp(-\alpha_p.p)\] \\ \[\alpha_p = \alpha_{p,ref} \exp(-M_{\alpha_{p}} \left(\rho_d-\rho_{d,ref}\right))\] | $\kappa_{s0}$ = KAPPAS0 \\ $\alpha_{p,ref}$ = KAPPAS1 \\ $M_{\alpha_{p}}$ = KAPPAS4 (Default value $M_{\alpha_{p}}$=0:\\ Reference case without density effects) | |
| |5| \[\kappa_s = \begin{cases} \kappa_{s0} & \quad \text{if } s>s^* \\ \kappa_{res} & \quad \text{if } s\leq s^*\end{cases}\] | $\kappa_{s0}$ = KAPPAS0 \\ $\kappa_{res}$ = KAPPAS1 \\ $s^*$ = KAPPAS2 | | |5| \[\kappa_s = \begin{cases} \kappa_{s0} & \quad \text{if } s>s^* \\ \kappa_{res} & \quad \text{if } s\leq s^*\end{cases}\] | $\kappa_{s0}$ = KAPPAS0 \\ $\kappa_{res}$ = KAPPAS1 \\ $s^*$ = KAPPAS2 | | ||
| |6| \[\kappa_s = \begin{cases} \kappa_{s0} & \quad \text{if } S_r\leq S_r^* \\ \kappa_{s0}(1-S_r)^{\gamma_{\kappa_s}}& \quad \text{if } S_r>S_r^*\end{cases}\] | $\kappa_{s0}$ = KAPPAS0 \\ $\gamma_{\kappa_s}$ = KAPPAS1 \\ $S_r^*$ = KAPPAS2 | | |6| \[\kappa_s = \begin{cases} \kappa_{s0} & \quad \text{if } S_r\leq S_r^* \\ \kappa_{s0}(1-S_r)^{\gamma_{\kappa_s}}& \quad \text{if } S_r>S_r^*\end{cases}\] | $\kappa_{s0}$ = KAPPAS0 \\ $\gamma_{\kappa_s}$ = KAPPAS1 \\ $S_r^*$ = KAPPAS2 | | ||
laws/bbm.1773733493.txt.gz · Last modified: 2026/03/17 08:44 by gilles
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