laws:bbm
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laws:bbm [2026/02/26 12:23] 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 | | + | | | \[\kappa_{s0}=\kappa_{s0,ref}\left(\frac{\rho_d}{\rho_{d,ref}}\right)^{N_{\kappa_{s}}}\] | $\kappa_{s0,ref}$ = 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 | | ||
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| |:::| > 0 : Variable KAPPA ($\kappa$) | | |:::| > 0 : Variable KAPPA ($\kappa$) | | ||
| |:::| = 1 : $\kappa = \kappa_0\left[1+\alpha_1. s + \alpha_2. \ln\left(\frac{s+u_{atm}}{u_{atm}}\right)\right]$ | | |:::| = 1 : $\kappa = \kappa_0\left[1+\alpha_1. s + \alpha_2. \ln\left(\frac{s+u_{atm}}{u_{atm}}\right)\right]$ | | ||
| - | |IELAS\\ (used in BBMINT)| = 0 : Constant KAPPAS ($\kappa_s$) | | + | |IELAS\\ (used in BBMINT)| = 0 : Constant KAPPAS ($\kappa_s=fct(\rho_d)$) | |
| - | |:::| > 0 : Variable KAPPAS ($\kappa_s$) | | + | |:::| > 0 : Variable KAPPAS ($\kappa_s=fct(\rho_d)$) | |
| |:::| = 1 : $\kappa_s = \kappa_{s0}\left[1+\alpha_p.\ln\left(\frac{p}{u_{atm}}\right)\right].\exp(\alpha_s.s)$ | | |:::| = 1 : $\kappa_s = \kappa_{s0}\left[1+\alpha_p.\ln\left(\frac{p}{u_{atm}}\right)\right].\exp(\alpha_s.s)$ | | ||
| |:::| = 2 : Not defined | | |:::| = 2 : Not defined | | ||
| |:::| = 3 : $\kappa_s = \kappa_{s0}.(1-\alpha_s.s)$ | | |:::| = 3 : $\kappa_s = \kappa_{s0}.(1-\alpha_s.s)$ | | ||
| - | |:::| = 4 : $\kappa_s = \kappa_{s0}.\exp(-\alpha_p.p)$ | | + | |:::| = 4 : $\kappa_s = \kappa_{s0}.\exp(-\alpha_p(=fct(\rho_d)).p)$ | |
| |:::| = 5 : if $s\leq s^*$ : $\kappa_s = \kappa_{res}$, else : $\kappa_s=\kappa_{s0}$ | | |:::| = 5 : if $s\leq s^*$ : $\kappa_s = \kappa_{res}$, else : $\kappa_s=\kappa_{s0}$ | | ||
| |:::| = 6 : if $S_r>S_r^*$ : $\kappa_s=\kappa_{s0}(1-S_r)^{\gamma_{\kappa_s}}$, else : $\kappa_s=\kappa_{s0}$ | | |:::| = 6 : if $S_r>S_r^*$ : $\kappa_s=\kappa_{s0}(1-S_r)^{\gamma_{\kappa_s}}$, else : $\kappa_s=\kappa_{s0}$ | | ||
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| |PHIE| Friction angle (in degrees) for extensive paths (only if ILODEF=2) | | |PHIE| Friction angle (in degrees) for extensive paths (only if ILODEF=2) | | ||
| |AN| Van Eekelen exponent (default value = -0.229) | | |AN| Van Eekelen exponent (default value = -0.229) | | ||
| - | ^ Line 4 (6G10) ^^ | + | ^ Line 4 (7G10) ^^ |
| |LAMBDA0| Plastic coefficient in saturated conditions | | |LAMBDA0| Plastic coefficient in saturated conditions | | ||
| |P0ST| Pre-consolidation pressure in saturated conditions | | |P0ST| Pre-consolidation pressure in saturated conditions | | ||
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| |LC_PAR2| 2nd parameter of the LC curve | | |LC_PAR2| 2nd parameter of the LC curve | | ||
| |LC_PAR3| 3rd parameter of the LC curve | | |LC_PAR3| 3rd parameter of the LC curve | | ||
| - | ^ Line 5 (6G10) ^^ | + | |KAPPAS4| 5th elastic parameter (relative to changes in suction) (default value = 0: no influence of dry density on $\kappa_{s0}$) | |
| + | ^ Line 5 (7G10) ^^ | ||
| |KAPPAS0| 1st elastic parameter (relative to changes in suction) | | |KAPPAS0| 1st elastic parameter (relative to changes in suction) | | ||
| |KAPPAS1| 2nd elastic parameter (relative to changes in suction) | | |KAPPAS1| 2nd elastic parameter (relative to changes in suction) | | ||
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| |PATM| Atmospheric pressure | | |PATM| Atmospheric pressure | | ||
| |S0| Yield limit in term of suction (SI curve) | | |S0| Yield limit in term of suction (SI curve) | | ||
| + | |KAPPAS3| 4th elastic parameter (relative to changes in suction) (default value = 0: no influence of dry density on $\alpha_p$) | | ||
| ===== Stresses ===== | ===== Stresses ===== | ||
laws/bbm.1772105016.txt.gz · Last modified: 2026/02/26 12:23 by gilles
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