laws:bbm
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laws:bbm [2020/08/25 15:46] 127.0.0.1 external edit |
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 (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| \[\kappa_s = \kappa_{s0}.\exp(-\alpha_p.p)\] | $\kappa_{s0}$ = KAPPAS0 \\ $\alpha_p$ = KAPPAS1 | | + | |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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| |ISOL| = 0 : Use of total stresses $\sigma_{t,ij}$ in the constitutive law | | |ISOL| = 0 : Use of total stresses $\sigma_{t,ij}$ in the constitutive law | | ||
| |:::| = 6 : Use of net stresses $\sigma_{ij}$ in the constitutive law. The net stresses are defined as \[\sigma_{ij}=\sigma_{t,ij}-\max(u_a,u_w)\;\delta_{ij}\] with $u_a$ and $u_w$ the air and water pressures and $\delta_{ij}$ the Kronecker delta | | |:::| = 6 : Use of net stresses $\sigma_{ij}$ in the constitutive law. The net stresses are defined as \[\sigma_{ij}=\sigma_{t,ij}-\max(u_a,u_w)\;\delta_{ij}\] with $u_a$ and $u_w$ the air and water pressures and $\delta_{ij}$ the Kronecker delta | | ||
| - | |IELA\\ (used in BBMELA)| = 0 : Non-linear elasticity \[K = \frac{1+e}{\kappa}.p/quad\text{and}\quad G=\frac{3}{2}.\frac{1-2\nu}{1+\nu}.K\] | | + | |IELA\\ (used in BBMELA)| = 0 : Non-linear elasticity \[K = \frac{1+e}{\kappa}.p\quad\text{and}\quad G=\frac{3}{2}.\frac{1-2\nu}{1+\nu}.K\] | |
| - | |:::| = 1 : Non-linear elasticity \[K = \frac{1+e}{\kappa}.p/quad\text{and}\quad G=G_0\] | | + | |:::| = 1 : Non-linear elasticity \[K = \frac{1+e}{\kappa}.p\quad\text{and}\quad G=G_0\] | |
| |IELAP\\ (used in BBMELA)| = 0 : Constant KAPPA ($\kappa$) | | |IELAP\\ (used in BBMELA)| = 0 : Constant KAPPA ($\kappa$) | | ||
| |:::| > 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 | | ||
| Line 125: | Line 126: | ||
| |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) | | ||
| Line 132: | Line 134: | ||
| |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.1598363185.txt.gz · Last modified: 2020/08/25 15:46 by 127.0.0.1
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