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laws:bbm
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BBM
Barcelona Basic Model
Description
Full law name : ALONSO-GENS BBM
An elasto-plastic constitutive law for saturated or partially saturated soils based on the CAMCLAY-type model.
It can take into account:
- the influence of the LODE angle;
- linear or non-linear elasticity;
- non-associated plasticity;
- the elasto-plasticity induced by the suction.
The model
This law is used for mechanical analysis of saturated and partially saturated elasto-plastic isotropic porous media undergoing suction changes.
Hardening forms
Elasticity
| IELAP | Expression | Parameters |
| 0 | \[\kappa=\kappa_0\] | $\kappa_0$ = KAPPA0 |
| 1 | \[\kappa = \kappa_0\left[1+\alpha_1.s+\alpha_2.\ln\left(\frac{s+u_{atm}}{u_{atm}}\right)\right]\] | $\kappa_0$ = KAPPA0 $\alpha_1$ = KAPPA1 $\alpha_2$ = KAPPA2 |
| IELAS | Expression | Parameters |
| 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 |
| 2 | Not defined | |
| 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 |
| 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 |
| 7 | \[\kappa_s = \begin{cases} \kappa_{s0} & \quad \text{if } S_r\leq S_r^* \\ \kappa_{res} & \quad \text{if } S_r>S_r^*\end{cases}\] | $\kappa_{s0}$ = KAPPAS0 $\kappa_{res}$ = KAPPAS1 $S_r^*$ = KAPPAS2 |
Yield surfaces
Files
Prepro: LBBM.F
Lagamine: BBMPIL.F
Availability
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | NO |
| Generalized plane state | NO |
Input file
Parameters defining the type of constitutive law
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 812 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (16I5) | |
|---|---|
| NINTV | > 0 : Number of sub-steps used to integrate numerically the constitutive equation in a time step |
| = 0 : NINTV will be calculated in the law with DIV | |
| 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 | |
| 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 \[K = \frac{1+e}{\kappa}.p\quad\text{and}\quad G=G_0\] | |
| IELAP (used in BBMELA) | = 0 : Constant KAPPA ($\kappa$) |
| > 0 : Variable KAPPA ($\kappa$) | |
| = 1 : $\kappa = \kappa_0\left[1+\alpha_1. s + \alpha_2. \ln\left(\frac{s+u_{atm}}{u_{atm}}\right)\right]$ | |
| IELAS (used in BBMINT) | = 0 : Constant KAPPAS ($\kappa_s$) |
| > 0 : Variable KAPPAS ($\kappa_s$) | |
| = 1 : $\kappa_s = \kappa_{s0}\left[1+\alpha_p.\ln\left(\frac{p}{u_{atm}}\right)\right].\exp(\alpha_s.s)$ | |
| = 2 : Not defined | |
| = 3 : $\kappa_s = \kappa_{s0}.(1-\alpha_s.s)$ | |
| = 4 : $\kappa_s = \kappa_{s0}.\exp(-\alpha_p.p)$ | |
| = 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 : $\kappa_s=\kappa_{s0}$ | |
| = 7 : if $S_r>S_r^*$ : $\kappa_s=\kappa_{res}$, else : $\kappa_s=\kappa_{s0}$ | |
| IVOID | = 0 : Initial void ratio |
| = 1 : Updated void ratio | |
| ILC | Shape of the LC curve in the $p-s$ plane |
| = 0 : Original formulation (Alonso et al., 1990) | |
| = 1 : Modified version for $S_r^*$ (Dieudonné, 2016) | |
| IDEV | Shape of the LC curve in the $p–q$ plane |
| = 0 : Original formulation (Alonso et al., 1990) | |
| ICS | Increase in cohesion with suction |
| = 0 : Original formulation (Alonso et al., 1990) | |
| IASSOC | = 0 : Non-associated plasticity (Alonso et al., 1990) |
| = 1 : Associated plasticity | |
| ILODEF | Shape of the yield surface in the deviatoric plane |
| = 0 : Circle in the deviatoric plane | |
| = 1 : Smoothed irregular hexagon in the deviatoric plane | |
| ILODEG | Shape of the flow surface in the deviatoric plane (meaningful if IASSOC$\neq$1) |
| = 0 : Circle in the deviatoric plane | |
| = 1 : Smoothed irregular hexagon in the deviatoric plane | |
Real parameters
| Line 1 (3G10) | |
|---|---|
| POROS0 | Initial porosity |
| RHO | Solid specific mass |
| DIV | Parameter for the computation of NINTV in the law (for NINTV=0 only) |
| Line 2 (5G10) | |
| KAPPA0 | 1st elastic parameter (relative to changes in stress) |
| KAPPA1 | 2nd elastic parameter (relative to changes in stress) |
| KAPPA2 | 3rd elastic parameter (relative to changes in stress) |
| NUG | Poisson’s ratio $\nu$ (if IELA = 0) |
| Shear modulus G (if IELA = 1) | |
| AI1MIN | Minimum value of $I_{\sigma}$ for non-linear elasticity |
| Line 3 (6G10) | |
| COH | Value of cohesion in saturated conditions |
| COH_PAR1 | 1st parameter for the evolution of cohesion with suction |
| COH_PAR2 | 2nd parameter for the evolution of cohesion with suction |
| PHIC | Friction angle (in degrees) for compressive paths |
| PHIE | Friction angle (in degrees) for extensive paths (only if ILODEF=2) |
| AN | Van Eekelen exponent (default value = -0.229) |
| Line 4 (6G10) | |
| LAMBDA0 | Plastic coefficient in saturated conditions |
| P0ST | Pre-consolidation pressure in saturated conditions |
| PCrel | Relative reference pressure P0ST/PC for the definition of the LC curve |
| LC_PAR1 | 1st parameter of the LC curve |
| LC_PAR2 | 2nd parameter of the LC curve |
| LC_PAR3 | 3rd parameter of the LC curve |
| Line 5 (6G10) | |
| KAPPAS0 | 1st elastic parameter (relative to changes in suction) |
| KAPPAS1 | 2nd elastic parameter (relative to changes in suction) |
| KAPPAS2 | 3rd elastic parameter (relative to changes in suction) |
| LAMBDAS | Plastic suction coefficient |
| PATM | Atmospheric pressure |
| S0 | Yield limit in term of suction (SI curve) |
Stresses
Number of stresses
6 for 3D state
4 for the other cases
Meaning
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates.
For the other cases:
| SIG(1) | $\sigma_{xx}$ |
| SIG(2) | $\sigma_{yy}$ |
| SIG(3) | $\sigma_{xy}$ |
| SIG(4) | $\sigma_{zz}$ |
State variables
Number of state variables
25 in all the other cases
List of state variables
| Q(1) | = 1 : Plane strain state |
| Circumferential strain rate ($\dot{\varepsilon}_{\theta}$) in axisymmetric state | |
| Q(2) | Specific mass |
| Q(3) | Porosity |
| Q(4) | Suction |
| Q(5) | = 0 if the current state is elastic |
| = 1 if the current state is elasto-plastic (LC) | |
| = 2 if the current state is elasto-plastic (SI) | |
| = 12 if the current state is elasto-plastic (LC + SI) | |
| Q(6) | Pre-consolidation pressure $p_0$ in saturated conditions |
| Q(7) | Current pre-consolidation pressure $p_0$ |
| Q(8) | Maximum suction $s_0$ |
| Q(9) | Apparent cohesion |
| Q(10) | Apparent resistance in extension |
| Q(11) | Elastic slope relative to changes in pressure ($\kappa$) |
| Q(12) | Cubic modulus (K) |
| Q(13) | Shear modulus (G) |
| Q(14) | Elastic slope relative to changes in pressure ($\kappa_s$) |
| Q(15) | Plastic slope relative to changes in pressure ($\lambda(s)$) |
| Q(16) | X deformation |
| Q(17) | Y deformation |
| Q(18) | Z deformation |
| Q(19) | XY deformation |
| Q(20) | Volumetric strain |
| Q(21) | Deviatoric strain |
| Q(22) | Number of sub-intervals used for the integration |
| Q(23) | Number of iteration used for the integration |
| Q(24) | Equivalent strain indicator $\alpha = \Delta\dot{\varepsilon}_{vol}\;\Delta t/\varepsilon_{vol}$ |
| Q(25) | = 0 if elastic, 1 if softening, 2 if hardening |
laws/bbm.txt · Last modified: 2024/06/20 16:35 by maximilian
