### Why does the deviatoric stress tend to infinity when modeling undrained behavior with the Hardening-Soil model?

Why does the deviatoric stress tend to infinity when modeling undrained behavior with the Hardening-Soil model?

ANSWER

This is because, in the original Hardening-Soil model formulation, the shear and volumetric plastic mechanisms are decoupled. The preconsolidation pressure *p _{c}*, being the hardening parameter of the cap yield surface, depends solely on the accumulated volumetric plastic strain

*ε*produced by this mechanism. Similar assumption is adopted for the shear yield surface that expands with increasing accumulated deviatoric plastic strain

_{v}^{p}*γ*produced by the shear mechanism. The latter plastic mechanism may also produce volumetric plastic strain (due to dilatancy) but it is not coupled with the hardening law for preconsolidation pressure.

^{PS}Evolution of the effective stress path in the undrained triaxial test assuming uncoupled shear/volumetric plastic mechanisms (OCR = 1)

The macroscopic behavior of cohesionless soils can be reproduced by the model reasonably well, regardless of drainage conditions (i.e. drained or undrained). **The ability to represent undrained behavior of overconsolidated, therefore usually dilative, cohesive soils is limited**. Lack of coupling of these two plastic mechanisms leads to an unlimited undrained shear strength increase regardless of the OCR value.

SOLUTION

The major drawback of the model is such that it is unable to appropriately reproduce the undrained shear strength in the case when dilatancy angle ψ is larger than zero. By applying a conservative assumption ψ = 0°, the computed undrained shear strength may be underestimated with respect to the true one (even a few times for larger values of OCR). On the other hand, by assuming ψ > 0°, the undrained shear strength will tend to infinity with the increasing shear strain amplitude.

### List of files used/created by calculation module

File extension | Content | Form | Needed for restart | Needed for postprocessing |

‘.dat’ | FE model data | ASCII | YES | YES |

.cfg’ | temporary config file for calculation module | ASCII | YES | NO |

‘.log’ | echo of execution | ASCII | YES | NO |

‘.opt’ | optimized nodes order for skyline solvers | BINARY | YES | NO |

‘.elb’ | current element storage | BINARY | NO | NO |

‘.sky’ | skyline block solver (obsolete as sparse is used for huge problems) | BINARY | NO | NO |

‘.sks’ | skyline block solver (obsolete as sparse is used for huge problems) | BINARY | NO | NO |

‘.exc’ | current excavation forces | BINARY | YES | NO |

‘.dis’ | nodal ASCII output (practicaly unused) | ASCII | YES | YES (if activated) |

‘.str’ | element ASCII output (practicaly unused) | ASCII | YES | YES (if activated) |

‘.his’ | summary history of execution | ASCII | YES | YES |

‘.rcf’ | results configuration setup (nodal results and element results) | ASCII | YES | YES |

‘.ers’ | element data storage produced by stability driver for restart purposes | YES | NO | |

‘.ern’ | element data storage produced by other drivers drivers used for restart purposes | BINARY | YES | NO |

‘.rst’ | other restart data | BINARY | YES | NO |

‘.fro’ | storage for frontal solver (obsolete) | BINARY | YES | NO |

‘.ech’ | fe data to be used for domain reduction and thermal loading | BINARY | YES | NO |

‘.eli’ | element storage for last accepted iteration | BINARY | YES | NO |

‘.eda’ | echo of input data | ASCII | YES | NO |

‘.rea’ | obsolete | NO | NO | |

‘.new’ | obsolete | NO | NO | |

‘.lay’ | results configuration file for beam/shell layers | ASCII | YES | YES |

‘.bgc’ | obsolete | NO | NO | |

‘.tgc’ | obsolete | NO | NO | |

‘.bfg’ | BFGS solver storage | BINARY | NO | NO |

‘.cdb’ | error log for postprocessor | ASCII | YES | YES |

‘.r00’ | reactions/residuals | BINARY | YES | YES |

‘.aux’ | temporary file | ANY | NO | NO |

‘.ovl’ | overlaid meshes info | BINARY | YES | YES |

‘.ctr’ | stage construction | BINARY | YES | YES |

‘.dps’ | pushover file | ASCII | YES | YES |

‘.rps’ | pushover file | ASCII | YES | YES |

‘.add’ | construction+large deformations | BINARY | YES | YES |

‘.v00’ | nodal velocities | BINARY | YES | YES |

‘.a00’ | nodal accelerations | BINARY | YES | YES |

‘.m00’ | eigenmodes | BINARY | YES | YES |

‘.fps’ | eigen-mode pushover force shape | BINARY | YES | YES |

‘.xof’ | x-ele offset in large deformations after morphing (continuum only) | BINARY | YES | YES |

‘.egv’ | eigenvalues | BINARY | YES | YES |

‘.psh’ | pushover results | ASCII | YES | YES |

‘.ppl’ | results in piles | ASCII | YES | YES |

‘.nal’ | results in nails | ASCII | YES | YES |

‘.rah’ | results in anchor heads | ASCII | YES | YES |

‘.rex’ | excavation forces for deleted BC | BINARY | YES | NO |

‘.arl’ | obsolete | |||

‘.ths’ | time history of selected nodes (used for tuning attenuation curve in dynamics) | ASCII | YES | YES |

‘.eig’ | output for eigenvalues | ASCII | YES | YES |

‘.msv’ | obsolete | |||

‘.uro’ | initial element deformations | BINARY | YES | YES |

‘.xst’ | temporary restart file | BINARY | YES | NO |

‘.xrn’ | temporary restart file for standard drivers | BINARY | YES | NO |

‘.xrs’ | temporary restart file for stability drivers | BINARY | YES | NO |

‘.xxc’ | temporary file to keep copy of excavation forces | BINARY | YES | NO |

‘.elj’ | element storage copy for Thomas initial stiffness method | BINARY | YES | NO |

‘.s00’ | nodal results | BINARY | YES | YES |

‘.s01’ | continuum results | BINARY | YES | YES |

‘.s02’ | shell results | BINARY | YES | YES |

‘.s03’ | truss results | BINARY | YES | YES |

‘.s04’ | beam results | BINARY | YES | YES |

‘.s05’ | beam/shell hinges results | BINARY | YES | YES |

‘.s06’ | unused | BINARY | YES | YES |

‘.s07’ | std contact results | BINARY | YES | YES |

‘.s08’ | unused | BINARY | YES | YES |

‘.s09’ | unused | BINARY | YES | YES |

‘.s10’ | unused | BINARY | YES | YES |

‘.s11’ | unused | BINARY | YES | YES |

‘.s12’ | unused | BINARY | YES | YES |

‘.s13’ | unused | BINARY | YES | YES |

‘.s14’ | unused | BINARY | YES | YES |

‘.s15’ | membrane results | BINARY | YES | YES |

‘.s16’ | ring (axisymm) results | BINARY | YES | YES |

‘.s17’ | node-segment contact results | BINARY | YES | YES |

‘.L02’ | shell layers results | BINARY | YES | YES |

‘.L04’ | beam layers results | BINARY | YES | YES |

### Why does the initial state analysis diverge for simulations with Modified Cam-Clay model

### Setting the initial stresses σ_{0} super element for Modified Cam-Clay model is required

The Modified Cam-Clay model (MCC) requires an initial guess for the initial effective stress state to be set by the user. In the initial state computation hardening is deactivated and MCC behaves as classical elasto-plastic model with deviatoric flow rule.

Notice that once the unloading branch, that we assume does not produce any plastic strains, is linear in e-ln(p) axes the soil stiffness must depend on the effective stresses. The bulk modulus is expressed as K = (1 + e_{o})/p.

**So every computation with Modified Cam-Clay model (also HSs) will require to set up the initial guess for the initial effective stress. No matter whether the initial state driver is active or not.**

Read more: Advanced model for soft soils. Modified Cam-Clay model (MCC)

### How to define initial stresses σ_{0} super element

How can we guess the initial stresses in that case?

Setting the initial effective stresses can be made exclusively at the FE level through the option in right menu:

**FE Model/Initial conditions/Initial stresses/On 4 nodes/points**(for 2D cases)**FE Model/Initial conditions/Initial stresses/On 8 nodes/points**(for 3D cases)

To define the initial stresses in quadrilateral regions (covering our FE mesh) we can set all stress components at each vertex separately or we can use a simplified method where we fix the vertical stress at the top and we define the in situ K_{o} coefficient and soil unit weight that will produce correct σ_{o} .

Note that by running the Initial State driver and assuming K_{o} coeficient locally at the material level we do not need to be very precise when we guess the initial in situ stress state. The driver will correct it anyway.

Read more: Advanced model for soft soils. Modified Cam-Clay model (MCC)

### How to simulate the undrained behavior?

Simulating the undrained behavior of soil can be carried out by means of three different approaches:

- Effective stress analysis using
**Consolidation**driver type for**Deformation+Flow**problem type - Effective stress analysis using
**Driven Load-Undrained**driver type for**Deformation+Flow**problem type - Total stress analysis using
**Driven Load**driver type for single-phase**Deformation**problem type

These approaches are described below.

**CONSOLIDATION**

*Driver setup: *Deformation+Flow, Time Dependent, Consolidation

*Input parameters: *always effective strength and stiffness parameters

*Advantages:
*

- undrained or partially drained conditions arise naturally depending on action time and soil permeability
- partial saturation effects are included
- consolidation analysis can be followed by any analysis type

*Disadvantages:*

- CPU time for very large boundary value problems

**DRIVEN LOAD – UNDRAINED**

*Driver setup: *Deformation+Flow, Time Dependent, Driven Load (Undrained)

*Input parameters: *effective strength and stiffness parameters

*Advantages:*

- fully undrained regime (no volume change) is obtained regardless defined soil soil permeability
- useful for dynamics

*Disadvantages:*

- Undrained driver cannot be followed by any other driver

Using Undrained driver type, special attention must be paid on appropriate selection of undrained driver settings. Undrained behavior can be disabled for material layers for which undrained behavior is not relevant.

**TOTAL STRESS ANALYSIS**

*Driver setup: *Deformation, Time Dependent, Driven Load

*Input parameters: *total stress strength and stiffness parameters

*Advantages:*

- relatively fast in terms of CPU

*Disadvantages:*

- undrained shear strength
*c = S*is stress independent (i.e. constant over depth; typically, not the case in natural conditions)_{u} - although « undrained » conditions imply no volume change, model’s preconsolidation pressure
*p*may evolve so not relevant for normally- and lightly overconsolidated soils_{c} - stiffness depends on
*φ*term because_{c}*c cot φ*= 0

The use of the Hardening-Soil model to simulate undrained behavior with the total stress approach demands the parameter setup which presented below.

**POST-PROCESSING**

*Pore** pressure*

For **Consolidation **analysis, pore pressure values can be standardily visualized using nodal quantities. In the case of **Undrained driver**, the results are stored in the Gauss points and visualization of pore pressure can be done using “Undrained pressure” under continuum element results.

*Suction pressure (S*p)*

Magnitudes of suction pressure are stored in the Gauss points and can be read using S*p + <dp_undr> under continuum element results.