Application |
PLAXIS 2D PLAXIS 3D |

Version |
PLAXIS 2D CONNECT Edition PLAXIS 3D CONNECT Edition |

Date created |
30 March 2022 |

Date modified |
30 March 2022 |

Original author |
Sean Johnson - Bentley Technical Support Group |

Occasionally, a PLAXIS analysis may report lower settlements in the case of a drained analysis compared to the settlements of a consolidation analysis, while applying the same surficial load. Why?

In general, a consolidation analysis in PLAXIS is driven by the dissipation of excess pore pressures. The soil will transition from an undrained state to a drained state as a function of the loading time, drainage path, and hydraulic conductivity of the soil. This is also outlined in the PLAXIS Scientific manual, specifically where the mathematics on Biot’s consolidation is described.

Conversely, in a drained plastic analysis, the soil remains in a drained state, whereby the stiffness of water will not have an influence on the stiffness or strength behavior of the soil.

Therefore, the effective stress path of the soil will be different in a consolidation analysis compared to a drained plastic analysis. Hence the stress state at failure might be different. Specifically, at failure, large plastic displacements will occur when the Mohr-Coulomb strength is exceeded in both a consolidation or plastic drained analysis.

In PLAXIS, the failure criteria are driven by the effective stress path in p’-q stress space.

Here we are working with the deviatoric applied effective stress and the mean octahedral stress. The Mohr-Coulomb failure criteria can be understood as a linear function that is driven by the tangent of effective phi’ (the input friction angle defines the soil strength) and the cohesion which is understood as the inherent soil strength when the mean effective stress is equal to zero (0).

Consider that undrained analysis adds water stiffness to the stiffness matrix so, in general, stiffer behavior (E_udr ~= 3 G, K_udr >> K_dr) is expected. Therefore, the bulk modulus of an undrained soil is dramatically different, which would naturally lead to a difference in stress-strain behavior. Moreover, because in the Finite Element method forces are coupled with matrix deformations, there is a possibility of a different strength between a drained and undrained soil. Especially, in a consolidation calculation, the effective shear strength of the soil is reduced since the Mohr-Coulomb failure is encountered during the development of excess pore pressure.

It follows from the figure, in an undrained case when pore pressures are not reduced there will be failure earlier in the analysis given a constant loading path. Therefore, in the consolidation analysis, this will develop more plasticity (and excess pore pressures of a few kPa) compared to a drained analysis.

Please note this only applies to a soil model that incorporates plasticity, which consists of all nearly all built-in soil models. For elastic materials, the two analysis types should converge to the same solution.

Figure 1. 3D symmetric loading with localized load

The above case with a shallow foundation consisting of symmetric vertical loading over a mat. The soil was modeled with the Hardening Soil model, which uses a Mohr-Coulomb failure criterion. As explained before, when you mobilize consolidation, much plasticity develops leading to higher deformation. This case was calculated with PLAXIS 3D CONNECT Edition V21,

To elaborate on the model, the vertical deformations directly under the center of the shallow foundation are provided. Please note that the only change to the model was the calculation type, no changes to the soil occurred.

- Plastic: 4.165m
- Consolidation short (100 Days): 3.482m
- Consolidation long (1100 Days): 4.693m

Figure 2. Drained Plastic loading

Figure 3. Long-term Consolidation