Safety analysis and displacements

When doing a safety analysis using the phi/c reduction method, tan(phi) and c are reduced according to the rule:
ΣMsf = tan(φ'_input) / tan(φ'_reduced) = c'_input / c'_reduced
Note that this relationship is different for models that do not have the Mohr-Coulomb failure criterion, like the Hoek-Brown model. See the Calculations chapter in the PLAXIS Reference Manual for more details.

Due to this ('artificial') strength reduction, you will introduce out-of-balance forces in the model. This out-of-balance will be solved by the calculation kernel, which will result in deformations.
These additional displacements that are generated do not have a physical meaning, but the incremental displacements and/or incremental shear strains in the final step (once a stable solution for ΣMsf is reached), give an indication of the likely failure mechanism. Note that the displacements júst before the maximum ΣMsf is reached may be used to get an order of magnitude of the displacements at the moment of failure.

The idea of phi/c reduction is that the soil strength is gradually reduced and when failure occurs the corresponding strength reduction factor can be considered a factor of safety on soil strength. We can recognize whether failure occurs based on the idea that when a small reduction of strength is applied this leads to a large change of strains and displacements.
Note that when more additional steps are used to calculate the safety factor by a phi/c reduction, and a stable value of ΣMsf is reached, you will generate more additional displacements.

In order to determine the safety factor as calculated by a phi/c reduction, please check if you have a stable value for ΣMsf: prior to the calculation select a control point that is likely to be in the failure zone. Afterwards, check if the control point is indeed in the failure zone and then plot the displacements of this point against ΣMsf and check if a stable value for ΣMsf is reached. If this is not the case, please calculate the phase with more additional steps.

For more details about this method, please see the Calculations chapter in the Reference Manual.