Iterative settings: Influence of Arc length control

ApplicationPLAXIS 2D
VersionPLAXIS 2D CE V20
Date created18 July 2011
Date modified7 September 2020

Assume on a certain geometry the user wants to apply a certain load, but during the calculation, it appears that the load to be applied is larger than the failure load. The calculation would then try to apply the load defined by the user over and over again without converging to a solution as the load can simply not be applied. Hence, the calculation will keep iterating. When using the arc-length control the calculation will in fact accurately find how much of the load can really be applied.

In principle using arc-length control or not makes no difference for the result of the calculation if no failure occurs. However, in case of failure, the results will differ because without arc-length control there is no accurate determination of the failure load. Generally, without using arc-length control the failure load is overestimated. This typically shows in a Safety factor determination (phi/c reduction) where the factor of safety obtained without arc-length control is generally higher than the factor of safety obtained with arc-length control. Since arc-length control is meant to determine failure accurately, it’s recommended to always do Safety analysis with arc-length control switched on.

Iterative settings: arc-length control

Additionally, in PLAXIS the use of arc-length control is combined with an automatic failure detection. This automatic failure detection says that if in 5 successive calculation steps the applied load has to be decreased in order for the calculation to converge, failure is assumed and the calculation stops. Without arc-length control, there are no automatic failure detections since without arc-length control it is not possible for the applied load to decrease. Therefore, if arc-length control is switched off and the calculation results give the impression of failure, the user has to check himself thoroughly whether failure occurs or not.

As mentioned, by using arc-length control it is possible for the calculation to determine accurately how much load is really applied from a load step determined by the user. This implies that the calculation won’t know how much load is really applied until the calculation has converged. For a plastic calculation, this is fine, but for consolidation, this is a problem. For a consolidation analysis, the stiffness matrix depends on the time step chosen, and therefore the time step must be determined before the calculation step when the stiffness matrix is made. Due to arc-length controlling the load step, and therefore the time step, is not known until áfter the calculation step when the calculation converged. Therefore arc-length control cannot be used for a consolidation analysis and is automatically switched off by PLAXIS.

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