A non-linear three-dimensional pile–soil model for vibratory pile installation in layered media

Athanasios Tsetas*, Apostolos Tsouvalas, Andrei V. Metrikine

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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This paper presents a computationally efficient model for vibratory pile installation. A semi-analytical finite element (SAFE) model for thin cylindrical shells is derived to represent the pile. The linear dynamic response of the soil medium is described by means of Green's functions via the Thin-Layer Method (TLM) coupled with Perfectly Matched Layers (PMLs) to account for the underlying elastic half-space. Furthermore, the non-linear pile–soil interaction is addressed through a history-dependent frictional interface and a visco-elasto-plastic tip reaction model that can be characterized on the basis of standard geotechnical in-situ measurements. The solution to the non-linear dynamic pile–soil interaction problem is based on the sequential application of the Harmonic Balance Method (HBM). The constituent components of the model are first benchmarked against established numerical schemes. Subsequently, model predictions are compared with experimental data collected from field tests. It is demonstrated that the proposed model amalgamates rigorous theoretical elements and promising prediction capabilities in a computationally efficient framework, applicable to engineering practice.

Original languageEnglish
Article number112202
Number of pages17
JournalInternational Journal of Solids and Structures
Publication statusPublished - 2023


This paper is associated with the GDP project in the framework of the GROW joint research programme. Funding from Topsector Energiesubsidie van het Ministerie van Economische Zaken, Netherlands under grant number TEHE117100 and financial/technical support from the following partners is gratefully acknowledged: Royal Boskalis Westminster N.V. Netherlands, CAPE Holland B.V. United States, Deltares, Netherlands, Delft Offshore Turbine B.V. Netherlands, Delft University of Technology, Netherlands, ECN, Netherlands, Eneco Wind B.V. Netherlands, IHC IQIP B.V. Netherlands, RWE Offshore Wind Netherlands B.V., SHL Offshore Contractors B.V. Netherlands, Shell Global Solutions International B.V. Netherlands, Sif Netherlands B.V., TNO, Netherlands, and Van Oord Offshore Wind Projects B.V, Netherlands.


  • Field tests
  • Green's functions
  • Harmonic Balance Method
  • Perfectly Matched Layers
  • Soil–structure interaction
  • Thin-Layer Method
  • Vibrations of shells
  • Vibratory pile driving


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