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Penetration of piles in soils is done over very large distances as compared to the radius of the pile. Soil deformations directly at the pile, or in the neighborhood of the pile, will become very large, such that the standard lagrangian calculations are not possible; the finite elements themselves would become severely distorted. A possible solution to this problem is the application of Eulerian calculations, where the material flow through the mesh, and so the finite elements of the mesh do not get deformed.

The figure here shows the velocity field for the penetration of a CPT cone into a soil. The soil, in this case sand, is modeled with the Drucker-Prager constitutive law. The soil flows at 20 mm/s a long the cone for a total displacement of 10 meters. The figure shows the velocity field [m/s].

This calculation is courtesy Delft University of Technology, Section Geoengineering, The Netherlands, .