How to Model Piles in PLAXIS
Richard Witasse, Principal Product Manager, Geotechnical
May 19, 2021 11:05:00 AM
https://blog.virtuosity.com/how-to-model-piles-in-plaxis
The problem of analyzing and designing deep foundations is relevant to many civil
engineering structures, because we are commonly and frequently constructing buildings on
soft soils. Pile foundation is a popular type of deep foundation technique used to transfer
superstructure load into subsoil and bearing layers. In this context, the accurate prediction of
piles’ settlement and proper evaluation of pile bearing capacity is a fundamental aspect of
deep foundation design. This could be a challenging task for the designer in the case of
complex pile-soil interaction or in situations involving a consolidation process.
Pile modeling is primarily a 3D problem
Due to the 3D nature of the pile geometry and the possible lateral component of the design
load, most pile foundation analyses should be set up in PLAXIS 3D. Ideally, the piles
themselves will be represented by volume elements. This will guarantee the most accurate
representation of the physical problem, especially regarding soil-structure interaction.
Figure 1: 3D model of a simple pile raft
With such 3D models, the piles are physically modeled, and the soil-structure interaction is
accounted for by means of surface interface elements with associated Coulomb-friction
behavior. Piles results will be primarily provided in terms of stresses which could later be
integrated into structural forces into the PLAXIS Output post-processing environment, either:


Through direct integration of stress through the Structural Forces in Volume Piles tool,
or
By introducing low stiffness beam elements along the neutral axis of the volume piles,
the purpose of which being to monitor the evolution of strains and change of curvature
along them and easily retrieve the structural forces based on beam theory.
Figure 2: Bending moment in simple pile raft model
The volume approach also requires the use of relatively small elements implicitly induced by
the relatively large slenderness of the pile element itself and, as a result, large number of
elements. This approach may find some limitations. A large number of piles would have to be
considered and the increasing number of elements (as the number of piles to be modeled
increased) might become simply impractical at some point.
Piles as embedded beams, or how to efficiently deal with many piles
The embedded beam is a special feature in PLAXIS 3D. This feature was developed to
simulate the behavior of piles in a simplified way. The embedded beam is particularly useful
in cases of large numbers of piles to be accounted for in a PLAXIS 3D model. In this
approach, the pile is represented by beam elements, while soil–pile interaction along the pile
shaft and at the pile tip is described by special interface elements that are constructed based
on node-to-node, non-linear coupling springs.
The generation of linear beam elements gives the opportunity to simulate piles as structural
elements with specified material properties. This saves a large number of elements needed in
the process, compared to volume piles being filled with tetrahedra elements. Another clear
advantage of using PLAXIS embedded beam elements is that the generation of the coupling
springs (for soil–pile interaction) does not require mesh node connectivity between the lines
supporting the pile/beam elements and the surrounding soil volume. Both pile lines and soil
volume could be meshed independently. The PLAXIS 3D calculation kernel automatically
takes care of finding intersection loci between beam pile element and soil element faces,
introducing at these points so-called “virtual” nodes where relative displacement between soil
mesh nodes and pile nodes can be computed. The simplification of both the geometry
description and the meshing process enables the consideration of hundreds of piles without
any difficulty.
Figure 3: The use of 3D embedded beam for modeling many piles
Embedded beam user input is divided into:

Beam properties for the pile: Material stiffness and weight along with cross section
shape and dimensions

Coupling spring properties: Interface normal stresses will always remain elastic
(they are not limited by any failure law), while the value of shear stress is limited by
the ultimate traction value Tmax which is provided by the user along the pile shaft. Pile
foot resistance is defined in a similar way, with a linear elastic-perfectly plastic spring
in pile axial direction where the base force is limited with value Fmax also provided as a
user input.
Figure 4: Property definition of 3D embedded beam for pile modeling
Results provided by embedded beams contain:

Displacements

Structural forces in the beam: Bending moments and axial forces

Interface results in terms of shaft friction (absolute and relative) and foot force
Embedded beam elements have demonstrated particularly good results for serviceability states
of pile groups under axial loading. It is important to note that the calculation time and the
number of elements required to analyze a certain pile–soil interaction problem are sufficiently
reduced by using embedded piles compared to using volume piles.
Figure 5: Available results for embedded beams in PLAXIS 3D
And what about 2D?
In the framework of a PLAXIS 2D analysis, it is possible to analyze axially loaded piles by
assuming axisymmetric conditions. Such models are very cost-effective, computationally
speaking, but can only be used in the case of axial loading, as any consideration of lateral
loading would not fulfill the axisymmetric conditions and would therefore require a proper 3D
model.
Figure 6: Axisymmetric model of an axially loaded pile in PLAXIS 2D
The embedded beam feature presented earlier is also available for 2D plane strain situations
but can only be used for the analysis of pile rows (rows extending in the out-of-modelingplane direction). The 2D nature of the plane strain analysis does not allow for the
consideration of a singular buried entity (that could only be considered in a 3D model). Thus,
it implicitly requires that any 2D embedded beam would represent a continuously spaced set
of piles in the out-of-plane direction with a pile-to-pile spacing value not too large compared
to the pile diameter, such that an average soil displacement as provided by the 2D soil mesh
between piles would remain an acceptable assumption.
When the assumption of continuously spaced piles is satisfied, the PLAXIS 2D model shows
very good agreement with equivalent 3D models, but at a fraction of the computational cost.
PLAXIS 2D with embedded beam row
PLAXIS 3D with volume pile
Figure 8: Pile model in PLAXIS 2D versus pile model in PLAXIS 3D
(a) Lateral displacement
b) Bending moment
Figure 9: Pile model comparison - PLAXIS 2D versus PLAXIS 3D
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