Introduction

In a lot of cases, there is a need to model piles in a 2D (plane strain) model. A typical situation may be the analysis of a superstructure that is (partly) founded on piles, such as a pile-raft foundation or a quay wall. In these cases, we want to approximate pile behaviour to be able to analyze deformations and forces of the superstructure and also obtain a first indication of axial and/or lateral loads on the piles.

It should, however, be realized that piles are true 3D elements and as such, it is not possible to model all relevant aspects of pile behaviour in a 2D model. Moreover, it should be realized that typical engineering aspects of pile behaviour (such as load-displacement behaviour) should, in general, be explicitly checked by the user before running the main analysis. As such the pile behaviour should be considered a USER INPUT instead of a MODEL OUTPUT or RESULT. Also, see this related article for a more detailed discussion on the reasons for the aforementioned behaviour (Attention points related to pile modelling in a 2D plane strain model). Nevertheless, it is quite feasible to model pile behaviour in a 2D model.

When modelling piles in a 2D model you can make use of the following modelling options (or combinations of options):

1. Volume elements (+ interfaces)
2. Plates (+ interfaces)
3. Node to node anchors (+ plates)
4. Embedded beam row

Before considering which modelling option is most suited for your situation you should first consider the center to center distance of the piles in relation to the dimensions/diameter of the piles to determine if the overall behavior is more wall, pile row or single pile -like.

Wall, pile row or single pile behaviour

Depending on the center to center (c.t.c.) distance of the piles in our project the global behaviour may be like a wall, a pile row or a single pile:

Let’s assume a pile with diameter D and a c.t.c. distance between the piles of L. Now if L/D = 1 the piles are directly next to each other and it is clear the behaviour will be like a wall. When moving the piles a bit apart (L/D is slightly larger than 1) probably the global behaviour will still be as a wall due to arching in the soil. However, when moving the piles further apart there is a point where global behaviour is no longer that of a wall but that of a pile row (i.e. the soil starts “flowing” in between the piles). Indications of the L/D ratios for which this happens can be found in geotechnical literature, but may typically be in the range of 1.5 to 5 (depending on soil type). When L/D becomes even larger than at a certain point we will have single pile behaviour (i.e. the piles no longer influence each other). We can visualize this also in the following figure:

Figure 1. Dependency of behaviour on L/D ratio

Possibilities and limitations of different pile modelling options

In the table below the suitability of the different pile modelling options are indicated for modelling the recognized types of behaviour.

Approach	Wall behaviour	Pile row behaviour	Single pile behaviour
Volume elements	A	C	-
Plate	A	C	-
Node to node anchor	-	C	-
Embedded beam row	-	B	C

Table 1. Suitability of different pile modelling options for the recognized types of behaviour

A   good approximation
B   reasonable approximation
C   first order (crude) approximation
-    not feasible/recommended

Now with regard to using volume elements or plates for modelling pile row behaviour some specific drawbacks can be mentioned:

• since we are basically modelling a wall the skin area may be different from the actual pile row. To obtain a correct transfer of forces to the skin you may need to adjust the Rinter, this, in turn, may influence the generation of an unrealistic shear plane (see Attention points related to pile modelling in a 2D plane strain model);
• soil cannot flow in between the piles since we are basically modelling a wall, this may give unrealistic behaviour especially in lateral loading;
• the bearing capacity of the shaft and tip cannot be directly controlled;
• in general, it is difficult/impossible to obtain a realistic load-displacement behaviour both in axial and lateral direction so the user has to decide which one is most relevant. By trial and error fitting of the smeared (out of plane) structural stiffness properties and the interface strength/stiffness the model should be set up in such a way that best results are obtained. This procedure has to be repeated for each new model;
• in general, a realistic distribution of forces between shaft and pile tip may be hard to obtain when the focus is on fitting the load-displacement behaviour.

The mentioned drawbacks are overcome to a large extent by using the embedded beam row element for modelling pile row behaviour. This element allows for direct input of strength of the shaft friction and the tip resistance. Due to the special interface used the embedded beamrow also allows for a more realistic load-displacement behaviour in axial and lateral loading compared to the volume elements and plate elements. A default setting is used for the stiffness of this interface. This default setting is derived for a specific set of conditions, for other conditions, the so-called Interface Stiffness Factors (ISF) need to be manually determined. Also see this article for further information on the embedded beam row element (Case study: embedded pile row).

Please also read this related article on some specific attention points and recommendations on pile modelling in a 2D plane strain model.