Introduction

Pile lateral support may be modeled using P-y curves. P-y curves, typically provided by the geotechnical engineer, describe the lateral soil resistance along the depth of a pile or drilled pier. For each layer of soil along the depth, the P-y curve represents a nonlinear relationship in which lateral pile displacement y mobilizes lateral soil reaction P per unit length.

The modeling of lateral soil support proceeds as follows:

Define links, and their associated properties, which will represent lateral support from the soil.

Draw discrete links at pile joints. For non-gapping soil behavior, draw one link per joint (Figure 1), and for gapping soil behavior, draw two links per joint, one on each side (Figure 2).

Fully restrain the grounded end of each link, which is away from the pile, as shown in Figures 1 and 2:

Link definition

Define nonlinear link properties, available through Define > Section Properties > Link/Support Properties, as follows:

Add a new link property of Multi-Linear Plastic type, then specify the nonlinear link stiffness for the axial (U1) DOF such that it matches the stiffness of the P-y curve, as described through the following process:
- Define the P-y curve as a force-deformation (F-D) relationship in which F is total force acting along the tributary length of a pile joint.
- Use the minimum number of points to characterize the P-y curve such that computation time may remain efficient.
- For soil with non-gapping behavior, link definition should extend stiffness through both sides of the F-D relationship, and the hysteretic model should be selected as Kinematic, as shown in Figure 3:
- For soil with gapping behavior, only compression should be specified. Tensile stiffness should be set to zero, and the hysteretic model should be selected as Takeda, as shown in Figure 4:

Link assignment

These link definitions should be assigned to link objects through Assign > Link/Support > Link/Support Properties.

Hysteretic behavior

To demonstrate hysteretic behavior, an increasing cyclic-displacement load is applied to a pile joint during nonlinear displacement-based quasi-static time-history analysis. Hysteretic response for the Kinematic and Takeda models are shown in Figures 5 and 6:

Distributed springs

Rather than drawing links as discrete elements, line springs may expedite the modeling process when assigned as follows:

Mesh the piles within each soil layer.

Define link properties using the tributary length assumed for the F-D relationship.

For each soil layer, select the pile frame elements and assign the corresponding P-y curve to its link using Assign > Frames > Line Springs.

Ground-displacement loading

The process for applying ground-displacement load along pile length is as follows:

Model discrete links within each soil layer along the depth of the pile.

For each layer with a common displacement history, define a single load pattern per loading direction, and a corresponding number of time functions.

For each load pattern, select the joint at the grounded end of each link, then assign a unit ground-displacement load along a single direction.

Create time-history load cases as needed to combine load patterns with time-history functions. Additional information is available in the Manual multi-support excitation article.

Pile lateral support based on P-y curves