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h1. 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|kb: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|kb:Link], and their associated properties, which will represent lateral support from the soil.

* Draw discrete links at pile [joints|kb:Joint]. 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|kb:Constraint] the grounded end of each link, which is away from the pile, as shown in Figures 1 and 2:

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{center-text}Figure 1 - Non-gapping soil behavior{center-text}

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{center-text}Figure 2 - Gapping soil behavior{center-text}


h1. Link definition

Define [nonlinear|kb:Nonlinear] link properties, available through Define > Section Properties > Link/Support Properties, as follows:

* Add a new [link|kb: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:
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** Define the P-y curve as a force-deformation (F-D) relationship wherein which F is total force acting along the tributary length of a pile joint.
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** Use the minimum number of points to characterize the P-y curve such that computation time may remain efficient.
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** 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:
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{center-text}Figure 3 - Non-gapping link definition{center-text}
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** 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:
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{center-text}Figure 4 - Gapping link definition{center-text}


h1. Link assignment

These [link|kb:Link] definitions should be assigned to link objects through Assign > Link/Support > Link/Support Properties.


h1. Hysteretic behavior

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

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{center-text}Figure 5 - Kinematic model simulates non-gapping behavior{center-text}

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{center-text}Figure 6 - Takeda model simulates gapping behavior{center-text}


h1. Distributed springs

Rather than drawing links as discrete elements, [line springs|tp:Line and area springs] may expedite the modeling process when assigned as follows:

* [Mesh|kb:Meshing] 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.


h1. 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|kb:Displacement time-history record], define a single [load pattern|kb: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|kb:Load case] as needed to combine load patterns with time-history functions. Additional information is available in the [Manual multi-support excitation|kb:Manual multi-support excitation] article.


h1. See Also

* [Line and area springs|tp:Line and area springs] test problem

* [Displacement time-history record|kb:Displacement time-history record] article

* [Manual multi-support excitation|kb:Manual multi-support excitation] article



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*Related Incident:*
* {incident:no=31866|comment=Inputting P-y curves, includes typical table with P-y curve data}
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