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This article was originally created for SAP2000, but the concept applies also to CSiBridge.
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This page describes how to model pile lateral support based on P-y curves.

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h1. Introduction

P-y curves describe the lateral soil resistance along the depth of a pile or drilled shaft and are typically provided by geotechnical engineer. For each layer of the soil along the depth of a pile, the P-y curve describes lateral soil reaction _P_ per unit length along the pile mobilized by lateral pile displacement _y_. The relationship between _P_ and _y_ is nonlinear.

The modeling of lateral soil support involves the following steps:
* Define the properties of links that will represent the lateral support provided by the soil.
* Draw discrete links at the joints of the pile: one link per joint for non-gapping soil behavior; and two links per joint at each side of the piles for gapping soils:

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*            One link per joint for non-gapping soil behavior* 
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*           Two links per joint at each side of the piles for gapping soils*

h1. Link Definition

Nonlinear link properties can be defined (in SAP2000) via "Define > Section Properties > Link/Support Properties" as follows:

      * Add new link property of "MultiLinear Plastic" type and specify nonlinear link stiffness for U2 degree of freedom to match the stiffness described by the P-y curve. 
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** For material with non-gapping behavior, define the link with stiffness in both sides of the curve, and select Kinematic as the hysteretic model:

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           *Link Definition Non-Gapping Behavior*
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**        For material with gapping behavior, define the link with the tension side stiffness equal to zero, and select Takeda as the hysteretic model, 


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*                 Link Definition Gapping Behavior*

h1. Link Assignment

      
Assign the above-defined links to the links using the Assign>Link/Support>Link/Support Properties menu command.

h1. Hysteretic

 Example of the hysteretic behavior obtained from a Displacement\- Based Quasi-Static Nonlinear Time History Analysis.  In this example, an increasingly cyclic displacement load was applied to the a pile

 joint.:
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             *The Kinematics model gives non-gapping behavior*
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           *The Takeda model gives gapping behavior when one side of the curve is all zero*

h1. Miscellaneous

* For non-gapping material, you can assign the links to the frame elements representing the piles as [line springs|https://wiki.csiberkeley.com/display/tp/Line+and+area+springs], instead of drawing them as discrete elements
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** Mesh the piles within each soil layer.
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**   Select the pile frame elements within a given soil layer and use the "Assign > Frames > Line Links" menu command to assign the P-y link with the properties corresponding to that layer. Repeat this for all layers.
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Related Incidents:

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