Laterally-Loaded Pile Foundation
Example Provided by: Christopher McGann, University of Washington
This article describes the OpenSees implementation of a simple laterally-loaded pile example. The problem is modeled as a beam on a nonlinear Winkler foundation (BNWF), utilizing displacement-based beam elements for the pile and nonlinear spring elements which represent the vertical and lateral response of the surrounding soil.
Provided with this article are the files needed to execute this analysis in OpenSees;
- the main input file, staticBNWFpile.tcl
- three procedures to define the soil constitutive behavior, get_pyParam.tcl, get_tzParam.tcl, and get_qzParam.tcl
- a file to define the pile section behavior, elasticSection.tcl
To run this example, the user must download each of the above files and place them in a single directory. Once this has been done, the user can then type "source staticBNWFpile.tcl" into the interpreter of the OpenSees.exe application to run the analysis. Representative results are presented in this article to verify the correct implementation of this example. Additionally, the pile response obtained from this analysis is compared to a similar analysis conducted using the commercial program LPile (http://www.ensoftinc.com) to provide verification the results of the OpenSees analysis.
Model Description
The BNWF model simulates the laterally-loaded pile problem using displacement-based beam elements to represent the pile and a series of nonlinear springs to represent the soil. The soil springs are generated using zero-length elements assigned separate uniaxial material objects in the lateral and vertical directions. An idealized schematic of the laterally-loaded pile model is provided in Fig. 1.
Geometry and Mesh
The geometry is rather simple in this example. There is only a single layer of cohesionless soil, and the groundwater table is assumed to be well below the tip of the pile. The pile geometry controls the meshing of the problem. The user can specify the length of the pile head (above the ground surface), L1, and the embedded pile length (below the ground surface), L2. The default values in staticBNWFpile.tcl are L1 = 1 m, and L2 = 20 m. The meshing is defined by the number of elements specified in the pile. The default value in this example is 84 elements (85 nodes). For the default pile geometry, this results in 80 elements over the embedded length and 4 elements above the ground surface.
The pile axis is oriented in the z-coordinate direction, and all of the nodes are initially located on the z-axis (x- and y- coordinates are zero). The model is created with three separate sets of nodes:
- fixed spring nodes (numbers 1-85)
- slave spring nodes (numbers 101-185)
- pile nodes (numbers 201-285)
Soil Modeling
The spring nodes are created with three dimensions and three translational degrees-of-freedom (no rotations). The input file is set up to automatically generate the necessary spring nodes and elements based upon the input geometry (pile head length, $L1, embedded length, $L2, and number of pile elements, $nElePile).