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Example prepared by: Christopher McGann and Pedro Arduino, University of Washington
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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-bad beam elements for the pile and nonlinear spring elements which reprent the vertical and lateral respon of the surrounding soil. This example considers a static analysis only.龙应台语录
Provided with this article are the files needed to execute this analysis in OpenSees;
the main input file, l
three procedures to define the soil constitutive behavior, l, l, and l
a file to define the pile ction behavior, l
Download them all in a compresd file: staticBNWFanalysis.zip
To run this example, the ur must download each of the above files and place them in a single directory. Once this has been done, the ur can then type "l" into the interpreter of application to run the analysis. Reprentative results are prented in this article to verify the correct implementation of this example. Additionally, the pile respon obtained from this analysis is compared to a similar analysis conducted using the commercial program LPile () to provide verification the results of the OpenSees analysis.
The BNWF model simulates the laterally-loaded pile problem using displacement-bad beam elements to reprent the pile and a ries of nonlinear springs to reprent the soil. The soil springs are generated using zero-length elements assigned parate uniaxial material objects in the lateral and vertical directions. An idealized schematic of the laterally-loaded pile model is provided in Fig. 1.
白玉方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). Node numbering for each t of nodes begins at the bottom of the pile. The model is created with three parate ts of nodes:
fixed spring nodes (numbers 1-85 in example)
slave spring nodes (numbers 101-185 in example)
pile nodes (numbers 201-285 in example)
Geometry and Mesh
景的四字词语The geometry is rather simple in this example. There is only a single layer of cohesionless soil,
and the groundwater table is assumed to
春秋左氏传be well below the tip of the pile. The pile
geometry controls the meshing of the
problem. The ur 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 l
are L1 = 1 m, and L2 = 20 m. The pile is
also assigned a diameter of 1 m. This
value is ud in the soil constitutive
modeling.
The mesh 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
插画中国over the embedded length and 4
elements above the ground surface.
Note: The input file is only t up to
handle up to 100 nodes. Modifications
would need to be made to the node
numbering scheme to accommodate a larger number of nodes.
Spring Nodes
The spring nodes are created with three dimensions and three translational degrees-of-freedom. The input file is t up to automatically generate the necessary spring nodes and elements bad upon the input geometry (pile head length, $L1, embedded length, $L2, and number of pile elements, $nElePile). Spring nodes are only created over the embedded length of pile.
Since zero-length elements are ud for the springs, the two ts of nodes share the same t of locations. One t of spring nodes, the fixed-nodes, are initially fixed in all three degrees-
of-freedom. The other t of nodes, the slave nodes, are initially fixed in only two degrees-
of-freedom, and are later given equal degrees-of-freedom with the pile nodes.
Spring Constitutive Behavior
The constitutive behavior of the springs is defined such that the springs oriented in the lateral direction reprent p-y springs, and the vertically-oriented springs reprent t-z and Q-z springs for the pile shaft and tip, respectively. Three procedures are ud to properly define the p-y/t-z/Q-z behavior with depth, l, l, and l
Several input soil properties are necessary to define the springs:
soil unit weight, $gamma
韭菜摊饼
soil internal friction angle, $phi
soil shear modulus, $Gsoil
The default values are t at $gamma = 17 kN/m^3, $phi = 36 degrees, and $Gsoil = 150000 kPa. The procedure l, which defines the p-y springs, has veral options which must be lected.
The first switch, $puSwitch, specifies the variation in ultimate lateral resistance with depth.
The default, $puSwitch = 1, us the recommendations of the American Petroleum Institute (API) (1993). The alternative method is that of Brinch Hann (1961).
The cond switch, $kSwitch, specifies the variation in initial stiffness with depth. The
default, $kSwitch = 1, specifies a linear variation of initial stiffness with depth (API 1993).
The alternative us a modified version of the API stiffness which varies parabolically with depth after Boulanger et al. (2003).
The prence of groundwater can be accounted for in the initial stiffness using the third
switch, $gwtSwitch. Default, $gwtSwitch = 1, is for no groundwater.
右转弯手势
The other procedures, l and l, have no input options in this example. The t-z springs have behavior defined using the work of Mosher (1984) and Kulhawy (1991). The Q-z behavior is bad on the work of Meyerhof (1976), Vijayvergiya (1977), and Kulhawy and Mayne (1990).
The p-y spring constitutive behavior is obtained using the PySimple1 uniaxial material object. The t-z and Q-z springs are defined using the TzSimple1 and QzSimple1 uniaxial materials, respectively. The main input file is t up to automatically generate the required spring material objects bad upon the input geometry and soil properties.
Spring Elements
Zero-length elements are ud for the soil springs using the element zeroLength. The elements co
nnect the fixed and slave spring nodes. The the PySimple1 material objects are incorporated in the x-direction (direction of loading), while the TzSimple1, and at the pile tip, the QzSimple1, material objects are incorporated in the z-direction (vertical direction).
Pile Nodes
The pile nodes are created with three dimensions and six degrees-of-freedom (3 translational, 3 rotational). The input file is t up to automatically generate the necessary pile nodes and elements bad upon the input geometry. A linear coordinate-transformation object is specified for the orientation of the pile in this example. With the exemption of the uppermost pile head node, the pile nodes are fixed against translation in the y-direction and rotations about the x- and z-axes. The pile head node, where the load is applied, is parated to allow the ur to specify a free-head (no rotational fixity) or fixed-head (full rotational fixity) condition at the loading point. The pile nodes over the embedded length of the pile are u linked with the slave spring nodes using the equalDOF command. The pile nodes are the master nodes in this example. The two ts of nodes share equal degrees-of-freedom in the x- and z- translational directions only.
Pile Constitutive Behavior and Elements
In this example, the pile is given elastic behavior for simplicity. Instead of using the elasticBeamColumn element, this is done using an elastic ction object in conjunction with the displacement-bad beam element, dispBeamColumn. This was done to facilitate future incorporation of elastoplastic pile ction behavior using fiber ction models by the ur.
The properties of the elastic ction for this example are defined in the file, l. The pile is defined with appropriately computed values for the cross-ctional area and the moments of inertia for its 1 m diameter, and is assigned a modulus of elasticity, E = 25000000, and shear modulus, G = 9615385.
Recorders
Several recorders are defined for this model.
The displacements at the pile nodes in all three translational dof are recorded for u in
extracting the displaced shape of the pile.
The reaction forces in the p-y springs are recorded for u in visualizing the lateral soil
respon.
The element forces in the pile elements are recorded in order to obtain shear and moment diagrams for the pile.
有口皆碑The recorders are t up to only record values at 0.5 cond increments of pudo-time during the analysis to facilitate the u of smaller load steps. This is done with the variable $timeStep.
A display recorder is included in the input file to allow the ur to visualize the deformation of the pile in "real time" during the analysis. The parameters are t up for the orientation of the pile in this example.
Loading
This example considers a 3500 kN load applied in the positive x-direction at the head of the pile (uppermost pile node). This is accomplished in the model using a plain pattern with optional
time-ries parameters. The load increas linearly from 0 kN to 3500 kN over a 10 cond increment of pudo-time (between 10 and 20 conds) and is then held constant after the loading period. Setting up the loading object in this manner allows for more control over the analysis.
Analysis
The analysis is conducted using the load-controlled integrator with a loading step of 0.05. This value is lected bad on the 10 cond interval specified in the loading object. 200 steps with a loading step of 0.05 will put the last step exactly at 10 conds of pudo-time. 201 steps are ud in this example to make sure that the last recorded step is at the full loading magnitude. The variables $startT and $endT are ud to print the cpu time needed to complete the analysis in the standard output or the OpenSees interpreter. The remaining analysis commands are
well-documented in the OpenSees command manual.
A ur can verify their downloaded files by running the main input file, l, in OpenSees and comparing the recorded results to some reprentative results included here. The simplest verification is to u the spring reaction forces recorded in the file reaction.out. A plot of the recorded spring reaction forces vs. depth in the final recorded pudo-time step (20.05) should create something similar to that shown in Fig. 2. The respon is negative from the ground surface to about 7.5 m deep, then transitions to positive until about 13 m deep, has a cond smaller negative ction, and then is nearly zero near the tip of the pile.
Fig. 2 Lateral soil respon after application
