Site Response Analysis of a Layered Soil Column (Total Stress Analysis)

Example posted by: Christopher McGann, University of Washington

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This article describes the OpenSees implementation of a site response analysis for a layered soil profile using total stress analysis. A single soil column is modeled in two-dimensions and is subject to an earthquake ground motion in a manner which accounts for the finite rigidity of the underlying medium.

Provided with this article is the main input file needed to execute this analysis in OpenSees, freeFieldDamp.tcl, along with several additional necessary and/or helpful files:

• ELCENTRO.EQ, the acceleration time history for the considered ground motion
• forceHistory.out, the path timeSeries information needed to run the analysis
• getForceHistory.m, a Matlab script which computes the timeSeries information from the acceleration time history
• getAccel.m, accelPlots.m, and depthPlots.m, Matlab scripts which produce the plots included in this article from the recorded results

Download them all in a compressed file: siteResponseSand.zip

To run this example, the user must download the files freeFieldDamp.tcl and forceHistory.out and place them in a single directory. Once this has been done, the user can then type "source freeFieldDamp.tcl" into the interpreter of the OpenSees.exe application to run the analysis. The Matlab scripts and the acceleration time history files are not essential to the analysis, however, they are provided to demonstrate how an alternative acceleration time history can be converted into the analysis and how certain plots can be obtained from the recorded output.

Model Description

File:SiteResponse.gif

Fig 1. Schematic representation of the model.

The site response analysis is performed for a soil profile with three layers of cohesionless soil. It is assumed that there is no groundwater, therefore, total stress analysis is used in this example. The soil is modeled in two-dimensions with two degrees-of-freedom using the plane strain formulation of the quad element. The nDMaterial model, PressureDependMultiYield, is used as a constitutive model for the cohesionless soil, and each layer is assigned separate material properties. A schematic of the model is shown in Fig. 1.

To account for the finite rigidity of the underlying medium (assumed to be bedrock in this example), a Lysmer-Kuhlemeyer (1969) dashpot is incorporated at the base of the soil column using a zeroLength element and the Viscous uniaxial material. The Lysmer-Kuhlemeyer (1969) dashpot is assigned a dashpot coefficient equal to the product of the mass density and shear wave velocity of the underlying bedrock layer. The soil column is excited at the base by a horizontal force time history which is proportional to the known velocity time history of the ground motion. Further information on this modeling approach can be found in Joyner and Chen (1975) and Lysmer (1978) among others.