Documentation for Model of Centrifuge Test of Liquefiable Site Treated with Drains
This OpenSees model is a full 2D, plane strain model of the SSK01 and RNK01 centrifuge tests performed at UC
Davis
as
part
of
the
project
NEES-GC:
Seismic
Risk
Mitigation
for
Port
Systems.
(Link:
http://nees.org/warehouse/project/86)
The finite element model includes two opposing areas of sloping ground underlain by liquefiable sand and
separated by a channel. One side of the model is treated with prefabricated vertical drains. The finite element
model includes the centrifuge model container.
The model consists of a .tcl file (for use in OpenSees), a series of .txt files (as input seismic ground motions), and a
note on the scaling of hydraulic conductivity k. The following is a description of these files.
1) Full2D_main.tcl: defines the centrifuge container and soil properties (nodes, elements, mesh), and adds
the gravity and dynamic load to the model.
The 2D centrifuge model consists of an untreated slope and a drain-treated slope, each comprised of
liquefiable sand overlain by a clay cap (Figure 1). It is established in prototype dimensions. The
drain-treated slope contains perfect drains spaced approximately 1.5 m apart. The soil was modeled using
four-node quadUP elements. These are bilinear isoparametric u-p elements in which the solid-fluid
response is fully coupled based on Biot's theory of porous medium (Yang et al., 2008). Each node has two
degrees of freedom for solid displacement and one degree of freedom for fluid pressure. The elements
were of varying size depending on their location in the model. A scaled hydraulic conductivity k is
necessary (see Scaling_k.pdf) for the treated slope in order to account for the fact that the drains act as
wall drains in a plane strain model, as well as for the untreated slope for continuity.
Figure 1: Drawing of the 2D centrifuge model.
2) SSK01/RNK01_XX_acc/time.txt: used as input time series seismic ground motions. In the name of the file,
SSK01 or RNK01 is the name of the centrifuge test, XX is the number of the shaking event, acc or time is a
data column of the seismic motion. A SSK01/RNK01_XX__acc.txt and a SSK01/RNK01_XX__time.txt file
with the same type of centrifuge test and shaking event number compose a pair of input data and should
be used in a single model computation.
3) Scaling_k.pdf: explains the scaling of the hydraulic conductivity k.
To use this model, you can run the Full2D_main.tcl file in OpenSees (either use OpenSees Laboratory, the
Workspace on the NEEShub servers or HPC venues, or OpenSees on your PC). Make sure the Full2D_main.tcl and
SSK01/RNK01_XX_acc/time.txt files are placed in the same folder so that the Full2D_main.tcl file runs properly.
Before you run it, you should specify the ground motion (Line 17 and Line 18) and scaled k (Line 133), and modify
other user defined model parameters according to your need. In addition to using the provided input ground
motions, you can use your own motions, as long as they are arranged in the same format as the provided input
files.
In the computing process, the model will ask you 3 times whether you wish to continue– upon elastic gravity
loading, upon plastic gravity loading, and upon drain loading. Note that drain loading simply sets the pore water
pressures of the nodes along the drains at hydrostatic levels, and dynamic loading starts after this phase. These
questions allow you to stop the analysis if a problem is encountered in the previous phase.
The output files are labeled XXX.out. They are recorded at different times of the computation. Some are at gravity
loading; the others are at dynamic loading. The descriptions are as follows:
For gravity loading -1) gdisplacement/gacceleration/gporePressure.out: records the displacement (horizontal and vertical),
acceleration (horizontal and vertical), and pore pressure for all soil nodes (from node 1 to node 2694).
2) gstress1/2/3/4.out: records the horizontal and vertical normal stresses as well as shear stress (11, 22,
12) for all elements (from element 1 to element 2570).
3) gstrain1/2/3/4.out: records the normal strains in x and y direction as well as shear strain (11, 22, 12)
for all elements (from element 1 to element 2570).
For 1) – 3), the first 40 values represent elastic gravity loading, and the remaining values represent plastic gravity
loading at 5 second increments.
For dynamic loading –
4) displacement/acceleration(optional)/porePressure.out: records the time series of displacement
(horizontal and vertical), acceleration (horizontal and vertical), and pore pressure for all soil nodes (from
node 1 to node 2694). To avoid unnecessarily large output file, the acceleration recorder is now
commented out so you will not obtain an acceleration.out currently. To obtain acceleration.out, please
get rid of the “#” in Line 6712.
5) stress1/2/3/4.out: records the time series of normal stresses in x and y direction as well as shear stress
(11, 22, 12) for all elements (from element 1 to element 2570).
6) strain1/2/3/4.out: records the time series of normal strains in x and y direction as well as shear strain
(11, 22, 12) for all elements (from element 1 to element 2570).
7) PPTTreated/PPTUntreated.out: records the time series of pore water pressure of the drain-treated area
(at mid-point between selected adjacent drains) and its corresponding location in the untreated area.
8) dispdepthTreated/dispdepthUntreated.out: records the time series of horizontal displacement of the
drain-treated area (at mid-point between selected adjacent drains) and its corresponding location in the
untreated area.
9) dispdepthContainer/dispdepthContainerSoil.out: records the time series of horizontal displacement of
the contact nodes between the container and soil.
10) accelerationmid.out: records the time series of acceleration at mid-depth and mid-slope node of the
untreated area (node 1715).
11) Treated/Untreated_xdisp/ydisp.out: records the time series of horizontal and vertical displacement of
the nodes at the base of the model in both the treated and untreated areas.
For 4) – 11), the time step is 0.1 s.
Additional documents
For more information on centrifuge tests SSK01 and RNK01:

A. Marinucci. Effectiveness of Prefabricated Vertical Drains on Pore Water Pressure Generation and
Dissipation in Liquefiable Sand. PhD thesis, University of Texas at Austin, 2010.

R. Kamai, S. Kano, C. Conlee, A. Marinucci, E. Rathje, R. Boulanger, and G. Rix. Evaluation of the
effectiveness of prefabricated vertical drains for liquefaction remediation: Centrifuge data report for
SSK01. Data report, Center for Geotechnical Modeling, University of California, Davis, 2007.

R. Kamai, R. Howell, C. Conlee, R. Boulanger, A. Marinucci, E. Rathje, and G. Rix. Evaluation of the e
ectiveness of prefabricated vertical drains for liquefaction remediation: Centrifuge data report for RNK01.
Data report, Center for Geotechnical Modeling, University of California, Davis, 2008.

R. Kamai, R. Howell, C. Conlee, R. Boulanger, E. Rathje, A. Marinucci, and G. Rix. Centrifuge test RNK01 on
prefabricated vertical drains for liquefaction remediation, 2013a. Network for Earthquake Engineering
Simulation (database), Dataset, DOI:10.4231/D3VX0628F.

R. Kamai, S. Kano, C. Conlee, A. Marinucci, R. Boulanger, E. Rathje, and G. Rix. Centrifuge test SSK01 on
prefabricated vertical drains for liquefaction remediation, 2013b. Network for Earthquake Engineering
Simulation (database), Dataset, DOI:10.4231/D32J6839J.
For more information on the scaling of hydraulic conductivity k, please refer to Hird et al. scaling law:

C. C. Hird, I. C. Pyrah, and D. Russell. Finite element modelling of vertical drains beneath embankments on
soft ground. Geotechnique, 42(3):499-511, 1992.