Documentation for 3D Unit Cell Model
This OpenSees model is a 3D unit cell infinite slope model of the area of influence around a single drain (or, in the
case of the untreated model, a free-field untreated area equal to the area of influence around a single drain). It
was developed to simulate lateral spreading in the in-plane horizontal direction (e.g. in the SSK01, RNK01, and
RLH01 centrifuge tests) and the out-of-plane direction (e.g. in the RLH01 centrifuge tests).
The geometry of this model is consistent with the geometry of the mid-slope sections of the centrifuge models. In
the centrifuge tests, the drains were placed in a triangular pattern at a center-to-center spacing of 1.5m
(prototype scale). Using equivalent areas, the center-to-center spacing of 1.5m equates to a square area of
influence with a 1.4m side length. Therefore, this model is 1.4m wide and extends 1.4m into the page, divided into
10 elements in the in-plane (x) and out-of-plane (y) horizontal directions. This model dimension corresponds to
the dimension of 1.578m * 1.578m in the 2D Unit Cell Model (Link: http://nees.org/resources/7293). The ground
water table is placed at the sand/clay interface. The model uses 8-node brickUP elements, which are hexahedral
linear 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). The eight corner nodes of each element have four degrees of freedom (three
for solid displacement and one for fluid pressure).
The model consists of four .tcl files for use in OpenSees (shakings parallel and orthogonal to the slope for the
treated condition and the untreated condition), and a suite of .txt files that contains the input seismic ground
motion. The following is a description of these files.
1) 3d_untreated_parallel.tcl: defines the elements and mesh to simulate the free-field untreated sloping
area, and adds the gravity and dynamic loads to the modeled area. The dynamic load is parallel to the
slope and a slope angle of 3° is applied, simulating the dynamic load in the SSK01 and RNK01 centrifuge
tests. The model consists of a 4.5m thick layer of liquefiable sand overlain by a 1m thick clay cap, divided
into 38 elements in the vertical direction (z) (Figure 1).
2) 3d_treated_parallel.tcl: defines the elements and mesh to simulate the area of influence around a single
drain, and adds the gravity and dynamic loads to the modeled area. The dynamic load is parallel to the
slope and a slope angle of 3° is applied, simulating the dynamic load in the SSK01 and RNK01 centrifuge
tests. The model is divided into 38 elements in the vertical direction (z) as in the untreated case (Figure 1).
A perfect drain is created by holding the pore water pressure at hydrostatic levels during shaking at the
nodes up the vertical centerline of the model.
3) 3d_untreated_orthogonal.tcl: defines the elements and mesh to simulate the free-field untreated sloping
area, and adds the gravity and dynamic loads to the modeled area. The dynamic load is orthogonal to the
slope and a slope angle of 10° is applied, simulating the dynamic load in the RLH01 centrifuge tests. The
model consists of a 5.5m thick layer of liquefiable sand overlain by a 1.5m thick clay cap, divided into 52
elements in the vertical direction (z) (Figure 1).
Figure 1: Drawing of the 3D unit cell model.
4) 3d_treated_orthogonal.tcl: defines the elements and mesh to simulate the area of influence around a
single drain, and adds the gravity and dynamic loads to the modeled area. The dynamic load is orthogonal
to the slope and a slope angle of 10° is applied, simulating the dynamic load in the RLH01 centrifuge tests.
The model is divided into 52 elements in the vertical direction (z) as in the untreated case (Figure 1). A
perfect drain is created by holding the pore water pressure at hydrostatic levels during shaking at the
nodes up the vertical centerline of the model.
5) SSK01/RNK01/RLH01_XX_acc/time.txt: used as input time series seismic ground motions. In the name of
the file, SSK01 or RNK01 or RLH01 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/RLH01_XX_acc.txt and a
SSK01/RNK01/RLH01_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.
To use this model, you can run the 3d_treated/untreated_parallel/orthogonal.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 .tcl and SSK01/RNK01/RLH01_XX_acc/time.txt files are placed in the same folder so that the .tcl file runs
properly. Before you run the model, you should specify the ground motion (Line 28 and Line 29), 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.
The model will ask you several times whether you wish to continue in the running process. These questions allow
you to stop the analysis if a problem is encountered in the previous phase. Note that in the drain treated case, the
drain loading simply sets the pore water pressures of the nodes along the drains at hydrostatic levels, and dynamic
loading starts after this phase.
The output files are labeled XXX.out or XXX.txt. They only provide output from the dynamic loading stage. The
descriptions are as follows:
Outputs from 3d_untreated_parallel.tcl –
1) accx.txt: records the time series of horizontal acceleration in x direction for all the nodes up the
centerline of the unit cell.
2) dispx/(dispy)/dispz.txt: records the time series of the displacement in x, (y,) and z direction for all the
nodes up the centerline of the unit cell.
3) dispx/dispz_cross.txt: records the time series of the displacement in x and z direction for the nodes at the
surface (from node 4599 to node 4719).
4) pwp.txt: records the time series of developed pore water pressure for all the nodes up the centerline of
the unit cell.
5) pwp_cross.txt: records the time series of developed pore water pressure for all the nodes at the bottom
(nodes 1 to 121).
6) pwp_interface.txt: records the time series of developed pore water pressure for the corner nodes in the
sand on the sand/clay interface (from node 3631 to 3751).
7) stress3.out: records the time series of stresses (11, 22, 33, 12, 13, 23, ) for the elements right
beside the centerline of the unit cell.
8) strain3.out: records the time series of strains (11, 22, 33, 12, 13, 23) for the elements right beside
the centerline of the unit cell.
9) stress3_cross.out: records the time series of stresses (11, 22, 33, 12, 13, 23, ) for a line of
elements at the bottom (elements 1 to 100).
These outputs are placed in the output3DUntreatedPa folder.
Outputs from 3d_treated_parallel.tcl – include the files (1) – (9) obtained in the untreated parallel case plus the
following additional five files:
a) dispx/dispz_cross2.txt: records the time series of the displacement in x and z direction for the nodes at
the height of 4.35m (from node 3510 to node 3630).
b) dispxLedge.out: records the time series of built-up pore water pressure for the nodes on the centerline of
the left face of the unit cell.
c) disp_all_x/y/z: records the time series of displacements in x, y, and z directions for all the nodes.
d) pwp_cross2.txt: records the time series of developed pore water pressure for all the nodes at the height
of 4.2m (nodes 3389 to 3509).
e) pwpLedge.txt: records the time series of developed pore water pressure for the nodes on the centerline
of the left face of the unit cell.
These outputs are placed in the output3DTreatedPa folder.
Outputs from 3d_untreated_orthogonal.tcl – the same as the files (1) – (9) obtained in the untreated parallel case.
These outputs are placed in the output3DUntreatedOr folder.
Outputs from 3d_treated_orthogonal.tcl – include the files (1) – (9) obtained in the untreated parallel case plus
the file (e) obtained in the treated parallel case. These outputs are placed in the output3DTreatedOr folder.
Additional documents
For more information on using single column models to simulate lateral spreading:

Z. Yang, A. Elgamal, and E. Parra. Computational model for cyclic mobility and associated shear
deformation. Journal of Geotechnical and Geoenvironmental Engineering, 129(12):1119-1127, 2003.

M. Seid-Karbasi and P. M. Byrne. Seismic liquefaction, lateral spreading and flow slides: a numerical
investigation into void redistribution. Canadian Geotechnical Journal, 44:873-890, 2007.

Mayoral, J. M., Flores, F. A., & Romo, M. P. (2009). A simplified numerical approach for lateral spreading
evaluation. Geofísica internacional, 48(4), 391-405.

Z. Cheng and B. Jeremic. Numerical modeling and simulation of soil lateral spreading against piles. In M.
Iskander, D. Laefer, and M. Hussein, editors, Geotechnical Special Publication No. 186: Contemporary
Topics in In Situ Testing, Analysis, and Reliability of Foundations (Proceedings of the International
Foundations Congress and Equipment Expo), pages 190-197, Orlando, Florida, 2009.

C. Phillips, Y. Hashash, S. Olson, and M. Muszynski. Signicance of small strain damping and dilation
parameters in numerical modeling of free-field lateral spreading centrifuge tests. Soil Dynamics and
Earthquake Engineering, 42:161-176, 2012.
For more information on the solid-fluid response of 8-node brickUP elements:

Z. Yang, J. L. Lu, and A. Elgamal. OpenSees soil models and solid-fluid fully coupled elements. User’s
Manual 2008 ver 1.0, Department of Structural Engineering, University of California, San Diego, October
2008.