Influence of Dense Granular Columns on the Performance of Level and Gently Sloping Liquefiable Sites

Influence of Dense Granular Columns on the Performance
of Level and Gently Sloping Liquefiable Sites
Mahir Badanagki, S.M.ASCE1
; Shideh Dashti, M.ASCE2
; and Peter Kirkwood3
Abstract: Dense granular columns are often used as a liquefaction mitigation measure to (1) enhance drainage; (2) provide shear reinforce-
ment; and (3) densify and increase lateral stresses in the surrounding soil during installation. However, the independent influence and con-
tribution of these mitigation mechanisms on the excess pore pressures, accelerations (or shear stresses), and lateral and vertical deformations
are not sufficiently understood to facilitate a reliable design. This paper presents the results of a series of dynamic centrifuge tests to fun-
damentally evaluate the influence of dense granular columns on the seismic performance of level and gently sloped sites, including a lique-
fiable layer of clean sand. Specific consideration was given to the relative importance of enhanced drainage and shear reinforcement. Granular
columns with greater area replacement ratios (Ar), for example Ar greater than about 20%, were shown to be highly effective in reducing the
seismic settlement and lateral deformations in gentle slopes, owing primarily to the expedited dissipation of excess pore water pressures. The
influence of granular columns on accelerations (and therefore, the shear stress demand) in the surrounding soil depended on the column’s Ar
and drainage capacity. Increasing Ar from 0 to 10% was shown to reduce the accelerations across a range of frequencies in the surrounding
soil due to the shear reinforcement effect alone. However, enhanced drainage simultaneously increased the rate of excess pore pressure
dissipation, helping the surrounding soil regain more quickly its shear strength and stiffness. At short drainage distances or higher Ar values
(for example, 20%), this could notably amplify the acceleration and shear stress demand on soil, particularly at greater frequencies that
influence PGA. The experimental insight presented in this paper aims to improve our understanding of the mechanics of liquefaction
and lateral spreading mitigation with granular columns, and it may be used to validate the numerical models used in their design.
DOI: 10.1061/(ASCE)GT.1943-5606.0001937. © 2018 American Society of Civil Engineers.
Author keywords: Soil liquefaction; Granular columns; Drains; Centrifuge modeling; Lateral spreading; Site performance.
Background and Introduction
Past earthquakes have provided many examples of damage to
important geotechnical structures such as slopes, retaining walls,
and embankments caused by soil liquefaction. For example, exten-
sive lateral slope deformations were reported by Seed (1987) and
Tokimatsu and Asaka (1998) during the earthquakes in Niigata,
Japan, in 1964; Loma Prieta, California, in 1989; and Kobe, Japan,
in 1995. Mitigation techniques are often warranted to prevent ex-
cessive lateral deformations in slopes founded on liquefiable depos-
its and the subsequent damage to infrastructure. A reliable and
performance-based design of liquefaction remediation techniques
for slopes requires a clear understanding of the influence of various
mitigation mechanisms that control performance.
Bartlett and Youd (1992) characterized liquefaction-induced lat-
eral spreading in mild (0.3–5%) slopes underlain by loose,
saturated granular soils. Despite the low angle of these slopes,
the lateral deformations produced during earthquake loading could
still exceed several meters, leading to extensive damage. Many
ground-improvement techniques such as densification, reinforce-
ment, and methods that enhance drainage can be used to reduce
the risk of liquefaction and its associated ground deformations.
In particular, the installation of dense granular columns made of
gravel or stone is an attractive mitigation method for slopes and
embankments (Seed and Booker 1977). Depending on its installa-
tion procedure, this method is believed to mitigate the soil lique-
faction hazard and its consequences through a combination of
densification, increased lateral earth pressures, shear reinforcement,
and enhanced drainage (Baez 1995; INA 2001; Rayamajhi et al.
2016a).
Previous case histories have generally demonstrated a success-
ful performance of different types of compacted granular columns
in loose, saturated cohesionless soils (e.g., Mitchell et al. 1995;
Mitchell 1986, 1988; Adalier 1996; Baez 1996; Boulanger et al.
1998; Koelling and Dickenson 1998; ISSMGE 2001). However,
although valuable insights can and must be drawn from case his-
tories, the influence and relative importance of each mechanism of
mitigation on the performance of the site and slope cannot be re-
liably evaluated from case histories alone in a systematic manner,
as is necessary for a reliable, performance-based mitigation design.
Seed and Booker (1977) introduced an analytical method for the
design of drains based on radial consolidation or excess pore pres-
sure (Δu) dissipation that is commonly used in practice. They rec-
ommended the use of gravel or stone columns with a hydraulic
conductivity at least two orders of magnitude greater than that of
the surrounding soil, to avoid significant Δu generation in the
drains. This study had a number of limitations, including (1) the
assumption of an infinite granular column permeability and ignor-
ing the well resistance or clogging potential; (2) the assumption of a
1
Graduate Research Assistant, Dept. of Civil, Environmental, and
Architectural Engineering, Univ. of Colorado Boulder, Boulder, CO 80309.
Email: mahir.badanagki@colorado.edu
2
Associate Professor, Dept. of Civil, Environmental and Architectural
Engineering, Univ. of Colorado Boulder, Boulder, CO 80309 (corresponding
author). Email: shideh.dashti@colorado.edu
3
Research Associate, Dept. of Civil, Environmental, and Architectural
Engineering, Univ. of Colorado Boulder, Boulder, CO 80309. Email: peter
.kirkwood@colorado.edu
Note. This manuscript was submitted on May 19, 2017; approved on
March 29, 2018; published online on July 6, 2018. Discussion period open
until December 6, 2018; separate discussions must be submitted for indi-
vidual papers. This paper is part of the Journal of Geotechnical and
Geoenvironmental Engineering, © ASCE, ISSN 1090-0241.
© ASCE 04018065-1 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2018, 144(9): 04018065
Downloadedfromascelibrary.orgbyColoradoUniversityatBoulderon07/24/18.CopyrightASCE.Forpersonaluseonly;allrightsreserved.

level ground condition (no slope); and (3) not considering shear
reinforcement in the gravel or stone columns. In practice, however,
engineers sometimes rely on the shear reinforcement provided by
granular columns and use design procedures (based on shear strain
compatibility) to reduce the cyclic stress ratios induced in the sur-
rounding soil (Rayamajhi et al. 2016a).
Rayamajhi et al. (2016a) numerically evaluated the contribution
of the shear reinforcement provided by granular columns in isola-
tion, with and without the generation and redistribution of excess
pore pressures. Their nonlinear, coupled, three-dimensional (3D)
finite-element analyses indicated that granular columns experience
shear strain deformations that are not compatible with the surround-
ing soil. As a result, the reduction in the cyclic stress ratios induced
in the treated soil was notably less than that predicted by the
conventional design approaches that assume strain compatibility.
They subsequently provided a modified design approach to esti-
mate the reduction in cyclic stress ratios provided by dense granular
columns.
Elgamal et al. (2009) and Asgari et al. (2013) performed a
numerical parametric study with a unit cell and showed that granu-
lar columns could help reduce lateral displacements in treated
soil due to a combination of drainage and shear reinforcement.
Rayamajhi et al. (2016b) numerically showed that granular col-
umns can be effective in reducing lateral spreading through shear
reinforcement, even if liquefaction or generation of large excess
pore pressures is not prevented. They also numerically identified
the surface pressure, length and diameter of the drains, area replace-
ment ratios, liquefiable soil depth, hydraulic conductivity, and
slope angle as some of the key parameters influencing the lateral
displacement. However, the results presented in these numerical
studies were not validated with rigorous physical model studies
or case history observations.
Although limited in quantity and scope, a number of physical
model studies (for example, 1g shake table and centrifuge tests)
have been conducted to evaluate the influence of different types
of drains on site response and lateral spreading. Due to the diffi-
culties of drain installation in flight, the centrifuge experiments fo-
cused primarily on the reinforcement and drainage mechanisms of
mitigation, as opposed to installation-induced densification or an
accurate representation of the increase in lateral earth pressures
in the surrounding soil, which may not be reliable in all cases, even
in the field. As an example, Adalier et al. (2003) performed cen-
trifuge experiments with stone columns in a uniform and level de-
posit of saturated, loose silt with an overlying model of a rigid
footing. This study showed that stone columns can be effective
in reducing the foundation settlement by reducing shear strains
and generation of excess pore pressures in the underlying soil. They
did not, however, evaluate the influence of granular columns and
their properties on the performance of sites with more realistic
layering and geometry and under different earthquake motions.
Centrifuge tests were more recently conducted by Howell et al.
(2012) to evaluate the performance of liquefiable slopes mitigated
with prefabricated vertical drains (PVDs). This method did not in-
troduce notable shear reinforcement and relied primarily on the
drainage mechanism of mitigation. The study showed that PVDs
could be effective in expediting the dissipation of excess pore pres-
sures and reducing the resulting lateral slope deformations, depend-
ing on the characteristics of the earthquake motion. The combined
or independent influence of shear reinforcement and enhanced
drainage in slopes has not been experimentally evaluated. It is
not clear, for example, whether the added shear reinforcement pro-
vided by stiffer drains (e.g., dense granular columns in comparison
with PVDs) would reduce the seismic demand or the deformations
in slopes.
Dashti et al. (2010) performed a series of centrifuge experiments
to identify the dominant mechanisms of settlement on layered
liquefiable soil deposits. The study classified the primary volumet-
ric settlement mechanisms active in the free-field as (1) sedimenta-
tion or solidification (εp-SED), which occurs after significant
strength loss, as settling particles from the uppermost part of the
liquefiable sand accumulate at the bottom to form a solidified zone.
This zone increases in thickness with time and concurrently con-
solidates under its own weight; (2) reconsolidation (εp-CON), which
occurs as the excess pore pressures dissipate and soil’s effective
stress regains its initial value; and (3) partial drainage and loss
of water during cyclic loading (εp-DR) that occur according to
the 3D transient hydraulic gradients. Volumetric deformations
caused by partial drainage can be notable, as they occur while
the hydraulic gradients are kept at their peak during shaking.
Drainage-enhancing granular columns, such as those investigated
in this study, locally reduce the duration, or the amplitude, of the
elevated excess pore pressures. This, along with the altered shear
stress and strain profiles, likely reduces the contribution of sedi-
mentation to the volumetric strains. However, the increased rate
of drainage likely increases the volumetric strains due to partial
drainage. The net effect of granular columns on the competing
mechanisms leading to volumetric strains is uncertain and requires
investigation.
This paper presents the results of three centrifuge experiments
that systematically evaluated the influence of dense granular col-
umns and their various mitigation mechanisms and properties on
the seismic performance of level and gently sloping sites underlain
by a layered liquefiable deposit consisting mostly of clean sand.
The data obtained from these experiments facilitated (1) the mecha-
nistic evaluation of the influence of granular columns and their dif-
ferent properties (for example, the area replacement ratio, shear
reinforcement, and enhanced drainage) on the site and slope per-
formance in terms of the acceleration, excess pore pressure, settle-
ment, and lateral spread; and (2) the provision of data for the
calibration and validation of advanced numerical models in the
future. Following validation, such models can be more reliably
used in the design or development of design guidelines for the
mitigation of lateral spreading hazards using dense granular
columns.
Experimental Procedure
Centrifuge Testing Plan
A series of three centrifuge experiments comprising five separate
models were designed and conducted at the University of Colorado
(CU) Boulder’s 400g-t (5.5-m-radius) centrifuge facility. In these
tests, the primary goal was to systematically evaluate the influence
and relative importance of various granular column parameters on
the performance of a level site and a gentle slope underlain by a
layered liquefiable deposit during one-dimensional horizontal
earthquake loading. Fig. 1 shows the detailed plan and elevation-
view drawings of the model tests and their instrumentation layouts.
The dimensions are presented at both prototype and model scales
following the accepted scaling relations (Tan and Scott 1985).
For all tests, as shown in Fig. 1, a dense layer (8 m thick in the
prototype scale) of Ottawa sand F65 was dry pluviated to attain a
relative density (Dr) of approximately 90% at the bottom of a
flexible-shear-beam (FSB) container constructed of aluminum and
rubber at CU. Subsequently, a loose layer of Ottawa sand (8 m
thick) with a Dr ≈ 40% was pluviated as the liquefiable material.
This layer was subsequently overlaid by a 0.5-m-thick layer of

Silica silt (Sil-Co-Sil 120) to restrict the rapid excess pore pressure
dissipation vertically and to represent a case with void redistribu-
tion, followed by a 1.5-m-thick layer of coarse Monterrey sand 0/30
with Dr ≈ 90%, to create a nonliquefiable, thin crust. For all the
treated models (Models 0, 1, 3, and 4), the granular columns with
diameter = 1.75 m (in prototype scale) were placed vertically at the
bottom of the container prior to sand pluviation to avoid localized
densification during their installation. This was done to isolate the
influence of drains from ground densification and to keep the den-
sity of the surrounding soil controlled and uniform within each
layer.
Test 1 (Model 0) examined the behavior of a single draining
granular column in level ground, before adding the complications
associated with multiple drains and a slope. Vertical arrays of ac-
celerometers (Accs), pore pressure transducers (PPTs), and linear
variable differential transformers (LVDTs) were placed at three dif-
ferent radial distances from the single drain to track the wave propa-
gation, pore water pressure generation and dissipation, and
volumetric deformations throughout the soil profiles, as shown
in Fig. 1.
In Tests 2 and 3, all soil models were constructed of two
symmetric slopes on the two sides of the container separated by
an open channel, as shown in Fig. 1. In Test 2, one side of the slope
(Model 1) was treated with a grid of 1.75-m-diameter dense granu-
lar columns encased in geotextile filters (to avoid clogging) sepa-
rated by 3.5 m (from center to center) with an Ar of 20%. The Ar is
ratio of the area of granular columns to the total treatment area
(Baez and Martin 1993). The other side of the slope (Model 2)
in Test 2 was left untreated to evaluate the effectiveness of the
granular columns as a mitigation technique. In Test 3, both sides
of the slope (Models 3 and 4) were treated with 1.75-m-diameter
dense granular columns separated by 5 m (from center to center)
with Ar ¼ 10%. In Model 3, the granular columns were encased in
geotextile filters, similarly to Model 1, whereas in Model 4 they
were encased in geotextile and a thin (0.2-mm-thick) latex mem-
brane to evaluate the influence of stiffness alone without drainage.
The groundwater table was at the soil surface in all tests (the highest
elevation in the cases with slope), and all model specimens were
spun to a centrifugal acceleration of 70 g prior to the application of
earthquake motions.
Properties of Sand, Silt, and Gravel
The response of Ottawa sand F65 at various relative densities was
evaluated under monotonic and cyclic, drained and undrained tri-
axial tests prior to the centrifuge experiments presented here (de-
tailed by Ramirez et al. 2017). The engineering properties of this
sand were measured by the authors as follows: maximum void ratio
ðemaxÞ ¼ 0.81; minimum void ratio ðeminÞ ¼ 0.53; coefficient of
uniformity ðCuÞ ¼ 1.56; specific gravity ðGsÞ ¼ 2.65; and hy-
draulic conductivity ðkÞ ¼ 1.19 × 10−2
to 1.41 × 10−2
cm=s at
1g with water (which were the same at 70g with viscous fluid
70 times more viscous than water) for the relative densities (Dr)
of 90 and 40%, respectively. The critical friction angle (ϕcs) of this
sand was estimated at approximately 31° (Ramirez et al. 2017).
Coarse Monterey 0/30 sand was selected for the thin, high-
permeability, dense surface layer. The properties of Monterey sand,
obtained from previous studies, were emax ¼ 0.84; emin ¼ 0.54;
Cu ¼ 1.3; k ¼ 5.29 × 10−2 cm=s; and Gs ¼ 2.64 (Dashti et al.
2010). Silica silt (Sil-Co-Sil 120) was selected as the thin, low-
permeability cap above the liquefiable layer. The properties of silica
silt, also obtained from previous studies (Walker and Stewart 1989),
were Cu ¼ 7.3; k ¼ 3 × 10−5
cm=s; and Gs ¼ 2.65; and the critical
friction angle (ϕcs) was approximately 25°. In this study, the material
428mm 428mm
[30m] [30m]
Treated side
(Model 1)
Untreated side
(Model 2)
3°
60°
Silica silt
Monterey sand
(Dr=90%)
Ottawa sand
Dr=90%
Ottawa sand
Dr=40%
Gravel column
(Diam.=25mm)
[1.75m]
150 mm Model
10.5 m [Prototype]
0 75
5.30
Acc. (A)
PPT (P)
LVDT (D)
Latex
Shaking table
Without latex
(Model 3)
With latex
(Model 4)
Model 0
Test #1
Test #2
Test #3
177mm144mm158mm
[12.4m][10m][11m]
956mm
[26.3m]
376mm
[66.9m]
R
35
[2.5m
]
R121
[8.5m]
[17.4m]
R249
Shaking table
Porous stone
Shaking table
228mm
328mm
[16m]
[23m]
21mm
7mm
[1.5m]
[0.5m]
[8m]
115mm
[8m]
115mm
Shaking
Shaking
3°
Fig. 1. (Color) Three centrifuge experiments with their instrumentation
layout.

representing the granular columns was made of relatively uniform,
clean, medium gravel with Cu ¼ 1.54. It had the critical and peak
friction angles (ϕcs and ϕpeak) of 35° and 40°, respectively, at a dry
unit weight of 17 kN=m3
, obtained from isotropically consolidated
drained triaxial tests conducted by the authors. The hydraulic con-
ductivity of these columns was estimated at k ≈ 2.9 cm=s from con-
stant head permeability tests (roughly 200 times more permeable
than Ottawa sand F65). Fig. 2 shows the grain-size distribution
curves for all four materials used in this study.
Model Construction
The Ottawa and Monterey sand layers were prepared using the air
pluviation reconstitution method with the automated pluviator at
CU [Fig. 3(a)], to improve the repeatability among tests and the
uniformity within each model. The silt layer was dry pluviated from
a constant height using a #10 sieve to avoid lumps and distribute silt
across a controlled area. It was then gently compacted using a static
surcharge pressure of 5 kPa to achieve a dry unit weight of approx-
imately 16 kN=m3
with a final thickness of approximately 0.5 m in
the prototype scale.
To prepare the dense granular columns, geotextile filters were
formed to the desired column’s shape and diameter, and they were
subsequently plugged and glued at the bottom. Then the gravelly
soil was poured inside and tightly compacted in the geotextile col-
umn in three layers (previously calibrated to achieve the desired dry
unit weight of approximately 17 kN=m3
) and subsequently glued
from the top by adhesive tape, to prevent sand from entering the
columns during pluviation. For Model 4, the granular columns
were encased first in geotextile filters and then in 0.2-mm-thick
latex membranes. At their base, the membrane latex was sealed
with silicone sealant and end-cap plates. This sealing process pre-
vented any water in the soil from moving into the constructed
granular columns in Model 4 from the bottom or sides. The granu-
lar columns in Models 0, 1, and 3 were capable of drainage and
were not encased with a latex membrane. The shear modulus ratio
(Gr), ratio of the small-strain shear modulus (Gmax) of granular col-
umns to that of the surrounding loose Ottawa sand, was approxi-
mately 3. The Gmax value was calculated for sand and gravel on the
basis of the empirical procedures detailed by Seed and Idriss (1970)
and Seed et al. (1986), respectively.
The construction of dense granular columns inside geotextile
may not be practical in loose saturated sandy deposits, based on
the existing construction techniques. Nevertheless, in this experi-
mental study, the geotextile was used to prevent clogging and
preserve the drainage capability of granular columns during sub-
sequent motions. This design also provided an upper-bound con-
dition for the shear stiffness and drainage ability of these columns,
enabling an easier evaluation of the underlying mechanisms.
Fig. 2. (Color) Particle size distribution curves for all soil types used in
this study.
Fig. 3. (Color) Photographs taken (a) during air pluviation of Ottawa Sand; (b) after model completion of Test 2; (c) showing horizontal LVDT
holders and setup designed for the centrifuge experiments; and (d) after model completion of Test 3.

To create accurate 3° slopes that were consistent among the
models, the sand surface was vacuumed rather than scraped (to
minimize soil disturbance) with the aid of guide rails clamped
along the length of the container. After the model completion in
Tests 2 and 3, the top surface of Monterey sand was sprayed with
a sugar solution (5% by mass), lightly heated, and left overnight to
dry. This treatment kept the slopes intact during the model transport
across the lab floor to the centrifuge, but cementation effects were
removed when the sugar dissolved during saturation.
For all the treated models (Models 0, 1, 3, and 4), the granular
columns were placed vertically at the bottom of the container at
predetermined positions in a grid prior to the pluviation of sand.
Rows and vertical columns of colored sand (Ottawa) were also
placed at various locations throughout the model, to enable meas-
urement and evaluation of various modes of deformation during
model excavation. Figs. 3(b and d) show photographs of the fully
assembled models. Figs. 3(b and c) also show the setup for meas-
uring vertical and horizontal soil movements. The vertical LVDTs
measured the settlement of bearing plates placed on the soil surface.
The vertical LVDT rods were free to slide horizontally across the
surface of the bearing plate, while the plate displaced with the soil
owing to the nails placed around its perimeter. The nails had a
diameter of 0.9 mm and height of 9 mm in the model scale,
and their effect on the soil response was assumed to be negligible.
The horizontal LVDTs recorded lateral displacements along an ini-
tially vertical slot in an aluminum plate. This permitted the vertical
settlement of soil without influencing horizontal displacement mea-
surements [Fig. 3(c)]. The bearing plate for horizontal LVDTs was
embedded in Monterey sand to resist the overturning moment aris-
ing from the inertia of LVDT rods. To minimize this moment, the
LVDT rod was initially positioned near the base of the slot.
After dry preparation, the models were saturated with a hydrox-
ypropyl methylcellulose solution of 64 cSt viscosity, prepared per
Stewart et al. (1998) and measured before use. The viscosity was
70 times greater than that of water, to satisfy both the diffusive and
the dynamic scaling laws (Taylor 1995). A computer-controlled sat-
uration system was designed and implemented to improve the qual-
ity and rate of saturation, similar to that proposed by Stringer and
Madabhushi (2009). Initially, the soil model was flushed with CO2
from the bottom of the container for about 1 h, after which it was
kept under constant vacuum. The fluid tank was placed on a scale,
and its vacuum level was subsequently controlled automatically to
maintain a safe and constant flow rate below that required for flow-
induced liquefaction (in this case, 19 g=minute just prior to reach-
ing the silt layer and then 2 g=min, based on Stringer and
Madabhushi 2009). Complete saturation of each model required
approximately 96 h.
Properties of Input Motions
Once they were under 70 g of centrifugal acceleration, a series
of one-dimensional horizontal earthquake motions were applied
to the base of each model using a servo-controlled hydraulic shake
table available at CU (Ketchum 1989). These motions were scaled
versions of the horizontal component of recorded earthquake
motions, selected to cover a range of characteristics in terms of am-
plitude, frequency content, and duration, thus enabling evaluation
of the impact of these properties on system performance. Table 1
provides a summary of the sequence and properties of the first three
earthquake motions applied at the base of the model container.
Fig. 4 shows the acceleration response spectra (5% damped) and
the Arias Intensity time histories of the base motions achieved in
the centrifuge (the mean and their range of variability among the
three tests). Ample time was allowed between each phase of shak-
ing to allow and monitor full excess pore pressure dissipation. The
1992 Mw 7.3 Landers Earthquake recording at the Joshua Tree sta-
tion was selected because of its longer duration and slower rate of
energy buildup relative to the other records. The 1995 Mw 6.9
Kobe Earthquake recording at the Takatori station had a more rapid
buildup of energy and a shorter duration, but it was scaled to have a
lower amplitude in comparison with the Landers event (for exam-
ple, in terms of the PGA). Finally, the 1994 Mw 6.7 Northridge
Earthquake recorded at the Newhall-WPC station was a near-fault
record with a significant velocity pulse. The three selected motions
also differed in their frequency content, as shown in Fig. 4, for the
achieved or measured base motions.
Centrifuge Experimental Results
During all tests, the data were recorded at a sampling rate of 3,500
samples per second. In the following sections, all the test results
are presented and discussed in prototype units. The responses of
Model 0 (level ground with a single drain), Model 1 (slope with
36 draining granular columns and Ar ¼ 20%), Model 2 (slope
without granular columns), Model 3 (slope with 25 granular col-
umns and Ar ¼ 10%), Model 4 (slope with 25 granular columns
and Ar ¼ 10%, encased with latex membrane) were analyzed and
compared on the basis of the recorded accelerations, pore water
pressures, and vertical and horizontal displacements, in order to
provide insight into the effects of granular columns and their vari-
ous properties on site and slope performance. Due to space limi-
tations, only selected, representative results are presented.
Table 1. Ground motion properties recorded at the base of the container during Test 3
Motion
number
Ground
motion identifier Event Station PGA (g)
Significant duration,
D5–95 (s)
Mean period,
Tm (s)
Arias intensity,
Ia (m=s)
1 Kobe 1995 Kobe Takatori 0.38 11.9 0.86 1.92
2 Joshua 1992 Landers Joshua Tree 0.58 27.6 0.66 7.54
3 Northridge 1994 Northridge Newhall-WPC 0.75 16.6 0.94 4.94
Fig. 4. (Color) Acceleration response spectra (5% damped) and Arias
Intensity time histories of the base motions recorded during the three
tests. The solid lines show the average of the three tests, and the
highlighted regions show the variation among tests.

In this paper, toe refers to the location of the instrument array closer
to the slope toe but still within the slope, whereas top refers to the
location of the instrument array closer to the slope top and container
boundaries.
Influence of a Single Granular Column on Site
Performance
The primary objectives of Test 1 (Model 0) were (1) to evaluate
site performance in the far field and in the vicinity of a single granu-
lar column in a level, layered soil profile in terms of accelerations,
pore pressures, and settlements; and (2) to provide a data set for
the calibration and validation of numerical models in the future,
before adding the complexities of a slope and multiple drains.
Furthermore, drain systems are often designed for a unit drain
cell surrounded by other drains on all sides. The performance of
a drain outside the unit cell framework (for example, drains at
the edge of a group or in isolation) has not been adequately studied
experimentally.
Fig. 5 shows a summary of the time histories of excess
pore pressure, vertical displacement, and horizontal acceleration
recorded at three different radial distances from the single granular
column at different depths in Model 0 during the Kobe motion.
Liquefaction, defined as an excess pore pressure ratio (ru ¼
Δu=σ0
vo) of 1.0, was observed quickly in the loose sand layer. Large
excess pore pressures were also generated in the lower dense layer
of Ottawa sand, causing liquefaction during the first motion but at a
slightly slower pace. The accelerations generally showed large,
high-frequency spikes due to dilation within dense Ottawa sand.
These were attenuated in loose sand.
The pore pressure recordings showed that a single granular col-
umn was unable to prevent liquefaction even at a radial distance of
2.5 m, a result that was not surprising given that the drain spacing
was effectively infinite. However, the rate of excess pore pressure
dissipation was increased after shaking ceased, leading to a faster
rate of dissipation near the granular column, particularly at the
lower depths. The net dissipation of excess pore pressures was
slower at higher elevations because of the upward flow from lower
elevations. The influence of a single granular column considered in
this study (in terms of its effects on pore pressures) appeared to fall
within a radius of 2.5–8.5 m. Further, the ru values greater than 1.0
at the top of the liquefiable layer may indicate the possible forma-
tion of a water film below the silt interface and/or the slight settle-
ment of PPTs with respect to the surrounding soil at that location.
The slight movement of those PPTs with respect to colored sand
was confirmed during the excavation.
The dynamic total head isochrones were used to show the di-
rection and magnitude of transient hydraulic gradients at different
times and the resulting flow tendencies around the drain. Fig. 6
shows a comparison of the dynamic total head isochrones obtained
from the PPT recordings at three different radial distances from
the granular column center during the Kobe and Joshua motions.
At different radial distances, the isochrones indicated that liquefac-
tion (ru ¼ 1.0) was achieved quickly within the loose layer
of Ottawa sand during all motions. The hydraulic gradients were
generally formed upward from the dense layer toward the surface.
Fig. 5. (Color) Acceleration, excess pore pressure, and vertical displacement time histories during the first motion (Kobe) at three radial distances
from the single granular column in Test 1.

The presence of a drain led to a radially inward and upward flow
pattern in its vicinity, which slightly reduced the duration of large
excess pore pressures near the drain, particularly in deeper layers,
in comparison with the far-field (for example, a radius of 17.4 m in
this experiment) that experienced only vertically upward flow.
More rapid drainage, particularly for the deeper liquefiable layers,
would be expected to reduce the duration of large lateral spreads in
the slopes and benefit their performance; this is explored in the next
section.
The acceleration time histories showed spikes at large strains
after significant pore pressure generation and softening of the soil.
The amplitude of the acceleration spikes increased as the shaking
intensity and soil density increased in the subsequent events (not
shown, for brevity), which may be attributed to increased soil di-
lation and restiffening (Dashti et al. 2010). The relative density of
the loose sand layer increased from approximately 40% prior to
Kobe to about 60% prior to the Northridge motion on the basis
of far-field LVDT recordings, assuming uniform settlement across
the far-field.
Fig. 7 shows the time-frequency Stockwell spectra (Stockwell
et al. 1996; Kramer et al. 2016) of the transverse accelerations at the
container base as well as the bottom, middle, and top of the lique-
fiable layer during the Kobe motion. These plots enable visualiza-
tion of the spectral changes in acceleration over time, which is more
appropriate and insightful than a Fourier transform in a highly non-
linear and nonstationary system. In this figure, the color scale is
constant across all plots to facilitate comparison, and the peak
ground acceleration (PGA) measured during the response is shown
in the top right corner of each plot. Significant deamplification of
accelerations occurred from the base toward the surface due to ex-
cessive softening, particularly in loose Ottawa sand.
Within the loose Ottawa sand layer, the acceleration’s frequency
content varied with distance from the granular column. Fig. 5
shows that the excess pore pressures developed in this layer were
relatively unaffected by the column for the duration of strong shak-
ing. Therefore, enhanced drainage was likely not primarily respon-
sible for this change in acceleration’s frequency content. It is
proposed that the shear stiffness increment due to the presence
of a gravel column shifted the site’s modal frequencies as a function
of the radius (R). Owing to the increased shear stiffness, the lower
frequency shear waves (less than approximately 1 Hz) experienced
deamplification in soil closer to the column in comparison with the
far-field. The frequency bandwidth of the deamplification may
have been more extensive in the absence of enhanced drainage.
However, the high-frequency accelerations (around 4–10 Hz), were
amplified near the granular column in comparison with the far-field
due to a slightly faster dissipation of excess pore pressures, even
during shaking, and hence the instances of recovery in the soil shear
stiffness (and the reduction in damping). This hypothesis is tested
in subsequent sections in which the effect of drainage is separated
from that of reinforcement.
When used on a gently sloping site (explored in the next sec-
tions), the increased shear stiffness close to the granular column
may help limit the lateral spreading. However, designers should
Fig. 6. (Color) Dynamic total head isochrones at three different radial distances from the granular column during the Kobe and Joshua motions.
Fig. 7. (Color) Time frequency (Stockwell spectra) of transverse
accelerations at the bottom, middle, and top of liquefiable layer and
container base at three different radial distances from the granular
column during the Kobe motion. (The PGA value is noted at the
top right corner of each figure.)

be aware of a consequential increase in PGA. The PGA of the sur-
face motion (controlled by higher-frequency vibrations) and hence
the cyclic stress ratio (commonly used in liquefaction-triggering
analyses as the measure of seismic demand) were increased by ap-
proximately threefold when the radial distance (R) to the drain was
decreased from 17.4 m (PGA ¼ 0.21 g) to 2.5 m (PGA ¼ 0.61 g),
during the Kobe motion. The adverse influence of the granular col-
umns on surface PGA and the cyclic demand must be considered in
design.
The readings from vertical LVDTs provided a measure of set-
tlement (positive readings) at the top and bottom of the loose sand
layer during different shaking events at three different radial dis-
tances from the drain center, as shown in Fig. 5, during the Kobe
motion. Generally, significant settlements occurred both in the
dense and loose layers of Ottawa sand during shaking due to sed-
imentation and partial drainage (εp-SED and εp-DR), followed by a
smaller contribution from post-shaking consolidation (εp-CON). As
the distance to the drain decreased, settlements within both loose
and dense layers of Ottawa sand generally reduced. Even though
the drain tended to amplify volumetric strains due directly to partial
drainage (εp-DR), it was shown to reduce the net volumetric settle-
ments at the surface by limiting the duration of large excess pore
pressures and therefore the extent of sedimentation (εp-SED). The
patterns were similar during other ground motions.
Influence of Granular Columns and Area Replacement
Ratio on Slope Performance
In this section, the effectiveness of granular columns is assessed in
reducing the extent of excess pore pressure generation, accelera-
tions, and lateral spreading in a gently sloping site. The influence
and relative importance of the area replacement ratio (Ar) of granu-
lar columns was assessed experimentally. Models 2, 3, and 1 con-
tained a gentle slope treated with granular columns that had
Ar ¼ 0% (no drains); Ar ¼ 10%; and Ar ¼ 20%, respectively.
Fig. 8 shows a comparison of the dynamic total head isochrones
for the Kobe motion, which were obtained from the PPT recordings
for Models 1 through 3 at the depths shown in Fig. 1. These
isochrones show that liquefaction was achieved quickly within
the loose layer of Ottawa sand in Models 2 and 3 with the Ar of
0 and 10%, respectively. Large excess pore pressures were mea-
sured in the dense layer of Ottawa sand, but liquefaction was typ-
ically not reached in this layer in the presence of a gentle slope
(even for the untreated case of Ar ¼ 0%). Importantly, the greater
Ar of 20% in Model 1 successfully reduced the extent and duration
of large excess pore pressures in all layers in comparison with the
other two models. Model 3 (Ar ¼ 10%) also appeared to slightly
increase the rate of excess pore pressure dissipation in comparison
with the untreated Model 2 (Ar ¼ 0%), but not as well as Model 1.
These patterns were consistent during different motions.
Fig. 9 shows a comparison of the excess pore pressure ratio (ru)
time histories at various depths together with the vertical and hori-
zontal displacements recorded at the top and toe of the slope during
the three shaking events in the three models. The container base
acceleration time histories are also provided for comparison.
The horizontal displacement is considered positive in the fall line
or downslope direction for all models. The rate of excess pore pres-
sure buildup at all depths was generally decreased and the rate of
post-
shaking dissipation increased when the Ar increased from 0 to 10%
and to 20%, as expected. Similar to Model 0, the fastest rate of
dissipation was observed at lower elevations, due to an upward flow
tendency, which is also shown in Fig. 8.
The time-frequency response (Stockwell spectra) of transverse
accelerations recorded in the three models during the Kobe motion
is shown in Fig. 10. The figure shows that the amplitude of soil
surface accelerations generally tended to decrease at lower frequen-
cies over an extended period of time, as the Ar increased from
0 to 10% (the left two plots on the top row of the figure). On the
other hand, the acceleration amplitudes increased considerably
when Ar was increased from 10 to 20% (the right two columns in
the figure), particularly at frequencies greater than 0.7 Hz during
and after strong shaking. This led to a notable increase in PGA in
the top half of the liquefiable layer. This response may be explained
by the counteracting effects of shear reinforcement and enhanced
drainage provided by granular columns. For both treated Models 3
(Ar ¼ 10%) and 1 (Ar ¼ 20%), the added shear stiffness of the col-
umns alone was expected to reduce the amplitude of accelerations
and shear stresses in the surrounding liquefiable soil, particularly at
lower frequencies. In the experiments, an Ar of 10% provided shear
reinforcement, resulting in a slight reduction of accelerations in
comparison with the unmitigated slope (Ar ¼ 0%) at frequencies
less than around 1 Hz. This model also enhanced the drainage rate,
but not sufficiently to noticeably amplify accelerations at higher
frequencies. At the accelerometer locations (midway between the
columns), the accelerations were in this case only marginally am-
plified or preserved at higher frequencies.
For the greater Ar of 20%, the drainage rates were increased
sufficiently to prevent soil liquefaction in most cases. Therefore,
the average soil stiffness was increased and the damping decreased
in comparison with Models 2 (Ar ¼ 0%) and Model 3 (Ar ¼ 10%).
This impacted the propagation and amplification of accelerations,
particularly above the dense Ottawa sand layer. The result was
more intense accelerations measured near the soil surface (the top
of loose Ottawa sand) across a range of frequencies, concentrated
around the strain-compatible fundamental frequency of the
treated slope (approximately 0.7–0.8 Hz as determined from the
Stockwell spectra) due to the combined effect of reinforcement
and drainage. These observations are in line with those in Model
0 and were consistent during various motions, despite their varia-
tions in intensity, frequency content, and duration. These effects on
the amplitude and frequency content of the motions near granular
Fig. 8. (Color) Dynamic total head isochrones recorded in sloped sites
with granular column treatment of Ar ¼ 0, 10, and 20%, during the
Kobe motion.

columns must be considered in evaluating liquefaction triggering
and consequences as well as the design of overlying structures.
Fig. 9 shows the surface settlements at the top and bottom of the
slope for each of the three models. These settlements were domi-
nated primarily by volumetric strains and to a smaller degree by
deviatoric or shear strains, due to the slope’s small angle. For ex-
ample, the settlements recorded at the top of the slope in Model 2
were quite similar to those of a similar profile with level ground in
Model 0. The settlements recorded at the top of the slopes generally
decreased with an increasing Ar due to the reduction in the extent
and duration of large excess pore pressures and hence the reduction
in volumetric strains caused by sedimentation and deviatoric strains
caused by the existing static and dynamic shear stresses. These fac-
tors were more significant than the increase in volumetric strains
due to partial drainage. At the toe of the slope, the settlements were
more strongly affected by the deviatoric strains and rotational
movements from the slope above, at times causing bulging or heave
in the central channel and close to the channel. Larger deviatoric
displacements downslope, for example, in Model 2 (Ar ¼ 0%), led
to smaller net settlements at the toe of the slope in comparison with
the top, or with other models, during the first motion (Kobe) due to
the bulging effect induced by rotational movements toward the cen-
tral channel. The settlements generally reduced during the sub-
sequent motions due to densification in the prior motions as
well as the cumulative reduction in slope’s angle.
Lateral displacements were recorded in the slopes with the
LVDT setup shown in Fig. 3(c) and the locations shown in Fig. 1.
It is noteworthy that these measurements were sensitive to the
rotation of the slotted aluminum plate and in many cases malfunc-
tioned. However, in comparison with the plates placed
perpendicular to the slope in previous experimental studies, the
horizontal LVDT measurement system had a far smaller impact
on the response of the slope and the development of lateral spread-
ing. The results from horizontal LVDTs that were subject to
Fig. 9. (Color) Base acceleration, excess pore pressure ratio, vertical and horizontal displacement time histories recorded in sloped sites with granular
column treatment of Ar ¼ 0, 10, and 20%, during the Kobe, Joshua, and Northridge motions.

excessive rotation are not shown in Fig. 9. The successful record-
ings as well as measurements obtained during model excavation
highlight the effectiveness of the granular columns, particularly
with Ar ¼ 20%, in reducing permanent lateral spreading, which
is a critical measure of slope performance. This was due partly
to the added shear reinforcement and partly to the faster dissipation
of excess pore pressures. The contribution of each mechanism is
subsequently evaluated for one case.
Lateral displacements were generally reduced as the Ar in-
creased. These lateral deformations, governed by deviatoric strains
under the existing static and dynamic shear stresses, were in all
cases greatest at the toe (shown in the second row in Fig. 9) of
the slope in comparison with the top (shown in the first row in
Fig. 9), and could be unacceptable even with Ar ¼ 20% (that is,
on the order of 15 cm or more during the first motion). The per-
manent lateral displacements reduced significantly after the first
motion (Kobe) in the treated slopes (both Ar ¼ 10% and
Ar ¼ 20%), whereas the large lateral deformations continued in
the untreated model (Ar ¼ 0%). However, the slope angle was re-
duced significantly in the untreated Model 2 after the first two mo-
tions (from 3° to about 0.6° during the Kobe and to about
0° during the Joshua, calculated roughly with the two vertical
LVDT recordings on the soil surface), which indicated negligible
static shear stresses driving the permanent lateral deformations be-
yond this point. Following the first two motions, the lateral dis-
placement recordings in the untreated Model 2 were therefore less
reliable and were strongly affected by the rotation of the aluminum
plate (hence, not presented during the Northridge). Nevertheless,
the recordings indicated excessive lateral spread potential in an
untreated slope.
Fig. 11 shows the cumulative settlements (greatest at the top of
the slope), lateral displacements (greatest at the toe of the slope),
and slope angles (calculated roughly from the two vertical LVDT
recordings on the surface of the Monterey sand), as recorded during
the application of three consecutive motions, when available. The
results generally support the conclusion that using granular col-
umns reduces the volumetric settlements and deviatoric lateral
displacements in gentle slopes. The magnitude of this reduction
was shown to depend strongly on Ar, the characteristics of shaking,
the initial preshaking soil properties, and the slope geometry. The
use of granular columns was highly effective in reducing the mag-
nitude of lateral spreading. The vertical settlements were also re-
duced, but additional mitigation measures may be required to limit
the deformations for structures or other sensitive infrastructure.
Relative Influence of Shear Stiffness and Drainage on
Slope Performance
The influence and relative importance of mitigation arising from
the mechanisms of shear reinforcement and enhanced drainage
in granular columns were evaluated experimentally by comparing
the responses of Models 3 and 4. Both models contained a gentle
slope treated with granular columns at Ar ¼ 10%. In Model 3, the
granular columns were encased only in geotextile to avoid clog-
ging, combining the drainage and shear reinforcement mechanisms.
In Model 4, the dense granular columns were encased in both a
geotextile and a thin (0.2-mm-thick) latex membrane to avoid
drainage and provide only shear reinforcement.
Fig. 12 shows the dynamic total head isochrones for Models 3
and 4 during the Kobe motion. As expected, the use of draining
granular columns (Model 3) slightly reduced the net excess pore
pressures generated during shaking (for example, it reduced the
peak ru values to slightly below 1.0 in the liquefiable layer) and
increased the rate of dissipation after shaking in comparision with
the nondraining columns in Model 4 (with latex). Fig. 13 shows the
faster rate of the pore pressure dissipation in Model 3 during all
shaking events. The faster drainage in Model 3 limited the
settlements both at the top and toe of the slope by limiting both
Fig. 10. (Color) Time frequency (Stockwell spectra) of transverse
accelerations at the bottom, middle, and top of liquefiable layer and
container base in sloped sites with granular columns of Ar ¼ 0, 10,
and 20%, during the Kobe motion.
Fig. 11. (Color) Cumulative vertical and horizontal displacements re-
corded in sloped sites with granular columns of Ar ¼ 0, 10, and 20%.

sedimentation and shear deformations. Similar effects were ob-
served in the comparison of lateral displacements shown in Fig. 13,
both at the top and toe of the slope. The nondraining granular col-
umns with latex extended the duration of large excess pore pres-
sures, which notably amplified lateral displacements in the slope
(for example, an increase from 25 to 50 cm at the slope toe during
Kobe).
Fig. 14 shows a comparison of the cumulative vertical and hori-
zontal displacements, as well as rough estimates of the slope angle,
in Models 3 and 4 during the three consecutive motions (in a man-
ner similar to that shown in Fig. 11). A reduction of approximately
20% was observed in the total surface settlements after two motions
due to the draining effect of granular columns. Similarly, a reduc-
tion of approximately 74% was observed in the lateral toe
displacements after three consecutive motions due to enhanced
drainage, even though Model 3 had a slightly steeper slope follow-
ing the first shake. The vertical and lateral deformations in Model 4
with the nondraining columns were quite similar to those in Model
2 without any treatment, which indicated a negligible influence
from shear reinforcement on slope performance in terms of defor-
mations for Ar ¼ 10%. The photographs taken during model
Fig. 12. (Color) Dynamic total head isochrones recorded in sloped
sites with granular columns of Ar ¼ 10%, draining (without latex,
Model 3), and nondraining (with latex, Model 4).
Fig. 13. (Color) Base acceleration, excess pore pressure ratio, vertical and horizontal displacement time histories in sloped sites with granular
columns of Ar ¼ 10%, draining (Model 3), and nondraining (Model 4).

excavation (Fig. 15) and the deformation of initially vertical col-
ored sand columns confirmed the significantly larger shear defor-
mations in loose Ottawa sand in Model 4 with nondraining
granular columns in comparison with Model 3, and similar to
Model 2. The photographs also show minimum lateral deforma-
tions in Model 1, which was consistent with the recordings
shown previously. These observations point to the critical impor-
tance and benefits of maintaining the drainage capabilities of
granular columns (for example, reducing the possibility of clog-
ging in the field after subsequent events) and of not relying solely
on the shear reinforcement mechanism of mitigation for reducing
slope deformations.
Fig. 16 shows the time-frequency Stockwell spectra of trans-
verse accelerations at the container base and various depths within
the loose layer of Ottawa sand during the Kobe motion in Models 2,
3, and 4. The same color scale is used at all depths to facilitate this
comparison. For all models, a significant deamplification of accel-
erations occurred from the base toward the surface due to soil soft-
ening. The higher shear stiffness provided by the nondraining
granular columns in Model 4 reduced the accelerations over a range
of frequencies. In this case, the high-frequency accelerations were
reduced in Model 4 in comparison with the untreated Model 2,
which led to a notable reduction in surface PGA (for example,
during Kobe, 0.31 g in the untreated Model 2 and 0.19 g in Model
4 with nondraining columns). The trends were consistent in other
motions. But the enhanced drainage (even by a slight amount in
Model 3 with Ar ¼ 10%) was shown to nullify this reduction
(PGA ¼ 0.29 g) or even cause notable amplifications of
accelerations in the surrounding soil (for example, as observed pre-
viously for Model 1 with Ar ¼ 20%, or near the granular column in
Model 0). The influence of granular columns on accelerations is
therefore expected to depend strongly on the column’s drainage
Fig. 14. (Color) Cumulative vertical and horizontal displacements in
sloped sites with granular columns of Ar ¼ 10%, draining (Model 3),
and nondraining (Model 4).
Fig. 15. (Color) Deformation of colored sand rows and columns after
the test during model excavation in sloped sites: draining granular
columns of Ar ¼ 20% (Model 1), no drains Ar ¼ 0 (Model 2), draining
granular columns of Ar ¼ 10% (Model 3), and nondraining granular
columns of Ar ¼ 10% (Model 4).
Fig. 16. (Color) Time frequency response (Stockwell spectra) of
transverse accelerations at different depths in sloped sites with granular
columns of Ar ¼ 10%, draining (Model 3) and nondraining (Model 4),
and Ar ¼ 0% (Model 2) during the Kobe motion.

ability and Ar as well as the soil properties, preshake slope geom-
etry, and motion characteristics.
Conclusions
A series of highly instrumented dynamic centrifuge model tests
were performed to evaluate the effectiveness of granular columns
as a liquefaction countermeasure and its properties on the perfor-
mance of level and gently sloping sites. The primary conclusions
drawn from the experimental results are the following:
• Drains in isolation or at the corner of a group cannot be relied
upon for preventing liquefaction if a large influx of fluid from
the far-field is possible. The conventional design charts do not
account for such cases. However, even drains without adjacent
drains can be somewhat effective in speeding up the dissipation
of excess pore pressures in their vicinity after shaking, and they
tend to reduce net volumetric settlements.
• The use of granular columns in gentle, layered, liquefiable
slopes was found to be effective in reducing the lateral and ver-
tical deformations. The drain’s area replacement ratio (Ar) was
experimentally shown to be a critical parameter in reducing both
settlements and lateral spreading in the slope. In this study, the
best performance was achieved when liquefaction was pre-
vented. The data presented here will be useful for the validation
of future numerical models used for optimizing design pro-
cedures.
• The influence of granular columns on the seismic demand and
accelerations experienced by the surrounding soil was shown to
depend on their Ar, drainage capability, and the frequency of
interest. Generally, shear reinforcement provided by the col-
umns tended to deamplify the accelerations over a range of fre-
quencies and reduced the PGA. However, enhanced drainage
could simultaneously increase the rate of excess pore pressure
dissipation and recovery of shear stiffness (and hence, reduction
in damping) in its surrounding soil, amplifying accelerations,
particularly at higher frequencies. The possible increase in
accelerations (and in particular, the PGA) at the surface of a
treated, draining site must be considered in evaluating liquefac-
tion triggering, consequences, and response of the overlying
structures.
• The possible reduction in accelerations and seismic demand due
to the shear reinforcement provided by granular columns cannot
be entirely relied upon for reducing the likelihood of liquefac-
tion triggering nor its consequences in terms of deformation. For
the particular Ar investigated (10%) here, the beneficial influ-
ence of granular columns on slope deformations was shown
to be due almost entirely to their ability to enhance drainage,
and not to shear reinforcement. However, this may not be the
case for higher Ar values or for cases in which notable ground
densification is expected during column installation. Neverthe-
less, the experimental results demonstrate that the influence of
enhanced drainage is vital. It is critical for engineers to avoid
clogging in these columns by using appropriate geotextile
filters.
• For soils with a high silt content, the hydraulic conductivity, and
thereby the zone of influence, is reduced. Therefore, the benefits
of drainage will be less visible (Adalier et al. 2003). This may
necessitate the use of higher area replacement ratios or possibly
different mitigation strategies.
Despite the inherent simplifications and uncertainties in centri-
fuge modeling, these experimental results and discussion are aimed
to guide the future field, physical, and numerical model studies to-
ward more reliable and performance-based liquefaction mitigation
design methodologies. Additional tests considering a wider range
of soil, slope, drain, and ground motion properties are needed with
parallel nonlinear numerical simulations in order to clarify the seis-
mic response of liquefiable deposits treated by granular columns
and the relative importance of reinforcement, drainage, and ground
densification in different kinds of soils; improve the existing design
procedures; and provide recommendations for practitioners.
Acknowledgments
The authors would like to acknowledge the support of the depart-
ment of Civil, Environmental, and Architectural Engineering at the
University of Colorado Boulder and the assistance of Mr. Balaji
Paramasivam, Mohamed Elmansouri, and Simon Petit in the execu-
tion of the centrifuge experiments presented in this paper.
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