Reduced-Scale Shake Table Testing of Seismic
Behaviors of Slurry Cutoff Walls
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Ming Xiao, Ph.D., P.E., M.ASCE 1; Martin Ledezma 2; and Jintai Wang 3
Abstract: This paper presents a reduced-scale shake table test on the seismic responses of a section of soil-cement-bentonite (SCB) slurry
cutoff wall. The geometric scale of slurry wall width was chosen as 1∶3 (model:prototype). A section of a slurry wall with dimensions of
150 cm long, 20 cm wide, and 160 cm tall was constructed and tested on a one-dimensional shake table. A 187 cm ðlongÞ × 150 cm ðwideÞ ×
180 cm (tall) steel-frame box was anchored on the shake table and contained the slurry wall and sandy soil that was compacted on both sides
of the wall. Spring-supported wood panels were installed at the bottom and on two sides of the box to create a boundary that has the stiffness
of dense sand. The slurry wall and the confining soil were instrumented with accelerometers, LVDT, linear potentiometers, and dynamic soil
stress gauges to respectively record the accelerations, vertical and horizontal deformations of the wall, and transient dynamic soil pressures on
the wall during the simulated seismic excitations. Dynamic scaling laws were implemented in the shake table testing to scale the seismic
excitation. Two shake table tests were conducted using the 1997 Loma Prieta earthquake motions and sinusoidal sweep-frequency motions
(from 0.2 to 6.0 Hz), respectively. The shake table tests provided a preliminary understanding of the seismic performances of the SCB slurry
wall in levees and earthen dams. DOI: 10.1061/(ASCE)CF.1943-5509.0000795. © 2015 American Society of Civil Engineers.
Author keywords: Slurry wall; Seismic performance; Shake table test.
Introduction
Slurry cutoff walls are commonly used as a mitigation of subsurface erosion in levees and earthen dams. Subsurface erosion in the
form of piping has been blamed for many catastrophic and highprofile failures such as the 1972 failure of the Buffalo Creak Dam in
West Virginia (Wahler 1973), the 1976 Teton Dam failure in Idaho
(Penman 1987; Sherard 1987), the 1990 Cyanide Dam failure in
North Carolina (Leonards and Deschamps 1998), the 2004 Upper
Jones Tract levee failure in northern California [California Department of Water Resources (DWR) 2004], and three levee breaches
during Hurricane Katrina in 2005 (Seed et al. 2008a, b; Sills et al.
2008). Slurry walls can provide impermeable barriers to seepage
through or beneath levees and are often considered as the first line
of defense against the initiation and progression of piping erosion
in levees. The slurries that are commonly used in the practice include the soil-bentonite (SB) slurry, cement-bentonite (CB) slurry,
and soil-cement-bentonite (SCB) slurry.
Although slurry cutoff walls have been used in the United States
for the past half a century and proved to be effective, their duringearthquake and postearthquake performances and conditions are
largely unknown. Failure of a slurry wall, as might be caused by
earthquakes, will undoubtedly subject levees, which are otherwise
protected by slurry walls, to piping erosion and subsequent breach.
1
Associate Professor, Dept. of Civil and Environmental Engineering,
Pennsylvania State Univ., University Park, PA 16802 (corresponding
author). E-mail: mxiao@engr.psu.edu
2
Staff Engineer, NCI Group, 550 Industry Way, Atwater, CA 95301.
E-mail: martinledezma07@hotmail.com
3
Graduate Student, Dept. of Civil and Environmental Engineering,
Pennsylvania State Univ., University Park, PA 16802. E-mail: jxw487@
psu.edu
Note. This manuscript was submitted on August 17, 2014; approved on
May 4, 2015; published online on July 9, 2015. Discussion period open
until December 9, 2015; separate discussions must be submitted for individual papers. This paper is part of the Journal of Performance of Constructed Facilities, © ASCE, ISSN 0887-3828/04015057(10)/$25.00.
© ASCE
For example, California’s levee system is located in the most
earthquake-prone region in the United States, adjacent to the San
Andreas Fault and other fault systems. The USGS estimated that a
magnitude 6.7 earthquake will occur in the greater San Francisco
Bay Area before the year 2032 with a 62% probability. Earthquake
damage is especially magnified during the wet season because of
flooding potential. The Phase 1 report by the Delta Risk Management Strategy (DRMS) of the California Department of Water
Resources (DRMS 2009) and the preliminary results presented by
the CALFED Bay-Delta Program (CALFED 2005) both indicated
that a large earthquake would not only cause widespread levee failures and island flooding but may also result in a multiyear disruption in the water supply and water quality. Although the threat is
realistic and present, the Delta levees have not been tested under
moderate to high seismic activities (CALFED 2000). Because of
the lack of historic damage and field and laboratory data, the dynamic responses of the built infrastructures such as levees and
slurry walls in an earthquake environment are not well understood.
Even if a levee survives a seismic shaking, the slurry wall inside the
levee could be damaged: microcracks and macrocracks can develop,
large lateral deformation can occur, and permeability may significantly increase. The damaged slurry wall may no longer serve as
a seepage barrier to existing piping channels, which may subsequently cause levee failure. Therefore, understanding the seismic
responses of slurry walls will help the evaluation of their postearthquake conditions, so that remediation measures can be timely taken.
Slurry cutoff walls are two-dimensional (2D), linear, underground structures, therefore the effects of soil-structure interaction are important. Such interactions include the dynamic soil
pressures on slurry walls, the acceleration-time histories of the
confining soil and slurry walls, the lateral deformations of
slurry walls with the seismic shaking, the possible resonance of
slurry walls with the site excitations, and dynamic settlement
of the confining soils and slurry walls. The objective of this
research is to provide a preliminary and quantitative insight of
the responses of a SCB slurry wall under simulated seismic
environments.
04015057-1
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Table 1. SCB Slurry Mixing Ratios by Mass
Slurry cutoff wall
Piping channel
Ground shaking
Constituents
Ratios (%)
Water
Sand
Cement
Bentonite
Defloculant
31.26
61.82
5.03
1.79
0.10
Gravelly sand
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Sandy clay
Ground shaking
Fig. 1. Simulation of a slurry wall section on shake table
Fig. 3. Instrumentation installation
Fig. 2. Shake table test of a slurry wall section
Methodology
Materials, Experimental Setup, and Instrumentation
A section of slurry wall was constructed and tested on a shake table.
The concept is illustrated in Fig. 1. The table can simulate ground
motions based on actual earthquake records. The dimensions of the
one-dimensional (1D) shake table were 2.44 × 2.13 m (8 ×
7 ft), and the load capacity was 177.9 kN (18.14 metric ton).
The table was driven in one dimension by an actuator that provided
245 kN (55 kip) hydraulic fluid driving force through a maximum
displacement of 25.4 cm (10 in.). A steel-frame box, as shown in
Fig. 2, was bolted on the shake table and had inside dimensions of
187 cm long in the shaking direction, 150 cm wide, and 180 cm tall.
Three walls of the box were made of 2.54 cm (1.0 in.) thick plywood and the fourth wall was made of 1.27 cm (0.5 in.) thick polycarbonate sheet, so that the construction and the segmental slurry
wall responses during shake table testing can be visually observed.
A section of soil-cement-bentonite (SCB) slurry wall was tested.
The SCB slurry was prepared following the mixing ratios and procedures used in the practice. The SCB mixing ratios were obtained
from a slurry wall construction company in California and are presented in Table 1. At the end of each shake table test, large specimens of the slurry wall section were obtained, and the density was
measured. The average density of the SCB slurry wall section was
1,743 kg=m3 . The dimensions of the slurry wall section were
150 cm long, 160 cm tall, and 20 cm wide. Selection of the slurry
© ASCE
wall section was restricted by the dimensions of the container on
the shake table. Because overburden stress was not applied on the
slurry wall and adjacent soil, the slurry wall section only simulated
a section of slurry wall adjacent to ground surface in the field.
Slurry was first poured in a formwork in the box. After four weeks
of hardening, the formwork was removed, the instrumentations
were installed, and a poorly graded sand was backfilled on both
sides of the wall. The backfill was compacted at 95% of its maximum dry density of 1,813.3 kg=m3 (based on the modified Proctor
test); this compaction ensured the relative density of the confining
sand was 80%, the minimum value specified by the U.S. Army
Corps of Engineers (USACE) in the engineer manual of “Design
and Construction of Levees” (USACE 2000). The USACE manual
also stipulates “any soil is suitable for construction levees, except
very wet, fine-grained soils or highly organic soils” (USACE
2000); accordingly, the poorly graded sand can be a suitable soil
used in levees. In the test, a 22.7 kg steel plate compactor was
manually used in the compaction. As the compactor was manually
controlled, the operator was careful when compacting soils adjacent to the slurry wall to ensure the slurry wall is not damaged
by the compaction. The confining soil was compacted on both sides
simultaneously to eliminate net lateral earth pressure on the wall.
Fig. 3 shows the instrumentation installation, and Fig. 4 illustrates the detailed layout of the instrumentations. Three linear
potentiometers were used to measure the transient lateral deflections of the wall in the bottom, middle, and top sections. The potentiometer’s wire was connected to a rigid steel rod outside of the
box, and the rigid steel rod went through the box and soil and was
fixed tightly to the slurry wall surface. Since the rigid rod was not
detached from the slurry wall during shake table testing, it was expected the rod followed the same lateral movements as the slurry
wall; so, the potentiometer recorded the actual lateral displacements
of the slurry wall section. The vertical deformations of the slurry
wall and the soil on both sides of the wall during shaking were
measured by linear variable displacement transformers (LVDTs)
that were anchored on the steel-frame box. The dynamic lateral soil
04015057-2
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FI ¼ ρL3 a
ð1Þ
FG ¼ ρL3 g
ð2Þ
FR ∼ σL2 ¼ εEL2
ð3Þ
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where ρ = material density; L = length; a = acceleration; g =
acceleration due to gravity; σ = stress; ε = strain; E = modulus
of elasticity. The ratio of the inertia force to the gravitational force
is known as the Froude’s number
Fr ¼
FI ρL3 a a
∼
∼
Fg ρL3 g g
ð4Þ
The ratio of the inertia force to the restoring force is known as
the Cauchy’s number
Fig. 4. Shake table configuration and instrumentation layout
Fr ¼
pressures on the wall were measured using dynamic soil pressure
cells. The accelerations of the wall and confining soil at different
elevations were measured by wire-free accelerometers, whose
dimensions were 10 × 6.3 × 2.9 cm. The wire-free accelerometers
avoided the interferences that might be caused by a wire during the
shaking. A timer was set in each accelerometer, and data recording
(100 data per second) automatically started at a predetermined time
when the shake table test was run. The instrumentations were connected to the National Instrument (NI SCXI, National Instrument,
Dallas, Texas) data-acquisition system that was located outside of
the shake table.
© ASCE
ð5Þ
To satisfy dynamic similitude, which includes geometric similitude and kinematic similitude, these two numbers must respectively
bear the same values for the model (lab scale) and the prototype
(field scale), as represented by the following expression:
FrðmodelÞ =FrðfieldÞ
¼1
CaðmodelÞ =FaðfieldÞ
ð6Þ
The above scaling law can also be expressed as
ðρLg
E Þmodel
ðρLg
E Þprototype
Dynamic Scaling Laws
Typical slurry walls in the field are 0.3–0.9 m (1–3 ft) wide depending on the width of backhoes that are used for excavation, and the
depths can vary from 5 to 30 m (15 to 100 ft). If assuming an average slurry wall width in the field is 0.6 m (2 ft), the width-to-depth
ratio may vary from 1∶7.5 to 1∶50 in the field. A section of slurry
wall on the shake table was chosen to be 20 cm wide and 160 cm
deep, so the width-to-depth ratio is 1∶8, at the lower end of the
width-to-depth ratio in the field. The effect of seismic wavelength
on the slurry wall was also considered. The wavelength is calculated using the shear wave velocity and the period. The shear wave
velocity of the top 30 m of the subsurface profile (VS30) varies
from <180 m=s for soft soils to 180–360 m=s for stiff soils (Wair
et al. 2012). The dominant earthquake frequency can range from 1
to 5 Hz. Therefore, the shear wavelength in the field can vary from
36 to 360 m, larger than the typical maximum depth of a slurry wall
of 30 m. In the lab testing, VS30 of 200 m=s was assumed for
the densely compacted soil (95% compaction based on modified Proctor test), and the simulated seismic frequency was from 0.2 to 6 Hz.
Therefore, the shear wavelength in the lab varies from 33 to 2,000 m,
also larger than the depth of the slurry wall model of 1.6 m.
Dynamic scaling laws were applied to address the similitudes of
the geometry, material properties, and loading. Scaling laws have
been widely studied and applied in the hydraulic and structural
engineering, and a wealth of literature is available. In this research,
the dynamic scaling laws followed the recommendations by
Moncarz and Krawinkler (1981).
The most important forces of a structure are inertia (FI ), gravitational (FG ), and restoring (FR ) forces, which depend on material
density, stiffness, and length, respectively, as shown as follows:
FI ρL3 a ρLa
∼
∼
E
FR εEL2
¼ 1;
ρr Lr gr
¼1
Er
also written as
ðDynamic scaling lawÞ
ð7Þ
In a true replica model, the above scaling law is satisfied. But
this scaling law poses one—but almost insurmountable—difficulty
in the selection of a suitable model material. Based on the desire to
use the same materials as in the prototype, the adequate model was
used in this research. The adequate model assumes the stresses induced by gravity loads are small and may be negligible compared
to the stress histories generated by seismic motions. So g in the
above scaling law was replaced by a. With the same E and ρ in
both model and prototype, the dynamic scaling law becomes
a
Lmodel −1
ar ¼ model ¼ L−1
r ¼
afield
Lfield
ðDynamic scaling law for adequate modelÞ
ð8Þ
In the reduced-scale shake table testing, a geometric scaling of
Lr ¼ 1∶3 was adopted, considering the available space in the steelbox on the shake table. Therefore, the acceleration induced by the
shake table should be three times of the measured acceleration
time-history in the field. The input acceleration-time history of
the shake table is controlled by the MTS system and can be defined
by the user. The dynamic scaling law for adequate model, although
the same as in centrifuge tests, is based on the assumption of negligible gravity field; while the centrifuge model fully satisfies the
dynamic scaling law without assumptions. In this research, the horizontal seismic stress is higher than the gravitational stress; therefore,
the dynamic scaling law for adequate model was adopted.
04015057-3
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Boundary Conditions
where L = half of the length of the foundation base; B = half of
the width of the foundation base; D = foundation embedment
= height of the shake table box in this research; d = height of
foundation that is actually in contact with soil = height of the
shake table box minus the freeboard in this research
The rigid boundary of the steel-frame box did not represent the true
boundary condition of the slurry wall and its confining soil. To address this boundary condition, spring-supported wood panels were
installed at the bottom and on two sides of the box, as shown in
Figs. 4 and 5(a). The idea was to create a flexible boundary that
has the same dynamic stiffness of dense sand. Gazetas (1991) derived
the dynamic stiffness of foundations embedded in homogeneous
half-space
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K dynamic ¼ K static kðωÞ
h ¼ D–d=2
where E = modulus of elasticity; and ν = Poisson’s ratio
χ¼
ð9Þ
where K dynamic = dynamic stiffness; K static = static stiffness; and
kðωÞ = dynamic stiffness coefficient.
1. The following is used to calculate static stiffness (K static ):
In vertical (z) direction
2=3 1
D
A
K staticðzÞ ¼ K z 1 þ
ð1 þ 1.3χÞ 1 þ 0.2 w
Ab
21
B
ð10Þ
In horizontal (y) direction, i.e., in the direction of shaking
0.5 0.4 D
h
Aw
K staticðyÞ ¼ K y 1 þ 0.15
1 þ 0.52
B
B
L2
Ky ¼
2 GL
ð2 þ 2.5χ0.85 Þ
2−ν
where G = shear modulus of foundation soil, and
G¼
E
2ð1 þ νÞ
ð13Þ
ð14Þ
where Ab = base contact area = ð2LÞð2BÞ; Aw = area of the
four sides of the embedded foundation = dð2L þ 2BÞ).
2. The following is used to calculate the dynamic stiffness coefficient, kðωÞ:
In z direction when ν ≤ 0.4
3=4 D
kz ðωÞ ¼ kz 1 − 0.09
ð15Þ
a20
B
where kz = dynamic stiffness coefficient for arbitrarily shaped foundations on the surface of homogeneous half-space in z direction
a0 ¼
ð11Þ
where K z and K y = static stiffness for arbitrarily shaped foundations on the surface of homogeneous half-space in z and y
directions, respectively; and
2 GL
Kz ¼
ð0.73 þ 1.54χ0.75 Þ
ð12Þ
1−ν
Ab
4 L2
ωB
Vs
ð16Þ
where ω is angular frequency; V s is shear wave velocity; and a0
ranges from 0 to 2. In this research, because of the lack of shear
wave velocity data, average value of 1.0 was used for a0 to account
for general soil condition. In y direction, ky ðωÞ also depends on
D=B and a0 and can be determined using Eq. (15). Table 2 shows
the initial parameters used in calculating dynamic stiffness of flexible boundary. Table 3 shows the calculation of the dynamic stiffness of the bottom boundary, and Table 4 shows the calculation of
the dynamic stiffness of the side boundaries.
Heavy-duty compression springs in parallel were used to
achieve the required stiffness on the three boundaries. A photo of
the bottom spring panel is shown in Fig. 5(a). The springs are
equally spaced, and the layout of the springs is also shown in
Fig. 5(a). Each spring’s stiffness coefficient is 1,386.5 N=mm, the
free length is 10 cm, and the maximum travel distance is 20 mm. To
Fig. 5. Spring panels used to generate seismic stresses on the confining soil of slurry wall: (a) photo of the bottom spring panel; (b) photo of the side
spring panel
© ASCE
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Table 2. Initial Parameters in Calculating Dynamic Stiffness of Flexible
Boundaries
4.5
Initial parameters
Symbols and units
Values
3.5
Given parameters
L (cm)
B (cm)
D (cm)
d (cm)
h (cm)
E (N=cm2 )
ν
G (N=cm2 )
a0
χ
83
75
180
160
80
3,500
0.4
1,250
1.0
0.90
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Derived parameters
Note: E¼ 3,500 N=cm2 is typical value for dense sand.
kz , using a0 as 1.0 and the chart of Gazetas (1991)
kz ðωÞ
K z (N=mm)
K staticðzÞ (N=mm)
K dynamicðzÞ (N=mm)
Values
0.8
0.66
74,606
144,441
95,500
Table 4. Calculation of Dynamic Stiffness of Side Boundaries in y
Direction
Calculated parameters
ky ðωÞ, using a0 as 1.0 and the chart of Gazetas (1991)
K y (N=mm)
K staticðyÞ (N=mm)
K dynamicðyÞ (N=mm)
Values
0.75
55,683
181,036
135,777
simulate dense sand around the confining soil, 187 springs were
needed on each side of the box, and 126 springs were needed at
the bottom. The total maximum weight of the slurry and sand backfill in the box was approximately 89,000 N. At the maximum spring
compression of 20 mm, the bottom spring-supported panel can support 1,910,000 N; this load capacity exceeds the total weight of the
slurry wall and soil in the box. In the horizontal direction, using a
horizontal acceleration of 10 g, the horizontal inertia force on the
vertical spring-supported panel is calculated as 890,000 N. The
spring-supported panel at full compression of 20 mm can sustain
2,715,540 N; this load capacity is 3.0 times the horizontal inertia
force (890,000 N) on the panel. Therefore, the springs will not be
fully compressed.
To simulate the cyclic stress variation with depth, the vertical
side spring-supported board on each side consisted of three panels
that moved independently. The side panel is illustrated in Fig. 5(b).
To reduce the friction between the slurry wall and the front and
back sides of the walls of the box, smooth Plexiglas sheets were
attached to the plywood walls of the box, so that the sides of
the slurry wall were in contact with the Plexiglas sheets. As shown
in Fig. 5(b), the bottom of the slurry wall rested on a springsupported plywood board at the bottom of the box; the transverse
cross-section of the slurry wall was in contact with the sidewalls of
the box. A plastic sheet was added between the slurry wall and the
sidewalls of the box in order to reduce interface friction and allow
relatively free movement of the wall during shaking. The top of the
slurry wall was open and had no restriction.
© ASCE
Displacement (cm)
3
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
Acceleration (g)
0.8
1
Fig. 6. Maximum displacements and maximum accelerations of Loma
Prieta earthquake recorded at various stations
Table 3. Calculation of Dynamic Stiffness of the Bottom Boundary in z
Direction
Calculated parameters
4
Selection of Input Seismic Excitations
In this research, the 1989 Loma Prieta earthquake (M ¼ 6.9) was
simulated, because of the earthquake’s proximity to the Sacramento-San Joaquin Delta levees and the earthquake’s well-recorded
time histories. The duration of the displacement-time history is
40 s. The earthquake’s displacement-time history and acceleration-time history data were obtained from the Pacific Earthquake
Engineering Research (PEER) Center Library of the University
of California at Berkeley and implemented into the input file to
the MTS (FlexTest SE, MTS, Eden Prairie, Minneapolis) control
system of the shake table. The seismic motions were recorded at
station 47125 in Capitola, California, at latitude of 36°58’27″ N
and longitude of 121°57’13″ W. Based on the dynamic scaling
law and using a geometric scaling factor of 3∶1 (prototype:model),
the input accelerations to the model test were three times the actually recorded accelerations in the field. Since the shake table is
controlled by displacements, the displacement-time history of the
shake table should be three times of the displacement-time history
recorded in the field. Considering the maximum displacement of
the table of 12.7 cm, the selected maximum ground motions
should be less than one third of 12.7 cm, or 4.2 cm. If the table
displacement exceeds the limit, the pump driving the actuator will
shut down. The Loma Prieta earthquake motions, in terms of
displacement-time history, velocity-time history, and accelerationtime history, were recorded at different field stations. The maximum displacement and acceleration at each station are plotted in
Fig. 6. To meet the displacement requirement and obtain the highest
possible acceleration, the station with the maximum acceleration
and displacement of 0.541 g and 2.6 cm was selected, as shown
in the circle in Fig. 6. Therefore, the maximum acceleration that the
table was expected to generate was 1.623 g. Fig. 7 shows the match
of the displacement-time history of the input file and the measured
displacements (output) of the shake table during the 40-s shaking.
Fig. 8 shows the measured acceleration-time history of the steel box
on the shake table during the 40-s shaking.
Low-amplitude (∼1.0 cm) sinusoidal excitations were also used
to investigate the fundamental seismic responses of slurry walls.
The vibration frequency increased in steps and was 0.2, 0.5, 1,
2, 3, 4, 5 and 6 Hz, with each frequency lasting 10 s. This frequency
range covers the dominant frequency range in most earthquakes.
Fig. 9 shows the measured acceleration-time history of the sinusoidal motions of the shake table. The purpose of using the sinusoidal sweep-frequency motions was twofold: (1) to determine
whether the natural frequency of the slurry wall with the soil confinement falls into the dominant frequency range of earthquakes,
and (2) to shake the slurry wall until failure if the scaled Loma
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Prieta earthquake motions could not fail the slurry wall, so that the
failure mechanisms of the slurry wall can be further investigated.
Moreover, sinusoidal waves can be easily input into numerical
models for future model development.
Effect of Seismic Shaking on Slurry Wall’s Strength
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When casting the slurry wall section on the shake table, cylindrical
specimens with dimensions of 10.2 cm ðdiameterÞ × 20.4 cm
(height) were also cast in cylindrical molds, from the same batch
of the slurry. The cylindrical specimens were sealed and allowed to
cure for the same time period as the slurry wall. These cylindrical
specimens did not experience seismic testing. After the shake table
testing, large blocks of samples were retrieved from the slurry wall
section and carefully trimmed to the same dimensions as the cylindrical samples that did not experience shaking. Then unconfined
compression tests were conducted on both specimens in order to
determine the effects of shaking on the slurry wall’s strength. Three
pairs of such specimens were tested for simulated Loma Prieta
earthquake motions and two pairs of such specimens were tested
for sinusoidal motions.
Results and Analyses
Fig. 7. Displacement-time histories of input and output motions of
simulated Loma Prieta earthquake
1. Simulated Loma Prieta Earthquake
The lateral deflections of the three sections of the wall, relative to the table movements, are shown in Fig. 10. The lateral
deflection increased from the bottom to the top of the slurry
wall. The maximum deflections of the bottom, middle, and top
sections of the slurry wall were 0.627, 0.955, and 1.204 cm,
respectively. The trend of the lateral deflections of the three
sections of the slurry wall followed the acceleration-time history of the shake table: higher acceleration apparently induced
higher lateral deflection.
The dynamic vertical deformations of the wall and the confining soil are shown in Fig. 11. The trend of the vertical
Fig. 8. Measured acceleration-time history of the box on shake table,
from simulated Loma Prieta earthquake
Fig. 10. Slurry wall lateral deflections caused by simulated Loma
Prieta earthquake
Fig. 9. Measured acceleration-time history of the shake table caused by
sinusoidal motions with increased frequency
Fig. 11. Vertical deformations of slurry wall and confining soil caused
by simulated Loma Prieta earthquake
© ASCE
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Fig. 14. Dynamic lateral pressure of the spring panels on confining soil
caused by simulated Loma Prieta earthquake
Fig. 12. Exposed slurry wall after simulated Loma Prieta earthquake
Table 5. Maximum Accelerations of Slurry Wall and Confining Soil
Caused by Simulated Loma Prieta Earthquake
System
component
Accelerometer position
and number
Acceleration
(g)
Occurrence
time (s)
Slurry wall
Bottom (1)
Middle (4)
Top (5)
Bottom (2)
Bottom (3)
Top (6)
Top (7)
(8)
(9)
1.46
1.81
2.33
1.54
1.58
2.35
2.47
1.88
1.78
8.51
8.50
9.57
8.52
8.50
8.58
9.56
9.77
6.23
Confining soil
Shake table
Box
Note: The numbers in Column 2 indicate the numbering of accelerometers
as shown in Fig. 4.
Fig. 13. Dynamic lateral earth pressures on slurry wall caused by
simulated Loma Prieta earthquake
deformations followed the trend of the accelerations of the
shake table: the intense shaking within the first 15 s induced
the majority of the vertical settlement; after that, the slurry wall
and the confining soil deformed little. The maximum vertical
settlements of the soil on the left and right sides of the slurry
wall were 1.265 and 1.080 cm, respectively. The maximum
vertical deformation of the slurry wall was 0.208 cm. Other
shake table tests on slurry walls by the authors showed that
vertical deformations of a slurry wall can indicate the occurrence of cracking and the time of occurrence of the wall: when
a slurry wall broke, the top portion tended to rotate, causing
the LVDT readings to suddenly increase, showing the wall
height increased. In this shake table test, the LVDT data did
not reveal sudden increase of the wall height. After removing
the soil on both sides, the slurry wall was examined and no
apparent crack was observed. Fig. 12 shows a photo of the
exposed slurry wall after shaking.
Fig. 13 shows the dynamic lateral earth pressures on the top
section (measured at 20 cm from top) and the bottom section
(measured at 20 cm from bottom) of the slurry wall during the
shaking. Fig. 14 shows the dynamic lateral pressures of the
spring panels on the confining soil. Both figures show that
the stabilized lateral pressures were higher at the bottom than
at the top because of the higher overburden effective stress at
© ASCE
the bottom. It seems the lateral pressure that was exerted by the
spring panel on the top section of the soil fluctuated more significantly; this agrees with the higher lateral deflection of
the slurry wall at the top. However, higher lateral pressure
on the soil (from the spring panel) in the top section did not
cause higher pressure on the slurry wall (as shown in Figs. 13
and 14).
The maximum accelerations and their time of occurrence of
the slurry wall and the confining soil are listed in Table 5. The
accelerometers are numbered and are shown in Fig. 4. The
maximum acceleration of the box on the shake table was
1.78 g, slightly higher than the maximum acceleration of
the input profile (1.62 g). The data show that acceleration increased from the bottom to the top of the slurry wall as well as
in the backfill. At the top section of the slurry wall and the
confining soil, the accelerations were amplified and higher
than the acceleration of the shake table.
2. Sinusoidal Sweep-Frequency Motions
The lateral deflections of the three sections of the wall,
relative to the table movements, are shown in Fig. 15. The
maximum deflections of the bottom, middle, and top sections
of the slurry wall were 2.182, 2.222, and 4.457 cm, respectively. The bottom portion of the wall showed similar movement to the sinusoidal movements of the table, whereas the
middle and top sections deflected independently, in magnitude, with the increased frequency of the table movements—
higher acceleration of the shake table did not induce higher
lateral movement of the slurry wall in the top and middle
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(b)
(a)
(c)
Fig. 15. Slurry wall lateral deflections caused by sinusoidal sweep-frequency motions: (a) bottom section; (b) middle section; (c) top section
sections. In the simulated Loma Prieta excitation, however,
higher acceleration induced higher lateral displacements in
all sections of the slurry wall. It is possible that different sections of the slurry wall resonated with the table movements,
i.e., the lateral deflections were more influenced by frequency
than by accelerations.
This research attempted to obtain the natural frequency of
the slurry wall using the experimental data. The maximum
lateral deflections of the top, middle, and bottom sections
of the slurry wall under each frequency were obtained from the
potentiometer readings. The maximum lateral deflection responses with frequency are plotted in Fig. 16. When the seismic frequency is equal to the natural frequency of the slurry
wall, the lateral deflections reach maximum. Fig. 16 showed
the top, middle, and bottom sections of the slurry wall
Fig. 16. Slurry wall lateral deflection responses with frequency
© ASCE
experienced the highest lateral deflection at 0.2, 2.0, and
4.0 Hz, respectively. Those frequencies, however, may not
be the natural frequencies of the different sections of the slurry
wall, since only a narrow band of frequencies (0.2–6.0 Hz)
was tested. Nevertheless, Fig. 16 indicates the slurry wall is
a complex system and may possess different natural frequencies at different sections.
The dynamic vertical deformations of the wall and the confining soil are shown in Fig. 17. At low frequencies (0.2, 0.5,
1.0 Hz), there was almost no vertical deformation. At frequency of 3.0 Hz, the slurry wall and the confining soil both
experienced large deformations. The recorded maximum vertical deformations of the soil on the left and right sides of the
slurry wall were 4.110 cm and 5.065 cm, respectively. The
recorded maximum vertical deformation of the slurry wall
Fig. 17. Vertical deformations of slurry wall and sand backfill caused
by sinusoidal sweep-frequency motions
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Table 6. Maximum Accelerations of Slurry Wall and Confining Soil
Caused by Sinusoidal Sweep-Frequency Motions
System
component
Accelerometer position
and number
Acceleration
(g)
Occurrence
time (s)
Slurry wall
Bottom (1)
Middle (4)
Top (5)
Bottom (2)
Bottom (3)
Top (6)
Top (7)
(8)
(9)
1.55
2.08
3.29
1.53
1.55
3.86
2.51
3.20
3.54
71.19
70.10
72.70
68.81
70.52
75.94
60.50
71.06
70.50
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Confining soil
Shake table
Box
Note: The numbers in Column 2 indicate the numbering of accelerometers
as shown in Fig. 4.
Fig. 18. Snapshot of slurry wall after sinusoidal sweep-frequency
motions
Table 7. Unconfined Compressive Strengths of Slurry Wall with and
without Being Subjected to Simulated Loma Prieta Earthquake Motions
Unconfined compressive strength (kPa)
Specimens
#1
#2
#3
Average
Without shaking
With shaking
173.40
118.52
131.69
141.20
141.56
160.23
185.58
169.79
Table 8. Unconfined Compressive Strengths of Slurry Wall with and
without Being Subjected to Sinusoidal Seismic Motions
Unconfined compressive strength (kPa)
Specimens
#1
#2
Average
Without shaking
With shaking
98.76
68.53
83.65
93.27
109.73
103.15
Fig. 19. Dynamic lateral earth pressures on slurry wall caused by
sinusoidal sweep-frequency motions
was 4.879 cm. At the end of the period with f ¼ 4 Hz
(t ¼ 60 s), the LVDT rods fell out of the LVDT tubes because
of the excessive settlements of the soil and wall; so, further
deformations of the slurry wall and the soil were not recorded.
The large settlement of sand may be caused by particle rearrangement under seismic load. It is also noted at t ¼ 51.7 s,
there was a sudden increase of the slurry wall height, this indicated a breakage of the slurry wall. When the wall broke, the
top portion rotated, pushing the LVDT rod back into the LVDT
tube; this was revealed in the LVDT readings as a sudden increase of the wall height. After removing the soil on both sides,
the slurry wall was examined, and a major crack was observed
and is shown in Fig. 18. Sand seeped into the crack throughout
the length of the wall, indicating a complete break of the top
section of the wall.
Fig. 19 shows the lateral earth pressures on the top section
(measured at 20 cm from top) and bottom section (measured at
20 cm from bottom) of the slurry wall during the shaking. At
lower frequency and accelerations, the dynamic lateral earth
pressure on the slurry wall remained unchanged. When seismic
frequency increased to 4 Hz (at t ¼ 50 s), lateral earth pressure
began to fluctuate. As expected, the lateral pressure on the bottom section of the wall is higher than that on the top section.
© ASCE
The maximum accelerations and their time of occurrence in
the slurry wall and the confining soil are listed in Table 6. The
accelerometers are numbered and are shown in Fig. 4. The data
showed that the accelerations of the slurry wall and the confining soil increased from the bottom to the top of the wall. It
should be noted that the maximum acceleration of the top section of the slurry wall occurred after the slurry wall broke. The
maximum acceleration of the top portion of the slurry wall
before the break was 1.137 g and occurred at 50.35 s, and
slurry wall broke at 51.70 s according to Fig. 17.
3. Effect of seismic shaking on slurry wall’s strength
The unconfined compressive strengths of the specimens
that were and were not subjected to simulated earthquake motions and sinusoidal motions, respectively, are summarized in
Tables 7 and 8. The preshaking specimens were made at the
same time of constructing the slurry wall; and the postshaking
specimens were obtained from the slurry wall during deconstruction. All compression tests were performed on the same
date, so that there was no time-effect on the strengths when
comparing the preshaking and postshaking specimens. The
strengths of the specimens that experienced shaking were
higher than those without shaking. The results suggested that
the shaking at least did not weaken the slurry wall. Apparently,
the preliminary compressive strength tests did not reveal the
seismic failure mechanisms of the slurry wall. A thorough
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material characterization of the slurry wall materials with and
without seismic excitations is needed. Such characterization
may include (1) density and water content; (2) one dimensional consolidation tests to determine the stress-void ratio
(stress-strain) relationship needed to assess volume changes
during consolidation of the slurry backfill in the model;
(3) consolidated-undrained triaxial shear strength tests with
pore pressure measurements to determine the stress-strain relationship, Young’s modulus and failure strain; (4) tension test to
derive the stress-strain relationship until failure; (5) fixed wall
permeability tests on 25 mm tall samples in consolidometers to
evaluate the relationship between hydraulic conductivity and
vertical stress under k0 conditions; and (6) flexible wall permeability tests on 70 mm tall samples to evaluate the hydraulic
conductivity under selected isotropic stresses. Although these
material characterizations were not conducted in this research,
they are under investigation in an attempt to understand the
failure mechanisms of slurry walls under various seismic
conditions.
Conclusions
This paper presents a reduced-scale shake table testing of soilcement-bentonite slurry wall. The seismic excitations used the
simulated 1989 Loma Prieta earthquake motions and low-magnitude
sinusoidal sweep-frequency motions. The Loma Prieta excitations
were scaled based on the dynamic scaling law for adequate model.
Spring-supported panels were used to simulate the sand boundary.
The slurry wall generally demonstrated increased lateral deflections
and accelerations from the bottom toward the top. A slurry wall
may possess different natural frequencies at different sections. The
simulated Loma Prieta excitation with maximum acceleration of
1.78 g did not break the slurry wall; while the sinusoidal sweepfrequency with maximum acceleration of 3.54 g broke the slurry
wall at the top portion.
The shake table results are not intended to be directly used to
evaluate the performances of slurry walls under earthquakes in field
conditions. The validity of the spring-supported boundaries needs
to be verified by numerical studies: the model can simulate the
spring-supported boundary exactly the way as in the shake table
tests and then simulate the boundary using infinitely long sandy
soil, the results from the two boundary conditions are compared
to see whether they yield the same results. Although a dynamic
scaling law was used, the scaling should be verified by numerical
analyses. Although this preliminary testing did not reveal the failure mechanisms of slurry walls under earthquakes, this paper presented a feasible testing methodology on the seismic responses of
slurry walls. A more thorough shake table testing, slurry wall
material characterizations with and without shaking, and numerical
analysis are needed to explain the failure mechanisms of slurry
walls under earthquakes.
© ASCE
Acknowledgments
The authors thank Diversified Minerals, Inc. (Oxnard, California)
for donating the bentonite and cement. The authors also thank Chris
Harris of Slurry Engineering Inc. (Sacramento, California) for
donating the deflocculation liquid and providing the mixing ratio
of the slurry.
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