SEISMIC COMPRESSION OF AS-COMPACTED FILL SOILS WITH VARIABLE LEVELS OF FINES CONTENT AND FINES PLASTICITY

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July 2004
CUREE Publication No. EDA-05
CUREE
Earthquake Damage Assessment and Repair Project
SEISMIC COMPRESSION OF AS-COMPACTED FILL SOILS
WITH VARIABLE LEVELS OF FINES CONTENT AND
FINES PLASTICITY
Consortium of Universities for Research in Earthquake Engineering
Jonathan P. Stewart
Daniel H. Whang
Matthew Moyneur
Pendo Duku
Department of Civil and Environmental Engineering
University of California, Los Angeles


CUREE, the Consortium of Universities for Research in Earthquake Engineering, is a non-profit organization incorporated in
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CUREE

Publishing


First Printing: July 2004



The goal of the Assessment and Repair of Earthquake Damage Project is to develop guidelines that provide a sound technical
basis for use by engineers, contractors, owners, the insurance industry, building officials, and others in the post-earthquake
context. Based on experimental and analytical research and a broad discussion of the issues involved, the guidelines produced
by the project will reduce disparities in the evaluation of building damage and the associated need for repairs.













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CUREE Publication No. EDA-05



SEISMIC COMPRESSION OF
AS-COMPACTED FILL SOILS WITH
VARIABLE LEVELS OF
FINES CONTENT AND FINES PLASTICITY

by

Jonathan P. Stewart, Daniel H. Whang, Matthew Moyneur, and Pendo Duku
Department of Civil and Environmental Engineering
University of California, Los Angeles


A report on research conducted under Subcontract No. 10 between the
Consortium of Universities for Research in Earthquake Engineering and the
Regents of the University of California


July 2004


CUREE
Consortium of Universities for Research in Earthquake Engineering
1301 South 46
th
Street
Richmond CA 94804-4698
Phone: 510.231.9557; Fax: 510.231.5664
e-mail: curee@curee.org
; website: www.curee.org





ABSTRACT
Seismic compression is defined as the accrual of contractive volumetric strains in unsaturated
soils during strong shaking from earthquakes, and has been recognized as a major cause of
seismically induced damage. As a result, there has been an increasing demand within the
engineering profession for seismic compression analysis procedures. Existing methods for
estimating seismic compression susceptibility include procedures proposed by Tokimatsu and
Seed in 1987 and Stewart and Whang in 2003. However, these two procedures are limited in
their applicability, because they only apply for a few specific soil characteristics. Accordingly,
there is a major research need for laboratory testing to develop relations between volumetric
strains, applied shear strains and number of strain cycles (termed a volumetric strain material
model) that cover a broad range of soil types.
The principal objective of this research was to perform laboratory simple shear testing to
provide insight into the seismic compression of sands, non-plastic silt-sand mixtures, and high
fines content/high plasticity sandy clays, and then to develop volumetric strain material models
for those soils. A total of 14 different clean sands, 8 silty sands, and one relatively plastic clay
were tested.
The sands were tested to characterize the effect of sand compositional factors on vertical
strain from seismic compression. The sands were selected to span a range of material gradation,
particle size and particle shape, and. specimens were prepared to varying levels of relative
density and saturation. As expected, vertical strains were found to decrease with increasing
relative density. No statistically significant trends in the variation of vertical strains with soil
compositional parameters were observed. However, vertical strains were found to decrease with
increasing secant shear modulus.
Artificial mixtures of sand and silt materials were used to manufacture the silty sand
materials. A series of eight different silty sands that span a range of fines contents (FC), relative
compaction (RC) levels, and degrees-of-saturation (S) were tested. The effect of intermediate S
≈ 30% was found to decrease vertical strains relative to values for dry and high saturation
conditions. The observed variation with saturation is likely related to matric suction in the soil.
Lastly, the effect of increasing FC was found to increase the seismic compression susceptibility
when using constant RC as a basis for comparison.
ii
The silty, sandy clay material is a natural soil with FC ≈ 77% and PI = 27. Specimens of the
soil were prepared to two relative compaction levels (RC = 87 and 92%) at degrees of saturation
that fall on the wet and dry sides of the line of optimums. It was found that soils with high
plasticity (PI = 27) can experience seismic compression, although the magnitudes of the vertical
strains are approximately one-half of those for PI = 15 soils. The trends of vertical strain with RC
and S are similar to those for PI = 15 soils, although the RC effect is not measurable for high
saturations (about 90%) and the S effect does not appear for RC = 92%.

iii
ACKNOWLEDGMENTS
Support for this work was provided by Subcontract No. 10 between the Consortium of
Universities for Research in Earthquake Engineering (CUREE) and the Regents of the University
of California, with funding provided by the California Earthquake Authority (CEA). Additional
support was provided by a CAREER grant from the National Science Foundation (NSF Award
No. 9733113) and the Cota Robles Fellowship at the University of California, Los Angeles (to
Pendo Duku). The views and conclusions contained in this document are those of the authors and
should not be interpreted as necessarily representing the official policies, either expressed or
implied, of the U.S. Government, CUREE, or the CEA.
Thanks are extended to Nirun Tungkongphanit, who helped provide soil materials tested in
this research. Thanks are also extended to Ryan Bulatao for his assistance in testing shape factors
for clean sands, and to Professor Wesley W. Chu and Dr. Yu Chen for their assistance with data
mining of the laboratory test data for sands.


iv
v
TABLE OF CONTENTS
ABSTRACT..................................................................................................................................iii
ACKNOWLEDGMENTS.............................................................................................................v
TABLE OF CONTENTS...........................................................................................................vii
LIST OF FIGURES.....................................................................................................................xi
LIST OF TABLES.......................................................................................................................xv
1 INTRODUCTION..............................................................................................................1
1.1 Compacted Structural Fills......................................................................................1
1.2 Observed Behavior of Structural Fills during Earthquakes.....................................2
1.3 Motivation and Objectives of Present Study...........................................................5

2 PREVIOUS LABORATORY STUDIES OF SEISMIC COMPRESSION..................7

2.1 Introduction..............................................................................................................7
2.2 Previous Investigations of Seismic Compression in Clean Sands...........................7
2.3 Previous Investigations of Seismic Compression in Compacted Soils Containing
Fines.......................................................................................................................13

3 SEISMIC COMPRESSION OF CLEAN SANDS........................................................19
3.1 Introduction............................................................................................................19
3.2 Sands Tested..........................................................................................................19
3.3 Laboratory Testing Equipment and Testing Procedures........................................23
3.3.1 General.............................................................................................................23
3.3.2 UCLA Digitally Controlled Simple Shear (UCLA-DCSS) Apparatus............23
3.3.3 Dry Specimen Preparation...............................................................................24
3.3.4 Moist Specimen Preparation............................................................................26

vi
3.4 Test Results............................................................................................................26
3.4.1 Data Reduction.................................................................................................26
3.4.2 Effects of Relative Density..............................................................................30
3.4.3 Effect of Saturation..........................................................................................32
3.4.4 Effect of Compositional Factors and Shear Stiffness......................................34
3.4.5 Effects of Specimen Preparation......................................................................41
3.4.6 Effects of Number of Cycles............................................................................42

4 SEISMIC COMPRESSION OF NON-PLASTIC SILTY SANDS..............................45
4.1 Introduction............................................................................................................45
4.2 Soils Tested............................................................................................................45
4.3 Testing Protocol.....................................................................................................49
4.4 Results of Cyclic Simple Shear Tests....................................................................50
4.4.1 Form and Parameterization of Results.............................................................50
4.4.2 Effect of Density..............................................................................................53
4.4.3 Effect of Saturation..........................................................................................55
4.4.4 Effect of Fines Content....................................................................................58
4.4.5 Effect of Number of Cycles.............................................................................65

5 SEISMIC COMPRESSION OF A HIGH-PLASTICITY CLAY...............................69
5.1 Introduction............................................................................................................69
5.2 Soil Tested.............................................................................................................69
5.3 Testing Protocols...................................................................................................71
5.4 Results of Cyclic Simple Shear Tests....................................................................72

vii
6 ANALYSIS PROCEDURE FOR SEISMIC COMPRESSION...................................75
6.1 Introduction............................................................................................................75
6.2 Tokimatsu and Seed Procedure for Clean Sands...................................................76
6.3 Procedure for Compacted Fill Soils.......................................................................78
6.4 Volumetric Strain Material Models.......................................................................83
6.4.1 Clean Sands......................................................................................................83
6.4.2 Soils with Non-Plastic Fines............................................................................86
6.4.3 Soils with Variable-Plasticity Fines.................................................................87

7 SUMMARY AND CONCLUSIONS..............................................................................91
7.1 Scope of Research..................................................................................................91
7.2 Research Findings and Recommendations............................................................93
7.3 Recommendations for Future Research.................................................................94

REFERENCES.............................................................................................................................97












viii





ix
LIST OF FIGURES
Figure 1.1 Typical geometries of compacted fills.....................................................................2
Figure 1.2 Site locations where fill movements caused significant damage during
Northridge earthquake.............................................................................................3
Figure 1.3 Schematic showing typical damage to fill slope......................................................5
Figure 2.1 Effect of relative density on settlement of dry sand
(Silver and Seed, 1971)
.............8
Figure 2.2 Settlement-number-of-cycles-relationships for D
R
= 60% (Silver and Seed,
1971)........................................................................................................................9
Figure 2.3
Comparison of vertical strains at 10 cycles for Ottawa sand at D
R
= 80% (Youd,
1972) and Crystal Silica sand at D
R
= 80% (Silver and Seed, 1971)
..............................10
Figure 2.4
Comparison of settlements of sand from shaking table tests performed (a) under
uni-directional and bi-directional stress-controlled loading and (b) under three-
directional stress-controlled loading (Pyke et al., 1975)
...............................................12
Figure 2.5 Volumetric strains measured in sandy soils with variable levels of
saturation (a) during undrained shear, (b) during post-shear consolidation,
and (c) sum of strains during and following shear Source: Tsukamoto et al.
(2004).....................................................................................................................13
Figure 2.6 Relationship between shear strain and vertical strain at N = 10 cycles for
fill material at Jensen Filtration Plant (after Pyke et al., 1975).............................14
Figure 2.7 The effect of w on settlements of a low-plasticity clay for N = 3, 10, and
40 cycles (Chu and Vucetic, 1992)........................................................................15
Figure 2.8 Seismic compression test results for low-plasticity silty sand (Whang et
al., 2004)................................................................................................................18
Figure 2.9 Seismic compression test results for medium-plasticity clayey sand
(Whang et al., 2004)...............................................................................................18
Figure 3.1 Grain size distributions of tested sands..................................................................20
Figure 3.2 Particle shape distribution for Vulcan sand...........................................................21
Figure 3.3 Digitally Controlled Simple Shear (UCLA-DCSS) apparatus...............................24
Figure 3.4 Specimen preparation equipment...........................................................................25
Figure 3.5 Typical cyclic simple shear test results (Irwindale Sand, γ
c
= 0.77%, D
R
=
60%).......................................................................................................................27

x
Figure 3.6 Volumetric strain model (Flint No. 13 at D
R
= 60%)............................................28
Figure 3.7 Seismic compression test results for 14 tested clean sands...................................29
Figure 3.8 Hysteretic curve for estimating secant shear modulus (Vulcan sand)...................30
Figure 3.9 Effect of density for dry sands (S = 0%)................................................................31
Figure 3.10 Effect of density at S = 30%..................................................................................31
Figure 3.11 Effect of density at S = 60%..................................................................................31
Figure 3.12 Effect of saturation on Vulcan sand.......................................................................33
Figure 3.13 Effect of saturation on Silica No. 2 sand...............................................................33
Figure 3.14 Effect of compositional factors on ε
v,N=15

c
= 0.2%)..........................................37
Figure 3.15 Effect of compositional factors on ε
v,N=15
(γ = 0.5%)............................................38
Figure 3.16 Effect of compositional factors on ε
v,N=15
(γ = 0.8%)............................................39
Figure 3.17 Effect of stiffness on seismic compression............................................................40
Figure 3.18 Effect of specimen preparation (test on Vulcan sand, D
R
= 60%, S = 0%)...........41
Figure 3.19 Histogram of R values for clean sands and fit of normal distribution to
data.........................................................................................................................42
Figure 3.20 Variation of slope parameter R for clean sand with various parameters...............43
Figure 4.1 Grain size distribution curve for sands and silt used in study...............................46
Figure 4.2 Correlation between matric suction and Whatman No. 42 filter paper.................47
Figure 4.3 Variation of index void ratios with silt content.....................................................49
Figure 4.4 Representative cyclic simple shear test result (Vulcan 50-50 mix, RC =
87%, γ
c
= 0.3%).....................................................................................................51
Figure 4.5 Volumetric strain model (Vulcan 50-50 mix)........................................................52
Figure 4.6 Volumetric strain model (Vulcan 50-50 mix)........................................................54
Figure 4.7 Effect of density on Silica 50-50 mix (incomplete data set for (b))......................54
Figure 4.8 Effect of saturation on Vulcan 50-50 mix..............................................................55
Figure 4.9 Effect of saturation on Silica 50-50 mix................................................................55

xi
Figure 4.10 Variation of normalized seismic compression with saturation..............................56
Figure 4.11 Variation of matric suction with saturation...........................................................57
Figure 4.12 Index void ratios at RC = 87%...............................................................................59
Figure 4.13 Effect of silt content on seismic compression of Vulcan host sand.......................61
Figure 4.14 Effect of silt content on seismic compression of Silica #2 host sand....................61
Figure 4.15 Seismic compression of pure silt at S = 0%...........................................................62
Figure 4.16 Effect of non-plastic fines on liquefaction resistance (Polito and Martin,
2001)......................................................................................................................64
Figure 4.17 Vulcan host sand: variation of R with (a) FC, (b) RC and (c) S............................67
Figure 4.18 Silica No. 2 host sand: variation of R with (a) FC, (b) RC and (c) S.....................68
Figure 5.1 Grain size distribution curve for the tested plastic clay soil..................................70
Figure 5.2 Results of Atterberg limits tests for clayey soil.....................................................70
Figure 5.3 Modified Proctor compaction curve for clayey soil..............................................71
Figure 5.4 Volumetric strains for high plasticity clayey soil..................................................73
Figure 5.5 Values of slope parameter R for high plasticity clayey soil...................................73
Figure 6.1 Variation of median values of N with distance and magnitude from Liu et
al. (2001) along with recommendations of Seed et al. (1975)...............................79
Figure 6.2 Modulus reduction curves from Iwasaki et al. (1978), Darendeli and
Stokoe (2001), and Vucetic and Dobry (1991) re-expressed in format for
estimation of shear strain amplitude, showing effects of effective
overburden stress and soil plasticity......................................................................81
Figure 6.3 Volumetric strains for clean sands at D
r
= 60%....................................................84
Figure 6.4 Volumetric strain models for clean sands at D
r
= 45%, 60%, and 80%................85
Figure 6.5 Volumetric strains for 50-50 sand-silt mixtures....................................................86
Figure 6.6 Volumetric strains for low plasticity fine-grained soil (PI = 2, LL = 27)
Source: Whang et al. (2004)..................................................................................88
Figure 6.7 Volumetric strains for medium plasticity fine-grained soil (PI = 15, LL =
33) Source: Whang et al. (2004)............................................................................89

xii
Figure 6.8 Volumetric strains for high plasticity fine-grained soil (PI = 27, LL = 47)..........90
xiii
LIST OF TABLES
Table 3.1 Index properties of tested sands.............................................................................20
Table 3.2 Particle shape classification scheme......................................................................22
Table 3.3 Shape factors for all tested sands...........................................................................22
Table 4.1 Sand-silt mixtures utilized in testing program.......................................................48


xiv





1
1 INTRODUCTION
1.1 COMPACTED STRUCTURAL FILLS
Structural fills are earth structures that are placed to create level building pads for building
construction. In hillside areas, these fills are generally constructed in wedge shapes and placed
along hillsides (as shown in Figure 1.1a) or are placed in canyons (Figure 1.1b).
There are a number of processes that can lead to deformations of compacted structural fills.
Static, long-term processes include hydro-compression, consolidation, and slope creep (e.g.,
Lawton et al., 1989; Brandon et al., 1990). Seismic processes include seismic slope instability
and seismic compression (e.g., Stewart et al., 2001). Deformations resulting from the above
processes can be damaging to the building structures, and hence engineers generally design fills
so as to minimize future ground deformations. Such analysis procedures are well developed for
static processes (e.g., Houston et al., 1988 for hydro-compression), but significant work remains
to be done before reliable ground deformation analysis procedures can be developed for seismic
applications.
The focus of the research described in this report is on seismic compression, which is defined
as volumetric strain accumulation in unsaturated soil during earthquake shaking. Seismic
compression only occurs in compacted fills whose voids are not fully filled with water (i.e.,
unsaturated soils); when such soils experience seismically induced shear deformations, the soil
grains tend to settle into a denser configuration.
2

Original
ground surface
Slope terrace
Another
building
pad below
1 to 2 m
overexcavation
Canyon fill
Excavated former ridges
Wedge Fill
Canyon Fill
(a)
(b)

Fig. 1.1. Typical geometries of compacted fills
1.2 OBSERVED BEHAVIOR OF STRUCTURAL FILLS DURING EARTHQUAKES
The performance of structural fills during earthquakes has been documented both in general field
reconnaissance and in detailed studies of specific sites. The reconnaissance work involves
observing the general characteristics of ground deformations across many sites. The detailed
studies involve more intensive examination of the geotechnical and damage characteristics at a
few specific sites (e.g., Pyke et al., 1975; Stewart et al., 2004). The focus here is on the general
reconnaissance work to establish the motivation for this research.
The performance of structural fills during earthquakes has been documented following the
1906 San Francisco, 1971 San Fernando, and 1994 Northridge earthquakes. Lawson (1908)
summarized observations of ground cracking in hillside areas from the 1906 San Francisco
earthquake by noting “roadways and artificial embankments were particularly susceptible to …
cracks.” After the 1971 San Fernando earthquake, McClure (1973) noted the influence of fills
on damage patterns, particularly when residences were constructed over cut/fills contacts. This
3
study found that “…ground failure occurred on a higher percentage of sites that were on fill or
cut and fill than those sites which were on cut or natural grade” and “dwellings on cut and fill or
fill had more relative damage than dwellings on cut or natural grade.”
After the 1994 Northridge earthquake, Stewart et al. (2001) documented locations of about
250 sites where fill movements caused damage. As shown in Figure 1.2, concentrated damage
occurred on the north flank of the Santa Monica Mountains, along the north rim of the San
Fernando Valley, and in the Santa Clarita Valley area. Other affected areas include isolated
portions of the south flank of the Santa Monica Mountains and portions of Simi Valley.
SURFACE PROJECTION OF
APPROXIMATE FAULT RUPTURE PLANE
EPICENTER
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Simi
Valley
Burbank
Malibu
Universal
City
Pacific
Palisades
M
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SANTA
Los
Angeles
Pasadena
Glendale
Granada
Hills
Hollywood
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San
Fernando
Canoga
Park
Northridge
Culver
City
Santa
Clarita
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Calabasas
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WALD AND HEATON (1994)

Fig. 1.2. Site locations where fill movements caused significant damage during Northridge
earthquake (Stewart et al., 2001)

The data in Figure 1.2 can be used to roughly evaluate the levels of shaking that were
required during the Northridge earthquake for seismic compression of fills to be a significant
problem. Areas with significant damage such as Sherman Oaks, the northern San Fernando
4
Valley, and Santa Clarita had peak accelerations in the range of 0.4 to 0.8 g (Chang et al., 1996),
whereas outlying areas where incidents of seismic compression induced damage are relatively
sparse (e.g., Calabasas, Universal City) had levels of shaking < 0.4 g. Based on analyses of
typical fill geometries reported in Stewart et al. (2001), approximate levels of peak shear strain
corresponding to those acceleration levels are generally on the order of > 0.1% in the areas with
damage and < 0.1% in areas without significant damage. Those shear strain levels can be
contrasted with volumetric threshold shear strains (i.e., the shear strains below which no volume
change would be expected) of γ
tv
≈ 0.01-0.02% for sands and γ
tv
≈ 0.04-0.09% for clays having
PI ≈ 30 (Hsu and Vucetic, 2004).
As seen in Figure 1.3, typical damage patterns at the mapped fill deformation sites included:
ƒ Cracks near cut/fill contacts: typically < 8 cm of lateral extension and 3 cm of
localized differential settlement relative to cut
ƒ Lateral extension in fill pad: observed in the form of tensile cracking parallel to the
top of the slope, which typically caused 3-10 cm of horizontal or vertical offsets.
ƒ Differential settlement on fill surfaces: observed as cracks with vertical offsets and
tilted floors and swimming pools.
ƒ Slope-face bulging: characterized by movement of surface drains running cross-slope
(terrace drains) and down-slope (down drains).
5
Cracking near
cut/fill contact
Ground cracks from
lateral extension
Settlement
Face bulging


Fig. 1.3. Schematic showing typical damage to fill slope (Stewart et al., 2001)

In order to objectively evaluate the significance of fill site conditions on damage patterns,
Stewart et al. (2001) compiled a complete inventory of damage within a subdivision with both
fill and cut sites. By comparing damage patterns for the two site conditions, an objective
assessment of the impact of fill materials on site performance was made. The results showed that
all broken water pipes were on fill near the cut/fill contact area. Moreover, damage to structures
was much more severe on fill and cut/fill sites that on cut sites. Those results clearly
demonstrated the significance of fill site conditions on damage patterns.
1.3 MOTIVATION AND OBJECTIVES OF PRESENT STUDY
Largely because of the significant damage that occurred to structures as a result of seismic
compression induced by the 1994 Northridge earthquake, there has been increasing demand
within the engineering profession for seismic compression analysis procedures that can be
utilized in practice. For example, in their report to the Governor of California following the 1994
Northridge earthquake, the California Seismic Safety Commission recommended that
“Seismically induced deformation caused by seismic compaction of fill and underlying alluvium
(should) be considered in the design and construction of residential fills.” More recently, the
6
California Geological Survey (CGS) has required analysis of seismic compression as part of the
design process for critical projects such as school and hospital structures (CGS, 2004).
The state-of-practice method for seismic compression analysis consists of a procedure by
Tokimatsu and Seed (1987), which is intended for application to clean sands. The principal
reason that the procedure is only applicable to clean sands is that a key component of the
procedure that relates shear strain demand and number of strain cycles to volumetric strains
(herein termed a volumetric strain material model) is based solely on laboratory test data for
clean sands by Silver and Seed (1971). The procedure has recently been extended to soil with
large fines content and low plasticity by Stewart and Whang (2003), and both procedures are
recommended for application by CGS (2004). However, these two procedures remain extremely
limited in their applicability, because they only apply for a few specific soil characteristics, and
thus they are not broadly applicable. Accordingly, there is a major research need for laboratory
testing to establish volumetric strain material models that cover a broader range of soil types.
The principal objectives of this research were to address this need by performing testing for soils
types that had not previously been investigated, and to develop from those results volumetric
strain material models that can be used in practice.
The remainder of this report is organized into five chapters. Chapter 2 describes previous test
results related to seismic compression. Chapters 3 – 5 describe the results of testing programs
that investigated the seismic compression behavior of clean sands, sands with non-plastic fines,
and high fines content/high plasticity materials, respectively. Chapter 6 presents a simplified
analysis procedure for seismic compression, which is an update to the Stewart and Whang (2003)
procedure. Finally, the report is concluded in Chapter 7 with a summary of the research results
and recommendations for future research.
7
2 PREVIOUS LABORATORY STUDIES OF
SEISMIC COMPRESSION
2.1 INTRODUCTION
The term “seismic compression” is used to describe volumetric strain accumulation in
unsaturated soil during earthquake shaking. Previous laboratory-based investigations of seismic
compression can be broadly divided into (1) a suite of studies on clean sands, mostly performed
in the late 1960s and early 1970s, but with some recent additions as well, and (2) a number of
studies regarding soils containing fines. That previous work is reviewed in this chapter. The
chapter is concluded by summarizing the critical conditions that had not been investigated at the
onset of this study, and by noting the conditions investigated herein.
2.2 PREVIOUS INVESTIGATIONS OF SEISMIC COMPRESSION IN CLEAN SANDS
The original studies of seismic compression were performed by Silver and Seed (1971), Youd
(1972), Seed and Silver (1972), and Pyke et al. (1975), who used laboratory testing to investigate
the volumetric strains induced in dry, clean sands undergoing cyclic loading with zero mean
(static) shear stress. Tsukamoto et al. (2004) has performed recent testing on sands to evaluate
the effect of saturation on the relative amounts of pre- and post-shaking volume change.
Silver and Seed (1971) and Seed and Silver (1972) performed strain-controlled simple shear
testing using an NGI-type device on dry quartz sand (Crystal Silica No. 20). The specimens were
prepared by dry pluviating a preweighed amount of sand, and then vibrating it to a specified
8
height such that the target density (D
R
= 45, 60, and 80%) was achieved. The tests were
performed by first applying a specified vertical stress to the specimen (values of σ
v
’ = 24, 96,
and 192 kN/m
2
were used), and then subjecting the specimens to a uniform cyclic shear strain
amplitude that varied from γ
c
= 0.01 to 0.5%. Continuous readings of vertical deformation were
made that enabled vertical strains to be evaluated as a function of the number of strain cycles
(N). Figure 2.1 shows a summary of test results at N = 15 cycles of loading for the three relative
densities. The vertical strain was seen to increase with cyclic shear strain amplitude, and to
decrease with increasing relative density. The vertical strains were found to be negligible below
a limiting value of shear strain. Denoted γ
tv
, this limiting strain has since come to be known as
the volumetric threshold shear strain (Vucetic, 1994). Typical values of threshold shear strains
for sands are γ
tv
= 0.01 to 0.02% (Hsu and Vucetic, 2004).

Fig. 2.1. Effect of relative
density on settlement of dry
sand (Silver and Seed, 1971)


9
The dependence of vertical strain on the number of strain cycles was relatively consistent for
the suite of test results, as shown in Figure 2.2. These results demonstrate a characteristic feature
of seismic compression, which is that a significant fraction of the overall volumetric strain
occurs within the first few cycles (e.g., 50% of the volumetric strain at 15 cycles occurs within
the first 3 cycles), and relatively little deformation occurs for N > 100. Several suites of tests
were performed at different vertical stresses (σ’
v
), but vertical strain was found to not be
significantly affected by σ’
v
.

Fig. 2.2. Settlement-number-of-cycles-relationships for D
R
= 60% (Silver and Seed, 1971)

Youd (1972) investigated seismic compression of Ottawa sand using simple shear laboratory
testing with an NGI-type device. The specimens were prepared by pouring sand into a membrane
and in some cases, vibrating the top cap to densify the specimen. Youd performed one subset of
tests on specimens that were saturated, consolidated under vertical stresses of σ’
v
= 5, 48 and 192
kN/m
2
, and then sheared under drained conditions. Volume change was monitored by a water
column (equipped with a pressure transducer) that was connected to the specimen. A second
subset of tests was performed using air-dry specimens. In both subsets of tests, specimens were
10
generally prepared to relative densities of D
R
= 70–80%. For each test, sinusoidal loading was
applied at a constant frequency that was varied from test-to-test across the range of f = 0.2 to 1.9
Hz. During an individual test, shear strain amplitudes varied somewhat with time as a result of
compliance in the loadcell. Accordingly, applied shear strains were reported as a range rather
than as a unique value.
The results of selected tests on Ottawa sand are presented in Figure 2.3, with the Silver and
Seed results also indicated for comparison. The Ottawa sand results confirm the finding of Silver
and Seed that vertical strains increase with increasing shear strain, but the vertical strains are
systematically higher (by factors of 4 to 6) than those of Silver and Seed for Crystal Silica No.
20 sand. The reasons for this difference are unknown. The results of Youd’s tests investigating
saturation and frequency of loading effects revealed no significant influence of either factor.

0.001 0.01 0.1 1
Shear Strain (%)
10
1
0.1
0.01
0.001
V
e
r
t
i
c
a
l

S
t
r
a
i
n

(
%
)
Test Series
Silver & Seed (1971)
Youd (1972)

Fig. 2.3. Comparison of vertical strains at 10 cycles for Ottawa sand at D
R
= 80% (Youd,
1972) and Crystal Silica sand at D
R
= 80% (Silver and Seed, 1971)
11
Pyke et al. (1975) investigated the seismic compression of dry Monterey No. 0 sand using
large-scale specimens tested on a shaking table. The disk-shaped specimens were prepared to D
R

= 40, 60, and 80% by raining sand from a spreader box into a 7.6 cm deep form, temporarily
mounted on top of the shaking table. The form was slightly overfilled and the excess sand was
removed with a screed. The specimens had sloping lateral boundaries, which were enclosed by a
rubber membrane. Vertical stresses were applied by the weight of a steel cap (7.7 kN/m
2
) placed
on top of the sand and vacuum pressures applied to the specimen. All testing was performed
under stress-controlled conditions, and the shear strains that occurred during the tests were not
reported.
The intent of the shaking table tests by Pyke et al. (1975) was to evaluate the effect of multi-
directional shaking (two horizontal directions and one vertical). The results of uni-directional, bi-
directional (two horizontal directions of shaking), and tri-directional (two horizontal and one
vertical direction of shaking) are compared in Figure 2.4. Based on the results, Pyke et al.
surmised that the settlements caused by the combined horizontal motions are about equal to the
sum of the settlements caused by the horizontal stresses acting separately. Since peak
accelerations in two horizontal directions are often similar, Pyke et al. recommended that
settlements under bi-directional shear generally be taken as about twice those under uni-
directional shear. Moreover, as indicated by the results in Figure 2.4, Pyke et al. found that
vertical accelerations superimposed on horizontal accelerations could cause an additional
increase in the settlements of as much as 50%.
12

Fig. 2.4. Comparison of settlements of sand from shaking table tests performed (a) under uni-
directional and bi-directional stress-controlled loading and (b) under three-directional
stress-controlled loading (Pyke et al., 1975)

Tsukamoto et al. (2004) performed a series of cyclic triaxial tests on sand specimens with
about 20% nonplastic fines. The specimens were prepared to consistent relative densities but
varying levels of saturation, and were sheared under undrained conditions. Volumetric strains
were monitored both during shaking and after the conclusion of shaking. Figures 2.5 (a) and (b)
show the relationship between volumetric and shear strains observed during shaking (2.5a) and
following shaking (2.5b). As expected, vertical strains during shaking are small for high
saturations and large for low saturations, with the converse being true for post shaking strains.
Figure 2.5c shows that the total volumetric strain is approximately the same for all three levels of
saturation. This implies that saturation does not significantly affect the seismic compression
(taken as total vertical strain) of this sandy material.

13





Fig. 2.5. Volumetric strains measured in sandy soils with variable levels of saturation (a)
during undrained shear, (b) during post-shear consolidation, and (c) sum of strains during
and following shear. Source: Tsukamoto et al. (2004)
2.3 PREVIOUS INVESTIGATIONS OF SEISMIC COMPRESSION IN
COMPACTED SOILS CONTAINING FINES
Pyke et al. (1975) performed a limited number of cyclic simple shear tests on a well-graded
clayey sand (SC) for back-analysis of settlements that occurred at the Jensen Filtration Plant
during the 1971 San Fernando earthquake. Tests were performed on an NGI-type apparatus at
14
one water content (w = 10%) and two Modified Proctor (ASTM D1557) densities (RC = 84.4 and
92%) under cyclic strain-controlled loading (γ
c
= 0.1 to 0.4%). The simple shear apparatus used
for this testing was the same as that used by Silver and Seed (1971). Figure 2.6 shows the
vertical strains obtained by Pyke et al. at 10 cycles of loading along with the Silver and Seed
results for sands at D
R
= 60% (a reasonable estimate of D
R
given the RC range of the fine-grained
fill soil). These test results indicate that vertical strains for the clayey sand were < 1/3 of the
vertical strains in sand at a comparable density. Another important finding from Pyke et al. is the
lack of sensitivity of seismic compression to variations in confining stress. As shown in Figure
2.6, Pyke et al. tested the Jensen fill under two vertical stresses (σ
v
= 95 and 191 kPa) and found
no detectable variation in vertical strain.
0 0.2 0.4 0.6 0.8
Shear Strain (%)
0.8
0.6
0.4
0.2
0
V
e
r
t
i
c
a
l

S
t
r
a
i
n

a
t

1
0

C
y
c
l
e
s

(
%
)
Jenson Fill, σ
v
= 95 kPa
Jenson Fill, σ
v
= 191 kPa
Clean Uniform Sand,
Silver & Seed (1971), D
R
= 60%
RC = 84.4%
RC = 92%

Fig. 2.6. Relationship between shear strain and vertical strain at N = 10 cycles for fill
material at Jensen Filtration Plant (after Pyke et al., 1975)

15
Chu and Vucetic (1992) investigated seismic compression of a low-plasticity (PI = 10.5)
clay using an NGI-type simple shear device. The testing was performed at three water contents at
very high relative compaction levels (Modified Proctor RC between 95 and 100%). Figure 2.7
shows the variation of vertical strain (ε
v
) with γ
c
for N = 3, 10 and 40 cycles of loading. From
these test results, Chu and Vucetic concluded that (1) for γ
c
> 0.1%, ε
v
for compacted clay
significantly increases with γ
c
and N, (2) ε
v
for this particular compacted clay does not depend
significantly on w for small γ
c
, and (3) the volumetric threshold strain, γ
tv
, of this compacted clay,
i.e., the shear strain below which the settlement is negligible, is around 0.1%.

Fig. 2.7. The effect of w on settlements of a low-plasticity clay for N = 3, 10, and 40 cycles
(Chu and Vucetic, 1992)

16
With respect to the second conclusion, it should be noted that specimens at different w in
this testing program also had different preconsolidation Modified Proctor RC, which ranged from
95% to 100%. Hence, the effect of w was not truly isolated from the effect of RC in these tests.
Moreover, the large compaction effort needed to produce the high RC in the tested samples
would be expected to break down macro-structural features such as clods that might have been
present at lower densities. Accordingly, the apparent lack of dependence of ε
v
on w in this testing
may not be applicable to the lower RC levels.
Hsu and Vucetic (2004) performed a similar set of tests to those reported above for Chu and
Vucetic (1992). In the more recent testing program, seven different sands and clays were
prepared to different saturations and tested in simple shear to evaluate the volumetric threshold
shear strain, γ
tv
. The threshold strains were found to be γ
tv
≈ 0.01-0.02% for sands and γ
tv
≈ 0.04-
0.09% for clays having PI ≈ 30.
Hsu and Vucetic (2004) interpret their findings for a range of saturations in a manner similar
to that of Tsukamoto et al. (2004) – namely, vertical strains occurring during shear are
distinguished from those occurring following shear. Hsu and Vucetic (2004) found that the
strains during shear are significantly impeded if the degree of saturation of the specimen is ≥
90%. The density of the specimens tested by Hsu and Vucetic was not maintained at consistent
values from specimen-to-specimen, and are not reported relative to a common standard such as
relative compaction. Accordingly, the results cannot be compared to those from other studies
discussed in this document.
Whang et al. (2004) performed a laboratory testing program on fill soils containing
significant fines with varying levels of fines plasticity. Testing was performed on four specimens
with nearly 50% fines contents and PI ranging from 2 to 15. The seismic compression
17
susceptibility of each specimen was evaluated using strain-controlled cyclic simple shear
laboratory testing with the UCLA digitally-controlled simple shear (UCLA-DCSS) apparatus.
Each soil material was compacted to a range of formation dry densities and degrees-of-
saturation.
The results for a low plasticity soil (PI = 2) are summarized in Figure 2.8. Figure 2.8a shows
a small effect of Modified Proctor relative compaction (RC) between RC ≈ 92 and 94%, and
negligible effects of as-compacted degree of saturation. Figure 2.8b compares the test results for
this low plasticity soil with fines to results for an equivalent clean sand prepared to a compatible
relative density. The results indicate that the soil with low plasticity fines experiences less
seismic compression than clean sands.
The results for a medium-plasticity soil (PI = 15) are summarized in Figure 2.9. Figure 2.9a
shows that the seismic compression decreases not only with increasing RC, but also for moderate
RCs decreases with increasing as-compacted degree-of-saturation (S). As shown in Figure 2.9b,
at low S, volumetric strains from seismic compression are comparable to those for sand (at a
common RC), whereas at high S the strains are approximately one-quarter of those for sand.
18
(a)
0.1 1
Shear strain,
γ
c
(%)
0
0.5
1
1.5
2
2.5
Vertical strain,
εv,N=15
(%)
Low Plasticity Soil (PI = 2)
RC = 90-92%; S = 55-80%
RC = 90-92%; S = 80-99%
RC = 93-95%; S = 55-80%
RC = 93-95%; S = 80-99%
RC = 90 - 92%
RC = 93 - 95%
(b)

Fig. 2.8. Seismic compression test results for low-plasticity silty sand (Whang et al., 2004)
(a)
0
0.5
1
1.5
2
2.5
Vertical Strain,
ε
v,N=15
(%)
0.1 1
Shear Strain,
γ
c
(%)
Moderate Plasticity Soil
S=87%
S=74%
S=61%
S=53%
RC=88%
RC=84%
RC=92%
(b)

Fig. 2.9. Seismic compression test results for medium-plasticity clayey sand
(Whang et al., 2004)
19
3 SEISMIC COMPRESSION OF CLEAN SANDS
3.1 INTRODUCTION
As described in Chapter 2, the first studies investigating the seismic compression of clean sands
were performed during the late 1960s and early 1970s, and were complimentary to the studies
investigating the dynamic response of saturated sands. While studies investigating the
liquefaction behavior of saturated sands would ultimately examine a myriad of compositional
and environmental factors, the seismic compression work was considerably more limited in
scope. Accordingly, an extensive laboratory testing program was undertaken to characterize the
effects of gradation, grain size, particle shape and saturation on seismic compression. That work
is the subject of this chapter.
3.2 SANDS TESTED
The cyclic simple shear testing program utilized 14 clean sand materials. The sands were
selected to span a range of material gradation, particle size and particle shape. Compositional soil
properties of the tested sands are presented in Table 3.1, and the grain size distribution curves are
shown in Figure 3.1. The maximum and minimum densities and void ratios of each of the sands
(shown in Table 3.1) were determined by the Modified Japanese method and dry tipping,
respectively. Those techniques are comparable to ASTM D4253 and D4254, respectively.
20
Table 3.1. Index properties of tested sands.

Sand D
10
(mm)
D
30
(mm)
D
50
(mm)
C
u
C
c
e
min
e
max
e
DR=60%

Flint#13

0.42

0.5

0.56

1.43

0.99

0.545

0.811

0.651

Flint#16

0.28

0.41

0.5
0

2.11

1.02

0.530

0.822

0.646

F
-
52

0.18

0.25

0.28

1.
72

1.12

0.533

0.837

0.658

F
-
110

0.0
8

0.1
0

0.13

1.90

0.84

0.616

0.884

0.722

Silica
#
0

0.65

0.77

0.89

1.45

0.97

0.674

0.983

0.797

Silica #2

1.4
0

1.5
0

1.6
0

1.29

0.89

0.689

1.016

0.820

Post O
f
fice

0.1
0

0.17

0.29

5
.00

0.72

0.449

0.706

0.553

Vulcan

0.21

0.3
7

0.51

2.90

1.07

0.501

0.839

0.634

Crystal
0.55

0.6
0

0.81

1.62

0.74

0.705

1.072

0.851

Nevada

0.15

0.17

0.19

1.30

0.99

0.553

0.907

0.694

Irwindale


0.3
0

0.61

1.00

4.67

0.89

0.485

0.749

0.591

Pacoima #1

0.15

0.25

0.38

3.07

0.91

0.564

0.920

0.7
05

Pacoima #3

0.22

0.35

0.55

3.18

0.80

0.535

0.882

0.674

Newhall

0.0
8

0.18

0.37

4.38

0.41

0.546

0.945

0.705



100 10 1 0.1 0.01
Grain Size (mm)
0
20
40
60
80
100
P
e
r
c
e
n
t

P
a
s
s
i
n
g

(
%
)
Pacoima No. 1
Pacoima No. 3
Flint No. 13
Flint No. 16
F-52
F-110
Irwindale Sand
Silica No. 2
Silica No. 0
Crystal Silica No. 30
Vulcan
Newhall
Post Office
Nevada
4 10 20 40 60 100 200
US Standard Sieve
Gravel
Coarse
MediumFine
Soil Type
Coarse
Fine
Sand
Silt/Clay

Fig. 3.1. Grain size distributions of tested sands
21
Particle shape was characterized for each sand using image analysis techniques similar to
those used by Zettler et al. (2000). Each soil was separated into three equal weight fractions by
grain size: coarse, medium and fine. Digital photographs of approximately 500 particles for each
soil fraction were taken and subsequently analyzed to quantify individual particle shapes using
Sigma ProScan™ V.5, a commercially available image analysis software program. The particle
shapes were characterized using a shape factor, which was defined as (Zettler et al., 2000):

2
)(
)4(
perimeter
area
S
f

=
π
(3.1)
Shape factor S
f
is one for a circle and zero for a line. The shape factors were found to have a log-
normal distribution based on Chi-Square statistical testing. Accordingly, a median in arithmetic
units and standard deviation in natural logarithmic units were computed for each weight fraction.
A typical distribution for one the tested sands (Vulcan) is shown in Figure 3.2. The computed
shape factors were then used to characterize the particle angularity based on the classification
scheme given in Table 3.2. The particle shape factors and shape classifications for all tested
sands are presented in Table 3.3.
0.5 0.6 0.7 0.8 0.9
1
S
h
a
p
e

F
a
c
t
o
r
0
20
40
60
F
r
e
q
u
e
n
c
y

Fig. 3.2. Particle shape distribution for Vulcan sand
22



Table 3.2. Particle shape classification scheme.
_______________________________________________________________
Particle Shape Shape Factor (S
f
)
_______________________________________________________________
Rounded S
f
≥ 0.823
Subrounded 0.823 >S
f
≥ 0.776
Subangular 0.776 > S
f
≥ 0.688
Angular 0.688 > S
f

_______________________________________________________________


Table 3.3. Shape factors for all tested sands.


Fine (S
f
) Medium (S
m
) Coarse (S
c
)
Sand Mean Std Mean Std Mean Std
Flint#13
0.876 0.074 0.864 0.083 0.873 0.067
Flint#16
0.811 0.114 0.784 0.136 0.809 0.132
F-52
0.829 0.127 0.820 0.127 0.806 0.125
F-110
0.939 0.146 0.943 0.121 0.852 0.113
Silica #0
0.782 0.073 0.789 0.066 0.790 0.054
Silica #2
0.731 0.095 0.744 0.083 0.733 0.092
Post Office
0.881 0.136 0.846 0.083 0.720 0.113
Vulcan
0.839 0.114 0.820 0.070 0.643 0.148
Crystal Silica #30
0.792 0.111 0.751 0.109 0.703 0.151
Nevada
0.951 0.118 0.999 0.120 0.866 0.089
Irwindale
0.829 0.110 0.719 0.136 0.548 0.205
Pacoima #1
0.956 0.148 0.809 0.106 0.837 0.080
Pacoima #3
0.845 0.102 0.832 0.094 0.711 0.131
Newhall
n/a n/a 0.945 0.113 0.695 0.117

23

3.3 LABORATORY TESTING EQUIPMENT AND TESTING PROCEDURES
3.3.1 General
Cyclic simple shear tests were performed under drained conditions to evaluate vertical strain
accumulation when uniform-amplitude cycles of shear strain are applied to the soil specimen.
Commercially available wire-reinforced membranes were used to laterally confine the cylindrical
soil specimens, which were prepared to a diameter of 102 mm and a height of 23 mm. These
membranes minimized lateral expansion of the test specimens, while providing negligible shear
stiffness. Since the effect of overburden pressure on vertical strain has previously been found to
be minor (e.g., Silver and Seed 1971, Youd 1972, Pyke et al. 1975), all tests were performed
under the same vertical stress of 101.3 kPa. A sinusoidal loading frequency of 1 Hz was used to
induce cyclic shear strain amplitudes between 0.1% ≤ γ
c
≤ 1.0%.
3.3.2 UCLA Digitally Controlled Simple Shear (UCLA-DCSS) Apparatus
The UCLA Digitally Controlled Simple Shear (UCLA-DCSS) apparatus, shown in Figure 3.3,
was used in this study. The UCLA-DCSS was designed using the UC Berkeley Bi-Directional
Cyclic Simple Shear apparatus (Boulanger et al., 1993) as a prototype. The UCLA-DCSS retains
all of the main features of the UCB-2D device such as inclusion of cell pressure for purposes of
backpressure saturation, limited mechanical compliance with respect to simple shear boundary
conditions (e.g. top and base platen “rocking”), and bi-directional loading capability. In addition
to these features, UCLA-DCSS incorporates several design improvements, including (a) the use
a tri-post frame with high performance track bearings to further reduce rocking; (b) a digitally
controlled hydraulic control system to allow for high frequency loading and high-precision
24
control; (c) a dual axis load cell to obtain post-friction shear stress measurements. Further details
on the UCLA-DCSS device are provided by Whang (2001).

Fig. 3.3. UCLA Digitally Controlled Simple Shear (UCLA-DCSS) apparatus
3.3.3 Dry Specimen Preparation
Dry specimens (S = 0%) were prepared using a dry pluviation method similar to that used by
Silver and Seed (1971) and Whang et al. (2004). A pre-weighed amount of oven-dried sand was
poured into a wire-reinforced membrane that was pre-mounted to the bottom specimen cap with
a screen placed at the base as shown in Figure 3.4(a). Then, the screen was pulled up through the
specimen to give each specimen essentially the same initial structure. After flattening the
specimen and mounting the top specimen cap, a high frequency (60 Hz) vibrator, shown in
Figure 3.4(b), was placed on the top cap to densify the specimen to a predetermined height that
would achieve the target relative density after application of the vertical stress of 1.0 atm.

25




(a) (b)
Fig. 3.4. Specimen preparation equipment
A small subset of dry sand specimens were also prepared using tamping and kneading
compaction methods to evaluate the effect of different specimen preparation techniques. In the
tamping method, specimens were prepared in two lifts using the same wire reinforced membrane
and compaction mold as shown in Figure 3.4(a). A pre-weighed amount of oven-dried sand was
loosely placed and gently tamped to a pre-determined height to achieve the target relative density
after application of 1.0 atm of vertical stress. The kneading method uses a Harvard miniature
compactor to induce shear strains during compaction and replicate what occurs in the field with a
sheepsfoot roller. The kneading compaction technique is commonly used for soils with fines, but
was adapted for clean sands in this study. This method is procedurally similar to the tamping
method, with the exception of kneading rather than tamping to densify the specimen.
26

3.3.4 Moist Specimen Preparation
Tamping and kneading compaction methods were used to prepare specimens at S > 0% to
evaluate the effect of saturation on the seismic compression behavior of clean sands. Water was
added to a pre-determined amount of oven-dried sand to achieve moisture contents
corresponding to saturation levels of S = 30, 60 and 90% at various relative densities. The
moistened sands were then allowed to cure for 24 hours in sealed buckets to ensure uniform
mixing, after which specimens were prepared using the tamping and kneading compaction
methods as described in the previous section.
3.4 TEST RESULTS
3.4.1 Data Reduction
The results of a typical strain-controlled cyclic simple shear test are shown in Figure 3.6
(Irwindale Sand, γ
c
= 0.77%, D
R
= 60%). Essentially uniform cyclic shear strain amplitudes are
achieved through a slight increase in the applied shear load during the first few cycles until the
soil’s shear modulus has stabilized. The soil’s equivalent shear modulus is essentially constant
after 10 cycles of loading. As shown in Figure 3.5(c), the majority of vertical strain accumulation
occurs within the first few cycles of loading.
27
-75
-50
-25
0
25
50
75
Shear Load (lbs)
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
Shear Strain (%)
0 5 10 15 20 25
Time (s)
0
0.25
0.5
0.75
1
1.25
1.5
1.75
Average Vertical Shear Strain (%)
(a)
(b)
(c)

Fig. 3.5. Typical cyclic simple shear test results (Irwindale Sand, γ
c
= 0.77%, D
R
= 60%)
A cyclic simple shear test can be summarized by the relationship between (a) γ
c
, the uniform
cyclic shear strain amplitude and (ε
v
)
N=15
,

the vertical strain associated with 15 cycles of loading
and (b) C
N
, the normalized vertical strain defined as (ε
v
)
N
/(ε
v
)
N=15
, versus N, the number of strain
cycles. These two relationships comprise the volumetric strain material model which can be
used in a simplified analysis procedure to estimate ground settlement from seismic compression
(Tokimatsu and Seed, 1987; Stewart and Whang, 2003).
28
For a specific sand, data from multiple simple shear tests at various cyclic shear strain
amplitudes (γ
c
) are available, as shown for example in Figure 3.6(a). A γ
c
-(ε
v
)
N=15
relationship is
defined using a power function curve-fit through the data as follows:

( )
b
tvcNv
a γγε −=
=15,
(3.2)

Where a, b, and γ
tv
are material-specific constants.
As shown in Figure 3.6(b), for a specific sand, the C
N
-N relationship is log-linear and hence
can be described by the following expression:
cNRC
N
+= )ln( (3.3)
All sands must have C
N
= 1 at N = 15, which implies that intercept parameter c = 1- ln(15)×R.
Consequently, the C
N
-N relationship for a given soil is fully described by slope parameter R. The
log-linear fit is shown in Figure 3.6 by the line.
1 10 100
Number of Cycles, N
1.4
1.2
1
0.8
0.6
0.4
0.2
Normalized Vertical Strain, C
N =
εv,N/εv,N=15
R
C
N
= R ln(N) + c
N=15
0.01 0.1 1
Shear Strain,
γ
c
(%)
0
0.4
0.8
1.2
Vertical Strain,
εv,N=15
(%)
ε
v,N=15
= a

c
-
γ
tv
)
b
(a)
(b)

Fig. 3.6. Volumetric strain model (Flint No. 13 at D
R
= 60%)
Figure 3.7(a) shows the γ
c
-(ε
v
)
N=15
data points for all tested sands at D
R
= 60% spanning a
range of sand compositional factors (gradation, grain size, particle shape), while Figure 3.7(b)
29
shows the median ± two standard deviations for C
N
based on the test results for all 14 sands. The
Silver and Seed (1971) results for Crystal Silica No. 20 sand are also included in both figures as
a basis for comparison.
0.01 0.1 1
Shear Strain,
γ
c
(%)
0
0.5
1
1.5
2
2.5
Vertical strain,
εv,N=15
(%)
14 Sands
D
R
= 60%
Silver and Seed, 1971
0 5 10 15 20 25
Number of Cycles, N
1.5
1.25
1
0.75
0.5
0.25
0
CN =
εv/εv, N=15
Range for clean sand (µ ± 2σ)
Mean, Silver & Seed (1971)
(a) (b)

Fig. 3.7. Seismic compression test results for 14 tested clean sands
In addition to the above parameters related to vertical strains, secant shear moduli (G) for
the soil specimens were computed for each cyclic simple shear test. This was done so that
potential effects of soil stiffness on seismic compression behavior could be investigated. The
shear modulus at a given γ
c
was computed by fitting a secant line through the shear stress-shear
strain hysteresis loop produced from the first half-cycle of loading as shown in Figure 3.8a. For
a specific sand, data from multiple tests at various γ
c
were used to construct a plot of G versus γ
c

which can be described by the following expression:

e
c
dG γ=
(3.4)
where d and e are material specific constants used to describe the sand. An example fit of Eq. 3.4
through the data is shown in Figure 3.8b.
30
-0.4 -0.2 0 0.2 0.4
Shear Strain (%)
-4
-2
0
2
4
Shear Stress (psi)
G
1
0 0.2 0.4 0.6 0.8
1
Shear strain,
γ
c
(%)
0
1
2
3
4
Secant shear modulus, G (psi)
(a)
(b)

Fig. 3.8. Hysteretic curve for estimating secant shear modulus (Vulcan sand)
3.4.2 Effect of Relative Density
A subset of simple shear tests was performed on three sands (Crystal Silica No. 30, Vulcan and
Silica No. 2) to characterize the effect of relative density on sand seismic compression. Figure
3.9 shows the variation of seismic compression with relative density between D
R
= 45, 60 and
80% at S = 0%. As expected, increasing relative density decreases (ε
v
)
N=15
, which is consistent
with previous findings for dry sands (Silver and Seed, 1971; Youd, 1972).
Additional tests were performed for Vulcan and Silica No. 2 sands to characterize the effect
of density across different saturations. Figures 3.10 and 3.11 show the test results for Vulcan and
Silica No. 2 sands at S = 30 and 60%, respectively. The tests on partially saturated specimens
were performed at high relative densities (D
R
= 80 and 100%) because it was difficult to prepare
loose specimens using kneading compaction specimen preparation techniques. As shown in
Figure 3.10, at S = 30%, the effect of density is similar to that for dry sand. At S = 60%, there is
no clear effect of density between D
R
= 80 and 100%.
31
0.11
Shear strain (%)
0
0.4
0.8
1.2
1.6
2
Vertical Strain,
ε
v,N=15
(%)
Silica #2
DR=45%
DR=60%
DR=80%
DR=100%
0.0010.010.11
Shear strain (%)
0
0.4
0.8
1.2
1.6
2
Vertical Strain,
ε
v,N=15
(%)
Crystal Silica
DR=60%
DR=80%
0.11
Shear strain (%)
0
0.4
0.8
1.2
1.6
2
Vertical Strain,
ε
v,N=15
(%)
Vulcan
DR=45%
DR=60%
DR=80%
(a)
(b)
(c)

Fig. 3.9. Effect of density for dry sands (S = 0%)
0.11
Shear Strain (%)
0
0.2
0.4
0.6
0.8
Vertical Strain,
ε
v,N=15
(%)
Vulcan
DR=80%
DR=100%
0.1
1
Shear Strain (%)
0
0.2
0.4
0.6
0.8
Vertical Strain,
ε
v,N=15
(%)
Silica No. 2
DR=80%
DR=100%
(a)
(b)

Fig. 3.10. Effect of density at S = 30%
32
0.1 1
S
h
e
a
r

S
t
r
a
i
n

(
%
)
0
0.2
0.4
0.6
0.8
1
Vertical Strain,
εv,N=15
(%)
Vulcan
D
R
=80%
D
R
=100%
0.1
1
S
h
e
a
r

S
t
r
a
i
n

(
%
)
0.2
0.4
0.6
0.8
1
Vertical Strain,
εv,N=15
(%)
Silica No. 2
D
R
=80%
D
R
=100%
(a)
(b)

Fig. 3.11. Effect of density at S = 60%
3.4.3 Effect of Saturation
Figures 3.12 and 3.13 show results of simple shear tests performed across a wide range of
saturations on Vulcan and Silica No. 2 sands, respectively. For each sand material, specimens
were prepared to S = 0, 30, 60 and 90% at relative densities of D
R
= 60, 80 and 100%.
Specimens at higher densities (D
R
= 80 & 100%) could not be prepared to S = 90% since they
approached the zero voids line. The results showed no consistent effect of saturation, with most
of the test results falling within the expected scatter of the seismic compression test data.
The above findings are generally consistent with the results of Tsukamoto et al. (2004),
which were discussed in Section 2.2. Tsukamoto et al. (2004) investigated the effect of
saturation (50 ≤ S ≤ 100%) on the volume change behavior of a non-plastic sandy soil subjected
to undrained shear and post-shaking re-consolidation. Tsukamoto et al. observed no effect of
saturation on the total volume change (i.e., sum of volume change during and following
shaking). In our tests, post-shaking volume change was negligibly small because the tests were
performed under drained conditions.
33
0.010.11
Shear Strain (%)
0
0.5
1
1.5
2
2.5
Vertical Strain,
ε
v,N=15
(%)
D
R=60%
S=0%
S=30%
S=60%
S=90%
0.11
Shear Strain (%)
0
0.2
0.4
0.6
0.8
Vertical Strain,
ε
v,N=15
(%)
DR=80%
S=0%
S=30%
S=60%
0.11
Shear Strain (%)
0
0.1
0.2
0.3
0.4
0.5
Vertical Strain,
ε
v,N=15
(%)
DR=100%
S=0%
S=30%
S=60%
(a)
(b)
(c)

Fig. 3.12. Effect of saturation on Vulcan sand
0.010.11
Shear Strain (%)
0
0.4
0.8
1.2
1.6
2
2.4
Vertical Strain,
ε
v,N=15
(%)
D
R=60%
S=0%
S=30%
S=60%
S=90%
0.11
Shear Strain (%)
0.2
0.4
0.6
0.8
1
Vertical Strain,
ε
v,N=15
(%)
DR=80%
S=0%
S=30%
S=60%
0.11
Shear Strain (%)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Vertical Strain,
ε
v,N=15
(%)
DR=100%
S=0%
S=30%
S=60%
(a)
(b)
(c)

Fig. 3.13. Effect of saturation on Silica No. 2 sand
34
3.4.4 Effect of Compositional Factors and Shear Stiffness
Figure 3.7(a) shows that the range of (ε
v
)
N=15
for clean sands can vary by more than a factor of
three even if specimens are prepared using the same method and tested at similar D
R
, S and
loading conditions. Conversely, Figure 3.7(b) shows that the C
N
-N relationship exhibits little
variability for the 14 tested sands. The purpose of this section is to investigate whether the
significant variability in the vertical strain data is truly random, or whether there are consistent
variations in (ε
v
)
N=15
with “secondary” factors such as compositional parameters or soil stiffness.
Due to the relatively small variability in the C
N
-N data, such effects are not investigated for slope
parameter R (defined in Eq. 3.3)
Our investigation of the dependence of vertical strains on secondary factors consists of
looking for trends in plots of (ε
v
)
N=15
data relative to composition/stiffness parameters. As shown
in Figure 3.6(a), the data for a given sand can possess significant variability, which could
potentially mask relatively weak data trends when comparisons are made between sands.
Therefore, we smooth individual test results (such as those shown in Figure 3.6a) by fitting Eq.
3.2 through the γ
c
-(ε
v
)
N=15
data, and by taking estimates from the regression equation at γ
c
= 0.2,
0.5 and 0.8% as vertical strain parameters to be utilized for trend identification. These
parameters are denoted ε
v,N=15
(γ = 0.2%), ε
v,N=15
(γ = 0.5%) and ε
v,N=15
(γ = 0.8%). In addition
to removing noise associated with intra-material data scatter, the use of these vertical strain
parameters also provides vertical strains at an exact γ
c
, which more easily facilitates comparisons
across different materials than the direct use of test data.
Figures 3.14-16 show trends in vertical strain parameters with soil compositional parameters
such as Coefficient of Uniformity (C
U
= D
60
/D
10
), median particle size (D
50
) and particle shape.
35
The results do not suggest the presence of a statistically significant trend in vertical strains with
respect to any of the investigated compositional factors.
These results can be compared with results of undrained liquefaction testing performed
across a range of material gradations by Kokusho et al. (2004) and Kuerbis et al. (1988).
Kokusho et al. (2004) performed a series of stress-controlled undrained tests on clean sands and
gravels with different particle gradations and different relative densities. Despite large
differences in gradation, for a given relative density, only small differences between materials
were observed in the cyclic stress required to initiate liquefaction. While Kokusho et al. found
the undrained monotonic shear strength at much larger strains to be affected by gradation, the
relatively small strain liquefaction triggering stresses are more appropriate for comparisons to
our results, which are associated with small cyclic shear strains. The liquefaction trigging results
are in close agreement with our findings with respect to the effects of gradation. Kuerbis et al.
(1988) identified apparent effects of C
U
and D
50
on the undrained behavior of sands subjected to
monotonic and cyclic triaxial testing (soil was reported to be more contractive as uniformity
increases and grain size increases). However, relative density in the tests was not carefully
controlled, which makes it difficult to reliably evaluate the effects of secondary compositional
factors on the soil behavior.
The effect of soil stiffness on vertical strain parameters is shown in Figure 3.17. For the
purpose of these comparisons, soil stiffness is taken as the secant shear modulus at γ
c
= 0.5%,
and is denoted G
γ=0.5%
. As shown in Figure 3.17, vertical strain parameters decrease with
increasing stiffness, sometimes by as much as a factor of three for a similar set of baseline
conditions, (i.e., compaction and loading).
36
It is important to recognize the context in which the above effect of shear modulus is
expressed by the data in Figure 3.17. It is well known that for a given ground surface motion at a
site, soil shear strains decrease with increasing shear stiffness, which will in turn result in
reduced volumetric strains. That effect is of first order importance in a seismic compression
analysis, and is considered in existing analysis procedures (e.g., Tokimatsu and Seed, 1987).
That effect is not what is expressed in Figure 3.17. Rather, the figure shows vertical strains for
fixed levels of shear strain, and illustrates the dependence of vertical strain parameters on shear
modulus as a “secondary” parameter.
The above effect of shear modulus on vertical strain parameters has not been previously
observed. The studies described in Chapter 2 by Seed and Silver (1971) and Youd (1972)
indirectly investigated the potential for such effects, because the simple shear tests in those
studies were run at varying confining stresses, which in turn resulted in varying shear moduli.
Since the effect of confining pressure on the γ
c
-(ε
v
)
N=15
relationship was found to be negligible,
by inference the effect of shear modulus must also have been negligible (since overburden
pressure affects shear modulus). However, the apparent contradiction between our results and the
previous results can be explained as follows. Seed and Silver (1971) and Youd (1972) utilized a
single material, and found no dependence of vertical strain on shear modulus for that material.
The present study utilized many materials, and the observed dependence of vertical strain on
shear modulus is likely associated with unquantified compositional factors that vary between
soils, and which both increase shear stiffness and decrease seismic compression susceptibility.
While we were unable to identify those compositional factors, as a practical matter it appears that
shear stiffness (or shear wave velocity) may be a useful parameter at both the primary and
secondary levels for evaluation of seismic compression susceptibility.
37
0.70.750.80.850.90.951
Fine Shape Factor, S
f
0.1
0.2
0.3
0.4
0.5
ε
v,N=15
(
γ
= 0.2%)
0.70.80.91
Medium Shape Factor, S
m
0.1
0.2
0.3
0.4
0.5
ε
v,N=15
(
γ
= 0.2%)
0.50.60.70.80.9
Coarse Shape Factor, S
c
0.1
0.2
0.3
0.4
0.5
ε
v,N=15
(
γ
= 0.2%)
00.40.81.21.6
D
10 (mm)
0.1
0.2
0.3
0.4
0.5
ε
v,N=15
(
γ
= 0.2%)
00.40.81.21.6
D
50
(mm)
0.1
0.2
0.3
0.4
0.5
ε
v,N=15
(
γ
= 0.2%)
12345
Uniformity Coefficient, C
u
0.1
0.2
0.3
0.4
0.5
ε
v,N=15
(
γ
= 0.2%)
(a)
(b)(c)
(d)
(e)
(f)

Fig. 3.14. Effect of compositional factors on
ε
v,N=15
(
γ
c = 0.2%)
38
0.70.750.80.850.90.951
Fine Shape Factor, S
f
0.2
0.4
0.6
0.8
1
1.2
ε
v,N=15
(
γ
= 0.5%)
0.70.80.91
Medium Shape Factor, S
m
0.2
0.4
0.6
0.8
1
1.2
ε
v,N=15
(
γ
= 0.5%)
0.50.60.70.80.9
Coarse Shape Factor, S
c
0.2
0.4
0.6
0.8
1
1.2
ε
v,N=15
(
γ
= 0.5%)
00.40.81.21.6
D
10 (mm)
0.2
0.4
0.6
0.8
1
1.2
ε
v,N=15
(
γ
= 0.5%)
00.40.81.21.6
D
50
(mm)
0.2
0.4
0.6
0.8
1
1.2
ε
v,N=15
(
γ
= 0.5%)
12345
Uniformity Coefficient, C
u
0.2
0.4
0.6
0.8
1
1.2
ε
v,N=15
(
γ
= 0.5%)
(a)
(b)(c)
(d)
(e)
(f)

Fig. 3.15. Effect of compositional factors on
ε
v,N=15
(
γ
= 0.5%)
39
0.70.750.80.850.90.951
Fine Shape Factor, S
f
0.4
0.8
1.2
1.6
2
ε
v,N=15
(
γ
= 0.8%)
0.70.80.91
Medium Shape Factor, S
m
0.4
0.8
1.2
1.6
2
ε
v,N=15
(
γ
= 0.8%)
0.50.60.70.80.9
Coarse Shape Factor, S
c
0.4
0.8
1.2
1.6
2
ε
v,N=15
(
γ
= 0.8%)
00.40.81.21.6
D
10 (mm)
0.4
0.8
1.2
1.6
2
ε
v,N=15
(
γ
= 0.8%)
00.40.81.21.6
D
50
(mm)
0.4
0.8
1.2
1.6
2
ε
v,N=15
(
γ
= 0.8%)
12345
Uniformity Coefficient, C
u
0.4
0.8
1.2
1.6
2
ε
v,N=15
(
γ
= 0.8%)
(a)
(b)(c)
(d)
(e)
(f)

Fig. 3.16. Effect of compositional factors on
ε
v,N=15
(
γ
= 0.8%)
40
1.21.41.61.8
Secant shear modulus, G
s,γ=0.5%
(psi)
0.1
0.2
0.3
0.4
0.5
ε
v,N=15
(
γ
= 0.2%)
1.21.41.61.8
Secant shear modulus, G
s,
γ=0.5%
(psi)
0.2
0.4
0.6
0.8
1
1.2
ε
v,N=15
(
γ
= 0.5%)
1.21.41.61.8
Secant shear modulus, G
s,γ=0.5%
(psi)
0.4
0.8
1.2
1.6
2
ε
v,N=15
(
γ
= 0.8%)
(a)
(b)
(c)

Fig. 3.17. Effect of stiffness on seismic compression
41
3.4.5 Effects of Specimen Preparation
Dry specimens of the Vulcan sand were prepared using dry pluviation, tamping and kneading
compaction to study the effects of specimen preparation. All tests were performed at D
R
= 60%
and S = 0%. The results are shown in Figure 3.18, and indicate no dependence of vertical strains
on the method of specimen preparation.
The findings in Figure 3.18 can be compared to several studies that investigated specimen
preparation effects on the results of both stress- and strain-controlled undrained liquefaction
tests. Previous stress-controlled testing programs have reported a significant specimen
preparation effect on the undrained behavior of sands (e.g., Mulilis et al., 1977; Ladd, 1974;
Vaid et al., 1999). However, strain-controlled liquefaction tests by Dobry and Ladd (1980) found
specimen preparation effects to be negligible, which is consistent with the results presented
herein.

0.1
1
S
h
e
a
r

S
t
r
a
i
n

(
%
)
0.4
0.8
1.2
1.6
2
Vertical Strain,
εv,N=15
(%)
Tamping
Dry pluviation
Harvard miniature

Fig. 3.18. Effect of specimen preparation
(test on Vulcan sand, D
R
= 60%, S = 0%)
42
3.4.6 Effects of Number of Cycles
As described in Section 3.4.1, the variation of normalized volumetric strain parameter C
N
=

v
)
N
/(ε
v
)
N=15
with number of cycles N is approximately log-linear, as described by Eq. 4.3. This
log-linear relationship is completely described by slope parameter R. In this section, the cyclic
simple shear test results are interpreted to evaluate R as a function of soil and test parameters.
Figure 3.19 presents a histogram of the R data. The data is found to be normally distributed
at a significance level of 99.5% per the Chi Square test (Ang and Tang, 1975, page 274). The
mean of the normal distribution is 0.33, and the standard deviation is 0.04.

0.20 0.24 0.28 0.32 0.36 0.40 0.44
Slope parameter, R
0
4
8
12
F
r
e
q
u
e
n
c
y

(
%
)
Mean = 0.33
σ
=0.04

Fig. 3.19. Histogram of R values for clean sands and fit of normal distribution to data

Figure 3.20 shows a summary of the R parameter for all the tested sands plotted against
shear strain amplitude (γ
c
), relative density (D
r
), degree of saturation (S), and shear modulus (G).
Linear regression curves fit through the data are shown on the figures along with their 95%
confidence intervals. The fit curves are seen to not have a significant slope, which is confirmed
43
by hypothesis testing that reveals that the level of confidence with which a zero slope model can
be rejected is 27% for γ
c
, 14% for D
r
, 70% for S, and 28% for G. This rejection confidence
should generally be greater than 90 to 95% before the slope can be considered significant. Given
the lack of dependence of R on these parameters, for practical purposes it is appropriate to take R
as the mean value of 0.33.

0 0.2 0.4 0.6 0.8 1
γ
c
(%)
0.2
0.3
0.4
0.5
R
± 95% significance level
Mean ± 1 sd

40 50 60 70 80 90
D
R

(%)
0.2
0.3
0.4
0.5
R

0 20 40 60 80
S (%)
0.2
0.3
0.4
0.5