The Japanese Geotechnical Society NII-Electronic Library Service The JapaneseGeotechnical Society SOILS AND FOUNDATIONS Japanese GeoLechnical SocietyVol. 48, No. 2, 255-265, Apr. 2008 IN-SITUEVALUATION OF STRENGTH AND DILATANCY SANDS BASED ON CPT RESULTS OF JuNHwAN LEEi),JoNGwAN EuNiD,KyuNGsuK LEEM),YOUNGHwAN PARKi") and MINKI KIMiV) ABSTRACT ln-situ testshave been increasingly used to estimate the shear strength of soils. In this paper, we propose methods to evaluate in-situ strength and dilatancy of sandy soils based on cone penetration test (CPT) results. Ittakes into account the silt content, relative density and stress state of the sand. A series of laboratory test results from fundamental property testsand triaxial testsare analyzed to developmethods for in-situ evaluation of strength and dilatancy for sands, Based on testresults, modified and simplified dilatancy equations, interms of the cone penetration resistance q, and intrinsic soil variables, are proposed. Results from proposed and original dilatancy indexes show close agreements forvarious soil conditions, Values of intrinsic variables forthe proposed dilatancy relationships were proposed as a function of silt content. Based on TX testresults, a direct CPT-based correlation, applicable to both clean and silty sands, is proposed as well. In order to verify the proposed methods, calibration chamber CPT results obtained inthis study and collected from the literature are adopted. Itisobserved that the results from the proposed methods show good agreement with the measured results. Key words: calibration chamber, CPT, dilatancy, D6/E2) friction angle, in-situ test,sands, shear strength, triaxial test (IGC: INTRODUCTION The shear strength of soils is the key design property that governs the stability of geotechnical structures and thus safety of overall structures, For clays, the undrained shear strength (s.) iscommonly adopted in design, while the friction angle ( ¢ ') is the sole property that represents the shear strength of sands, Estimation of these proper- ties is still a challenging task for geotechnical engineers, primarily due to complex soil constitutions, non- homogeneity, and non-linearity of soil behavior. For sandy soils, the challenge iseven greater, as strength is highlystate-dependent and undisturbed soil sampling is not an economically and practically feasible option, As a result, various empirical correlations based on in-situ test results, such as SPT blow count IVsipT from the standard penetration test (SPT) or cone resistance q, from the cone penetration test (CPT), have been proposed (Dunham, 1954; Durgunoglu and Mitchell, 1975; Robertson and Campanella, 1983; Chen and Juang, 1996), Application of IVkpT to the estimation of ¢ ' has been popular in practice. Results from itare however subject- ed to various uncertainties due to crude correlations be- tween O' and IVsipT and experimental procedure of SPT. In this context, the CPT-based approach may be a better alternative since the cone resistance q, itself represents state-dependent strength characteristics of soils and con- tinuous depth profiles ef q, can be obtained. Less ex- perimental uncertainties of CPT due to automated data acquisition system and quasi-static penetration mechan- ism is another important advantage, There have been several methods for the estimation of the shear strength in sands using CPT results, defining direct correlations between q. and the peak friction angle ipS. While these have provided useful tools forthe interpretation of CPT measurements, further investigation isstill necessary as no specific consideration of the state-dependent dilatancy and soil constitution were addressed in detail. The peak friction angle of granular soils consists ef two components: the critical-state friction angle and the dilatancy angle (Bolton, 1986). The critical-state friction angle isan intrillsic soil variable, independentof stress- state, history, and density, The dilatancy angle, on the other hand, isa state soil variable that varies with relative density DR and confining stress. In order to quantify the dilatancy angle of sandy soils, several stress-dilatancy models have been proposed (DeJosselin de Jong, 1976; Bolton, 1986),While these models have been validated experimentally and analytically for known soil and stress states, direct application to fieldconditions is not yet /)ibm)i") Associate Professor, School of Civil& Environmental Engineering, Yonsei Ulliversity, Korea "[email protected]). Post-Master Research Assistant,ditto. Geotechnical Engjneer, Division of Geoteehnical Design, Hyundai Construction, Co. Ltd., Korea. GraduaLe Research Assistant,School ef Civil & Environmental Engineering, Yonsei University,Korea. The manuscript forthis paper was received for review on July 20, 2007; approved on November 22, 2007. Writtcn discussions oii this paper should be submitted before Novernber 1, 20e8 te tbe Japanese Geotech]ical Society, 4-38-2, Sengoku, Bunkyo-ku, Tokyo 112-OOI1, Japan. Upon rcquest the closing date may be extended onc month. 255 NII-Electionic
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In-situevaluation of Strength and Dilatancy Sands Based on Cpt Results
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The Japanese Geotechnical Society
NII-Electronic Library Service
The JapaneseGeotechnical Society
SOILS AND FOUNDATIONS
Japanese GeoLechnical SocietyVol.
48, No. 2, 255-265, Apr. 2008
IN-SITUEVALUATION OF STRENGTH AND DILATANCY
SANDS BASED ON CPT RESULTS
OF
JuNHwAN LEEi),JoNGwAN EuNiD, KyuNGsuK LEEM),YOUNGHwAN PARKi") and MINKI KIMiV)
ABSTRACT
ln-situ tests have been increasingly used to estimate the shear strength of soils. In this paper, we propose methods toevaluate in-situ strength and dilatancy of sandy soils based on cone penetration test (CPT) results. It takes into account
the silt content, relative density and stress state of the sand. A series of laboratory test results from fundamentalproperty tests and triaxial tests are analyzed to develop methods for in-situ evaluation of strength and dilatancy forsands, Based on test results, modified and simplified dilatancy equations, in terms of the cone penetration resistance q,and intrinsic soil variables, are proposed. Results from proposed and original dilatancy indexes show close agreements
for various soil conditions, Values of intrinsic variables for the proposed dilatancy relationships were proposed as a
function of silt content. Based on TX test results, a direct CPT-based correlation, applicable to both clean and silty
sands, is proposed as well. In order to verify the proposed methods, calibration chamber CPT results obtained in thisstudy and collected from the literature are adopted. It is observed that the results from the proposed methods show
friction angle, in-situ test,sands, shear strength, triaxial test (IGC:
INTRODUCTION
The shear strength of soils is the key design propertythat governs the stability of geotechnical structures and
thus safety of overall structures, For clays, the undrained
shear strength (s.) is commonly adopted in design, whilethe friction angle (¢ ')
is the sole property that representsthe shear strength of sands, Estimation of these proper-ties is still a challenging task for geotechnical engineers,
primarily due to complex soil constitutions, non-
homogeneity, and non-linearity of soil behavior. Forsandy soils, the challenge is even greater, as strength ishighly state-dependent and undisturbed soil sampling isnot an economically and practically feasible option, As a
result, various empirical correlations based on in-situ test
results, such as SPT blow count IVsipT from the standard
penetration test (SPT) or cone resistance q, from the cone
penetration test (CPT), have been proposed (Dunham,1954; Durgunoglu and Mitchell, 1975; Robertson and
Campanella, 1983; Chen and Juang, 1996),
Application of IVkpT to the estimation of ¢'
has been
popular in practice. Results from it are however subject-
ed to various uncertainties due to crude correlations be-tween O' and IVsipT and experimental procedure of SPT.
In this context, the CPT-based approach may be a better
alternative since the cone resistance q, itself represents
state-dependent strength characteristics of soils and con-
tinuous depth profiles ef q, can be obtained. Less ex-
perimental uncertainties of CPT due to automated dataacquisition system and quasi-static penetration mechan-
ism is another important advantage, There have beenseveral methods for the estimation of the shear strength
in sands using CPT results, defining direct correlations
between q. and the peak friction angle ipS. While these
have provided useful tools for the interpretation of CPTmeasurements, further investigation is still necessary as
no specific consideration of the state-dependent dilatancyand soil constitution were addressed in detail. The peak friction angle of granular soils consists ef twocomponents: the critical-state friction angle and thedilatancy angle (Bolton, 1986). The critical-state frictionangle is an intrillsic soil variable, independent of stress-
state, history, and density, The dilatancy angle, on theother hand, is a state soil variable that varies with relative
density DR and confining stress. In order to quantify the
dilatancy angle of sandy soils, several stress-dilatancy
models have been proposed (DeJosselin de Jong, 1976;
Bolton, 1986), While these models have been validated
experimentally and analytically for known soil and stress
states, direct application to field conditions is not yet
/)ibm)i")Associate Professor, School of Civil & Environmental Engineering, Yonsei Ulliversity, Korea "[email protected]).Post-Master Research Assistant, ditto.
Geotechnical Engjneer, Division of Geoteehnical Design, Hyundai Construction, Co. Ltd., Korea.GraduaLe Research Assistant, School ef Civil & Environmental Engineering, Yonsei University, Korea.The manuscript for this paper was received for review on July 20, 2007; approved on November 22, 2007.Writtcn discussions oii this paper should be submitted before Novernber 1, 20e8 te tbe Japanese Geotech]ical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-OOI1, Japan. Upon rcquest the closing date may be extended onc month.
255
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256 LEE ET AL.
fully possible as soil and stress states in the field are not,
in general, known unless extensive soil exploration is per-formed.
In the present study, we propose methodology to esti-
mate the in-situ strength and dilatancy characteristics of
sandy soils based on the CPT cone resistance q.. The vaTi-
ables evaluated in this study include the silt content ofthe
sand, relative density and confining stress. A series of
laboratory test results obtained for various soil condi-
tions are used in the analysis and investigation. For each
soil and stress condition, cone penetration analysis is per-formed and used to develop the CPT-based methodology
for in-situ evaluation of dilatancy. In order to verify the
It is well known that the peak friction angle O6 of sands
is a stress- and density-dependent variable (Bolton, 1986).
The critical-state friction angle OE is on the other hand an
intrinsic soil variable, independent of stress state, history,
and density, and thus can be uniquely obtained even byusing completely disturbed samples. It follows that the
dilatancy angle (OS-OE) varies with both relative densityand confining stTess. As a result, the peak-strength enve-lope is not linear. In order to quantify the dilatancy ofsandy soils, Bolton (1986) proposed the followingrelationship based on experimental test results:
ip fi =g5t+RD・Ik (1)where RD =dilatancy ratio=3 and 5 for triaxial and
plane-strain conditions, respectively. The dilatancy indexIl・ is given by:
lt=Ib [e-ln (10;.a""P)]-R (2)
where Ib == relative density as a number between O and 1;
pA=reference stress=100kPa; a:,,=mean efiective
stress at peak strength (in the same units as pA); and 9and R=intrinsic soil variables. According to Bolton
(1986), values of e and R are equal to 10 and 1 for clean
quartz sands, respectively. As Bolton's dilatancy re-
lationship of Eqs. (1) and (2) reflects effects of both rela-
tive density and confining stress, it has been widely used
and adopted for strength evaluation of sands experimen-
tally and analytically.
As indicated by Eq, (2), state variables that control the
dilatancy of sands are DR and ofu. DR is a state soil varia-
ble that is uniquely defined for given soil conditions. As
alnp represents the mobilized mean effective stress at peak,it depends on a number of factors, includjng initial verti-cal and horizontal effective stress (oC-o and afio), DR, andother state and intrinsic soil variables. For laboratory test
conditions, where stress and soil conditions are knownfor a given confining stress aC, afi. can be easily deter-
mined. Field evaluation of afi,,, however, is diMcult dueto unknown stress states mobilized upon loading. For this
reason, Eqs. (1) and (2) have not been fully applied forfield evaluation of strength. As an approximation, empir-
ical relationships are sornetimes adopted to estimate oih,.
For example, Perkins and Madson (2000) proposed asimple empirical relationship between al., and the limitunit base resistance qbL of footings:
a,'i"f-t
(o.s2-o.o4 i) (3)
where L and B=length and width of footing, respec-
tively. It can be seen that Eq, (3) still requires evaluation
of qbL, which is unknown, given by mobilized strength.
Estimation of Shear Strength Based on CPT Cone Re-
slstance
There have been several CPT-based methods for theestimation of the friction angle ipS for sands (Janbu andSunneset, 1974; Durgunoglu and Mitchell, 1975; Rober-
tson and Campanella, 1983; Chen and Junag, 1996;
Schnaid and Yu, 2007). Methods frequently used in prac-tice include those proposed by Durgunoglu and Michell(1975) and Robertson and Campanella (1983). Thesewere developed based on the bearing capacity theory and
empirical correlation between q, and Oe, respectively. De-sign application of these methods is often made through
charts that give graphical correlations between q, and ip".According to Chen and Jung (1996), the correlations be-tween q, and ¢ fi for both methods can be closely approxi-
mated by the following equation:
tan dis=a ln (qcZgCo) (4)
where a(,o=vertical effective stress at the depth of the
cone tip; Ci and Q=correlation parameters. For Dur-
gunoglu and Michell (1975) and Robertson and Cam-
panella (1983), Ci =7.629 and 6.820 and C2=O.194 and
O.266, respectively.
It is known that Robertson and Campanella's correla-
tion is suitable for medium-compressible sands, while
Dungunoglu and Mitchell's correlation is effective forlow-compressible sands. Schnaid and Yu (20e7), on theother hand, proposed a methodology for the estimation
of the state parameter, which defines dilatancy of sands,
using the cone resistance q,, This method, however, re-
quires knowledge of the initial shear modulus Go that can
be obtained from the down-hole seismic cone penetrationtest,
EXPERIMENTS FOR CHARACTERIZATION OFSHEAR STRENGTH
Tiriaxiat Zests In this study, triaxial (TX) test results from Salgado et
al. (2000) and Lee et al. (2004) were adopted for charac-terizing the shear strength of sands at various conditions.
Test soils in both Saigado et al, (2000) and Lee et al.
(2004) were Ottawa sand containing different amount of
non-plastic silts in O to 20% range by weight. The maxi-
mum silt content (s..) of 20% was considered, as the be-
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IN-SITU EVALUATION OF STRENGTH 257
havior of sandy soils at s.. up to about this limit is
governed by the larger sand particles (Salgado et al.,
2000). For fines contents above thls limit, the behavior ofthe soil is dominated by the fines (silt in this case) rather
than by the sand. Other detailed test procedures and
properties of Ottawa sand can be found in Salgado et al.
(2000) and Lee et al. (2004). Additional triaxial and fundamental property tests
were performed in this study using Jumunjin sand, a
standard sand in Korea. Test results obtained for Jumun-
jin sand will be used for the method verification that will
1OO
*- 80Y2
6oi=
40sa
¢ 20
o
O.Ol O.1 1 10
Partic[e size (mm)
Fig, i, Grain size distribution curves for Ottawa and Jumulljin sands
be discussed in Iater sections. Relative densjties in rangeof 45-90% and confining stresses in range of 50-400 kPawere considered in triaxial tests to characterize state-
dependent shear strength of Jumunjin sand. Figure 1 andTable 1 show the grain size distributions and basic soil
properties of Ottawa and Jumunjin sands.
Cltlibratii n enamber Cone Penetration 71ists
As the goal of this study is to develop CPT-basedmethodology for in-situ shear strength and dilatancy esti-
mation, calibration chamber CPTs were adopted and
used in the verification. Calibration chamber tests adopt-ed herein include those performed in this study and select-
ed from the literature. The calibration chamber used inthis study was made of steel and had a diameter andheight equal to 77,5 and 125 cm, respectively. Inside thechamber, two rubber mernbranes were attached on the
bottom and lateral sides, Through these membranes,
compressed air pressure was supplied for achieving a
Table 1. Basic soil properties of Ottawa and Jumunjin sands
"coeficjent ofun"iforml'ty, bcrl'tical state fricti6n anEie
-'
'-'
''
Oilpressurecylinder
Connectionrod
Guideframe
Coneprobe
Lateral liII/membrane
Compressedair
Bottom
l・ll/l/iil//li'i・II
llililll・llilli
llil・l・l]ll'
llii'
llllililiiiiittt/t'
:1,1././.../.
{.s.ertdiitt
f・!l?.Sim・e'l・/
illililillli/[/l
/
illlilil・i
'
iiliifilllllll・lllliiil1
membrane 111・1/-//1111,ilil
Compressedair
77.5cm
Guiderod
125 cm
(b)
(a) (c)
Fig. 2, Calibration chamber colle penetration test: (a) schematic of cnlibration chamber tesiag equipment, (b) calibration ehamber and (c) cone p"netra"en test in pTogress
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258 LEE ET AL.
desired stress state of the calibration chamber specimen.
Figure 2 shows details of the calibration chamber and
cone penetrorneter used in this study.
Calibration chamber specimens were prepared with
Jumunjin sand by the raining rnethod using a sand
diffuser. The sand diffuser consisted of a sand cQntainer
and two screen sieves (see Fig. 2(b)). The raining method
was effective to simulate the process of natural soil depo-sition, and to achieve homogeneous soil condition. Therelative density DK of the specimen was controlled by the
fall height and hole size of the sand diffuser, which were
predetermined at a desired DR through several prelimina-ry tests. Two relative densities of DR == 55 and 86% were
adopted in tests at different stress states.
The cone penetrometer used in the calibration chamber
tests in thjs study consists of the cone probe with exten-
sion rods, pushing device, depth encoder, and data acqui-
sition system. The cone probe was of a miniature type
with a diameter of 1.6cm (cross-sectional area of 2.0cm2), manufactured by AP van der Berge. The miniature
type of the cone was used to reduce the chamber size
effect that has significant effect on results of calibration
charnber tests due to limited size of the chamber. As the
cone resistance is given as a unit of pressure, the size of
the cone does not significantly affect values of the cone
resistance. In order to fit the cone penetrometer into thecalibration chamber, the pushing deice, which consisted
of the hydraulic jaek of 25-kN capacity, four steel bars,and rod connection, was specifically designed and
manufactured. For data acquisition, a 24-channel data
logger manufactured by Tokyo Sokki Kenkyujo Co.,Ltd, was used. Figure 2(c) shows details of the cone and
pushing device.
SEM 7lests
In order to investigate effects of soil fabrics on mechan-
ical properties of silty sands, scanning electron micro-
scope (SEM) tests were performed for Jumunjin sands,
Figure3 shows microphotographs of clean Jumunjinsand, silt, and silty sand obtained from SEM tests, TheJumunjin sand particles are rounded to sub-round while
the silt particles are very angular. In the case of silty sand
mixtures, silt particles tend to separate and adhere to the
larger sand particles and to fi11 voids.
According to Salgado et al. (2000) and Lee et al.
(2004), strength and stiffness of sands were found to
deerease and increase respectively with increasing fines
content. This observation may be explained, at least in in-
tuitive point of view, from the particle arrangements
shown in Fig, 3. For the initial shear modulus Go, as an
example of stifThess, the presence of silt would reduce
friction between the larger sand particles, causing a
decrease in the overall magnitude of Go with increasing
fines content, The presence of non-plastic fines, however,
would have the opposite effect on the shear strength and
dilatancy, due to the higher degree of interlocking and
wedging of the fines with the sand particles, resulting inhigher values of friction angle (Salgado et al., 2000).
・ee
(a)
(c)
'f
,ve
l$ee"g'l.
l
va
(b)
(d)
Fig. 3. SEM pictures of (a) clenn Jumunjin sand (magnification ratio
of 50), (b) non-plastic silt (magnrncntion rntio of 50), (c) no"-plns- tic silt (magpification ratio of 2000} and (d) siJt)' sand mixturc (mag- nification Tatio of 50)
CPT-BASED DILATANCY RELATIONSHIP FORIN.SITU EVALUATION OF SHEAR STRENGTH
Modiped Ditatanqy Relationship
As discussed previously, Bolton's dilatancy relation-ship given by Eqs. (1) and (2) cannot be directly applied
into field evaluation of shear strength due to the
unknown variable of afu,. In this study, rnethodology forthe field application of the dilatancy equation based on
CPT cone resistance q, is investigated. For the CPT-
based dilatancy relationship, the same framework of the
dilatancy relationship proposed by Bolton (1986) isadopted. TX test results with Ottawa sands (Salgado et
al,, 2000; Lee et al., 2004) are used in the analysis. Figure
4 shows the values of ¢ S measured from triaxial tests and
estimated using Bolton's equation, It is seen that values
of ip fi from Bolton's equation are in good agreement with
the values of ipS measured from triaxial tests.
The confining stress (oO in TX tests is routinely deter-
mined from in-situ vertical (o;o) and horizontal (aAe)stresses at a certain target depth. As illustrated in Fig. 5,for TX test of a soil at a certain depth z, aE is typically
given as the mean effective stress ahn equal to (aCo + 2aAo)f3. Based on this procedure, a series of in-situ stresses
(i.e., aC-o and ofio), equivalent to oE values adopted in TXtests, were obtained at three Kb values of O.45, O.7, and
1.0. For each in-situ stress state and DR, values of qc were
obtained from the cone penetration analysis using the
program CONPOINT, which has been widely examined
and yalidated (Salgado et al,, 1998; Salgado and Ran-dolph, 2001), The cone resistance q, from CONPOINT isdetermined using the cylindrical cavity expansion theory.
For uncemented granular soils, it is generally possible to 'wrlte:
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IN-SITU EVALUATION OF STRENGTH 259
50-ev=
45,9ts=crdi
40.e=o--o
35mE2'
3o'e"
25
1 1 1 1 1
t/ / 1
1 1--1------+--- 1
1
1 1 1ttltttttt
t t
ii,
.erk
- tvi/////
11.:-!-
/
/-1Lt!
...!... 1 1
/
i i I Q 1・ ・・ ・----
Qa ol
eloO ei
o. ..1...... 1'" i 1 1 1
t Soo = e% (Ottawa)
' . Sco=2% (Ottawa) i Sco
= 5% (Ottawa)
a Sco=1O% (Otawa)' Q Sco = 15% (Ottawa) A Sco
= 2o% (ottawa)
X Sco = O% (Jumunjin)
30
¢,
35 40 45
p from triaxial test (e}
50
1,5
1,2T.=b
O.9s2'b
O.6E'
(a)
O.3
o,o3.0
25
Comparison of thS between Bo]ton's equation and triaxial tests
O.4
O.3
4.0
Fig, 4.
rff-'
'lllll
I/I/sl// /ta;,+2・a;,
d O.2
o.ri
5.0ln(qctu'ho)6.0 7.0
z
ff q,<CPT>
Fig. 5.
fi'v/J
i g'ho
-----[?t:
<In-situstate>
eeof :
3
< Triaxial test >
Stress states for in-siin, CPT, nnd TX tcst conditions
q,=:q.(DR, a(・o, aAo) (5)
where q.=function containing intrinsic variables; DR=
relative density of sand beforepenetration; and a<,e and
aAo=initial vertical and lateral effective stresses. The de-tails of the theoretical development, evaluation, and vali-
dation of the function represented by Eq, (5) are available
in Salgado et al. (1998) and Salgado and Randolph
(2001), Figure6(a) shows relationships between the mean
efiective stress at peak aF.p, measured from TX tests forOttawa sands, and the cone resistance q, obtained fromCONPOINT with equivalent in-situ stresses a(,o and a{o at
Kb=O.4S, O.7, and 1.0. Both al., and q, were normalized
with the in-situ horizontal effective stress cAo. As can beseen in Fig. 6(a), the correlation between afu,fage and
q,/afio appear to be fairly unique for all the soil condi-
tions considered in this study. It should be noticed that
test data points plotted in Fig. 6(a) include results forboth clean and silty Ottawa sands at s,.=O, 2, 5, 10, 15and 20%, This result indicates that afi, and q, representsimilar dependency on DR and initial confining stress.
Correlations in Fig. 6(a) can be given by;
ln ac,Ml,'
±= cM (ln aqfC,)
fi
(6)
where af.,=mean effective stress at peak observed from
versus cone resistmice both normalized with respect to the horizon-
tal effectiye stress nt different Kh yalues nlld (b) values of or and fi as a fullctioll of Kh for IR,cpT
TX tests; afio= in-situ horizontal effective stress; q, == cone
resistance; and or and rs= correlation parameters, As can
be seen in Fig, 6(b), values of cr and fi were found to varyas a function of Ko, For Ko
= O.45, yalues of cr and fi were
O,263 and O,848, respectively.
Based on the results in Fig. 6 and Eq. (6), the dilatancyindex lk given by Eq. (2) and the peak friction angle ¢fican be rewritten as:
ik,cpT=h Ie-a・ (in ::/;.)fi-in (iO;.aAo)]-R (7)
q5S=q5E+RD'Jk,cpT (8)
where Ik,cpT= modified dilatancy index in terrns of q.; eand R=intrinsic soil variables as adopted in original
dilatancy equation of Eq. (2); (aAo=in-situ horizontalefiective stress; p,x = reference stress= 1OO kPa; and RD=
dilatancy ratio =
3 and 5 for triaxial and plane-strain con-
ditions, respectively. The modified dilatancy equation of
Eq, (7) may be more efibctive and straightforward in thatit is based on a quantity that can be measured from thefield Ci.e., q,), instead of relying on empirical correlations
to estimate the field afi, values. Figure 7 shows values of
IR versus Ik,cpT. In Fig. 7, values of Ii{ were obtained
from Eq, (2) by Bolton (1986), while lk,cp・i・ were calculat-
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260 LEE ET AL.
5
R4Ycr-3Eoe2to.gl
oo
1 2 3
IR from Eq. {2)
4 5
as
e 129ts.V98{6I・
i3
oo.o
Fig. 8.
O.2 O.41.O,6 O.8 1.0
Rcgressio" analysis for acpT alld RcpT determinationFig. 7. Comparison between lh and Jlt,cpT
ed from Eq. (7) using q, from CONPOINT. As can beseen in the figure, both methods produce virtually thesarne results, irrespective of Kb values.
SimpICfied Dilatanqy Relationship
Both q, and atsp are primarily governed by DR and the
confining stress, Based on the assumption of similar de-
pendency of qc and aAip on DR and af,o, the Botton's
dilatancy index and diS equations of Eqs. (2) and (1) mayfurther be modified as a sole function of q. as follows:
ik,cp・r*=ib [ecpr-in (iOO qcll-Rc,. (g) L XPA I]
diS==¢ E+R.・Ik,.,,* (1O)
where Iii,cpT.=simplified dilatancy index in terms of q,;
9cpT and RcpT = intrinsic soil variables that are analogous
to e andR in Eq, (2). In Eq. (9), values of ecpT and RcpTare different from those of e and R in Eq, (2), due to nu-
merical difrerences between q, and ain,. While Eq. (7) wasobtained in a fairly rigorous fashion based on experimen-
tal results, the semi-empirical formulation of Eq. (9) isbased on simple replacement of afl, with q,, Detailed
comparison between two approaches with reference to
the Bolton's dilatancy relationship wM be further
presented in the later section,
ln oTder to obtain values of QcpT and RcpT, a regression
analysis was performed using TX test results and values
of q, from CONPOINT for Ottawa sand sarnples, Figure
8 shows results frorn the regression analysis for sands at
s,.=O and 10%. For sands at other silt contents,
surnciently tight correlations, showing R2 greater than
O.98, were also observed. In Fig, 8, the slope of regres-
sion lines and the y-intercept represent values of the in-trinsic parameters gcpT and RcpT, respectively. Figure 9shows values of Q, R, 9cm and Rcpb as a function of silt
content, obtained frorn the regression analysis. Values of9 and R in Fig. 9 were from previously reported results
obtained by Salgado et al, (2000) and Lee et al. (2004),From Fig. 9, yalues of ecp・r im case s..=O, 2, 5, 10, 15 and
18
ri 5F8
12av9=N6cr3
o
-
i/
1t t ttt ltttttt tt/tttt ttt tt tt ttt
1 / 1 1 1.... .. tll. .... 1....... .... 1 1
=!N-- T-----÷'XKilLL:IL
1 1 1tttttttltttttttt tlttt tt t ttrttt t tttt
! : ---Q 1
l .Qcpt /
2
o 5 la "5
Silt Content (% )
(a)
20
Hltrvorvo:or
-a
-2
1 1 1
1
tttttttltttttt tt ttttttt
/
:////
////L
nttN - 1
1 1
ttttttt tt ttttttt ttt 1
1 1
/
1
1
/
/ /
/ /
/
: :-----
---R
+Rcpt
/
o 5 10 15
Silt Conte nt (% }
(b)
20
Fig, 9. Iptrinsic soil yariab]es Q, Qc?・J・, R and Rcvr versus silt conte"t:
(a) e and QcpT a"d (b) R and Rcpi
20% cases were found to be 14,O, 15.4, 14,O, 14.3, 11,8and 12.1, while values ofRcpT were 1.0, -O,12,
-O.l2,-O.Ol,
O.Ol and O.12 respectively. It is seen that values of
9cpT vary in 12-15 range. The difference between 9cpT
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15
Aov
12ps-."
9E9`'-.
6-eLbe3
Aevp8g"
E9-"'e
o
50
45
40
35
30
25
IN-SITU EVALUATION OF STRENGTH
o 3
¢'p-thIC
6 9 f2
from triaxial test (O}
(a)
15
25 30
¢
35 40
'p
from triaxial test (
(b)
45o} 50
Fig. 10. Comparison of (a) dilatanc}, angles and (b) peak friction an-
gles measurcd and estimated "s;ng IR,cp・r'
and e is approximately constant regardless of the silt
content, and equals to around 3 to 4. The difference be-tween RcpT and R appears to be, on the other hand,negligible, showing both RcpT and R values ranging from-1
to 1. For clean sand, 9cpT and RcpT were around 14
and 1, respectively.
Figure 1O(a) shows values of the dilatancy angle (di 3-ip:)calculated from Eq. (1O) using Ik,cpT. of Eq. (9) and those
measured from triaxial test results with Ottawa sand sarn-
ples, As shown in Fig. 10(a), difference between meas-ured and calculated (ipS-¢ S) values is no more than 20.Figure 1O(b) shows calculated and measured values of the
peak frietion angle thS. Calculated di6 values were ob-
tained from Eq. (10) for given values of diC. Similar to the
results in Fig. 1O(a), both measured and calculated values
of ¢ " show good match with difference less than 2
o.=bs.
orr
o.=bny..-
ov
o
100
200
300
400
500
o
1OO
200
300
400
500
¢'p
-e'. from triaxial test (O)O 5 10 15 20
(a)
O'p -¢',
from triaxial test (O)O 4 8 12 ri620
(b)
261
Fig. 11. Correlations between dilatamcy angle and normalized co"e
resistallcc for (a) snilds of different silt contents and (b) different .Kli vallles
degrees,
Direct Correlation between Cone Resistance andDiiatan-
qy Angie for Sancts Several direct correlations between q, and OS have beenproposed to estimate the shear strength of sands (Dur-gunoglu and Mitchell, 1975; Robertson and Campanella,1983; Chen and Juang, 1996; Lee et al,, 2004), Whilethese correlations have been frequently used for analysis
and interpretation of CPT results, further investigation is
necessary for soils at different fines contents and 1(b con-ditions. Since diC can be uniquely identified even using
completely disturbed sand samples, a focus for the corre-
lation investigated in this study is on the estimation of
dilatancy angle (ipS-ipE) directly from cone resistance.
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262 LEE ET AL,
Figure 1 1(a) shows va]ues of ¢ fi-thE obtained from triax-ial tests versus q. normalized with oto for clean and silty
Ottawa sands under Ko=O.45, Values of q, in Fig. 11(a)
were obtained from CONPOINT at the same mean effec-
tive stress as adopted in each triaxial test with Ottawasand samples. As can be seen in Fig. 11(a), a quite unique
correlation, applicable to both clean and silty sands, ap- .pears to exlst.
Correlations between q./aAo and (¢ S-thS) for other 1<b
values were also obtained and plotted in Fig, 11(b). Fromthe trends of the regression lines in Fig. 11(b), it is ob-served that slight increase of dilatancy occurs with in-creasing Ko for a given normalized cone resistance q./aAo.Correlations obtained from Fig, 11(b) can be given as:
dis-dia--±・ln (qc/bafio) (11)
where aAo=in-situ horizontal effective stress; a and b=correlations parameters that depend on Kb values, For Kb=O.45, a and b were found to be O,148 and 73,6, respec-tjvely. For other Kb values, based on resuits in Fig, 11(b),values of a and b were found to be approximated as:
a=o,13s・K,iO・ii5 a2) b=64,og・Ko'O・ii (13)Equations (11)-(13) can be used to estimate dilatancy and
peak friction angles directly from CPT results for bothclean and silty sands with silt contents up to approximate-
ly 15-20%, In Eq. (11), as the normalized cone resistance
q./aAo is adopted, values of q, mainly reflect the effect of
the relative density on ipS-g6E correlation, while q, in Eq,
(9) was considered as a component for refiecting the efiect
of the confining stress.
COMPARISON AND VERIFICATION USING
CALIBRATION CHAMBER TESTS
Calibration Chamber 7lest Results with fumunjin Sand The methods for in-situ evaluation of shear strength
and dilatancy using CPT proposed in this study can besummarized into the following three cases: (1) Method1-Modified dilatancy equation of Eq, (7); (2) Method2-Simplified dilatancy equation ef Eq. (9); and (3)Method 3-Direct correlation equation of Eq. (11). De-tailed descriptions and procedure for each method are
given in Table 2 and Fig. 12, From Fig. 12, it is noticedthat soil characteristic properties, such as stress state, DRand ipE, other than q, are still required, This is a common
situation since strength is not given as a sole function of
q,, but typically represents infiuence of various mechani-
cal soil properties, As collection of undisturbed soil sam-
pling is not practically available in sands, determination
Method
Table 2. Summary or CPT-based strength alld dilatancy estimation methods
Equation of dilatancy Model parameters
iR tpT=in [e-or (ln E/:,)fi-in (iO;.aiCO)]-R ll: IR3 Fiigg
6g
Ik,,..-=I. [g...-ln (10pO.q')]-R.,. Re.C:.T FFIgg g
of DR is commonly based on in-situ test results. Various
methods for the determination of DR using CPT can be
found from Salgado (2006). In order to evaluate the proposed methods, calibration
chamber cone penetration tests using Jumunjin sand were
conducted and used in comparison and verification. Atotal of 11 calibration chamber CPTs were perforrned at
different relative densities and stress states. Table 3 shovvsrelative densities and stress states considered in the tests.
It has been well recognized that size effect exists incalibration chamber tests due to the limited size ef cham-
ber (Schnaid and Houlsby, 1991; Kurup and Voyiadjis,1994; Salgado et al., 1998, 2001; Lee and Salgado, 2000),Due to the size effect, values of q, measured from calibra-
tion chambers are smaller than those measured in the fieldfor the same stress states and soil conditions. As soils are
more dilatant, in general, degree of underestimation of q.in chambers increases.
In order to obtain values of q, corrected for the size
effect, correction factors for the chamber size effect
(CLi.,) obtained by Salgado et al, (1998) were adopted.
Using CEi.., the cone resistance for field conditions (i.e.,qr,f{eid) can be obtained from the calibration chamber
cone resistance (i,e., qe.chambcr) as follows:
q,, ,,,,d ==
qcc・ cTL,kail.ier
(1 4)
According to Salgado et al. (1998), size effect correction
factors vary as a function of DR, stress states, and cham-
ber-to-eone diameter Tatios. For each calibration cham-
ber test in Table 3, values of CIFLi,, were obtained basedon stress states and DR actually adopted in the test. Thechamber-to-cone diameter ratio was 48 considering di-ameters of cone and chamber equal to O.Ol6 and O.77 m,respectively.
Figure 13 shows typical examples of q, profiles ob-
tained from calibration chamber tests. Values of q, inFig. 13 are those corrected with the chamber size effect.
As shown in Fig. 13, due to the boundary effect of the
chamber, q, increases down to a certain depth belowwhich the profile becomes stabilized. Accordingly, valuesof q, adopted for the estimation of ipS were selected at thisrange of middle depths of the specimen. Values of q. ob-tained from each calibration chamber test were summa-
rized in Table 3,
Figure 14 shows measured and predicted values of ipSfor each calibration chamber test case. Measured values
of ip fi were obtained from the triaxial tests using Jumunjinsand samples. For pTedicted ipS, proposed methods of
AEvs-aoo
o.o
O.2
O.4
e.6
O,8
a.o
rt.2
o5
q. {Mpa)rie ri5 20 25 30
Fig, 13. J)epth profiles of q, for calibration chamber tests
Eqs, (7), (9), and (11) were used. For comparison, two
otheT existing methods by Durgunoglu and Mitchell<1975) and Robertson and Campanella (1983), which can
be classified as direct approach similar to Eq, (11), were
also included in Fig. 14.
Figure 14(a) shows values of diS obtained from TX testsand proposed methods of Eqs. (7), (9), and (11). It is ob-
served that predicted ipbvalues from Eqs. (7) and (9) showreasonable agreement with those from TX tests. Somecases obtained from the direct correlation of Eq. (11)show overestimated difi values compared to those fromTX tests for dense sand cases, This overestimation was
also obseived from other similar types of correlations byDurgunoglu and Mitchell (1975) and Robertson and
Campanella (1983) in Fig. 14(b).
Calibration Chamber Tk7st Results fi'om Literature
Houlsby and Hitchman (l988) conducted calibration
chamber cone penetration tests using Leighton Buzzard
sand. The critical state friction angel Ol of Leighton Buz-zard sand is equal to 33O. Calibration chamber samples
were prepared at three relative density levels of DR =
20-26%, 47-61%, and 82-90% under 1(h=O.5, 1.0, and
Fig. 14. Measured versus predictcd dil, yalues forjum"lljin sand with
(a) proposed methods and (b) existing methods
2.0. As Ko equals to 1,O may be regarded as the upper
limit for highly overconsolidated sands, calibratjon
chamber test results for Kb=O.5 and 1.0 were used in the
comparison and results with Kb ==2.0
were not included.
The chamber was of height and diameter equal to 1.0 and
O.9 m, respectively, whereas CPTs were conducted using
the standard 36-mm cone. More detailed test eonditions
can be found from Houlsby and Hitchman <1988). A
total of 15 calibration chamber CPT results were adopted
in this comparison. Table 4 shows soil conditions and
cone resistances corrected with the size effect for each
calibration chamber test, Values of q, shown in Table 4are those measured at a depth of O.5 rn (i.e., at the middle
depth of calibration chamber sample) from the top of
calibration chamber samples.
Figure 15 shows values of the peak friction angle ¢ fiobtained for each calibration chamber test with differentrnethods. As Houlsby and Hitchman (1988) suggested
and no TX test results were available, reference values of
ipS adopted in the cornparison were those obtained from
Fig. 15. Comparison of ipa va]ues ror Leighton Bnzzard sand (Houl- sby and Hitchman, 19SS) with (a) Bolten's versus proposed
methods and (b) Bo]ton's and existing mcthods
Bolton's dilatancy relationship given by Eq.
previous examples, two other methods by(2), As in the
Durgunoglu
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IN-SITU EVAI.UATION OF STRENGTH 265
and Mitchell (1975) and Robertson and Campanella
(1983) were also included. Figure 15(a) shows values of
thB obtained from Bolton (1986) and proposed methods of
Eqs, (7), (9), and (11). It is observed that the modified
dilatancy equation based on Ik,cpT of Eq. (7) (i,e.,Method 1) produces virtually the same results as those
from Bolton's relationship. The simplified dilatancy equ-ation of Eq. (9) (i,e,, Method 2), on the other hand,tends to underestimate values of ¢S as soil becomes more
dilatant. This result indicates that the modified dilatancyequation with consideration of afle would give more ac-
curate field evaluation of shear strength, while the simpli-
fied dilatancy equation using Ift,cpT. may still be applica-
ble for practica] purpose. The direct q,-based correlation of Eq. (11) shown inFig. 15(a), on the other hand, results in overestimated OSvalues compared to those from Bolton's dilatancyrelationship. For results from Durgunoglu and Mitchell
(1975) and Robertson and Campanella (1983) in Fig.15(b), while both methods show overestimated thS values,degree of overestimation for Robertson and Campanella(1983) was slightly higher than for Durgunoglu and
Mitchell (1975), From Fig, 15, it can be concluded that
the modified dilatancy equation based on q, can be effec-
tively used for field evaluation of shear strength without a
need for laboratory testing to obtain a;,,. For direct cor-relation between q, and dilatancy or peak friction angle,
unconservative estimation of 03 may result in.
Summar;y and Conctusions
Bolton's dilatancy relationship has been widely adopt-
ed in various strength analyses, It cannot be, however, di-rectly applied into field evaluation of shear strength dueto the unknown variable of the mean efiective stress at
peak. In this study, methodology for the field appiicationof the dilatancy equation based on CPT cone resistance q.is investigated for sandy soils containing fines, Resultsfrom a series of laboratory tests and cone penetrationanalysis were used for the development of CPT-basedmethods of strength and dilatancy evaluation for sands,
Based on empirical correlations between q. and ath, 'for
a given TX and equivalent field stress state, a modified
dilatancy index lk, cpT in terms of q, was proposed and in-vestigated for different Kh conditions. Results from both
modified and original dilatancy indexes (i,e,, IR, and
Ik,cpT) showed close agreements for soils at all the siltcontents and Kb values considered, As both q, and oin, are
primarily governed by DR and the confining stress with
similar dependency, further simplified dilatancy indexIk,cpT# in terms of q, was proposed, Values of intrinsic
vaTiables 9cpT and Rcp・r for Ii{,cprF were proposed as a
function of silt content. Based on TX test results, a directcorrelationbetween (¢ S-ipO and q,laAo, applicable to both
clean and silty sands, was proposed as well,
In order to verify the proposed CPT-based methods
for in-situ evaluation of shear strength and dilatancy forsands, calibration chamber CPT results were adopted
and used for comparison. The calibration chamber test
results include those obtained in this study and collected
from the literature. Various soil conditions were used inboth tests, It was observed that modified dilatancyrelationships based on Jk,cpT produces results reasonably
close to those measured from triaxial tests and estimated
from Bolton's original dilatancy relationship, while sim-
plified relationship of Ik,cpTs tends to show underesti-
mated results at higher range of ¢ S values, Direct q.-basedcorrelations, on the other hand, were found to result inoverestimated ipfi values compared to those from Bolton's
dilatancy relationship,
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