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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

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 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 "unlee@yonsei.ac.kr).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

proposed methods, results frorn calibration chamber tests

are adopted and used in the comparison.

SHEAR STRENGTH OF SANDY SOILS

State-Dupendent Shear Strength and Dilatancy

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

TsYP.fid"f

G, e... e.,. (kgl:}"fi,]) (kS17w'fi i) c.e ipE(o)b-. ..-. . . . 0ttawa 2.62 O.782 O.482 17.34 14.//2"L48 ti9Jumynjin

2.61

O.878

O.631 IS.69 13.63 1.47 31

"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

(b)

oO,2O,4O,6Ko

O.8 1 1.2

1,5

1.2

O,9 1D

O.6

O,3

Fig. 6. Modified dilatancl, relationships: (a} moan peak effective strcsg

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

aba=! ths-ip:!-l;- in e"fbak") Zi EEqql

((1:))

Equation of ip5

Modified dilatancy equation

(Methed 1)¢ "= ¢ {+3Jk,cpL

SimpLifieddilatancyequation

(Method 2)th r, = ip :. + 3IR, c,..

Direct correlation

(Method 3)¢ s=di:+ipg

Characterizebasicsoiistate/DR,abc,GAo,qc

Method1/Modifieddilatancyequationof{R,cpT[Eq,(7)]

Method2/SimplifieddilatancyequationIR,cpT+[Eq.(9)]

Method3/Directcorrelation

Q',[Eq.(rt1)]

Determinemodelparameters/(x,P,Q,R(Figs.6and9)

Determinemodelparameters/QcpT,RcpT(Fig.9)

Determinemodelparameters/a,b[Eqs.C12)and(13)]

Estimatethedilatancy/IR,cpT{Eq,(7)]

Estimatethedilatancy/[R,cpT･[Eq.(9)]

Estimatethedilatancy/

O'd[Eq.(M)l

Estimate¢'p/

O'p=Oc+3[R,cpTEstimateO'p/

-Fp=O'.+31R,cpT'Estimate-'p/

O'p=tpFc+a)'d

Fig. 11.Procedure for pToposcd CPT-based strength and dilatancy estimation mcthods

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IN.SITU EVALUATION OF STRENGTH / Soil cortditiolls adapted calibration chamber tests

263

T- DR=5S%T

& afo (kPa) ffr,o (kPa)

ecFkizcqc,

fit]a (MPa)/i

O,27100

27O.713.39

O,27150

40O.755.32

O,40100

40'O.735.39

O,705740O.705.36O,70100

70O.776.92

1.00100100O.788.42O.27150

40O.698.68

aCFk,,: correction factor for chamber size effect

O,40100

40O.6518.69

D.;86%

O.70 100

40

O.63 15.40

O.70100

70O.7019.65

1.00too100

O.7222.64

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

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50

LEE ET AL.

Table 4.

1988)Calibrationchamber

testres-lts(Hou]sby a"dHltchma",

45Aevv

40 eEb'

9 35 idi'e

30

25

50

45{i8

4og,

g 35i-e-

30

25

25 30 35 40 45

¢'P,

Measured (Tx) (O) (a)

50

25 30 35 40

{b 'p,

measured (Tx) (e}

(b)

45

Da {%)o:o (kPa)

50

of,e (kPu)

644761S9S723202024269086878588

-ov

ve

,g v e q.ae

106.2149.749.063.0IS5Ji51.2151,663.3103.143,1151.066.750.3113.3163.1

50

45

40

96.975.840.532.214S.8149.076.931.0101,I39.776.935.140.598.9147.7

&qc,chamber(MPa)C fiLizeq.,fi.ld(MPa)

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

Aov

vs

.! -

e a.ae

35

30

25

50

45

40

35

30

25

O.913O.506O.826O.512O.936O.98SO.508O.490O,980O.922O.509O,527O.805O.873O.90616.0713.469.4607.97019.79

5.650 3.990 1.9904.240

1.97020.8212,eo12.8722.4330.28

O.62O.65O.58O.58O.73O.80O.7SO.66O.75O.63O.60O.53O.53O,60O.6725.9220.7116.3113.7427.117.0625.3203,O155.6533.12734.7022.6424.2837.3845,19

2530 35 40

¢'p,LrcBoiton}(e)

(a)

4550

2530 35 40

(P 'P,tr(Betton)

{O)

(b)

4550

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,

REFERENCES

1) Bolton, M, D. <19S6): The strength and dilatancy ef sands,

Geotechnique, 36(1), 65-7S,

2) Chen, J. W. and Juang, C. H. (1996): DezeTmjnation of drained

frietion angle of sands from CPT, Journai of Geotechnicat En-

gineering, ASCE, 122(5), 374-380.

3) De Josselin de Jong, G. (1976): Rowe"s stress-dilatancy re]ation

based on friction, Geotechnique, London, 26{3), 527-534.

4) Dunhanm, J. W, (19S4): Pile foundaLion for buildings, Journat of the Soil Mechanics and foundation Division, ASCE, 80(1), 1-21,5) Durgunoglu, H. T. and Mitchell, J. K. (1975): Statie penetration

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Situ Measuretnent of Soit Rroperties. ASCE, New York, 1,

151-171.

6) Heulsby, G. T, and Hizchman, R. (t988)/ Calibration chamber

tests of a cone penetremeter in sand, Geotechnique, 38(1), 39-44.

7) Janbu, N. and Senneset, K. (1974): Eil'ectiveness stress interpreta-

tien of insitu static cone penctration tests, Proc. Ist Eur. Symp. on Penetration Tlesting, 2(1), 181-193.

8) Kurup, P. U. and Voyiadjis, G. Z. (1994): Calibration chambeT stu-

dies of piezocone test in cohesive soils, Journal of Geotechnicat En-

gineering, ASCE, 120(1), 81-107.9) Lec, J. and Salgado, R. (2000): Analysis of calibration chamber

plate load tests, Canadian Geoteehnical Journa4 37(1), 14-2S.

10) Lee, J., Salgado. R. and CarTuro, A. (X)04): Stiffriess degradation

and shear strength of silty sands, Canadian Geotechnical Jburnal,

41C5),831.843.

") Perkins, S. and Madson, C, (2000): Bearing capacity of shallow

foundations on sand: A re]ative density approach, Journal ofGeo- technicai and Geoenvironmental Engineering, ASCE, 126(6),

521-530.

12) Robertson, P. K. and Campane!la, R. G, (1983): Interpretation of

cone penetration tests 1: sand, Canadian Geotechnicai lo"rnal,

109(11), 1449-14S9.

13) Salgado, R., Mitchell, J. K, and Jamiolkowski, M. (1998): Calibra-

tion chamber size effects on penetration resistance measured in

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mentat Engineering, ASCE, 124(9), 878-S88,

l4) Salgado, R., Bandini, P. and Karirn, A. (2000): Stiffness and

stremgth of silty sand, Journal of Ceoiechnical and Geoenviron- mental Engineering, ASCE, 126(5), 451-462.

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sion in sands, international ,fournal of Geomeehanics, 1(2), 175-192.

16) Salgado, R,, Mitchelr, J. K. and Jamiolkowski, M. (2001): Closure to calibration chamber size effects on penetration resistance meas-

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17) Salgado, R. {2006): Tke Engineering of Foundations, McGraw- HM.18)

Schnaid, F. and HouLsby, G. T. (1991): An assessment of chamber

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