anbazhagan sdee print version

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ReviewofcorrelationsbetweenSPTNandshearmodulusAnewcorrelationapplicabletoanyregion

ARTICLEinSOILDYNAMICSANDEARTHQUAKEENGINEERINGmiddotMAY2012

ImpactFactor122middotDOI101016jsoildyn201201005

CITATIONS

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IndianInstituteofScience

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SEEPROFILE

AdityaParihar

ThaparUniversity

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Retrievedon08December2015

Soil Dynamics and Earthquake Engineering 36 (2012) 52ndash69

Contents lists available at SciVerse ScienceDirect

Soil Dynamics and Earthquake Engineering

0267-72

doi101

n Corr

fax thorn9

E-m

anbazha

aditpari

URL

journal homepage wwwelseviercomlocatesoildyn

Review of correlations between SPT N and shear modulus A new correlationapplicable to any region

P Anbazhagan n Aditya Parihar HN Rashmi

Department of Civil Engineering Indian Institute of Science Bangalore 560012 India

a r t i c l e i n f o

Article history

Received 19 July 2011

Received in revised form

2 January 2012

Accepted 8 January 2012Available online 1 February 2012

Keywords

Shear modulus

SPT N

MASW

Seismic survey

Hammer energy

Correlation

61$ - see front matter Crown Copyright amp 2

016jsoildyn201201005

esponding author Tel thorn91 80 2293246794

1 80 23600404

ail addresses anbazhaganciviliiscernetin

gan2005gmailcom (P Anbazhagan)

hargmailcom (A Parihar) rashmihn88re

httpwwwciviliiscernetin~anbazhagan

a b s t r a c t

A low strain shear modulus plays a fundamental role in earthquake geotechnical engineering to

estimate the ground response parameters for seismic microzonation A large number of site response

studies are being carried out using the standard penetration test (SPT) data considering the existing

correlation between SPT N values and shear modulus The purpose of this paper is to review the

available empirical correlations between shear modulus and SPT N values and to generate a new

correlation by combining the new data obtained by the author and the old available data The review

shows that only few authors have used measured density and shear wave velocity to estimate shear

modulus which were related to the SPT N values Others have assumed a constant density for all the

shear wave velocities to estimate the shear modulus Many authors used the SPT N values of less than

1 and more than 100 to generate the correlation by extrapolation or assumption but practically these N

values have limited applications as measuring of the SPT N values of less than 1 is not possible and

more than 100 is not carried out Most of the existing correlations were developed based on the studies

carried out in Japan where N values are measured with a hammer energy of 78 which may not be

directly applicable for other regions because of the variation in SPT hammer energy A new correlation

has been generated using the measured values in Japan and in India by eliminating the assumed and

extrapolated data This correlation has higher regression coefficient and lower standard error Finally

modification factors are suggested for other regions where the hammer energy is different from 78

Crown Copyright amp 2012 Published by Elsevier Ltd All rights reserved

1 Introduction

Many countries have initiated seismic microzonation studieswith emphasis on site effects around the world because of theincreasing earthquake damages due to ground motionsite effectsResearchers are trying to develop regional level hazard mapsconsidering different earthquake effects Earthquake damages aremainly because of the changes in the seismic waves and soilbehavior during dynamic loading These are called as site effectsand induced effects which are primarily based on geotechnicalproperties of the subsurface materials Site effects are the combi-nation of soil and topographical effects which can modify(amplify and deamplify) the characteristics (amplitude frequencycontent and duration) of the incoming wave field Induced effectsare liquefaction landslide and Tsunami hazards Amplificationand liquefaction are the major effects of earthquake that cause

012 Published by Elsevier Ltd All

48100410 (Cell)

diffmailcom (HN Rashmi)

(P Anbazhagan)

massive damages to infrastructures and loss of lives Recent studyby USGS revealed that among deadly earthquakes reported for thelast 40 years loss of lives and damages caused by ground shakinghazard was more than 80 of the total damages [24] Subsurfacesoil layers play a very important role in ground shaking modifica-tion Most of the earthquake geotechnical engineers are workingto estimate and reduce the hazards due to geotechnical aspects

Site specific response and seismic microzonation studies arecarried out by considering the local geotechnical properties ofsubsurface layers Dynamic shear modulus of subsurface layer isthe most important geotechnical property used in the site specificresponse analysis The shear modulus of subsurface layers areusually measured in situ by means of seismic exploration andsometimes by the dynamic triaxial compression test or theresonant column test of undisturbed soil samples in the labora-tory [28] A large number of researchers have presented thelaboratory based shear modulus studies Even though SPT N dataare widely used for site response and seismic microzonation veryfew studies are available for in situ correlation between shearmodulus versus standard penetration test (SPT) N values usingthe field experiments [59] Seismic microzonation requires soilparameters in the form of shear wave velocity for site classifica-tion and shear modulus to estimate the site specific ground

rights reserved

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P Anbazhagan et al Soil Dynamics and Earthquake Engineering 36 (2012) 52ndash69 53

response parameters [6ndash8384] The input soil parametersrequired essentially are thickness (h) density (r) and shearmodulus (Gmax) for each subsurface layer The soil type andthickness of each layer are generally obtained by drilling bore-holes and logging the borehole information (bore log) The in-situdensity of each layer is usually obtained from the undisturbed soilsamples collected from boreholes However such measuringtechniques are expensive time consuming and require specia-lized techniques [28] Borelogs with SPT N values are widely usedin most of the microzonation studies Shear modulus (Gmax) forsite response analysis is evaluated by using the existing correla-tions between SPT N values and shear modulus The SPT is one ofthe oldest popular and most common in situ tests used for soilexploration in soil mechanics and foundation engineering Thistest is being used for many geotechnical projects because of thesimplicity of the equipment and test procedure In particular SPTsare used for seismic site characterization site response andliquefaction studies for seismic microzonation [25]

This paper reviews available correlations between SPT N andshear modulus The existing correlations were developed by Imaiand Yoshimura [17] Ohba and Toriumi [27] Ohta et al [29]Ohsaki and Iwasaki [28] Hara et al [16] Imai and Tonouchi [18]Seed et al [3436] and Anbazhagan and Sitharam [5] Most of theold correlations are listed in the popular textbook of Ishihara [20]and Kramer [23] Ishihara [20] has presented the summary of SPTN values and Gmax correlations based on the above first fiveresearch works Kramer [23] has modified the correlation devel-oped by Imai and Tonouchi [18] for a sandy soil by replacing themeasured N values with energy corrected N values [N60] Seedet al [34] presented the correlation based on their previousstudies Seed et al [36] have presented Gmax correlation basedon the Ohta and Goto [30] data Correlation proposed by Seedet al [3436] and Kramer [23] is being used in SHAKE2000 siteresponse software to estimate the shear modulus from the SPT N

values A correlation by Anbazhagan and Sitharam [5] is a recentlydeveloped one after 27 years of gap This paper presents thesummary of the above correlations and comparisons A newcorrelation has been developed considering the measured oldand new data from Japan and India where N values are measuredwith a hammer energy of 78 The modification factor for old andnew correlations is suggested for other regions where the SPT N

values are measured with different hammer energies

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2 Existing correlations between SPT N and Gmax

Many regression equations of SPT N versus shear wave velocityare available in the literature for different soils by many research-ers Among these correlations few were developed consideringcorrected SPT N and shear wave velocities But few regressionequations are available for SPT N versus shear modulus whencompared to SPT N versus shear wave velocity relation Summaryof SPT N versus shear modulus correlation in original form andconverted in SI units is presented in Table 1 and discussed below

Imai and Yoshimura [17] presented the very first correlationbased on downhole shear wave velocity measurements in varioussoil layers Here authors calculated shear modulus by assuming aunit weight of 17 tm3 (1667 kNm3 or 17 gcm3) and high-lighted that their correlation is valid for different soil types (seeEq (1) in Table 1) provided that the small changes are needed inthe numerical value of Poissonrsquos ratio

In the same year Ohba and Toriumi [27] have also given acorrelation based on their experimental study at Osaka Theauthors have estimated the shear wave velocity by manipulationof measured Rayleigh wave velocities and have assumed a unitweight of 17 tm3 (see Eq (2) in Table 1)

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110

Measured SPT N value

Shea

r mod

ulus

(MPa

)

Overall dataAlluvial clayAlluvial sand Diluvial clayDiluvial sand

Fig 2 Comparison of correlations developed by Imai and Tonouchi [18] for

different soils

P Anbazhagan et al Soil Dynamics and Earthquake Engineering 36 (2012) 52ndash6954

Ohta et al [29] have presented the correlation between SPT N

versus shear modulus using 100 sets of data from 18 locations(see Eq (3) in Table 1) Data are derived from Tertiary soilDiluvial sandy and cohesive soil and Alluvial sandy and cohesivesoil The authors observed that the sandy soil possessed a littlelower shear modulus than the cohesive soils for the same valuesof N but the difference was not so definitive

Ohsaki and Iwasaki [28] presented a summary of all the aboveequations and proposed new correlations from well shooting andSPTs The authors and Evaluation Committee collected these datajointly on High Rise Building Structures The authors developedthis correlation by considering the SPT N value of 05 instead ofzero also by considering the different soil category and soil typesThese data sets contain the data from Tertiary soil Diluvial sandysoil Diluvial cohesive soil Alluvial Sandy soil and Alluvialcohesive soil Correlations were developed based on soil category(Tertiary Diluvial and Alluvial) and soil type (Sandy intermediateand cohesive) The authors have observed that based on soilcategories there was no appreciable difference between thecoefficients of correlation The correlation considering all the datasets is given in Eq (4) in Table 1 and correlation for each soil typeis given in Eqs (5)ndash(7) in Table 1 The authors have highlightedthat among the above correlations the correlation obtained forcohesive soils (Eq (7)) is well correlated and correlation forintermediate soils (Eq (6)) is fairly correlated since soils of toomuch variety are incorporated in this category In order to use acorrelation regardless of soil type and geological age authorsrounded up Eq (4) as given in Eq (8) (see Table 1)

Fig 1 shows the comparison of correlation developed byOhsaki and Iwasaki [28] The figure clearly shows that up to theN values of 30 all correlations give similar shear modulus beyondthat value the shear modulus of cohesive (Eq (7)) and inter-mediate soil (Eq (6)) are less than that of the sandy soil (Eq (5))The rounded correlation (Eq (8)) and correlation for sandy soil(Eq (5)) match closely for the values of N above 40 which may bedue to a large number of data sets for sandy soil than cohesivesoil The correlation considering all the data sets (Eq (4)) is in-between the Eq (5) and Eqs (6) and (7) Cohesive data sets areclustered in between SPT N value of 2 and 20 and the N value ofless than 2 is found only in cohesive soils

Hara et al [16] have developed a correlation using the data setof 25 sites which consisted of 15 Alluvial deposits 9 Diluvialdeposits and 1 Tertiary deposit Cohesive soil data were onlyconsidered to develop correlation between Gmax and SPT N valueShear wave velocity was measured by the well-shooting test andthe developed correlation is Eq (9) in Table 1

Imai and Tonouchi [18] developed correlations between SPT N

with shear wave velocity and shear modulus and presented them

0

100

200

300

400

500

0 10 20 30 40 50 60 70 80 90 100Measured SPT N value

Shea

r mod

ulus

(MPa

)

RoundedOriginal Sandy soilIntermediate soilCohesive soil

Fig 1 Comparison of correlations developed by Ohsaki and Iwasaki [28] for

different soils

in the Second European Symposium on Penetration Testing Theauthors have accumulated the above data in the year 1967 whichcontains 400 boreholes data throughout Japan They have mea-sured S wave and P wave velocity separately considering averageN values for single velocity layer and have presented the correla-tion for different soil geological categories and soil types The N

values of less than 1 and above 50 are substituted for the numberof blows required to achieve a penetration depth of 30 cm fromthe actual amount of penetration achieved in blows Data setincludes alluvial peat clay sand and gravel diluvial clay sandand gravel Tertiary clay and sand Fill clay and sand and Specialsoil of loam and Sirasu A large number of data are from alluvialclay and sand diluvial clay and sand Eqs (10)ndash(14) in Table 1give the correlation developed for different soil types with anumber of data sets considered along with their range N values

Fig 2 shows the comparison of correlation developed by Imaiand Tonouchi [18] (Eqs (10)ndash(14)) It is interesting to note thatthe correlation for all the soil types (Eq (14)) matches with thecorrelation for Diluvial sand (Eq (13)) and clay (Eq (12)) Thecorrelation for alluvial clay (Eq (10)) is comparable with thecorrelation for all the soil types (Eq (14)) up to the SPT N value of40 The alluvial sand correlation (Eq (11)) is not comparable withthe correlation for all the soil types (Eq (14)) for any N value

Seed et al [34] developed a correlation based on their previousstudies The correlation is available but other information regard-ing the number of points data sets and soil types is missing Co-author Arango (personal e-mail communication October 2009)has also confirmed that the above details are not available Thecorrelation presented by Seed et al [34] is given by Eq (15)

Review shows that Eqs (1) and (2) were developed by assum-ing uniform density Remaining equations were developed assum-ing SPT N values less than 1 and extrapolating SPT N values morethan 50 using shear wave velocity measured by well shootingThese studies were carried out in Japan except by Seed et al [34]Recently Anbazhagan and Sitharam [5] developed a correlationbetween measured SPT N and shear modulus values using datagenerated for seismic microzonation study of Bangalore India

3 SPT and MASW comparison and correlation

Shear wave velocity used for old correlations is obtained fromwell shooting tests The recent and very popular method forcomputation of shear wave velocity is Multichannel Analysis ofSurface Wave (MASW) This method is widely used for seismicmicrozonation A MASW is a seismic surface method widely used

10

100

001011

Mea

sure

d sh

ear m

odul

us (M

Pa)


G = 2428N

R = 088

Fig 3 Correlation developed by Anbazhagan and Sitharam [5] with data and

upper and lower sides on 95 confidence interval


for subsurface characterization and is increasingly being appliedfor seismic microzonation and site response studies [6] It is alsoused for the geotechnical characterization of near surface materi-als [314125217] MASW is used to identify the subsurfacematerial boundaries spatial and depth variations of weatheredand engineering rocks [3] and also used in railway engineering toidentify the degree and types of fouling [10] MASW generates aVs profile (ie Vs versus depth) by analyzing Raleigh-type surfacewaves recorded on a multichannel Anbazhagan and Sitharam[35] have used the MASW system consisting of 24 channelsGeode seismograph with 24 vertical geophones of 45 Hz capacityand have carried out a number of field experiments close to SPTborehole locations The authors compared soil layers and rockdepth using their experimental data It is found that the shearwave velocities using MASW match well with soil layers in theboreholes

Anbazhagan and Sitharam [5] selected 38 locations MASW andSPT results and generated 215 data pairs of SPT N and Gmax valueswhich they have used for the regression analysis Fig 3 shows theshear modulus correlation recently developed by Anbazhagan andSitharam [5] with data The shear modulus corresponding to SPTN value was estimated using measured shear wave velocity anddensity from the in-situ samples [5] The correlation developedbetween Gmax and N is given by Eq (16) The correlation betweenSPT N and Gmax presented in logndashlog plot and the best-fit equationhas the regression coefficient of 088 In addition 95 confidencebands enclose the area that one can be 95 sure of the true curvegives a visual sense of how well the data define the best-fit curve[26] Regression equations corresponding to 95 confidenceintervals are given in Eqs (16a) and (16b) respectively

Upper side on 95 confidence interval

Gmax frac14 2912N060eth16aTHORN

Lower side on 95 confidence interval

Gmax frac14 1943N051eth16bTHORN

These N values are measured values and no extrapolation orassumptions were made The authors have compared newlydeveloped correlation with widely used correlations and alsodeveloped correlation between corrected SPT N with measuredand corrected shear modulus [5]

4 SPT N values and corrections

The Standard Penetration Test (SPT) is one of the oldest andmost common in situ tests used for soil exploration in soilmechanics and foundation engineering because of the simplicity

of the equipment and test procedures Standard Penetration Test N

values become very important in earthquake geotechnical engi-neering because of a good correlation with an index of soilliquefaction and also provides the basis for site response andmicrozonation studies Many researchers have published site-specific response parameters and liquefaction maps using theSPT data This test is quite crude and depends on many factorsdue to the test procedure and some equipment used in the testMany factors include the drilling methods drill rods boreholesizes and stabilization sampler blow count rate hammer config-uration energy corrections fine content and test procedure[33221539] The combined effect of all these factors can beaccounted by applying the correction factors separately ortogether The SPT N values may vary even for identical soilconditions because of the sensitivity to operator techniquesequipment malfunctions and boring practice So the SPT N basedcorrelations may be used for projects in preliminary stage orwhere there is a financial limitation [5]

SPT data are most likely to be used in case of seismicmicrozonation and related site response and liquefaction studiesSPT data can be used effectively if proper corrections are appliedto N values based on field record and lab results Detailed SPTcorrections and range of correction values followed for micro-zonation and liquefaction study are given in Youd et al [43]Anbazhagan [1] and Anbazhagan and Sitharam [85] Most of theshear modulus correlations are developed using the measuredSPT N values But Kramer [23] has given the correlation betweencorrected N values for hammer energy [N60] and shear modulusIn order to account this correlation a brief summary of hammerenergy correction is discussed here and more details can be foundin Seed et al [35] and Youd et al [43] The actual energy deliveredto the drill rods while performing the SPT is different from thetheoretical energy which varies from region to region dependingon the procedure and equipment used Hammer energy generallyvaries from 40 to 90 of theoretical free-fall energy The mainreason for this variation is the use of different methods for raisingand then dropping the hammer [223335] The widely used SPThammers are Donut hammer Safety hammer and Automatic tripdonut type hammer Seed et al [35] have reviewed differenthammers used in practice in Argentina China Japan and theUnited States with their energy measurement The authors haveconsidered 60 hammer energy as a base (safety hammermdashmostcommonly used in the United States) and have produced correc-tion factors Corrected N value considering hammer energy can becalculated as follows [35]

N60 frac14NmERm

60eth17THORN

where N60 is the corrected N value for 60 energy delivery Nm isthe measured SPT N value and ERm is the hammer energy ratio forthe method used in the investigation The safety hammer withrope and pulley is mostly used in the US where N60 for the sameis equal to Nm Hammer used in Japan is Donut type Seed et al[35] have highlighted that rope and pulley with special throwrelease was followed in Japan in the year around 1983 Previouslythe free fall hammer release was practiced in Japan hence SPT N

values used for correlation before 1983 were measured by thefree fall hammer release The Gmax correlation papers do not haveany information about hammer energy So the SPT N valuemeasured using the Japan Donut hammer with the free fall energyrelease is 130 times (ERmfrac1478) greater than US safety hammerwith rope and pulley release (ERmfrac1460) Hence an energy correc-tion factor of 130 is applicable only for the data measured before1983 Similarly the SPT N values measured using the JapaneseDonut hammer with rope and pulley with a special throw releaseis 112 times (ERmfrac1467) greater than US safety hammer with rope


and pulley So an energy correction factor of 112 is applicable forN values measured around 1983 and later These SPT N valuedifferences between the Japan and US practices are also high-lighted in [20]

Correlation developed by Anbazhagan and Sitharam [5] isbased on the SPT N value measured in Bangalore India Theprocedure and hammer used in India are in concord with BIS 2131[19] standard which are similar to international specificationsregarding weight and height of fall Donut hammer is widely usedin India but limited information is available regarding hammerenergy measurement Personal discussion with leading geotech-nical consultants reveals that the SPT N values are measuredusing the Donut hammer with free fall release manually (pullinghammer rope by hand and dropping them after reaching markedheight) or Donut hammer with pulley and rope release (pullinghammer by machine with operator) These are similar to Japanesepractice to measure the SPT N value before 1983 No record isavailable for SPT energy measurement in India However leadinggeotechnical consultant Mr Anirudhan (personal communicationDecember 2009) has measured energy release by Donut hammerin 2000 He has found that energy varies from about 70 to 86which is similar to Japanese Donut hammer and hence N values inIndia are almost similar to Japanese N values

Table 2Coefficient of constants for N versus Gmax correlations given in Ishihara [20] and

revised constants of lsquolsquoarsquorsquo value

Value of

lsquolsquoarsquorsquo as per

Ishihara

[20] (kPa)

Value

of b

Modified lsquolsquoarsquorsquo value

suggested by Ishihara

on Sep 28 2009a

(MPa)

Suggested lsquolsquoarsquorsquo

value by authors

in this paper

(MPa)

References and

respective

equations in

this paper

1 078 10 981 Imai and

Yoshimura

[17] and

Eq (1a)

122 062 122 1196 Ohba and

Toriumi [27]

and Eq (2a)

139 072 139 1363 Ohta et al [29]

and Eq (3a)

12 08 12 1177 Ohsaki and

Iwasaki [28]

and Eq (8a)

158 067 158 1549 Hara et al [16]

and Eq (9a)

a By e-mail personal communication on September 2009

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(kPa

)

Imai and Yoshimura (1970)

Ohba and Toriumi (1970)

Ohta et al (1972)

Ohsaki and Iwasaki (1973)

Hara et al (1974)

Fig 4 Plot of correlations given in Ishihara [20] (Table 64) (modified after

Anbazhagan et al [11])

5 Converted and modified correlations

Most of the correlations were developed in Japan and therelated articles were published in Japanese These correlationshave come to light through a standard textbook of Soil DynamicsEarthquake Engineering by Ishihara [20] and Geotechnical Earth-quake Engineering by Kramer [23] Few Gmax and SPT N basedcorrelations are also listed in SHAKE2000 software [37] The veryfirst converted correlation was presented by Seed et al [36] Theauthors have presented a correlation between corrected N con-sidering effective vertical stress and shear modulus based on theOhta and Goto [30] studies Ohta and Goto [30] developedcorrelation between measured Vs and Japanese SPT N values withdepth by including soil factors Seed et al [36] have simplifiedoriginal correlation by averaging soil factors and replacing Japa-nese N value by US N values with depth Further Seed et al [36]have assumed a unit weight of 192 gcm3 (120 pcf) and con-verted depth in effective stress by assuming water table isrelatively shallow Final correlation derived by above assumptionsby Seed et al [36] is given below

Gmax frac14 35 1000N03460 eths

00THORN

04 psfeth THORN eth18THORN

where N60 is the N value measured in SPT delivering 60 of thetheoretical free fall energy to the drill rods and s00 is the effectivevertical stress Seed et al [36] further modified Eq (18) byconsidering Nfrac14N1CN and for normally consolidated depositss0m frac14 065s00 Final correlation proposed by Seed et al [36] isgiven below

Gmax frac14 20 1000ethN1THORN1=360 eths

0mTHORN

1=2ethpsfTHORN eth19THORN

where (N1)60 is the N-value measured in SPT delivering 60 of thetheoretical free fall energy to the drill rods and corrected for aneffective overburden pressure of 1 tsft and s0m is the effectiveconfining pressure

The summary and compilation of relations between SPT N

values and Gmax was presented by Ishihara [20] The author hasplotted the summary of relations developed by others using astraight line logndashlog plot and have tabulated the constants lsquolsquoarsquorsquoand lsquolsquobrsquorsquo for the equation given below

Gmax frac14 aNbeth20THORN

The coefficient of lsquolsquoarsquorsquo takes a value between 10 and 16 kPa andthe exponent of N takes the value between 06 and 08 Table 2columns 1 and 2 shows the lsquolsquoarsquorsquo and lsquolsquobrsquorsquo values presented byIshihara [20] and respective references This is the first textbookwhich summarizes many SPT N versus shear modulus relationsdeveloped by others In this book the author has also highlightedthat the SPT N value in Japanese practice is approximately12 times [E(13thorn112)2] greater than the N60 values used inthe US practice [20] Fig 4 shows the correlation presented byIshihara [20] considering the Japanese SPT N values Anbazhaganet al [11] had noticed that Gmax values vary from 12 to 25 kPa forthe SPT N value of 1 and 21ndash48 kPa for the N value of 100 whichare very less This has been brought to the notice of Ishihara bythe first author and had requested clarification for the same (e-mail communication with Ishihara on June 2009) Ishihara hasgiven the clarification by e-mail that the constant lsquolsquoarsquorsquo presented incolumn 3 Table 2 (Table 64 p 119 in [20]) should have values of10 122 139 y with the unit MPa This means that the shearmodulus correlation given by Ishihara [20] in Table 64 p 119 is9810 times less than the actual values reported by the originalresearchers Hence the modified lsquoarsquo values based on this study aregiven in Table 2 column 4

Another SPT N based correlation given by Kramer [23] text-book of Geotechnical Earthquake Engineering (p 235 SPT Eq (2))

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

Seed et al (1983)Kramer (1996)

Fig 6 Comparison of correlation developed by Seed et al [34] and reproduced by

Kramer [23] these are also used in SHAKE2000


is given by Eq (21) in Table 1 This correlation was cross referredby the original authors Imai and Tonouchi [18] for sandy soil butSPT N values were replaced by hammer energy corrected N valuesin the original correlation Personal communication with Kramerconfirms that N60 is the hammer energy corrected N value for 60energy release It can be noticed that no information is availableregarding hammer type energy level and releasing mechanism inImai and Tonouchi [18] Kramer [23] has not highlighted how N60

was estimated According to Seed et al [35] two types ofhammers were used in Japan with different hammer energiesHammer used before 1982 had the energy release of 78 oftheoretical values which is 13 times larger than that of 60hammer release in the US [35]

In order to compare the original correlation developed by Imaiand Tonouchi [18] and reproduced sand correlation by Kramer[23] N values in the original correlation for alluvial clay and sanddiluvial sand and all soils (Eqs (10) (11) (13) and (14)) aremultiplied by 13 (ie N60frac1413N) Fig 5 shows the comparison ofreproduced correlation by Kramer [23] (Eq (21)) for sand withoriginal Imai and Tonouchi [18] correlation for alluvial clay andsand diluvial sand and all the soil types (Eqs (10) (11) (13) and(14)) Similar to Fig 2 correlations of diluvial sand and all the soiltypes (13 and 14) are comparable for hammer energy corrected N

values It can be easily observed that the reproduced correlation(Eq (21)) is not comparable with Imai and Tonouchi [18]correlations applicable for alluvial and diluvial sand or all thesoil types for any N value But the reproduced correlation byKramer [23] is well comparable with alluvial clay (Eq (10)) for allthe N values Kramer [23] has suggested the correlation (Eq (21))for sand but which closely matches with alluvial clay

SHAKE2000 is a widely used ground response software whichis used by many researchers for site specific response studies andmicrozonation mapping Correlations given in Eqs (15) (18) (19)and (21) (Eqs (3) (5) (6) and (13) in SHAKE2000) are inbuilt inSHAKE2000 to calculate the shear modulus using SPT N valuesEqs (18) and (19) require the effective vertical and mean stressand hence these are not considered for comparison in this paperwith other correlations Eqs (15) and (21) are compared byconsidering N60 and N values measured in the US are the same[35] Fig 6 shows the comparison of Seed et al [34] correlation(Eq (15)) and reproduced Kramer [23] correlation (Eq (21)) Twocorrelations are comparable up to the SPT N values of 25 beyondwhich both correlations are not compatible

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50 60 70 80 90 100 110Corrected SPT N value (N60)

Shea

r mod

ulus

(MPa

)

Overall dataKramer Sand -N60Alluvial sand Diluvial sand Alluvial clay

Fig 5 Comparison of original correlations developed by Imai and Tonouchi [18]

for corrected N values for 60 hammer energy and reproduced correlation given in

Kramer [23]

6 Comparison of existing correlations

Review of shear modulus correlations clearly shows thatlimited study has been carried out in this area Most of thestudies were carried out during the 1970s and 1980s using thewell shooting technique except that by Anbazhagan andSitharam [5] A few correlations were developed by assumingthe density Rest of them has assumed N values less than 1 andhas extrapolated N value more than 100 or 50 to estimate theshear modulus One similarity is that the above correlations weredeveloped between measured SPT N values and shear modulusexcept that Kramer [23] and Seed et al [36] reproduced correla-tions between the corrected N values to measured shear modulusIt is also observed that these correlations are based on theexperimental studies carried out in Japan the United States andIndia In Japan and India the hammer energy is almost samebecause of similarities in hammer type and releasing mechanismIn the US the hammer energy is 077 times that of the Japaneseand Indian hammer energy

Seed et al [34] have not given any information about N values(corrected or measured) and hammer energy In order to compareSeed et al [34] correlation (Eq (15)) with other correlations Eq(15) is considered two cases (a) assuming N value is similar toother correlations and (b) N values are 077 times less than theother correlations and similar to US measured values (called asEq (15) modified) Fig 7 shows the comparison of final correla-tions proposed by different researchers (Eqs (1)ndash(4) (8) (9)(14)ndash(16) and (15) modified)

Fig 7 shows that the shear modulus is almost same for all thecorrelations for N value up to 20 beyond which shear modulus isinconsistent The correlation proposed by Ohba and Toriumi [27][Eq (2)] gives the least shear modulus for all the values of N whencompared to other correlations Similarly the correlation pro-posed by Seed et al [34] [Eq (15) and (15) modified] gives thehighest shear modulus for the entire values of N when comparedto other correlations The shear modulus obtained from correla-tions proposed by Imai and Yoshimura [17] [Eq (1)] Ohta et al[16] [Eq (3)] Hara et al [29] [Eq (9)] Imai and Tonouchi [18][Eq (14)] and Sitharam and Anbazhagan [38] [Eq (16)] iscomparable The shear modulus obtained from Ohsaki and Iwa-saki [28] [Eqs (4) and (8)] is comparable with the above correla-tions up to SPT N value 60 and for N value above 60 it givesslightly higher shear modulus Among the Ohsaki and Iwasaki[28] correlations the original correlation [Eq (4)] is closer to

0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

6

14

15

16

15 modified

Fig 8 Comparison of correlations developed using all the soil types

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100 110

Measured SPT N values

Shea

r Mod

ulus

(MPa

)

5

11

13

Fig 9 Comparison of correlations developed using the sandy soil

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110Measured SPT N values

Shea

r Mod

ulus

(MPa

)

7

9

10

12

Fig 10 Comparison of correlations developed using the cohesive soil

0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

8

9

14

15

16

15 modified

Fig 7 Comparison of final correlations developed by different researchers


other five correlations and rounded correlation [Eq (8)] givesslightly higher shear modulus when compared to Eq (4) Correla-tions developed by Imai and Yoshimura [17] [Eq (1)] and Ohbaand Toriumi [27] [Eq (2)] have a similar density assumption toestimate the shear modulus but Eq (1) matches closely withother four correlations Out of five comparable correlationscorrelation developed by Hara et al [16] [Eq (9)] has considereddata from cohesive soil but it matches well with the other fourcorrelations developed for all soil types

In order to discuss the correlations developed for specific soiltype the above correlations are broadly divided as three groupsapplicable to (a) all the soil types (b) sandy soil and (c) cohesivesoil Final correlation and correlation developed for intermediatesoil are included in the first group Fig 8 shows the comparison ofcorrelations coming under the first group Here similar to Fig 7Eqs (2) and (15) give lesser and higher shear modulus whencompared to other correlations The correlation given for inter-mediate soil (Eq (6)) by Ohsaki and Iwasaki [28] matches closelywith other correlations (Eqs (1) (3) (14) and (16)) The correla-tion proposed by Ohsaki and Iwasaki [28] considering all the soiltypes (Eq (4)) shows the higher shear modulus for the SPT N

value of above 60 Correlations developed by Imai and Yoshimura[17] [Eq (1)] Ohta et al [29] [Eq (3)] Ohsaki and Iwasaki [28][Eq (6)] Imai and Tonouchi [18] [Eq (14)] and Sitharam andAnbazhagan [38] [Eq (16)] show comparable shear modulus forall the soil types irrespective of the N values However slightdifference can be observed for the N value of above 80 whichmight be due to data variations

Fig 9 shows correlations for sandy soil Ohsaki and Iwasaki [28][Eq (5)] and Imai and Tonouchi [18] [Eq (11) for Alluvial and

Eq (13) for Diluvial] have developed correlation considering sandysoil data These three correlations show similar shear modulusup to the N value of 20 beyond which Eqs (5) and (13) are compar-able up to the N value of 50 For N values above 50 correlationdeveloped by Imai and Tonouchi [18] [Eqs (11) and (13)] shows thelower shear modulus when compared to Eq (5) which may beattributed by the data Imai and Tonouchi [18] have consideredmore data points of N value 50 and below and Ohsaki and Iwasaki[28] have considered more data points of N value 50 and above N

values above 50 were extrapolated by Imai and Tonouchi [18] butthe same might be measured by Ohsaki and Iwasaki [28]

Group three correlations are developed using the cohesive soiland are shown in Fig 10 Ohsaki and Iwasaki [28] [Eq (7)] Haraet al [29] [Eq (9)] and Imai and Tonouchi [18] [Eq (10) forAlluvial and Eq (12) for Diluvial] developed the correlation appli-cable to cohesive soil These four correlations give similar shearmodulus up to the N value of 40 beyond which the correlationdeveloped by Imai and Tonouchi [18] [Eq (10)] gives the lowershear modulus when compared to the other three correlationsThis may be attributed by data set used by Imai and Tonouchi[18] which contains a maximum N value of 40 Other threecorrelations are comparable for all the N values This comparisonshows that correlations developed by different researchers areunique and have limited applications for other region-based SPTprocedures and soil types A new correlation considering themeasured data and which is applicable to all types of soilsand regions will be appropriate for practical application Manyresearchers are using single or textbook cited correlations world-wide for site response and microzonation studies without realiz-ing its suitability for their region


7 New correlations based on two data set combinations

This study shows that about 10 independent publications weregiven SPT N versus shear modulus correlations The correlationgiven by Seed et al [36] and Kramer [23] was reproduced thecorrelations from other researcherrsquos data with required assumptionsAmong the remaining eight correlations five correlations arecomparable to each otherrsquos one correlation is partially comparableand two correlations are not comparable Among these five compar-able correlations the correlation by Imai and Yoshimura [17] [Eq(1)] has developed by assuming the density to calculate the shearmodulus Among the remaining four correlations three were devel-oped in Japan and one was developed in India Even though thesecorrelations are comparable they may not be directly applicable toother regions because of different SPT practice and extrapolateddata Hence new correlations have been attempted in this section

G = 1703NR = 085

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1431NRsup2 = 073

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1603NRsup2 = 089

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1440NRsup2 = 075

1

10

100

1000

10000

01 10 100 1000 10000SPT N value

Shea

r mod

ulus

(MPa

)

Fig 11 New correlations by combining Anbazhagan and Sitharam [5] and others data (

the SPT N value of 1ndash100 with 10 error

by combining the authors data with the available old data Most ofthe earlier correlations were developed including the SPT N value ofless than 1 and more than 100 Researchers have assumed the SPT N

values of less than 1 and extrapolated the SPT N values of more than100 Data set used by Anbazhagan and Sitharam [5] has a measuredN value of up to 109 and assumed the N value of 100 for reboundcorresponding to rock In few locations the N value of more than 100was also recorded

In this study eight combinations have been attempted to developnew SPT N versus Gmax correlations Shear modulus reported byother researchers is converted to SI units of MPa and used forregression analysis Two correlations have been developed for eachcombination the first one is considering all the data sets and thesecond one is eliminating the assumed data sets ie considering theSPT N value of 1ndash100 with 10 error The N values from 09 (10 lessthan 1) to 110 (10 more than 100) are considered in the second

G = 1850NRsup2 = 082

1

10

100

1000

01 1 10 100 1000Measured SPT N value

Shea

r mod

ulus

(MPa

)

G = 1343NRsup2 = 068

1

10

100

1000

10000

1 10 100 1000Measured SPT N value

Shea

r mod

ulus

(MPa

)

G = 1689NRsup2 = 087

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1482NRsup2 = 064

1

10

100

1000


Shea

r mod

ulus

(MPa

)

a) (c) (e) and (g) are considering all the data and (b) (d) (f) and (h) are considering


combination to account the digitalization error Fig 11andashh showsthe combination of author data with other researchers data andresulted best fit correlation Fig 11a c e and g for all the data sets

Table 3New correlations based on two three or more data set combinations

Case Correlations

Authors data are combined with

I Ohta et al [29]

Ohta et al [29]

II Ohsaki and Iwasaki [28]

Ohsaki and Iwasaki [28]

III Hara et al [16]

Hara et al [16]

IV Imai and Tonouchi [18]

Imai and Tonouchi [18]

V Ohta et al [29] and Hara et al [16]

Ohta et al [29] and Hara et al [16]

VI Ohta et al [29] Hara et al [16] and Ohsaki and Iwasaki [28]

Ohta et al [29] Hara et al [16] and Ohsaki and Iwasaki [28]

VII Ohta et al [29] Hara et al [16] and Imai and Tonouchi [18]

Ohta et al [29] Hara et al [16] and Imai and Tonouchi [18]

VIII Ohta et al [29] Hara et al [16] Ohsaki and Iwasaki [28] and Imai and Tonouchi

Ohta et al [29] Hara et al [16] Ohsaki and Iwasaki [28] and Imai and Tonouchi

Gmdashlow strain measured shear modulus and Nmdashmeasured SPT lsquolsquoNrsquorsquo value

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

22

23

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

24

25

Fig 12 Comparison of newly developed correlation by combining authors data and oth

(d) case IV

with correlation and Fig 11b d f and h for measured data set withcorrelation Details of each combination and resulting correlationsare given in Table 3

Remarks

Eqs in (MPa) Eq no

Gmax frac14 1703N064 eth22THORN 100 data give R2 value 085Gmax frac14 185N062 eth23THORN

9677 data give R2 value 082

Gmax frac14 1431N070 eth24THORN100 data give R2 value 070












[18] Gmax frac14 1415N069 eth36THORN100 data give R2 value 076


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

26

27

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

28

29

ers data with five comparable old correlations (a) case I (b) case II (c) case III and

0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data

Measured DataAll data

05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV


Fig 14 Comparisons of R-squared value and standard error of correlations

developed considering the four cases


The authors data have been combined with the Ohta et al [29]data and two correlations have been generated Fig 11a and bshows a typical plot for the correlations using the data from[529] The first combination of 100 data set gives Eq (22) andthe second combination of 9677 total data set gives Eq (23) (seeTable 3) Developed correlations (Eqs (22) and (23)) are com-pared with the original five comparable correlations (Eqs (1) (3)(9) (14) and (16)) in Fig 12a These two correlations matches wellwith the five correlations when compared to the original correla-tions developed by Ohta et al [29] and [5] Eq (22) ie firstcombinations resulting lesser shear modulus for N values lessthan 50 and higher shear modulus for N values more than 50when compared to Eq (23) ie second combinations The authorsdata are combined with Ohsaki and Iwasaki [28] and twocorrelations have been generated and presented as Eqs (24) and(25) in Table 3 Fig 12b shows the comparison of new correlations(Eqs (24) and (25)) with five original correlations Both thecorrelations give similar shear modulus for all the N values Thesenew correlations give comparable shear modulus up to the N

value of 50 and higher modulus shear modulus for the N value ofabove 50 Data used by Hara et al [16] is combined with theauthors data and new correlations have been generated andpresented as Eqs (26) and (27) in Table 3 These two newcorrelations (Eqs (26) and (27)) give similar shear modulus forall the values of N and match well with the correlation developedby Imai and Tonouchi [18] Fig 12c shows the comparison of twonew correlations with the old five correlations The authors dataare combined with the Imai and Tonouchi [18] data and two newcorrelations have been generated Imai and Tonouchi [18] haveused the extrapolated N values of less than 1 and more than 50for the second combinations these data are removed (Fig 11h)The comparison of these two new correlations (Eqs (28) and (29))with five correlations is shown in Fig 12d The first combinationgives slightly lesser shear modulus when compared to the secondone up to the N value of about 20 beyond which the firstcorrelation gives the higher shear modulus The first correlation(Eq (28)) is comparable with five correlations but the secondcorrelation (Eq (29)) by eliminating extrapolated data (N valuesless than 1 and more than 50) from Imai and Tonouchi [18] is notcomparable The second correlation (Eq (29)) shows the leastshear modulus for the N value of more than 50

Newly developed eight correlations for four cases are com-pared in Fig 13 Five correlations (Eqs (22) (23) (26)ndash(28))match closely for all the values of N Two correlations (Eqs (24)and (25)) obtained by the combination of the Anbazhagan andSitharam [5] and Ohsaki and Iwasaki [28] data give higher shear

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29

Fig 13 Comparison of newly developed correlation by considering two data

combinations

modulus when compared to the other five correlations for the SPTN value above 60 The correlation (Eq (29)) obtained consideringmeasured data of Anbazhagan and Sitharam [5] and Imai andTonouchi [18] gives lesser shear modulus when compared to theother correlations for the SPT N value of above 50 Standard errorof each case has been estimated and the correlations fitness iscompared The standard error is a measure of the amount of errorin the prediction of Gmax(y) for an individual N(x)

Fig 14 shows the R-squared values and standard error of thefirst four cases The measured data standard errors are slightlylower than all the data standard errors Differences in standarderror for cases IndashIII are negligible The measured data are 50 lesswhen compared to all the data for case IV R-squared values of allthe data combinations are slightly higher than the measured datacombinations R-squared value for case III shows the highest andcase IV is the least among the four cases Difference in R-squaredvalue is negligible for cases I and III and is considerable for cases IIand IV Data combination of cases I and III show relatively lessstandard error and higher R-squared values Data combinationscases II and IV shows relatively higher standard error and lesserR-squared values Further cases I and III data sets are combinedtogether and are used to generate new correlations

8 New correlations based on three and more data setcombinations

The first four cases with two combinations have resulted ineight correlations among which cases I and III ie author datacombined with Ohta et al [29] and Hara et al [16] give correla-tions with less standard error and higher R-squared values Inorder to improve the correlations these three data sets Anbazha-gan and Sitharam [5] Ohta et al [29] and Hara et al [16] arecombined together to develop the correlations which is callusedas case V Case V data set is combined with Ohsaki and Iwasaki


[28] [case VI] and Imai and Tonouchi [18] [case VII] and used togenerate two correlations Further Anbazhagan and Sitharam [5]Ohta et al [29] Hara et al [16] Ohsaki and Iwasaki [28] and Imaiand Tonouchi [18] data sets are combined (case VIII) to generatethe correlations In each case two correlations have been devel-oped by considering all the data sets and measured data set (SPTN value of 1ndash100 with 10 error) separately The summary ofthese combinations is given in the first three columns in Table 3Fig 15a c e and g and Fig 15b d f and h show data set with acorrelation for all data and measured data Newly developedcorrelations by combining three and more research works arecompared with the original five comparable correlations (Eqs (1)(3) (9) (14) and (16)) in Fig 16andashd Newly developed correlationsby combining three and more research works are compared withnew five comparable correlations (Eqs (22) (23) (26)ndash(28))developed in the previous sections in Fig 17andashd Fig 15a and bshows combined data from Anbazhagan and Sitharam [5] Ohtaet al [29] and Hara et al [16] and newly arrived Eqs (30) and (31)

G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

Fig 15 New correlations by combining three and more researchers data (a) (c) (e) an

value of 1ndash100 with 10 error

(see Table 3) These two correlations (Eqs (30) and (31)) matchwell with original five correlations (Fig 16a) Fig 17a shows thatcorrelation considering all the data (Eq (30)) matches with newfive comparable correlations up to the N value of 60 beyondwhich it gives slightly higher shear modulus The correlationconsidering the measured data (Eq (31)) matches well with fiveold and five new comparable correlations for all the values of NCase VI gives two new correlations (Eqs (32) and (33) in Table 3)and which are shown in Fig 15c and d These two correlations arecompared with the old and new five comparable correlations areshown in Figs 16b and 17b These correlations are comparablewith the original old five correlations (Fig 16b) Fig 17b showsthat these two correlations are comparable with five new correla-tions up to the N value of 50 beyond which both the correlationsgive higher shear modulus Anbazhagan and Sitharam [5] Ohtaet al [29] and Hara et al [16] data are combined with Imai andTonouchi [18] data and generated Eqs (34) and (35) (Fig 15eand f) These two correlations are comparable up to the SPT N

G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

d (g) are considering all the data and (b) (d) (f) and (h) are considering the SPT N

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37

Fig 16 Comparison of newly developed correlations with five original comparable correlations old correlations and new correlations from (a) Anbazhagan and Sitharam

[5] Ohta et al [29] and Hara et al [16] (b) Anbazhagan and Sitharam [5] Ohta et al [29] Hara et al [16] and Ohsaki and Iwasaki [28] (c) Anbazhagan and Sitharam [5]

Ohta et al [29] Hara et al [16] and Imai and Tonouchi [18] and (d) Anbazhagan and Sitharam [5] Ohta et al [29] Hara et al [16] Ohsaki and Iwasaki [28] and Imai and

Tonouchi [18]


value of 50 beyond which the measured data correlation givesthe lesser shear modulus Fig 16c shows the comparison of thesetwo correlations with the original five comparable correlationsThese two correlations reasonably match with five originalcorrelations (Fig 16c) Fig 17c shows the comparison of thesetwo correlations with the new five comparable correlationsCorrelation using all the data (Eq (34)) is well comparable withthese new five correlations Correlations considering the mea-sured data (Eq (35)) are comparable up to the N value of 50beyond which it gives the lower shear modulus Case VII data setsare combined with the Ohsaki and Iwasaki [28] data and two newcorrelations have been generated This is called as case VIII anddata set with correlation is shown in Fig 15g and h Both thecorrelations (Eqs (36) and (37)) are comparable with the fiveoriginal correlations (Fig 16d) A comparison with the new fivecorrelations (Fig 17d) shows that the correlation using all thedata (Eq (36)) gives higher shear modulus for the value N above70 and measured data correlation match with others correlations

Fig 18 shows the correlations developed in this sectionconsidering data from three data sets and more research worksFrom Fig 18 it can be observed that combining more datareduces the differences in estimating the shear modulus andimproves the correlations coefficient ie two data combinedcorrelation shows larger difference in the shear modulus for thesame values of N when compared to three or more data combina-tions Fig 19 shows the R-squared values and standard error offour cases discussed above The highest R squared value of 088and lower standard error were obtained for case V all data and

measured data combinations The R squared value and standarderror of measured data correlation are very close to all the datacorrelations In general measured data correlations are having lessstandard error when compared to all the data correlations

9 Result and discussion

Eight independent correlations are developed between shearmodulus and measured SPT N values by various researchers Fiveof them are comparable and rest of them are not Each equationhas its own limitations with respect to the data distribution anddensity assumptions In order to find a good correlation applic-able for all the regions different combinations are attempted Thisstudy shows that correlations resulting by adding the Ohsaki andIwasaki [28] data to any other data give higher predication ofshear modulus particularly for the SPT N value of above 50Similarly resulting correlation by adding the Imai and Tonouchirsquos[18] measured data to any other data gives lower predication ofshear modulus for any N value Correlations obtained by combi-nation of any other data with Imai and Tonouchi [18] are veryclose to Imai and Tonouchi [18] original correlation This isattributed by a large number of data points in Imai and Tonouchi[18] when compared to others

A comparison of R squared value and standard error of all thedata and measured data combinations shows that the correlationdeveloped by using Anbazhagan and Sitharam [5] Ohta et al [29]and Hara et al [16] data having higher R squared value and less

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35

Fig 17 Comparison of newly developed correlations with five comparable correlation developed by combining authors data with others data (a) Anbazhagan and

Sitharam [5] Ohta et al [29] and Hara et al [16] (b) Anbazhagan and Sitharam [5] Ohta et al [29] Hara et al [16] and Ohsaki and Iwasaki [28] (c) Anbazhagan and

Sitharam [5] Ohta et al [29] Hara et al [16] and Imai and Tonouchi [18] and (d) Ohta et al [29] Hara et al [16] Ohsaki and Iwasaki [28] and Imai and Tonouchi [18]

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37

Fig 18 Comparison of correlations developed considering the three and more

data sets


standard error All the data correlations have slightly higher R

squared value and lower standard error when compared to themeasured data correlation Both correlations are comparable andmeasured data correlation matches very well with the original oldand new comparable correlations This correlation (Eq (31)) hasbeen considered as a reference to compare other correlations interms of percentage of Gmax error (PGE) Typical PGE is calculatedaccording to the relation given below

PGE for correlation 1

frac14Gmax from correlation 1Gmax from correlation 31

Gmax from correlation 31 100 ethTHORN

eth38THORN

Percentage error in between correlations 30 and 31 is veryless about 5 up to the N value of 5 and less than 3 for the N

value of above 5 (see Fig 20a) Percentage error in betweencorrelation 15 [34] and 31 is very high (more than 300 andabove) Hence this is removed from the comparison plot Fig 20ashows the PGE for the original old correlations with new correla-tion (Eq (31)) PGE is reduced up to a certain value of N and

0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII


Fig 19 Comparisons of standard error and R squared value of correlations

developed by considering the three and more data sets


increased or constant for all the correlations except the correla-tions by Ohba and Toriumi [27] [Eq (2)] and Kramer [23][Eq (21)] where PGE increases with increasing N value PGE isless than 20 for the correlations developed by Ohta et al [16][Eq (3)] Hara et al [29] [Eq (9)] and Imai and Tonouchi [18][Eq (14)] PGE is more than 20 up to the N value of 8 andgradually decreases approaching zero and less than 10 for restof the N values in the correlation developed by Imai andYoshimura [17] [Eq (1)] and Anbazhagan and Sitharam [5][Eq (16)] PGE is less than 15 for the N value of 3ndash30 and morethan 15 for rest of the N values for the correlation given by Ohsakiand Iwasaki [28] [Eq (4)] PGE is more than 15 for all the N valuesfor correlations presented by Ohba and Toriumi [27] [Eq (2)] andKramer [23] [Eq (21)]

Fig 20b shows the PGE for correlations developed consideringtwo data combinations (cases IndashIV) PGE for the correlation consider-ing the measured data (Eqs (23) (25) (27) and (29)) are less whencompared to correlations (Eqs (22) (24) (26) and (28)) consideringall the data PGE is less than 5 for correlations developed combiningthe authors data with Ohta et al [29] and Hara et al [16] [Eqs (22)(26) and (27)] A correlation considering the measured data of theauthor and Ohta et al [29] [Eq (23)] shows a PGE of more than 5 upto the N value of 10 and PGE approaches less than 5 for rest of the N

values A similar trend is also observed up to the value of N of 15 forcorrelations developed using all the data of the author and Imai andTonouchi [18] [Eq (28)] The same combinations have constant PGEfor all the N values using the measured data The correlationsdeveloped considering the author data and Ohsaki and Iwasaki[28] show large variations in PGE In general PGE is reducedconsiderably for new correlations developed considering the twodata combinations

Fig 20c shows the PGE for correlations developed consideringthe three and more data combinations (cases VndashVIII) Fig 20cshows the similar trend and pattern like Fig 20b but PGE values

decrease considerably when compared to new correlations bytwo data combinations PGE values for the correlations consider-ing all the data are relatively more up to the SPT N value of 10 andbeyond which PGE is reduced to about 3 except for correlations32 33 and 35 These three correlations have PGE more than 3 forall the values of N due to adding Ohsaki and Iwasaki [28] data andremoving extrapolated data from Imai and Tonouchi [18]

10 Correlations for all regions

Proposed correlations with high R2 and less standard errormatch well with the originally proposed correlations and arelower in percentage of Gmax error for all the N values Thiscorrelation cannot be directly applicable to other regions becausethe SPT N values used for correlations are measured in Japan andIndia with a hammer energy of 78 Hammer energy and otherparameters control the SPT N which is region specific and varyfrom region to region The SPT N values depend on drillingmethods drill rods borehole sizes and stabilization samplerblow count rate hammer configuration energy corrections finecontent and test procedure [332215395] These correlations canbe used for other regions if proper correction factors are appliedto the SPT N values

The first and foremost correction factor is the hammer energycorrection factor which depends on the energy applied to count N

values The SPT N values used for correlations were measured byapplying average 78 of theoretical energy If the SPT N valuesmeasured other than 78 theoretical energy the correctionsfactor has to be applied so that these shear modulus correlationcan be used in any region

Hammer energy correction factor CES can be calculated usingthe below equation

CES frac14ERU

ERMfrac14

78

ERMeth39THORN

where ERU is the hammer energy used for Gmax correlations ie78 and ERM the average measured hammer energy applied in theregion (percentage with respect to theoretical energy) This factorcan be multiplied with measured N value in the region and usedin the correlation (Eq (31)) Energy level in different regionsand respective correction factor is given in Table 4 Table 4 alsoshows energy corrected correlation constant lsquoarsquo corresponding toEq (31) here constant lsquobrsquo remains same as 065 By consideringthe average reported energy in different regions correlationconstant can be modified This constant can be directly used withthe measured value of N in the respective region Based onhammer energy one can choose the constant lsquoarsquo for example ifthe correlation is used in the United States (60 hammer energy)the value of lsquoarsquo can be taken as 2123 with measured N valuesSimilarly for other regions based on the energy measurementsvalue of lsquolsquoarsquorsquo can be obtained from Table 4 Fig 21a shows thehammer energy corrected N value for the hammer energy of 7065 60 55 50 and 45 with respect to measured N values(hammer energy of 78) used for Gmax correlations Fig 21bshows the Gmax variation for the hammer energy of 70 6560 55 50 and 45

In addition to hammer energy variations other factors alsoaffect N count which are listed in the beginning of this sectionThese factors can be accounted by applying necessary correctionsWidely applied correction factors in addition to the hammerenergy (CE) are (a) overburden pressure (CN) (b) borehole dia-meter (CB) (c) presence or absence of liner (CS) (d) rod length (CR)and (e) fines content (Cfines) [3435404312325] Daniel et al[14] reviewed SPT short rod length correction and suggesteddetailed investigation for rod length corrections Youd et al [42]

-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33

Fig 20 Percentage of Gmax error reference to new correlation Eq (31) developed in this study with other correlations (a) original old correlations (b) correlations

developed by considering the two data combinations and (c) correlations developed by considering the three and more data sets combinations

Table 4Energy correction factor for shear modulus correlations

Average measured energya () Hammer type and release Country Correction factor with respect to

original correlations

Modified constant of lsquoarsquo

corresponding to Eq (31)

78 Donutmdashfree fall Japan and India 7878frac14100 1640

67 Donutmdashrope and pulley Japan after 1982 7864frac141219 1999

60 DonutmdashFree fall China 7860frac14130 2132

60 Safetymdashrope and pulley United States

50 Donutmdashrope and pulley China 7850frac14156 2558

45 Donutmdashrope and pulley United States 7845frac141733 2843

45 Donutmdashrope and pulley Argentina

a Measured the hammer energy values after Seed et al [35]


have carried out field experiments and have concluded that thecorrection factor for rod length is increasing with the length ofrod as given in Youd et al [43] Changho et al [13] have studiedthe secondary impacts on SPT rod energy and samplerpenetration

Anbazhagan and Sitharam [5] have applied all the correctionsand developed correlation between measured and corrected N

values The authors have used the hammer energy correction

factor of 07 for 60 hammer energy but in this study it can benoticed that the hammer energy correction factor should be 077Hence correlations developed by Anbazhagan and Sitharam [5]are modified and presented with data in Fig 22a and b Modifiedcorrelations between measured N values and corrected N values[(N1)60 and (N1)60cs] are given below

ethN1THORN60 frac14 105ethNTHORN090eth40THORN

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue

N used for correlations (78)N measured by 70

N measured by 65N measured by 60N measured by 55N measured by 50

N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110

Measured SPT N value with different hammer energy

Shea

r mod

ulus

(MPa

)

N used Gmax correlationN for 70N for 65N for 60N for 55N for 50N for 45

Fig 21 (a) Plot of measured and corrected SPT N values for different hammer

energies and (b) comparison of shear modulus variation for measured and

different hammer energies corrected N values considering correlation 31

(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110

Measured SPT N value with 78 hammer energy

(N)

Data

Anbazhagan and Sitharam (2010)

(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110Measured SPT N value with 78 hammer energy

(N)

Data


Fig 22 Correlation between measured and corrected SPT N values (a) N versus

corrected N value for 60 hammer energy and other corrections excluding fines

content correction [(N1)60] and (b) N versus corrected N value for 60 hammer

energy and other corrections including fines content correction [(N1)60cs]


ethN1THORN60cs frac14 286ethNTHORN068eth41THORN

where (N1)60 is the corrected N value for 60 hammer energy andother corrections excluding fines content correction and (N1)60cs isthe corrected N value for 60 hammer energy and other correc-tions including fines content correction Fig 22a and b also showsthe presently developed correlation between measured andcorrected N values with old correlations proposed by Anbazhaganand Sitharam [5] considering CE as 07 This variation is consider-able for N values corrected without considering fines correctionand negligible by considering fines content corrections Gmax

correlation (Eq (31)) is also modified with respect to the abovetwo corrected N values considering 60 hammer energy Fig 23aand b shows correlations between corrected N values and shearmodulus for data used in correlation 31 The regression coefficientof R2 values does not vary for measured or corrected values of NCorrelations for corrected values of N are given below

The correlation for corrected N value for 60 hammer energyand other corrections excluding fines content correction [(N1)60]

Gmax frac14 1509frac12ethN1THORN60074 eth42THORN

The correlation for corrected N value for 60 hammer energyand other corrections including fines content correction [(N1)60cs]

Gmax frac14 603frac12ethN1THORN60cs095 eth43THORN

These correlations can be directly used in Japan and India Inother regions based on hammer energy the value of N should bemodified and (N1)60 or (N1)60cs can be evaluated using Eqs (40)

and (41) and correlations (42) and (43) can be used Before using(N1)60 or (N1)60cs the researcher should take into account theparameters suitable for their region

11 Conclusions

This paper presents a review of available correlations betweenSPT N values and shear modulus Eight independent and tworeproduced correlations are published till date The followingobservations have been made while analyzing these correlationsin this study

(1)

Reproduced Gmax correlations given in Ishihara [20] is notcomparable with the original published correlations Correla-tion coefficient of constant lsquolsquoarsquorsquo values given in Ishihara [20]are 9810 times less than the actual value The authors haveidentified this and suggested modified constant lsquolsquoarsquorsquo values (inTable 2) for the correlation given in Ishihara [20] afterpersonal communication with Ishihara (e-mail from Ishiharain 2009)

(2)

The reproduced correlation given by Kramer [23] for sandysoil with a corrected N value of 60 hammer energy iscomparable with Imai and Tonouchi [18] alluvial clay correla-tion with corrected N value

G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000

01 1 10 100Corrected N value [(N ) ]

Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011

Corrected N value [(N ) ]

Shea

r mod

ulus

(MPa

)

Fig 23 Correlation between shear modulus and corrected N values (a) corrected

N value for 60 hammer energy and other corrections excluding fines content

correction [(N1)60] and (b) corrected N value for 60 hammer energy and other

corrections including fines content correction [(N1)60cs]


(3)

The two correlations proposed by Seed et al [34] and Kramer[23] and used in site response program SHAKE2000 are notcomparable even though Seed et al [34] have developedcorrelation considering the US data These data were mea-sured using 60 hammer energy and Kramer [23] has mod-ified the Imai and Tonouchi [18] equation for similar 60hammer energy

(4)

Eight independent researchers have developed SPT measuredN versus Gmax correlations The comparison shows that thecorrelation proposed by Ohba and Toriumi [27] [Eq (2)] givesthe least shear modulus for all the values of N when comparedto the other correlations Similarly correlation proposed bySeed et al [34] [Eq (15)] gives the highest shear modulus forall the values of N when compared to the other correlations

(5)

Correlations proposed by Imai and Yoshimura [17] [Eq (1)]Ohta et al [29] [Eq (3)] Hara et al [16] [Eq (9)] Imai andTonouchi [18] [Eq (14)] and Sitharam and Anbazhagan [38][Eq (16)] are comparable These correlations may be used byknowing the limitations with respect to hammer energy soiltypes and extrapolated SPT N values

(6)

Correlation proposed by Ohsaki and Iwasaki [28] [Eqs (4) and(5)] is comparable with the above five correlations up to theSPT N value of 60 and beyond which it gives slightly highershear modulus

(7)

Grouping of correlations based on soil type shows thatcorrelation proposed by Imai and Yoshimura [17] [Eq (1)]Ohta et al [29] [Eq (3)] Ohsaki and Iwasaki [28] [Eq (6)]Imai and Tonouchi [18] [Eq (14)] and Sitharam and Anbaz-hagan [38] [Eq (16)] may be applicable to all types of soil

(8)

The correlations proposed for sandy soil by Ohsaki andIwasaki [28] [Eq (5)] and Imai and Tonouchi [18] [Eq (11)for Alluvial and Eq (13) for Diluvial] are not comparable

(9)

The correlations proposed for cohesive soil by Ohsaki andIwasaki [28] [Eq (7)] Hara et al [16] [Eq (9)] and Imai andTonouchi [18] [Eq (10) for Alluvial and Eq (12) for Diluvial]are comparable up to an N value of 40 and the first threecorrelations (Eqs (7) (9) and (10)) are comparable for all thevalues of N

New correlations are proposed by combining the authors datawith available old data from each researcher separately in twoways (a) using all the data and (b) eliminating assumed andextrapolated data ie measured data This study shows thatcorrelations using measured data are better than correlationsusing all the data (including extrapolated) Further another set ofcorrelations is developed by combining three and more data setsby considering all the data and measured data separately Threeand more data combinations give the best correlation whencompared to the original independent correlations and two datacombined correlations Correlation obtained by combining Anbaz-hagan and Sitharam [5] Ohta et al [29] and Hara et al [16]measured data shows less standard error and highest R squaredvalue Existing correlations and new correlations are developedusing the SPT N values measured by the hammer energy of 78 inJapan and India This correlation can be directly used in otherregions where hammer energy is same For regions with differenthammer energies correction factors and modified coefficient ofconstant values of lsquoarsquo for Gmax correlation are suggested based onthis study Correction factors are obtained considering the widelyavailable hammer energy measurement of 45ndash70 Correlationbetween uncorrected and corrected SPT N values for 60 hammerenergy is studied and presented in this paper Correlationbetween measured shear modulus and corrected 60 hammerenergy N values is also presented The proposed correlations arenew and applicable to all types of soils This correlation can beused in other regions with different hammer energies by applyingthe necessary correction factor suggested in this study based onthe available hammer energy measurement

Acknowledgments

The author thanks Prof Ishihara Prof Tonouchi Prof Kramerand Prof Arango for their valuable input through emails Specialthanks to Prof Tonouchi and Dr Akio Yamamooto TechnicalManager OYO Corporation for supplying a soft copy of data usedby Imai and Tonouchi [18] Thanks to Dr JS Vinod LecturerUniversity of Wollongong NSW Australia for his valuable sugges-tions and discussions The authors also thank Dr AnirudhanGeotechnical Solutions Chennai Dr Parthasarathy Sarathy Geo-tech amp Engineering Services Bangalore Dr Narasimha Raju CIVIL-AID Technoclinic Pvt Bangalore and Mr Peter Elite EngineeringConsultancy Bangalore for exchanging their field experience anddetails The author also thank Seismology Division Ministry ofEarth Sciences Government of India for funding the project lsquolsquoSiteResponse Studies Using Strong Motion Accelerographsrsquorsquo (Ref noMoESPO(Seismo)1 (20)2008)

References

[1] Anbazhagan P Liquefaction hazard mapping of Bangalore South IndiaDisaster Advances 20092(2)26ndash35

[2] Anbazhagan P Sitharam TG Site characterization and site response studiesusing shear wave velocity Journal of Seismology and Earthquake Engineering200810(2)53ndash67


[3] Anbazhagan P Sitharam TG Spatial variability of the weathered andengineering bed rock using multichannel analysis of surface wave surveyPure and Applied Geophysics 2009166(3)409ndash28

[4] Anbazhagan P Sitharam TG Vipin KS Site classification and estimation ofsurface level seismic hazard using geophysical data and probabilisticapproach Journal of Applied Geophysics 200968(2)219ndash30

[5] Anbazhagan P Sitharam TG Relationship between low strain shear modulusand standard penetration test lsquoNrsquo values ASTM Geotechnical Testing Journal201033(2)150ndash64

[6] Anbazhagan P Sitharam TG Seismic microzonation of Bangalore Journal ofEarth System Science 2008117(S2)833ndash52

[7] Anbazhagan P Sitharam TG Mapping of average shear wave velocity forBangalore region a case study Journal of Environmental amp EngineeringGeophysics 200813(2)69ndash84

[8] Anbazhagan P Sitharam TG Estimation of ground response parameters andcomparison with field measurements Indian Geotechnical Journal200939(3)245ndash70

[9] Anbazhagan P Thingbaijam KKS Nath SK Narendara Kumar JN Sitharam TGMulti-criteria seismic hazard evaluation for Bangalore city India Journal ofAsian Earth Sciences 201038186ndash98

[10] Anbazhagan P Indraratna B Rujikiatkamjorn C Su L Using a seismic surveyto measure the shear modulus of clean and fouled ballast Geomechanics andGeoengineering An International Journal 20105(2)117ndash26

[11] Anbazhagan P Sitharam TG Aditya P Correlation between low strain shearmodulus and standard penetration test lsquoNrsquo values In Proceedings of the fifthinternational conference on recent advances in geotechnical earthquakeengineering and soil dynamics 2010 p 10 (Paper no 113b)

[12] Cetin KO Seed RB Kiureghian AD Tokimatsu K Harder Jr LF Kayen RE et alStandard penetration test-based probabilistic and deterministic assessmentof seismic soil liquefaction potential Journal of Geotechnical and Geoenvir-onmental Engineering 2004121314ndash40

[13] Changho L Jong-Sub L Shinwhan A Woojin L Effect of secondary impacts onSPT rod energy and sampler penetration Journal of Geotechnical andGeoenvironmental Engineering 2010136(3)512ndash26

[14] Daniel CR Howie JA Jackson S Walker B Review of standard penetration testshort rod corrections Journal of Geotechnical and Geoenvironmental Engi-neering 2005131(4)489ndash97

[15] Farrar JA Nickell J Alien MG Goble G Berger J Energy loss in long rodpenetration testingmdashterminus dam liquefaction investigation In Proceed-ings of the ASCE specialty conference on geotechnical earthquake engineer-ing and soil dynamics III vol 75 1998 p 554ndash67

[16] Hara A Ohta T Niwa M Tanaka S Banno T Shear modulus and shear strengthof cohesive soils Soils and Foundations 1974141ndash12

[17] Imai T Yoshimura Y Elastic wave velocity and soil properties in soft soilTsuchito-Kiso 197018(1)17ndash22 [in Japanese]

[18] Imai T Tonouchi K Correlation of N-value with S-wave velocity and shearmodulus In Proceedings of the 2nd European symposium on penetrationtesting 1982 p 57ndash72

[19] IS 2131 Indian standard method for standard penetration test for soils NewDelhi Bureau of Indian Standards 1981

[20] Ishihara K Soil behaviour in earthquake geotechnics Oxford New YorkClarendon Press 1996

[21] Kanli AI Tildy P Pronay Z Pinar A Hemann L Vs30 mapping and soilclassification for seismic site effect evaluation in Dinar region SW TurkeyGeophysics Journal International 2006165223ndash35

[22] Kovacs WD Salomone LA Yokel FY Energy measurement in the standardpenetration test Washington (DC) US Department of Commerce andNational Bureau of Standards 1981

[23] Kramer SL Geotechnical earthquake engineering Delhi (India) Pearson

Education Ptd Ltd 1996 [Reprinted 2003][24] Marano KD Wald Dj Allen TL Global earthquake casualties due to secondary

effects a quantitative analysis for improving rapid loss analyses Natural

Hazards 201052319ndash28[25] Miller RD Xia J Park CB Ivanov J Multichannel analysis of surface waves to

map bedrock The Leading Edge 199918(12)1392ndash6[26] Motulsky H Confidence and prediction bands graphing nonlinear regression

GraphPad Prism version 500 for Windows San Diego (CA USA) GraphPad

Software httpwwwgraphpadcomS [last accessed on 23-08-2008][27] Ohba S Toriumi I Research on vibration characteristics of soil deposits in

Osaka part 2 on velocities of wave propagation and predominant periods of

soil deposits Abstract Technical meeting of Architectural Institute of Japan

1970 [in Japanese][28] Ohsaki Y Iwasaki R On dynamic shear moduli and Poissonrsquos ratio of soil

deposits Soils and Foundations 197313(4)61ndash73[29] Ohta T Hara A Niwa M Sakano T Elastic moduli of soil deposits estimated by

N-values In Proceedings of the 7th annual conference The Japanese Society

of Soil Mechanics and Foundation Engineering 1972 p 265ndash8[30] Ohta Y Goto N Estimation of S-wave velocity in terms of characteristic

indices of soil Butsuri-Tanko 197629(4)34ndash41 [in Japanese][31] Park CB Miller RD Xia J Multi-channel analysis of surface waves Geophysics

199964(3)800ndash8[32] Pearce JT Baldwin JN Liquefaction susceptibility mapping St Louis Missouri

and Illinois Final Technical Report 2005 Published in wwwweberusgs

govreportsabstract2003cu03HQGR0029pdfS[33] Schmertmann JH Palacios A Energy dynamics of SPT ASCE Journal of

Geotechnical Engineering Division 1979105(GT8)909ndash26[34] Seed HB Idriss IM Arango I Evaluation of liquefaction potential using field

performance data Journal of Geotechnical Engineering 1983109(3)458ndash82[35] Seed HB Tokimatsu K Harder LF Chung RM The influence of SPT procedures

in soil liquefaction resistance evaluations Journal of Geotechnical Engineer-

ing ASCE 1985111(12)1425ndash45[36] Seed HB Wong TR Idriss IM Tokimatsu K Moduli and damping factors for

dynamic analyses of cohesionless soils Journal of Geotechnical Engineering

1986112(11)1016ndash32[37] SHAKE2000 A computer program for the 1-D analysis of geotechnical

earthquake engineering program Users manual 2009 p 258[38] Sitharam TG Anbazhagan P Seismic microzonation principles practices and

experiments EJGE special volume bouquet 08 2008 p 61 Online http

wwwejgecomBouquet08PrefacehtmS[39] Sivrikaya O Togrol E Determination of undrained strength of fine-grained

soils by means of SPT and its application in Turkey Engineering Geology

20068652ndash69[40] Skempton AW Standard penetration test procedures Geotechnique

198636(3)425ndash47[41] Xia J Miller RD Park CB Estimation of near-surface shear-wave velocity by

inversion of Rayleigh wave Geophysics 199964(3)691ndash700[42] Youd TL Bartholomew HW Steidl JH SPT hammer energy ratio versus drop

height Journal of Geotechnical and Geoenvironmental Engineering

2008134(3)397ndash400[43] Youd TL Idriss IM Andrus RD Arango I Castro G Christian JT et al

Liquefaction resistance of soils summary from the 1996 NCEER and 1998

NCEERNSF workshops on evaluation of liquefaction resistance of soils

Journal of Geotechnical and Geoenvironmental Engineering 2001817ndash33

Soil Dynamics and Earthquake Engineering 36 (2012) 52ndash69

Contents lists available at SciVerse ScienceDirect

Soil Dynamics and Earthquake Engineering

0267-72

doi101

n Corr

fax thorn9

E-m

anbazha

aditpari

URL

journal homepage wwwelseviercomlocatesoildyn

Review of correlations between SPT N and shear modulus A new correlationapplicable to any region

P Anbazhagan n Aditya Parihar HN Rashmi

Department of Civil Engineering Indian Institute of Science Bangalore 560012 India

a r t i c l e i n f o

Article history

Received 19 July 2011

Received in revised form

2 January 2012

Accepted 8 January 2012Available online 1 February 2012

Keywords

Shear modulus

SPT N

MASW

Seismic survey

Hammer energy

Correlation

61$ - see front matter Crown Copyright amp 2

016jsoildyn201201005

esponding author Tel thorn91 80 2293246794

1 80 23600404

ail addresses anbazhaganciviliiscernetin

gan2005gmailcom (P Anbazhagan)

hargmailcom (A Parihar) rashmihn88re

httpwwwciviliiscernetin~anbazhagan

a b s t r a c t

A low strain shear modulus plays a fundamental role in earthquake geotechnical engineering to

estimate the ground response parameters for seismic microzonation A large number of site response

studies are being carried out using the standard penetration test (SPT) data considering the existing

correlation between SPT N values and shear modulus The purpose of this paper is to review the

available empirical correlations between shear modulus and SPT N values and to generate a new

correlation by combining the new data obtained by the author and the old available data The review

shows that only few authors have used measured density and shear wave velocity to estimate shear

modulus which were related to the SPT N values Others have assumed a constant density for all the

shear wave velocities to estimate the shear modulus Many authors used the SPT N values of less than

1 and more than 100 to generate the correlation by extrapolation or assumption but practically these N

values have limited applications as measuring of the SPT N values of less than 1 is not possible and

more than 100 is not carried out Most of the existing correlations were developed based on the studies

carried out in Japan where N values are measured with a hammer energy of 78 which may not be

directly applicable for other regions because of the variation in SPT hammer energy A new correlation

has been generated using the measured values in Japan and in India by eliminating the assumed and

extrapolated data This correlation has higher regression coefficient and lower standard error Finally

modification factors are suggested for other regions where the hammer energy is different from 78

Crown Copyright amp 2012 Published by Elsevier Ltd All rights reserved

1 Introduction

Many countries have initiated seismic microzonation studieswith emphasis on site effects around the world because of theincreasing earthquake damages due to ground motionsite effectsResearchers are trying to develop regional level hazard mapsconsidering different earthquake effects Earthquake damages aremainly because of the changes in the seismic waves and soilbehavior during dynamic loading These are called as site effectsand induced effects which are primarily based on geotechnicalproperties of the subsurface materials Site effects are the combi-nation of soil and topographical effects which can modify(amplify and deamplify) the characteristics (amplitude frequencycontent and duration) of the incoming wave field Induced effectsare liquefaction landslide and Tsunami hazards Amplificationand liquefaction are the major effects of earthquake that cause

012 Published by Elsevier Ltd All

48100410 (Cell)

diffmailcom (HN Rashmi)

(P Anbazhagan)

massive damages to infrastructures and loss of lives Recent studyby USGS revealed that among deadly earthquakes reported for thelast 40 years loss of lives and damages caused by ground shakinghazard was more than 80 of the total damages [24] Subsurfacesoil layers play a very important role in ground shaking modifica-tion Most of the earthquake geotechnical engineers are workingto estimate and reduce the hazards due to geotechnical aspects

Site specific response and seismic microzonation studies arecarried out by considering the local geotechnical properties ofsubsurface layers Dynamic shear modulus of subsurface layer isthe most important geotechnical property used in the site specificresponse analysis The shear modulus of subsurface layers areusually measured in situ by means of seismic exploration andsometimes by the dynamic triaxial compression test or theresonant column test of undisturbed soil samples in the labora-tory [28] A large number of researchers have presented thelaboratory based shear modulus studies Even though SPT N dataare widely used for site response and seismic microzonation veryfew studies are available for in situ correlation between shearmodulus versus standard penetration test (SPT) N values usingthe field experiments [59] Seismic microzonation requires soilparameters in the form of shear wave velocity for site classifica-tion and shear modulus to estimate the site specific ground

rights reserved

Co

nv

ert

ed

inS

Iu

nit

s(M

Pa

)N

o

of

da

tase

tsN

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s

Min

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s

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ndashndash

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00

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ta

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09

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nd

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erc

en

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ay

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od

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om

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nd

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i[1

8]

Sa

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il

PT


va

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Ta

ble

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tin

gco

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ee

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Na

nd

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ax

Co

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on

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n

o

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nd

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ura

[17

]G

ma

xfrac14

10

00

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8eth1THORN

tm

2

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ba

an

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7]

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axfrac14

12

20

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2eth2THORN

tm

2

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l[2

9]

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13

90

N07

2eth3THORN

tm

2

Oh

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ia

nd

Iwa

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i[2

8]

Gm

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12

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8eth4THORN

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2

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Iwa

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8]

Gm

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65

0N

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8]

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8]

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00

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eth8THORN

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2

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6]

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axfrac14

15

8N

06

68

eth9THORN

kg

cm

2

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nd

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i[1

8]

Gm

axfrac14

17

6N

06

07

eth10THORN

kg

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2

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nd

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8]

Gm

axfrac14

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06

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2

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8]

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axfrac14

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05

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kg

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2

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i[1

8]

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axfrac14

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06

31

eth13THORN

kg

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2

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]G

ma

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tft

2

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ga

na

nd

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[5]

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axfrac14

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a

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3]

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Eq

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G

mdashlo

wst

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me

asu

red

she

ar

mo

du

lus

an

dN

isth

em

ea

sure

dS





0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)



different soils









0

100

200

300

400

500


Shea

r mod

ulus

(MPa

)



different soils








10

100

001011

Mea

sure

d sh

ear m

odul

us (M

Pa)


G = 2428N

R = 088
















N60 frac14NmERm

60eth17THORN








Value of


Ishihara

[20] (kPa)

Value

of b



on Sep 28 2009a

(MPa)


value by authors

in this paper

(MPa)

References and

respective

equations in

this paper

1 078 10 981 Imai and

Yoshimura

[17] and

Eq (1a)

122 062 122 1196 Ohba and

Toriumi [27]

and Eq (2a)

139 072 139 1363 Ohta et al [29]

and Eq (3a)

12 08 12 1177 Ohsaki and

Iwasaki [28]

and Eq (8a)

158 067 158 1549 Hara et al [16]

and Eq (9a)


0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(kPa

)



Ohta et al (1972)


Hara et al (1974)






00THORN




0mTHORN








0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)










0

50

100

150

200

250

300

350

400

450


Shea

r mod

ulus

(MPa

)




Kramer [23]





0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

6

14

15

16

15 modified


0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r Mod

ulus

(MPa

)

5

11

13


0

50

100

150

200

250

300

350

400


Shea

r Mod

ulus

(MPa

)

7

9

10

12


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

8

9

14

15

16

15 modified













G = 1703NR = 085

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1431NRsup2 = 073

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1603NRsup2 = 089

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1440NRsup2 = 075

1

10

100

1000

10000

01 10 100 1000 10000SPT N value

Shea

r mod

ulus

(MPa

)






G = 1850NRsup2 = 082

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1343NRsup2 = 068

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1689NRsup2 = 087

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1482NRsup2 = 064

1

10

100

1000


Shea

r mod

ulus

(MPa

)





Case Correlations


I Ohta et al [29]

Ohta et al [29]



III Hara et al [16]

Hara et al [16]












0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

22

23

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

24

25


(d) case IV


Remarks

Eqs in (MPa) Eq no

















0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

26

27

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

28

29


0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29


combinations







G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































Co

nv

ert

ed

inS

Iu

nit

s(M

Pa

)N

o

of

da

tase

tsN

va

lue

use

dR

em

ark

s

Min

Ma

x

Gfrac14

98

1N

07

8M

ixe

dso

ilty

pe

Gfrac14

119

6N

06

2A

llu

via

lsa

nd

cl

ay

Gfrac14

136

3N

07

21

00

05

15

0T

ert

iary

soil

d

ilu

via

lsa

nd

ya

nd

coh

esi

ve

soil

Gfrac14

119

4N

07

82

20

05

10

0A

llso

ilty

pe

s

Gfrac14

63

74

N09

4ndash

ndashndash

Sa

nd

yso

il

Gfrac14

115

9N

07

6ndash

ndashndash

Inte

rme

dia

teso

il

Gfrac14

137

3N

07

1ndash

ndashndash

Co

he

siv

eso

il

Gfrac14

117

7N

08

ndashndash

ndashA

llso

ilty

pe

s

Gfrac14

154

9N

06

68

25

site

sd

ata

All

uv

ial

dil

uv

ial

an

dte

rtia

ryd

ep

osi

t

Gfrac14

172

6N

06

07

32

50

24

0A

llu

via

lcl

ay

Gfrac14

122

6N

06

11

29

41

70

All

uv

ial

san

d

Gfrac14

246

1N

05

55

22

21

51

70

Dil

uv

ial

cla

y

Gfrac14

173

6N

06

31

33

82

30

0D

ilu

via

lsa

nd

Gfrac14

141

2N

06

81

65

40

23

00

All

soil

typ

es

Gfrac14

62

2N

No

ta

va

ila

ble

Gfrac14

242

8N

05

52

15

21

09

Sil

tysa

nd

wit

hle

ssp

erc

en

tag

eo

fcl

ay

Gfrac14

155

6ethN

60THORN06

8M

od

ifie

dfr

om

Ima

ia

nd

To

no

uch

i[1

8]

Sa

nd

yso

il

PT


va

lue






Ta

ble

1E

xis

tin

gco

rre

lati

on

sb

etw

ee

nS

PT

Na

nd

Gm

ax

Co

rre

lati

on

sa

va

ila

ble

inli

tera

ture

Au

tho

rsO

rig

ina

lE

q

no

Eq

n

o

Un

it

Ima

ia

nd

Yo

shim

ura

[17

]G

ma

xfrac14

10

00

N07

8eth1THORN

tm

2

Oh

ba

an

dT

ori

um

i[2

7]

Gm

axfrac14

12

20

N06

2eth2THORN

tm

2

Oh

tae

ta

l[2

9]

Gm

axfrac14

13

90

N07

2eth3THORN

tm

2

Oh

sak

ia

nd

Iwa

sak

i[2

8]

Gm

axfrac14

12

18

N07

8eth4THORN

tm

2

Oh

sak

ia

nd

Iwa

sak

i[2

8]

Gm

axfrac14

65

0N

09

4eth5THORN

tm

2

Oh

sak

ia

nd

Iwa

sak

i[2

8]

Gm

axfrac14

11

82

N07

6eth6THORN

tm

2

Oh

sak

ia

nd

Iwa

sak

i[2

8]

Gm

axfrac14

14

00

N07

1eth7THORN

tm

2

Oh

sak

ia

nd

Iwa

sak

i[2

8]

Gm

axfrac14

12

00

N08

eth8THORN

tm

2

Ha

rae

ta

l[1

6]

Gm

axfrac14

15

8N

06

68

eth9THORN

kg

cm

2

Ima

ia

nd

To

no

uch

i[1

8]

Gm

axfrac14

17

6N

06

07

eth10THORN

kg

cm

2

Ima

ia

nd

To

no

uch

i[1

8]

Gm

axfrac14

12

5N

06

11

eth11THORN

kg

cm

2

Ima

ia

nd

To

no

uch

i[1

8]

Gm

axfrac14

25

1N

05

55

eth12THORN

kg

cm

2

Ima

ia

nd

To

no

uch

i[1

8]

Gm

axfrac14

17

7N

06

31

eth13THORN

kg

cm

2

Ima

ia

nd

To

no

uch

i[1

8]

Gm

axfrac14

14

4N

06

8eth1

4THORN

kg

cm

2

Se

ed

et

al

[34

]G

ma

xfrac14

65

Neth1

5THORN

tft

2

An

ba

zha

ga

na

nd

Sit

ha

ram

[5]

Gm

axfrac14

242

8N

05

5eth1

6THORN

MP

a

Kra

me

r[2

3]

Gm

axfrac14

32

5ethN

60THORN06

8eth2

1THORN

kip

ssq

f

Eq

mdashe

qu

ati

on

G

mdashlo

wst

rain

me

asu

red

she

ar

mo

du

lus

an

dN

isth

em

ea

sure

dS





0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)



different soils









0

100

200

300

400

500


Shea

r mod

ulus

(MPa

)



different soils








10

100

001011

Mea

sure

d sh

ear m

odul

us (M

Pa)


G = 2428N

R = 088
















N60 frac14NmERm

60eth17THORN








Value of


Ishihara

[20] (kPa)

Value

of b



on Sep 28 2009a

(MPa)


value by authors

in this paper

(MPa)

References and

respective

equations in

this paper

1 078 10 981 Imai and

Yoshimura

[17] and

Eq (1a)

122 062 122 1196 Ohba and

Toriumi [27]

and Eq (2a)

139 072 139 1363 Ohta et al [29]

and Eq (3a)

12 08 12 1177 Ohsaki and

Iwasaki [28]

and Eq (8a)

158 067 158 1549 Hara et al [16]

and Eq (9a)


0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(kPa

)



Ohta et al (1972)


Hara et al (1974)






00THORN




0mTHORN








0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)










0

50

100

150

200

250

300

350

400

450


Shea

r mod

ulus

(MPa

)




Kramer [23]





0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

6

14

15

16

15 modified


0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r Mod

ulus

(MPa

)

5

11

13


0

50

100

150

200

250

300

350

400


Shea

r Mod

ulus

(MPa

)

7

9

10

12


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

8

9

14

15

16

15 modified













G = 1703NR = 085

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1431NRsup2 = 073

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1603NRsup2 = 089

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1440NRsup2 = 075

1

10

100

1000

10000

01 10 100 1000 10000SPT N value

Shea

r mod

ulus

(MPa

)






G = 1850NRsup2 = 082

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1343NRsup2 = 068

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1689NRsup2 = 087

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1482NRsup2 = 064

1

10

100

1000


Shea

r mod

ulus

(MPa

)





Case Correlations


I Ohta et al [29]

Ohta et al [29]



III Hara et al [16]

Hara et al [16]












0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

22

23

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

24

25


(d) case IV


Remarks

Eqs in (MPa) Eq no

















0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

26

27

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

28

29


0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29


combinations







G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)



different soils









0

100

200

300

400

500


Shea

r mod

ulus

(MPa

)



different soils








10

100

001011

Mea

sure

d sh

ear m

odul

us (M

Pa)


G = 2428N

R = 088
















N60 frac14NmERm

60eth17THORN








Value of


Ishihara

[20] (kPa)

Value

of b



on Sep 28 2009a

(MPa)


value by authors

in this paper

(MPa)

References and

respective

equations in

this paper

1 078 10 981 Imai and

Yoshimura

[17] and

Eq (1a)

122 062 122 1196 Ohba and

Toriumi [27]

and Eq (2a)

139 072 139 1363 Ohta et al [29]

and Eq (3a)

12 08 12 1177 Ohsaki and

Iwasaki [28]

and Eq (8a)

158 067 158 1549 Hara et al [16]

and Eq (9a)


0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(kPa

)



Ohta et al (1972)


Hara et al (1974)






00THORN




0mTHORN








0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)










0

50

100

150

200

250

300

350

400

450


Shea

r mod

ulus

(MPa

)




Kramer [23]





0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

6

14

15

16

15 modified


0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r Mod

ulus

(MPa

)

5

11

13


0

50

100

150

200

250

300

350

400


Shea

r Mod

ulus

(MPa

)

7

9

10

12


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

8

9

14

15

16

15 modified













G = 1703NR = 085

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1431NRsup2 = 073

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1603NRsup2 = 089

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1440NRsup2 = 075

1

10

100

1000

10000

01 10 100 1000 10000SPT N value

Shea

r mod

ulus

(MPa

)






G = 1850NRsup2 = 082

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1343NRsup2 = 068

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1689NRsup2 = 087

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1482NRsup2 = 064

1

10

100

1000


Shea

r mod

ulus

(MPa

)





Case Correlations


I Ohta et al [29]

Ohta et al [29]



III Hara et al [16]

Hara et al [16]












0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

22

23

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

24

25


(d) case IV


Remarks

Eqs in (MPa) Eq no

















0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

26

27

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

28

29


0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29


combinations







G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































10

100

001011

Mea

sure

d sh

ear m

odul

us (M

Pa)


G = 2428N

R = 088
















N60 frac14NmERm

60eth17THORN








Value of


Ishihara

[20] (kPa)

Value

of b



on Sep 28 2009a

(MPa)


value by authors

in this paper

(MPa)

References and

respective

equations in

this paper

1 078 10 981 Imai and

Yoshimura

[17] and

Eq (1a)

122 062 122 1196 Ohba and

Toriumi [27]

and Eq (2a)

139 072 139 1363 Ohta et al [29]

and Eq (3a)

12 08 12 1177 Ohsaki and

Iwasaki [28]

and Eq (8a)

158 067 158 1549 Hara et al [16]

and Eq (9a)


0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(kPa

)



Ohta et al (1972)


Hara et al (1974)






00THORN




0mTHORN








0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)










0

50

100

150

200

250

300

350

400

450


Shea

r mod

ulus

(MPa

)




Kramer [23]





0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

6

14

15

16

15 modified


0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r Mod

ulus

(MPa

)

5

11

13


0

50

100

150

200

250

300

350

400


Shea

r Mod

ulus

(MPa

)

7

9

10

12


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

8

9

14

15

16

15 modified













G = 1703NR = 085

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1431NRsup2 = 073

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1603NRsup2 = 089

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1440NRsup2 = 075

1

10

100

1000

10000

01 10 100 1000 10000SPT N value

Shea

r mod

ulus

(MPa

)






G = 1850NRsup2 = 082

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1343NRsup2 = 068

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1689NRsup2 = 087

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1482NRsup2 = 064

1

10

100

1000


Shea

r mod

ulus

(MPa

)





Case Correlations


I Ohta et al [29]

Ohta et al [29]



III Hara et al [16]

Hara et al [16]












0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

22

23

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

24

25


(d) case IV


Remarks

Eqs in (MPa) Eq no

















0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

26

27

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

28

29


0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29


combinations







G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References
































































Value of


Ishihara

[20] (kPa)

Value

of b



on Sep 28 2009a

(MPa)


value by authors

in this paper

(MPa)

References and

respective

equations in

this paper

1 078 10 981 Imai and

Yoshimura

[17] and

Eq (1a)

122 062 122 1196 Ohba and

Toriumi [27]

and Eq (2a)

139 072 139 1363 Ohta et al [29]

and Eq (3a)

12 08 12 1177 Ohsaki and

Iwasaki [28]

and Eq (8a)

158 067 158 1549 Hara et al [16]

and Eq (9a)


0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(kPa

)



Ohta et al (1972)


Hara et al (1974)






00THORN




0mTHORN








0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)










0

50

100

150

200

250

300

350

400

450


Shea

r mod

ulus

(MPa

)




Kramer [23]





0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

6

14

15

16

15 modified


0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r Mod

ulus

(MPa

)

5

11

13


0

50

100

150

200

250

300

350

400


Shea

r Mod

ulus

(MPa

)

7

9

10

12


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

8

9

14

15

16

15 modified













G = 1703NR = 085

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1431NRsup2 = 073

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1603NRsup2 = 089

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1440NRsup2 = 075

1

10

100

1000

10000

01 10 100 1000 10000SPT N value

Shea

r mod

ulus

(MPa

)






G = 1850NRsup2 = 082

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1343NRsup2 = 068

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1689NRsup2 = 087

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1482NRsup2 = 064

1

10

100

1000


Shea

r mod

ulus

(MPa

)





Case Correlations


I Ohta et al [29]

Ohta et al [29]



III Hara et al [16]

Hara et al [16]












0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

22

23

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

24

25


(d) case IV


Remarks

Eqs in (MPa) Eq no

















0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

26

27

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

28

29


0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29


combinations







G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)










0

50

100

150

200

250

300

350

400

450


Shea

r mod

ulus

(MPa

)




Kramer [23]





0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

6

14

15

16

15 modified


0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r Mod

ulus

(MPa

)

5

11

13


0

50

100

150

200

250

300

350

400


Shea

r Mod

ulus

(MPa

)

7

9

10

12


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

8

9

14

15

16

15 modified













G = 1703NR = 085

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1431NRsup2 = 073

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1603NRsup2 = 089

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1440NRsup2 = 075

1

10

100

1000

10000

01 10 100 1000 10000SPT N value

Shea

r mod

ulus

(MPa

)






G = 1850NRsup2 = 082

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1343NRsup2 = 068

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1689NRsup2 = 087

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1482NRsup2 = 064

1

10

100

1000


Shea

r mod

ulus

(MPa

)





Case Correlations


I Ohta et al [29]

Ohta et al [29]



III Hara et al [16]

Hara et al [16]












0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

22

23

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

24

25


(d) case IV


Remarks

Eqs in (MPa) Eq no

















0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

26

27

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

28

29


0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29


combinations







G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

6

14

15

16

15 modified


0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r Mod

ulus

(MPa

)

5

11

13


0

50

100

150

200

250

300

350

400


Shea

r Mod

ulus

(MPa

)

7

9

10

12


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

2

3

4

8

9

14

15

16

15 modified













G = 1703NR = 085

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1431NRsup2 = 073

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1603NRsup2 = 089

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1440NRsup2 = 075

1

10

100

1000

10000

01 10 100 1000 10000SPT N value

Shea

r mod

ulus

(MPa

)






G = 1850NRsup2 = 082

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1343NRsup2 = 068

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1689NRsup2 = 087

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1482NRsup2 = 064

1

10

100

1000


Shea

r mod

ulus

(MPa

)





Case Correlations


I Ohta et al [29]

Ohta et al [29]



III Hara et al [16]

Hara et al [16]












0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

22

23

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

24

25


(d) case IV


Remarks

Eqs in (MPa) Eq no

















0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

26

27

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

28

29


0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29


combinations







G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References






























































G = 1703NR = 085

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1431NRsup2 = 073

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1603NRsup2 = 089

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1440NRsup2 = 075

1

10

100

1000

10000

01 10 100 1000 10000SPT N value

Shea

r mod

ulus

(MPa

)






G = 1850NRsup2 = 082

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1343NRsup2 = 068

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1689NRsup2 = 087

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1482NRsup2 = 064

1

10

100

1000


Shea

r mod

ulus

(MPa

)





Case Correlations


I Ohta et al [29]

Ohta et al [29]



III Hara et al [16]

Hara et al [16]












0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

22

23

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

24

25


(d) case IV


Remarks

Eqs in (MPa) Eq no

















0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

26

27

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

28

29


0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29


combinations







G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References






























































Case Correlations


I Ohta et al [29]

Ohta et al [29]



III Hara et al [16]

Hara et al [16]












0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

22

23

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

24

25


(d) case IV


Remarks

Eqs in (MPa) Eq no

















0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

26

27

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

28

29


0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29


combinations







G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































0

50

100

150

Stan

dard

Err

or

Case I

Case II

Case III

Case IV

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case I

Case II

Case III

Case IV








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

24 25

26 27

28 29


combinations







G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References





























































G = 1543NR2 = 088

1

10

100

1000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 080

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1438NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)

G = 1415NR2 = 076

1

10

100

1000

10000

01 1 10 100 1000SPT N value

Shea

r mod

ulus

(MPa

)




G = 1640NR2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1412NR2 = 067

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)

G = 1483NR2 = 066

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 1410NR2 = 076

1

10

100

1000

10000


Shea

r mod

ulus

(MPa

)


0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

34

35

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

1

3

9

14

16

36

37




Tonouchi [18]








0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 30

31

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 36

37

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 32

33

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

Shea

r mod

ulus

(MPa

)

22 23

26 27

28 34

35




0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

SPT N value

Shea

r mod

ulus

(MPa

)

30 31

32 33

34 35

36 37


data sets







eth38THORN



0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































0

50

100

150

Stan

dard

Err

or

Case V

Case VI

Case VII

Case VIII

MeasuredData

All data


05

06

07

08

09

1

R-S

quar

ed V

alue

Case V

Case VI

Case VII

Case VIII















CES frac14ERU

ERMfrac14

78

ERMeth39THORN



-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































-45

-35

-25

-15

-5

5

15

25

35

45

0 10 20 30 40 50 60 70 80 90 100 110SPT N value

G

max

var

iatio

n

30 31 1 2

3 4 9 14

16 21

-19

-16

-13

-10

-7

-4

-1

2

5

8

11

14

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31 22

23 24 25

26 27 28

29

-15

-12

-9

-6

-3

0

3

6

9

0 10 20 30 40 50 60 70 80 90 100 110

SPT N value

G

max

var

iatio

n

30 31

32 34

35 36

37 33






















0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


Mod

ified

N v

alue



N measured by 45

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100 110


Shea

r mod

ulus

(MPa

)





(N1)60 = 105N090

R2 = 096

0

10

20

30

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80 90 100 110


(N)

Data


(N1)60cs = 286N068

R2 = 094

0

10

20

30

40

50

60

70

80

90

100

110


(N)

Data
















11 Conclusions


(1)


(2)


G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































G = 1509[(N1)60] 074

R2 = 085

1

10

100

1000


Shea

r mod

ulus

(MPa

)

G = 602[(N1)60cs] 095

R2 = 085

1

10

100

1000

001011


Shea

r mod

ulus

(MPa

)






(3)


(4)


(5)


(6)


(7)


(8)


(9)



Acknowledgments


References



























































anbazhagan sdee print version

Documents

site response

shear modulus studies

shear modulus of subsurface

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seismic microzonation

major effects of earthquake

site specic groundurl