probabilistic identification of soil stratification · probabilistic identification of soil...

Probabilistic identification of soil stratification

J. LI�, M. J. CASSIDY†, J. HUANG‡, L. ZHANG§ and R. KELLY‡

Identification of soil stratification is vital to geotechnical structural design and construction wherethe soil layer, soil type and properties are necessary inputs. Although methods are available forclassifying the soil profiling using measured cone penetration test (CPT) data, the identification of soilstratification at unsampled locations is still difficult due to significant variability of natural soil. Theidentification is further complicated by the considerable uncertainties in the CPT measurements andsoil classification methods. This study aims to develop a probabilistic method to predict soilstratification at unsampled locations by explicitly filtering the uncertainties in soil classification systems.An established Kriging interpolation technique is used to estimate the CPT parameters which arefurther interpreted to identify the soil stratification. Equations are derived to quantify the degree ofuncertainties reduced by this method. The approaches are illustrated using a database of 26 CPT testsrecently sourced from a dike near Ballina, Australia. Results show that the majority of the uncertaintiesin the soil parameters are screened by a soil classification index. The remaining uncertainties are furtherfiltered by the soil classification systems. A clear stratification with a high degree of confidence isobtained in both horizontal plane and vertical unsampled locations, which shows excellent agreementwith the existing CPT tests. This study provides a methodology to clearly identify the soil strata andreduce the uncertainties in prediction of design properties, paving the way for a more cost-effectivegeotechnical design.

KEYWORDS: geology; site investigation; soil classification; statistical analysis

INTRODUCTIONSoil stratification is essential in geotechnical site character-isation and structural design (Houlsby & Houlsby, 2013;Wang et al., 2014). Recent studies have reported the signific-ant effect of soil stratification on the design of foundations,tunneling and pipelines (Burd & Frydman, 1997; Padrónet al., 2008; Huang & Griffiths, 2010; Zhang et al., 2012; Leeet al., 2013; White et al., 2014). The identification of soilstratification includes determining soil types, the number ofsoil layers, the thickness of each layer and soil properties.

The standardised cone penetration test (CPT) and piezo-cone (CPTU) have been widely used to infer the soil type bydirectly interpreting measured CPT/CPTU parameters (e.g.Schmertmann, 1978; Douglas & Olsen, 1981; Robertson &Campanella, 1983; Robertson, 1990; Jefferies & Davies,1993; Olsen & Mitchell, 1995; Eslami & Fellenius, 1997;Lunne et al., 1997; Schneider et al., 2008). Hence, theidentity of the soil type can only be obtained at the location atwhich a CPT is conducted. When the soil stratification atnearby locations is required during a design or constructionprocess, the results at the existing location generally cannotbe used directly due to the significant variability of natural

soils (Lloret-Cabolt et al., 2014). The stratification of naturalsoil may change greatly within a small horizontal distance of,say, 15 m (Das, 2010). The evaluation of soil stratification atunsampled locations with no available data remains anunsolved problem.EN 1990 (CEN, 2002) provides a method for the

calibration of partial factors, which, however, cannot beused to estimate parameters at unsampled locations. Themaximum likelihood method can be used to estimatethe optimal value of a parameter of interest by maximisingthe likelihood function or the chance for observing the data.This maximum likelihood method assumes that the obser-vations are statistically independent; ignoring the inherentcorrelation among the observations. The interpolation tech-nique can give a rough estimation of a certain soil parameterat unsampled locations based on existing CPT data (Lacasse& Nadim, 1996; Beacher & Christian, 2003). Traditionalinterpolation techniques that approximate the variable ofinterest by a specified function (e.g. polynomials) cannotaccommodate the correlations among the CPT data. Krigingis a probabilistic-based approach that produces an interp-olation function based on a variogram model derived fromthe data rather than a prior model of the interpolatingfunction (Chilès & Delfiner, 2012). This estimation willinevitably vary over a wide range due to the considerablevariability of CPT measurements as well as the uncertaintiesassociated with soil classification methods (e.g. Zhang &Tumay, 1999; Kurup & Griffin, 2006; Jung et al., 2008; Cetin& Ozan, 2009; Wang et al., 2013). Therefore, clear determi-nation of soil stratification from a scattered and obscured esti-mation of soil parameters is difficult (Houlsby & Houlsby,2013).This study aims to predict soil stratification at unsampled

locations by explicitly filtering the uncertainties in soilclassification systems. Considering the spatial variability ofexisting CPTU tests, estimates of soil parameters at locationsof interest are first obtained, with their variations clearlydemonstrated. The uncertainties that propagate from this

� Centre for Offshore Foundation Systems and ARC CoE forGeotechnical Science and Engineering, University of WesternAustralia, Crawley, Australia.† Lloyd’s Register Foundation Chair of Offshore Foundations,Centre for Offshore Foundation Systems and ARC CoE forGeotechnical Science and Engineering, University of WesternAustralia, Crawley, Australia.‡ ARC CoE for Geotechnical Science and Engineering, Universityof Newcastle, Newcastle, Australia.§ Department of Civil and Environmental Engineering, The HongKong University of Science and Technology, Hong Kong.

Manuscript received 27 November 2014; revised manuscriptaccepted 2 July 2015. Published online ahead of print 16September 2015.Discussion on this paper closes on 1 June 2016, for further details seep. ii.

Li, J. et al. (2016). Géotechnique 66, No. 1, 16–26 [http://dx.doi.org/10.1680/jgeot.14.P.242]

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Downloaded by [ University Of Western Australia] on [14/11/16]. Copyright © ICE Publishing, all rights reserved.

estimation to the soil stratification are then significantlyreduced through a soil classification system. Ultimately, aclear soil stratification in three dimensions is identified with alimited number of CPTU tests.

KRIGING ESTIMATION AT UNSAMPLEDLOCATIONSKriging is an advanced interpolation procedure that uses

the correlation among existing data (Matheron, 1971). Thecorrelation is often described by a semivariogram, the valueof which for separation distance h is calculated by the averagesquared difference in property values between pairs of inputsample points separated by h

γh ¼12E pi � piþhð Þ2h i

ð1Þ

where γh is the semivariogram value for the data pairs withproperty values of pi and piþh. In geotechnical practice, CPTlocations are often irregularly spaced, requiring the distanceand directions to be grouped into subsets (Olea, 1999;Dasaka & Zhang, 2012) and for the semivariogram to beevaluated based on the subsets. To evaluate the spatialvariability using Kriging techniques it is essential that thedata are stationary; that is, the mean and covariance of thedata depend only upon separation, not on absolute location.If the semivariogram does not level off for long separationdistances, this indicates that the data set is non-stationary(Kulatilake & Ghosh, 1988). If the data are non-stationary,treatment must be given to transform the data to a stationaryset by removing the deterministic component called thetrend, and the stationary residual random component is thenanalysed.The properties at an unsampled location can be estimated

using a linear weighting of all measured data within theeffective domain around the location

p̂0 ¼XNi¼1

λipi ð2Þ

where λi is the weight for the measured property pi, and p̂0is the estimated property at the unsampled location. Kriginguses the semivariogram to assign a weight to each measureddata point. To ensure the estimated value is unbiased, thesum of the weights λi must equal to one. The weights areselected to minimise the expected mean squared errorbetween the estimation and the true value. The solution tothe minimisation, constrained by the unbiased estimation,gives the Kriging equations (Murakami et al., 2006)

γ11 � � � γ1N 1

..

. . .. ..

. ...

γN1 � � � γNN 1

1 � � � 1 0

266664

377775�

λ1

..

.

λNm

266664

377775¼

γ10

..

.

γN0

1

266664

377775

ð3Þ

where γij denotes the modelled semivariogram values basedon the distance between the two samples pertaining to the ithand jth locations. The unknownm is a Lagrange multiplier toensure the unbiased constraint.The semivariogram can be evaluated using nugget (i.e. a

small offset of the semivariance when the separation is zero),range (i.e. the distance where the model first flattens out) andsill (i.e. the value that the semivariogram model attains at therange). If a high-quality semivariogram with a small nugget/sill ratio and a large range is obtained, Kriging can beperformed with only a few data (Jernigan, 1986). An

important parameter to quantify the accuracy of theestimation is the Kriging variance (σ2)

σ2 ¼ Eðp̂0 � p0Þ2 ð4Þwhere σ is the Kriging standard error. This Kriging variancedepends only on the locations of the data but not on theirvalues. To measure the relative variation of the estimation, aKriging variation is defined as

ε ¼ σ

p̂0ð5Þ

The quality of semivariogram affects the Kriging vari-ation, an indicator measuring the estimation accuracy. Boththe quality of semivariogram and the Kriging variation aredependent on the following aspects.

(a) CPT plan and data quality. The distances between theCPTs and the number of CPTs are essential to theestimation. If the distances between the CPTs are largerthan the correlation length, the correlation structurecannot be obtained properly, which directly influencesthe accuracy of the estimation. High-quality data thatlead to a small nugget and a large range in thesemivariogram maintain small measurement errorsand give better estimation.

(b) Correlation of existing data. Good correlation of theexisting data results in a good estimation of thesemivariogram, which, in turn, leads to a smallKriging variation.

(c) Distance between the location of interest and existingCPTs. As the estimation relies more heavily onneighbouring CPTs, the accuracy is better in the vicinityof existing tests.

(d) Estimated value of the property. Kriging variance isdependent on location and correlation structure, whichare not related to the estimated value of the property.However, the Kriging variation is a value relative to theestimated value, which depends on the estimated value.If the estimated value is relatively small, its Krigingvariation tends to be large.

The range within which the true value of the estimatedproperty lies with a prescribed probability is often of practicalinterest. This range (with lower and upper limits) can bedefined by assuming a normally distributed parameter with amean value of p̂0 and a variance of σ2 (Ang & Tang, 2007)

k p0l1�α ¼ p̂0 þ kα=2σ; p̂0 þ kð1�α=2Þσ� � ð6Þ

in which kp0l1�α is the (1�α) confidence interval for theestimation, kα/2¼�Φ�1(1�α/2) and k(1�α/2)¼Φ�1(1�α/2).Φ is the cumulative distribution function of the standardnormal variate. α is a parameter to specify the probability.Particularly, the 95% confidence interval (with α equal to0·05) of the estimation is p̂0 � 1�96σ; p̂0 þ 1�96σð Þ.

UNCERTAINTY IN SOIL CLASSIFICATION BASEDON CPTU TESTSThe soil classification method proposed by Robertson

(1990) is one of the most widely used methods and adoptsthree parameters based on CPTU tests

(a) normalised cone resistance

Qt ¼ qt � σv0σ′v0

ð7Þ

PROBABILISTIC IDENTIFICATION OF SOIL STRATIFICATION 17


(b) normalised friction ratio

FR ¼ fsqt � σv0

� 100% ð8Þ

(c) pore pressure ratio

Bq ¼ u� u0qt � σ′v0

ð9Þ

where σv0 is total overburden stress, σ′v0 is effective over-burden stress, fs is sleeve friction, u is pore pressure measuredbetween the cone tip and the friction sleeve, u0 is equilibriumpore pressure, qt is corrected cone penetration resistance toaccount for unequal end area effects

qt ¼ qc þ ð1� aÞu ð10Þwhere qc is measured cone penetration resistance, a is the netarea ratio between load cell support diameter, d, and conediameter, D

a ¼ d2

D2 ð11Þ

A soil classification chart using these three parameters wasproposed by Robertson (1990). This method was furtherimproved by Jefferies & Davies (1993) to make the chartmore amendable to spreadsheet analysis by introducing a soilclassification index, Ic, to define the boundary of soil type

Ic ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif3� log ½Qtð1� BqÞ�g2 þ ½1�5þ 1�3 ðlog FRÞ�2

q

ð12ÞWithin this classification, soil types are attributed from Ic,

as summarised in Table 1. This CPT classification methodmay not provide accurate predictions of soil type based ongrain size distribution but provides a guide to soil behaviourtype (Lunne et al., 1997). This classification inevitablycontains uncertainties, such as measurement errors and trans-formation uncertainty. Experience has shown that measure-ment errors are mainly from the measurement of conepenetration resistance (qc), sleeve friction ( fs) and porepressure (u).

In the following sections, the cone penetration resistance,sleeve friction and pore pressure are interpolated separatelyat locations of interest, which quantify the variation in eachparameter. The soil types are examined using the soilclassification method proposed by Jefferies & Davies (1993)based on inferred parameters. The transformation uncer-tainty can then be expressed in an explicit manner. In the nextsection, equations will be derived to quantify the uncertain-ties that are filtered by soil classification.

UNCERTAINTY FILTERING THROUGH SOILCLASSIFICATION

The change in soil classification index, ΔIc, can beexpressed in terms of changes in normalised cone resistance

(ΔQt), normalised friction ratio (ΔFR) and pore pressureratio (ΔBq)

ΔIc ¼ @Ic@Qt

ΔQt þ @Ic@FR

ΔFR þ @Ic@Bq

ΔBq ð13Þ

in which

@Ic@Qt

¼ 3� log Qt 1� Bq� �� 2þ 1�5þ 1�3 log FRð Þ½ �2

� 1=2

� 3� log Qt 1� Bq� �� 1

Qt ln 10

ð14Þ

@Ic@FR


� 1=2

� 1�5þ 1�3 logFRð Þ½ � 1 � 3FR ln 10

ð15Þ

@Ic@Bq


� 1=2

� 3� log Qt 1� Bq� �� 1

ln 101

1� Bq

ð16ÞThe change in soil classification index with the only

change in normalised cone resistance (assuming the changesin FR and Bq are zero) can then be expressed as

ΔIc=IcΔQt=Qt

¼ log Qtð1� BqÞ� �� 3

I 2c ln 10ð17Þ

Similarly, the change in soil classification index with theonly change in normalised friction ratio or pore pressureratio can be expressed by equations (18) and (19)

ΔIc=IcΔFR=FR

¼ 1�3 1�5þ 1�3 log FRð Þ½ �I2c ln 10

ð18Þ

ΔIc=IcΔBq=Bq

¼ Bq 3� log Qt 1� Bq� ��

1� Bq� �

I2c ln 10ð19Þ

Equations (17)–(19) quantify the relative change of soilclassification index with a relative change in cone penetrationresistance, sleeve friction or pore pressure. A ratio smallerthan 1 indicates that the magnitude of change in the soilclassification system is smaller than the magnitude of changein the measured qc, fs and u, which means that uncertaintiesin the predictions of these parameters are filtered by the soilclassification index as described by equation (12).Furthermore, the uncertainty in the soil classification indexcan be filtered by the soil classification system, as indicatedby Table 1. For example, if a variation of 5% in ΔIc/Ic occursfor Ic of 3·02, Ic can then vary from 2·87 to 3·17. However,any value in this range is classified as clay (see Table 1). Thissoil classification system further filters the uncertainty in thesoil classification index.

CASE STUDYIn total, 26 CPTU tests (as shown in Fig. 1) have been

performed on a soft clay site near the town of Ballina, NewSouth Wales, Australia. The tests were conducted over a totalarea of 100�100 m. In each test, the cone penetrationresistance, sleeve friction and pore pressure were measured

Table 1. Soil behaviour types from classification index, Ic (afterJefferies & Davies, 1993)

CPTU index, Ic Zone Soil classification

Ic,1·25 7 Gravelly sands1·25, Ic,1·90 6 Sands – clean sand to silty sand1·90, Ic,2·54 5 Sand mixture – silty sand to sandy silt2·54, Ic,2·82 4 Silt mixture – clayey silt to silty clay2·82, Ic,3·22 3 ClaysIc.3·22 2 Organic clays

LI, CASSIDY, HUANG, ZHANG AND KELLY18


every 0·02 m in depth. The profiles of the measured qc, fs andu of a typical CPTU test are shown in Fig. 2. These para-meters at a designated depth can be used to estimate the sameparameters at unsampled locations at the same depth, whichis the first step towards the identification of soil stratificationat unsampled locations. The estimation of these parametersand their accuracy for a plane at 2 m depth are first detailed.The uncertainty filtering process is then performed and thesoil types at the same plane are predicted. Finally, the soilprofile and properties at two unsampled locations, B1 and B2(also shown in Fig. 1), are examined. B1 is located within thesampling cluster where enough information can be used toevaluate the rationality of the prediction. B2 is far away fromthe existing CPTU tests and represents a typical predictionwhere only limited information is available in the field. Theaccuracy of the predictions from the two locations will beexamined separately.

Prediction of CPTU parameters at unsampled locations andtheir accuracyThe cone penetration resistance, sleeve friction and pore

pressure measured at 2 m depth of the 26 CPTU tests aredemonstrated in Fig. 3. The vertical axis of the dot pointsgives the property values, and the vertical lines attachedto the points indicate the locations of the tests. The soil at1·82 m depth at location (14·95, 0·75) is classified as siltmixtures according to the Jefferies & Davies method (1993).Laboratory sieve analysis of the soil taken at the samelocation shows that the soil has 43·4% clay, 53·6% silt and3·0% sand. Hence the soil is classified as a silt mixture, whichis consistent with the classification using the Jefferies &Davies method (1993). As this method is not the focus of thepresent study, more discussion on its reliability can be foundin, among other sources, the book by Lunne et al. (1997).Previous researchers have reported that the range of

semivariograms in the horizontal direction is larger thanthat in the vertical direction. The ranges in different direc-tions in a horizontal plane are often assumed the same withan isotropic correlation structure, especially for small datasets (Jernigan, 1986). In this study no direction-dependencyis observed among the data in the horizontal plane at a depthof 2 m (see Fig. 3). Hence a lateral isotropic correlationstructure is assumed. Trends which are equal to the averagesof the cone penetration resistance, sleeve friction and porepressure are first removed, respectively. Then the semivario-grams of the three parameters are calculated using aself-developed code according to equation (1) and plottedas shown in Fig. 4. Results show that the semivarianceincreases first with the separation distance and then levels off.A theoretical exponential model is used here to fit the samplesemivariogram. For the cone penetration resistance andsleeve friction the model starts from zero, which indicatesthat the measurement error is negligible. In contrast, thenugget effect in pore pressure is much higher. This means thatthe measurement error in pore pressure is large, which isconsistent with the field observation. The semivariograms forthe cone penetration resistance and sleeve friction have smallnugget/sill ratios and relatively large ranges, which indicatesfairly good semivariograms. However, with the same set of

0

20

40

60

80

100

0 20 40 60 80 100

Nor

thin

g: m

Easting: m

B1B2Existing CPTU

Fig. 1. Locations of existing CPTU tests and unsampled locations(B1 and B2)

0

–2·0

–4·0

–6·0

–8·0

–10·0

–12·0

–14·0

–16·0

–18·0

Dep

th: m

0

–2·0

–4·0

–6·0

–8·0

–10·0

–12·0

–14·0

–16·0

–18·0

Dep

th: m

0

–2·0

–4·0

–6·0

–8·0

–10·0

–12·0

–14·0

–16·0

–18·0

Dep

th: m

0 0 20 40 60 –100 0 100 200 3001·5 3·0 4·5 6·0

qc: MPa fs: kPa u: kPa

(a) (b) (c)

Fig. 2. Profiles for CPTU test NS 19: (a) cone penetration resistance; (b) sleeve friction; (c) pore pressure



data the quality of the semivariogram for the pore pressure isunsatisfactory. The influence of the quality of the semivar-iogram on the estimation will be further discussed in thefollowing sections.

The Kriging interpolation was performed, which resultsin the estimated qc, fs and u values at 2 m depth, as shownin Fig. 5. The accuracy of this estimation can be evaluatedby the Kriging variation, as defined by equation (5). TheKriging variation values of qc, fs and u for unsampled

locations at 2 m depth are shown in Fig. 6. The variations incone penetration resistance are smaller than 0·27. In par-ticular, the variations are extremely low at locations near theexisting CPTs (see Fig. 6(a)). The variations in sleeve frictionare relatively large (a maximum variation of 0·74), especiallyin the areas with sparse CPT tests (Fig. 6(b)). The variationsin pore pressure are extremely large (a maximum variation of11) in the areas with small pore pressures (Fig. 6(c)). Suchlarge variation is partly due to the poor quality in the

10075

5025

0 0 25 50 75 100Northing: m

Easting: m

0·4

0·3

0·2

0·1

0Con

e re

sist

ance

: MP

a

(a)

10075

5025

0 0 25 50 75 100Northing: m

Easting: m

10

8

6

4

2

0Sle

eve

frict

ion:

kP

a

(b) (c)

10075

5025

0 0 25 50 75 100Northing: m

Easting: m

80

40

0

–40Por

e pr

essu

re: k

Pa

Fig. 3. Measured (a) cone penetration resistance (qc), (b) sleeve friction ( fs) and (c) pore pressure (u) at 2 m depth

0·0020 3 1500

1000

500

0

2

1

0

0·0015

0·0010

0·0005

0

Sem

ivar

ianc

e: M

Pa2

Sem

ivar

ianc

e: k

Pa2

Sem

ivar

ianc

e: k

Pa2

0 20 40 60 0 5 10 15 20 0 5 10 15Separation distance: m Separation distance: m Separation distance: m

Sample semivariogramExponential model



(a) (b) (c)

Fig. 4. Semivariogram for: (a) cone penetration resistance (qc); (b) sleeve friction ( fs); (c) pore pressure (u) at 2 m depth

10075

5025

0 0 25 50 75 100Northing: m

Easting: m

100

10

5

0

7550

250 0 25 50 75 100

Northing: mEasting: m

10075

5025

0 0 25 50 75 100Northing: m

Easting: m

0·4

0·3

0·20·1

Con

ere

sist

ance

: MP

a

Sle

eve

frict

ion:

kP

a 100

50

–50

0Por

epr

essu

re: k

Pa

(a) (b) (c)

Fig. 5. Estimated (a) penetration resistance (qc), (b) sleeve friction ( fs) and (c) pore pressure (u) at 2 m depth

10075

5025

0 0 25 50 75 100Northing: m

Easting: m

0·4

0·3

0·2

0·1

0

Varia

tion

in q

c

(a)

10075

5025

0 0 25 50 75 100Northing: m

Easting: m

0·8

0·6

0·4

0·2

0

Varia

tion

in f s

(b)

100 75 50 25 0 0 25 50 75 100

Northing: m Easting: m

12

10

8

6

4

20

Varia

tion

in u

(c)

Fig. 6. Kriging variation of (a) penetration resistance; (b) sleeve friction; and (c) pore pressure at 2 m depth



measurement and semivariogram of pore pressure, which willbe analysed further in the following sections.A confidence interval for each parameter can be estimated

using the predicted value and the Kriging variance byequation (6). For example, the predicted cone penetrationresistance is 0·202MPa at location B1 and 0·171MPa atlocation B2. The Kriging standard error is 0·019MPa atlocation B1 and 0·038MPa at location B2. A larger standarderror occurs at location B2 because the CPT data around B2are sparse. The 95% confidence intervals are (0·165, 0·238) atlocation B1 and (0·096, 0·246) at location B2. The largerstandard error at location B2 results in a wider confidenceinterval at this location.A similar procedure can be performed for sleeve friction

and pore pressure. The estimators, standard errors and 95%confidence intervals (shown as CI on column headings)for locations B1 and B2 are shown in Table 2. The Krigingstandard error values for pore pressure are extremely largedue to the large variations in pore pressure and the poorsemivariogram. Although such large variations lead to wideintervals of pore pressure, the quantification of the variationsis one of the strengths of the proposed method.

Soil typeIf the soil parameters (i.e. qc, fs and u) at a certain location

are estimated, the soil type at this location can be classifiedusing equation (12). As the soil parameters may be distrib-uted in an interval, the soil type may also vary. An alternativesoil type can be obtained using the lower bound values of the95% confidence interval for the soil parameters at eachlocation. Similarly, a soil type can be obtained using theupper bound of the confidence interval.The soil classification index, Ic, for location B1 calculated

from the estimator is 3·02. The soil classification index is 2·86using the lower bound value of cone penetration resistance(0·165MPa), sleeve friction (2·41 kPa) and pore pressure(�26·72 kPa). The soil classification index is 3·09 usingthe upper bound value of cone penetration resistance(0·238MPa), sleeve friction (7·29 kPa) and pore pressure(64·00 kPa). Hence the uncertainties in the measured CPTUdata lead to a range of soil classification index values from 2·86to 3·09. A poor quality of data with large uncertainties willresult in a wide range of the soil classification index. Thevariations that propagate from the estimated soil parameters tothe soil classification index can be calculated using equations(17) and (18). The variations in the estimated qc, fs and u are0·09, 0·26 and 1·24, respectively. The variations in Ic caused bythose in qc, fs and u are 0·009, 0·034 and 0·062, respectively.The variations in Ic are only approximately 10% of thevariations in qc, fs and u, which indicates that the majority ofthe uncertainties in the predicted qc, fs and u are filtered.The soil type can be classified by the soil classification

index according to Table 1. When the soil classification indexis larger than 2·82 and smaller than 3·22, the soil is classifiedas a clay. The soil classification index at location B1 is in therange of 2·86–3·09, which indicates that the soil is clay. Inother words, with 95% probability, the soil at location B1 at

2 m depth is clay. This process shows that the relatively smallvariations in the soil classification index are further filteredby the soil classification systems, which leads to a consistentconclusion of clay at unsampled location B1. Althoughthe variations in the estimated qc, fs and u are large, theclassification of soil type consistently indicates that the soil isclay. Such uncertainty filtering gives a clear indicator of thesoil type with high confidence.At location B2, the soil classification index at 2 m depth is

3·22, which is on the boundary of clay and organic clay. Thesoil classification index calculated from the lower boundvalues of the parameters is 3·27, which indicates that thesoil behaves like organic clay. The soil classification indexcalculated from the upper bound values is 3·17, which isclassified as clay. The results indicate that the soil at locationB2 at 2 m depth may situate in a transition zone from clay toorganic clay. The transition may be due to

(a) soil behaviour, which is influenced by the soil ahead andbehind the cone tip (Ahmadi & Robertson, 2005)

(b) the variation in soil classification (e.g. the variations inthe soil classification index, Ic, caused by variations inqc, fs and u are 0·02, 0·04 and 0·02, respectively; onlylimited influence is caused by such small variations)

(c) soil located in a transition zone that consists of mixturesof clay and organic clay. The presence of a transitionzone can be further examined by the neighbouringCPTs around location B2. The nearest neighbouringCPT tests are NS12, NS28 and NS30. The soils at 2 mdepth at NS12, NS28 and NS30 are clay, organic clayand organic clay, respectively, which confirms that B2 islocated in a transition zone from clay to organic clayfrom south to north.

Soil stratificationSoil stratification in the horizontal direction. Soil stratifica-tion in the horizontal direction can be examined by exploringthe soil types at a horizontal plane. The soil types of thewhole site at 2 m depth are calculated for each small zone(1·5�1·5 m) using the aforementioned method. Fig. 7(a)shows a soil type map that is classified based on the estimatedcone penetration resistance, sleeve friction and pore pressure.Organic clay behaviour is present at the west of this area,which changes to clay towards the east and further to siltmixtures at the southeast corner of the site. The soil atlocation (14·95, 0·75) is classified as clay in this predicted soiltype map. The particle size distribution at this location at2·27 m depth shows that there is 54·7% of clay, 41·3% of siltand 4% of sand. Therefore, the soil particle size distributionalso indicates that this is fine-grained soil (i.e. silty clay).Different soil types may be present due to variations in the

estimated soil parameters. For example, the soil typesclassified using the lower bound and upper bound values ofthe 95% confidence interval are not exactly the same as thosein Fig. 7(a). Therefore, three soil types at each location arepredicted using the estimator, the lower bound and the upperbound of the soil parameters, respectively. By randomly

Table 2. Predicted value, standard error and 95% confidence interval of qc, fs, u at locations B1 and B2

Parameters Location B1 Location B2

Estimator Standard error 95% CI Estimator Standard error 95% CI

Cone penetration resistance, qc: MPa 0·202 0·019 [0·165, 0·238] 0·171 0·038 [0·096, 0·246]Sleeve friction, fs: kPa 4·85 1·24 [2·41, 7·29] 5·22 1·66 [1·97, 8·48]Pore pressure, u: kPa 18·64 23·15 [�26·72, 64·00] 40·53 29·82 [�17·93, 98·98]



sampling the soil type from the three classifications thatreflect the variation in the soil parameters, different soil typemaps can be obtained. Figs 7(b)–7(f) show five randomsamples, which demonstrate the possible presence of soft,sensitive clay, silt mixture and sand mixture in the northeastof the site. The soil type maps show a consistent transitiontrend, despite the large variations in the estimated qc, fs and u.The boundary between different soil types is vague whenconsidering the variation in estimation.

Soil profile in the vertical direction. The soil profile in thevertical direction is examined at locations B1 and B2 in thissection. Values of the cone penetration resistance, sleevefriction and pore pressure at 2, 5, 8 and 11 m depths are firstestimated for location B1. The estimated values and 95%confidence intervals of qc, fs and u are shown in Fig. 8.Considerable variations are present in these parameters. Soilclassification at location B1 is performed and shown inFig. 9. At 2 m depth, clay is consistently identified, despite

Soft, sensitive clay Organic clay Clay Silt mixture Sand mixture

80

60

40

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thin

g: m

Easting: m20 40 60 80

(a)

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g: m

Easting: m20 40 60 80

(b)

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Easting: m20 40 60 80

(c)

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Easting: m20 40 60 80

(d)

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thin

g: m

Easting: m20 40 60 80

(e)

80

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40

20

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thin

g: m

Easting: m20 40 60 80

(f)

Fig. 7. Interpreted soil type maps at 2 m depth: (a) from predicted parameters; (b) sampling 1; (c) sampling 2; (d) sampling 3; (e) sampling 4;(f) sampling 5

00

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0·2 0·4 0·6 0 5 10 15 –100 0 100 200 300

Predicted qc: MPa Predicted fs: MPa Predicted u: MPa

Dep

th: m

0

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10

12

Dep

th: m

Prediction95% CI

0

2

4

6

8

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Dep

th: m

Prediction95% CI

Prediction95% CI

Fig. 8. Estimated value and 95% confidence intervals at location B1: (a) penetration resistance; (b) sleeve friction; (c) pore pressure



considerable variation in the estimated qc, fs and u. At 5 mdepth, the prediction from the estimator and upper boundvalues indicate that the soil in this area is clay. However, theclassification from the lower bound values of the intervalindicates organic clay behaviour. Hence, the soil at 5 m depthmay be in a transition zone from clay to organic clay. At 8 mdepth, the estimator and the lower bound values lead to theconclusion of organic clay. The upper bound values identifythe soil as clay, which further confirms the presence of atransition zone from clay to organic clay. At 11 m depth, allof the estimators, lower bound values and upper bound

values of the 95% confidence interval indicate that the soilbehaves as organic clay.These results indicate clear soil stratification at location

B1, which is clay at 2 m depth, transitioning to organic clay at11 m depth. This estimation can be examined by comparingthe stratification at location B1 with neighbouring tests (seeFig. 10). CPT test NS14 is located approximately 2 m southof B1. NS15 is located 3 m north of B1. NS 19 is located 5 meast of B1. The stratification of the three existing CPT testsand the soil types at 2, 5, 8 and 11 m are clearly demonstratedin the figure. The soils at 2 m depth at the three locations areall clay, which supports the conclusion that the soil at B1 isclay. At 5 m depth, the soil at NS15 is in a transition zone,and the soils at NS14 and NS19 are clay, which also indicatethat a transition zone at B1 is possible. At 8 m depth, the soilin NS19 is clay. The soils in NS15 andNS14 are located in thetransition zone. Hence, with a high probability, location B1 issituated in a transition zone. At 11 m depth, the soils in thethree CPT tests are all organic clay. Organic clay at 11 mdepth at location B1 is logical. The boundary of thestratification can be accurately identified if predictions areobtained at more depths.Figure 11 shows the estimators and 95% confidence

intervals of qc, fs and u at location B2. The variations inthe three parameters at location B2 are larger than those atlocation B1. The soil types classified from the estimator, thelower bound and upper bound values of the confidenceinterval are shown in Fig. 12. In the upper 2 m, the soil variesfrom clay to organic clay. From approximately 5 m, theprediction from the estimator and the 95% confidenceinterval consistently indicate that the soil behaves likeorganic clay. Hence, a layer of organic clay from 5 to 11 mcan be concluded with high confidence.

Soil propertiesWith a clear definition of soil stratification, the property of

each layer of soil can be established. Here, the layer of organicclay at location B2 is used as an example. The undrainedshear strength, su, of clay can be calculated based on CPTUtests as

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7

Dep

th: m

Soil classification

PredictionLowerUpper

Clay

Organic clay

Transition zone

Fig. 9. Soil classification and stratification at location B1

SandClayTransition Organic clay

2 m

5 m

8 m

11 m

NS19

?

B1

2 m

5 m

8 m

11 m

NS14

2 m

5 m

8 m

11 m

NS15

22

23 24

25 26

27

0

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11 12

13 14

15 16

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th: m

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Easting: m

Fig. 10. Comparison of soil strata at unsampled location B1 with neighbouring CPT tests



su ¼ qt � σv0Nc

ð20Þ

where Nc is a cone factor. The cone factor values typicallyrange from 7 to 15 (Robertson & Campanella, 1983),depending on the sensitivity and the overconsolidation ratioof the clay. Although affecting the absolute value of shearstrength, the cone factor does not affect the trend of thestrength. Kelly et al. (2014) have calibrated the cone factorfor the Ballina clay relative to laboratory triaxial com-pression strength, which results in Nc¼11·2.

Parameters qc, fs and u are first estimated using the Krigingtechnique at various depths, which are further used to derivethe corrected penetration resistance, qt, according toequation (10). The profile of corrected cone penetrationresistance for the layer of organic clay (from 5 to 11 m) at

location B2 is shown in Fig. 13. The cone penetrationresistance increases with depth. The range of cone pen-etration resistance with 95% probability is also given inFig. 13. The shear strength of this organic clay layer can thenbe obtained using equation (20). The estimated shearstrength and its 95% confidence interval along the depthare shown in Fig. 14. The undrained shear strength increasesalmost linearly with depth. The strength profile in this layer isestimated by su¼8·0þ1·5z kPa, with a strength of 15·5 kPaat the layer surface (i.e. 5 m) and a gradient of 1·5 kPa/m.

CONCLUSIONSA method has been developed for the prediction of soil

stratification at unsampled locations. The strength of thismethod is in its ability to greatly filter the uncertainties in

00

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4

6

8

10

12

0·2 0·30·1 0·4 0·5 0 5 10 15 –100 0 100 200 400300

Predicted qc: MPa Predicted fs: MPa Predicted u: MPa

Dep

th: m

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Dep

th: m

Prediction95% CI

0

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Prediction95% CI

Prediction95% CI

Fig. 11. Estimated value and 95% confidence intervals at location B2: (a) penetration resistance; (b) sleeve friction; (c) pore pressure

0

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8

10

12

1 2 3 4 5 6 7

Dep

th: m

Soil classification

PredictionLowerUpper

Organic clay

Transition zone

Fig. 12. Soil classification and stratification at location B2

4

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7

8

9

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12

0 200 400 600

Dep

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Predicted qt: kPa

Prediction95% CI

Fig. 13. Corrected tip resistance (qt) of the organic clay layer atlocation B2



prediction in an explicit manner, which leads to clearstratification with a high degree of confidence. The resultingsoil types and stratification were validated against existingCPTU tests. Excellent agreement was obtained between thepredicted stratification and that based on sampling and sieveanalysis.Equations were derived to quantify the degree of uncer-

tainties reduced by the proposed method. The majority of theuncertainties in the soil parameters (i.e., qc, fs and u) arescreened by the soil classification index. The remaininguncertainties are further filtered by the use of a soilclassification system. This method leads to a consistentconclusion on soil type, despite considerable variations in soilparameters. Better prediction accuracy can be obtained forCPTU data of higher quality, better correlation of existingdata and locations closer to existing tests.Another advantage of this method is that the soil

properties at locations without CPTU tests can be estimatedat various depths with high confidence (and with confidenceintervals calculated). The undrained soil strength profile ofan organic clay layer at an unsampled location was found toincrease linearly with soil depth, with a strength of 15·5 kPaat the layer surface and a gradient of 1·5 kPa/m with depth.Although this paper illustrates the procedure using a claylayer, the method is equally applicable to sand layers.

ACKNOWLEDGEMENTSThis research was supported by the Australian Research

Council Centre of Excellence for Geotechnical Science andEngineering and by the Lloyd’s Register Foundation. Thissupport is gratefully acknowledged.

NOTATIONa net area ratio

Bq pore pressure ratioFR normalised friction ratiofs sleeve frictionh separation distanceIc soil classification index

m Lagrange multiplierNc cone factorpi property value at location i

piþh property value at location iþhp̂0 estimated property at the unsampled location

kp0l1�α (1�α) confidence intervalQt normalised cone resistanceqc measured cone penetration resistanceqt corrected cone penetration resistancesu undrained shear strengthu pore pressureu0 equilibrium pore pressureγh semivariogram value for the data pairs with property

values of pi and piþh

ε Kriging variationλi weight for measured property piσ Kriging standard error

σv0 total overburden stressσ′v0 effective overburden stressΦ cumulative distribution function of standard normal

variate

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0 10 20 30 40

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