Stratigraphic profiling by cluster analysis and fuzzy soil classification from mechanical cone penetration tests

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Stratigraphic profiling by cluster analysis and fuzzy soil classification from mechanical cone penetration tests

J. Facciorusso & M. Uzielli

Department of Civil Engineering, University of Florence, Italy

Keywords: geologic uncertainty, stratigraphy, cone penetration testing, clustering, fuzzy

ABSTRACT: Cone penetration testing has gained increasing popularity in geotechnical site characterization due to its speed and economy, and to the good quality of its data in terms of precision, accuracy, repeatability and continuity of measurement when compared to other in-situ tests. In the present paper, cluster analysis and fuzzy soil classification from mechanical cone penetration tests are applied for stratigraphic delineation in the harbor area of the southern Italian town of Gioia Tauro. The main features of the clustering and fuzzy algorithms adopted are described. The results of stratigraphic profiling by cluster analysis and fuzzy classification for a number of soundings are shown and compared; the applicability of the adopted site characterization techniques is assessed through comparison with adjacent borehole logs and standard penetration tests.

1 INTRODUCTION

Cone penetration testing is increasingly employed in geotechnical site characterization due to the precision, accuracy, and repeatability of its output data.

Data deriving from mechanical cone penetration testing, however, are affected by larger uncertainties than those from electrical cone penetration and piezocone testing; furthermore, the data sampling inter- val is greater and the distance between cone-tip resistance and sleeve friction measures is larger.

Nonetheless, in Italy, at present, a considerable number of databases used for important geotechnical analyses - such as liquefaction susceptibility evaluation - consists of data from mechanical cone tests.

Thus, it appears advisable to apply different techniques and compare their results to obtain reliable stratigraphic profiling from such data.

In the geotechnical literature, results of cone penetration tests have been interpreted to delineate stratigraphic profiles in one or more of the following ways: 1) visual examination of raw data; 2) empirical soil classification charts; 3) statistical methods;

4) fuzzy soil classification techniques; and 5) neural networks. Here, the applicability of cluster analysis and fuzzy soil classification to mechanical cone penetration test data for stratigraphic profiling is evaluated for the harbor area of the town of Gioia Tauro, in southern Italy; this study also assisted with liqufaction risk analysis in this area.. A description of the basic features of the algorithms employed is

provided, as well as an overview and an assessment of the main results.

2 GEOLOGICAL FEATURES AND SOURCE DATA

The harbour area of Gioia Tauro, in the southern Italian region of Calabria, is located in a flat plain, originating from a depression, spreading along its length in a N-S direction and filled by continental sediments of Quaternary Age. The plain primariliy comprises granular saturated soils in its surficial layers (up to a depth ranging from 50 m to 70 m from ground level), overlying a layer of compacted clays and silty clays of considerable thickness (500m or more). The bedrock is located at variable depths of 500-600 m (Facciorusso and Vannucchi, 2003).

Figure 1 shows a representative cross-section from borehole log data and the locations of CPT and SPT tests. As may be observed, the first 20 meters (represented by a dashed area) of the cohesionless deposit - the maximum depth commonly investigated for liquefaction risk analyses - include a thick layer of made ground, overlying, with increasing depth:

− Soil A: coarse to medium loose aeolian sands, with a thickness varying between 3 and 5 m;

Proceedings ISC-2 on Geotechnical and Geophysical Site Characterization, Viana da Fonseca & Mayne (eds.)

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− Soil B: coarse and medium to coarse sands with polygenic gravels or sandy polygenic alluvial gravels, with a thickness of about 10 m;

− Soil C: medium and fine to medium dense sands, having a thickness ranging from 30 m to 70 m, including a sequence of lenses and thin layers of sands, gravelly sands and fine silty sands; the top of layer C is found at depths ranging from 7 to 19 m from ground surface. While borehole logs frequently indicate the presence of heterogeneous layers in terms of composition, these are, nevertheless, indicated as single stratigraphic units.

The water table level is estimated at 2.3 m above sea level, corresponding to depths varying from 0.0 m to 3.2 m below the ground surface. The reference water table is the highest measured at the site (with daily fluctuations of 0.35-0.4 m).

Extensive geological and geotechnical surveys have been performed in the past (CPT and SPT tests, geotechnical boreholes, laboratory tests, etc.) to characterize the area, which hosts one of the most important trade port junction of southern Europe.

The results of 6 boreholes, of 25 profiles of mechanical CPT tests and 19 profiles of SPT tests were selected for the present study. The maximum investigated depth ranges between 40 and 91.3 m, for boreholes, between 20.5 m and 39.5 m, for SPT tests, from 20.5 m and 72 m, for CPT tests. The main characteristics of the CPT tests, such as investigated depth and spatial distance from other in situ investigations, are summarized in Table 1. CPT re- sults, in terms of cone tip resistance, qc, and friction ratio, Rf, in the upper 20m are plotted in Figure 2.

The qc values show a certain variability around an average value of 24 MPa, with a a maximum value of 44 MPa; the Rf, values generally fall below 2%, though a peak of 7% is reached.

3 CLUSTER ANALYSIS

In general terms, cluster analysis is the art of finding groups in data showing a certain degree of similarity in their mathematical description. The delineation of stratigraphies based on visual inspection of CPT profiles is a complex, subjective procedure, relying on expert judgement. Previous investigations (Hegazy 1998; Hegazy and Mayne 2002) have shown that the application of clustering to piezocone CPT results may allow for the objective detection of inherent correlations between data, and for the consequent assessment of the stratigraphic profile. Thus, in the context of the less accurate and reliable mechanical CPT testing, the attempt will be made herein to identify the presence and location of primary layers (arbitrarily defined as those having a thickness greater than 1 m), secondary layers (having a thickness between 0.5 m and 1 m), lenses, transitions layers, soil mixture, and other features, as defined by Hegazy and Mayne (2002), while excluding all data outliers deriving from accidental or systematic errors, as shown in Figure 3.

The clustering method adopted herein refers to the following succession of operations: 1) the data are arranged into n objects, (i.e. each set of measures performed at each depth investigated during CPT testing) and p attributes, (i.e. soil properties directly measured or derived during CPT testing) in a nxp matrix (in which each row represents all the considered properties at the corresponding depth); 2) two or more attributes are chosen to identify the structure present in the data and, if necessary, standardized to avoid their dependence on the choice of measurement units; 3) a set of proximity (distance) values between all possible pairs of objects is stored in a nxn matrix; 4) the objects are grouped in clusters on the basis of mutual distance.

Figure 2 – Comprehensive plots of cone tip resistance, qc, and friction ratio, Rf, for the 23 investigated soundings, limited to 20 m below ground level

GEOLOGICAL SETTING

S 218 S 119 S 203 S 209 S 213S 212 S 244

LEGEN

Riporto

Formaz

Formaz 6 m

0 m s.l.m.

10 m

20 m 30 m 40 m 50 m 60 m

70 m 80 m 90 m

200 m 0 m

Debris

Soil B Soil C Soil D Soil E LEGEND*

*

Soil A

GEOLOGICAL SETTING

S 218 S 119 S 203 S 209 S 213S 212 S 244

LEGEN

Riporto

Formaz

Formaz 6 m

0 m s.l.m.

10 m

20 m 30 m 40 m 50 m 60 m 70 m

80 m 90 m

200 m 0 m

Debris

Soil B Soil C Soil D Soil E LEGEND*

*

Soil A

Figure 1 –Representative cross-section of soil stratigraphy in the Gioia Tauro harbor area with bore-hole (indicated as S) and CPT and SPT (represented by a dashed line) location.

S S S S S S S

20 m

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Clustering can be performed by various algorithms which differ from each other in terms of: (a) the input data (e.g. type and number of variables, standardization method, etc.); (b) the mathematical

function adopted to represent the distances between objects (e.g. euclidean, cosine, etc.); (c) the number of clusters (fixed in “partitioning methods”, variable in “hierarchical methods”); (d) the procedure of grouping objects to generate clusters (merging objects by means of “agglomerative techniques” or splitting them by means of “divisive techniques”);

and (e) the definition of the type of distance (e.g.

minimum, maximum, average, etc., )between clusters (e.g. Kaufman and Rousseeuw, 1990).

In the present study, the selection of the most suitable algorithm to perform clustering analysis was based on the nature of the data (continuous variables), their spatial distribution (generally irregular and widely spaced) and the past, still limited, ex- periences in the field of geotechnics (Máynarek and Lunne, 1987). A hierarchical agglomerative method was adopted, whereby clusters are merged using the average distance criterion. The algorithm, referred to by the acronym HAMAD, is shown schematically in Figure 4 and detailed hereinafter.

The Minkowski distance, selected as the prox- imity parameter, is given, between the i-th and the j- th object, by:

( )

¹^q

p

1 k

q jk

ik x

x ) j , i (

d ¸¸

¹

·

¨¨

©

§ −

= ¦

=

(1)

where i and j vary between 1 and the number of ob- jects, n; p is the number of variables considered and q is set equal to 2.

The HAMAD algorithm was applied to the nor-

Choice of variables (q_c, f_s) Normalization

Standardization (Z-score)

Distance matrix (Minkowski)

q = 2; i,j = 1:n; n = number of measures

Building of clusters Nc = n Finding minimum distance

“Average Distance”

between each pair of clusters

Associating to each cluster a stratigraphical feature (primary, secondary and transition layers, lenses, mixed soil) and finding outliers

PRELIMINARY TREATMENT

CLUSTERING N_c> 1

N

0 v a a

0 v c

c '

p p

Q q ¸¸

¹

·

¨¨©

§

¸¸¹

·

¨¨©

§ −

= σ σ ₁₀₀

q F f

0 v c

s

R ⋅

= −σ

deviation absolute mean

average ' X

X_i= ⁱ−

( ) ( )

[

^Q^'^ci ^Q^'^cj^q ^F^'^Ri ^F^'^Rj^q

]

¹^q

) j , i (

d = − + −

Merging the corresponding clusters (N_c= N_c-1)

N_c= 1

Finding the maximum

number of clusters (N_cmax):

- derivative of the distance function, K_D(N_c) < 0.5

-- correlation coefficient, ρρρρc= 1

INTERPRETATION N_c= 1

Number of primary layers increases or is constant Yes

No Nc= Nc+1< Ncmax

N_cf Choice of variables (q_c, f_s)

Normalization

Standardization (Z-score)

Distance matrix (Minkowski)

q = 2; i,j = 1:n; n = number of measures

Building of clusters Nc = n Finding minimum distance

“Average Distance”

between each pair of clusters

Associating to each cluster a stratigraphical feature (primary, secondary and transition layers, lenses, mixed soil) and finding outliers

PRELIMINARY TREATMENT

CLUSTERING N_c> 1

N

0 v a a

0 v c

c '

p p

Q q ¸¸

¹

·

¨¨©

§

¸¸¹

·

¨¨©

§ −

= σ σ ₁₀₀

q F f

0 v c

s

R ⋅

= −σ

deviation absolute mean

average ' X

X_i= ⁱ−

( ) ( )

[

^Q^'^ci ^Q^'^cj^q ^F^'^Ri ^F^'^Rj^q

]

¹^q

) j , i (

d = − + −

Merging the corresponding clusters (N_c= N_c-1)

N_c= 1

Finding the maximum

number of clusters (N_cmax):

- derivative of the distance function, K_D(N_c) < 0.5

-- correlation coefficient, ρρρρc= 1

INTERPRETATION N_c= 1

Number of primary layers increases or is constant Yes

No Nc= Nc+1< Ncmax

N_cf

Figure 4 – Flow chart of the HAMAD algorithm

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a

a

A

B

C

outlier

soil mixture

soil transition

primary layer (> 1 m) missing data

Figure. 3 – Main definitions for soil categories used in the clustering procedure of mechanical CPT data

1 cluster rank 17

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malized cone tip resistance, Qc, and friction ratio, FR:

N

0 v a a

0 v c c

' p p

Q q ¸¸

¹

·

¨¨©

§

¸¸¹

·

¨¨©

§ −

= σ

σ (2)

q 100 F f

0 v c

s

R ⋅

= −

σ (3)

wherepa = 0.1 MPa, σv0 and σ’v0 are the vertical to- tal and effective stresses, respectively, and N is an exponent depending on soil type (Robertson, 1990), ranging from 0.5 (for sands) to 1 (for clays). Qc and FR were selected in place of qc and fs as normalization allows to remove the influence of depth.

To avoid the dependence on the choice of measurements units, which may have a strong effect on the results of clustering, the two reference variables were subsequently standardized into the unitless input variables to the HAMAD algorithm, X1’ and X2’, using a modified Z-score method:

X X i i

s m

X' =X − (4)

whereXi is the variable to be standardized (X1=Qc, X2=FR) and

(

^X

)

ⁿ

m_X = ¦ⁿ_i₌₁ _i / (5)

(

^X ^m

)

ⁿ

s_X =¦ⁿ_i₌₁ _i− _X / (6)

are the average and mean absolute deviation, respectively, of the sets of measurements to be standardized (i.e. X1 and X2). Kaufman and Rousseeuw (1990) suggested that using sX instead of the standard deviation – the latter commonly used in the standard z-score method – allows for a more robust identification and treatment of outliers.

The Minkowski distance was calculated between pairs of standardized objects (X1i,X2i) and (X1j,X2j), measured at depths i and j, respectively, by means of Eq. 1.

Prior to implementing the HAMAD algorithm, each of the n objects initially constitued a single cluster (with the number of clusters, Nc, initially equal to number of objects, n). At the first step of the HAMAD algorithm, the two closest clusters were merged to form a new cluster. In each following step, the distance between all clusters was recalcu- lated considering the average of the Minkowski distances between all pairs of objects in the two clusters (Figure 5); two clusters now closest were merged, andNc decreased by 1.

While the procedure could be iteratively repeated until all data are merged into a single cluster (Nc=1), the algorithm was stopped for Nc=Ncmax. The thresh-

old value, Ncmax, was defined arbitrarily in terms of the following conditions: 1) the derivative, KD, of the Minkowski distance function, D(Nc), represented by the minimum distance between clusters at each step, was definitively less than 0.1 (Figure 6b); 2) the correlation coefficient, ρ^c, approached a value of 1 (Figure 6c) or was characterized, for Ncmax, by a significant variation (i.e. maximum relative peaks).

The correlation coefficient, ρc, is calculated between two adjacent cluster configurations (corresponding to two consecutive steps), as defined by Neter et al. (1990):

( )( )

( )

¦

( )

¦

= + +

=

= + +

−

= n

1 i

2 ) 1 j ( ) 1 j ( i n

1 i

2 ) j ( ) j ( i n

1 i

) 1 j ( ) 1 j ( i ) j ( ) j ( i c

m x

ρ (7)

wherexi(j) is the cluster rank to which the i-th object X₁

X2

-4 +4

0

10 _{cluster 2}

cluster 3 cluster 1

avg. dist.

1-2 avg. dist.

2-3

avg. dist.

1-3

Figure 5 – Example of average distance clustering visual scheme

24

20

a)

b)

c)

Figure 6 – Minkowski distance function, D(Nc), its derivative, KD(Nc), and correlation coefficient, ρ(Nc), for the selection of Ncmax (Ncmax = 20 in the example shown)

1

(q=2)

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belongs at the j-th step and m(j) is a weigthed average of the number of objects included in each cluster at thej-th step.

All cluster configurations were then analyzed, and the resulting subdivision of data into clusters with depth (conceptually related to a possible soil stratigraphy) were interpreted visually on the basis of the criteria and definitions established by Hegazy (1998) (see, for example, Figure 3). The minimum number of clusters, Ncf, able to provide a reliable soil stratigraphy is defined as the value of Nc corresponding to the last step at which no primary layers (with thickness greater than 1.0 m) were formed as a result of HAMAD agglomeration.

4 FUZZY CLASSIFICATION

Zhang and Tumay (1999) proposed a possibilistic- fuzzy approach with the objective of addressing the observed uncertainty in the correlation between existing soil composition and the mechanical response to penetration in existing CPT-based classification charts, as investigated in previous works (Zhang and Tumay 1996a; Zhang and Tumay 1996b).

Zhang (1996a) observed two basic tendencies in existing soil behavior classification charts, as two almost orthogonal curve shapes: soil type changes in one direction, and in situ soil state (OCR, sensitivity, age, cementation, liquidity index, K0, etc.) in the other.

The operation of soil chart simplification as proposed by Zhang and Tumay consists of the deriva- tion of two independent indices (the soil classification index, U, and the in-situ state index, V) representing the two primary tendencies in the soil behavior classification chart by Douglas and Olsen (1981) shown in Figure 7, through the empirical su- perposition of a curvilineal orthogonal coordinate system along the principal tendencies in the original chart and, successively, the transformation of the curvilineal coordinate system into a cartesian coordinate system by conformal mapping (Zhang and Tumay 1996a), as shown in Figure 8.

Given qc and Rf, from the Douglas and Olsen (1981) semi-logarithmic chart (Rf is in % and qc is in tsf), the intermediate variables x, y, and u(x,y) are calculated from the following relations:

( )

³^.³⁵

log 8870 . 0 1539 .

0 + −

= Rf qc

x (8)

( )

⁰^.³⁷

log 4617 . 0 2957 .

0 + −

−

= Rf qc

y (9)

( )( )

( ) ( )

( )( )

( ) (

2 1 2

)

²

2 2 1

2 1 2 2 1 2

2 2 1 2 2 2 1

1 2 1 1 2 1

1 1

d y c x c d y c x c

d y c x c b y a x a

d y c x c d y c x c

d y c x c b y a x u a

+ + + +

−

+ + + + +

−

+

− +

− −

=

(10)

Finally the soil classification index U=-u is defined, while the in-situ soil index, V, is not used in the fuzzy classification procedure.

In a subsequent paper, Zhang and Tumay (1999) introduced three fuzzy soil types: highly probable sandy soil (HPS), highly probable mixed soil (HPM) and highly probable clayey soil (HPC). The membership functions of the three fuzzy soil types, given in Eq. 11, Eq. 12 and Eq. 13, and shown in Figure 9, are functions of the soil classification index U:

°¯

°®

» ≤

»

¼ º

«

¬ ª

¸¹

¨ ·

©

§ −

−

>

= 2.6575

834586 . 0

6575 . 2 2 exp 1

2.6575 0

. 1

2

U U

U

µs (11)

Figure. 7 - Douglas and Olsen soil behavior classification chart (1981)

Figure 8 - Transformed Douglas and Olsen chart with su- perimposed U-V plane and boundary curves of soil classifi- cation criteria (Zhang 1994)

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∞

<

∞

» −

»

¼ º

««

¬ ª

¸¹

¨ ·

©

§ −

−

= U U

m

2

724307 . 0

35 . 1 2 exp 1

µ (12)

°¯

°®

<

» ≥

»

¼ º

«

¬ ª

¸¹

¨ ·

©

§ −

= −

0.1775 0

. 1

0.1775 86332

. 0

1775 . 0 2 exp 1

2

U U U

µc (13)

They approximate the normal distributions for the three soil type groups as defined in a preceeding sta- tistical analysis relating the average U value, repre- senting soil behavior type, to the soil composition characteristics for eight sets of CPT sounding and boring data (Zhang and Tumay 1996b).

For any calculated value of U, by applying Equa- tions 11, 12 and 13, it is thus possible to describe a continuous profile in terms of soil behavior, quanti- fying the degree of possibility that, at each depth, the penetrated soil behaves like a cohesionless, mixed or cohesive soil.

5 EVALUATION OF RESULTS

Clustering and fuzzy soil classification analyses were performed on the 25 mechanical CPT soundings selected for the study. For each sounding, the results were compared with the stratigraphic profiles of adjacent borehole logs and SPT profiles.

Poor to good agreement between the clustering outputs and the borehole logs was generally ob- served with a final number of clusters Ncf varying between 7 and 17. The agreement was assessed as being “good” if the main stratigraphic interfaces (di- viding soils A, B, and C), and also the minor interfaces in the heterogeneous soil C were identified with sufficient accuracy, consistently with the limitations of the source CPT and SPT in-situ tests and with the subjectivity of borehole logs; “fair” if only the main units were identified; and “poor” if not even the main stratigraphic units were delineated ac-

curately. In most cases, clustering also allowed to mark the presence lenses, soil transitions and heterogeneous layers, the latter being generally reported as single units in the borehole logs.

The results are summarized in Table 1, which re- ports, for each CPT considered: (a) CPT identification code from original data; (b) elevation of ground surface above sea level; (c) distance from the closest bore-hole or other in situ test; (d) final number of cluster adopted on the basis of the criteria treated previously; and (e) qualitative assessment of consis- tency with the stratigraphical interpretation from bore-hole and SPT results.

Figure 10d shows a typical example of a “good”

final cluster configuration for one of the investigated CPT soundings, the results of which are reported in Figure 10a and 10b in terms of normalized cone tip resistance, Qc, and friction ratio, FR. In the example, Ncf=17. It may be seen that the main stratigraphic interfaces (continuous lines in Figure 10) as delineated by the borehole log (Figure 10 f) performed at a distance of 12.2 m (see Table 1) from the CPT vertical, are correctly detected by the cluster subdivision (at depth 4.95 m between the soils denoted as A and B, at depth 8.95 m, between soils B and C, respectively). Moreover, the soil previously indicated as C,

Table 1 - List of CPT considered in this study, with elevation of ground surface above sea level, Z, distance from the closest bore-hole or SPT test, dB, final number of cluster adopted, Ncf, and qualitative assessment of agreement with bore-hole and SPT results

ID Z (m ) dB (m) Ncf Agreement 415 5.51 10.7 8 fair 436 5.56 8.1 12 good 444 5.50 8.3 10 poor 445 5.48 10.5 9 fair

447 5.34 8.4 8 fair

450 5.5 12.7 10 poor

452 4.11 3.5 10 poor 454 4.18 6.7 10 good 455 5.54 8.2 10 good 456 5.48 10.5 13 good 457 5.43 11.5 9 poor 458 5.49 6.0 10 fair 459 5.54 9.2 12 fair 460 5.55 10.4 11 fair 461 5.39 8.2 12 fair

462 5.47 9.5 7 good

465 5.55 8.8 17 good 468 5.46 10.5 8 fair 469 5.47 10.4 15 good 480 5.24 5.8 10 good 481 5.20 11.1 14 good 483 2.30 12.4 12 good 484 2.30 12.2 10 poor

488 2.89 8.8 9 fair

498 4.19 9.0 10 fair 0.00

0.25 0.50 0.75 1.00

-2 0 U 2 4

µµµµ

µµµµS

µµµµm

µµµµc

Figure 9 - Membership functions for HPS, HPM and HPC fuzzy soil types

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defined as being markedly heterogeneous by the geological description of the area and borehole logs (and whose heterogeneity may also be inferred by the SPT values reported in Figure 10e), is described by means of 6 distinct clusters identifying a set of secondary stratigraphic boundaries (dashed lines in Figure 10). It is also possible to recognize a transition zone (at depth of 11.9 m) and a mixed soil zone

(at depth of 10.2 m). Finally, three outliers result from the cluster representation at various depths, as shown in Figure 10d. Shifts in the depths of the main stratigraphic interfaces between cluster profiles, borehole logs and SPT logs were acknowledged in some cases; these do not exceed 0.5 m in the soundings examined, and are most probably due to the

Fig. 10 - Example of final cluster configuration (d) obtained by applying HAMAD to one of the considered CPT (a, b), compared t to Robertson (1990) soil classification and to SPT results (e) and bore-hole log interpretation (f) obtained at the nearest site

non-cohesive behavior (HPS) mixed behavior (HPM) cohesive behavior (HPC)

Fig. 11 - Example of results of fuzzy analysis

cohesionlessbehavior(HPS)

Mixed soil

Transition zone

Outliers

Medium to fine sand Coarse sand

Coarse to medium sand

Medium to fine sand

Medium sand

Medium to fine sand

A

B

C

a) b) c) d) e) f)

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well recognized uncertainty, existing in the true depth of CPT and SPT measurements.

Besides the expected, markedly cohesionless nature of the investigated soil layers, emphasized by the consistently high values of µs (seldom falling below 0.8) the fuzzy classification approach allowed to acknowledge a variable degree of “mixed” behavior with depth, with µ^m ranging between 0 and 0.6, with peaks around 0.8, and a very low degree of cohesive behavior, with µc rarely ranging beyond 0.1. The presence of intermediate-behavior soils in essentially cohesionless layers, which may be observed in Fig- ure 11, in the example output of the same CPT previously considered, is consistent with the visual de- scriptions provided in the borehole logs, and with the variability of NSPT values.

6 MAIN CONCLUSIONS

Clustering techniques and fuzzy soil classification were employed in an integrated approach for stratigraphic profiling. Even in a case of relatively homo- geneous soil profiles in terms of soil compositions, and in presence of relatively less reliable and accurate input data - as are the results of mechanical CPT tests – it was possible to assess the capability of cluster analysis to identify the presence and position of stratigraphic discontinuities in the investigated soundings, and to gain a better comprehension of the variability of soil mechanical behavior with depth by the fuzzy membership functions.

The information gained from the successive application of the two techniques allows for the ac- knowledgement of the possible heterogeneity of layers, and for the direct quantification of the uncertainty in soil classification through the generally non-zero values of the fuzzy membership functions.

On the basis of the assessment of the agreement between the borehole logs, the results of adjacent SPT tests and the results obtained in the present study, it may be stated that the clustering-fuzzy integrated approach can provide an objective method for the subdivision of data on the basis of soil mechanical response to penetration, thus allowing to over- come the limitations and uncertainty, and lack of one-to-one correspondence between soil composition and mechanical behavior, inherent in a stratigraphic profiling based on composition criteria and visual inspection of CPT profiles.

Thus, it may assessed with sufficient confidence that clustering and fuzzy soil classification could be employed in the case examined, even in absence of numerous boreholes logs and other in-situ tests, for the delineation of soil stratigraphy from mechanical CPT data.

ACKNOWLEDGMENTS

This research has been carried out within the frame- work of a project financed by the MIUR (Ministry of Education University and Research) with the aim of performing geotechnical and seismological analyses in the Messina Strait area.

REFERENCES

Douglas, B.J., Olsen, R.S. (1981), “Soil Classification Using Electric Cone Penetrometer. Cone Penetration Testing and Experience.” Proceedings of the ASCE National Conven- tion, St. Louis, MI, U.S.A., 209-227.

Facciorusso, J., Vannucchi, G. (2003), “Liquefaction Hazard Maps of the Harbour Area of Gioia Tauro (Italy) by Geo- statistical Methods”, Proc. SEE4, Teheran (Iran)

Hegazy, Y.A. (1998), “Delineating Geostratigraphy by Cluster Analysis of Piezocone Data ”, Ph. D Thesis, Georgia Insti- tute of Technology, 464 pp.

Hegazy, Y.A., Mayne, P.W. (2002), “Objective Site Charac- terization Using Clustering of Piezocone Data”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 128(12): 986-996.

Kaufman, L., Rousseeuw, P.J. (1990), “Finding Group in Data:

An Introduction to Cluster Analysis”, John Wiley & Sons, Inc.

Máynarek, Z., Lunne, T. (1987), “Statistical estimation of ho- mogeneity of a North Sea overconsolidated clay”, Proc. Of 5^th ICASP, Vancouver, Vol. 2, 961-968.

Neter, J., Wasserman, W., Kutner, M.H. (1990), “Applied Lin- ear Statistical Models: Regression Analysis of Variance and Experimental Designs”, Richard D. Irwin, Inc., Boston, Massachusetts, 1012 pp

Robertson, P.K. (1990), “Soil Classification Using the Cone Penetration Test”, Canadian Geotechnical Journal, Vol.

27, 151-158.

Zhang & Tumay (1996a), “Simplification of Soil Classification Charts Derived from the Cone Penetration Test”, Geotech- nical Testing Journal, Vol. 19, No. 2, 203-216.

Zhang, Z., Tumay, M.T. (1996b), “The Reliability of Soil Clas- sification Derived from Cone Penetration Test.” Uncer- tainty in the Geologic Environment: From Theory to Prac- tice, ed. C.D. Shackleford, P.P. Nelson and M.J.S. Roth, ASCE Geotechnical Special Publication No. 58, Madison, WI, U.S.A., 383-408.

Zhang, Z., Tumay, M.T. (1999), “Statistical to Fuzzy Approach Towards Soil Classification”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 125(3):179-186.