GeotechnicalVariability Phoon&Kulhawy 1999

5/20/2018 GeotechnicalVariability Phoon&Kulhawy 1999

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Characterization of geotechnical variability

Kok-Kwang Phoon and Fred H. Kulhawy

Abstract: Geotechnical variability is a complex attribute that results from many disparate sources of uncertainties. The

three primary sources of geotechnical uncertainties are inherent variability, measurement error, and transformation

uncertainty. Inherent soil variability is modeled as a random field, which can be described concisely by the coefficient

of variation (COV) and scale of fluctuation. Measurement error is extracted from field measurements using a simple

additive probabilistic model or is determined directly from comparative laboratory testing programs. Based on an

extensive literature review, the COV of inherent variability, scale of fluctuation, and COV of measurement error are

evaluated in detail, along with the general soil type and the approximate range of mean value for which the COVs are

applicable. Transformation uncertainty and overall property uncertainty are quantified in a companion paper.

Key words: inherent soil variability, measurement error, coefficient of variation, scale of fluctuation, geotechnical vari-

ability.

Rsum : La variabilit gotechnique est un caractre complexe qui rsulte de nombreuses sources dincertitudes. Les

trois causes principales dincertitude gotechnique sont la variabilit intrinsque, lerreur de mesure et lincertitude de

transformation. La variabilit intrinsque peut-tre modlise par un champ alatoire pouvant tre dcrit succinctementpar le coefficient de variation (COV) et lchelle de fluctuation. Lerreur de mesure est extraite des relevs en place, en

utilisant un modle probabiliste simple additif. Elle peut aussi tre dtermine directement par des programmes dessai

comparatifs de laboratoire. A partir dun examen fouill de la littrature, le COV de variabilit intrinsque, lchelle de

fluctuation et le COV de lerreur de mesure ont t valus en dtail, de mme que le type gnral de sol et la plage

approximative des valeurs moyennes sur laquelle on peut appliquer les COV. Lincertitude de transformation et

lincertitude gnrale sur la proprit tudie sont quantifies dans un papier conjoint.

Mots cls : variabilit intrinsque su sol, erreur de mesure, coefficient de variation, chelle de fluctuation, variabilit

gotechnique.

[Traduit par la Rdaction] P hoon and K ulhaw y 62 4

Introduction

Since the early 1980s, an extensive research study to de-velop a sound reliability-based design (RBD) approach forfoundations has been in progress at Cornell University underthe sponsorship of the Electric Power Research Institute. Asa part of this RBD methodology, it was necessary to estab-lish realistic statistical estimates of the variability of designsoil properties. A series of five studies on geotechnicalvariabilities (Spry et al. 1988; Orchant et al. 1988; Filippaset al. 1988; Kulhawy et al. 1992; Phoon et al. 1995) wasconducted to quantify realistic best case and worst casescenarios and provide property guidelines for the calibrationof the RBD equations. These results are useful for all typesof RBD studies. For foundations, extensive calibration stud-

ies by Phoon et al. (1995) indicated that the foundation re-sistance factors in the RBD equations are functions of thedesign soil property coefficient of variation (COV).

Ideally, a designer should select the appropriate resistancefactors based on the variability of the soil data at a specific

site. In the absence of site-specific data, or where the soi

data are too limited for meaningful statistical analyses to bperformed, guidelines on the probable range of soil propertCOV are useful as first-order approximations. Even whethere is sufficient information for statistical analyses, a morrobust estimate of geotechnical variability can be obtaineby combining the site-specific data with prior informatiofrom these generalized guidelines using Bayesian updatintechniques. Details on the application of Bayesian techniques to site characterization are described elsewhere (e.gSpry et al. 1988; Filippas et al. 1988) and are not repeateherein. Finally, the establishment of typical soil propertCOV values would help design engineers develop an appreciation for the probable range of variability inherent in thoverall estimation of common design soil properties an

therefore identify atypical geotechnical variabilities.Unfortunately, a number of the soil property statistics re

ported in the geotechnical literature are not suitable for thigeneral use, primarily because they were determined fromtotal variability analyses that implicitly assume a uniform

Can. Geotech. J. 36 : 612624 (1999) 1999 NRC Canad

61 2

Received March 11, 1998. Accepted February 16, 1999.

K.-K. Phoon. Department of Civil Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260.F.H. Kulhawy.1 School of Civil and Environmental Engineering, Hollister Hall, Cornell University, Ithaca,NY 14853-3501, U.S.A.

1 Author to whom all correspondence should be addressed.


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source of uncertainty. However, geotechnical variability ismore complex and results from many disparate sources ofuncertainties, as illustrated in Fig. 1. As shown, the threeprimary sources of geotechnical uncertainty are inherentvariability, measurement error, and transformation uncer-tainty. The first results primarily from the natural geologicprocesses that produced and continually modify the soil

mass in situ. The second is caused by equipment, proce-duraloperator, and random testing effects. Collectively,these two sources can be described as data scatter. In situmeasurements also are influenced by statistical uncertaintyor sampling error that result from limited amounts of infor-mation. This uncertainty can be minimized by taking moresamples, but it is commonly included within the measure-ment error at this time (Kulhawy 1992). The third source ofuncertainty is introduced when field or laboratory measure-ments are transformed into design soil properties using em-pirical or other correlation models. The relative contributionof these three sources to the overall uncertainty in the designsoil property clearly depends on the site conditions, degree

of equipment and procedural control, and precision of thcorrelation model. Therefore, soil property statistics that ardetermined from total variability analyses only can be ap

plied to the specific set of circumstances (site conditionsmeasurement techniques, correlation models) for which thdesign soil properties were derived.

In this paper, the inherent soil variability is modeled as random field, which can be described concisely by the COVand the scale of fluctuation. Measurement error is extractefrom field measurements using a simple additive probabilistic model or is determined directly from comparative laboratory test results. Based on an extensive literature review, thCOV of inherent variability, the scale of fluctuation, and thCOV of measurement error are evaluated in detail, alonwith the general soil type and the approximate range omean value for which the COVs are applicable. A companion paper (Phoon and Kulhawy 1999) discusses the transfor

mation uncertainty and illustrates how these componenuncertainties can be combined consistently, for a variety ocommon soil parameters, to quantify the variability of design soil properties for general geotechnical use.

Modeling inherent soil variability

Soil is a complex engineering material that has beeformed by a combination of various geologic, environmental, and physicalchemical processes. Many of these processes are continuing and can be modifying the soil in situBecause of these natural processes, all soil properties in sitwill vary vertically and horizontally. As shown in Fig. 2, thispatial variation can be decomposed conveniently into

smoothly varying trend function [t(z)] and a fluctuating component [w(z)] as follows:

[1] (z) = t(z) + w(z)

in which is the in situ soil property, and z is the depth. Thfluctuating component defined in eq. [1] represents the inherent soil variability.

A rational means of quantifying inherent variability is tmodel w(z) as a homogeneous random function or fiel(Vanmarcke 1983). The function w(z) is considered to bstatistically homogeneous if (i) the mean and variance of wdo not change with depth; and (ii) the correlation betwee

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P hoon and K ulhaw y 61

Fig. 1. Uncertainty in soil property estimates (source: Kulhawy 1992, p. 101).

Fig. 2. Inherent soil variability.


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the deviations at two different depths is a function only oftheir separation distance, rather than their absolute positions.Note that this correlation is a measure of linear dependencebetween two random quantities and varies between +1 and 1.

A correlation of +1 or 1 implies that a perfect linear rela-tionship exists between the two random quantities, with thesign indicating a positive or negative slope. The condition ofconstant mean can be satisfied if the data are detrended asshown in Fig. 2. In fact, the mean ofw is a constant value ofzero, because it is fluctuating equally about the trend line.Aside from a constant mean, the fluctuations also should beapproximately uniform to satisfy the variance and correla-tion conditions given above. Fluctuations in the soil propertyprofile are likely to be uniform if the data are extracted froma homogeneous soil layer.

For data sets that satisfy the above conditions, the inherentsoil variability can be evaluated in a straightforward manner.First, the standard deviation of the inherent soil variability

(SDw) is evaluated as

[2] SD 1

1w =

=

nw zi

i

n

[ ( ) ] 2

1

in which n is the number of data points, and w(zi) is the fluc-tuation at depth zi. Then a more useful dimensionless repre-sentation of inherent variability can be obtained bynormalizing SDw with respect to the mean soil propertytrend (t) as follows:

[3] COV SD

ww=

t

in which COVw

is the coefficient of variation of inherentvariability.

Another statistical parameter that is needed to describe in-herent variability is the correlation distance or scale of fluc-tuation (Fig. 2), which provides an indication of the distancewithin which the property values show relatively strong cor-relation. A simple but approximate method of determiningthe scale of fluctuation is given by Vanmarcke (1977) as

[4] v 0.8 d

in which v is the vertical scale of fluctuation, and d is theaverage distance between intersections of the fluctuatingproperty and its trend function, as shown in Fig. 3. Addi-

tional details on modeling inherent soil variability can bfound elsewhere (e.g., Vanmarcke 1977; Baecher 1985; Spret al. 1988; Filippas et al. 1988).

Coefficient of variation of inherent soilvariabilit y

An extensive literature review was conducted to estimatthe typical COV values of inherent soil variability. Howeverthis task was complicated because most COVs reported ithe geotechnical literature are based on total variability analyses, as noted above. Therefore, the reported COVs may beconsiderably larger than the actual inherent soil variabilitbecause of four potential problems: (i) soil data from different geologic units are mixed, (ii) equipment and proceduracontrols generally are insufficient, (iii) deterministic trendin the soil data are not removed, and ( iv) soil data are takeover a long time period.

The first problem can be minimized by ensuring that thsoil data are classified properly into geologic units befor

statistical analyses are performed (Morse 1971). In the absence of relevant documentation, it is reasonable to assumthat soil data taken over restricted locales and limited depthintervals are sufficiently homogeneous for the evaluation oinherent variability.

The second problem is related to measurement errorswhich should be separated from inherent variability if thstatistical results are to be extended for general use (e.gBaecher 1985; Orchant et al. 1988). A detailed discussion onmeasurement errors is given later in this paper. Documentation on equipment and procedural controls during soil testing usually is not detailed sufficiently to permit quantitative evaluation of measurement errors. However, it ireasonable to assume that measurement errors are minimafor soil data obtained in research programs, where gooequipment and procedural controls are likely to be maintained (Orchant et al. 1988).

The third problem, which concerns the removal of deterministic trends from the soil data, is not well recognizedConsider a hypothetical soil property that varies linearlwith depth with no random fluctuations about the lineatrend. The soil property takes on the values of 10, 20, an30, at depths of 1, 2, and 3, respectively. If the obvious linear trend is not removed, the sample mean and standard deviation of the data set would be evaluated as 20 and 10respectively. Therefore, the COV of the soil data is 50%. Aproperly detrended data set, however, would reveal that th

fluctuations are zero at all three depths, and the inherenvariability clearly is zero. A number of the statistical analyses reported in the geotechnical literature are based on thoriginal data set, rather than the detrended data set. From rigorous statistical point of view, the results from such analyses do not represent inherent soil variability, unless thoriginal data set contains no obvious trends. This situation inot likely, because most soil properties exhibit variationwith depth to some degree. However, the depth variatiomight not be significant if the sampling interval is sufficiently small. Under this condition, the COV of the data sewould be a valid, albeit approximate, indicator of inherenvariability.

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614 C an. G eotech. J. Vol. 36, 199

Fig. 3. Estimation of vertical scale of fluctuation (source: Spry

et al. 1988, p. 2-12).


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The fourth problem is associated with the variation of soilproperties with time. If the samples were collected over aperiod of 12 weeks, the soil properties may be regarded astime-invariant (Rthti 1988). However, over longer time pe-riods, additional variability could be introduced into the dataset because of the changes in the soil mass occurring withtime. This variation with time can be rather significant (e.g.,McCormack and Wilding 1979; Reyna and Chameau 1991).Unfortunately, most studies do not report the time frameover which the soil data are collected. Therefore, it is notpossible to determine if the temporal changes in the soilmass are significant.

The reported COVs in the geotechnical literature were ex-amined critically based on the considerations given above. Ingeneral, only the COVs of soil data from similar geologicorigins that were collected over limited spatial extents withgood equipment and procedural controls were considered tobe representative of inherent soil variability. However, theproblems associated with extraneous sources of variabilitycould not be removed completely because of limited docu -mentation. Therefore, the COVs should be somewhat higherthan those representing inherent soil variability alone. Thislimitation applies to all the inherent variability results pre-sented later in the paper.

Laboratory strength properties

Table 1 summarizes the available data on the inheren

variability of the undrained shear strength, effective stresfriction angle, and tangent of the effective stress friction angle. Full details are given elsewhere (Phoon et al. 1995)Where possible, the test types are reported because the tesboundary conditions can have a considerable effect on thundrained shear strength and the friction angle (e.gKulhawy and Mayne 1990). Unfortunately, not all the datcan be classified properly, because the importance of reporting test types with the strength properties is only graduallybeing recognized. Table 1 also summarizes the general soitype, the number of data groups and tests per group, and thmean and COV of the soil property. A description of soitype is useful because the site-specific COVs tabulated cabe extrapolated to other locations, provided the soil deposit

are of similar geologic formation and environmental history(Kay and Krizek 1971; Vanmarcke 1978, 1989; Tang 1984)The number of tests is a useful indicator of the accuracy othe mean and COV estimates. The number of tests per grouptypically is fairly large, which implies that the errors in thstatistical estimates are minimal. The presentation of thmean in conjunction with the COV also is important to ensure that the COV is not misinterpreted as being applicablto all possible mean values.

Undrained shear strength

The variation of the COV of inherent variability of the undrained shear strength (su) is plotted versus the mean su i

Fig. 4. The lower bound of the COV remains relatively constant at about 10% over the range of mean values shownHowever, the upper bound on the COV seems to decreaswith increasing mean. The effect of test type on the COValso can be seen. The typical ranges of COV for unconfinedcompression tests (UC), unconsolidatedundrained triaxiacompression tests (UU), and consolidated isotropic undrainetriaxial compression tests (CIUC) are 2055%, 1030%, and2040%, respectively. The differences between UU and CIUCtests are particularly evident because the soil types corresponding to these two tests are primarily London ClaysTherefore, the differences in COV cannot be attributed to thdifferences in the soil types used in the various tests. Mor

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Propertya Soil type

No. of data

groups

No. of tests per group Property value Property COV (%

Range Mean Range Mean Range Mean

su(UC) (kN/m2) Fine grained 38 2538 101 6412 100 656 33

su(UU) (kN/m2) Clay, silt 13 1482 33 15363 276 1149 22

su(CIUC) (kN/m2) Clay 10 1286 47 130713 405 1842 32

su (kN/m2)b Clay 42 24124 48 8638 112 680 32 () Sand 7 29136 62 3541 37.6 511 9 () Clay, silt 12 551 16 933 15.3 1050 21

() Clay, silt 9 1741 33.3 412 9tan (TC) Clay, silt 4 0.240.69 0.509 646 20tan (DS) Clay, silt 3 0.615 646 23tan b Sand 13 6111 45 0.650.92 0.744 514 9

asu, undrained shear strength; , effective stress friction angle; TC, triaxial compression test; UC, unconfined compression test; UU, unconsolidatedundrained triaxial compression test; CIUC, consolidated isotropic undrained triaxial compression test; DS, direct shear test.

bLaboratory test type not reported.

Table 1. Summary of inherent variability of strength properties (source: Phoon et al. 1995, p. 4-7).

Fig. 4. COV of inherent variability of su versus mean su.


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data on other soil types are needed to confirm this observa-tion.

Friction angle

The variation of the COV of inherent variability of the ef-fective stress friction angle () is plotted versus the mean in Fig. 5. Both the COV ofand tan are plotted. There isno apparent difference between the COV of these two pa-rameters. The effect of soil type on the COV also is illus-trated in Fig. 5, in which the soil type is classified broadlyinto sand and clay. The COV for clay generally is higher

than that for sand. A possible reason for this effect can befound in eq. [3], which states that the COV is inversely pro-portional to the mean if the standard deviation (SD) is a con-stant. This relationship is plotted in Fig. 5 for two constantSD values of 1.5 and 5.0. It is evident that this range ofstandard deviation is applicable to both sand and clay.Therefore, the differences in the COV for sand and clay pri-marily are caused by the differences in the mean friction an-gle. Note that the differences in the COV for sand and clayonly are apparent because the mean friction angles of theclays shown in Fig. 5 are very low. For most soils, the meanfriction angle typically is between 20 and 40. The COVwithin this range of mean friction angle essentially is 515%.

Laboratory index parametersThe inherent variability of some common index parame

ters is summarized in Table 2, along with the soil type, number of data groups and tests per group, and the mean andCOV of the index parameter. Full details are given elsewher(Phoon et al. 1995).

Natural water contentThe variation of the COV of inherent variability for th

natural water content (wn) is plotted versus the mean wn iFig. 6. No trends in the COV are present as the mean variefrom 13 to 105%. The typical range of COV for w

n is be

tween 8 and 30%.

Liquid and plastic limitsThe variations of the COV of inherent variability for the

liquid limit (wL) and plastic limit (wP) are plotted versus thmean wL and w P in Fig. 7. As with wn, no trends in the COVare present as the mean w L and w P vary from 27 to 89% an14 to 27%, respectively. The typical range of COV is between 6 and 30% for both index parameters, which is comparable to that for wn.

Plasticity and liquidity indicesThe variations of the COV of inherent variability for the

Fig. 5. COV of inherent variability of versus mean .

No. of data

groups

No. of tests per group Property value Property COV (%)

Propertya Soil typeb Range Mean Range Mean Range Mean

wn (%) Fine grained 40 17439 252 13105 29 746 18

wL (%) Fine grained 38 15299 129 2789 51 739 18

wP (%) Fine grained 23 32299 201 1427 22 634 16

PI (%) Fine grained 33 15299 120 1244 25 957 29

LI Clay, silt 2 32118 75 0.094 6088 74

(kN/m3) Fine grained 6 53200 564 1420 17.5 320 9

d (kN/m3) Fine grained 8 4315 122 1318 15.7 213 7

Dr (%)c Sand 5 3070 50 1136 19

Dr (%)d Sand 5 3070 50 4974 61

awn, natural water content; w L, liquid limit; w P, plastic limit; PI, plasticity index; LI, liquidity index; , total unit weight; d, dry unit weight; D r, relativdensity.

b Fine-grained materials derived from a variety of geologic origins, e.g., glacial deposits, tropical soils, and loess.c Total variability for direct method of determination.dTotal variability for indirect determination using standard penetration test (SPT) values.

Table 2. Summary of inherent variability of index parameters (source: Phoon et al. 1995, p. 4-16).

Fig. 6. COV of inherent variability of wn versus mean wn.


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plasticity index (PI) and liquidity index (LI) are plotted ver-sus the mean PI and LI in Fig. 8. As with , the smallerCOVs at larger mean values are primarily the result of divid-ing a relatively constant standard deviation by larger means.The larger COVs in Fig. 8 typically are associated withsmaller means for the converse reason. By plotting eq. [3]onto Fig. 8, it can be seen that a relatively limited range ofstandard deviation (312%) can explain the large variationsin the COV. This typical range of standard deviation appearsto be applicable to both PI and LI. However, this observa-tion only can be considered as tentative, because the statisti-cal data on LI are too limited.

Total and dry unit weightsThe variations of the COV of inherent variability for the

total unit weight () and dry unit weight (d) are plotted ver-sus the mean and d in Fig. 9. The typical COVs for bothparameters are less than 10%. No trends in the COV can beobserved as the mean varies from about 13 to 20 kN/m 3. Thetwo outliers with COV of 20% are associated with the tidalswamp and tropical soils of Nigeria (Ejezie and Harrop-Williams 1984).

Relative densityStatistical information on the inherent variability of rela-

tive density Dr appears to be lacking. A statistical analysion the total variability ofDr suggests that the range of COVis between 11 and 36% for the direct method of determination (Haldar and Tang 1979). However, the COV varies withthe mean, as shown in Fig. 10. Most of the variation in thCOV can be adequately explained using eq. [3] with a standard deviation of 8%. Figure 10 also presents the results of statistical analysis on the total variability of Dr for an indirect method of determination using standard penetration tesN values (Haldar and Miller 1984). The COVs are muchigher, which is to be expected. The COV decreases almoslinearly from 74% for a mean D r of 30% to 49% for a meanDr of 70%.

Field measurementsThe inherent variabilities of some common field measure

ments are summarized in Table 3. Full details are given elsewhere (Phoon et al. 1995). Note that there are importansubdivisions within each field test. For example, cone tip resistance qc can be measured using a mechanical or electricone. However, these subdivisions cannot be established athis time because of inadequacies in the data base. The soitype, number of data groups and tests per group, and thmean and COV of the field measurement also are summarized in Table 3.

The COV of inherent variability for these test measure

Fig. 7. COV of inherent variability of wL and wP versus mean

wL and wP.

Fig. 8. COV of inherent variability of PI and LI versus mean PI

and LI.

Fig. 9. COV of inherent variability of and d versus mean and d.

Fig. 10. COV of inherent variability of Dr versus mean Dr.


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ments has been discussed by Phoon and Kulhawy (1996)and will not be repeated herein. However, since these spe-cialty conference proceedings have rather limited circulationinternationally, it is wise to repeat key data where pertinent.Therefore, the basic data plots of COV of inherent variabil-ity versus the mean in situ tests parameters are given in theAppendix. These data support the interpretations given inTable 3.

Scale of fluctuation

An extensive literature review was conducted to estimatethe typical scales of fluctuations for a variety of commongeotechnical parameters. The results of this review are sum-marized in Table 4. Full details are given elsewhere (Phoonet al. 1995). The scales of fluctuation are generally calcu-lated using the method of moments. Information on the soiltype and the direction of fluctuation also are included in thetable. It is apparent that the amount of information on the

scale of fluctuation is relatively limited in comparison to theamount of information on the COV of inherent soil variabil-ity. Therefore, the observations given below should beviewed with caution, because there seldom are enough datato establish their generality on a firm basis.

The vertical scale of fluctuation (v) for the undrainedshear strength is on the order of 12 m, although it can be aslarge as 6 m. For the cone tip resistance, v typically is lessthan 1 m. The value of v for the corrected cone tip resis-tance seems to be smaller than the corresponding v valuefor the uncorrected cone tip resistance. The typical value ofv for the corrected cone tip resistance is less than 0.5 m.For the vane shear test, the value of v seems to vary be-

tween 2 and 6 m. The upper bound of this range appears tobe somewhat larger than that for the laboratory measuremenof the undrained shear strength. The single reported value ov for the standard penetration test N value falls within thpreviously noted range of 26 m. For the index parametersmost of the v values are within the range of 210 m.

The horizontal scale of fluctuation (h) is more than onorder of magnitude larger than the vertical scale of fluctua

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Test

typeaNo. of data

groups

No. of tests per group Property value Property COV (%

Propertyb Soil type Range Mean Range Mean Range Mean

CPT qc (MN/m2) Sand 57 102039 115 0.429.2 4.10 1081 38

CPT qc (MN/m2) Silty clay 12 3053 43 0.52.1 1.59 540 27

CPT qT (MN/m2) Clay 9 0.42.6 1.32 217 8

VST su(VST) (kN/m2) Clay 31 431 16 6375 105 444 24SPT N Sand 22 2300 123 774 35 1962 54

SPT N Clay, loam 2 261 32 763 32 3757 44

DMT A (kN/m2) Sand to clayey sand 15 1225 17 641335 512 2053 33

DMT A (kN/m2) Clay 13 1020 17 119455 358 1232 20

DMT B (kN/m2) Sand to clayey sand 15 1225 17 3462435 1337 1359 37

DMT B (kN/m2) Clay 13 1020 17 502876 690 1238 20

DMT ED (MN/m2) Sand to clayey sand 15 1025 15 9.446.1 25.4 992 50

DMT ED (MN/m2) Sand, silt 16 10.453.4 21.6 767 36

DMT ID Sand to clayey sand 15 1025 15 0.88.4 2.85 16130 53

DMT ID Sand, silt 16 2.15.4 3.89 848 30

DMT KD Sand to clayey sand 15 1025 15 1.928.3 15.1 2099 44

DMT KD Sand, silt 16 1.39.3 4.1 1767 38

PMT pL (kN/m2) Sand 4 17 16173566 2284 2350 40

PMT pL (kN/m2) Cohesive 5 1025 4282779 1084 1032 15

PMT EPMT (MN/m2) Sand 4 5.215.6 8.97 2868 42

aCPT, cone penetration test; VST, vane shear test; SPT, standard penetration test; DMT, dilatometer test; PMT, pressuremeter test.bqc, CPT tip resistance; q T, corrected CPT tip resistance; s u(VST), undrained shear strength from VST; N, SPT blow count (number of blows per foot o

per 305 mm); A and B , DMT A and B readings; ED, DMT modulus; ID, DMT material index; KD, DMT horizontal stress index; p L, PMT limit stress;EPMT, PMT modulus.

Table 3. Summary of inherent variability of field measurements (source: Phoon et al. 1995, p. 4-10).

Propertya Soil type

No. of

studies

Scale of fluctuation (m

Range Mea

Vertical fluctuation

su Clay 5 0.86.1 2.

qc Sand, clay 7 0.12.2 0.

qT Clay 10 0.20.5 0.

su(VST) Clay 6 2.06.2 3.

N Sand 1 2.4

wn Clay, loam 3 1.612.7 5.

wL Clay, loam 2 1.68.7 5.

Clay 1 1.

Clay, loam 2 2.47.9 5.Horizontal fluctuation

qc Sand, clay 11 3.080.0 47.

qT Clay 2 23.066.0 44.

su(VST) Clay 3 46.060.0 50.

wn Clay 1 170.asu and s u (VST), undrained shear strength from laboratory tests and

vane shear tests, respectively; , effective unit weight.

Table 4. Summary of scale of fluctuation of some geotechnical

properties (source: Phoon et al. 1995, p. 4-20).


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tion, with a typical range of between 4060 m. This result is

not surprising because soil properties tend to be more vari-able in the vertical direction than in the horizontal direction.The single reported h value of 170 m for the natural watercontent is about three to four times larger than the h valuesfor the other soil parameters. This result is consistent withthe observation that the v values for index parameters alsoare the largest. It would appear that index parameters gener-ally are less variable in both vertical and horizontal direc-tions, in comparison with other soil parameters. It isimportant to note that the scale of fluctuation is strongly in-fluenced by the sampling interval (DeGroot and Baecher1993). Some of the scales of fluctuation reported in Table 4possibly might be biased because of sampling limitation.

Measurement errorAll soil properties have to be measured by some physical

means. This process of measurement introduces additionalvariability into the soil data. The total variability of a mea-sured property (m) can be described by the following simplemodel (Lumb 1971; Orchant et al. 1988):

[5] m(z) = (z) + e(z)

in which is the in situ property, and e is the measurementerror. Equation [5] can be expanded by substituting eq. [1]for as follows:

[6] m(z) = t(z) + w(z) + e(z)

in which t is the deterministic trend, and w is the inherentvariability. The two uncertain components, w and e, gener-ally are assumed to be uncorrelated because they are derivedfrom unrelated sources (e.g., Lumb 1971; Baecher 1985;Filippas et al. 1988; Kulhawy et al. 1992). As mentionedpreviously, inherent variability is caused primarily by thenatural geologic processes that are involved in soil forma-tion. Measurement error, on the other hand, arises fromequipment, proceduraloperator, and random testing effects.Equipment effects result from inaccuracies in the measuringdevices and variations in equipment geometries and systemsemployed for routine testing. Proceduraloperator effectsoriginate from the limitations in existing test standards and

how they are followed. In general, tests that are highly oper

ator dependent and that have complicated test procedurewill have greater variability than those with simple procedures and little operator dependency. Random testing errorefers to the remaining scatter in the test results that is noassignable to specific testing parameters and is not causedby inherent soil variability. A more complete discussion omeasurement error is given elsewhere (Orchant et al. 1988).

Laboratory tests

In principle, measurement error can be determined directly by analyzing the variation of the results obtained by representative group of soil testing companies performinthe same test on nominally identical soil samples. Comparative testing programs of this type are available (e.gHammitt 1966; Johnston 1969; Sherwood 1970; Singh andLee 1970; Minty et al. 1979), but they are rather limited. Asummary of the total measurement error in terms of thCOV is given in Table 5 for a variety of common laboratortests. Full details are given elsewhere (Phoon et al. 1995)None of the studies reported the contribution from equipment, proceduraloperator, and random testing effects separately. Table 5 also summarizes the soil type, the number odata groups and tests per group, and the mean and COV othe measurements.

Undrained shear strength

The variation of the COV of measurement error of the un

drained shear strength (su) is plotted versus the mean su iFig. 11. The su tests can be classified broadly into (i) triaxiacompression (TC), (ii) direct shear (DS), and (iii) laboratorvane (LV). No apparent differences in the COV for the different test types can be observed, and most of the COVs arless than 20%. Note that the clayey silt specimens shown inTable 5 were compacted separately by each participant before testing. Therefore, the water content and dry density othe soil specimens were different and could contribute to thlarger measurement errors (Singh and Lee 1970). Withouthe additional variability introduced by compaction, thrange of measurement error for thesesu tests probably woulbe about 515%.

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Propertya Soil type

No. of data

groups

No. of tests per group Property value Property COV (%)

Range Mean Range Mean Range Mean

su(TC) (kN/m2) Clay, silt 11 13 7407 125 838 19

su(DS) (kN/m2) Clay, silt 2 1317 15 108130 119 1920 20

su(LV) (kN/m2) Clay 15 4123 29 537 13

(TC) () Clay, silt 4 913 10 227 19.1 756 24 (DS) () Clay, silt 5 913 11 2440 33.3 329 13 (DS) () Sand 2 26 26 3035 32.7 1314 14

tan (TC) Sand, silt 6 222 8tan (DS) Clay 2 622 14wn (%) Fine grained 3 8288 85 1621 18 612 8

wL (%) Fine grained 26 4189 64 17113 36 311 7

wP (%) Fine grained 26 4189 62 1235 21 718 10

PI (%) Fine grained 10 4189 61 444 23 551 24

(kN/m3) Fine grained 3 8288 85 1617 17.0 12 1aLV, laboratory vane shear test.

Table 5. Summary of total measurement error of some laboratory tests (source: Phoon et al. 1995, p. 4-22).


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Friction angleThe variation of the COV of measurement error of the ef-

fective stress friction angle () is plotted versus the mean in Fig. 12. The friction angle tests can be classified broadlyinto (i) triaxial compression (TC), and (ii) direct shear (DS).No apparent differences in the COV for the different testtypes are evident, and most of the COVs are less than 20%.As for su, part of the variability was not related to thestrength tests, but to the compaction procedure. In addition,it was observed that significant differences in the friction an-gles were caused by the linearization of the curved failureenvelope over different ranges of confining pressure (Singhand Lee 1970). Based on these considerations, the measure-ment error for the friction angle tests also is judged to be be-tween 5 and 15%, as for the su tests.

Natural water content and liquid and plastic limitsThe variation of the COV of measurement error of the

natural water content (wn), liquid limit (wL), and plastic limit(wP) are plotted versus the mean wn, wL, and wP in Fig. 13.No trends in the COV can be observed as the mean variesfrom 12 to 113%. The measurement error for the liquid limittest appears to be somewhat smaller than that for the plasticlimit test. The probable ranges of measurement error for theliquid and plastic limit tests are 510% and 1015%, respec-tively. The limited data for natural water content seem tosuggest that the measurement error is intermediate between

those of the liquid and plastic limit tests.

Plasticity indexThe variation of the COV of measurement error of th

plasticity index (PI) is plotted versus the mean PI in Fig. 14As in Fig. 8, the association of larger COVs with smallemeans, or vice versa, can be explained adequately usineq. [3]. Note that the standard deviation for measurement error, which is about 4%, is considerably smaller than thstandard deviation for inherent variability shown in Fig. 8which averages about 8%.

Total unit weightThe COV of measurement error for the total unit weigh

also is summarized in Table 5. The measurement error of 12% is the smallest among all the tests given in the table.

Field testsFor the field tests, a detailed analysis of the measuremen

error already has been conducted (Kulhawy and Trautman1996) and is summarized in Table 6. In the study by Kulhawand Trautmann (1996), regression analyses were performeon the results of laboratory calibration studies to determinthe amount of variation assignable to each test parameteWhere replicate data were available, second-moment statistic(mean and coefficient of variation) were evaluated to estimatrandom testing error. Inherent soil variability was assumed t

Fig. 13. COV of total measurement error of wn, wL, and wPversus mean wn, wL, and wP.

Fig. 14. COV of total measurement error of PI versus mean PI.Fig. 12. COV of total measurement error of versus mean .

Fig. 11. COV of total measurement error of su versus mean su.


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be small in these laboratory calibration studies, because thesoil deposits generally were prepared under controlled laboratoryconditions. Field data also were analyzed using second-momentstatistical techniques. However, only total variability could beobtained because of the difficulty in separating the inherentvariability of the soil deposit from the variability of the testmeasurements.

As shown in Table 6, the measurement error for the stan-dard penetration test is the largest, and the measurement er-rors for the electric cone penetration test and the dilatometer

test are the smallest. Because of the limited data availabland the need to use judgment to estimate these errors, thlast column of Table 6 represents the range of probable tesmeasurement variability one can expect in typical field isitu tests. Full details are given elsewhere (Kulhawy anTrautmann 1996).

Summary and conclusions

Realistic estimates of the variability of soil parameters ar

Coefficient of variation, COV (%)

Test Equipment Procedure Random Totala Rangeb

Standard penetration test (SPT) 575c 575c 1215 14100c 1545

Mechanical cone penetration test (MCPT) 5 1015d 1015d 1522d 1525

Electric cone penetration test (ECPT) 3 5 510d 712d 515Vane shear test (VST) 5 8 10 14 1020

Dilatometer test (DMT) 5 5 8 11 515

Pressuremeter test, prebored (PMT) 5 12 10 16 1020e

Self-boring pressuremeter test (SBPMT) 8 15 8 19 1525e

aCOV(Total) = [COV(Equipment)2 + COV(Procedure)2 + COV(Random)2]0.5.bBecause of limited data and judgment involved in estimating COVs, ranges represent probable magnitudes of field test measurement error.cBest to worst case scenarios, respectively, for SPT.dTip and side resistances, respectively, for CPT.eIt is likely that results may differ for p o, p f, and p L, but the data are insufficient to clarify this issue.

Table 6. Summary of measurement error of common in situ tests (source: Orchant et al. 1988, p. 4-63; Kulhawy and Trautmann 1996,

p. 283).

Test type Property Soil type Mean COV(%)

Lab strength su(UC) Clay 10400 kN/m2 2055su(UU) Clay 10350 kN/m

2 1030

su(CIUC) Clay 150700 kN/m2 2040

Clay and sand 2040 515CPT qT Clay 0.52.5 MN/m

2


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needed for the development and application of reliability-based design. The variability of design soil parametersshould be evaluated as a function of inherent soil variability,measurement error, and transformation uncertainty. The rel-ative contribution of these components to the overall vari-ability in the design parameter depends on the siteconditions, degree of equipment and procedural control dur-

ing testing, and quality of the transformation model.An extensive literature review was conducted to estimate

the statistics of inherent soil variability and measurement er-ror. A summary of the COV of inherent variability for vari-ous test measurements is given in Table 7. The general soiltype and the approximate range of mean value for which theCOV is applicable also are included in the table. With re-spect to soil type, the COV of inherent variability for sand ishigher than that for clay. With respect to measurement type,the COVs of inherent variability for index parameters are thelowest, with the possible exception of the relative density.The highest COVs of inherent variability seem to be associ-ated with measurements in the horizontal direction and mea-surements of soil modulus.

Another important descriptor of inherent variability is thescale of fluctuation. However, information on this parameteris limited. The vertical scale of fluctuation for laboratorymeasurement of undrained shear strength is in the range of12 m. For the cone tip resistance and the corrected cone tipresistance, the vertical scale of fluctuation is less than 1 mand 0.5 m, respectively. The vertical scales of fluctuation forvane shear and standard penetration test measurements are inthe range of 26 m. The horizontal scale of fluctuation forthese laboratory and field measurements is on the order of4060 m. The vertical and horizontal scales of fluctuationfor index parameters were the largest.

Statistical information on measurement error is rather lim-ited. Based on the statistics reported by comparative testingprograms, the COVs of measurement error for most labora-tory strength tests were estimated to be between 5 and 15%.The COVs of measurement error for the plastic and liquidlimit tests were in the range of 1015% and 510%, respec-tively. The COV of measurement error for the natural watercontent was intermediate between those of the limit tests.For the plasticity index, the standard deviation of the measure-ment error was between 2 and 6%. The unit weight determi-nation had the lowest COV of measurement error (1%).The COVs of measurement error for field tests were givenelsewhere.

Acknowledgments

This research was supported, in part, by the ElectricPower Research Institute (EPRI) under RP1493. The EPRIproject manager was A. Hirany.

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List of symbols

A: dilatometer A reading

B: dilatometer B reading

COV: coefficient of variation

COVw: coefficient of variation of inherent variability

Dr: relative density

ED: dilatometer modulusEPMT: pressuremeter modulus

ID: dilatometer material index

KD: dilatometer horizontal stress index

LI: liquidity index

N: standard penetration test value

PI: plasticity index

SD: standard deviation

SDw: standard deviation of inherent variability

d: average distance between intersections of the fluctuatingproperty and its trend function

e: measurement error

n: number of data points

li, lj, ll: layer depthspf: pressuremeter yield stress

pL: pressuremeter limit stress

po: pressuremeter seating stress

qc: cone tip resistance

qT: corrected qcsu: undrained shear strength

t(): trend function

t: mean soil property trend

w(): inherent soil variability

wL: liquid limit

wP: plastic limit

wn: water content

z: depthzi: ith depth coordinate

: total soil unit weight: effective unit weightd: dry unit weightv: vertical scale of fluctuationh: horizontal scale of fluctuation: in situ soil propertym: measured soil property: effective stress friction angle

Appendix

This appendix includes basic data plots (Fig. A1, see following page) of COV of inherent variability versus the meanin situ test parameters that support the interpretations givein Table 3.

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Fig. A1. COV of inherent variability versus mean in situ test parameters: (a) CPT qc and qT; (b) su(VST); (c) SPT N; (d) DMT A and

B readings; (e) PMT pL; (f) DMT ID; (g) DMT KD; (h) DMT ED and PMT EPMT.

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