Copyright 2007, Offshore Technology Conference This paper was prepared for presentation at the 2007 Offshore Technology Conference held in Houston, Texas, U.S.A., 30 April–3 May 2007. This paper was selected for presentation by an OTC Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Papers presented at OTC are subject to publication review by Sponsor Society Committees of the Offshore Technology Conference. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, OTC, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Abstract The paper discusses expressions such as "characteristic value", "best estimate", "upper bound" and "lower bound" used to describe a design soil profile in practice through the reanalysis of case studies. Characteristic (design) values of undrained shear strength were compared with the results of unbiased statistical analyses. It would seem that when one relies on laboratory test results to establish the characteristic (design) strength, the experienced engineers tend to lie much lower than the average, perhaps one standard deviation below the mean. On the other hand, when one relies on the results of in situ piezocone tests, the characteristic strength can be much closer to the mean of the interpreted measurements in situ. The authors suggest that the profession adopts a univocal definition for the term "Best Estimate" and for parameter variability. This suggestion is proposed as a subject for debate in the coming months so that agreement can be established for use in practice. The authors also suggest that the geotechnical profession should use more extensively than before statistical analysis when establishing design values, look beyond using exclusively statistical analyses and start addressing the variability and uncertainty in soil parameters explicitly by implementing probability theory and reliability analyses. Introduction A detailed geohazards assessment at an offshore site often involves the assessment of the stability of submarine slopes under static and dynamic (ocean wave and seismic) loading. Even the simplest geotechnical calculation models for slope stability and seismic response require mechanical soil properties. These can never be established with complete certainty. Soils are naturally variable because of the way they are formed and the continuous processes of the environment that alter them. The uncertainty in the mechanical properties of offshore soils is due to both the natural variability from point

to point within a soil volume, and imperfect interpretation models, measurement errors and other sources.

The selection of soil properties for use in geotechnical assessment is often based on subjective judgment and accumulated experience. The uncertainties in the soil properties are only indirectly accounted for when the characteristic (design) value(s) are chosen.

Statistics and probability are useful tools for the quantification of the mean (most probable, expected) value and the possible range of values of a parameter. Statistical and probabilistic methods can quantify the uncertainties and make it possible to account for them in a rational and consistent manner. They are however rarely used in practice to establish the design soil parameters. The reason for this is unclear, but perhaps it has become a habit that no one questions, or the restricted use of statistical methods may be a reflection that often there are not enough data available to actually implement statistical methods with confidence. DNV (2006) prepared a guidance note on the statistical representation of soil data. The tools are explained in detail. The profession now needs to make a recommendation of which values to use in design.

In this paper, examples of design soil parameters recom-mended by NGI for offshore sites over the past two decades were reevaluated using statistical methods, and comparisons of characteristic value with best estimates and variance are made. Background for study When describing the design soil profile, expressions such as "characteristic", "best estimate", "upper bound" and "lower bound" values are used in practice. There does not exist a common understanding or a standard criterion for either the selection of "best estimate", "upper bound" and "lower bound" values or the uncertainty that is covered by these expressions. The paper attempts to quantify some of these concepts through the reanalysis of case studies in the North Sea and elsewhere, where characteristic (design) values had been selected by experienced engineers. The characteristic values were compared with the results of unbiased statistical analyses. To ensure neutrality for the statistical analysis, the cases were analyzed by an engineer not having had any prior involvement in the original selection of the characteristic parameters.

Six analyses are presented. Three of the case studies were for geohazards assessment while the other three were for foundation design for offshore installations. Several parame-ters are key to the such calculations. Important parameters needed for slope stability evaluation, seismic response analysis

OTC 19117

Statistical Description of Characteristic Soil Properties Suzanne Lacasse and Farrokh Nadim, Intl. Centre for Geohazards, Norwegian Geotechnical Inst. (NGI); Amir Rahim, NGI; and Tom R. Guttormsen, Norsk Hydro Production

2 OTC 19117

and the evaluation of the load capacity of anchored foundations include undrained shear strength, shear modulus at small strains, unit weight of soil, pore pressure generation, etc. Focus is placed on the undrained strength of the soil in the paper. The characteristic (design) undrained shear strength in the case studies was based on laboratory tests under different stress conditions, the interpretation of in situ piezocone penetration test or correlations for normalized undrained shear strength as a function of overconsolidation ratio. Uncertainties in soil properties The selection of characteristic values of soil properties for use in geotechnical design is often based on subjective judgment and accumulated experience, and the uncertainties which are involved with the soil properties are only to a limited extent brought into the picture when the characteristic values are chosen and reported to the client.

In the engineering literature - and geotechnical engineering is no exception - the terms variability and uncertainty are often employed interchangeably. While the two terms refer to concepts which are significantly related, a clarification in terminology would positively contribute to reducing the confusion and ambiguities associated with the statistical characterization of mechanical soil parameters for geotechnical assessment.

Technically, variability can be defined as an observable manifestation of one or more physical processes. In principle, a variable property could be described, for instance, if a sufficient number of measurements were available and if the quality of the measurements themselves was sufficient to ensure confident evaluation of the observations. Hence, the observation of variability implicitly provides a more or less detailed assessment of the level of knowledge on a phenomenon of interest and of the capability to measure and model the phenomenon itself. Variability, which represents the natural randomness of the property, is also referred to as aleatory (or inherent) uncertainty.

Uncertainty can also be epistemic. Epistemic uncertainty refers to the lack of knowledge for a given soil property. Given the inherent nature of a physical process and the available level of knowledge and/or technology related to the process itself, it is impossible in many situations to model the variability rigorously. In other situations, it may be practical to assume that a phenomenon is indeterminate (uncertain) when a detailed description of variability is expected to be uneconomic or redundant. Figure 1 (Uzielli et al. 2006a) shows the integrated descriptive and inferential analysis for probabilistic modeling of a random variable.

The main sources of uncertainty in estimated mechanical soil properties within a nominally uniform layer are:

• Limited geo-exploration • Measurement errors • Limited parameter evaluation • Spatial variability of mechanical properties

These sources, except for the inherent spatial variability, are epistemic uncertainties. This type of uncertainty can be reduced by, for example, by increasing the number of tests or improving the measurement methods.

Statistical description of soil properties A quantitative geotechnical variability investigation must rely on sets (samples in statistical terms) of measured data which

Fig. 1 Descriptive and inferential analysis for the probabilistic

modeling of a random variable.

are limited in size and quality. Hence, it is necessary to refer to sample statistics. Sample statistics are imperfect estimators of the “real” population parameters. Hence, they are never completely representative of the real distribution of the data, and are biased to some degree. “Sample statistics” refers to any mathematical function for a sample. For most engineering purposes, sample statistics are more useful than the comprehensive frequency distribution (as given by a histogram, for instance). An infinite number of sample statistics may be calculated from any given data set. For most geotechnical engineering applications, however, it is usually sufficient to calculate the first two statistical moments of a sample, i.e. the mean and standard deviation. Higher moments are unreliable when estimated from usual sample sizes available for offshore sites. Parameter estimation for independent soil variables Let X be a soil parameter, for example the unit weight, for which n observations, x1... xn exist. The mean value of X is µ and the standard deviation is σ. Any dependency on depth or on any other conditioning quantity is disregarded in this example, i.e. X is a so-called independent variable.

The mean value µ is estimated by the sample mean deno-ted x and the standard deviation σ is estimated by the sample standard deviation, where n is the number of data points:

∑==

n

iix

nx

1

1

OTC 19117 3

( )∑ −−

==

n

ii xx

ns

1

2

11

The sample estimates x and s are central estimates of µ and σ. The coefficient of variation is the ratio of the standard deviation to the mean (CoV = σ/µ).

Parameter estimation for dependent soil variables Let Y be a soil variable, for example the shear strength, whose variation with depth z can be reasonably well modeled as a li-near function: Y is then a so-called dependent variable, where-as z is independent. Assuming that n observations of pairs (zi, yi) where i = 1, 2, 3,... n are available from a soil investigation, the variation of Y with depth can be expressed as: Y = ao + a1 z + ε where the term a0 + a1z represents the linear mean variation with depth, the term ε the natural variability of Y about the mean, and z the depth below the soil surface. The variable Y vs. z is shown in Fig. 2. The coefficients a0 and a1 represent the surface intercept and the depth gradient, respectively, of the mean of Y. The variability term ε has zero mean and standard deviation σ. The standard deviation σ is assumed to be constant, i.e. it is assumed to be independent of depth z. The coefficients a0 and a1 in the linear expression can be estimated from the n observed data pairs (z, y) as

( )( )( )∑ −

∑ −−=

=

=n

ii

n

iii

zz

yyzza

1

21

1

and

zaxao 1−= in which

∑==

n

iiy

ny

1

1 and ∑==

n

iiz

nz

1

1

The standard deviation σ of the natural variability term is

estimated by the sample standard deviation:

( )( )∑ +−−

==

n

iioi zaay

ns

1

212

1

When the standard deviation or variance of ε is not

constant with depth, the derivation above is no longer valid. DNV (2006) provides the equations for a0 and a1 for the situation where the standard deviation of ε increases with depth, and the increase is proportional with depth z.

Undrained shear strength, su The three geohazards assessment sites are designated as A, B and C. The soil profiles at Sites D, E and F were established

for stability analysis of offshore installations. In sites A and F, the characteristic undrained shear strength was based on triaxial and/or direct simple shear laboratory tests. At site, B, D and E, CPTU profiles were used to determine undrained

Fig. 2 Variability of a depth-dependent soil parameter.

shear strength, while at site C, several series of different labo-ratory and in situ shear strength tests were used.

Although the geotechnical specialists who established the characteristic (design) undrained shear strength profiles were aware of the variability of the measurements at these three sites and the uncertainty in the estimation of the undrained shear strength, no attempt was made at the time to quantify the variability or uncertainties. su from laboratory measurements When undrained shear strength is measured in the laboratory, the shear strength profile vs. depth consists of discrete measurements, and the characteristic (design) undrained shear strength is often selected as a conservative estimate representative of the available data. For the statistical study, the mean and standard deviations were obtained from the parameter estimation method for dependent variables as described above. Only the triaxial compression data were used, as they represent the most reliable test results.

su from interpreted from CPTU results When the characteristic undrained shear strength profile is es-tablished on the basis of piezocone penetration (CPTU) tests, the results can be interpreted from theoretical or empirical cor-relations. The empirical approach was used in this study. To interpret undrained shear strength from CPTU test results, three main categories can be used:

1. su interpretation using “total” cone resistance 2. su interpretation using “effective” cone resistance 3. su interpretation using excess pore pressure

In most of the cases presented in this paper, the estimation of su from CPTU tests used the corrected total cone resistance. The interpretation was done with the following equation:

kt

votu N

qs σ−=

1

a1

ao Y

z

ε

4 OTC 19117

where qt is the corrected cone resistance (measured cone resistance plus measured pore pressure behind the cone), σvo is the total overburden stress and Nkt is the cone factor.

There are two main sources of uncertainty in the evaluation of su from the above equation: the corrected cone resistance qt and the cone factor Nkt. The uncertainty in the total overburden stress is considered as small as σvo is calculated from the unit weight of the clay times the depth. Data in the literature show little variability in the unit weight of clay within a layer. Therefore, in the derivation below, the uncertainty in the overburden stress is ignored.

The mean and standard deviation of the undrained shear strength su were evaluated using the first-order, second-moment (FOSM) approach (Ang and Tang, 1984). The FOSM approach provides an effective means of investigating the propagation of second-moment uncertainties. It provides an approximate estimate of the central tendency parameter (e.g. mean) and the dispersion parameter (e.g. standard deviation) of a random variable which is a function of other random variable. The statistical parameters for the undrained shear strength were evaluated as follows:

kt

votu N

qs σ−=

with mean at any depth as:

( )kt

votu

N

qs σ−=

Ignoring the uncertainty which may be present in the

estimation of the overburden stress, the variance of the undrained shear strength su, accounting for the uncertainties for both qt and Nkt, becomes:

( ) 24

2

2

22

kt

u N

kt

vot

kt

qs

N

q

Nσ

σσσ

⎟⎠⎞⎜

⎝⎛

−+≈

where the mean and standard deviation of the cone resistance are given by:

n

qq

n

iti

t

∑== 1

( )∑ −−

==

n

ittiq qq

nt 1

2

11σ

The soil design parameter reports that were used in this study often provide upper bound and lower bound estimates of the cone factor. If the average cone factor was not given, the statistical analyses assumed that the cone factor had a normal probability distribution and that the mean and standard deviation of Nkt were:

2

boundLowerkt

boundupperkt

ktNN

N+

=

4

boundLowerkt

boundupperkt

NNN

kt

−≈σ

If one should interpret the undrained shear strength from CPTU with one of the other two interpretation methods mentioned above (effective cone resistance or excess pore pressure), the derivation of the mean and standard deviation of su using the effective cone resistance or the excess pore pressures can be done in a manner similar to the procedure outlined above.

For Site E, the estimation of su from CPTU tests used two alternative approaches; (1) correlation between corrected cone resistance Nkt and the pore pressure factor Bq (Lunne et al 1997); and (2) site-specific correlation between the pore pressure factor Bq and the overconsolidation ratio (OCR) followed by calculation of the su from the OCR using the SHANSEP approach (Ladd et al 1977). The pore pressure factor Bq is defined as:

where qt is the corrected cone resistance, σvo the total overbur-den stress and ∆u the measured excess pore pressure.

Characteristic soil profiles used in design vs. statistical soil parameters The statistical results are shown as the mean of the undrained shear strength µsu, and the standard deviation represented by the µsu ± σsu. The dispersion σsu represents both the spatial variability of the undrained shear strength in the soil layer in question (aleatory uncertainty) and the uncertainty in the estimation of the in situ values (epistemic uncertainty). Site A At Site A, anisotropically consolidated triaxial compression tests were used to establish the characteristic undrained shear strength under triaxial conditions. Twenty-two tests were available between depths of 45 and 95 m. Figure 3 presents the results for Site A. The statistical analysis is shown as the means and ± one standard deviation (±1 std. dev.). The characteristic (design) undrained shear strength profile was taken at the lower bound of the measured CAUC-values. The characteristic su

C selected was even lower than the mean minus one standard deviation below depth 65 m.

Site B At Site B, six fairly uniform CPTU profiles were analyzed statistically. Figures 4 and 5 present the available CPTU data and the results of the statistical analysis at Site B compared with the characteristic values. The undrained shear strength was interpreted from the CPTU's to correspond to loading under triaxial compression conditions, su

C. The statistical mean and the recommended characteristic value compare quite well, and are in agreement at depth 1 to 2 m and at about 8 m depth. Otherwise, the statistical mean is only a few percentage points (up to 5%) below the characteristic value. The coefficient of variation was higher, approximately 16%.

Site C At Site C (Fig. 6), strength index tests (torvane, pocket pene-trometer, lab vane), in situ vane tests, unconsolidated undrai-

votvot

oq q

uq

uuB

σσ −∆

=−−

=

OTC 19117 5

ned (UU) tests were available. More recent anisotropically and isotropically undrained triaxial compression tests (CIUC and CAUC) were run at depths 28 m and 69 m. These are the most reliable results. The characteristic undrained shear strength in triaxial compression, su

C, was obtained from a correlation with in situ overburden stress (p'o) and overconsolidation ratio, where the undrained shear strength was taken as 0.31·p'o. Figure 7 presents the statistical analysis. Using the method described above, the coefficient of variation about the means was between 10 and 15%. Since there were only 4 data points available, the standard deviation was verified using the Snedecor and Cochran (1964) approximation, where the range of values at a given depth is multiplied by a weighting factor (see Lacasse and Nadim, 1996). This led to a coefficient of variation between 6 and 14%. For a more complete study, one should also include the statistics for the field vane tests. The field vane showed a shear strength profile close to the triaxial compression results, and is considered to be reliable.

The strength index and UU tests show linearly increasing shear strength with depth down to a depth of 70 m, and a de-crease in strength down to 90 m. The data below 70 m are probably affected by sampling disturbance. The triaxial data at a depth of 70 m may also have been affected by sample disturbance, though probably to a smaller degree than the strength index tests.

Figure 7 compares the characteristic undrained shear strength with the statistical analysis results. The mean is 10-15% higher that the characteristic undrained shear strength. The characteristic shear strength is close to the mean minus one standard deviation. The characteristic shear strength below a depth of 50 m tends to be higher than the mean minus one standard deviation. The relative position of the characteristic profile and triaxial data at 69 m can confirm that the triaxial data may have also been affected by sample disturbance at 70 m, if there is no change in the layering at that depth. Site D At Site D, four highly variable CPTU profiles were available. Figure 8 reproduces the corrected cone resistance and Fig. 9 presents the characteristic lower and upper bound interpreted su

C (corresponding to triaxial compression) in the design report. The strength recommendations were made for calculations associated with skirt penetration. Figure 9 also shows the statistical mean ± one standard deviation based on the four CPTU results. The characteristic upper bound agrees well the mean + one standard deviation in the top 3 m, but is much higher than that below 3m. On the other hand, the characteristic lower bound is about 2 standard deviations lower than the mean in the top 3m, and one standard deviation below the mean between 3 and 6 m. Site E At Site E, two CPTU profiles were available in two locations that had very different soil profiles. Figures 10 and 11 present the results of the analyses (sites E1 and E2). For this site, the effect of using two different methods of interpretation for the CPTU results was studied, and the undrained shear strength profiles form the two methods was compared. The two interpretations were used to obtain the undrained shear strength for a direct simple shear state of stress su

DSS. The

results illustrate the uncertainty in the interpretation method. For Site E1, the two interpretations gave very different results. The characteristic profile was selected as close to the lower of the two interpretations. For Site E2, the two interpretation methods gave similar results. The characteristic strength was again selected close to the lower of the two interpretations.

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700 800su

C (kPa)

Dep

th (m

)

CAUC testCharacteristicmeanmean +1 std.dev.mean -1 std.dev.

Fig. 3 Characteristic undrained shear strength in triaxial

compression at Site A (1984) compared with result of statistical analysis.

0

1

2

3

4

5

6

7

8

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4

qt (MPa)

Dept

h (m

)

Mean_qtDW50DW51DW51ADW51BDW37DW38

Fig. 4 Results of 6 CPTU tests at Site C (2003). Site F Site F had a very uniform soft clay profile where both labora-tory tests and CPTU tests were very uniform. Figure 12a pre-sents the laboratory data set analyzed statistically (CAUC and DSS tests) and Fig. 12b the mean ± one standard deviation in the two soil units for the DSS undrained shear strength. The statistical analysis (Uzielli et al. 2006b) included not only the statistical uncertainty, represented by the standard deviation of

6 OTC 19117

the data about the mean trend, but also the uncertainty in the measurements and the uncertainty due to the limited number of measurements. The resulting standard deviation represents therefore the total uncertainty. The coefficient of variation was 22% for the CAUC in soil units I and II, and 29% in unit I and 23% in unit II for the DSS tests. Statistical analysis was also done for the CPTU results, and the CoV was lower. The characteristic strength profile was only slightly lower than the statistical mean of the laboratory data.

0

1

2

3

4

5

6

7

8

0,0 5,0 10,0 15,0 20,0 25,0

suC (kPa)

Dep

th (m

)

Characteristicmeanmean +1 std.dev.mean -1 std.dev.

Fig. 5 Characteristic triaxial compression undrained shear

strength compared with result of statistical analysis at Site B.

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250su

C (kPa)

Dep

th (m

)

in-situ vane

UU

Pocket penetrometer

Torvane

Lab vane

CIUC/CAUC

Fig. 6 Undrained shear strength tests at Site C (2003). Discussion In a deterministic framework, the stability situation for a slope is expressed by the factor of safety. The factor of safety is defined as the ratio of the characteristic resisting force to the characteristic load (driving force). The conventional approach does not address the uncertainty in load and resistance in a consistent manner. The ambiguous definition of “characte-ristic” value requires that the engineer implicitly account for uncertainties by choosing conservative values of load (high) and resistance parameters (low). The choice, however, does

not reflect a consistent safety margin and because of this appears to be somewhat arbitrary, while remaining conserva-tive. Slopes with nominally the same factor of safety could have significantly different safety margins because of the uncertainties and how they are dealt with.

0

10

20

30

40

50

60

70

80

0 50 100 150 200 250su

C (kPa)

Dep

th (m

)

CAUC/CIUCCharacteristic

meanmean +1 std.dev.

mean -1 std.dev.

Fig. 7 Characteristic triaxial compression undrained shear

strength at Site C compared with result of statistical analysis.

0

1

2

3

4

5

6

7

0 100 200 300 400 500 600 700

qt (kPa)

Dep

th (m

)

qt KS01qt KR02qt-KP01qt KN01mean_qt

Fig. 8 Results of 4 CPTUs at Site D (2001).

The characteristic shear strength profile for sea floor stability evaluation recommended by the experienced engineer seems to fit well with the statistically-determined mean value minus one-half to one standard deviation.

The case studies suggest that in the early 80's, the characteristic undrained shear strength was selected close to the mean value minus one standard deviation. Characteristic

OTC 19117 7

undrained shear strengths from more recent case studies lie close to the mean value minus one-half standard deviation, although there are exceptions.

Fig. 9 Characteristic upper and lower bound undrained shear

strength from CPTUs at Site D compared with result of statistical analysis.

Fig. 10 Characteristic direct simple shear undrained shear

strength from CPTUs interpreted with 2 methods at Site E1 (2003).

When the engineer is faced with two sets of data for the

shear strength profile, he tends to choose the lowest value of the two as the characteristic profile. It may be more logical to combine the two sets of data through e.g. a Bayesian model.

A characteristic strength equal to the mean minus 1 to 2 standard deviations would probably fit well with the characteristic profiles for situations where much of the available data are strength index tests and tests of unknown quality. This is also rational if the point values are of concern. If the undrained shear strength averaged over, for example, a critical sliding surface or the length and periphery of long

skirts are of interest, this is believed to be too conservative because of spatial averaging effects.

Fig. 11 Characteristic direct simple shear undrained shear

strength from CPTUs interpreted with 2 methods at Site E2 (2003).

(a)

(b)

Fig. 12 (a) Undrained shear strength from laboratory tests at

Site F (1989), (b) Characteristic undrained shear strength in direct simple shear at Site F compared with result of statistical analysis.

The statistical data also provided useful additional

information, for example confirming the effects of sample disturbance on the specimens tested in the laboratory.

Although some patterns seem to emerge on the relationship between the characteristic design soil parameters and the statistically-derived ones through the cases considered in this study, the geotechnical engineers should look beyond using exclusively simple statistical analyses, and start addressing the variability and uncertainty in soil parameters explicitly.

Probability theory and reliability analyses provide a ration-al framework for dealing with uncertainties and decision-

Characteristic

0

1

2

3

4

5

6

7

8

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0

Su (kPa)

Dep

th (m

)

SuC_recommended_UpperSuC_recommended_LowerSuC_mean+std-std

suC recom. Upper Bound

suC recom. Lower Bound

suC mean

mean +1 std.dev. mean -1 std.dev.

suDSS (kPa)

0

5

10

15

20

25

0 20 40 60 80 100

120

140

Dep

th (m

)

Based on Nkt &Bq

calculated mean (Nkt&Bq)

Based on Bq&OCR

calculated mean (Bq&OCR)

Design, Capacity

suDSS (kPa)

Based on Nkt & Bq Mean Nkt & Bq

Based on Bq & OCR

Mean Bq & OCR

Characteristic

0

5

10

15

20

25

0 20 40 60 80 100

120

140

SuDSS (kPa)

Dep

th (m

)

Based on Nkt &Bqcalculated mean (Nkt&Bq)Based on Bq&OCRcalculated mean (Bq&OCR)Design

Based on Nkt & Bq Mean Nkt & Bq

Based on Bq & OCR Mean Bq & OCR Characteristic

suDSS (kPa)

8 OTC 19117

making under uncertainty. Depending on the level of sophisti-cation, the analyses provide the following output: probability of failure or unsatisfactory performance, reliability index, the most probable combination of parameters leading to failure and sensitivity of result to any change in parameters

Conclusions and recommendations The study aims at setting the premises for a discussion in the profession on the consistency in the selection of design parameters. The profession should aim at providing consistent safety margins in design, as was the intention with LRFD codes. Yes the study shows that there can be large and highly variable uncertainties in the soil parameters. Probability ap-proaches or some simplified version of this is probably the only rigorous way to approach a consistent safety margin. Ideally characteristic parameters should be estimated to be above/below a threshold within a distribution in which the user has a reasonable level of confidence. Threshold recommendations are made below. Such an approach would also give recognition to the necessity and cost-effectiveness of high quality and reliable soil sampling and testing.

From the case studies, it would seem that when one relies on laboratory test results to establish the characteristic (design) strength, the experienced engineers tend to lie much lower than the mean, perhaps at about one standard deviation below the mean. On the other hand, when one relies on the results of in situ piezocone tests, the characteristic strength can be much closer to the mean of the interpreted measurements in situ. This may be due to the fact that one feels that for CPTU's in clays, the selection of the cone resistance values is already based on the data that lie towards the lower bound of the measured data.

A study of the case study data bank suggests that the experienced engineer was more conservative in the early to mid-80's than in the past 10-15 years.

There is a need to unify the vocabulary used in the description of soil parameters used in design. "Characteristic" strength is probably fairly well understood by most practitioners to be the recommended value for design. The authors recommend that "best estimate" be used to designate the statistical mean obtained by methods similar to those described herein. The use of the expressions "Lower Bound" and "Upper Bound" should be discouraged, but one should express the "uncertainties" (or the "variability") as the standard deviation or the coefficient of variation.

The profession should encourage the use of the characteristic value for design. There should be a series of characteristic profiles for different design cases, e.g. skirt penetration, stability of skirted gravity foundations, seismic response (Nadim et al 2007). The characteristic profile could be more sophisticated, and include a range or a standard deviation to account for uncertainty and specific modifications to account for shape or depth effects. The standard deviation considered should represent the total uncertainty, and not only the statistical uncertainty represented by the standard deviation of the data about the mean trend. This means that the uncertainty in the measurements and the uncertainty due to the limited number of measurements should also be evaluated and represented in the standard deviation.

When determining the characteristic undrained shear strength, using ±0.5 or ±1 standard deviations in the analyses will depend on what the parameters will be used for (for example, stability analysis versus skirt penetration analysis). A wider bound would be logical if one is mainly concerned with the punctual values of the undrained shear strength. If the undrained shear strength is averaged over a larger depth and/or volume of soil, the wide range is however probably too conservative because of spatial averaging effects.

The authors recommend the following when the parame-ters are based on high quality laboratory or in situ tests: for design over large volumes of soil, the characteristic undrained shear strength could be set equal to the mean minus 0.5 standard deviation; for design of installations over smaller areas or volumes (e.g. penetration of short skirts), one should use a characteristic value equal to the mean minus one standard deviation. For design based on less reliable test data, the range should be one to two standard deviations, depending on the volume of interest. Furthermore for the stability assessment of natural submarine slopes, the mean undrained shear strength should be used. These definitions and suggest-ions are set forth as a subject for debate in the coming months so that the issue can be discussed and agreement can be reached for use in practice.

The authors believe that the geotechnical profession should use more extensively and more routinely statistical analysis of the parameters. Patterns emerge on the relationship between characteristic soil parameters and statistically-derived ones. The authors recommend however that the profession should look beyond simple statistical analyses, and address the variability and uncertainty in soil parameters explicitly by implementing probability theory and reliability analyses.

References Ang, A.H.S. and W.H. Tang: Probability concepts in engineering

planning and design, New York. Wiley & Sons, 409 p, 1975. DNV/Norsk Hydro Technical Report No. 2006-1437: “Guidance

Notes Statistical Representation of Soil Data”, 30 August 2006. Lacasse, S., and F. Nadim: “Uncertainty in characterizing soil

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