Managing risk and achieving reliable geotechnical designs using Eurocode 7 - Risk and Reliability in Geotechnical Engineering - page 407

Table 10.4 COV inher values for soil parameters
Soil parameter Symbol Range of COV values Recommended COV inher
Weight density γ 0.01-0.10 0
Angle of internal friction tan ϕ′ 0.05-0.15 0.1
Cohesion c ′ 0.30-0.50 0.4
Undrained shear strength c u 0.30-0.50 0.4
Source: Schneider H.R. and Schneider M.A. 2013. Modern Geotechnical Design Codes of Practice , eds. P. Arnold, G.A. Fenton,
M.A. Hicks, T. Schweckendiek and B. Simpson, IOS Press, Amsterdam, 87-101.

and the characteristic value determined using Equation 10.22 . At this point, it is safe to say
that the recommendations presented in Equation 10.11 through 10.22 are crude approxima-
tions in need of more rigorous calibrations to ascertain their associated errors.
Due to the way soil is normally stratified in horizontal layers, the SOF is usually much
smaller in the vertical direction than in the horizontal direction with the consequence that
the extent of the failure mechanism in the vertical direction has more effect on the charac-
teristic value than the extent in the horizontal direction. Phoon and Kulhawy (1999), from
an extensive literature survey, reported mean values of 2.5 and 50.5 m for the vertical and
horizontal scales of fluctuation, δ v = δ z and δ h = δ x = δ y , respectively, of clay from laboratory
and vane shear tests. Schneider and Fitze (2013) recommended values of 2.0 and 50.0 m for
δ v and δ h . Since the SOF is normally so different in the vertical and horizontal directions,
Equations 10.21 and 10.22 may not provide appropriate X k values for some design situa-
tions as the variance reduction factor may be excessive.
Equations 10.21 and 10.22 are used to examine the effect of the extent of the failure
mechanism in the vertical direction, L z on the characteristic value, X k . A correlation factor
ξ = X mean /X k is defined for determining the characteristic soil parameter value, similar to
the correlation factors in Eurocode 7 for determining the characteristic pile resistance as
described in the next section. The characteristic parameter value is therefore obtained by
dividing the mean value X mean by this correlation factor, which is greater than unity:

X k = X mean /ξ (10.23)

ξ is plotted against L z in Figure 10.5 for COV inher = 0.1, assuming a normal distribu-
tion curve ( Equation 10.21 ) , and for COV inher = 0.4, assuming a log-normal distribution
( Equation 10.22 ), with δ z = 2 m, when the extent of the failure mechanism in the horizontal
direction is equal to zero and ΓΓ
x

==.. The graphs in Figure 10.5 show the effect of
the extent of the failure mechanism in the vertical direction, that is, the L z value, on the
characteristic value; it can be seen that the correlation factor, ξ approaches closer to unity,
that is, the characteristic value becomes closer to the mean value, as the extent of the failure
zone increases.
The graphs of ξ, obtained from Equations 10.8 and 10.9 for X k , are also plotted in
Figure 10.5 for comparison. These graphs, with constant ξ values as L z increases, show
tha t Equation 10.8 for the 5% fractile gives a much too high ξ value, equal to 2.92, hence
a much too cautious X k value, while the Schneider (1997) Equation 10.9 provides a reason-
ably cautious ξ value, equal to 1.25, compared to the lower ξ values given by both Equations
10.21 and 10.22 , except for soil parameters with COV inher ≥ 0.4 and when, for the assumed
conditions, the extent of the failure mechanism is less than 17 m and Equation 10.22 gives
a more conservative ξ value. The graphs in Figure 10.5 demonstrate the need to take into
account the extent of the failure mechanism when selecting characteristic parameter values,
particularly in the case of the undrained shear strength with a high COV value.

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