Characteristic values of geotechnical parameters

Eurocode 7 defines the characteristic value of a geotechnical parameter as “a cautious estimate of the value affecting the occurrence of the limit state” [EN 1997, Clause 2.4.5.2(2)]. This definition is worded to allow experienced designers to exercise their judgment, whilst directing less experienced designers to choose safe and reasonable values (Simpson and Driscoll 1998). Hicks (2013) commented on some clauses in Eurocode 7 regarding characteristic value (Table 2.3).

15

Table 2.3 Extracts from Section 2.4.5.2 of Eurocode 7 (after Hicks 2013)

No. Clause Hick’s comments

(4)P The selection of characteristic values for geotechnical parameters shall take account of

the following:

• geological and other background information, such

as data from previous projects; Reduces uncertainty

• the variability of measured property values and other relevant information, e.g. from existing knowledge;

Should account for soil variability

• the extent of the field and laboratory investigation; Affects uncertainty

• the type and number of samples; Affects uncertainty

• the extent of the zone of ground governing the behavior of the geotechnical structure at the limit state being considered;

Spatial aspect of soil variability is important

• the ability of the geotechnical structure to transfer loads from weak to strong zones in the ground

Characteristic values are problem-dependent

(7)

The zone of ground governing the behavior of a geotechnical structure at a limit state is usually much larger than a test sample or the zone of ground affected in an in-situ test. Consequently the value of the

governing parameter is often the mean of the range of values covering a large surface or volume of the ground.

The characteristic value should be a cautious estimate of this mean value

If the behavior of the geotechnical structure at the limit state considered is governed by the lowest or highest value of the ground property, the characteristic value should be a cautious estimate of the lowest or highest value occurring in the zone governing the behavior.

Extreme scenario implying local failure

(11)

If statistical methods are used, the characteristic value should be derived such that the calculated probability of a worse value governing the occurrence of the limit state under consideration is not greater than 5%.

5% refers to probability of failure of the structure; not to parameter values

NOTE: In this respect, a cautious estimate of the mean value is a selection of the mean value of the limited set of geotechnical parameter values, with a confidence level of 95%; where local failure is concerned, a cautious estimate of the low value is a 5% fractile.

Percentages refer to parameter values; not to structure performance

There are two main aspects in the definition of characteristic values: (a) a cautious estimate, and (b) the value affecting the occurrence of the limit state. The first aspect is related to uncertainties, such as spatial variability (Vanmarcke 1977a), transformation uncertainty (Phoon and Kulhawy 1999), statistical uncertainty, and model uncertainty. The second aspect is related to mechanics (e.g., spatial variability, force equilibrium, boundary conditions, etc.).

For the uncertainty (or statistical) aspect, a cautious estimate can be selected based on statistical methods, as Clause 2.4.5.2(11) elaborates that “If statistical methods are used, the characteristic value should be derived such that the calculated probability of a worse value governing the occurrence of the limit state under consideration is not greater than 5%”. Note that the value of 5% (instead of, for example, 10% or 20%) is adopted from the head Eurocode (EN 1990). The determination of the “cautious estimate” requires the statistics (e.g., mean and variance) of various uncertainties. To address this, a growing body of research aims to derive such statistics based on site investigation data (Yang, Xu, and Wang 2017; Zhao et al. 2018; van der Krogt, Schweckendiek, and Kok 2019). It is clear that spatial variability of soil properties plays a role in the statistical aspect of the characteristic value, because spatial variability constitutes one important source of uncertainties.

For the physical or mechanical aspect, Eurocode 7 provides some guidelines on the “value affecting the occurrence of the limit state”. For instance, Clause 2.4.5.2(4) lists factors to account for when selecting the characteristic value, which includes, among other factors, “the extent of the zone of ground governing the behavior of the geotechnical structure at the limit state being considered”. This is well known since Boussinesq established a solution for stress distribution in a homogeneous and isotropic subgrade subjected to a vertical point load on the ground surface in 1885. Clause

17

2.4.5.2(7) further states that “the value of the governing parameter is often the mean of a range of values covering a large surface or volume of the ground”. This is in line with the proposition made by Vanmarcke (1977a) that the performance of a geotechnical structure is often governed by the spatial average of soil properties over some influence zone (such as the spatial average of Young’s modulus over a soil volume beneath a footing or the spatial average of shear strength along a critical slip curve) rather than by the property at a certain point, referred to as the “point property”. It is clear that spatial variability of soil properties plays a role in the mechanical aspect of the characteristic value. It is not surprising that spatial variability is influential in both aspects, statistical and mechanical, although the former statistical aspect is more widely studied in the literature. In fact, most existing simplified formulas for characteristic value presented in the next section are based on statistical considerations. The mechanical aspect has not fully been considered. It is important to point out that the two aspects interact very strongly with each other.

Although the definition of characteristic value is sensible, Phoon (in a discussion in Wang 2017) opined that “there is an under-stated difficulty in making this statement [definition of characteristic value] sufficiently concrete for codification”. In fact, there is a considerable degree of subjectivity in the selection of characteristic value using Eurocode 7. As an example, this is demonstrated by Bond and Harris (2008), where they asked more than a hundred engineers to estimate the characteristic value of undrained shear strength for a particular soil profile. Figure 2.4 illustrates the outcome.

Solid dots represent data points, while gray lines represent engineers’ estimations. It can be seen that there is a wide range of estimations, and engineers are inconsistent when it comes to selecting the characteristic value.

Figure 2.4 Engineers’ interpretation of the characteristic value for a soil profile. Solid dots represent data points, while gray lines represent engineers’ interpretations (after

Bond and Harris 2008)

As discussed in Orr (2012), based on a questionnaire survey, 94% of engineers asked for more guidance on selecting characteristic soil parameter to be considered for the next revised version of Eurocode 7, which is due for publication in 202x. In fact, as listed in Table 1, it is the second most challenging and hot topic in Eurocode 7.

Considering these difficulties, a number of simplified formulas for determining

19

characteristic values have been proposed in the literature, which is reviewed in the next section.

Table 2.4 Top five topics as voted by the UK engineers to be considered for the next revised version of Eurocode 7 (after Orr 2012)

Rank Topic % of respondents

who chose topic

1 Add new parts to Eurocode 7 covering detailed design (e.g.

footings, walls, pile and slopes) 100

2 Improve general guidance on selecting characteristic soil parameter 94

3 Improve guidance on selecting water pressures 70

4 Add new parts to Eurocode 7 covering reinforced soil 59

5 Simplify/reduce number of DAs 43