Y

n r„ y v^x y where mX and sX are the measured mean and standard deviation of X; pX and oX are the mean and standard deviation of X expected from prior knoweldge;

and m x and s x are the updated values of m of X is then given by:

X and sX. The characteristic value

Suitable values of pX may be obtained, for example, from the literature or from well-established experience (see Section 5.3.6). Values of oX are more difficult to obtain, but studies have suggested suitable values for the coefficient of variation oX/pX (see Section 5.3.1) that can be used in lieu of better data.

^autocorrelation' is the correlation between the elements of a series and others from the same series separated from them by a given interval.

5.5.5 Use or abuse of statistics?

There is something fascinating about science...

'In the space of [176] years the Lower Mississippi has shortened itself by [242] miles. That is ... a trifle over one mile and a third per year. Therefore, any calm person ... can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi was upward of [1,300,000] miles long, and stuck out over the Gulf of Mexico like a fishing rod... There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact'

Mark Twain, Life on the Mississippi (1874)

We conclude this sub-section with a warning about the naive application of statistics to geotechnical data:

'Attempts by statisticians to tackle geotechnical design have often ended in ridicule, and it is very difficult for one person to have sufficient grasp of both disciplines that he can use them sensibly.'32

Statistical analysis of geotechnical data is a useful adjunct to engineering judgement of the characteristic value. However, for statistical outcomes to make sense, the following simple rules should be observed:

• Only use statistics if you have sufficient data

• Use the simplest form of statistics that captures the data trend

• Exclude rogue data points

• Apply simple physical principles to choose which data to exclude

• Analyse data sets independently of each other as well as together

• Be careful to choose appropriate correlations when combining data

• Choose the outcome on the basis of judgement, not the statistics alone

And remember what Benjamin Disraeli once said:

'There are lies, damned lies, and statistics.' 5.6 Summary of key points

The selection of characteristic values of relevant ground parameters is probably the single most important task that a geotechnical engineer undertakes in design. Although partial factors provide a degree of reliability (for example, by reducing soil strengths from their expected values), they cannot compensate for gross errors of judgement in interpretation of the operational conditions in the ground.

In view of the alarming spread of interpretations of characteristic values that we have discovered in our research for this book, it is essential that engineers acquaint themselves with the fundamental assumptions that underpin Eurocode 7, especially with regard to the selection of ground parameters.

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