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Mean value m'

© This characteristic value is half the standard deviation below the mean.

© The critical state angle of shearing resistance of Leighton Buzzard Sand, the relative dilatancy index IR, and the formula for determining 9 from IR are all taken from Bolton's paper 33 on the strength and dilatancy of sands.

© The 'modal' value here is calculated using a simple rule-of-thumb that depends on the sand's particle shape, grading, and density. The maximum and minimum values are obtained from the same rule-of-thumb, assuming extreme values for the components A, B, and C.

& This characteristic value is a simple weighted average of the minimum, modal, and maximum values.

© The coefficient of variation of 9 is assumed to be 0.1, based on observed values for a wide range of different soils.

© The mean m9 and standard deviation s9 from the laboratory measurements are updated using the mean and standard deviation o9 obtained from previous experience.

® This characteristic value is half the updated standard deviation below the updated mean. The full range of values of 9k obtained in this example vary from 46.8° to 49.6°.

5.8 Notes and references

1. Ang, A. H.-S. And Tang, W. H. (2006) Probability concepts in engineering: emphasis on applications in civil and environmental engineering (2nd edition), John Wiley and Sons Ltd, 406pp.

2. Data provided by Stent Foundations (pers. comm., 2007).

3. BS EN 1997-2: 2006, Eurocode 7 - Geotechnical design, Part 2 - Ground investigation and testing, British Standards Institution, London, 999pp.

4. Definition from Merriam-Webster's Online Dictionary, www.m-w.com.

5. Terzaghi, K. and Peck, R. B. (1967) Soil mechanics in engineering practice (2nd edition), John Wiley & Sons, Inc, 729pp.

7. Schneider, H. R. (1997) Definition and determination of characteristic soil properties, 12th Int. Conf. Soil Mech. & Fdn Engng, Hamburg: Balkema.

8. See, for example, Phoon, K. K. and Kulhawy, F. H. (1999) 'Characterization of geotechnical variability', Can. Geotech. J. 36(4), pp. 612-624.

9. See Schneider, ibid., and Phoon, K. K. and Kulhawy, F. H. (1999) 'Evaluation of geotechnical property variability', Can. Geotech. J. 36(4), pp.625-639.

10. Ground Board of the Institution of Civil Engineers (1991) Inadequate site investigation, Thomas Telford.

11. Pearsall, J. (ed.) (1999) The Concise Oxford Dictionary (10th edition), Oxford University Press.

12. BS 8002:1994 Code of practice for earth retaining structures, British Standards Institution, London.

13. Padfield, C. J. and Mair, R. J. (1984) Design of retaining walls embedded in stiff clays. CIRIA RP104.

14. Pearsall, ibid.

15. Gaba, A. R., Simpson, B., Powrie, W. and Beadman, D. R. (2003) Embedded retaining walls - guidance for economic design, London, CIRIA C580.

16. Pearsall, ibid., see definition of 'experience'.

18. For example, see Tomlinson, M. J. (2000) Foundation design and construction, Prentice Hall; or Bowles, J.E. (1997) Foundation analysis and design, McGraw-Hill.

20. Data kindly provided by Viv Troughton and Tony Suckling of Stent Foundations (pers. comm., 2007).

21. Data kindly provided by Dr Toh and the Singapore Building and Construction Authority (pers. comm., 2007).

22. Bjerrum , L. (1972) 'Embankments on soft ground', Proc. Speciality Conf. on Performance of Earth and Earth Supported Structures, ASCE, 2, pp. 1-54.

23. Suckling T. (2003) 'Driven cast insitu piles, the CPT and the SPT - two case studies', Ground Engineering, 36(10), pp. 28-32 (and pers. comm., 2007).

24. Simpson, B. and Driscoll, R. (1998) Eurocode 7 - a commentary, BRE.

25. This follows from the central limit theorem — 'one of the most important theorems in probability theory' according to Ang and Tang, ibid., p. 168.

26. Mortensen, J. K., Hansen, G., and Sorensen, B. (1991) 'Correlation of CPT and field vane tests for clay tills', Danish Geotechnical Society Bulletin, 7, 62pp.

28. Schneider, ibid.

29. Schneider, ibid.

31. Ang and Tang, ibid., pp. 361-2 and Schneider, ibid.

32. Simpson and Driscoll, ibid.

33. Bolton, M. D. (1986) 'The strength and dilatancy of sands', Géotechnique, 36(1), pp. 65-78.

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