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Are there any standard classification of clay based on undrained shear strength?

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I'm from the old school - North America: we use the following (see Terzaghi, Peck and Hanson (Table 7.1 - but be careful that this is compressive strength = 2xSu (Su = undrained shear strength) - this is as per your attachment. Don't have time to try to find an ASTM Standard . . .

This has become automatic for me (the "N" correlations are generally accepted but depending on the plasticity there are "other correlations" - best if site specific for general use):
0 to 12.5 kPa - very soft (N = 0 to 2)
12.5 to 25 kPa - soft (N = 2 to 4)
25 to 50 kPa - firm (N = 4 to 8)
50 to 100 kPa - stiff (N = 8 to 15)
100 to 200 kPa - very stiff (N = 15 to 30)
>200 kPa - hard (N > 30)

You can find a similar thing though in BS 2004 CP Table 6. As typical the Brits have a slightly different take on things (have put the accepted North American range in parentheses):
< 20 kPa - very soft (0 to 12.5)
20 to 40 kPa - soft (12.5 to 25)
40 to 50 kPa - soft to firm
50 to 75 kPa - firm (25 to 50)
75 to 100 kPa - firm to stiff
100 to 150 kPa - stiff (50 to 100)
> 150 kPa - very stiff (100 to 200)
hard: (> 200)

Bottom Line - when you use the descriptor terms - be careful if "accepted Practice" or BS Code of Practice.
 
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