In the context of standard penetration test, what is the relation between N and N_o during correction for overburden? (where N = actual value of penetration resistance; No = corrected value of penetration resistance; C_n = normalising correction factor) 

Concept:

The observed SPT number (No) is corrected for

• Overburden pressure 
• Dilatancy 

These corrections are applied in sequence. It mean corrected value for overburden pressure is further corrected for dilatancy.

Overburden pressure correction:

(i) The SPT values at shallow level are too low but greater depth the same soil having same density index would give higher penetration resistance. In order to make average computation of SPT number at a given value of relative density, this correction is required.

The corrected SPT number of overburden pressure is given by,

\({N_o} = {N} × \frac{{350}}{{̅ σ + 70}}\) = N×Cn

Where, N = Observed or actual value of SPT, Cn = normalising correction factor, and σ̅  = Effective overburden pressure in kN/m2

Dilatancy or water table correction:

(i) In case of fine sand or silt below water table, apparently high values may be noted for No. In such cases the following correction is applied.

(ii) The value of SPT, corrected for overburden pressure i.e. N1 is further corrected for dilatancy 

\(N_1 = 15 + \frac{1}{2}\left( {{N_o} - 15} \right)\)

Where, N_o = Corrected SPT value after overburden correction

N₁ = Finally corrected value