Drilled Shaft Sand QZ (Reese and O'Neill) [O’Neil et al., 1999]

$q_u$, the ultimate end bearing resistance, can be found in tsf units as $0.6N_{SPT}$ if $N_{SPT}$ is between 0 and 50. Otherwise, $q_u$ equals 30 tsf. If the shaft's base diameter exceeds 50 inches, the ultimate bearing resistance may be reduced using the following equation.

$$\tag{1} q_{ur} = \frac{50}{D}q_u$$

where,

$q_{u}$ = ultimate end bearing (tip) resistance $D$ = pile diameter

Nonlinear curve of the end bearing resistance calculated as follows:

$$\tag{2} q = q_u(-0.0001079Z^4 + 0.0035584Z^3 - 0.045115Z^2 + 0.34861Z)$$

$$\tag{3} Z = \frac{z}{D}*100$$

where,

$q$ = end bearing resistance $Z$ = normalized settlement

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[O’Neil et al., 1999] O’Neil, M. W., Reese, L. C., et al. (1999). Drilled shafts: Construction procedures and design methods. Technical report, United States. Federal Highway Administration. Office of Infrastructure.