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

$$\tag{1} t_u=\alpha c_{uz} \leq 2.75 \quad tsf$$

where,

$t_u$ = ultimate skin friction $c_{uz}$ = undrained shear strength at depth z $\alpha$ = unitless shaft friction factor, 0 from the ground surface to a depth of 5 ft and also 1 diameter of drilled shaft, otherwise 0.55

$$\tag{2} t = t_u(4.943R) \quad for \quad Z \leq 0.12$$

$$\tag{3} t = t_u(\frac{R}{0.0951+0.893R}) \quad for \quad 0.12 < R \leq 0.74$$

$$\tag{4} t = t_u(0.9789-0.1158(R-0.74)) \quad for \quad 0.74 < R \leq 2.0$$

$$\tag{5} t = 0.833t_u \quad for \quad Z > 2.0$$

$$\tag{6} Z = \frac{z}{D}*100$$

where,

$t$ = skin friction $Z$ = normalized settlement $D$ = pile diameter

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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.