Driven Pile (McVay) QZ [McVay et al., 1989]

$$\tag{1} z = \frac{q(1-\nu)}{4r_bG_i(1-\frac{q}{q_u})^2}$$

where $q$ = axial end bearing (tip) resistance $z$ = vertical displacement (settlement) $r_b$ = pile radius at the base $G_i$ = Initial (small-strain) shear modulus of soil $q_u$ = ultimate axial end bearing resistance $ν$ = Poisson's ratio of soil

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[McVay et al., 1989] McVay, M., Townsend, F., Bloomquist, D., O’Brien, M., and Caliendo, J. (1989). Numerical analysis of vertically loaded pile groups. Foundation Engineering, pages 675–690