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

(1)

where,

t = skin friction (side friction) z = vertical displacement (settlement) r = pile radius Gi = initial (small-strain) shear modulus of soil rm = outward radius were the transferred shear stress to soil is negligible β = side resistance parameter

The parameter β is computed as,

(2)

where,

tu = ultimate side resistance

rm is assumed to be initially equal to:

(3)

where L = pile length ν = Poisson’s ratio of soil Gmid = shear modulus of soil at mid-depth Gtip = shear modulus of soil at the pile tip

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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