Liquefied Sand (Rollins) [Rollins et al., 2005]

p-y curve model recommended by [Rollins et al., 2005], derived from full-scale lateral load tests, is used to analyze piles subjected to lateral loads in the presence of a liquefied sand layer. The resulting p-y relationship does not require input values other than pile width.

$$\tag{1} p = p_dA(By)^{C}$$

where,

$p$ = horizontal soil resistance per unit length in (kN/m)

$p_d$ = pile diameter correction factor

$y$ = horizontal displacement in (mm)

$A,B,C$ = coefficients

$$\tag{2} A = 3*10^{-7}(z+1)^{6.05} \quad B = 2.8(z+1)^{0.11} \quad C = 2.85(z+1)^{-0.41}$$

where,

$z$ = depth (m)

$$\tag{3} p_d = 3.81ln(b) + 5.6$$

$b$ = diameter or width of the pile or shaft (m)

The pile diameter correction factor, $p_d$, is equal to 1 when the pile diameter is 0.3 m. According to[Rollins et al., 2005], Eqn. (2) may not be appropriate for foundations with diameters smaller than 0.3 m or greater than 1.0 m. Moreover, the maximum horizontal resistance, $p_u$, for the tested piles is 15 kN/m. In other words, Eqn. (1), with $p_d$ = 1, equals 15 kN/m.

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[Rollins et al., 2005] Rollins, K. M., Gerber, T. M., Lane, J. D., and Ashford, S. A. (2005). Lateral resistance of a full-scale pile group in liquefied sand. Journal of Geotechnical and Geoenvironmental Engineering, 131(1):115–125