Sand (API) [API, 2010]

To develop the p-y curve for API Sand the friction angle and initial modulus of subgrade reaction is required. Hyperbolic p-y relationship for sand for both short-term static and cyclic loading conditions are recommended by [API, 2010].

At a given depth, pu is taken as the lesser of the calculated pus and pud.

(1)

(2)

(3)

where,

b = pile diameter γ = sand unit weight pus = horizontal ultimate resistance per unit length at shallow depths pud = horizontal ultimate resistance per unit length at greater depths

and

(4)

(5)

(6)

where,

ϕ = internal friction angle α = ϕ/2 β = π/4 + ϕ/2 K0 = coefficient of earth pressure at rest Ka = coefficient of Rankine’s active earth pressure Kp = coefficient of Rankine’s passive earth pressure

The p-y curve is computed on pu based on:

(7)

where,

k = initial modulus of subgrade reaction z = depth y = horizontal displacement p = horizontal resistance per unit length pu = horizontal ultimate resistance per unit length A = factor depending on loading type: 0.9 for cyclic loading;

for static loading

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[API, 2010] American Petroleum Institute (2010). Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms-Working Stress Design. API RP 2A.