Subsea Pipeline - 2D Cross-Section and Stability Check

Per metre of pipe, the horizontal force from the flow is the Morison sum F = 1/2 rho CD D |U| U + rho CM (pi D^2/4) dU/dt with CD = 1.05, CM = 2.0, and a lift force FL = 1/2 rho CL D U^2 with CL = 0.9. The near-bed velocity is a steady current plus the linear-wave amplitude Uw = pi H / (T sinh(kh)), where the wavenumber k solves the dispersion relation omega^2 = g k tanh(k h).

Resistance is Coulomb friction on the net downward force plus passive soil resistance of the embedded part: R = mu (Ws - FL) + 1/2 gamma' Kp (e D)^2, with mu = 0.6, soil gamma' = 8 kN/m3 and Kp = 3. The submerged weight is Ws = (SG - 1) rho g pi D^2/4. Burial (embedment fraction e) shields the pipe: the drag and inertia forces are cut by (1 - 0.7 e) and the lift by (1 - 1.25 e), a simplified trend of the shielding factors used in pipeline design practice.

The safety factor is SF = R / |F|, evaluated every instant; the minimum over a wave cycle decides stability, and below 1 the pipe accelerates with its own mass plus added mass until friction stops it. The time-domain slide here uses the same forces.

Simplifications: a 2D rigid pipe on a flat sand bed, no scour, no span, no unsteady lift, no soil penetration. This is an educational model and not a design method.

• Press Storm and watch the pipe slide while the safety factor dips under 1 each time the force peaks.
• Raise the embedment: lift vanishes first, then the force falls and soil resistance appears.
• Read the critical current on the graph: the point where the safety-factor curve crosses 1.