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Pipe/Soil interactions

The seabed contact is ruled by so-called contact elements connecting a node of the riser with a node on the seabed. Following the relative positions of these two nodes, each contact element generates reaction and friction forces. It is important to note that the reaction forces are concentrated on the nodes.

The normal reaction force is proportional to the penetration DZ except close to DZ=0 where a quadratic formula is used to ensure tangent continuity :

  • If \(\Delta Z \geq 0\)     Fn = 0

  • If \(\Delta Z \lt 0\) then

  • If \(\lvert\Delta Z\lvert \le EPSZ\) then Fn \(=\) Kn \(\Delta Z^2/(2EPSZ)\)

  • otherwise : Fn = -Kn\((\Delta Z-EPSZ/2)\)

where Kn is the normal contact stiffness.

The nodal reactions must balance the apparent weight of all the elements connected to each node. For a binodal element, if Lo is the length and wo its apparent weight, the nodal penetration is roughly be given by : DZ = wo Lo / 2Kn.

As for the lateral displacements, two friction coefficients are introduced along with two given directions u1 and u2. The total friction force is Ffric = F1 + F2 and the Coulomb criteria is separately checked on both directions :

  • If \(\|F_1\| \leq \mu 1 F_n\)     \(F_1=K_t1 \Delta x_1\)

  • Otherwise \(F_1 = \mu 1 F_n u_1\)


  • If \(\|F_2\| \leq \mu 2 F_n\)      \(F_2=K_t2 \Delta x_2\)

  • Otherwise \(F_2 = \mu 2 F_n u_2\)

The Coulomb law is slightly modified for numerical reasons. A given lateral displacement \(\Delta S_R\) is allowed even when the Lateral force \(F_T\) is under the Coulomb threshold \(\mu F_N\). The contact element acts like a spring with a given stiffness \(K_T\) and the lateral force is \(K_T \Delta s_R\).

It comes : \(Ds_R = mF_n/K_t\).

Note

the longer an element is, the higher the Coulomb threshold and the greater the reversible displacement can be.