The upper bound approach of the theory of perfect plasticity has been applied to develop a method for geotechnical stability analysis of unburied submarine pipelines. The coefficient of? lateral resistance of the soil and the corresponding displacements of the pipe depend on seven geometrical, loading and material parameters. Compared to the comfits based on Coulomb friction, the coefficients obtained by the present method are, in general, higher for pipes on sand and lower for pipes on clay.


The complex problem of the interaction between water, pipe and soil for an unburied submarine pipeline is traditionally separated into two parts:

  • the determination of wave and current action on the pipe in the form of lift, drag and inertia forces (in this paper termed as hydrokinetic forces); and

  • the investigation of lateral stability of the pipe exposed to known hydrodynamic forces.

Lateral stability is often the critical factor for determining the necessary weight of pipe coating, especially in Shallow waters (?100 - 120 m).

Appreciable attention has been devoted to the solution of part (a) of the problem,' including the pertinent gathering of environmental data and experimental results. If this effort is to gain the intended meaning, attention must be paid also to part (b) of the problem - transmission of the hydrodynamic forces into the soil.

This paper describes a method for-predicting the lateral soil resistance to a pipe. The method employs a limit analysis by upper bound technique 1, 2,3 afforded by the theory of perfect plasticity.


The lateral resistance of soil to a submarine pipeline is commonly treated as Coulomb sliding friction, the lateral soil resistance Rl being written as:

(Mathematical equation available in full paper)

where f = friction coefficient and Wn net Submerged weight of the pipe defined as:

(Mathematical equation available in full paper)

Here Ws submerged weight of the pipe, and Pv = vertical component of hydrodynamic forces, taken as positive upwards

This approach is based on the assumptions that:

  • the support is rigid,

  • the pipe is sliding parallel to the surface of the support, and

  • Rl is independent of lateral displacement

These assumptions fail for most actual physical problems. The soil is not rigid, the sliding does not develop along the soil surface, and the soil resistance depends on the displacements of the pipe. Thus it should be expected that this approach will fail for the most actual loading - soil - pipe conditions. Reliable results, however, can be obtained for "light" pipelines supported by dense sand using the approach based on Coulomb friction.

Lyons7 has concluded that "Coulomb friction is not valid for lateral sliding on soft clay". For this case he has presented some results derived by a finite element procedure. These results alone, however, are not sufficient for determination of lateral resistance of pipes with other geometrical, loading and soil parameters.

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