This is an interesting topic, and I would like to share the following information on how the non-linear behavior of soil restraint has been addressed in the past, and has been generally accepted by the soil-structure interaction community.

It well documented that the soil load-displacement response to beam-on- elastic foundation types of structural movements is highly non-linear. The soil response or the general shape of the soil load-displacement curve can exhibit two distinct types of behavior which can be described as either "soft" or "brittle".

The "soft" behavior is characterized by a hyperbolic smooth strain hardening type of load-diplacement soil response where the soil load smoothly increases at a decreasing rate where the ultimate soil response becomes asymptotic to a constant value at large structureal (pipeline) displacements. This type of behavior is generally associated with "loose" to medium dense granular soils (i.e. sands or silty sands).

The "brittle" behavior is characterized by an initially "stiff" response to increasing structural displacements where the soil load increases to an ultimate value, and then drops off to a lower residual or mobilized soil response and becomes asymptotic to a constant value at continued increased structural displacements. This type of behavior is generally associated with dense granular soils and/or cohesive fine grained clayey materials. This characterisic is also associated with frictional load-displacment behavior and pipeline sea bottom resistance against lateral loads as mentioned above by a previous respondee.

For either case, the question is, how to mathmatically characterize these types of non-linear soil response using the bi-linear soil model available in CAESAR II? A bi-linear soil model is restricted to characterizing soil behavior using two straight lines. The accepted way of using a bi-linear soil model to approximate non-linear soil response involves an iteritive trial and error type procedure to match the soil response (soil force) and corresponding displacment from the CAESAR output with the predicted "actual" non-linear soil displacement funtion by changing the slope or stiffness of the bilinear CAESAR II soil model at different segments along the buried pipeline.

This is very much considered to be an advanced analysis approach, is not necessarily for "beginners", and implies that the the user be very familiar with the technical literiture that addresses how to generate non-linear soil-load displacement functions, and the he or she has a good working knowledge of soil mechanics focusing on soil-structure interation problems.

Some literiture that is helpful to understand the soil mechanics side of the problem are as follows:

Nyman, K. J., "Thaw Settlement Analysis For Buried Pipelines In Permafrost", Preocedings, Pipelines In Adverse Environments II, ASCE, San Diego 14-16 Nov. 1983, pp 300-325

Audibert, J.M.E., Nyman, K.J., "Soil Restraint Against the Horizontal Motion of Pipes, Journ. Geotechnical Eng. Div., ASCE, GT10, Oct 1977, pp 1119-1142

"Guidelines for the Design of Buried Pipe", July 2001, American Lifelines Alliance (avialable for free on the Web...look it up)