Seismic risk assessment for oil and gas pipelines - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 692

The pipeline is modeled with pipe elements that are essentially beam
elements that are capable of accounting for internal pressure effects. Soil
restraint is modeled with non-linear spring elements that act independently
in the axial, horizontal, and vertical directions relative to the axis of the
pipeline as illustrated schematically in Fig. 25.2. Ground displacement
induced by earthquakes is modeled as displacements applied to the base of
the soil springs. There are no restrictions on the analysis software that can
be used as long as it is capable of capturing the nonlinear behaviour of soil

Z

Pipe in soil continuum

X

Y

T

Z

P

X

Q

Y

Discrete soil spring analog

Q T

Relative
displacement

Nonlinear soil
spring response

25.2 Representation of pipe-soil interaction using nonlinear spring
elements.