Page 176 - Buried Pipe Design

150 Chapter Three

1. The soil properties are strain-dependent (nonlinear).
2. Different elements, than those used to represent the soil, are usu-
ally used to represent the structure (pipe in this case).
3. For flexible pipe, the assumption that displacement gradients are
small often is incorrect and the solution will need to incorporate
geometrically nonlinear capability.
4. It may be necessary, in some instances, to allow movement between
the soil and the walls of the pipe (soil slip).

The stress-strain behavior of the soil is nonlinear; thus the solution
procedure must follow the stress condition incrementally. The con-
struction of the soil structure must be followed in steps, and the exter-
nal loads must be added incrementally for the FEA program to follow
the nonlinear stress-strain properties of the soil. This particular non-
linear behavior of the soil system has resulted in a special type of
analysis that is commonly used in most soil mechanics FEA programs.
The basic procedure followed is outlined below. The steps that are
described are those that are used in PIPE5.
A wide range of buried pipe problems can be modeled using a two-
dimensional plane-strain approach. In the two-dimensional finite ele-
ment model, the pipe is modeled using beam elements. These elements
are capable of accommodating shear, moment, and thrust. The nodes of
the pipe elements are connected to the adjacent soil elements at their
common nodal points. Slip between the pipe and soil can be accommo-
dated in the finite element analysis by placing “interface” or “gap” ele-
ments between the pipe nodes and the soil element nodes. These
interface elements have essentially no size, but kinematically allow
movement between nodes when a specified friction force is exceeded.

PIPE5 analysis procedure
1. Initial estimates of the stresses and elastic parameters of the soil
elements are assumed. Soil properties are nonlinear and are stress-
and strain-dependent. Due to the soil nonlinearities, the solution
procedure requires modeling that allows for incremental construc-
tion of the soil structure and the incremental addition of loads.
Initial elastic parameters must be known or assumed to compute
the stiffness matrix.
2. An incremental load vector is computed in one of two ways. If incre-
mental construction is being modeled, the load vector is computed
as the weight of the added soil and/or structure elements for the
increment. Alternatively, the load vector may comprise external
loads resulting from external forces.