Page 183 - Buried Pipe Design

Design of Gravity Flow Pipes 157

One very significant feature of the PIPE5 program is its ability to
detect when an element should be on the unload/reload curve and shift
from using Eq. (3.36) to Eq (3.43) for evaluation of the element stiff-
ness matrix of that element.

Determining the maximum stress. The most desirable condition is to
provide a means of monitoring the stress history of each soil element
and to use an unloading modulus when the soil stresses are detected
to be less than a maximum previous stress. An improved soil model
was developed which includes both primary loading parameters and
unloading-reloading parameters. The stress condition of a soil element
is uniquely determined by the values of the maximum and minimum
principal stresses. For plane-strain analysis, the intermediate princi-
pal stress is assumed to be equal to or greater than the minimum prin-
cipal stress. Several different schemes have been tested to monitor the
stress history of each soil element: maximum deviator stress, maximum
confining pressure, maximum principal stress, and maximum average
stress.
The schemes were investigated in view of Mohr’s circle analysis.
These investigations show the best variable for testing the stress con-
dition of the soil elements is the average stress (or the center of Mohr’s
circle). The center of Mohr’s circle gives a general indication of the
stress condition, dependent on both maximum and minimum principal
stresses. If the position of the center of the circle is decreasing, an
unloading modulus is in effect. The unloading-reloading modulus is
also in effect until the position of the center of the circle exceeds a max-
imum position indicated by the stress history.
The average principal stress is monitored for each element and com-
pared to the highest previously recorded average principal stress for
that element. The soil model uses an unloading modulus if the average
stress is less than the maximum average stress value. A mechanism is
provided to simulate maximum past pressures by inputting values for
maximum stresses for each soil element, similar to the preexisting
stress concept.

Behavior of other soil parameters. The discussion given by Duncan
et al. indicates that the only soil parameter that is a function of stress
6
history is the elastic modulus constant. However, there appears to be
an insufficient database to substantiate these remarks. Poisson’s ratio
ν is computed based on the bulk modulus B and elastic modulus E by
Eq. (3.40). Duncan’s recommendation is that the modulus of elasticity
be from 1.2 to 3.0 times greater on unloading than on primary loading
depending on the soil density. If the bulk modulus is invariant of
stress history, the value of Poisson’s ratio will become very small if the