Page 112 - Buried Pipe Design

88 Chapter Three

Spangler’s equation or the Iowa formula and may be so referenced in
this text.
D L KW c r 3
X (3.5)
EI 0.061E′r 3

Two other observations from Watkins’ work are of particular note.
(1) There is little point in evaluating E by a model test and then
using this modulus to predict ring deflection, as the model gives ring
deflection directly. (2) Ring deflection may not be the only perfor-
mance limit.
Another parameter that is needed to calculate deflections in the
Iowa formula is the deflection lag factor, D L . Spangler recognized that
in soil-pipe systems, as with all engineering systems involving soil, the
soil consolidation at the sides of the pipe continues with time after
installation of the pipe. His experience had shown that deflections
could increase by as much as 30 percent over a period of 40 years. For
this reason, he recommended the incorporation of a deflection lag fac-
tor of 1.5 as a conservative design procedure. However, recall that the
load proposed by Spangler was the Marston load for a flexible pipe. For
most sewer pipe installations, the prism load is at least 1.5 times
greater than the Marston load (see Chap. 2 for soil loads on pipe). If
the prism load is used for design, a design deflection lag factor D L 1.0
should be used.

Soil modulus E analysis. The remaining parameter in the modified
Iowa formula is the soil modulus E . Spangler’s Iowa formula predicts
ring deflection based on elastic pipe and elastic soil. Spangler, a soil
engineer, included a horizontal elastic soil modulus E which he called
modulus of passive resistance of soil. In fact, horizontal passive resis-
tance is K
y where K (1 sin
)/(1 sin
). Soil slip planes occur at
45°
/2—not at 45°.
Eventually (at a high enough load), general soil shear will occur. By
Mohr’s circle analysis, horizontal soil resistance is K
y . Accordingly,
soil slip planes should occur at spring lines at angle 45°
/2 with the
horizontal. The analysis is conservative. The soil friction angle
is not
constant. It varies with depth of cover and ring deflection. In a con-
trolled test, planes of soil slip were observed in the sand embedment
of a flexible ring. See Fig. 3.8.
Soil modulus E may vary as the depth of cover (confining pressure
increases). In a confined compression test of soil, the slope of the
stress-strain (load-deflection) curve increases as the load increases.
That is, the load deflection curve is concave upward. Thus, the slope
of the curve increases with load or depth. There have been suggestions