Page 157 - Buried Pipe Design

Design of Gravity Flow Pipes 131

Critical depth Z is a convenient measure of soil strength. It is
defined as the maximum depth of a trench at which the walls stand
in vertical cut. At greater depths the trench walls slip or cave in.
Critical depth Z may be determined by excavation in the field, or it
may be calculated from the dimensionless stability number Z /C. See
Fig. 3.31.

2C
tan 45° (3.27)
Z 2
where Z critical depth of trench in vertical cut,
unit weight of soil, lb/ft 3
C soil cohesion, lb/ft 2

soil friction angle of trench wall

Depth Z can be found from Eq. (3.27) if soil properties , C, and
are
provided by laboratory tests.
To investigate the four fundamental variables, three pi terms are
required. One possible set is X/D, H/D, and H/Z. Tests show that H/D
is not pertinent. Only X/D and H/Z remain as pertinent pi terms.
For a vertical trench wall excavated parallel to a flexible pipe:

1. If the ring has some stiffness, and if soil cover H is not great enough
to collapse the ring, soil may slough off the pipe into the trench.
This is not considered failure because the soil can be replaced dur-
ing backfilling.
2. The ring collapses under a free-standing prism of soil that breaks
loose on top of the pipe.
3. Failure is sudden and complete collapse.
Test data are plotted in Fig. 3.29, which shows X/D as a function of
H/Z. The best fit straight line equation is X/D 1.4H/Z. The probable
error in X/D is ±0.1, so the probable error in side soil cover X is roughly
±D/10. Because field conditions may be less reliable than laboratory
conditions, the safety factor should be 2. Therefore, the minimum side
cover X might be specified as

X 3H
(3.28)
D Z
Of interest in Fig. 3.29 are the data points indicated by squares.
These do not represent collapse. The ring stiffness for the test pipes
was great enough that part of the shallow soil cover merely
sloughed off the pipes after the soil wedge fell into the trench. If
ring stiffness were to be included as a fundamental variable, ring