Page 161 - Buried Pipe Design

Design of Gravity Flow Pipes 135

Failure Plane Strength Envelope
Soil
Unit Weight f f

C Mohr’s Circle
z
f
Failure Plane z C z

z
f f
x
x
z
Trench z
(Vertical Cut) Mohr’s Circle for Critical Stresses at 0
Figure 3.31 Mohr’s circle analysis for finding critical depth Z for a vertical trench wall
in a brittle soil cohesion C and a soil friction angle
, where 2C/( Z) tan(45°
/2).

From tests, Eq. (3.27) provides a reasonable analysis for brittle soil.
If the soil is plastic, soil slip does not occur until shearing stresses
reach shearing strength C. Consequently, in plastic soil, the critical
depth equation is 2C/( Z) 1. Below the water table, critical depth is
essentially doubled.

Example Problem 3.5 What is the critical depth Z of a vertical, opencut,
2
3
trench wall if C 600 lb/ft , 120 lb/ft , and
30°?
Substituting into Eq. (3.27) gives Z 17.3 ft. This is a lower limit if the
soil has some plasticity (is not brittle).
Example Problem 3.6 Suppose that a sloped trench wall exposes a pipe as
shown in Fig. 3.30. Pressure P x must be resisted by ring stiffness. What is
the required pipe stiffness for a 72-in HDPE pipe to prevent buckling?
Assume the soil is granular with unit weight of 120 pcf. Since there is no
soil on one side of the pipe, assume the pipe is unsupported and must be
able to withstand the pressure P x r.
From Eq. (3.14),

3EI
P cr 3 r
2
(1 ) R
Assume the following:

E 110,000 lb/in 2
0.4