Page 73 - Buried Pipe Design

External Loads 49

From Eq. (2.20), the minimum soil cover is H 724 mm (28.5 in). In this
analysis, the pipe section is a simply supported beam (no support from the
soil). Minimum cover is 724 mm (28.5 in). This is an upper limit.
It is prudent to specify good bedding and embedment, and to require a
minimum cover of 0.9 m (3 ft) for the impact loads of heavy construction
equipment. To place and compact embedment under the haunches, a
windrow of soil along the pipe can be shoved into place by laborers with
J-bars working on top of the pipe, by flushing the windrow under the
haunches with a water jet, or by mechanical compactors. Some installers
pour soil cement or slurry under the haunches. The slump should be about
2
10 in, and the strength should be low—maybe 100 lb/in .
Example Problem 2.7 What is the minimum cover H for the pipe in the
above examples based on maximum longitudinal tensile stress Mc/I in
the bottom of a simply supported beam? With a uniform load w at
2
midspan M wL /8, where w is the load per unit length of beam; that is,
4
4
2
w P(OD) 4W/ (32 in H) . And I/c ( /32)[(OD) (ID) ]/OD. If ten-
sile strength is f 7 MPa (1 ksi), substituting values into the equation
f M/(I/c), H 665 mm (26.2 in). Failure by a broken bell is slightly
more critical.
Similitude. Engineering is basically design and analysis with atten-
tion paid to cost, risk, safety, etc. In this section, the design considered
is a buried pipe. Analysis is a model that predicts performance.
Performance must not exceed performance limits. Mathematical models
are convenient. Physical, small-scale models are better for complex
pipe-soil interaction. The most dependable models are full-scale proto-
types. Mathematical models are often written to describe prototype
performance because it is impractical to perform a full-scale prototype
study for every buried pipe to be installed. The set of principles upon
which a model can be related to the prototype for predicting prototype
performance is called similitude. Similitude applies to all models—
mathematical, small-scale, and prototype.
There are three basic steps in achieving similitude.
1. Fundamental variables (FVs) are all the variables that affect the
phenomenon. All the FVs must be uniquely interdependent.
However, no subset of FVs can be uniquely interdependent. For
example, force, mass, and acceleration of gravity cannot all be
used as fundamental variables in a more complex phenomenon,
because force equals mass times acceleration. Therefore the sub-
set is uniquely interdependent. Only two of the three fundamen-
tal variables could be used in the phenomenon to be investigated.
2. Basic dimensions (BDs) are the dimensions in which the FVs can
be written. The basic dimensions for buried pipes are usually
force F, distance L, and sometimes time T and temperature.