a. Longitudinal Extension. The maximum horizontal strain of a conduit
beneath an embankment or earth dam occurs under the center of the fill.
Maximum strain depends on the ratios b/h, b/d, and the average vertical
strain in the foundation beneath center of the fill. (See Figure 22 for the
definitions and the relationship between vertical strain and horizontal
b. Joint Rotation. Besides the horizontal extension of the conduit,
additional joint opening may occur at the bottom of the pipe because of
settlement under the embankment load. For concrete pipe in sections about
12 feet long, compute additional joint opening due to settlement by Equation
Opening = ))))))))))
[delta] = settlement of base of pipe at embankment centerline (in)
b = embankment base width (in)
c = constant, varying from 5 for uniform foundation
conditions to 7 for variable foundation conditions
r = pipe radius (in)
c. Pipe Selection. Compute total settlement below embankment by
methods in Chapter 5. From this value, compute maximum joint opening at
pipe mid-height as above. Add to this opening the spread at the top or
bottom of the pipe from joint rotation computed from Equation (4-8).
Specify a pipe joint that will accommodate this movement and remain
watertight. If the joint opening exceeds a safe value for precast concrete
pipe, consider cast-in-place conduit in long sections with watertight
expansion joints. Corrugated metal pipe is generally able to lengthen
without rupture, but it may not be sufficiently corrosion resistant for
water retention structures.
5. LONG SPAN METAL CULVERTS. The above methods are not applicable to very
large, flexible metal culverts, i.e., widths in the range of 25 to 45 feet.
For analysis and design procedures for these see Reference 19, Behavior and
Design of Long Span Metal Culverts, by Duncan.
DEEP UNDERGROUND OPENINGS
1. GENERAL FACTORS. Pressures acting on underground openings after their
completion depend on the character of the surrounding materials, inward
movement permitted during construction, and restraint provided by the tunnel