Page 40 - Buried Pipe Design
P. 40
18 Chapter Two
All the above discussed parameters affect the load on the pipe and
are incorporated in Marston’s load equation for positive projecting
(embankment) conduits
2
W c C c B c (2.5)
where
c 1
e ±2K (H/B )
C c (2.6)
±2K
or
e ±2K (H /B ) H H e
c 1
e
C e ±2K (H /B ) (2.7)
c
e
c
±2K B c B c
Equation (2.6) is for the complete condition. The minus signs are for
the complete ditch, and the plus signs are for the complete projection
condition. Equation (2.7) is for the incomplete condition, where the
minus signs are for the incomplete ditch and the plus signs are for the
incomplete projection condition. And H e is the height of the plane of
equal settlement. Note that if H e H, the incomplete case of Eq. (2.7)
becomes the complete case and Eq. (2.6) applies for C c .
Although the above equations are difficult and cumbersome, they have
been simplified and can be found in graphical form in many references.
Note that value C is a function of the ratio of height of cover to pipe-
c
diameter ratio, the product of the settlement ratio (r ) and the projec-
sd
tion ratio (p), Rankine’s constant (K), and the coefficient of friction ( ).
The vertical distance from the natural ground surface to the top of the
pipe is expressed as pB , where p is the projection ratio.
c
H
C c f , r sd p, K,
B c
The value of the product K is generally taken as 0.19 for the projec-
tion condition and 0.13 for the ditch condition. Figure 2.5 is a typical dia-
gram of C c for the various values of H/B c and r sd p encountered. Table 2.2
gives the equations of C c as a function of H/B c for various values of r sd p
and K .
The settlement ratio r sd is difficult, if not impossible, to determine
even empirically from direct observations. Experience has shown that
the values tabulated in Table 2.3 can be used with success. Note that
when r sd p 0, C c H/B c and W c H B c . This is the prism load (i.e.,
the weight of the prism of soil over the top of the pipe). When r sd 0,
the plane at the top of the pipe, called the critical plane, settles the
