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Pr oject Considerations for Horizontal Dir ectional Drilling 217

Direction of Bore

Bore/pipe path Product pipe entry
β D A α

H
Product
pipe exit C B
L 4 L 3 L 2 L 1

L bore
FIGURE 5.20 Nominal Maxi-HDD route (river crossing). (Source: Outside Plant
Consulting Services.)

5.5.1 Pipe Load Calculations
Figure 5.20 illustrates a typical geometry for a major (Maxi-HDD)
operation, corresponding to a river crossing. The indicated path cor-
responds to that shown in ASTM F1962 and comprises four segments,
including those spanning the pipe entry to exit point (L , L , L ) and
2 3 4
the excess length (L ) remaining after the span has been accomplished.
1
Thus, the length of the actual crossing, L , is given by
bore
L = L + L + L
bore 2 3 4
In some cases, the intermediate horizontal segment, L , may be of
3
zero length. Due to the typically low pipe entry angle, α, and exit
angle, β, and gradual path curvature, the depth of the crossing, H, is
small compared to the transition distances L and L .
2 4
Pull Force
Using the above terminologies, ASTM F1962 provides a set of recur-
sive relations to predict the required pull force ––T , T , T , and
A B C
T –– corresponding to the leading end of the pipe reaching point A,
D
B, C, and D (see Fig. 5.20). Thus,
υa α
T = e · υ · w · (L + L + L + L ) (5.12a)
A a a 1 2 3 4
υb α
T = e · (T + υ · |w |· L + w · H – υ · w · L · e υa α ) (5.12b)
B A b b 2 b a a 2
υb α
T = T + υ · |w |· L – e · (υ · w · L · e υa α ) (5.12c)
C B b b 3 a a 3
υb α
υb β
T = e · (T + υ · |w |· L – w · H – e · [υ · w · L · e υa α ]) (5.12d)
D C b b 4 b a a 4
where w and w are the empty (above ground) and buoyant weights of
a b
the pipe, respectively, and υ and υ . are the corresponding coefficients
a b