Page 256 - Trenchless Technology Piping Installation and Inspection

220 Cha pte r F i v e

these equations to relatively simple formulae and practical proce-
dures, albeit at a possible loss of precision, would be beneficial, as
described in the following sections.

Pull Force
In order to reduce the complexity of Eq. (5.12) for Mini-HDD installa-
tions, the procedure is limited to polyethylene pipe without the use of
anti-buoyancy techniques. Such techniques are typically not employed
for Mini-HDD operations. Substituting specific (conservative) values
for several of the parameters, and a comparison of the typical magni-
tudes of the resulting calculations, allows a major simplification of
the predicted pull force at the end of the installation, T . In particular,
D
values of the frictional coefficients υ and υ are assumed to be equal
a b
to 0.5 and 0.3, respectively, and pipe entry and exit angles, α and β,
are assumed to be 20°. Thus, it may be shown that Eq. (5.12d) can be
simplified to

T ≈ L · w · (1/3) (5.15)
D bore b
It is recognized that, under appropriate conditions and actual instal-
lations, the pull force may achieve its maximum level prior to point D
in Fig. 5.20. However, with the present basic theoretical model, under
the assumed conditions and conservative parametric values, the pre-
dicted tension at point D would be a maximum, or reasonably close
in magnitude to a previously occurring (predicted) maximum value.
For Mini-HDD installations, the above estimate T must be mod-
D
ified to account for the possibility of additional path curvature due to
deliberate route bends as well as the likelihood of unplanned undula-
tions resulting from path corrections. The presence of such character-
istics in the final (as-built) path will increase the required pull force,
consistent with the capstan effect described above. These effects may
be conservatively estimated by the applying the exponential term in
Eq. (5.13) to the tension T , such that
D
1
T = T · e υb θ (5.16)
D D
represents the net final tension, for which the angle θ is selected as
equal to the total additional route curvature. The latter may be
expressed as
θ = n· (π/2) (5.17)

where n is equal to the number of additional 90° route bends due to
the cumulative route curvature, as described below. Considering the
assumed value of υ of 0.3, combining Eqs. (5.15) to (5.17) yields:
b
T ≈ [L · w · (1/3)] · (1.6) n (5.18)
1
D bore b