Pipe resistance to pullback in the bore hole depends primarily on the frictional force created between the pipe and the hole or the pipe and the ground surface in the entry area, the frictional drag between pipe and drilling slurry, the capstan effect at bends, and the weight of the pipe. Equation 7-4 gives the frictional resistance or required pulling force for pipe pulled in straight, level bores or across level ground (Figure 7-2).

where:

FP = pulling force in pounds ^ = coefficient of friction between pipe and slurry (typically 0.3) or between pipe and ground (typically 0.5 or 0.1 when pipe is on rollers) WB = net downward (or upward) force on pipe in pounds per foot L = length in feet

FIGURE 7-2 Frictional Resistance

When slurry is present, WB is the upward buoyant force of the pipe and its contents. Filling the pipe with fluid significantly reduces the buoyancy force and thus the pulling force. If the pipe is installed empty using a closed nose-pull head, the pipe will tend to float on the crown of the bore hole leading to the sidewall loading and frictional drag through the buoyancy-per-foot force and the wet soil to pipe coefficient of friction. If the pipe is installed full of water, the net buoyant force is drastically reduced. During pullback, the moving drill mud lubricates the contact zone. If drilling, pipe, or mud flow stops, the pipe can push up and squeeze out the lubricating mud.

For curves in the bore hole, the force can be factored into horizontal and vertical components (Figure 7-3). When drilling with steel pipe there is an additional frictional force that occurs due to the pressure required by the bore hole to keep the steel pipe curved. When drilling with plastic pipe using a radius of curvature similar to that used for steel pipe, these forces are likely insignificant. However, when using tight bends these forces should be taken into consideration. The frictional resistance during a pull is compounded by the capstan effect. Compounding forces caused by the direction of the pulling vectors are created as the pipe is pulled around a curve or bend, creating an angle. The pulling force due to the capstan effect is given in Equation 7-5. This equation and the preceding one are applied recursively to the pipe for each section along the pullback distance. This method is credited to Larry Slavin of Bellcore (Middletown, NJ).

where:

e = natural logarithm base (e = 2.71828)

^ = coefficient of friction between the pipe and slurry (typically 0.3) ^ = angle of bend in pipe in radians WB = weight of pipe or buoyant force on pipe in pounds per foot L = length of pull in feet

Equation 7-5

Pulling Force

Pulling Force

FIGURE 7-3 Capstan Effect

174 Chapter 7 ■ HDD Pipe Stress Analysis for Plastic Pipe

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