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Pr oject Considerations for Horizontal Dir ectional Drilling   215

          grade. Thus, for the simplification purposes, the bore entry and exit
          angles are defined relative to the average grade. For large surface
          depressions or mounds (e.g., of height greater than the depth of inter-
          est and extending over a long expanse, on the order of the minimum
          drill rod bend radius or greater), the bore should attempt to follow a
          path at the nominal specified depth below the average surface pro-
          file. Available industry tools may be used to provide assistance dur-
          ing the planning and construction phases.
             The path should avoid unnecessary bends and consecutive left and
          right, or upward and downward curves. Such trajectories are difficult
          to follow and may lead to over-steering and excessive bends, resulting
          in increased stresses in the drill rods and greater pulling forces during
          the installation of the pipe. A heavy rope or line placed on the surface
          may serve as a convenient means of defining a gradual curve consis-
          tent with the desired path radius of curvature. The radius of curvature
          of the path may be estimated by:

                                R  = ΔS/Δφ                     (5.11)
                                 avg
          where R avg  = average radius of curvature along path segment, ft
                 ΔS = distance along path, ft
                 Δφ = angular change in direction, radians

             Thus, a change of 0.1 radian (approximately 6°) per 10 ft corre-
          sponds to a radius of curvature of approximately 100 ft.

          Accuracy and Tolerance
          The deviation of the actual bore route from the proposed path should
          be within a specified tolerance and such as to meet the intent of
          required separations from existing facilities. Both vertical and hori-
          zontal limits should be specified by the owner, consistent with local
          regulations. Some regulations require that new construction activities
          be a minimum of 18 in. from either side of the outer edge of existing
          facilities (Telcordia, 2007).
             Unintentional bore path deviations may result from attempting
          to follow a bend with sharp curvature, drill head misalignments
          caused by cobbles or other obstacles, or soil conditions in general.
          Deviations may be reduced by decreasing the interval between suc-
          cessive drill head location determinations. Unless otherwise speci-
          fied, the drill head should exit at the surface or access pit within a
          12-in. radius of the target point. It is generally less difficult to meet
          such a condition for a target point in a pit than at the surface in a
          gradually rising bore profile (see Fig. 5.16). The allowable horizontal
          and vertical deviations along the bore route should also be specified
          by the owner. Typically, horizontal and vertical deviations along the
          bore route should be within ± 18 in. of the proposed path.
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