The installation loads are gone once the pipe is in place and connected, but a Horizontal Directional Drilling installation leaves behind one operating condition that a conventionally trenched pipeline does not: a locked-in elastic bend. Because the pipe is pulled into a pre-formed curved hole rather than bent to fit an open ditch, it retains an elastic bending stress in service. This article covers the operating load cases for an HDD line and the combined-stress check that governs them.
The Three Operating Loads
- Internal pressure from the transported fluid, producing hoop stress and an associated longitudinal component.
- Elastic bending as the pipe conforms to the curved shape of the drilled hole — the HDD-specific term.
- Thermal stress from the difference between the locked-in (constructed) temperature and the operating temperature.
Apart from the elastic bend, these are the same loads any buried pipeline sees, so established stress procedures apply — the bending term is simply added to the mix and checked in combination with the others.
The Individual Formulas
Bending stress uses the same expression as the installation analysis, fb = (E × D) / (24 × R), so the design radius sets the operating bend stress just as it sets the installation one. Hoop stress from internal pressure is fh = (Δp × D) / (2 × t); in the operating case Δp is the difference between internal fluid pressure and external groundwater pressure. The longitudinal stress from internal pressure is fp = fh × ν, where ν is Poisson’s ratio (0.3 for steel).
Thermal stress follows the standard restrained-pipe expression from ASME B31.4: ft = E × k × (T1 − T2), where k is the coefficient of thermal expansion for steel (about 0.0000065 in/in/°F), T1 is the constructed temperature, and T2 the operating temperature. A line locked in cold and operated warm goes into longitudinal compression; the reverse puts it in tension.
Combining the Stresses: Maximum Shear
The combined operating check is done by finding the maximum shear stress on a small element of pipe wall and limiting it to 45% of SMYS, per ASME B31.4. The maximum shear stress is fv = (fhoop − flong) / 2, where the total hoop stress comes from the pressure term and the total longitudinal stress is the sum of the bending, thermal, and pressure-induced longitudinal contributions (tensile positive, compressive negative). The critical element is on the compressive side of an elastic bend, at the greatest distance from the neutral axis — exactly where the locked-in HDD bend adds most to the longitudinal stress.
Why It Rarely Governs — But Must Be Checked
For a properly designed crossing the bending stresses imposed by HDD are generally not severe, because the minimum design radius (typically about 100 feet of radius per inch of diameter — see radius of curvature design) keeps fb modest. As a result the operating check is usually satisfied comfortably. But it still must be run: a crossing that was drilled tighter than design, or one operating with a large temperature swing and high pressure, can push the combined shear toward the 45%-SMYS limit. The as-built curvature verified during construction is the right radius to use in this check, not the design value.