Dent Strain — Engineering Fundamentals

1. Dent types

Pipelines suffer three classes of mechanical damage:

• Plain dent — smooth indentation, no gouge or metal loss. Most common from third-party equipment impact or backfill rock. B31.8 App R addresses this case.
• Kinked dent — sharp angular change in shell, often from heavy machinery. Always requires repair per 49 CFR.
• Dent with gouge / metal loss — combined damage; App R doesn't apply, use API 579 Part 12.

Plain dents are routinely tolerated up to ~6% depth when off-weld and showing low strain.

2. Parabolic geometry

App R approximates the dent shell-surface as parabolic in both axial and circumferential directions. Given dent depth d, axial length L, and circ length C, the radii of curvature at the deepest point are:

Both directions get smaller-radius (higher-curvature) with deeper dents — generating more bending strain per unit wall thickness.

3. Combined strain invariant

Three strain components contribute:

• ε₁: axial bending = −t / (2·R₁) (negative if concave outward)
• ε₂: circumferential bending = t/(2·R₂) − t/D (subtract original cylinder curvature)
• ε₃: extensional / membrane = 0.5·(d/D)² (shell stretches over the dent)

The B31.8 Eq R-2 combines via a von-Mises-style invariant scaled by 2/√3:

Acceptance: ε_total ≤ 6%. This limit was derived from full-scale burst testing of dented pipe and represents the strain at which fatigue life drops sharply.

4. Repair criteria

Per 49 CFR 192.711 / 195.422, a dent must be repaired if any of:

• Depth > 6% of OD (regardless of strain) — gas / liquid pipelines.
• Depth > 2% on a weld.
• Located in an HCA (more stringent).
• Associated with gouge, crack, or metal loss.
• Kinked or sharp shoulder.

Repair methods range from grinding (small gouges only), composite sleeve (Type A), to full pipe replacement.

5. References

• ASME B31.8 (2022). Appendix R — Estimating Strain in Dents.
• API 1156 (2nd ed). Effects of Smooth Rock Dents on Pipelines.
• API 579-1 / ASME FFS-1. Part 12 — Dents.
• 49 CFR 192.711, 195.422. Repair procedures.
• Folias, E.S. Stress analysis basis carried into bending strain.