Pipeline · ground movement
OOS Strain Estimator
Rapid bending and axial strain estimate for a pipeline pushed laterally by ground movement, from field-staked out-of-straightness (Fathi et al. 2020 sine-shape method).
Deflected shape
Method checks
Tensile strain demand vs ground displacement
Strain along the span
Following the paper, axial strain is uniform within each limb, so it steps at the peak when the limbs differ in length. In reality axial force is continuous at the peak; the per-limb form is kept because it is the form the paper calibrated against FEA.
Strain at girth welds
Calculation detail
About this tool · v1.0.0
Purpose. Screening-level estimate of bending and axial strain in a pipeline deflected roughly perpendicular to its axis by ground movement, from a field-staked or IMU-derived out-of-straightness (OOS) profile, and how that strain grows with further movement.
Method. Fathi et al. (2020), IPC2020-9259. Each limb is fitted with a half-cosine (Eq. 1). Peak curvature κ = Δ/2·(π/Lshort)² and bending strain κD/2 (Eqs. 2–3). Axial strain is the arc-length elongation of each limb (Eq. 4). The short-limb axial strain plus peak bending strain is the governing tensile demand. In the paper's 1,296 FEA cases the method was conservative 71% of the time, with a mean overestimate of about 19%.
Validated range (paper). Δmax 0.3–7.3 m; LUS 4.8–69.2 m; L 11.2–165.3 m; D/t 25.5–96. Results outside this range are flagged.
Strain localization. The method assumes smooth bending and uniform axial strain along each limb. As strain localizes at bends, girth welds or sharp slide margins, those assumptions break down. Experience comparing the rapid method with IMU: below about 0.3% peak bending, localization is unlikely and agreement is generally good. From 0.3% to 0.5% it becomes increasingly likely. Above 0.5%, treat the estimate with caution and consider FEA.
Limitations. Perpendicular loading only; the oblique or axial-dominated cases are not covered. It does not capture sharp, block-like slide margins where the S-bend is shorter than the fitted limb, or pre-existing field bends. Internal pressure and temperature effects on axial strain are not included. Results are screening estimates and do not replace engineering judgement or FEA.
Comparison values. The span-average axial strain and an empirical axial strain used in some legacy workbooks, 2.3485·(Δ/L)1.9893, are reported in the calculation detail for comparison with legacy workbooks. They are not used for the governing result.
Change log.
- 1.0.0 (2026-10-26): First Outcrop release. Standalone HTML (no external libraries). Generic example only. Comparison rows added for the empirical axial formula used in some legacy workbooks. Optional project number recorded in the PDF and spreadsheet outputs. Replaces the "Updated Axial Strain Estimate Workbook for OOS – Fathi et al. (2020)" spreadsheet, which it reproduces exactly except for a corrected upstream-limb axial strain in the profile.
Owner: Pipeline team (BGC). Reviewer and sign-off are recorded in the Outcrop listing.
Method: A. Fathi, O. Ndubuaku, N. Yoosef-Ghodsi, M. Hill (2020), Rapid strain demand estimation of pipelines deformed by lateral ground movements, IPC2020-9259. Shape: Eq. 1. Bending: Eqs. 2–3 on the shorter limb. Axial: Eq. 4 arc-length elongation per limb, assuming no strain leaks outside the span; the maximum tensile strain adds the short-limb axial strain to the peak bending strain, as in the paper. The span-average axial value is shown for comparison only. In the paper's 1,296-case FEA comparison the max tensile estimate was conservative in 71% of cases (mean overestimate about 19%); bending was generally underestimated and axial slightly overestimated. The paper treats this as a screening estimate, not a replacement for FEA.