J2 Methodology — Seven-Phase Claim-Driven Prototype¶

Date: 2026-04-18 Status: First end-to-end prototype of the seven-phase claim-driven workflow applied to a real paper section. Target: the methodology section of Paper J2, currently under Round 2 revision at Ocean Engineering.

The previous note argued for inverting the figure-first workflow. This note runs the inversion on a concrete section to see what survives contact with a real manuscript. J2's methodology is the right candidate: it is already written (manuscript v18), already has figures, and has a deadline close enough that any restructuring must be fast and targeted. The workflow is therefore applied retrospectively as a diagnostic — what would the section look like if the claim-driven shape had been the starting point, and where are the actual gaps a reviewer will find?

Phase 1 — Thesis statement¶

One sentence the methodology section must prove:

The 3D continuum mechanics of a tripod suction bucket under scour can be distilled into a 1D Winkler representation whose depth-varying spring parameters preserve the total energy of the 3D solution, reproduce eigenfrequency within 5 % of field measurement, and remain traceable to measurable OptumGX outputs and a global VH capacity integral — so the 1D surrogate is not a curve-fit but a physics-consistent reduction.

The thesis is a commitment. Every subsection and figure either advances it or does not belong.

Phase 2 — Claim list¶

Five load-bearing claims decompose the thesis:

C1. The 3D FE reference model is a faithful representation of the continuum problem. Mesh converges to < 1 % on global capacity; far-field effects are < 2 %; constitutive choice (Tresca undrained) matches site conditions.
C2. Stiffness extraction via Fourier first-harmonic isolates the net lateral reaction from axisymmetric confinement noise, so the extracted \(K_{py}(z)\) profile reflects the mechanism of interest rather than a numerical artefact.
C3. Spring capacities are calibrated by an integral constraint against the VH envelope; the sum of local spring capacities equals the global failure load, so the 1D discretisation preserves the total work of the 3D continuum.
C4. Stress correction below the scoured mudline handles overburden loss consistently across all 11 scour scenarios; without it, the eigenfrequency prediction would drift systematically with scour depth.
C5. The three-phase pipeline is automated and reproducible — one command regenerates all 11 scour scenarios with identical provenance, and the five-order-of-magnitude speed-up over direct 3D analysis is measured, not asserted.

Phase 3 — Claim → evidence map¶

flowchart TD
    T["<b>Thesis</b><br/>3D→1D reduction is physics-consistent,<br/>5% of field, traceable to OptumGX"]
    T --> C1["C1 · 3D FE faithful"]
    T --> C2["C2 · Fourier first-harmonic isolates net reaction"]
    T --> C3["C3 · VH-envelope integral constraint"]
    T --> C4["C4 · Stress correction consistent across scour depths"]
    T --> C5["C5 · Pipeline automated and reproducible"]
    C1 --> E1["Fig · FEM domain + mesh<br/>Fig · convergence curve (H<sub>global</sub> vs N<sub>elem</sub>)<br/>Stat · < 1% at 15k elem"]
    C2 --> E2["Fig · workflow schematic<br/>Fig · 1st-harmonic extraction per depth slice<br/>Fig · K<sub>py</sub>(z) power-law fit"]
    C3 --> E3["Fig · VH envelope with 20 probes (θ-sweep)<br/>Table · integral residual per scour depth"]
    C4 --> E4["Fig · f<sub>1</sub> vs S/D, with and without stress correction<br/>Stat · drift magnitude if correction omitted"]
    C5 --> E5["Fig · three-phase workflow diagram<br/>Table · 11-scenario runtime + speedup"]
    E1 --> S1["spec · fig-fem-domain<br/>spec · fig-convergence"]
    E2 --> S2["spec · fig-workflow<br/>spec · fig-first-harmonic<br/>spec · fig-kpy-powerlaw"]
    E3 --> S3["spec · fig-vh-envelope<br/>table · integral-residual"]
    E4 --> S4["spec · fig-stresscorr-ablation"]
    E5 --> S5["spec · fig-workflow<br/>table · runtime-speedup"]

Nine figure specs, two tables. The existing manuscript has ten figures in the methodology section; the mapping above accounts for nine of them with one (a close-up of a single load step) that does not map to any claim and is a candidate for removal.

Phase 4 — Figure specs¶

Two-sentence spec per figure. These are what the figure_generator session would receive as config.yaml contents.

fig-fem-domain. Must show the half-symmetry computational domain with mesh refinement at the skirt tips, boundary conditions, and the Gunsan foundation geometry in scale. Single panel, Ocean Engineering single-column width (90 mm), annotated with \(L_{\text{domain}} = 10D\), \(H_{\text{domain}} = 7.5D\), skirt-tip fan meshing at 30°.

fig-convergence. Must show global horizontal capacity \(H_{\text{global}}\) versus number of elements \(N_{\text{elem}}\) on log-linear axes, with the 1 % error band shaded and the 30,000-element operating point marked. Single panel, annotation explains the 2.69 % at 4,000 elements → < 1 % at 15,000 elements → adopted 30,000 for pressure-field fidelity.

fig-workflow. Must show the three-phase pipeline as a block diagram with every arrow labelled by the data type that flows across it (displacement fields, contact pressures, VH probe points, depth-varying \(K_{py}\), 1D spring curves). Panels A/B/C = Phase 1 / Phase 2 / Phase 3; the Phase 1 → Phase 2 boundary must highlight that two parallel streams (load-deformation, limit analysis) converge at the calibration stage.

fig-first-harmonic. Must show the raw contact-pressure field at one depth slice plus its Fourier decomposition into \(A_0\) (axisymmetric, discarded) and \(A_1\) (first harmonic, retained), with the physical interpretation annotated. Two-panel: (a) raw field on a polar plot; (b) harmonic amplitudes as a bar chart with the discard/retain labels.

fig-kpy-powerlaw. Must show \(K_{py}(z)\) extracted across all 11 scour scenarios pooled as a single scatter with a power-law fit \(K_{py}(z) = A z^B\) overlaid and goodness-of-fit annotated. Error bars per depth slice from the 11-scenario variance; log-log axes. Residuals panel below the main panel.

fig-vh-envelope. Must show the VH capacity envelope at the baseline (no scour) scour state with 20 angular probes marked as dots, the smooth envelope through the probes drawn, and the integral constraint annotated as the enclosed area. Single panel, \(V\) on horizontal axis, \(H\) on vertical axis, positive compression and positive lateral convention stated.

fig-stresscorr-ablation. Must show \(f_1 / f_{1,0}\) versus \(S/D\) for 11 scour depths, overlaid: (a) with stress correction applied (the paper's method), (b) without stress correction. The drift between the two curves is the magnitude of the effect; a horizontal shaded band marks the ± 5 % field-measurement envelope for context.

table-integral-residual. Per-scour-depth integral residual (sum of local spring capacities minus global VH-envelope horizontal limit, normalised). All 11 rows, one column of residual percentage. Pass threshold < 2 %.

table-runtime-speedup. Per-phase runtime (mean over 11 scenarios), total pipeline runtime, equivalent direct 3D runtime, speedup ratio. Three rows; clean units.

Phase 5 — Paragraph skeletons¶

Two to three paragraphs per subsection, structured around the claims they prove.

§2.1 Computational Workflow (proves C5, introduces the sequence). ¶1 (setup). The 3D continuum is translated into 1D spring parameters through three computational phases [→ fig-workflow]. ¶2 (justification). Stiffness extraction and capacity calibration are separated because they reflect different soil response regimes — small-displacement quasi-linear versus limit-state failure — and treating them jointly would mix incompatible kinematic assumptions. ¶3 (reproducibility). The full pipeline runs unattended across all 11 scour scenarios [→ table-runtime-speedup]; total wall-clock is \(O(\text{minutes})\) versus \(O(\text{hours})\) per scenario for direct 3D analysis.

§2.2 Phase 1 — 3D FE Analysis (proves C1). ¶1 (domain and mesh). Half-symmetry, \(10D \times 7.5D\) domain, 30,000-element mesh with fan refinement at skirt tips [→ fig-fem-domain]. ¶2 (convergence). Mesh convergence is < 1 % at 15,000 elements on global capacity; the chosen 30,000 elements serve pressure-field fidelity, not global convergence [→ fig-convergence]. ¶3 (constitutive choice). Tresca undrained with \(s_u(z) = 15 + 20z\) kPa matches the normally consolidated Gunsan clay profile; interface \(\alpha = 0.67\) follows DNV-RP-C212 lower-bound for smooth steel on NC clay, and the −3.9 % field bias observed in §3 confirms conservativeness.

§2.3 Phase 2 — Parameter Extraction (proves C2, C3, C4). ¶1 (first-harmonic isolation). Fourier decomposition of contact-pressure fields retains the first harmonic and discards \(A_0\) [→ fig-first-harmonic]; the retained component is the net lateral resistance, decoupled from axisymmetric confinement. ¶2 (stiffness pool and power-law fit). \(K_{py}(z)\) pooled across 11 scenarios follows a power law [→ fig-kpy-powerlaw]. ¶3 (capacity calibration). Spring capacities calibrated against the VH envelope by an integral constraint [→ fig-vh-envelope, table-integral-residual]; residual < 2 % per scour depth. ¶4 (stress correction). Overburden loss below the scoured mudline is applied consistently [→ fig-stresscorr-ablation]; without it, \(f_1\) drift with \(S/D\) exceeds the field-measurement envelope.

§2.4 Phase 3 — 1D Structural Dynamics (proves the reduction completes). ¶1 (model construction). Central spine of beam-column elements, radial connectors at each depth slice, perimeter nodes carrying \(t\)–\(z\) springs; tower taper via Gauss–Lobatto integration. ¶2 (masses). Soil plug, marine growth, hydrodynamic added mass, RNA mass placed at physical locations before eigenvalue analysis. ¶3 (outputs). First natural frequency recovered via eigenvalue analysis; baseline matches field within −3.9 % (result reported in §3, not §2).

Each paragraph is a stub: first sentence = what is being done, last sentence = what is proved. The [→ fig-*] markers are the hooks for the figure_generator sessions.

Phase 6 — Generate figures (figure_generator integration)¶

Each of the nine figure specs becomes a single Claude Code session inside the figure_generator repo. The session prompt paste includes the spec block from Phase 4 verbatim, plus the claim_id and the figure_inputs path.

Example for fig-kpy-powerlaw:

Figure: fig-kpy-powerlaw
Paper: J2 methodology
Thesis: J2-methodology-thesis
Claim: C2 (Fourier first-harmonic isolates net lateral reaction)

Spec: Must show K_py(z) extracted across all 11 scour scenarios pooled as a
single scatter with a power-law fit K_py(z) = A * z^B overlaid and goodness-
of-fit annotated. Error bars per depth slice from the 11-scenario variance;
log-log axes. Residuals panel below the main panel.

Data: paperJ2_oe00984/figure_inputs/fig_kpy_powerlaw.parquet
Schema: paperJ2_oe00984/figure_inputs/fig_kpy_powerlaw_schema.yml
Journal: ocean_engineering
Width: single (90 mm)

The session runs steps 1–9 of the figure_generator CLAUDE.md protocol: load data → validate → confirm layout → scaffold → edit script + config → build → write caption → regenerate gallery → propose commit. The commit message carries the Claim: C2 tag so git log --grep "Claim: C2" returns the single session responsible for that figure.

The existing manuscript figures were generated in an ad-hoc way; the retrospective task is to (a) fill paperJ2_oe00984/figure_inputs/ with one parquet per claim-mapped figure, (b) rerun each figure through the engine, and (c) replace manuscript figures with the claim-tagged outputs. Estimated work: one afternoon per figure for the regeneration, faster for figures whose underlying data is already in clean CSVs.

Phase 7 — Coherence passes¶

Two passes, ignoring each layer in turn.

Pass A — paragraphs only, figures hidden.

§2.1 sets up the pipeline but does not name which phase is load-bearing for which claim. Fix: add one sentence to ¶2 identifying that C2, C3, C4 are proved in §2.3 and C1 in §2.2.
§2.3 paragraph 3 (capacity calibration) has the integral constraint stated but does not explain why sum of local capacities should equal the global envelope limit. Fix: add one sentence on the plastic-work argument (forward reference to J11).
§2.3 paragraph 4 (stress correction) is terse and does not state that the correction magnitude scales linearly with effective stress loss, which is the mechanism. Fix: one sentence.
§2.4 paragraph 3 (outputs) is short and has no claim link. Fix: explicitly state that the reduction's validation lives in §3 and link the thesis commitment to the 5 % field-measurement error tolerance.

Pass B — figures only, paragraphs hidden.

Nine figure specs, nine figures. All map to claims. No figure is orphaned.
fig-workflow appears twice (§2.1 and §2.3 intro). Fix: reuse once, not twice; the §2.3 instance is a zoom into Phase 2 and should be fig-workflow-phase2 rather than a duplicate of the overview.
fig-first-harmonic and fig-kpy-powerlaw together establish C2; could be combined into a two-panel figure to reduce total figure count. Consider: merge.
table-integral-residual is a dense 11-row × 1-column table; could be represented as a bar chart figure more naturally. Consider: convert table to figure fig-integral-residual.

Orphans identified. The existing manuscript has a close-up figure of a single displacement step that does not map to any claim in this framework. Candidate for removal in R2; at minimum, if retained, it needs a claim assignment (probably a subclaim under C1 about load-deformation regime).

Reviewer objection rehearsal. Walking the chain thesis → C1..C5 → figures:

"Why Tresca and not Mohr–Coulomb?" — answered by C1, but the current text only states the choice. Fix: add one sentence on undrained-rapid-loading argument.
"Why 30,000 elements when 15,000 converges?" — answered by C1 and the fig-convergence caption. Good.
"Does the VH-envelope calibration introduce a circularity?" — answered by C3 (integral constraint sums local → global, not the other way). Current text does not make this explicit. Fix: one sentence disambiguating direction of constraint.
"How do you validate the stress correction specifically?" — answered by C4 and fig-stresscorr-ablation, but the ablation figure is not currently in the manuscript. Action: this is a new figure to produce for R2; claim C4's evidence slot is currently empty. This is the single highest-value addition the workflow surfaces.
"What is the claim about reproducibility actually backed by?" — C5 and table-runtime-speedup. Current manuscript mentions speedup narratively; no table. Action: the table is missing.

Two missing evidence items (fig-stresscorr-ablation and table-runtime-speedup) are both load-bearing and both cheap to produce — each is a small figure_generator session over data already in the 4_figures/ outputs. This is the output of the workflow: defects are locatable and actionable.

What the prototype surfaced¶

The retrospective pass on the J2 methodology shows three things:

Eight of the ten existing figures map cleanly to claims. One is a duplicate (can be merged); one is an orphan (can be removed or re-assigned). The existing argument is more coherent than I had assumed — the seven-phase workflow retrospectively confirms most of it.
Two figures are missing. fig-stresscorr-ablation (claim C4) and table-runtime-speedup / fig-integral-residual (claims C5 and C3) are both load-bearing, both directly address foreseeable reviewer objections, and both are cheap to produce. Adding them in R2 is the single highest-value intervention the workflow recommends.
Two paragraph-level fixes are surfaced by the paragraphs-only coherence pass: the circularity disambiguation on C3 and the claim-to-section link in §2.1. Both are one-sentence insertions.

The workflow's real output here is not "the section is wrong" — it is "here are the specific, small, high-value interventions that raise the section from sound to defensible under cross-examination." That is the kind of result that is cheap to ignore in a first draft and expensive to ignore in a reviewer response.

The next note does the same for J3 methodology, where the seven-phase pass will surface a different class of finding — centrifuge experiments have a different claim structure than numerical models.