J3 Results — Seven-Phase Claim-Driven Prototype¶

Date: 2026-04-18 Status: Sixth prototype; companion to the J3 methodology prototype. Applied to J3 results sections (§3 Results + §4 Discussion + §6 Innovation) ahead of R1 submission 2026-05-06. All 18 reviewer comments on J3 are closed; this prototype verifies the results-section evidence chain is equally complete.

Experimental results carry a different burden of proof than numerical results: reviewers expect per-test-series transparency, repeatability evidence, and mechanism-level explanations for observed effects. The workflow picks up this class of defect distinctly.

Phase 1 — Thesis statement¶

Ten saturated-sand centrifuge test cases (T4 dense, T5 loose) across four scour stages plus two backfill stages extend the dry-sand baseline of Paper J1 to quantify three mechanism-level effects: a 1.94 × saturation correction, a 3 × density amplification, and an asymmetric 41 %-vs-158 % backfill recovery — the last of which exposes a bending-to-tilting regime transition in loose saturated sand that frequency monitoring alone does not detect.

Phase 2 — Claim list¶

R1 — Saturation ratio 1.94. Scour sensitivity in saturated sand is approximately half that in dry sand across the tested range. Analytical \(\sqrt{\gamma_d / \gamma'} = 1.23\) accounts for roughly half; secondary density and stress-path effects account for the rest.
R2 — Density amplification 3×. Loose saturated sand (T5) shows 2.58 % frequency drop at \(S/D = 0.58\); dense saturated sand (T4) shows 0.85 %. Threefold amplification attributed to confining-stress-dependent stiffness contrast.
R3 — Asymmetric backfill recovery. Coarser No. 5 sand backfill recovers 41 % of frequency loss in dense native soil and overshoots by 158 % in loose native soil, explained by stiffness contrast between backfill and native.
R4 — Bending-to-tilting regime transition. Displacement amplification 4.27 ×, bending-strain reversal (+21 % → −11 %), and asymmetric settlement (13.2 mm vs 0.3 mm in T5 at \(S/D = 0.58\)) evidence a kinematic mode change in loose saturated sand that the 2.58 % frequency decline does not flag.
R5 — Prototype-to-model reconciliation. The 9.5 % RNA over-representation and 2.3 % \(EI_{\text{eq}}\) under-match produce directionally offsetting biases that cancel in relative \(f/f_0\), as disclosed in §2.2.1.
R6 — Cross-paper consistency with J2. Centrifuge power-law exponent \(b \approx 1.5\) matches the J2 numerical Winkler model within the combined error envelope, with the OCR-artefact offset in \(|a|\) (centrifuge 0.044–0.086 vs numerical 0.167) accounted for.

Phase 3 — Claim → evidence map¶

flowchart TD
    T["<b>Thesis (J3 results)</b><br/>Saturation 1.94× · Density 3× · Backfill 41%-vs-158% ·<br/>Bending→tilting regime transition"]
    T --> R1["R1 · Saturation ratio 1.94"]
    T --> R2["R2 · Density amplification 3×"]
    T --> R3["R3 · Asymmetric backfill recovery"]
    T --> R4["R4 · Bending-to-tilting regime transition"]
    T --> R5["R5 · Prototype-to-model reconciliation"]
    T --> R6["R6 · Cross-paper consistency with J2"]
    R1 --> E1["Fig · saturated-vs-dry f1(S/D) overlay<br/>Fig · 3-panel effective-stress + G_max schematic<br/>Stat · sqrt(gamma_d/gamma') = 1.23"]
    R2 --> E2["Fig · dense-vs-loose f1(S/D) overlay<br/>Table · slope alpha per series"]
    R3 --> E3["Fig · backfill recovery bar chart (dense vs loose)<br/>Fig · grain-size distribution (No. 5 vs No. 7)"]
    R4 --> E4["Fig · displacement · strain · settlement across T5 stages<br/>Text · three-mechanism explanation for abrupt transition"]
    R5 --> E5["Table · prototype-to-model error budget<br/>Fig · RNA-bias vs EI-bias cancellation in relative f/f0"]
    R6 --> E6["Fig · centrifuge-vs-numerical power-law comparison<br/>(with OCR-induced offset band)"]
    E1 --> S1["spec · fig-sat-vs-dry-f1<br/>spec · fig-stress-scour-schematic"]
    E2 --> S2["spec · fig-density-comparison<br/>table · slope-per-series"]
    E3 --> S3["spec · fig-backfill-recovery<br/>spec · fig-grain-size"]
    E4 --> S4["spec · fig-displacement-strain-settlement"]
    E5 --> S5["table · proto-model-error-budget<br/>spec · fig-bias-cancellation"]
    E6 --> S6["spec · fig-centrifuge-vs-numerical-powerlaw"]

Nine figures (some already in the R1 manuscript; some new), three tables.

Phase 4 — Figure specs (focused on ones not already in the R1 manuscript or needing reinforcement)¶

fig-centrifuge-vs-numerical-powerlaw (R6). Same axes: \(|\Delta f / f_0|\) vs \(S/D\) on log-log. Two power-law fits overlaid: centrifuge \(|a| = 0.044\)–\(0.086\) (range bar, T4 and T5) and numerical \(|a| = 0.167\) (single line from J2). Shaded band: OCR-induced 15–25 % stiffness bias that directionally aligns the centrifuge as a lower bound. Annotation: centrifuge is a directionally conservative lower bound on field sensitivity; J2 numerical provides the upper envelope.

fig-bias-cancellation (R5). Two-panel. Panel a: model-scale \(f_1\) with +9.5 % RNA bias error bar vs prototype-scale \(f_1\) reference. Panel b: model-scale \(f_1/f_{1,0}\) relative metric where the bias cancels within 0.8 %. Caption: the relative metric \(f/f_0\) is robust to the deliberate mass deviation.

fig-grain-size (R3). Already in the R1 manuscript per the R1.5 change log. Verify it shows No. 5 (\(d_{50} = 1.99\) mm) clearly coarser than No. 7 (\(d_{50} = 0.22\) mm) native — coarseness is the mechanism of the 158 % overshoot.

fig-stress-scour-schematic (R1). Already in the R1 manuscript per the R1.8 change log. Three-panel schematic of effective-stress and \(G_{\max}\) profiles pre- and post-scour for dry vs submerged. Ensure the analytical \(\sqrt{\gamma_d / \gamma'} = 1.23\) annotation sits next to the observed T2/T5 ratio 1.25 for direct visual comparison.

fig-backfill-recovery (R3). Two-panel bar chart. Panel a: dense series (T4) showing pre-scour \(f_1\), post-scour \(f_1\), post-backfill \(f_1\); 41 % recovery annotated. Panel b: loose series (T5) showing the 158 % overshoot with the pre-scour level as the reference horizontal line.

fig-displacement-strain-settlement (R4). Three stacked time-series panels for T5 across four scour stages: (i) lateral displacement amplitude; (ii) bending strain at the mid-elevation gauge; (iii) bucket settlement. Vertical dashed line at \(S/D = 0.39\) marks the onset of the bending-to-tilting transition. Caption: the 2.58 % frequency decline missed this mechanism change — monitoring-relevant.

Phase 5 — Paragraph skeletons¶

§3 Results. ¶1 (saturation effect) [→ fig-sat-vs-dry-f1]. T1/T4 at dense: dry 4.2 % vs saturated 2.2 % at \(S/D = 0.58\); ratio 1.94. T2/T5 at loose: 5.1 % vs 2.6 %; ratio 1.96. Mean ratio 1.94. Headline. ¶2 (density amplification). Across saturated series: T4 (dense, 0.85 %) vs T5 (loose, 2.58 %) at \(S/D = 0.58\). Threefold amplification. ¶3 (backfill) [→ fig-backfill-recovery, fig-grain-size]. 41 % recovery in dense native; 158 % overshoot in loose native. Attributed to backfill-native stiffness contrast. ¶4 (regime transition) [→ fig-displacement-strain-settlement]. At \(S/D = 0.39\) in T5, displacement amplification of 4.27 ×, bending-strain reversal, asymmetric settlement — mechanism change that \(f_1\) does not flag.

§4 Discussion. ¶1 (saturation mechanism) [→ fig-stress-scour-schematic]. Hardin \(\sqrt{\gamma_d / \gamma'} = 1.23\) explains ~half the ratio; the rest is secondary density + stress-path effects. Written to address R1.8 explicitly. ¶2 (monitoring implications). Frequency-only monitoring misses kinematic regime changes. Recommendation: multi-channel monitoring (foreshadows Paper A). ¶3 (engineering correction factor). Engineers applying dry-sand centrifuge calibrations to saturated field sites should apply a correction of approximately 2. Addresses R3.5 generalisation caveat. ¶4 (cross-paper consistency) [→ fig-centrifuge-vs-numerical-powerlaw]. Centrifuge \(b \approx 1.5\) agrees with J2 numerical within combined error; centrifuge is directionally conservative lower bound. ¶5 (prototype-to-model reconciliation) [→ table-proto-model-error-budget, fig-bias-cancellation]. Addresses R3.4 transparently.

§6.1 Innovation vs J2. ¶1 (threefold innovation). First saturation quantification on TSB; first backfill measurement on multi-footing foundation; discovery of bending-to-tilting transition. ¶2 (complementarity, not redundancy). J2 is the mechanism paper; J3 is the experimental evidence. The two should be consulted jointly.

Phase 6 — Generate figures (figure_generator integration)¶

All nine figures exist or are in the R1 change log. Focus is confirmation and reinforcement:

Verify fig-centrifuge-vs-numerical-powerlaw is in the manuscript (check the R1 draft; add if missing — this is the single highest-value figure tying J3 to J2).
Verify fig-bias-cancellation shows the bias-cancellation argument visually, not just in prose (R3.4).
Spot-check that fig-displacement-strain-settlement has the \(S/D = 0.39\) transition boundary marked (R2.1).
Each is at most one figure_generator session.

Phase 7 — Coherence passes¶

Pass A — paragraphs only. - §3 ¶1 (saturation) leads with a number (1.94) before establishing that this is a headline ratio. Fix: one sentence ahead of ¶1 that declares saturation ratio as the first quantitative finding of the paper. - §4 ¶2 (monitoring implications) currently ends on a recommendation without naming the audience. Fix: name the audience — "asset owners deploying vibration-based scour monitoring on saturated field sites." - §4 ¶5 (reconciliation) is technical; may read as defensive. Reframe: lead with the positive result ("relative \(f/f_0\) metric is robust to the 9.5 % RNA deviation") rather than the limitation.

Pass B — figures only. - Nine figures is acceptable for a 10,000-word results-heavy paper. No orphans identified. - fig-centrifuge-vs-numerical-powerlaw is the figure that makes J3 + J2 read as companions rather than disconnected. Confirm it is load-bearing in the introduction or discussion framing, not just as a late-stage comparison. - fig-displacement-strain-settlement should be the hero for the bending-to-tilting finding (R4). In the current R1 draft this finding may be text-heavy; the figure earns the mechanism-level claim.

Reviewer objection rehearsal (results-specific for J3):

"Are T4 and T5 repeatable? Did you rerun any test to confirm?" — the programme is single-run per case. Acknowledge this in §4 limitations; cite the in-flight CPT as independent verification of soil state per flight.
"What is the 95 % CI on the 1.94 saturation ratio?" — bootstrap from the per-stage measurements. If not already in the R1 draft, add in a one-line annotation on fig-sat-vs-dry-f1 caption.
"Why is loose native soil more susceptible to backfill overshoot?" — explain via stiffness contrast: the backfill is stiffer than the loose native and becomes the new load path; in dense native the backfill is weaker and does not take the load. One sentence.
"Does the bending-to-tilting transition occur earlier in the field?" — unknown without bathymetric ground truth. Flag as limitation + future work (second-site field validation).

Actionable items before R1 submission:

#	Item	Driving consideration	Cost
1	Confirm `fig-centrifuge-vs-numerical-powerlaw` in R1 draft	R6 cross-paper consistency	15 min check + 1 session if missing
2	Confirm \(S/D = 0.39\) transition line on displacement/strain/settlement fig	R2.1 mechanism claim	10 min check
3	Add 95 % CI on saturation ratio 1.94 (bootstrap if not present)	Preempt reviewer scepticism	30 min
4	Rewrite §4 ¶5 to lead with positive reconciliation result	Coherence pass fix	15 min
5	Name audience in §4 ¶2 monitoring implications	Coherence pass fix	5 min
6	Add one sentence on backfill-stiffness mechanism in §3 ¶3	Reviewer-objection preempt	10 min

Six actions, roughly 2–3 hours of work. Deadline 2026-05-06 leaves comfortable margin.

What this pass surfaced that the methodology pass did not¶

Results-section figures carry mechanism-level burden of proof. Methodology figures demonstrate that a procedure was followed; results figures must demonstrate that a mechanism operated. The fig-displacement-strain-settlement figure (bending-to-tilting) is the one that carries the paper's most novel finding, and it must read as mechanism, not just data.
Cross-paper consistency figures belong in results, not methodology. The fig-centrifuge-vs-numerical-powerlaw figure reconciling J3 with J2 belongs in J3 §4 discussion, not anywhere in methodology. This is a results-section-specific class of figure.
Audience-naming in monitoring-implication paragraphs is a cross-paper pattern now confirmed on two results-prototype passes (J2 and J3). Every results paper should explicitly name the engineer / asset owner / committee member who benefits from the result.