Resistance collapse by unjamming

Resistance collapse by unjamming and liquefaction — The strongest objection is that under a continent-scale load any thin water layer is squeezed out, so lubrication cannot persist. This section answers it not with a qualitative "water is slippery" claim but with effective-stress reduction and an unjamming/liquefaction transition that collapses basal resistance. Gate verdict: PASS.

“Under enormous normal stress beneath a continent-scale load, a thin water layer will simply squeeze out sideways. Tire hydroplaning (cm-scale films) is not comparable.” (LOCK → Derive → Gate).

The strongest critique (scale): “water immediately squeezes out”

A natural critique is:

“Under enormous normal stress beneath a continent-scale load, a thin water layer will simply squeeze out sideways. Tire hydroplaning (cm-scale films) is not comparable.”

Accordingly, this white paper does not rely on a purely qualitative “water is slippery” claim. Instead it upgrades the narrative by (i) collapsing solid friction via effective-stress reduction (hydraulic jacking), and then (ii) modeling the residual resistance by a viscous-shear (hydroplaning) term.

Core equations: Terzaghi/Biot effective stress and friction collapse

In rock/soil mechanics, friction is governed primarily by effective normal stress. Terzaghi/Biot effective stress is

where σₙ is total normal stress, P_f is pore-fluid pressure, and α~ 1 is the Biot coefficient. If solid–solid contact dominates (dry friction regime), a Coulomb-like shear scale is

so if P_f→ σₙ/α and σ'→ 0, then τ_coul→ 0 even if μ_dry is large. This is hydraulic jacking: friction collapses not because water is a good lubricant, but because overpressure effectively lifts/decouples the interface and removes solid friction.

Primary collapse from VP jamming: unjamming–liquefaction (not melting)

The effective-stress route (Eq. §14, hydraulic jacking) is retained as a corroborating mechanism, but the primary resistance-collapse mechanism is derived from the project's own VP jamming theory (jamming spine S2.2–S2.4), so friction is not an imported fault-mechanics assumption.

State picture. The basal shear zone is a granular gouge in one of two VP states: jammed (State 4: load-bearing contact backbone, finite yield stress, behaves as a solid) or unjammed/liquefied (State 3: backbone dissolved, viscous flow). The control variable is the mean coordination number z relative to the isostatic value zᵢₛₒ=2d (zᵢₛₒ=6 in 3D).

Friction law (mixture). With jammed fraction ξ∈[0,1] (1 = fully jammed),

τᵣₑₛ = ξ μ_dry σ' + (1-ξ) η_flowV/h, eq:jam_friction

a Coulomb (jammed) term that vanishes as the gouge unjams plus a viscous (liquefied) term. In the jammed limit Eq. §14 reduces to the combined resistance Eq. §14; it adds the physically essential collapse channel ξ→ 0.

Liquefaction rule (key step). Frictional shear heating raises the gouge temperature, driving z→ zᵢₛₒ. At isostaticity the relaxed shear modulus and the yield stress vanish while the bulk modulus stays finite:

G_relaxed(z) ∝ (z-zᵢₛₒ)→ 0, σ_y ~ G_relaxed γ_y ∝ (z-zᵢₛₒ)→ 0, eq:sigmay_vanish

so the shear backbone dissolves (State 4 → 3) before melting: grains stay solid, only the collective load-bearing network is lost — liquefaction by unjamming, distinct from melting.

Derived (not assumed) constants. The rule form of Eqs. §14–§14 is derived from first-principles soft-disk jamming simulations (2D bidisperse; generalizing to the spine's 3D), reproducing classical and spine results:

Quantity	Result (derived)
Jamming onset φ_jam	0.840 (classical 2D bidisperse ≈ 0.842)
Isostatic coordination zᵢₛₒ=2d	4 (2D); 6 (3D = spine S2.4)
Excess contacts	(z-zᵢₛₒ)=4.0 (φ-φ_jam)⁽1/2)
Pressure	p = 0.33 (φ-φ_jam)
Relaxed shear modulus (Hessian)	G_relaxed=0.068 (z-zᵢₛₒ)→ 0
Affine (Born) modulus	G_Born≈ 0.20 (finite)

Prototype outcome. For a representative mid-crustal gouge, the unjamming channel on gives μ_eff≈ 2.2×10⁻³ (inside Ω-NoGo omega_nogo.mu_eff_hold_min=10⁻²) at Δ T≈ 25 K (no melting). The melt-only counterfactual needs Δ T≈ 1462 K; unjamming reaches low friction at ~ 1.3% of the melt energy.

Bistability: a liquefied zone cannot creep slowly. Liquefaction is self-consistent only while shear heating outpaces conduction. For the viscous branch the steady temperature rise is Δ Tₛₛ=η_flowV²/(8k), so sustained unjamming (Δ Tₛₛ≥Δ T_unjam) requires

V ≥ V_crit=√8 k Δ T_unjamη_flow ≈ 10⁻²--1 m s⁻¹ eq:vcrit

across η_flow=10²–10⁶ Pa s. Since V_crit exceeds cm yr⁻¹ (~ 3×10⁻¹⁰ m s⁻¹) by ~ 10⁸, there is no stable slow-liquefied branch: τₛₛ(V) drops by ~10²–10³ across unjamming, giving velocity-weakening (dτₛₛ/dV<0) and a stick–slip instability. The motion mode is stuck-or-fast; an apparent slow steady rate is a time-average of brief fast slips (cumulative actual sliding to open a 3000 km half-basin ~ 70 days at V~0.5 m s⁻¹). This is the honest replacement for “slow residual viscous creep.”

Corroborating routes (demoted). (i) Thermal pressurization (Rice 2006): the same heating raises P_f and lowers σ' in Eq. §14; a coupled 1-D prototype gives ~ 82% undrained weakening (atl_bundle/engine/tp_dilatancy_prototype.py). (ii) Granular fluidization/dilatancy. A sign-discriminator R_md governs basal weakening vs tip dilatant strengthening. These reinforce, not replace, unjamming.

Derivation status (honest). The material law (Eqs. §14–§14) is lab-grounded and scale-invariant (jamming is a material property; cf. O'Hern–Silbert–Liu–Nagel). Its application at continental scale is gated by the master-scale constraint (Section §16).

Falsifier (WP-T1). (A) signature: basal shear zones should record unjamming/fluidization (gouge fluidization, injection/hydrofracture textures, grain-intact but fabric-destroyed gouge), with melting only on segments that failed to unjam (cf. P4-a/P4-b). (B) data: exhumed detachment petrofabrics; gouge microstructure; pseudotachylyte presence/absence. (C) test: is μ_eff≤ 10⁻² reached without violating Ω-NoGo (h≥ 10⁻⁶ m, Δ P≤ 500 MPa)? (D) FALSIFIER: if shear zones show neither unjamming/fluidization nor fluid-overpressure signatures, or μ_eff≤10⁻² only by violating Ω-NoGo, WP-T1 is FAIL and the rapid-motion core reverts to HOLD.

Rebutting squeeze-out: drainage timescale and undrained loading

For overpressure to matter, P_f must persist over the event window. A simplest criterion is a drainage timescale. With hydraulic diffusivity D_h, a characteristic equilibration time over length is

τ_drain ~ ²/D_h (D_h = k/(η_f Sₛ)) eq:drainₜimescale

where k is permeability, η_f fluid viscosity, and Sₛ specific storage. The key requirement is

i.e., the event window τ is shorter than the drainage time so that an undrained regime exists (AR-10). If this holds, “water immediately escapes” is weakened automatically. If instead τ≳τ_drain, maintaining overpressure is difficult and hydroplaning assumptions should be downgraded to HOLD/FAIL.

Geologic reinforcements (qualitative). Event-like shear can induce (i) comminution/gouge that reduces permeability via self-sealing, (ii) localized trapped pockets created by hydrofracturing, and (iii) low-permeability films via fine particles/clay formation. These mechanisms must be testable via P4.

Residual resistance: viscous shear and “combined resistance”

If hydraulic jacking reduces σ', solid friction drops sharply but does not necessarily become zero. Residual shear resistance can be modeled by viscous shear. Under a Newtonian approximation,

A conservative combined shear resistance is

τᵣₑₛ ≈ μ_dry (σₙ-α P_f) + /h. eq:combinedᵣesistance

The total resisting force is F_friction≈ τᵣₑₛA_base, and the effective friction coefficient (normalized by total normal stress) is

Interpretation. (1) As P_f grows and σ' shrinks, the first (solid-friction) term collapses, (2) the bottleneck becomes the second (viscous-shear) term, and (3) the feasibility question becomes whether plausible (η,v,h) keep μ_eff within Ω-NoGo limits.

Geological signatures of lubrication/overpressure (P4): “hydrofracturing” may matter more than “melting”

A common attack is: “If it slid that fast, frictional heat must have melted everything.” But this mechanism aims to reduce resistance rather than increase it. Therefore it is more honest to pre-register two branches of expected signatures:

(P4-a) Overpressure/hydrofracturing dominated (recommended default). Widespread melting (vitrification) is not mandatory. Instead, signatures of fluid overpressure should appear near shear zones: hydrofracturing, injection veins, brecciation, and gouge fluidization.
(P4-b) Local melting dominated (alternative branch). If some segments failed to achieve low friction, localized melting/vitrification (e.g., pseudotachylyte) may appear. In that case the model must explain why those segments are exceptions (local differences in permeability/drainage/fluid supply).

Multiphase fluid details: what is the “lubrication film”?

Fluid composition strongly affects viscosity η and state behavior. We therefore register candidate fluid classes (AR-8):

(F1) seawater/brine (low viscosity),
(F2) supercritical fluid / high-T steam mixture (variable viscosity; strong pressure sensitivity),
(F3) melt involvement (high viscosity; strong thermal signatures),
(F4) particle–fluid mixture (granular fluidization; nonlinear effective viscosity/yield stress).

ID	Composition/state	η (order examples)	Expected P4 signatures (examples)
F1	seawater/brine (liquid)	~ 10⁻³ Pa· s	infiltration/salinity, low-T alteration, possible injection veins
F2	supercritical water / steam mixture	10⁻⁵–10⁻³ Pa· s (variable)	phase-change/vesicularity, hydrothermal alteration, pressure-oscillation signatures
F3	melt involvement	10¹–10⁴ Pa· s (high)	localized melting/vitrification (pseudotachylyte), quench textures
F4	particle–fluid mixture (fluidization)	η_eff nonlinear (may include yield)	gouge fluidization, grain alignment/sorting, injection breccias

Important note. These viscosity ranges are not definitive; they are order examples to be updated by references/datasheets in a release. The role of this table is to lock sensitivity-analysis inputs for “which candidate can create the μ_eff bottleneck.”

Viscosity sensitivity (summary).

In Eq. §14, η controls the residual resistance. Therefore for each candidate, (η,h,v) ranges must be pre-registered and judged by whether μ_eff stays within Ω-NoGo constraints.

Phase change and cavitation.

Strong suction can rapidly drop pressure along contacts/crack networks. If fluid vaporizes or cavitates, (1) the pathway for transmitting suction changes, and (2) the lubrication film can become discontinuous, raising friction. Conversely, if shear/heating raises P_f, hydraulic jacking can strengthen, while phase transitions may absorb energy as latent heat (see the energy budget subsection). Accordingly, P4 should include not only “hydrothermal” signatures but also microstructures that can indicate rapid pressure fluctuations/hydrofracturing/phase change (porosity/vesicles, injection veins, breccias, quench textures).

Fluid budget and sources: a quantitative answer to “where did the fluid come from?”

Claiming hydroplaning/hydraulic jacking immediately raises: “Where does the fluid come from?” A key point is that the mechanism does not require an ocean-scale volume. It requires a thin, high-pressure film (h_film) maintained over an interface during an event window τ. Thus, check area × thickness first.

A simplest required volume estimate is

Example (order). If A_base~ 10⁷ km²=10¹³ m² and h_film~ 1 mm=10⁻³ m, then

This is tiny compared with total ocean volume; the bottleneck is not total volume but maintaining overpressure (undrained) and distribution/trapping.

h_film	V_req (assume A_base=10¹³ m²)	Interpretation (order)
10⁻⁴m (0.1 mm)	10⁹ m³≈ 1 km³	“Microfilm” regime; total-volume constraint is negligible.
10⁻³m (1 mm)	10¹⁰ m³≈ 10 km³	Thin film; distribution/overpressure maintenance is key.
10⁻²m (1 cm)	10¹¹ m³≈ 100 km³	Total volume grows; source assumptions become important.

Candidate sources (AR-12). We do not lock a single fluid source; instead we register competing modules (H-S1–H-S3):

(H-S1) External infiltration: seawater/brine intrusion along rupture/fault/damage zones.
(H-S2) In-situ generation: dehydration reactions of hydrous minerals (e.g., serpentinized mantle/crust) releasing fluids during high-T/P events.
(H-S3) Multiphase transitions: generation/condensation of supercritical water/steam (phase change) and particle–fluid mixture fluidization (F4).

Strict falsification rule. If (1) required h_film becomes so large that V_req is unrealistic, or (2) P4 shows systematic absence of signatures corresponding to infiltration/dehydration/hydrothermal alteration/injection veins, then AR-12 (fluid supply) and the corresponding C3 branch must be downgraded to HOLD or FAIL.

Convergence

The friction-collapse rule here is derived from the project’s foundational vacuum-as-jammed-solid theory (jamming → unjamming) and shares the marginal, just-rigid flow state treated in the configured-continuum paper; it is not imported fault mechanics.