Pfc Freeze Thaw Damage

PFC Freeze-Thaw Damage

Explicitly simulate stress-freeze-thaw coupling in PFC using a two-particle system (mineral grains plus pore-water particles) and the particle-expansion method: cyclic temperature -> unfrozen water content -> pore-water particle volume growth -> rock-rock bond breakage = frost-heave damage. A constant axial stress applied by end walls before cycling gives "freeze-thaw under real-time load", as opposed to the traditional "freeze-thaw first, mechanical test afterwards" route.

Two output tracks:

• Frost-heave deformation: axial / radial / volumetric strain versus cycle number.
• Fracture evolution: crack density banding, dip-angle distribution, tensile/shear ratio.

Parent Skill Relationship

pfc-freeze-thaw-damage is a child skill of pfc-workflow, plugging into P2 (modeling), P4 (solve) and P5 (post-processing).

• Parent pfc-workflow: owns the full project lifecycle and decides when freeze-thaw support is needed.
• Child pfc-freeze-thaw-damage: owns the two-particle specimen, the three bond families, the temperature -> unfrozen-water -> volume driver, and freeze-thaw-specific statistics.
• Complementary skill (high-temperature route): thermo-mechanical models that use the PFC thermal module with heat conduction driving grain thermal expansion. This skill does not enable the thermal module; temperature is assigned uniformly and mapped directly to pore-water particle volume.
• Sibling pfc-servo-calibration / pfc-modeling-techniques: wall servo control and curve-based parameter extraction.
• Sibling pfc-postprocessing: generic figures and exports after solve.

When To Use

• Freeze-thaw deformation and damage assessment for cold-region tunnels, slopes and other rock masses.
• Numerical tests that need coupled "real-time load + freeze-thaw" rather than load-after-thaw.
• Meso-mechanism outputs of frost damage: crack density banding, dip-angle distribution, tensile/shear ratio.

Physical Picture -> Numerical Mapping

Operating Rules

1. Water-rock and water-water bond strengths are set large (e.g. 100 MPa) so they only transmit force and never break; only rock-rock bonds represent damage.
2. After every pore-water volume change, cycle to mechanical equilibrium before advancing temperature (quasi-static driving).
3. Set the minimum temperature where unfrozen water content approaches zero (about -25 to -30 C). Temperature is assigned uniformly; no hold time for full freezing/thawing is required, and the T > 0 C branch need not be simulated.
4. Apply and servo-stabilize the axial stress sigma_1 before entering the freeze-thaw loop; history axial/radial strain and crack counts throughout.
5. Calibrate UCS and E to within a few percent before any freeze-thaw run (reference case: 2.2% / 3.3%).

Required Inputs

Ask for these if missing:

• PFC version and dimensionality (the reference case is PFC3D, cylinder 50 x 100 mm).
• Rock type, dry density, porosity, target UCS and E for calibration.
• Particle sizes and densities for mineral and pore-water particles.
• Axial stress level(s) as a fraction of pre-freeze UCS, and the number of freeze-thaw cycles.
• Temperature schedule: amplitude, period, and minimum temperature.
• Required outputs: strain histories, crack-count/temperature curves, radial density banding, dip-angle bins, tensile/shear ratio.

Pipeline

S1 two-particle specimen
 -> S2 three bond families + UCS/E calibration
 -> S3 end walls apply and servo constant sigma_1
 -> S4 freeze-thaw main loop (temperature -> unfrozen water -> particle volume -> equilibrium)
 -> S5 deformation and crack statistics (banding / dip angle / tensile-shear)
 -> S6 cross-check against measured trends

SOP: Freeze-Thaw Main Loop (7 steps)

1. Build the specimen: mineral particles, pore-water particles, and the rock-rock / water-rock / water-water bond families.
2. Record the initial volume V0 of every pore-water particle and assign properties per bond family.
3. Read the current mechanical time and compute the current temperature from Eq. (4).
4. Compute the unfrozen water content w_u at that temperature from Eq. (3).
5. Compute the target volume of every pore-water particle from Eqs. (1)-(2).
6. Set the pore-water particle volumes to the target and cycle to mechanical equilibrium.
7. Repeat 3-6 until the target number of cycles is reached.

For stress-freeze-thaw coupling, apply and hold sigma_1 with the end walls before step 3.

Meso Parameters and Calibration Baseline

Reference case: Sichuan yellow sandstone, dry density 2.25 g/cm3, cylinder 50 x 100 mm.

• Mineral particles: density 2500 kg/m3, radius 0.8-1.0 mm.
• Pore-water particles: density 920 kg/m3, radius 0.6-0.8 mm.
• Calibration result: numerical UCS 73.40 MPa and E 8.72 GPa against test values 75.05 MPa and 9.02 GPa (about 2.2% and 3.3% error). Match the pre-freeze stress-strain curve before starting freeze-thaw runs.

Post-Processing Recipe (P5)

• Deformation: axial/radial strain histories; volumetric strain versus cycle number. In the companion laboratory test, strain gauges use quartz-glass temperature compensation to remove gauge-resistance drift while retaining rock thermal deformation.
• Crack-temperature curve: within a single cycle, crack count rises quickly during cooling and flattens below about -25 C (where w_u -> 0).
• Radial crack density banding: Eqs. (5)-(6) with a 5 mm sampling interval; verify "surface > interior".
• Dip-angle distribution: angle between crack and specimen axis, binned every 5 degrees.
• Tensile/shear classification: fraction of tensile bond-failure cracks (analogous to AE mechanism statistics).

Canonical Script Map

Staged save chain: ftc_ini -> ftc_bonded -> ftc_state1 -> ftc_cycle_n.

Result-Verification Checklist

• No axial stress: axial and radial strain grow then stabilize after roughly 10 cycles; radial strain exceeds axial strain (the axial dimension is longer and more constrained); their difference grows then shrinks and oscillates near 100e-6 after 30 cycles.
• With axial stress: radial strain grows with cycles and accelerates nonlinearly beyond 30 cycles; axial strain is negative and decreases with cycles (damage accumulation); volumetric strain keeps growing. In the 0.6 sigma_0 case the specimen fails at about 45 cycles.
• Spatial distribution: crack density near the surface clearly exceeds the interior. For 0.6 sigma_0, the 0-20 mm band from the axis holds 0.90e7 to 1.17e7 cracks/m3, while the 20-25 mm edge band jumps to 2.45e7 cracks/m3 (interior is triaxially constrained, the surface is nearly free).
• Directionality: low dip angles (0-20 deg) dominate and 80-90 deg is rare. Increasing axial stress raises the low-angle share (0-5 deg: 10.86% -> 15.01%, +38.21%) and lowers the high-angle share (85-90 deg: 0.52% -> 0.24%, -85.85%): axial compression suppresses radial crack initiation.
• Mechanism: freeze-thaw failure is tension-dominated (tensile crack fraction > 50% in all cases). As sigma_1 goes from 0 to 0.6 sigma_0, the tensile share falls 68.76% -> 58.97% (compression induces some shear).

Limitations and Improvements

• Specimen temperature is uniform and heat conduction is ignored. Improvement: impose a cyclic temperature boundary on the specimen surface with the PFC thermal module and compute ice-particle volume from the local real-time temperature.
• Migration of pore water to the freezing front is ignored. Improvement: add a moisture-migration equation during freezing and scale ice-particle volume by local water content.

Output Contract

A complete handoff back to pfc-workflow should include:

• Calibrated meso parameters and the pre-freeze UCS/E match.
• Bond-family assignment and the justification for unbreakable water bonds.
• Temperature schedule, minimum temperature and the unfrozen-water form used.
• Volume-increment convention actually implemented (see references/unfrozen-water.md).
• Axial stress level, servo tolerance, cycle count, and the staged save chain.
• Strain histories plus crack banding / dip-angle / tensile-shear statistics.
• Explicit statement of the uniform-temperature and no-migration assumptions.

Local Contents

• references/unfrozen-water.md: governing equations, temperature schedule, minimum-temperature choice, and the volume-increment consistency check.
• references/bond-scheme.md: three bond families and how to assign them.
• references/findings.md: measured-trend quick reference for result verification.
• scripts/: specimen generation, freeze-thaw driver, axial servo, crack statistics.
• templates/params.yaml: meso parameters and case matrix.
• examples/README.md: how to validate the bundled workflow.