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arxiv: 1907.00698 · v1 · pith:R5LHTVV6new · submitted 2019-06-20 · ⚛️ physics.geo-ph · physics.comp-ph

Contact phase-field modeling for chemo-mechanical degradation processes. Part II: Numerical applications with focus on pressure solution

Alexandre Guevel , Hadrien Rattez , Manolis Veveakis This is my paper

Pith reviewed 2026-05-25 18:43 UTC · model grok-4.3

classification ⚛️ physics.geo-ph physics.comp-ph
keywords pressure solution creepphase-field modelingmicrostructural geometrychemo-mechanical degradationgeomaterialsgrain contactsstrain concentrationcatalyzing effects
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The pith

Grain arrangement in packs sets pressure solution creep rates by controlling local strain at contacts.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies contact phase-field modeling to digital grain packs and tracks how microstructural geometry shapes chemo-mechanical degradation. Numerical runs on pressure solution creep show that irregular grain shapes concentrate strain at stressed contacts and thereby speed dissolution. Catalyzing and inhibiting multipliers let the model include temperature and clay influences without adding those features explicitly. The authors conclude that the missing unique creep description in earlier work stems from this geometry dependence. If the claim holds, simulations built on real scanned microstructures should produce consistent long-term deformation rates.

Core claim

Contact phase-field modeling with catalyzing/inhibiting multipliers reproduces the chemo-mechanical response of digitalized geomaterials at the grain scale. Application to pressure solution creep shows that microstructural geometry governs strain concentration at contacts, which directly controls creep rate. This geometry dependence accounts for the absence of a single constitutive description of pressure solution in the literature.

What carries the argument

Contact phase-field formulation with catalyzing/inhibiting multipliers that track evolving interfaces while modulating local equilibrium rates according to conditions such as temperature or clay presence.

If this is right

  • Creep rates rise in packs whose geometry produces higher local strain concentrations at contacts.
  • Temperature enters the model as a single multiplier on reaction rates at contacts.
  • Clay inhibition reduces dissolution rates through a multiplier without explicit particle modeling.
  • Digitized natural microstructures yield creep responses that vary systematically with packing geometry.
  • A unique description of pressure solution requires explicit input of microstructural geometry.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Lab experiments that use idealized spherical grains may systematically understate field creep rates because they produce lower strain concentrations.
  • The same modeling approach could be applied to other grain-scale degradation processes such as chemical compaction or corrosion.
  • Direct import of micro-CT scans of real rock samples would provide a direct test of whether geometry alone accounts for observed scatter in creep data.
  • Coupling the contact multipliers to larger-scale fluid transport could link local dissolution to changes in bulk permeability.

Load-bearing premise

The contact phase-field model with multipliers can reproduce the chemo-mechanical response of real grain packs without resolving explicit clay particles or fluid flow inside contacts.

What would settle it

Compare measured creep rates from laboratory tests on two natural grain packs that share the same mineralogy but differ in scanned grain arrangement; the observed rate difference should match the model's predicted difference in strain concentration.

Figures

Figures reproduced from arXiv: 1907.00698 by Alexandre Guevel, Hadrien Rattez, Manolis Veveakis.

Figure 1
Figure 1. Figure 1: 4 main PSC processes and 2 main models for grain contacts [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Graph of the double-well potential Gg(φ) ≈ B(φ) with G = 10 in blue and of the tilted double-well potential B(φ, ) = Gg(φ) + H¯ (, φ) with G = 10, HA() = 0.1 and HB() = 10 in orange Thus we want to observe the nucleation of the phase A under mechanical loading. Let us consider the extreme case where there is no phase A at beginning, with initial conditions randomly fluctuating in the phase B, i.e. φ ∈ … view at source ↗
Figure 3
Figure 3. Figure 3: Cracks nucleation in solid phase under isotropic compression at initial time, onset [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Initial conditions for the oedometric compression of the circle-shaped inclusion [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Oedometric compression of a circle inclusion of weak phase (blue), just after softening [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Graph of the double-well potential Gg(φ) ≈ B(φ) with G = 10 in blue and of the tilted double-well potential B(φ, ) = Gg(φ) + H¯ (, φ) with G = 10, HA() = 0.1 and HB() = 10 in orange 9 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Initial conditions for the benchmark of PSC model: two ideal spherical grains [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Influence of β on the the system’s mechanical response: the higher its value the later the failure finer and finer meshes. It appears that the finer the mesh the less accentuated the jump. In the light of the mesh convergence, we can choose a mesh of 100∗100 elements. ● ● ● ● ● 50 60 70 80 90 100 110 120 0 5 10 15 20 25 Mesh size Time of failure (ks) [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Mesh convergence: measured failure time converges approximately for a mesh with [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: PSC of two-grain benchmark at during dissolution until the rounded surfaces get [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Digitalization of a LV60A sandpack’s CT scan obtained from [23] [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Simulations outputs for CT scans simulations for a same vertical shortening of [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Maximum mean stress and dissipation for µ = 0 and µ = 1. The dissipation has two components D = Dn + Dt = τ1φ˙2 + τ2||∇φ˙ ||2 (Dt = 0 for the case µ = 0). the Laplacian rate term is activated or not. In the latter case (µ = 0), the dissipation is more irregular whereas in the former case (µ = 1) the dissipation evolution consists in two peaks, mostly due to the tangential component, corre￾sponding to the … view at source ↗
Figure 14
Figure 14. Figure 14: Influence of β on the microstructure’s response: the higher its value the slower the compression. However this is less obvious for the present microstructure than for the ideal two-grain benchmark Then we choose α = 0.01 and D∗ = 0.1 to keep α < D∗ . 4.2.2. Chemo-mechanical response As expected from the model’s equations, dissolution should happen in high stress/strain zones ( ˆχ(, c) > 0) and conversely… view at source ↗
Figure 15
Figure 15. Figure 15: Visualization of the microstructure’s state at [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Dynamic Andrade creep laws ((t) ∼ t 1/3 ), separated by weakening events (differ￾ent MGs have different primitive processes) Furthermore, we fit power laws in the cubic root of time, the so-called An￾drade creep law, with good agreement. The adequateness between Andrade creep (from metallurgy initially) and PSC has been shown in [25] and [22], with 18 [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Influence of µ on the microstructure’s response: no qualitative change (grains rereorganization followed by major phase change) but delayed as µ increases Laplacian rate term is shown to control the variations of the interfaces curva￾tures and as such acts as a CI for degradation processes. For PSC, that could correspond to temperature or clay content, both enhancing the process. Sec￾ondly, the tracking o… view at source ↗
read the original abstract

The microstructural geometry (MG) of materials has a significant influence on their macroscopic response, all the more when the process is essentially microscopic as for microstructural degradation processes. However, the MG tends to be approximated by ideal spherical packings with constitutive description of the microstructural contacts. Interfaces tracking models like phase-field modeling (PFM) are promising candidates to capture the microstructures dynamics. Contact PFM (CPFM) enables to include catalyzing/inhibiting (CI) effects, accelerating/delaying equilibrium, such as temperature or the presence of certain constituents. To emphasize the influence of geometry and CI effects, we study numerically the chemo-mechanical response of digitalized geomaterials at the grain scale. An application to pressure solution creep (PSC) shows the importance of the MG and how the influence of temperature and clay can be taken into account without explicit modeling. As already inferred in previous works on PSC, the lack of MG considerations could be the reason why a unique description of PSC is missing. A simple reason could be that PSC is directly dependent on the strain concentration, which is directly dependent on the MG. This is our motivation here to investigate and suggest the influence of the MG on a degradation process like PSC.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper presents numerical applications of a contact phase-field model (CPFM) for chemo-mechanical degradation processes, with emphasis on pressure solution creep (PSC) in digitized grain packs. It argues that microstructural geometry (MG) controls strain concentration and thus PSC rates, and that catalyzing/inhibiting (CI) multipliers can incorporate temperature and clay effects without explicit particle or fluid-flow modeling at contacts. The central motivation is that insufficient MG consideration explains the lack of a unique PSC description in the literature.

Significance. If the CPFM formulation with CI multipliers is shown to produce quantitatively accurate chemo-mechanical evolution, the work would provide a practical route to embed geometry-dependent strain effects into PSC models and to modulate environmental influences via multipliers rather than explicit interfaces. This could address variability in experimental PSC rates by linking them directly to digitized MG.

major comments (3)
  1. [Abstract] Abstract: the claim that 'PSC is directly dependent on the strain concentration, which is directly dependent on the MG' is load-bearing for the motivation, yet the numerical demonstrations are described only qualitatively; no error bars, mesh-convergence metrics, or direct comparison to independent PSC rate data are referenced to establish the quantitative dependence.
  2. [Abstract] Abstract (paragraph on CI effects): the assertion that CI multipliers allow temperature/clay effects 'without explicit modeling' of particles or fluid flow is central to the modeling strategy, but the text provides no benchmark against experiments containing clay or against a reference model with resolved interfaces; without such validation the numerical examples cannot confirm that the multipliers faithfully reproduce local dissolution rates or contact stresses.
  3. [Motivation] Motivation section: the inference that 'the lack of MG considerations could be the reason why a unique description of PSC is missing' requires a sensitivity study across multiple digitized geometries showing that MG-induced rate variations match the scatter in published PSC data; the current presentation leaves this link as a plausible but untested hypothesis.
minor comments (1)
  1. Notation for the CI multipliers and their temperature/clay dependence should be defined explicitly with units and ranges before the numerical results are presented.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. This is Part II of the work, presenting numerical applications of the contact phase-field model to illustrate the role of microstructural geometry (MG) and catalyzing/inhibiting (CI) multipliers in pressure solution creep (PSC). The study is demonstrative rather than a quantitative validation exercise. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'PSC is directly dependent on the strain concentration, which is directly dependent on the MG' is load-bearing for the motivation, yet the numerical demonstrations are described only qualitatively; no error bars, mesh-convergence metrics, or direct comparison to independent PSC rate data are referenced to establish the quantitative dependence.

    Authors: The abstract condenses the central observation from the grain-scale simulations: different digitized geometries produce different local strain concentrations and consequently different PSC rates. The full manuscript reports the quantitative outcomes of these simulations as trends across multiple geometries. Because the computations are deterministic, statistical error bars are not applicable; mesh-convergence checks are documented in the numerical-methods section. Direct comparison with independent experimental rate data lies outside the scope of this numerical demonstration paper and is reserved for future validation studies. We will revise the abstract to make the qualitative, illustrative character of the reported dependence explicit. revision: partial

  2. Referee: [Abstract] Abstract (paragraph on CI effects): the assertion that CI multipliers allow temperature/clay effects 'without explicit modeling' of particles or fluid flow is central to the modeling strategy, but the text provides no benchmark against experiments containing clay or against a reference model with resolved interfaces; without such validation the numerical examples cannot confirm that the multipliers faithfully reproduce local dissolution rates or contact stresses.

    Authors: The CI multipliers are introduced precisely to embed temperature and clay influences at the continuum scale without resolving explicit particle contacts or fluid-flow fields. The numerical examples show the resulting change in macroscopic creep rates when these multipliers are varied. We agree that the manuscript contains no direct benchmark against clay-bearing experiments or against a fully resolved-interface reference model; such comparisons would require additional data sets and are beyond the present scope. The paper therefore demonstrates the modeling convenience of the multipliers rather than claiming quantitative fidelity to local dissolution kinetics. revision: no

  3. Referee: [Motivation] Motivation section: the inference that 'the lack of MG considerations could be the reason why a unique description of PSC is missing' requires a sensitivity study across multiple digitized geometries showing that MG-induced rate variations match the scatter in published PSC data; the current presentation leaves this link as a plausible but untested hypothesis.

    Authors: The motivation section offers this inference as a working hypothesis supported by the literature and by the MG-dependent rate variations obtained in our simulations. While a systematic sensitivity campaign that quantitatively reproduces the entire scatter of published PSC rates would be valuable, it would constitute a separate, substantially larger study. The present work supplies concrete numerical illustrations across several digitized grain packs to show that MG alone can produce order-of-magnitude differences in creep rate, thereby lending credence to the hypothesis within the paper’s demonstrative remit. revision: no

Circularity Check

0 steps flagged

Numerical applications of CPFM to PSC exhibit no circular derivation chain

full rationale

The manuscript is Part II and consists of forward numerical simulations on digitized grain packs using the contact phase-field model (with CI multipliers) to illustrate effects of microstructural geometry on pressure solution creep. No equations are presented that derive a closed-form result or prediction; the text instead reports simulation outcomes. The reference to prior PSC literature is purely motivational and does not serve as a load-bearing premise that reduces the numerical demonstrations to self-citation. The work therefore remains self-contained as an application study rather than a derivation that collapses to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the modeling framework is presumed to inherit standard phase-field assumptions (diffuse interface, mobility parameters) whose specific values are not stated.

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