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arxiv: 2605.17081 · v1 · pith:VTLMPZ7Unew · submitted 2026-05-16 · ⚛️ physics.geo-ph

Analyzing the role of tensile and hybrid fractures on the max-imum relief topography

Julien Gargani This is my paper

Pith reviewed 2026-05-20 15:11 UTC · model grok-4.3

classification ⚛️ physics.geo-ph
keywords slope stabilityGriffith criterionMohr-Coulomb lawtensile fractureshybrid fracturesmaximum reliefescarpment heightCarrara marble
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The pith

The Mohr-Coulomb law overestimates maximum escarpment height compared to the modified Griffith criterion by amounts similar to those from seismic activity or different destabilization processes.

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

The paper examines how using a fracture criterion that accounts for tensile and hybrid fractures affects predictions of maximum relief topography in slopes. It compares the modified Griffith criterion with variable rock traction to the traditional Mohr-Coulomb law in a modeling approach for large-scale relief. The difference in estimated maximum heights is large enough to be comparable to variations caused by geological factors like earthquakes or whether the slope fails by tilting or landslide. This is illustrated with Carrara marbles as a case study, highlighting implications for understanding Earth morphology and assessing risks.

Core claim

When the modified Griffith criterion is used instead of the Mohr-Coulomb law, the predicted maximum escarpment height is lower. The difference in maximum relief estimates between these two rupture criteria is of the same order as differences caused by geological phenomena such as seismic activity or destabilization processes like tilting versus landslide.

What carries the argument

The modified Griffith criterion with variable rock traction, which describes shear, tensile, and hybrid fractures in a single equation and is applied to model slope stability at the scale of mountain ranges.

If this is right

  • Maximum relief topography thresholds depend on the choice of fracture criterion including tensile modes.
  • The Mohr-Coulomb law overestimates escarpment heights relative to the Griffith approach.
  • Predicted differences are comparable in scale to effects of seismic activity or process variations.
  • Application to Carrara marbles provides a concrete case for the theoretical framework.

Where Pith is reading between the lines

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

  • Models of landscape evolution might need to incorporate hybrid fracture modes for better accuracy at large scales.
  • Testing the criterion on other rock types could reveal how general the overestimation is.
  • Field observations of fracture types in natural escarpments could validate the scale application.

Load-bearing premise

The assumption that the Griffith criterion with variable rock traction can be applied at all scales from the laboratory to the mountain range.

What would settle it

Direct comparison of observed maximum escarpment heights in a region with known rock tensile strength against model predictions using both the Mohr-Coulomb law and the modified Griffith criterion.

Figures

Figures reproduced from arXiv: 2605.17081 by Julien Gargani.

Figure 1
Figure 1. Figure 1: Schematic diagram of forces acting on rock block tilting. (A) 3D representation of the rock block, (B) 2D representation of the forces, including the forces triggered by the seismicity (hmg and vmg), acting on the rock block tilting. The balance of moments of forces is given by the sum of all the moments of forces which oppose the tipping  MR on the one hand, and all the moments of forces which tend to … view at source ↗
read the original abstract

Slope stability description through mechanical laws has important implication for Earth morphology understanding and risk assessment. Previous researches have showed that shear, tensile, and hybrid fractures can be observed experimentally and in the field, but their descriptions by a single equation is still an open debate. Fracture envelope able to describe contemporaneously these three fracture modes differ signif-icantly from the Mohr-Coulomb law. Despite the need to apply such a law at all scales, from the laboratory to the mountain range, the fracture criterion that characterizes all types of fractures is rarely used in geotechnical engineering and geological investiga-tions. In order to analyze the stability thresholds of large-scale relief, the current work examines the effects of considering the Griffith criterion with a variable rock traction instead of the Mohr-Coulomb law using a modelling approach. The difference esti-mated on maximum relief using these two different rupture criterions could be of the same order than the one caused by geological phenomena, such as with or without seismic activity, or from the one caused by the destabilization processes (tilting vs. landslide). When compared to the modified Griffith criterion, the Mohr-Coulomb law tends to overestimate the maximum escarpment height. The results are examined in relation to the Carrara marbles, which serve as a case study for the theoretical frame-work.

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

2 major / 2 minor

Summary. The manuscript uses a modeling approach to compare the Mohr-Coulomb law against the modified Griffith criterion (with variable rock traction) for determining maximum relief and escarpment heights in slope stability. It concludes that Mohr-Coulomb overestimates maximum escarpment height relative to modified Griffith, with the magnitude of this difference comparable to that arising from geological factors such as seismic activity or tilting versus landslide processes. Results are discussed in relation to the Carrara marbles as a case study for applying the criterion at mountain-range scales.

Significance. If validated, the quantitative demonstration that tensile/hybrid fracture modes can produce relief differences on the order of seismic or destabilization effects would strengthen the case for using comprehensive fracture envelopes in geomorphological modeling and hazard assessment. The work correctly identifies the under-use of such criteria in large-scale applications and provides a direct comparison that could inform revised stability thresholds.

major comments (2)
  1. [Case Study] The central claim that the relief difference between criteria is comparable to geological phenomena (seismic activity, tilting vs. landslide) rests on direct application of the modified Griffith envelope at kilometer scales. The Carrara marbles case study is invoked only for qualitative context and does not include a quantitative comparison of model-predicted versus observed maximum relief under field heterogeneity and stress gradients (Case Study section).
  2. [Modeling Approach] The modeling comparison assumes the laboratory-derived variable traction in the modified Griffith criterion remains predictive at mountain-range scales without additional terms for time-dependent processes or heterogeneity. No explicit check or sensitivity test is reported to confirm that the overestimation result is robust once these field-scale factors are included (Modeling Approach section).
minor comments (2)
  1. [Abstract] Abstract contains hyphenation artifacts ('max-imum', 'signif-icantly') that should be corrected for clarity.
  2. [Abstract] The abstract would benefit from a brief statement of the specific modeling technique (analytical, numerical) and the exact rock-property values or ranges used in the variable-traction implementation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify the scope and limitations of our modeling study. We address each major comment below and indicate planned revisions to the manuscript.

read point-by-point responses

  1. Referee: [Case Study] The central claim that the relief difference between criteria is comparable to geological phenomena (seismic activity, tilting vs. landslide) rests on direct application of the modified Griffith envelope at kilometer scales. The Carrara marbles case study is invoked only for qualitative context and does not include a quantitative comparison of model-predicted versus observed maximum relief under field heterogeneity and stress gradients (Case Study section).

    Authors: The central claim is grounded in the modeling results, which show that the difference in maximum escarpment height between the Mohr-Coulomb law and the modified Griffith criterion is on the same order as variations arising from seismic activity or tilting versus landslide processes. This is a direct outcome of applying the two envelopes under the same boundary conditions at large scales. The Carrara marbles example is presented as a qualitative illustration of how the modified Griffith framework might be applied to a real mountain-range setting, not as a quantitative validation against field observations. We agree that a direct quantitative comparison of model predictions with observed relief, incorporating field heterogeneity and stress gradients, would strengthen the work. However, obtaining the necessary high-resolution field data for such a comparison lies outside the current scope of this modeling paper. We will revise the Case Study section to more explicitly state the illustrative purpose of the example and to note the absence of quantitative field validation as a limitation. revision: partial

  2. Referee: [Modeling Approach] The modeling comparison assumes the laboratory-derived variable traction in the modified Griffith criterion remains predictive at mountain-range scales without additional terms for time-dependent processes or heterogeneity. No explicit check or sensitivity test is reported to confirm that the overestimation result is robust once these field-scale factors are included (Modeling Approach section).

    Authors: The modeling comparison is intentionally simplified to isolate the effect of switching from the Mohr-Coulomb law to the modified Griffith criterion with variable traction. The laboratory-derived parameters are used as a first-order approximation to demonstrate the potential magnitude of the difference at large scales. We acknowledge that time-dependent processes and spatial heterogeneity are not explicitly modeled and that no dedicated sensitivity tests for these factors were performed. The overestimation result is therefore presented under the stated assumptions. We will expand the Modeling Approach section to discuss these assumptions more thoroughly, highlight the first-order nature of the comparison, and add a brief sensitivity discussion on how heterogeneity or time-dependent weakening might modulate the reported difference. revision: yes

Circularity Check

0 steps flagged

Direct modeling comparison of established criteria shows no circular derivation

full rationale

The paper conducts a modeling comparison of maximum relief using the Mohr-Coulomb law versus the modified Griffith criterion with variable rock traction. No equations or steps are shown that reduce the estimated difference in escarpment height to a fitted parameter, self-referential definition, or load-bearing self-citation chain. The central claim follows directly from applying the two known criteria to the stability thresholds, making the derivation self-contained. The scale-bridging assumption is a modeling choice but does not create circularity within the paper's own chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only information; no explicit free parameters, axioms, or invented entities are detailed beyond the choice of fracture criterion and variable traction.

pith-pipeline@v0.9.0 · 5758 in / 1110 out tokens · 51085 ms · 2026-05-20T15:11:56.301657+00:00 · methodology

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