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| 22 Apr 2024
Localized shear versus distributed strain accumulation as shear-accommodation mechanisms in ductile shear zones: Constraining their dictating factors
Abstract. Understanding the underlying mechanisms of strain localization in Earth’s lithosphere is crucial to explain the mechanics of tectonic plate boundaries and various failure-assisted geophysical phenomena, such as earthquakes. Geological observations suggest that ductile shear zones are the most important lithospheric structures of intense shear localization, sharing a major part of tectonic deformations. Despite extensive studies in the past several decades, the factors governing how they accommodate the bulk shear, whether by distributed homogeneous strain (i.e., development of S tectonic foliation normal to the principal shortening strain axis) or by localized shearing (formation of shear-parallel C bands) remain largely unexplored. This article aims to address this gap in knowledge, providing observational evidences of varying S and C development in ductile shear zones from two geological terrains of Eastern India. The field observations are complemented with 2D-viscoplastic numerical simulations within a strain-softening rheological framework to constrain the factors controlling the two competing shear-accommodation mechanisms: homogeneously distributed strain accumulation versus shear band formation. The model based analysis recognizes the bulk shear rate (γb), the bulk viscosity (ηv) and the initial cohesion (Ci) of a shear zone as the most critical factors to determine the dominance of one mechanism over the other. For a given Ci, low γb and ηv facilitate the formation of S foliation (uniformly distributed strain), which transforms to C-dominated shear-accommodation mechanism with increasing ηv. However, increasing γb, facilitates shear accommodation in a combination of the two mechanisms leading to CS- structures. The article finally discusses the conditions in which ductile shear zones can enormously intensify localized shear rates to produce rapid slip events, such as frictional melting and seismic activities.
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RC1: 'Comment on egusphere-2024-1077', Anonymous Referee #1, 29 May 2024
Comments on the manuscript «Localized shear versus distributed strain accumulation…” by Chatterjee, Roy, and Mandal
The manuscript describes modeling results and field examples of shear bands and shear zones. The results are presented in a clear, well-written, and concise text. The modeling results appear reasonable and sound. The field examples are presented at the mesoscale observation level. However, the manuscript requires some major revisions before it can be published. The first problem that I see lies in some confusion of terms that is related to nomenclature:
For a large part of the text, especially the modeling part, the authors use a continuum mechanics rheology nomenclature, consistent with their modeling approach, which is continuum-mechanics-based. In this nomenclature “plastic” refers to “pressure-sensitive, temperature-insensitive” deformation with a yield criterion, and “viscous” refers to “temperature-sensitive and pressure-insensitive” deformation without a yield criterion. These definitions are not clear to all geologists or may be used differently by them and therefore should be defined in the introductory section. Furthermore, the term “ductile” is problematic in geology and rock mechanics. “Ductile” in rock mechanics primarily refers to brittle, distributed deformation, e.g., cataclastic flow, and in this sense, the brittle-ductile-transition is a purely confining-pressure-dependent transition from discrete fractures to zones of distributed cracking. Friction-controlled sliding may agree with the term “plastic” in the purely rheological sense defined above. However, the term “ductile shear zone” is used by most geologists as a zone where viscous deformation processes (intracrystalline plasticity or diffusion creep) dominantly accommodate the strain and thus a viscous rheology prevails. Obviously, from the short outline above, it becomes clear that the terms “ductile” and “plastic” have very different meanings in the different communities. Large parts of the discussion suffer from this confusion of terms. Again, the terms should be clearly defined and probably the terms “ductile” and “plastic” (without the prefix “crystal”) should be avoided or their use should be checked for consistency in every instance.
The second problem of the manuscript lies in the lack of microstructural analysis in the field examples. The microstructures could provide information on the deformation mechanisms in each shear band or -zone. Once the deformation mechanism is established, rheological consequences are implied. E.g., for cataclastic-frictional microstructures (perhaps the quartzite examples?), the rheology may be “ideal-plastic” in the rheological sense or “ductile” in the rock mechanics sense, but not in the common structural geology sense. The S-foliation-dominated microstructures may indicate crystal plastic or diffusion-creep-type deformation mechanisms and therefore could imply dominantly “viscous” deformation in the rheological sense. The discussion would become much clearer, far more relevant, and less speculative with such information provided. Furthermore, rate-dependent and viscosity-related inferences are made from the mechanical modeling and discussed. Such a discussion should only use the field examples when deformation mechanisms are established for the examples – otherwise the field examples are black-box cases.
Detailed comments:
Line 21: omit “intense”
Lines 83-107: The discussion should include the possibility that the S- and C- fabric elements may not develop simultaneously as poposed by Berthe et al. 1979. Recent studies by Bukovska et al. 2013, 2016 indicate a different origin and should be mentioned and discussed here.
Line 86-87: there is important experimental evidence for the formation of shear bands in the semi-brittle deformation regime, and this should be considered here, too: Pec et al. 2016, Marti et al. 2017, 2018, 2020, Schmocker et al. 2003.
Line 95: definition of terms “viscous” and “plastic”, see introductory comments above. It will not be clear to most geologists how or why the terms viscous and plastic are used in a distinguishing of differing sense here. Furthermore, it is not clear why the strain accommodating processes in S and C bands have to different.
Line 99: “accommodates” instead of “accommodate”
Line 100: how is it determined that the deformation in the localized zones is not viscous?
Fig. 1: please give scales in km, not just in degrees of latitude and longitude. CGGC does not appear in the maps but in the text – please indicate the abbreviation in the maps or refer to other units (NPSZ?)
Lines 158-162: by foliation you refer to a S-foliation? Please specify.
Fig. 3: the C-bands show a coarse grain and have a melt-like appearance within the feldspar-biotite matrix. Such melt segregations will have a different mechanical property compared to the matrix. Please comment on this aspect, especially with respect to the relevance to modeling and in terms of rheological development.
Fig. 4: the shear zones are considerably coarser grained than what is termed “wall-rock” here and appear to have a melt-origin, while the wall rock does not show clear evidence for melt. Again, as in Fig. 3, a considerably weaker rheology is expected for these shear domains. Modeling such structures appears difficult: have the melt segregations formed first, so that they localize the deformation? In such a case, a homogeneous matrix cannot be assumed for modeling. Or has melt material filled pre-existing shear bands? If this is the case, why are such bands so dilatant?
Lines 178-180: C-band formation appears to be in contrast with viscous deformation here – why? Please define or describe the difference between viscous deformation and localized shear band formation. Why should localized deformation not be viscous? Commonly, shear bands can be considered localized zones of viscous deformation.
Line 276: “accommodates” instead of “accommodate”
Lines 276-278: this statement implies that plastic yield will produce some strain localization. In principle, plastic deformation may produce homogeneous strain – depending, in part, on the definition of “plastic”. That is why it is important to define the terms, see introductory comments
Lines 318-322: the terms viscous and plastic appear to be used in a strictly continuum mechanics rheological sense here. As many geologists may have a somewhat different understanding of these terms, it is important to explain them in the introductory part. Furthermore, the difference in plastic and viscous strain accommodation mechanisms may follow from the modeling, but the mechanisms are not demonstrated for the field examples. For a complete discussion, this aspect of the analysis needs to be performed or at least some evidence for supporting an interpretation of different deformation processes needs to be given.
Lines 323-329: these few lines discuss very important aspects of definitions and identification of deformation mechanisms in conjunction with rheology. The identification of viscous deformation mechanisms is fairly straightforward from thin sections. As for “plastic” deformation in the rheological sense, this can manifest itself in cataclastic deformation processes, because these are pressure-sensitive. Such processes can also be identified from thin sections. The term “ductile” in some rock mechanics literature (e.g. Byerlee) can include distributed brittle deformation (e.g. cataclasis). Geological literature often refers to ductile as a viscous deformation. See general introductory remarks above.
Lines 330-344: the occurrence of different types of shear zones is less dependent on the tectonic setting but, instead, strictly temperature- and strain rate-dependent. Of course, higher temperatures and lower strain rate favor viscous deformation, whereas cataclastic deformation processes dominate in lower temperature regimes and at higher strain rate.
Line 351: “ductile shear zones” – see general comments above. Probably, this term should be avoided altogether.
Citation: https://doi.org/10.5194/egusphere-2024-1077-RC1 -
RC2: 'Comment on egusphere-2024-1077', Anonymous Referee #2, 21 Jun 2024
This article analyzes homogeneous distributed strain versus shear band formation in shear zones in Eastern India and tries to find governing rheological and kinematic parameters controlling the formation of natural C, S, and CS fabrics using 2D, visco-plastic numerical shear deformation models. The paper is well written and clearly structured. The description and explanation of the natural fabrics in the different outcrops is detailed and accurate and the discussion tries to connect the numerical results and the natural observations in a good way.
However, I do struggle with some of the terminology, especially in combination with the numerical models. In the current way and how the authors argue for a correlation between the numerical results and the natural fabrics, the numerical model setup seems inappropriate to describe the natural fabrics. Especially, considering the simple rheology of the numerical models and no discussion on how a simple visco-plastic rheology can explain or represent/mimic complex microscopic features leading to strain localization and shear band formation.
I like the combination of the numerical models with clear and precise natural examples. However, in the current way it is hard to believe, that a simple visco-plastic rheology is enough to explain complex natural C,S, and CS fabrics. It is very nice to see how they connect the different fabrics with the main rheological and kinematic parameters (shear rate and viscosity). However, no discussion or explanation is made on how one could correlate shear bands due to plastic failure in the models with natural shear bands forming C fabrics, besides their simple pattern.
Also, I am not convinced that the numerical results are specifically new. Figure 9 simply states, that for a certain yield stress one obtains yielding above a threshold viscosity for a given shear rate. This is expected though, since the stress increases with increasing viscosity in simple shear deformation assuming a constant shear rate! Using a different cohesion results in different regimes again!
The connection between natural examples and numerical models is interesting as well as the classification of the different fabrics in the shear-rate – viscosity regime would be interesting for the geoscientific community. Thus, I believe this article, is worth publishing, however, only after a major revision. I do hope the comments below help the authors to do so.
Major comments
Visco-plastic rheology and correlation with natural fabrics
That the parameter combination of ductile viscosity, shear rate and cohesion result in regimes of homogeneous distributed strain, localized plastic shear bands, and a combination thereof is clear. How those patterns can be link to the natural fabrics not!
My major concern is the rheological configuration of the numerical models and how the results of the numerical models are correlated to the natural fabrics in the shear zones. Besides the fact, that the rheology is not purely viscous (plasticity is included), I am missing an explanation on how the numerical results can explain the natural fabrics. How does a purely viscous simple shear deformation result in S fabric (homogeneously distributed strain sure, but this does not tell us anything about the fabrics)? If this is the case, then we should see fabrics in all viscously deforming rocks. Is this really the case? A more detailed discussion or explanation thereof would be very helpful.
This is even more concerning regarding the correlation between plastic failure and the localized shear bands. Yes, the pattern look similar and one could explain the natural fabrics via such a pattern in the numerical models. But, clearly the natural localized shear bands are not formed via plastic failure. An explanation or discussion should be given on what the plastic failure represents or mimics such that it can be linked to the natural shear zone. This is currently missing, or not very clearly described. Current research on plastic strain-weakening processes help to link plastic strain-softening and hardening to micro-physical mechanisms like a grain-size sensitive composite olivine rheology. While healing is not specifically applied in this research here, a similar way to argue for the connection between a visco-plastic rheology including strain-dependent weakening mechanisms and complex micro-physical mechanisms would be helpful. Considering the fact, that strain-localization is not only driven by grain-size reduction other potential mechanisms could be discussed a little bit in more detail to link the numerical patterns observed in the models with the natural fabrics.
I believe a discussion in that direction would benefit the manuscript, maybe also additional models with a more complex rheology (or an argument why to stick to a simple visco-plastic rheology) is really necessary. Multiple micro-physical mechanisms can lead to strain localization, which are also described in the natural examples (grain size refinement in the localized shear bands), however, which dominates is still unclear. To mimic those mechanism by a simple visco-plastic rheology would be to easy, without a clear definition why, which, I believe is currently missing. Considering a more complex rheology in the discussion of the numerical results might also put the final conclusion in Figure 9 into a different perspective, since I strongly doubt that it is so simple to classify the natural fabrics by purely visco-plastic rheology.
Terminology of "Ductile shear zones"
I find the term “ductile shear zones” a little misleading. Maybe, this is a general term in geology, but considering that multiple deformation mechanisms are observed, brittle and viscous, it might be not the appropriate term. The brief explanation of both mechanisms in shear zone (lines 32-36) is good, however, I suggest to generally talk about "shear zones" (maybe “crustal” or “lithospheric shear zones”) when describing and discussing the field evidence and the numerical results. Calling them ductile shear zones already implies, that you only consider ductile deformation processes, like grain-size sensitive diffusion creep, non-linear creep, melt interaction (in a simplified formulation) and such. While this might be the case for the natural shear zones, non of the more complex mechanisms are considered in the numerical models. In fact the numerical models are just visco-plastic models with a constant viscosity. The occurrence of the different deformation mechanisms is already discussed in the introduction. However, in the current version, I do not feel like this is enough to justify calling them ductile shear zones. If you do insist on calling them ductile shear zones, I think the numerical models are not appropriate to analyze the natural structures without a discussion on how to link the plastic failure to shear band formation and corresponding strain localization via any kind of microphysical mechanism (such as grain size reduction).
Minor comments
Line 29: augment … processes
Line 37: I find “irrespective” a little to hard. Yes on a large scale the evolution of shear zones might be scaled by strain partitioning along macroscopic shear bands. However, the internal deformation mechanisms are important, not only for strain partitioning, but also for strain localization processes.
Line 60: deformation not deformations
Line 63: … Mair and Abe (2008),…
Line 67: depends
Line 76: do you mean … (Rutter et al., 1986), …?
Line 76: what brittle features? The feedback mechanism shown by Bercovici and Karato (2002) are not brittle features!
Line 81: lead
Line 85: occurs
Line 94: deformation … occurs …
Line 162: Definition on how the area is evaluated is unclear.
Equation 4: you mean (1/eta_v + 1/eta_p)^-1, correct.
Equation 6: what is Chi (X)?
Line 223: “decreases non-linearly”. Is this really the case? Looking at equation (8) the cohesion decreases linearly with increasing strain.
Equation (7): This equation does not explain how the flow stress is equated by the yield stress. What is the absolute of the strain rate? Where does the yield function F occur?
Equation (8): Is the pressure that important? I assume, in that case it would simply be the dynamic pressure.
Line 260: I would not call it bulk viscosity, since this would mean the viscosity of the shear zone. Maybe call it ductile viscosity.
Table 1: I assume the Cohesion is also the Scaling value for the stress, correct. The correct way is 2.7 10 -14 s-1 and 10 21 Pa s.
Line 270: Supplementary videos do not work!
Line 279: … deformation emerges …
Line 415: parentheses missing
Line 422-426: Little unclear, maybe rephrase a bit. What exactly is an „enormous shear rate enhancement„?
Line 426: Ductile shear zone can not produce earthquakes, since an earthquake is a brittle event! Even a dramatic viscosity reduction within a shear band and a high viscosity contrast do not produce Earthquakes, but simple a high strain rate event. To obtain an earthquake you need brittle failure. Maybe, shear localization in the ductile regime can trigger an earthquake in shallower brittle regimes.
Line 288: what is lambda*?
Figures 1b and 1c: What are the red squares? The regions of you field studies?
Figures 2 and 3: Scale is not very good visible
Figure 5: What is the color scale in the background? Is is simply a gradient showing the different regimes? In that case, you should leave it out! Maybe call the x-axis like in the text: “areal percentage of S foliage on domains” or similar.
Figure 7c(iv): what is the white arrow?
Figure 8: How did you obtain the values from the models? Are the interpolated over the particles?
Citation: https://doi.org/10.5194/egusphere-2024-1077-RC2
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