|The revised manuscript is greatly improved, and I thank the authors for taking the time to consider my previous comments. The introduction and discussion are much clearer in the revised version, and I find the inclusion of the absolute porosity changes to be intriguing. There are a couple of primary points I’d like to raise related to the revised text and to the response to my initial comments. I still think the content of the article is timely and worth publishing. My comments relate to the fact that I’m having trouble making some logical connections among different parts of the paper, and therefore some clarification would be welcome in a revision.|
I admit that I did find the expanded discussion on the thermodynamics of creep to be difficult to follow at times. I appreciate the emphasis on the boundary conditions, and the possibility for constant velocity boundary conditions to prevent localization. However, I’m not sure I understand why a macroscopic response related to the porosity evolution must be linked to localization. There should still be some effect on the mechanical response associated with a 1% increase in the pore fraction, even if there isn’t localization. This effect is well documented in the literature on partially molten rocks (e.g., see part 1 and part 2 of Hirth and Kohlstedt, 1995). Because of the reduction in grain-grain contact area, the local stresses are higher, and therefore higher strain rates are generated for the same macroscopic stress. The details of this reduction in apparent viscosity clearly depend on the specific microstructure, but for the basalt-olivine system in dislocation creep, you’d expect a reduction in viscosity of about 10% (factor of 1.5 increase in strain rate at constant stress, or a factor of 1.1 decrease in stress at constant strain rate, for a stress exponent of 3.5). Some of the experiments in Barnhoorn et al. (2004) may have weakening of this amount at strains >5, but the majority seem pretty stable.
I find it particularly interesting that the porosity doesn’t increase until after gamma = 5. Considering that you are only counting open pores (as documented in the revised manuscript), this must mean the sample has increase in volume by 1% between a gamma of 5 and a gamma of 10. I understand the hypothesis that porosity is generated by recrystallization, but there is still plenty of recrystallization (perhaps even more) at low strains. So it remains unclear to me why there is a porosity increase only after very large strains (and as noted above, in association with essentially no change in flow stress). I think it would be useful to include some explanation, even if speculative, for this phenomenon.
Regarding the link to partially molten rocks, I understand the authors’ point that to properly treat that connection is a major undertaking. And I understand that this comparison has been made already by Spiess et al. (2012). However, I still feel that something needs to be said in this manuscript, even if it is just a single sentence referring the reader to Spiess et al. I should also note that the authors’ second reason for not including this topic (that these experiments represent single phase aggregates) does not sound quite right to me. If there is a fluid phase in the pores (as the authors suggest there is in the revised version), then this is a multiphase system. Much of the relevant literature on partially molten rocks focuses on a single solid phase and a single fluid phase.
I also appreciate the expanded discussion on how failure associated with cavity formation is not easily predicted in existing experiments in rocks. My comment here is intended to point out that there is an extensive literature on failure by cavity formation in metals, and the time to failure is a primary concern for engineering applications. Correspondingly, there are a variety of efforts to establish constitutive equations that predict the time to failure, which is exactly what the authors seem to be advocating for. Some well cited examples include Ashby and Dyson (1984, https://doi.org/10.1016/B978-1-4832-8440-8.50017-X) and Kowalewski et al. (1994, https://doi.org/10.1243/03093247V294309). As with the discussion of partially molten rocks, it seems unfortunate to not, at least, acknowledge that significant effort has already been made on this front outside the geological literature and refer the reader to this vast resource.
Line 26: “by” instead of “with”
Line 27: Perhaps it is worth starting a new paragraph at “In contrast” since the topic sentence of this paragraph is about existing models. Also, “that” instead of “which”.
Line 29: Why capitalize “Generalized Thermodynamic”? This can’t be the only generalized thermodynamic model.
Lines 29 to 30: Is it really a paradigm if much remains to be tested? I guess it sounds more like a hypothesis to me.
Lines 54 to 55: I’m not sure I fully understand this statement. Indeed, the energetics are critical to consider, but they are, to some extent, already included in the mechanics. For example, the typical quantities to measure in tests of viscous materials are stress and strain rate. The product of these two quantities is the total energy dissipation (in Watts per unit volume). Therefore, the energetics of the system are generally being measured and considered in traditional treatments of these data. Perhaps some additional clarification is necessary here.
Lines 58 to 59: T should be italicized.
Line 75: I think a slight rewording is needed to clarify that it is the clusters (rather than the pores) that are systematically oriented.
Line 89: Perhaps include “dominant” before “spatial”.
Line 120: This statement caught me off guard a bit. I suppose my instinct is that the evolution of the porosity and porosity distribution will depend large on the nature of the pore fluid and the pore-fluid pressure. I think the only way to say that these features of the porosity depend on bulk material properties like the elastic modulus is to demonstrate that the porosity is different for different materials, rather than the suggestion that the porosity reaches steady state, as is implied here.
Line 129: “affected” → “affect”
Line 131: Remove “concerning” or “of”
Line 148: Is “flux” the right word here? What is there a flux of? This discussion is about the boundary conditions, but flux refers to some sort of transport. Is this the flux of energy into the system? Some clarification would be useful.
Line 195: “evolved”→ “evolve”
Line 198: Again, shouldn’t the pore-fluid pressure factor into this discussion?
Line 200: Remove “a” prior to “fracture”
Line 230: An “e.g.” makes sense before the citation to Hobbs since there are many documented observations of frictional melting in the geological record.