Review

The effect of stiffness contrasts at faults on stress orientation

Ziegler et al.

submitted to Solid Earth

General comments and recommendation

This is a useful contribution that expands on the present knowledge about the influence of mechanical inhomogeneities (faults and fractures) on stress magnitude and orientation in homogeneous rock. It is well suited for publication in Solid Earth.

The manuscript still has some serious shortcomings in its present form:

• The Results chapter lacks a proper introduction that explains the problem focused upon and which strategy is selected to solve those. This chapter and its affiliated figures seem to me to be not to utilized to its full potential (see comments below) and gives a slightly whimsical impression.
• I recommend that the Discussion-chapter is re-written in full, starting with a definition of which (scientific) elements to be treated (it should harmonized with the introduction to the Results-chapter). This list of scientific items should be strictly used in the following discussion. Many interseting items are treated in the present version of the discussion, but they are mentioned under headings that may not all be well taken and sometimes also fail to go in sufficent depth, e.g. when (geological) implications and present status of knowledge in the literature are concerned. My recommendation will be that the Discussion-chapter is completely re-written. It seems that the observations given in Results and Discussion/evaluation-chapters have not been consequently systematized in all cases.
• I think some figures (Figures 2 and 3) should be redrafted to display some more details clearly. If I understand correctly that the outer part of the zonation is an artifact (see comment Lines 127-130) the color code should be modified: Artifacts should not have a color code in the fiure). I also suggst that other figures (particularly 4 and 5) are described and discussed more coherently in the text. The figure cations should also be more focused on explaining the meaasge to he reader.
• The English language needs some more attention. It is sometimes a little clumsy and some phrasings and sometimes ambiguous or unclear.  It is therefore recommended that the authors approach a colleague (who is familiar with this field of research) with English as his/her first language to assist in linguistic matters.

It is concluded that this article deserves publication in Solid Earth after rewriting of the description and discussion, reworking of a couple of figures and affiliated figure captions and improvement of the English language in general.

Specific comments

Title

I suggest that the authors adjust the title of the paper slightly, perhaps something like:

“The influence of rock stiffness contrast on stress configuration along and within faults”.

Abstract

Generally, I find the abstract to be a little “soft”. The initial sentence has the flare of a general introduction and should be condensed. I suggest that the abstract separate clearly between 1) the definition of the problem investigated in this study, 2) specification of which methods were and 3) sharpen even more the conclusions of this work and that all three items are expanded upon, more completely to cover the intention of the paper and its important findings.

Line 1: I think “body forces” are better than “gravitational volume forces”. Perhaps “contemporary stress” and associated concepts as defined by e.g. Engelder (1983) is preferrable (Engelder,T.,1993: Stress Regimes in the Lithosphere. Princeton University Press, 467pp.)

.

Line 4: This is fine and is where the important information really starts: “We investigate….”

Lines 2-3: “when faults are crossed …..”. Suggestion: “along or in the vicinity of faults ….. control the amount of principal stress axes.”

Line 7: “General findings….” You mean findings in the present work. Please clarify.

Introduction

Line 15: parameter in the stability assessment

Line 16: “exploitation” rather than “usage”?  Add safety assessment?

Line 17: Most frequently? You mean: “Information about S_Hmax is most easily obtained from…”?

Lines 19-24: You mean far-field stress, locally imposed by stress imposed by local……. like topography. Perhaps an advanced textbook (e.g. Engelder 1983) with a summary of such stress systems should be referred to and nomenclature and definitions adapted to that source (see also above).

e.g. Lines 23-28 and generally: The authors have a tendency to over-use adverbs in beginnings of phrases: “Furthermore, it has……”, “However, Reiter ….”, “Nevertheless, on a meters scale….”. These examples are taken from sentences that follow each other.

Line 29: “across the world” is a surplice phrase: (Where else?)

Line 33: Borehole breakouts: Again, I think it would be convenient to refer to an advanced textbook – Again, I think Engelder (1983) can be used.

Line 47: Perhaps this section should start with reference to empiric data/observations: Examples are given in lines 58-60, so I suggest that this is moved here.

Lines 43-49: Not well phrased. Please separate int two statements and clarify.

Line 50: Rather: “This raises questions as to which parameters determine….”

Lines52-53: Rephrase. Suggestion: (if this is what the authors mean to say. If I misread this, a full rephrasing is necessary). “The potential for stress rotation and the magnitude for such rotation are assumed to be determined by…. , the contrast in rock stiffness between …..  and the angle between S_Hmax and the fault strike”.

Lines 61-74: I think this is well phrased. Please include a short version of this in the abstract.

Line 76: I do see the rationale in the application of a plain strain situation in a strike-slip regime. Most faults will be influenced by shear whatever the overall tectonic regime. Perhaps this generic situation should be explained (to the unprepared reader), and perhaps the term shear” (rather than-strike slip) should be applied (for the same reason).

Line 77: Why S_Hmax and S_hmin: Misprint or some hidden significance? Either correct or explain.

Line 84: Isn’t the term tria-elements commonly written with capital T?

Line 85: In the order of about 75,00 elements?? Either 75,000 elements were used or not? Or did the model define the grid itself? If so, based on what? Whatever: “In the order of about” is a superfluous double description.

Lines 90ff: Why not E_host and E_fault to bring it in harmony with e.g. S_Hmax

Line 93: “Non-existence of a fault”: Why not “intact rock”? When I walk in a street, the street may be empty, which is congruent with “filled with non-existent cars”. But we don’t say that.

Line 94ff: In my opinion care should be taken so that the conclusions gave a consequent grammatical time sence in distinguishing between what was observed in the experiments and what is generally valid for such systems. In other words: We tested the influence…., scenarios were analysed…. .

Results

This important section of the paper comes on a little abruptly. Perhaps a short introduction that describes the dynamics of the experiments should serve as an introduction to this section. Particularly, the reader should be reminded which relations and which hypoteses are subject to investigation, and informed about the strategy selected to attack the problem (which parameters are at stake, which are kept constant and which are varied). Some of the general statements on the experiments given in the previous section and also spread out in the following description could perhaps be moved here.

At this stage he authors should reveal to the reader also their strategy for illustration of the observations and the analyses, which is revealed in Figures 3, 4 and 5: In oher words, The relation between figures 3 - 5 showing the stress configuration within the faults should be highlighted from the start in this section.

I think the use of tables 1 and 2 should be utilized more actively in the descriptive part. Now a very summaric summary is given in the text: “A more comprehensive comparison is shown in Table 2” (line 113).

Some crucial information seems to be lacking: Are the situations illustrated in Figure 3 initial or advanced stress configurations? In other words: did the configuration change with time or did it become stabilised?

The general observaton should be stated and highlighted in the closing part of this section: Now the summary of the key observations are a little bit spread out and the (important) observatios are presented rather summarily.

General: See comment to line 94ff above.

Line 98: Please rephrase: this sentence is complex to the extent that is messsage is obscured. Start with the subject “The orientation of ……”, refer immediately to Figure 3, and use Figure 2 more actively.

Line 98 -101: Again, why not s_xx, s_yy etc, since s and _xx describe different qualities, namely principal stress and vector components?

Line 103: Please expand the text somewhat to help the reader a bit here, e.g. “….. an angle (g) of 15^o between the strike of the fault and the far field stress (S₁) a moderate stiffness contrast (R_E)…”.

Line 104: Take out “There,”

Lines 103-105: I think that the potential of Figure 3 is not fully exploited here, and the reader should be informed to read Figure 3 in concert with Figures 4 and 5. And why is only Figure 3a referred to in the text, completely neglecting b-f?

Furthermore, Figure 3 is rather nitty-gritty and it is mpossible to read all the details. (Particularly 3b is unclearly displayed). I understand that the displayed zonation (e.g.yellow-red-magneta) in e.g. is an artifact (lines 126-130). If so, the color symbols are misleading and the “artifical” color zones should be removed from the figure display and rather commented upon in the figure caption.

Lines 105-108: I think this information should be given in the very inroduction to the Results-section on a general basis and combined with a description of the strategy for the prsentation of the results (see general comments to the Results-chapter above).

Line 108: You mean: “S1-S2 remains constant”. Please state clearly whether this implies absolute stress magnitude, or the difference only?

Line 115: Rather: “Thus, greater R_E promotes less stress rotation”

Line 123: Moved to introductory remarks in this chapter?

Line 127-130: This is a strange phrasing and rather confusing.You mean: “The data on stress orientation at the material borders show here are not valid, because…..the apparent stress rotation result from interpolation of what?...... please rephrase/explain” Also the following sentence (“At material contrasts….”) needs to be rewritten e.g.: “At the borders between bodies with different material properties ….”.

I understand that the apparent zonation (displayed in Figures 3a, b,c,d) are artifacts. This is technical information that should be kept isolated form the valid observations done in the interpretation of the data (perhaps transferred to the introductory section of “Results”).

Lines 130-150: I think I understand what the authors try to state her, but the messages are blurred by overly complex sentences and uclear language:  Pleaese straighten out and avoid over-complex statements like “…(g = 0_o) may exhibit the maximally possible stress rotation of 90^o which signifies a mutual replacement of S₁ and S₂ orientation, respectively”. This is unclear at the best, and should be rephrased.

Figure 3, figure caption: “… dependent on different setting” meaning what? I assme you mean: ”resulting from contrasting sets of model input parameters”. Details in this figure are not easily readable (see e.g. 3b). A better explanation is needed and the crucial differnces should be pinted out. E.g. The only difference between a and b is the Rs-value of 1,4 and 1,2. So please axplain what you want to demonstrate.

Figure 4, figure caption: This figure is not well explained. Rather: “Intrinsic stress rotation in the fault zone as a function of increasing ……”. The figure caption needs much more attention. Please lead the attention of the reader more clearly to the important relations here, for example the abrupt termination of stress rotation at the fault border. A comment on geological consequences and limitations would be appropriate (see e.g. Gabrielsen et al. 2017 referred to below).

1. Discussion

After a very short introduction the discussion chapter jumps directly onto a mention of the practical application of the results (4.1 Application). Thereby the entire scientific discussion and the evaluation of the results in the framework of established knowledge of stress configurations in the framework of present knowledge becomes deluted. This is a bit disappointing and particularly so because elements several principal elemnts for discussion pop up.

I recommend that the Discussion-chapter is re-written in full, starting with a definition of which (scientific) elements to be treated. This list should be strictly used in the following discussion. Many interseting items are treated in the present version of the discussion, but they are mentioned under headings that may not all be well taken and also fail to go in sufficent depth, e.g. when (geological) implications and present status of knowledge in the literature are concerned.

Thereafter the chapter on practical applications of the reults  could be included before the Conclusions are given

Since I reommend that the Discussion-chapter is re-written, I have not included specific comments here.

In the present version the  “Discussion” slides over from “4.1 Application” to “Implementation (4.2)”. Relevant elements that should be addressed in a scientific discussion are touched upon, but are immeiately abandoned, preventing  discussion in any depth (e.g. the element of plastic (vs brittle, which is not mentioned) deformation and strain softening/hardening).

The authors touch upon the complexities of mature fault zones “Material gradient (4.3)”. I do agree that mature natural fault zones frequently host damage zones (as mentioned) and often include structural elements sparated by abrupt changes in mechanical properties (see e.g. Gabrielsen et al. 2017; Figure1; (Gabrielsen,R.H., Braathen,A., Kjemperud,M. & Valdresbåten,M.L.R., 2017: The geometry and dimensions of fault core lenses, Geological Society London, Special Publication, 439, 249-269, doi.org/10.1144/SP439.4). Nevertheless, the present contribution has a nucleus for a more profound discussion of this in the light of their new data, that I think it could be expanded upon.

The authors use data well data to illustrate patterns of break-out (4.4 Well data vs modeling results). The concept of wellbore break-out is well established in the literature and I again miss reference to basic advanced textbooks (again Engelder 1983). I think these would give a good background for the discussion of rotated stress, which is tricky in wellbores since the drilling process can influence the stress and fracture patterns.

The final part of the Discussion (4.5 Limitations) has a flare of afterthought. I think it would be better that elements from this section be transferred to the discussions of in subchapters 4.1 - 4.4 and placed where there should is a limitation in the conclusion for each topic.

4.6. Other reasons for stress rotations. I think this section should be amalgamated with section. 4.4.

1. Conclusions

The most significant conclusions from Chapter 4 should be summarized here and referred to in the abstract.

References

The references have not been controlled by me, neither when consistency between text and reference list, nor when format is concerned.

The paper conducted extensive numerical studies to investigate the effect of stiffness contrasts, stress ratio, and the angle on stress orientation. It has essential contribution to the community to understand the difference between in situ stress and local stress field. It also calls for attention that breakouts do not necessarily correspond to the far field Shmin direction, but need more in-depth investigation since local stress fields could be rotated. Revisions are required before publication to address questions/clarifications that have been listed below:

Title: The study is not only about stiffness contrasts, but also includes stress ratio, and the angle between strike and SHmax. Please consider changing the title.  

Line 25: Reiter et al. (2024) says stress changes beyond a few hundred meters are too small to see. However, from Fig 4, the rotation is zero as when the distance is >=3m. Could you please explain the order difference (hundred meters in Reiter versus only 3m in Fig 4)? In the current study, it seems the stress changes are indiscernible whenever the distance is >= 3m.

Line 77: In the Strike-slip stress regime, shouldn’t S1=SHmax and S3=Shmin? I understand the model is in 2D, but I feel it is a bit confusing to say S2=Shmin. Please consider change that.

Line 79: Have you conducted a mesh convergence study in FEM? It could be great to have plots (maybe in the supplement) to show the validation of mesh convergence.

Table 2: The row name should be “S1-S2 [MPa]”, instead of “S1-2 [MPa]”.

Line 113: “A reduction of RE=0.4 to RE=0.7” seems to be an increase, not reduction. I understand that from the value, it is “increase”. However, based on the meaning, it could say a reduction of stiffness contrast between fault and the host rock. Please make it clear in the text.

Figure 6: the color-coding looks different as it is in the legend.

Section 4.2: section 4.2 could be combined with section 2 model setup. It is all about how you set the model. You didn’t do contact modelling, right?

Section 4.4 and Table 3: The table caption of table 3 shows “parameters in italics are derived”. However, the parameters in Table 3 is in italics. In addition, in order to do comparison of well data with the modelling result, intuitively, I will expect authors use Rs, Re, angle from the reference, and have a column called “modeled stress rotation” and compare it with the column “observed stress rotation”. However, in the manuscript, it seems authors sometime derived for input parameters, not for modeled stress rotation. Please have more clarifications in the text.