the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Nov 2022
Time-dependent Frictional Properties of Granular Materials Used In Analogue Modelling: Implications for mimicking fault healing during reactivation and inversion
Abstract. Analogue models are commonly used to model long-term geological processes such as mountain building or basin inversion. The majority of these models use granular materials like sand or glass beads to simulate the brittle behaviour of the crust. In granular materials deformation is localized into shear bands that act as analogues to natural fault zones and detachments. Shear bands aka faults are persistent anomalies in the granular package and are frequently reactivated during an experimental run. This is due to their lower strength in comparison to the undeformed bulk material. When fault motion stops, time dependent healing immediately starts to increase the strength of the fault. Therefore, older faults show a higher strength in comparison to younger faults. This time dependent healing, also called time consolidation, can therefore affect the structural style of an analogue model due to evolution of fault strength over time. Time consolidation is a well known mechanism in granular mechanics but remains poorly characterized for analogue materials and on the timescales of typical analogue models. In this study, we estimate the healing rate of several analogue materials and evaluate the consequences on the reactivation potential of analogue faults. We find that the healing rates are generally below 3 % per tenfold increase in hold time which is comparable to natural fault zones. We qualitatively compare the frictional properties of the materials with grain characteristics and find a weak correlation of healing rates with sphericity and friction with an average quality score. In models where predefined faults exist or reactivation is forced by blocks, the stability region of fault angles that can be reactivated can accordingly decrease by up to 7° over the duration of 12 hours. The stress required to reactivate a preexisting fault can double in the same time which may favor the creation of new faults. In a basin inversion scenario, normal faults can not be inverted due to severe misorientation and therefore time consolidation plays only a minor additional role for such models.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(1580 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-1178', Hanna Elston, 23 Dec 2022
The manuscript provides new and valuable information on the material and frictional properties of many granular materials that are frequently used in analog models to simulate crustal faulting processes. The findings presented in the manuscript will have a great value to the analogue modelling community. One major contribution of this study is that the authors define the grain characteristics and quantitatively estimate the friction coefficient, cohesion, and healing rates for a large set of granular materials. Rudolf et al. present a possible explanation for the general absence of fault reactivation during basin inversion models that has been observed in several previous studies that use granular materials. Furthermore, the authors provide new insight on the suitability of a set of granular materials for fault models that aim to explore basin inversion scenarios, fault healing processes, and more general faulting processes. I have a few suggestions that could strengthen the paper, but overall I recommend that the manuscript be accepted with revisions.
The methodology section could be strengthened in two ways: 1) Whether ring-shear tests were conducted for this study specifically or results from previous studies were reanalyzed for this study is not entirely clear. Lines 73-76 insinuate that the authors collected samples of 14 granular materials and conducted ring-shear and slide-hold-slide tests, however, lines 121-122 indicate that the ring-shear test data is taken from previous studies and reanalyzed for this study. I believe the results are from a combination of new and previous test, but a sentence either in the last paragraph of the introduction or early on in the methodology would clear up any potential confusion. 2) The method to assign grain characteristics or quality scores and associated uncertainties is unclear unless reading the background literature. A brief explanation of how quality scores are assigned and how precise the quality scores are would be helpful, especially when interpreting Figure A1 and the calculated correlation coefficients. Additionally, including some description of the correlation coefficients and comparisons between the quality scores and healing rates, friction coefficients, and cohesion would strengthen the methodology section.
The correlations, or lack thereof, between the quality scores and healing rates, friction coefficients, and cohesion are a key conclusion. The basis for this conclusion could be solidified if the authors address the following: 1) What is the reason to use Pearson and Spearman correlation coefficients for the comparisons between healing rate/friction/cohesion and the qualitative properties? 2) What is uncertainty for each quality score, and how does such uncertainty impact the correlation coefficients? In other words, how much weight should be placed in the correlation coefficients and p values? 3) Figure A1 supports the conclusion regarding the correlation between sphericity and healing rates and friction coefficients. As such, Figure A1 should be included in the main text.
The discussion section addresses many valid points relating to fault reactivation in basin inversion models. The findings of this manuscript may be more broadly applicable. More specifically, lines 382-389 include a key interpretation that is relevant to many analogue models. The authors introduce potential implications in the introduction that could be addressed in the discussion section to further emphasize the impact of the findings on a range of analogue models that use granular materials. Two examples of such discussion topics are 1) How could healing impact fault behavior within models with erosion/sedimentation that are stopped to remove/add material? and 2) How could consolidation and healing time impact repeatability?
Specific comments
Formatting/grammar: Some paragraphs have indentations, but others do not.
Add spaces between numbers and units (e.g., lines 186 and 187)
Add commas before ‘which’ (lines 16, 22, 42, 56, 116, 121, 133, 221, 235, 238, 245, 288, 307, 341)
6-7: By older faults do you mean faults that have been inactive longer? This sentence is not entirely clear.
29: Remove ‘e.g.’
40-42: Use of ‘it’ is slightly confusing. I presume you mean analogue models?
51: I would recommend citing Reber et al. 2020, which covered a range of analogue modelling benefits, applications, and material properties https://doi.org/10.1016/j.earscirev.2020.103107
112: Change ‘materials’ to ‘material’
116: Remove ‘and’ following ‘fault zone’
138: vl doesn’t seem to appear elsewhere. Maybe it doesn’t need a variable assigned.
208: Remove repeated ‘increase of hold time’
241-243: Complex sentence that could be clarified
267: Change ‘which’ to ‘and’ and remove ‘therefore’
296: Change ‘which’ to ‘that’
306: Insert comma after gray
359: Out of curiosity, would you expect that healing may have a larger role for materials that exhibit stick-slip behavior (e.g., Utrecht sand?)?
Results section: Reorganizing to present the grain characteristics first would provide context for how the different materials compare to one another, which could help the reader more readily digest the differences in healing rates and reactivation. This reorganization could also improve the flow from results to discussion.
Discussion section: Sections 4.1 and 4.4 are closely related and the reader could benefit from the two sections being next to each other or integrated.
Figure 3: Including a simple note on what the numbers next to the material name mean could add clarity. Indicating which materials were included in Klinkmüller et al., 2016 is a nice touch.
Figure 6: Very helpful
Figure A1: Needs a legend. It would be beneficial to include in the main text since the discussion relies on the correlations that the plots demonstrate.
Citation: https://doi.org/10.5194/egusphere-2022-1178-RC1 -
AC1: 'Reply on RC1', Michael Rudolf, 30 Jan 2023
Dear reviewers, we have considered your comments in the attached comment file. Since some of your questions and comments were very similar, they have been merged at the appropriate places. The roughest changes briefly summarized:
- Slight linguistic revision of the abstract.
- New chapter: 'Materials' partly with text and table from the previous version. This now describes in detail the materials and measurements made before and during this study.
- Better description of the particle properties, the determination and relevance of the quality score in 'Grain Characteristics'.
- Results for 'Grain Characteristics' moved to the beginning of the Results chapter.
- An error in the calculation of the weighting factors has been corrected. This has only a minor impact on the overall result.
- First chapter of the discussion slightly revised and a more general part (4.1.3) added. (former 4.1 and 4.4 are now together in 4.1.1 and 4.1.2).
- Added the stick-slip sand aspect from Utrecht for discussion.
- Figure A1 moved to main text and revised.
- Added another conclusion as a result of 4.1.3.
All comments on spelling, grammar, and placement of units have been addressed.
-
AC1: 'Reply on RC1', Michael Rudolf, 30 Jan 2023
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RC2: 'Comment on egusphere-2022-1178', Anonymous Referee #2, 17 Jan 2023
This manuscript focuses on the time-dependent frictional properties of granular materials that are frequently used as analog in laboratory experiments to simulate the brittle behaviour of the crust. The authors provide a quantitative estimate of the friction coefficient, cohesion and healing rates of a wide range of granular materials and attempts to find correlations of these parameters with the physical characteristics of the grains. I think the outcomes of this study represent an important contribution to the analog modelling community, as properties of materials used for experiments are crucial for similarity with the natural prototype. The manuscript is well written, but I have some suggestions that could improve paper structure and strengthen the importance of the findings. Overall, I recommend the paper to be accepted after revision.
Major comments:
- The paper is not clear about whether new tests were performed for this study or results from previous studies were used. Line 73-75 seems to state that new tests were conducted, but then lines 121-123 indicate that data were taken from previous studies and reanalysed. I believe you have conducted new measurements and reanalysed previous data, but this is an important point that should be clarified. In addition, Table 1 includes multiple references, but the legend in figure 3 only highlights data from Klinkmüller et al. (2016). Does this mean that data from the other papers cited in this table were not considered in this study?
- I would probably move section 3.3 Grain characteristics (and Figure 6) before the other results sections to give the reader an idea of the materials of this study and differences/similarities between them. I also think this would be helpful to more easily link grain and frictional properties. Another option could be to add a brief material section where all materials tested are introduced. This might also help clarifying what has been tested in this work and what has been reanalysed (see previous comment)
- It is not clear just by reading the paper how quality scores and weights were assigned and I think a brief explanation needs to be provided, especially to interpret Figure A1. In addition, I think Figure A1 should be moved to the main text because it shows correlations that are discussed in the section 4.2.
- The introduction section mentions the impact of healing time on the repeatability of the experiments, which is a crucial aspect for modellers working with analog materials. The introduction also mentions the impact of healing on models with erosion and sedimentation. I think these two points could be discussed more to strengthen the importance of the findings of this paper. This would be also of interest for modellers working with granular materials but not specifically on basin inversion.
Minor comments: see pdf
-
AC2: 'Reply on RC2', Michael Rudolf, 30 Jan 2023
Dear reviewers, we have considered your comments in the attached comment file. Since some of your questions and comments were very similar, they have been merged at the appropriate places. The roughest changes briefly summarized:
- Slight linguistic revision of the abstract.
- New chapter: 'Materials' partly with text and table from the previous version. This now describes in detail the materials and measurements made before and during this study.
- Better description of the particle properties, the determination and relevance of the quality score in 'Grain Characteristics'.
- Results for 'Grain Characteristics' moved to the beginning of the Results chapter.
- An error in the calculation of the weighting factors has been corrected. This has only a minor impact on the overall result.
- First chapter of the discussion slightly revised and a more general part (4.1.3) added. (former 4.1 and 4.4 are now together in 4.1.1 and 4.1.2).
- Added the stick-slip sand aspect from Utrecht for discussion.
- Figure A1 moved to main text and revised.
- Added another conclusion as a result of 4.1.3.
All comments on spelling, grammar, and placement of units have been addressed.
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-1178', Hanna Elston, 23 Dec 2022
The manuscript provides new and valuable information on the material and frictional properties of many granular materials that are frequently used in analog models to simulate crustal faulting processes. The findings presented in the manuscript will have a great value to the analogue modelling community. One major contribution of this study is that the authors define the grain characteristics and quantitatively estimate the friction coefficient, cohesion, and healing rates for a large set of granular materials. Rudolf et al. present a possible explanation for the general absence of fault reactivation during basin inversion models that has been observed in several previous studies that use granular materials. Furthermore, the authors provide new insight on the suitability of a set of granular materials for fault models that aim to explore basin inversion scenarios, fault healing processes, and more general faulting processes. I have a few suggestions that could strengthen the paper, but overall I recommend that the manuscript be accepted with revisions.
The methodology section could be strengthened in two ways: 1) Whether ring-shear tests were conducted for this study specifically or results from previous studies were reanalyzed for this study is not entirely clear. Lines 73-76 insinuate that the authors collected samples of 14 granular materials and conducted ring-shear and slide-hold-slide tests, however, lines 121-122 indicate that the ring-shear test data is taken from previous studies and reanalyzed for this study. I believe the results are from a combination of new and previous test, but a sentence either in the last paragraph of the introduction or early on in the methodology would clear up any potential confusion. 2) The method to assign grain characteristics or quality scores and associated uncertainties is unclear unless reading the background literature. A brief explanation of how quality scores are assigned and how precise the quality scores are would be helpful, especially when interpreting Figure A1 and the calculated correlation coefficients. Additionally, including some description of the correlation coefficients and comparisons between the quality scores and healing rates, friction coefficients, and cohesion would strengthen the methodology section.
The correlations, or lack thereof, between the quality scores and healing rates, friction coefficients, and cohesion are a key conclusion. The basis for this conclusion could be solidified if the authors address the following: 1) What is the reason to use Pearson and Spearman correlation coefficients for the comparisons between healing rate/friction/cohesion and the qualitative properties? 2) What is uncertainty for each quality score, and how does such uncertainty impact the correlation coefficients? In other words, how much weight should be placed in the correlation coefficients and p values? 3) Figure A1 supports the conclusion regarding the correlation between sphericity and healing rates and friction coefficients. As such, Figure A1 should be included in the main text.
The discussion section addresses many valid points relating to fault reactivation in basin inversion models. The findings of this manuscript may be more broadly applicable. More specifically, lines 382-389 include a key interpretation that is relevant to many analogue models. The authors introduce potential implications in the introduction that could be addressed in the discussion section to further emphasize the impact of the findings on a range of analogue models that use granular materials. Two examples of such discussion topics are 1) How could healing impact fault behavior within models with erosion/sedimentation that are stopped to remove/add material? and 2) How could consolidation and healing time impact repeatability?
Specific comments
Formatting/grammar: Some paragraphs have indentations, but others do not.
Add spaces between numbers and units (e.g., lines 186 and 187)
Add commas before ‘which’ (lines 16, 22, 42, 56, 116, 121, 133, 221, 235, 238, 245, 288, 307, 341)
6-7: By older faults do you mean faults that have been inactive longer? This sentence is not entirely clear.
29: Remove ‘e.g.’
40-42: Use of ‘it’ is slightly confusing. I presume you mean analogue models?
51: I would recommend citing Reber et al. 2020, which covered a range of analogue modelling benefits, applications, and material properties https://doi.org/10.1016/j.earscirev.2020.103107
112: Change ‘materials’ to ‘material’
116: Remove ‘and’ following ‘fault zone’
138: vl doesn’t seem to appear elsewhere. Maybe it doesn’t need a variable assigned.
208: Remove repeated ‘increase of hold time’
241-243: Complex sentence that could be clarified
267: Change ‘which’ to ‘and’ and remove ‘therefore’
296: Change ‘which’ to ‘that’
306: Insert comma after gray
359: Out of curiosity, would you expect that healing may have a larger role for materials that exhibit stick-slip behavior (e.g., Utrecht sand?)?
Results section: Reorganizing to present the grain characteristics first would provide context for how the different materials compare to one another, which could help the reader more readily digest the differences in healing rates and reactivation. This reorganization could also improve the flow from results to discussion.
Discussion section: Sections 4.1 and 4.4 are closely related and the reader could benefit from the two sections being next to each other or integrated.
Figure 3: Including a simple note on what the numbers next to the material name mean could add clarity. Indicating which materials were included in Klinkmüller et al., 2016 is a nice touch.
Figure 6: Very helpful
Figure A1: Needs a legend. It would be beneficial to include in the main text since the discussion relies on the correlations that the plots demonstrate.
Citation: https://doi.org/10.5194/egusphere-2022-1178-RC1 -
AC1: 'Reply on RC1', Michael Rudolf, 30 Jan 2023
Dear reviewers, we have considered your comments in the attached comment file. Since some of your questions and comments were very similar, they have been merged at the appropriate places. The roughest changes briefly summarized:
- Slight linguistic revision of the abstract.
- New chapter: 'Materials' partly with text and table from the previous version. This now describes in detail the materials and measurements made before and during this study.
- Better description of the particle properties, the determination and relevance of the quality score in 'Grain Characteristics'.
- Results for 'Grain Characteristics' moved to the beginning of the Results chapter.
- An error in the calculation of the weighting factors has been corrected. This has only a minor impact on the overall result.
- First chapter of the discussion slightly revised and a more general part (4.1.3) added. (former 4.1 and 4.4 are now together in 4.1.1 and 4.1.2).
- Added the stick-slip sand aspect from Utrecht for discussion.
- Figure A1 moved to main text and revised.
- Added another conclusion as a result of 4.1.3.
All comments on spelling, grammar, and placement of units have been addressed.
-
AC1: 'Reply on RC1', Michael Rudolf, 30 Jan 2023
-
RC2: 'Comment on egusphere-2022-1178', Anonymous Referee #2, 17 Jan 2023
This manuscript focuses on the time-dependent frictional properties of granular materials that are frequently used as analog in laboratory experiments to simulate the brittle behaviour of the crust. The authors provide a quantitative estimate of the friction coefficient, cohesion and healing rates of a wide range of granular materials and attempts to find correlations of these parameters with the physical characteristics of the grains. I think the outcomes of this study represent an important contribution to the analog modelling community, as properties of materials used for experiments are crucial for similarity with the natural prototype. The manuscript is well written, but I have some suggestions that could improve paper structure and strengthen the importance of the findings. Overall, I recommend the paper to be accepted after revision.
Major comments:
- The paper is not clear about whether new tests were performed for this study or results from previous studies were used. Line 73-75 seems to state that new tests were conducted, but then lines 121-123 indicate that data were taken from previous studies and reanalysed. I believe you have conducted new measurements and reanalysed previous data, but this is an important point that should be clarified. In addition, Table 1 includes multiple references, but the legend in figure 3 only highlights data from Klinkmüller et al. (2016). Does this mean that data from the other papers cited in this table were not considered in this study?
- I would probably move section 3.3 Grain characteristics (and Figure 6) before the other results sections to give the reader an idea of the materials of this study and differences/similarities between them. I also think this would be helpful to more easily link grain and frictional properties. Another option could be to add a brief material section where all materials tested are introduced. This might also help clarifying what has been tested in this work and what has been reanalysed (see previous comment)
- It is not clear just by reading the paper how quality scores and weights were assigned and I think a brief explanation needs to be provided, especially to interpret Figure A1. In addition, I think Figure A1 should be moved to the main text because it shows correlations that are discussed in the section 4.2.
- The introduction section mentions the impact of healing time on the repeatability of the experiments, which is a crucial aspect for modellers working with analog materials. The introduction also mentions the impact of healing on models with erosion and sedimentation. I think these two points could be discussed more to strengthen the importance of the findings of this paper. This would be also of interest for modellers working with granular materials but not specifically on basin inversion.
Minor comments: see pdf
-
AC2: 'Reply on RC2', Michael Rudolf, 30 Jan 2023
Dear reviewers, we have considered your comments in the attached comment file. Since some of your questions and comments were very similar, they have been merged at the appropriate places. The roughest changes briefly summarized:
- Slight linguistic revision of the abstract.
- New chapter: 'Materials' partly with text and table from the previous version. This now describes in detail the materials and measurements made before and during this study.
- Better description of the particle properties, the determination and relevance of the quality score in 'Grain Characteristics'.
- Results for 'Grain Characteristics' moved to the beginning of the Results chapter.
- An error in the calculation of the weighting factors has been corrected. This has only a minor impact on the overall result.
- First chapter of the discussion slightly revised and a more general part (4.1.3) added. (former 4.1 and 4.4 are now together in 4.1.1 and 4.1.2).
- Added the stick-slip sand aspect from Utrecht for discussion.
- Figure A1 moved to main text and revised.
- Added another conclusion as a result of 4.1.3.
All comments on spelling, grammar, and placement of units have been addressed.
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Michael Rudolf
Matthias Rosenau
Onno Oncken
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1580 KB) - Metadata XML