the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 May 2023
Geotechnical controls on erodibility in fluvial impact erosion
Abstract. Bedrock incision by rivers is commonly driven by the impacts of moving bedload particles. The speed of incision is modulated by rock properties, which is quantified within a parameter known as erodibility that scales the erosion rate to the erosive action of the flow. Although basic models for the geotechnical controls on rock erodibility have been suggested, large scatter and trends in the remaining relationships indicate that they are incompletely understood. Here, we conducted dedicated laboratory experiments measuring erodibility using erosion mills. In parallel, we measured compressive strength, tensile strength, Young’s modulus, bulk density and the Poisson ratio for the tested lithologies. We find that under the same flow conditions, erosion rates of samples from the same lithology can vary by a factor of up to sixty. This indicates that rock properties that may vary over short distances within the same rock can exert a strong control on its erosional properties. The geotechnical properties of the tested lithologies are strongly cross-correlated, preventing a purely empirical determination of their controls on erodibility. The currently prevailing model predicts that erosion rates should scale linearly with Young’s modulus and inversely with the square of the tensile strength. We extend this model using first-principle physical arguments, taking into account the geotechnical properties of the impactor. The extended model provides a better description of the data than the existing model. Yet, the fit is far from satisfactory. We suggest that the ratio of mineral grain size to the impactor diameter present a strong control on erodibility that has not been quantified so far. We also discuss how our laboratory results upscale to real landscapes and long timescales. For both a revised stream power incision model and a sediment-flux-dependent incision model, we suggest that long-term erosion rates scale linear with erodibility and that, within this theoretical framework, relative laboratory measurements of erodibility can be applied at the landscape scale.
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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
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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.
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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-2023-76', Anonymous Referee #1, 29 May 2023
The submitted manuscript presents a study designed to explore the controls on rock erodibility. The manuscript is interesting and well written. I recommend publication after the following minor comments have been considered.
Line 12: "uniaxial compressive strength"
Line 13: "Poisson's ratio"
Line 21: "presents"
Line 93: So, these discs were 191 to 193 mm in diameter? Perhaps this should be stated here?
Line 95: What lithology is the Passwang Formation? Perhaps this should be stated here?
Line 104: The samples were dried following preparation? If so, how were they dried?
Line 136: What does LDPE stand for?
Line 137: How was trapped air removed exactly? Typically, fully saturating samples in the laboratory requires a vacuum pump. How are the authors sure that their samples were completely saturated?
Line 141: What type of glass were the beads made from? What was the diameter of the glass beads? They are spherical?
Line 149: Did any material spall from the samples during rinsing? Was this material collected?
Line 161: This sentence suggests that bulk sample density was measured using an MTS load frame. Reword?
Line 164: I think it's important to clearly state, if true, that these measurements were performed on dry samples. The strength of rock is typically lower when saturated with water. Since this "water-weakening" varies from rock type to rock type, it could explain some of the scatter in the experimental data (since the erosion tests are performed on wet rock and the petrophysical parameters are measured on dry rock).
Line 165: I assume this is the dry bulk density? How did the authors dry their samples prior to the measurement of dry mass?
Line 172: By "conversion rate", do the authors mean "displacement rate"? Can the authors also quote the strain rate here too? How was the displacement measured?
Line 174: Surely this is the stress, not the pressure? Unless the authors are talking about the pressure inside the piston that is used to calculate the force, which is in turn used to calculate the stress using the sample radius?
Line 176: Why would you use a constant force? Do the authors mean a constant force rate?
Line 177: By "convergence speed", do the authors mean "displacement rate"?
Line 178: "before fracture" is ambiguous. The authors mean the maximum force obtained immediately prior to the formation of the tensile fracture?
Line 181: The authors are sure that the behaviour is elastic at 50% of the UCS in all the experiments?
Line 182: "Poisson's ratio"
Line 188: The authors are sure that the behaviour is elastic at 50% of the UCS in all the experiments?
Line 212: What about bedding orientation? Did this influence the erosion rate?
Line 244: Poisson's ratio and UCS do not look particularly correlated (Figure 5d).
Figure 5: "Poisson's ratio"
Figure 5: Why were these cross-plots chosen? I'm not suggesting that the authors should plot every combination, but why do the authors only show how tensile strength, Young's modulus, Poisson's ratio, and density vary as a function of UCS?
Line 245: Can the authors explain Kendall's rank coefficient? How is this calculated?
Line 259: How can the authors explain the large differences in erosion rates between samples cut from the same core (e.g., the data on Figure 4a)? This cannot be explained by differences in grain size etc.
Figure 7: These data were collected using the same (similar) impactor material and geometry (shape and diameter)? If not, is it not useful to state these parameters in the figure caption?
Line 265: Tensile strength can also be influenced by pore size and shape, as shown in Heap et al. (2021). Although this study focusses on volcanic rocks, the modelling results are relevant for other rock types, such as porous sedimentary rocks.
Heap, M. J., Wadsworth, F. B., Heng, Z., Xu, T., Griffiths, L., Velasco, A. A., ... & Deegan, F. M. (2021). The tensile strength of volcanic rocks: Experiments and models. Journal of Volcanology and Geothermal Research, 418, 107348.Line 269: If the impactor type/size is important, I think this information should be provided in the figure caption for each of the datasets.
Line 276: Perhaps the authors should/could cite a few papers here that have previously demonstrated these relationships for rocks?
Line 302: The "elastic modulus" is the Young's modulus?
Line 308: This constant does not therefore depend on rock type or rock properties? This has been previously demonstrated?
Figure 9: Do these plots show the same experimental erosion rate data?
Line 355 and elsewhere: The authors often refer to a "linear fit", which is actually a power law. Is this not misleading?
Line 363: Also pore size and shape.
Line 383: Unless I'm mistaken, I don't think the size of the impactors (the glass beads) used in this study is stated in the manuscript. Surely, based on this paragraph, it's very important for future studies to clearly state the impactor size?
Citation: https://doi.org/10.5194/egusphere-2023-76-RC1 -
CC1: 'Comment on egusphere-2023-76: data publication', Gunnar Pruß, 08 Jun 2023
We are unfortunately experiencing some delays with the cited data publication, i.e. Pruß et al. (2023). The given URL is not active yet, but a preview version of the data can be found here:
https://dataservices.gfz-potsdam.de/panmetaworks/review/25c25d36f66d2c9723f58def1c2cccfaa260d58e9fd13df9c490f6c8ba28f118/
Citation: https://doi.org/10.5194/egusphere-2023-76-CC1 -
RC2: 'Comment on egusphere-2023-76', Anonymous Referee #2, 12 Jun 2023
Summary:
This is very impressive work on the experiments of the controls of rock properties on erosion rate. I suggest major revision. I have two major comments. 1) there needs to be much more details on the results. Currently the results section is so short, especially, when it comes to the interesting results of figure 5 and 6, there is less than 100 words! The authors choose different rock types, and different rock from the same sample for this impressive experiment. They have so much information that is missing here. 2) The discussion section can go much deeper, and there is a disconnection between results and discussion. The authors test different rock types, and found the erosion rate vary a lot. The discussion should focus on explaining the variation of results and the implications. With the new two theories, the authors can apply two theories to the results, and try to explain the scatter more specifically and carefully, rather than just saying there is a better trend or the theory probably works better with no proof. Also without a solid theory or solid explanation, expanding the results to bedrock rivers is a big stretch.
Individual Comments:
- Line 35-36: “In the field,..., poor exposure”, this is a confusing sentence, something is missing here.
- I found it was difficult to interpret the results shown in Table 1, Figure 3 and Figure 4. The axis of Figure 3 tells me nothing about the rock, I have to go back to Table 1 for every sample id and unit id. The authors decided to used locations as IDs of individual rocks, but as a reader, I am more interested in results from different rock types, rather than different locations. I suggest to use rock type as a primary id, and location and others as a secondary one, to differentiate them.
- Line 141-145, how much is the glass bead abrasion and what is the difference of glass bead abrasion for weaker and harder rock? For a harder rock, more glass bead will probably be eroded, while not much for a weaker rock. Also more time is ran, more glass beads can be eroded. Given that the experiments use different rock types and run time, it is expected there will be different amount of glass beads that got eroded. If the glass bead gets eroded a lot, it will directly influence the erosion rates on the rock, which means the erosion rate is not solely controlled by rock properties here. The authors need to add more information here, and also potentially in the discussion since impactor properties influence kζa (Sklar and Dietrich, 2004).
- Line 140-150. I am confused with the experimental runs. “For each experiment two independent bead sets of 150 g each were prepared to run in alternation.”, so this means each experiment has more than 1 run? Then “Run duration was set depending on the erosion rates to between 4 hrs and 52 days to achieve a total mass loss of 1 - 10 g”, this means only one run? And “To keep track of bead abrasion, after each run the bead set was oven-dried for 24 hours at 40°C”, after how much time? Between 4 hrs and 52 days?
- Line 209. I cannot see how figure 5 give uncertainties, figure 5 shows rock properties, not erosion rates.
- Line 241-245, “All measured rock geotechnical properties are correlated,” it seems all properties correlate with compressive strength based on figure 5, rather than they are all correlated.
- Figure 5 and 6 are the key results, but are only written in very short two sentences, less than 100 words! I highly suggest the authors to go into more details and guide the readers to the interesting results. For example, how erosion rate correlates with compressive strength, what is the best fit relation, and what is the comparison of each correlation.
- Line 256-259, again, key results, but are difficult to get from the current use of ids.
- Figure 8, what value of rock resistance coefficient kζa is used here? And how did you choose the value? Is it possible that the remaining trends with compressive strength, tensile strength, Young’s modulus, and density are due to kζa, especially when kζa captures controls on erodibility (e.g., Turowski et al., 2013; Auel et al., 2015) and also the glass beads (Sklar and Dietrich, 2004)?
- Line 340, why “It is related to f by the square of Poisson’s ratio ν”? There needs more explanation and references.
- Equation 3, there is kζa, but equation 11, there is 𝑘𝜁. Are they the same, if not, what values?
- Equation 7. I am confused here. In equation 4, you use f, but how does it change into fc in equation 7 when you use equation 4 to get equation 7. So if it is supposed to be fc in equation 7, all the equations after equation 7 and the results are supposed to change correspondingly.
- Line 361-364, there is a strange conclusion. The experiment already measure a lot of properties, and the lack of fit is not because of the lack of measurements, but the lack of theory. Regardless how many things you measure, without a good theory, no one knows what to measure and to fit, not to mention how to fit.
- Line 368-369, Why is assumed to scale with impactor size? What is the reference?
- Line 369-370, what is the reasoning and reference of this assumption?
- It is a bummer that the paper stopped here, when readers go through the paper, find the current fit is not good, and think there is a better way, but do not have any idea of how better this will be. I suggest to connect this to the results of this paper in some way, and give a discussion of how this will explain the scatter in the current theory.
- Due to the lack of good explanation and good fit of the results, it seems too much to apply them to natural bedrock rivers and other erosional processes in Section 4.3 and 4.4. Also the authors state that they can be applied to natural systems, but there are no indirect or direct measurements to support that. I suggest to cut sections 4.3 and 4.4, or shorten into one section. At the same time, I suggest to expand on section 4.2, focusing on using the current theory to explain the trend and scatter more specifically and carefully, and the new two theory to guide reads to understand and to explain the results, from the same rock type and the different rock types.
Citation: https://doi.org/10.5194/egusphere-2023-76-RC2 -
EC1: 'Comment on egusphere-2023-76', Tom Coulthard, 13 Jun 2023
Dear Authors,
We now have two reviews on your MS and whilst the discussion remains open for some more days there will be no more reviews, so you may start working on your response and revisions if you wish,
All the best
Tom Coulthard
Citation: https://doi.org/10.5194/egusphere-2023-76-EC1 - AC1: 'Reply to comments, egusphere-2023-76', Jens Turowski, 07 Aug 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-76', Anonymous Referee #1, 29 May 2023
The submitted manuscript presents a study designed to explore the controls on rock erodibility. The manuscript is interesting and well written. I recommend publication after the following minor comments have been considered.
Line 12: "uniaxial compressive strength"
Line 13: "Poisson's ratio"
Line 21: "presents"
Line 93: So, these discs were 191 to 193 mm in diameter? Perhaps this should be stated here?
Line 95: What lithology is the Passwang Formation? Perhaps this should be stated here?
Line 104: The samples were dried following preparation? If so, how were they dried?
Line 136: What does LDPE stand for?
Line 137: How was trapped air removed exactly? Typically, fully saturating samples in the laboratory requires a vacuum pump. How are the authors sure that their samples were completely saturated?
Line 141: What type of glass were the beads made from? What was the diameter of the glass beads? They are spherical?
Line 149: Did any material spall from the samples during rinsing? Was this material collected?
Line 161: This sentence suggests that bulk sample density was measured using an MTS load frame. Reword?
Line 164: I think it's important to clearly state, if true, that these measurements were performed on dry samples. The strength of rock is typically lower when saturated with water. Since this "water-weakening" varies from rock type to rock type, it could explain some of the scatter in the experimental data (since the erosion tests are performed on wet rock and the petrophysical parameters are measured on dry rock).
Line 165: I assume this is the dry bulk density? How did the authors dry their samples prior to the measurement of dry mass?
Line 172: By "conversion rate", do the authors mean "displacement rate"? Can the authors also quote the strain rate here too? How was the displacement measured?
Line 174: Surely this is the stress, not the pressure? Unless the authors are talking about the pressure inside the piston that is used to calculate the force, which is in turn used to calculate the stress using the sample radius?
Line 176: Why would you use a constant force? Do the authors mean a constant force rate?
Line 177: By "convergence speed", do the authors mean "displacement rate"?
Line 178: "before fracture" is ambiguous. The authors mean the maximum force obtained immediately prior to the formation of the tensile fracture?
Line 181: The authors are sure that the behaviour is elastic at 50% of the UCS in all the experiments?
Line 182: "Poisson's ratio"
Line 188: The authors are sure that the behaviour is elastic at 50% of the UCS in all the experiments?
Line 212: What about bedding orientation? Did this influence the erosion rate?
Line 244: Poisson's ratio and UCS do not look particularly correlated (Figure 5d).
Figure 5: "Poisson's ratio"
Figure 5: Why were these cross-plots chosen? I'm not suggesting that the authors should plot every combination, but why do the authors only show how tensile strength, Young's modulus, Poisson's ratio, and density vary as a function of UCS?
Line 245: Can the authors explain Kendall's rank coefficient? How is this calculated?
Line 259: How can the authors explain the large differences in erosion rates between samples cut from the same core (e.g., the data on Figure 4a)? This cannot be explained by differences in grain size etc.
Figure 7: These data were collected using the same (similar) impactor material and geometry (shape and diameter)? If not, is it not useful to state these parameters in the figure caption?
Line 265: Tensile strength can also be influenced by pore size and shape, as shown in Heap et al. (2021). Although this study focusses on volcanic rocks, the modelling results are relevant for other rock types, such as porous sedimentary rocks.
Heap, M. J., Wadsworth, F. B., Heng, Z., Xu, T., Griffiths, L., Velasco, A. A., ... & Deegan, F. M. (2021). The tensile strength of volcanic rocks: Experiments and models. Journal of Volcanology and Geothermal Research, 418, 107348.Line 269: If the impactor type/size is important, I think this information should be provided in the figure caption for each of the datasets.
Line 276: Perhaps the authors should/could cite a few papers here that have previously demonstrated these relationships for rocks?
Line 302: The "elastic modulus" is the Young's modulus?
Line 308: This constant does not therefore depend on rock type or rock properties? This has been previously demonstrated?
Figure 9: Do these plots show the same experimental erosion rate data?
Line 355 and elsewhere: The authors often refer to a "linear fit", which is actually a power law. Is this not misleading?
Line 363: Also pore size and shape.
Line 383: Unless I'm mistaken, I don't think the size of the impactors (the glass beads) used in this study is stated in the manuscript. Surely, based on this paragraph, it's very important for future studies to clearly state the impactor size?
Citation: https://doi.org/10.5194/egusphere-2023-76-RC1 -
CC1: 'Comment on egusphere-2023-76: data publication', Gunnar Pruß, 08 Jun 2023
We are unfortunately experiencing some delays with the cited data publication, i.e. Pruß et al. (2023). The given URL is not active yet, but a preview version of the data can be found here:
https://dataservices.gfz-potsdam.de/panmetaworks/review/25c25d36f66d2c9723f58def1c2cccfaa260d58e9fd13df9c490f6c8ba28f118/
Citation: https://doi.org/10.5194/egusphere-2023-76-CC1 -
RC2: 'Comment on egusphere-2023-76', Anonymous Referee #2, 12 Jun 2023
Summary:
This is very impressive work on the experiments of the controls of rock properties on erosion rate. I suggest major revision. I have two major comments. 1) there needs to be much more details on the results. Currently the results section is so short, especially, when it comes to the interesting results of figure 5 and 6, there is less than 100 words! The authors choose different rock types, and different rock from the same sample for this impressive experiment. They have so much information that is missing here. 2) The discussion section can go much deeper, and there is a disconnection between results and discussion. The authors test different rock types, and found the erosion rate vary a lot. The discussion should focus on explaining the variation of results and the implications. With the new two theories, the authors can apply two theories to the results, and try to explain the scatter more specifically and carefully, rather than just saying there is a better trend or the theory probably works better with no proof. Also without a solid theory or solid explanation, expanding the results to bedrock rivers is a big stretch.
Individual Comments:
- Line 35-36: “In the field,..., poor exposure”, this is a confusing sentence, something is missing here.
- I found it was difficult to interpret the results shown in Table 1, Figure 3 and Figure 4. The axis of Figure 3 tells me nothing about the rock, I have to go back to Table 1 for every sample id and unit id. The authors decided to used locations as IDs of individual rocks, but as a reader, I am more interested in results from different rock types, rather than different locations. I suggest to use rock type as a primary id, and location and others as a secondary one, to differentiate them.
- Line 141-145, how much is the glass bead abrasion and what is the difference of glass bead abrasion for weaker and harder rock? For a harder rock, more glass bead will probably be eroded, while not much for a weaker rock. Also more time is ran, more glass beads can be eroded. Given that the experiments use different rock types and run time, it is expected there will be different amount of glass beads that got eroded. If the glass bead gets eroded a lot, it will directly influence the erosion rates on the rock, which means the erosion rate is not solely controlled by rock properties here. The authors need to add more information here, and also potentially in the discussion since impactor properties influence kζa (Sklar and Dietrich, 2004).
- Line 140-150. I am confused with the experimental runs. “For each experiment two independent bead sets of 150 g each were prepared to run in alternation.”, so this means each experiment has more than 1 run? Then “Run duration was set depending on the erosion rates to between 4 hrs and 52 days to achieve a total mass loss of 1 - 10 g”, this means only one run? And “To keep track of bead abrasion, after each run the bead set was oven-dried for 24 hours at 40°C”, after how much time? Between 4 hrs and 52 days?
- Line 209. I cannot see how figure 5 give uncertainties, figure 5 shows rock properties, not erosion rates.
- Line 241-245, “All measured rock geotechnical properties are correlated,” it seems all properties correlate with compressive strength based on figure 5, rather than they are all correlated.
- Figure 5 and 6 are the key results, but are only written in very short two sentences, less than 100 words! I highly suggest the authors to go into more details and guide the readers to the interesting results. For example, how erosion rate correlates with compressive strength, what is the best fit relation, and what is the comparison of each correlation.
- Line 256-259, again, key results, but are difficult to get from the current use of ids.
- Figure 8, what value of rock resistance coefficient kζa is used here? And how did you choose the value? Is it possible that the remaining trends with compressive strength, tensile strength, Young’s modulus, and density are due to kζa, especially when kζa captures controls on erodibility (e.g., Turowski et al., 2013; Auel et al., 2015) and also the glass beads (Sklar and Dietrich, 2004)?
- Line 340, why “It is related to f by the square of Poisson’s ratio ν”? There needs more explanation and references.
- Equation 3, there is kζa, but equation 11, there is 𝑘𝜁. Are they the same, if not, what values?
- Equation 7. I am confused here. In equation 4, you use f, but how does it change into fc in equation 7 when you use equation 4 to get equation 7. So if it is supposed to be fc in equation 7, all the equations after equation 7 and the results are supposed to change correspondingly.
- Line 361-364, there is a strange conclusion. The experiment already measure a lot of properties, and the lack of fit is not because of the lack of measurements, but the lack of theory. Regardless how many things you measure, without a good theory, no one knows what to measure and to fit, not to mention how to fit.
- Line 368-369, Why is assumed to scale with impactor size? What is the reference?
- Line 369-370, what is the reasoning and reference of this assumption?
- It is a bummer that the paper stopped here, when readers go through the paper, find the current fit is not good, and think there is a better way, but do not have any idea of how better this will be. I suggest to connect this to the results of this paper in some way, and give a discussion of how this will explain the scatter in the current theory.
- Due to the lack of good explanation and good fit of the results, it seems too much to apply them to natural bedrock rivers and other erosional processes in Section 4.3 and 4.4. Also the authors state that they can be applied to natural systems, but there are no indirect or direct measurements to support that. I suggest to cut sections 4.3 and 4.4, or shorten into one section. At the same time, I suggest to expand on section 4.2, focusing on using the current theory to explain the trend and scatter more specifically and carefully, and the new two theory to guide reads to understand and to explain the results, from the same rock type and the different rock types.
Citation: https://doi.org/10.5194/egusphere-2023-76-RC2 -
EC1: 'Comment on egusphere-2023-76', Tom Coulthard, 13 Jun 2023
Dear Authors,
We now have two reviews on your MS and whilst the discussion remains open for some more days there will be no more reviews, so you may start working on your response and revisions if you wish,
All the best
Tom Coulthard
Citation: https://doi.org/10.5194/egusphere-2023-76-EC1 - AC1: 'Reply to comments, egusphere-2023-76', Jens Turowski, 07 Aug 2023
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Jens Martin Turowski
Gunnar Pruß
Anne Voigtländer
Andreas Ludwig
Angela Landgraf
Florian Kober
Audrey Bonnelye
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1481 KB) - Metadata XML