Influence of a Meandering Channel on the Threshold of Sediment

Round 1

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

This study examines how bed curvature affects sediment movement, which is important for river restoration projects, especially when the river is navigable. It is an interesting and useful study. Based on these studies, it is possible to forecast the movement of sediments, the places where entrainment and deposition of alluvial particles take place. Effective measures can be established to maintain the designed parameters of the beds, especially for navigation, respectively for ballast quarries. It is possible to estimate the places favorable for the extraction of sand and gravel from the riverbeds, i.e. the places where the respective deposits are restored quite quickly.

Author Response

We extend our heartfelt gratitude for your encouraging comment and support. Thank you for taking the time to review our manuscript.

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

An interesting, well done, and timely paper that looks at how river meanders influence sediment transport. The flume work appears sound and applicable to the study; I don't have the background/expertise to comment on the modeling/statistical section of the Results and Discussion. 

A couple of comments:

First, why were the depths of 13, 15, and 17 cm used?  I did not see any justification for using these depths and not a depth closer to the water surface. Some additional discussion would be helpful.

Second, the abstract notes that the results of the study could be informative for river restoration. The first sentence of the Conclusions section makes the same observation. But beyond this, there is no discussion as to how the findings could be used in river restoration. Would they be useful in determining channel patterns? Setting river curvature?  At least some linkage of the findings to the issues surrounding river restoration should be presented since the authors note river restoration at the outset of the paper. 

Author Response

First, why were the depths of 13, 15, and 17 cm used?  I did not see any justification for using these depths and not a depth closer to the water surface. Some additional discussion would be helpful.

Response by the authors: The depths of 13, 15, and 17 cm were selected for the experiments based on several practical considerations:

1. Flume Structure: The flume has a total height of 60 cm, with 30 cm covered by sediment particles and 10 cm reserved as freeboard (the distance from the water surface to the edge of the flume). This leaves a maximum water depth of 20 cm for experiments.
2. Equipment Constraints: The stand for the ADV (Acoustic Doppler Velocimeter) device had limitations that influenced the chosen depths.
3. Pump Capacity: Achieving larger water depths would require a higher flow rate to reach sediment movement threshold conditions, which was not feasible given the pump’s capacity.

Given these constraints, 13, 15, and 17 cm depths were deemed optimal for the study. Velocity data were collected throughout the water column, with particular attention to maintaining a 3 mm distance between points in the lower 20% near the bed and a 1 cm distance for the remaining 80% of the depth. Additionally, the choice of these depths aligns with the characteristics of shallow water in coarse-bed rivers commonly found in mountainous regions.

Second, the abstract notes that the results of the study could be informative for river restoration. The first sentence of the Conclusions section makes the same observation. But beyond this, there is no discussion as to how the findings could be used in river restoration. Would they be useful in determining channel patterns? Setting river curvature?  At least some linkage of the findings to the issues surrounding river restoration should be presented since the authors note river restoration at the outset of the paper. 

Response by the authors: River restoration projects indeed demand substantial budgets from governmental agencies, and a significant portion of these costs stem from managing sediment transport and altering river patterns. These changes can significantly impact river management and water supply policies at the watershed scale, sometimes leading to conflicts and social issues in urban and agricultural areas.

Our study offers practical insights into meander dynamics, which are crucial for river restoration efforts, particularly in stabilizing canals or rivers and improving water quality. Meanders naturally undergo lateral migrations due to erosion, causing shifts in their positions. These movements affect bed slope, canal width, radius of curvature, and flow patterns. By identifying sensitive points in meanders, restoration projects can implement measures like vegetation planting to stabilize banks and beds, thereby enhancing water quality.

Our findings on sediment movement at different bend angles provide valuable information for stabilizing riverbeds and banks. This knowledge contributes to the success of restoration projects by maintaining the health of aquatic ecosystems. We have added this discussion to the text to better link our findings with river restoration efforts.

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

Dear Authors,

this work is interesting and in line with the scope of the Journal but, in my opinion, not yet ready for publication.

I have major concerns regarding sections 2 and 3, as they are not well developed and need very major revision to both guarantee the reproducibility of the study and show its novelty when compared with the current literature.

I hope my comments will help you in better developing the manuscript, to have it eventually published.

 

Abstract

- please consider revising it to better clarify the key message and what approach you used, eventually citing some methods

- what do you mean by "The findings indicate that the interaction between the curved channel and incipient sediment motion affects the velocity distribution"? Is not the incipient motion which is affected by changes in velocity due to the channel curvature?

 

Introduction

- a more in-depth review of the state of the art is needed, as there are many works on incipient motion which are not considered here. Moreover, when revising past studies, a few additional details on the specific experimental conditions should be provided, as some of them are very different and the results could be not comparable

- the study goals, rationale and novelty could be better described

 

Material and Methods

- please add details on the lab facility (where is it located?)

- more details on both the experimental study and the MLR part should be provided, to allow other researchers to replicate your study

 

Results and Discussion

- I strongly advise separating this into two sections, presenting the study outcomes in the Results, and critically discussing them against the existing literature in the Discussion section

- line 262: please use the same nomenclature used in the subsections (Laboratory achievements & Statistical equation). You can also consider changing the naming of these subsections

- actually, there is almost no Discussion here. Results are properly presented, but a major effort should be made to critically compare them with existing studies and the large literature body on incipient motion (also in curved channels). A better-developed Discussion section is needed to show what is the novelty of this work, and what it adds to our knowledge of how bends drive sediments in open channel flow

 

Conclusions

- please revise this section to drive only key messages in a clear manner, eventually adding some comments on future steps needed to address the current study limitations (described, in detail, in the Discussion section)

 

Figures

- please provide figures of higher quality, in particular Fig. 1

- please check that you have the right to reproduce all figures. What about Fig. 1?

- Figures 2 and 3 could be combined

- please check the language in all figures (Figure 7 has a typo in the legend)

 

Text formatting

- please be consistent (why sometimes units are in italics, or with the first capital letter?)

Comments on the Quality of English Language

There are some typos along the manuscript, and a double-checking by a native English speaker could help in improving the readability.

Author Response

Abstract

- please consider revising it to better clarify the key message and what approach you used, eventually citing some methods

Response by the authors: We have revised the abstract to clarify the key message and describe the approach used, citing relevant methods.

Revised Abstract:

River meanders and channel curvatures play a significant role in sediment motion, making it crucial to predict incipient sediment motion for effective river restoration projects. This study utilizes an artificial intelligence method, Multiple Linear Regression (MLR), to investigate the impact of channel curvature on sediment incipient motion at a 180-degree bend. We analyzed 42 velocity profiles for flow depths of 13, 15, and 17 cm in a laboratory flume. The results indicate that the velocity distribution is influenced by the sediment movement threshold conditions due to channel curvature, creating a distinct convex shape based on the bend's position and flow characteristics. Reynolds stress distribution is concave in the upstream bend and convex in the downstream bend, underscoring the bend's impact on incipient motion. Bed Reynolds stress is highest in the first half of the bend (0 to 90 degrees) and lowest in the second half (90 to 180 degrees). The critical Shields parameter at the bend is approximately 8-61% lower than the values suggested by the Shields diagram, decreasing from 0.042 at the beginning to 0.016 at the end of the bend. Furthermore, our findings suggest that the MLR method does not significantly enhance the understanding of sediment movement, highlighting the need for a more comprehensive physical rationale and an expanded dataset for studying sediment dynamics in curved channels. Additional discussion on these findings can be found in the updated manuscript.

- what do you mean by "The findings indicate that the interaction between the curved channel and incipient sediment motion affects the velocity distribution"? Is not the incipient motion which is affected by changes in velocity due to the channel curvature?

Response by the authors: You are correct that the incipient motion is affected by changes in flow velocity due to channel curvature, and this interaction is indeed complex and bilateral. Our experiments indicate that both solid and moving velocities play distinct roles in flow structures. To clarify, the sentence has been revised. The revision highlights the dynamic interaction between flow velocity and sediment motion in curved channels.

Introduction

- a more in-depth review of the state of the art is needed, as there are many works on incipient motion which are not considered here. Moreover, when revising past studies, a few additional details on the specific experimental conditions should be provided, as some of them are very different and the results could be not comparable

Response by the authors: We agree that a more comprehensive review of the state of the art is essential, particularly given the numerous studies on incipient motion. We have revised our discussion to include additional details on past experimental conditions, recognizing that different results may not always be comparable.

Buffington and Montgomery (1997) emphasize a stochastic approach to incipient motion rather than a universal approach due to the variability in threshold conditions and behavior under similar flow conditions. While extensive research exists on sediment movement thresholds, there is limited focus specifically on curved channels. Most discussions have centered on sediment transport in bends, often neglecting the significance of studying sediment movement thresholds in these settings. This gap has necessitated the inclusion of studies conducted under different experimental conditions in our review.

We have expanded our literature review to provide a more comprehensive overview:

1. Mohtar et al. (2020): They modified the representation of the Shields parameter by incorporating turbulent strength, conducting experiments under steady, uniform flow conditions with eight sediment sizes varying in particle Reynolds numbers. Their findings indicate that turbulent fluctuations are crucial for predicting incipient sediment motion, showing a trend similar to the traditional Shields curve but with greater accuracy.
2. Khosravi et al. (2021): This study investigated hydraulic parameters related to incipient motion, comparing uniform and graded sediments as well as round and angular sediment types. Their experiments included rounded uniform bed sediments of various sizes, angular uniform sediment, and graded sediment. Results showed that angular sediment had a higher critical shear velocity for incipient motion than rounded sediment. Additionally, critical Shields stress and relative roughness increased with bed slope, while the particle Froude number decreased. Graded sediments demonstrated higher critical shear stress compared to finer uniform sediments, with finer fractions having higher particle Froude numbers and coarser fractions showing lower stability.
3. Dodangeh and Afzalimehr (2022): This study focused on the incipient motion of sediment particles under non-uniform flow conditions, emphasizing the impact of bed forms on flow dynamics and sediment transport. They challenged the traditional use of the Shields diagram based on uniform flow assumptions, highlighting the importance of considering pressure gradients in non-uniform flows. Their findings indicate that the Shields diagram underestimates particle motion in both laboratory and river settings, with bed forms, changes in river width, and flow non-uniformity playing significant roles. Differences in incipient motion were observed between accelerating and decelerating flows, with greater motion occurring in accelerating conditions.

We have incorporated these additional works and their findings into our manuscript to ensure a more thorough and comprehensive review of the state of the art.

- the study goals, rationale and novelty could be better described.

Response by the authors: We have revised the description of the study goals, rationale, and novelty to provide a clearer and more comprehensive overview.

Material and Methods

- please add details on the lab facility (where is it located?)

Response by the authors: In each profile, data collection is conducted at 3 mm intervals within the lower 20 percent of the water column depth, and at 10 mm intervals for the remaining 80 percent. The ADV used for data collection must be positioned so that its sensors are submerged in the water, with the initial measurement point typically set 60 mm below the water surface. In this study, the distance between the sampling volume and the transmitter is maintained at 50 mm, resulting in the final data point being located 53 mm above the bed. All measurements were conducted in the fully developed flow region, where the boundary layer depth is equal to the flow depth.

 

- more details on both the experimental study and the MLR part should be provided, to allow other researchers to replicate your study

Response by the authors: All necessary explanations are provided in the text. The MLR section was not expanded as it did not offer a practical or improved prediction for incipient motion based on the data collected in this study.  

Results and Discussion

- I strongly advise separating this into two sections, presenting the study outcomes in the Results, and critically discussing them against the existing literature in the Discussion section.

Response by the authors: The results have been separated from the discussion. The following discussion has been added to the revised manuscript:

Previous studies have predominantly focused on sediment incipient motion in straight river channels, with limited research on river bends. The flow structures in a river bend are influenced by sediment incipient motion, resulting in more complex processes due to secondary currents. As the river channel's plane changes, the spatial distribution of flow velocity varies, leading to changes in longitudinal and transverse flow velocities, and consequently, variations in hydraulic parameter estimations. To the authors' knowledge, no study has examined the incipient motion in a 180° bend considering turbulent flow structures, which hinders the comparison of this study's results with existing literature.

An examination of the vertical velocity profile reveals that central axis velocities have a small gradient in flow depth but point downward, creating strong vortices and placing the maximum velocity below the water's surface. The sediment movement and curved channel interaction affect Reynolds stress distribution, showing that the bend degree influences the secondary current's strength, leading to different patterns and locations of maximum velocity. When the maximum velocity tends towards the bed, the secondary currents become stronger in the bend, though this phenomenon is complex and requires extensive data and analysis.

Changes in velocity profiles affect the calculations of key hydraulic parameters, including the friction factor and Shields parameter. This suggests that applying a constant value for hydraulic parameters along a path may not yield accurate results or reasonable modeling. Bed shear stress results indicate that lower bed shear stress enhances the threshold condition. This experimental research allowed for the observation of complex flow separation and particle motion along the inner side of the curve. High turbulence in the separation zone causes particle movement, which depends on the pressure gradient and the sign of vorticity. Both factors can be calculated using velocity components in different flow directions, though accounting for vorticity in the critical Shields parameter is not currently feasible. Additionally, the Shields diagram requires modification to incorporate Reynolds stress distribution along a curved path. Applying Reynolds stress in incipient motion studies provides practical tools for designers and engineers in fluvial projects, allowing consideration of turbulent flow details rather than relying on average values in fluvial hydraulic models.

The bed shear stress, used in the numerator of the Shields parameter and particle Reynolds number in the Shields diagram, can only be estimated using statistical methods. However, the physical interpretation of this statistical analysis is performed using the momentum (Reynolds) equation. Before the bend apex, the flow experiences a favorable pressure gradient, showing no separation and a concave Reynolds stress distribution without inflection points in flow depth from the bed to the water surface. Conversely, after the apex, flow separation occurs in regions with an unfavorable pressure gradient, leading to a different Reynolds stress distribution. A strong pressure gradient can cause a stall, observed as a dead zone in the downstream part of the bend. These effects of instantaneous velocity fluctuations in 3D are reflected in the critical threshold condition, considering the turbulent flow structure analyzed by ADV in this study. Consequently, the critical Shields parameter is influenced by flow structures and the estimation of Reynolds stress, taking into account favorable or unfavorable pressure gradients in different curve regions.

Figure 6 shows that for the curved channel, Reynolds stress has a concave shape and lower bed shear stress compared to a straight path. The concave Reynolds stress distribution emphasizes that the bent channel accelerates incipient motion compared to the straight path with a mildly convex (quasi-linear) Reynolds stress distribution. Bed maximum Reynolds stress occurs in the bend's first half (0 to 90 degrees), while bed minimum Reynolds stress occurs in the second half (90 to 180 degrees). Therefore, more sediment transport is expected in the bend's second half with considered minimum Reynolds stresses for sediment incipient motion.

This study uses the Shields parameter for different angles on a 180-degree bend. The Shields parameter defines the particle movement threshold, assuming uniform flow conditions, which may not hold in bends with non-uniform flow conditions. Curved channels alter Reynolds stress distribution from linear to nonlinear shapes, potentially overestimating or underestimating bed shear stress. This study calculates bed shear stress for estimating the Shields parameter and particle Reynolds number. Different methods exist for shear stress calculation, but more investigation is needed to determine the best method for non-uniform flow conditions due to flow curvature. Many studies have applied the equation τ_0=γRS to compute shear stress, where R is the hydraulic radius and S is the energy slope. However, this method only works for uniform and straight channels with linear stress distribution. This research deals with non-uniform flow due to channel curvature, causing non-linear stress distribution. Therefore, this method is unsuitable. This study employs the Reynolds stress method to estimate channel bed shear stress from the Reynolds shear stress distribution (Figure 6), involving fitting a polynomial function to measured Reynolds stress profiles. The bed shear stress is the intersection point of the fitted curve and the bed on the Reynolds stress.

Using the Reynolds stress method, this study obtained Shields parameters ranging from 0.041 to 0.043 on the straight path, with particle Reynolds numbers up to 39. These values matched the Shields parameter of incipient motion in the Shields diagram, which assumes uniform flow conditions. For the 180-degree bend, the Shields parameter ranged from 0.018 to 0.041 for h = 13 cm, 0.013 to 0.042 for h = 15 cm, and 0.014 to 0.042 for h = 17 cm. This result showed that the Shields parameter was higher on the straight path than on the 180-degree bend, except for a few cases below the Shields curve (Figure 7). This indicated that bed sediment moved more easily on the bent path. The critical Shields parameter value on the bent path was about 8-61% lower than in the Shields diagram. Even though particles moved, the critical Shields parameter was below the Shields curve, suggesting that the Shields diagram overestimated the critical Shields parameter for flow on the 180-degree bend. This overestimation could result from various factors, such as flow non-uniformity in the bend, while the Shields diagram relies on uniform flow, or inappropriate shear stress determination methods. Lastly, the unrealistic estimation and agreement of the Shields parameter in the curved channel with the straight path was because this parameter did not include variables reflecting the curve path and lateral forces' effects. Therefore, a better estimation of sediment movement threshold conditions in curved channels would consider the convex Reynolds shear stress distribution effect, differing from the straight path's convex distribution. This study expects a lower critical Shields stress for 60 to 120 degrees than other angles, but the critical Shields parameter results do not clearly show the movement threshold conditions for the 180-degree bend.

- line 262: please use the same nomenclature used in the subsections (Laboratory achievements & Statistical equation). You can also consider changing the naming of these subsections

Response by the authors: Done.  

- actually, there is almost no Discussion here. Results are properly presented, but a major effort should be made to critically compare them with existing studies and the large literature body on incipient motion (also in curved channels). A better-developed Discussion section is needed to show what is the novelty of this work, and what it adds to our knowledge of how bends drive sediments in open channel flow.

Response by the authors: Please see the response to the previous comment.

Conclusions

- please revise this section to drive only key messages in a clear manner, eventually adding some comments on future steps needed to address the current study limitations (described, in detail, in the Discussion section)

Response by the authors: The Conclusions section is updated.

Figures

- please provide figures of higher quality, in particular Fig. 1

Response by the authors: Done.

- please check that you have the right to reproduce all figures. What about Fig. 1?

Response by the authors: Figure 1 has a reference and belongs to our research group.

- Figures 2 and 3 could be combined

Response by the authors: To maintain quality, both figures are being considered separately.

- please check the language in all figures (Figure 7 has a typo in the legend)

Response by the authors: Done.

Text formatting

- please be consistent (why sometimes units are in italics, or with the first capital letter?)

Response by the authors: Corrected.

Comments on the Quality of English Language:

There are some typos along the manuscript, and a double-checking by a native English speaker could help in improving the readability.

Response by the authors: The entire manuscript is re-checked and the English language is improved.

Round 2

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

Dear Authors,

thank you for having addressed my previous comments.

I still would like to see a more in-depth discussion of the results, where you critically compare your outcomes with the existing literature, to show where the novelty of your work is, and what other scholars can learn from it.

Figures should be improved.

Comments on the Quality of English Language

The language is rather fine, and some improvements could help in further improving the readability.

Author Response

Dear Authors,

Thank you for having addressed my previous comments.

I still would like to see a more in-depth discussion of the results, where you critically compare your outcomes with the existing literature, to show where the novelty of your work is, and what other scholars can learn from it.

Response by the authors:

Thank you for your valuable feedback and for acknowledging our previous revisions. We understand the importance of a more thorough discussion and critical comparison of our results with the existing literature to highlight the novelty and contributions of our work.

In our study, we have built upon several prior investigations into flow dynamics in 180° sharp bends.

For instance, Moghaddassi et al. (2021) examined a meandering channel with two consecutive 180-degree mild bends flanked by straight upstream and downstream reaches. They investigated the impact of varying mean velocity-to-critical velocity ratios at the upstream straight reach on bed topography variations along the meander. Additionally, they studied how the geometry of the upstream bend influenced bed topography in the downstream bend and how the downstream straight end affected the upstream bend. They discovered that variations in bed topography at the upstream bend indicate the downstream bend's influence on incipient motion conditions along this bend. Furthermore, they found that for each flow velocity to critical velocity ratio (U/Uc) at the upstream bend, the maximum scour occurred 5% of the channel width from the outer bank, within the 178 to 180-degree range. However, Moghaddassi et al. (2021) did not examine turbulent flow structures, including 3D velocity components, Reynolds normal stress, and Reynolds shear stress, nor did they discuss the limitations of the Shields parameter.

 

Akbari and Vaghefi (2017) reported that in a 180° sharp bend, the secondary flow strength and the size of the vortex formed from the beginning to the bend apex increased. They also determined the average horizontal angle of the streamlines, as well as the vector and locus of maximum velocity at different levels. However, they did not discuss turbulent flow characteristics or 3D Reynolds stresses.

 

Vaghefi et al. (2016) investigated the influence of streamline variations, maximum velocity distribution, and secondary flow strength on bed shear stress distribution along a 180-degree sharp bend in a laboratory setting. They reported that maximum secondary flow strength occurred in the second half of the bend. They evaluated bed shear stress distribution using the TKE, modified TKE, and Reynolds methods within the turbulent boundary layer. Additionally, they found that maximum shear stress occurred from the entrance of the bend to the bend apex near the inner wall. They observed that maximum shear stress in the lower layer shifted from the 40-degree cross-section to the 60-degree cross-section in the upper layer. However, they did not present any patterns for Reynolds stress distribution or its application for determining the Shields parameter and predicting incipient motion.

 

Graf and Blanckaert (2002) reported that the magnitude and distribution of normal stresses and turbulent kinetic energy are concentrated over the thalweg, with the magnitude increasing through the first half of the bend. The streamwise-cross-stream and cross-stream vertical Reynolds stresses increase as the flow moves through the bend, while the streamwise vertical stresses near the bank become less dominant. Additionally, it was found that the magnitudes of streamwise-cross-stream stresses at the outer bank are relatively high compared to other stresses.  

 

Barman et al. (2022) stated that despite many years of research, the structure of turbulence in meander bends remains unclear. They suggested that future work should focus on accurately measuring the fluid stresses exerted on the adjacent boundaries in meander bends.

Additionally, the following paragraph is added at the end of the Conclusions:

The novelty of the present study lies in examining the effect of 3D turbulent flow structures on sediment thresholds at various bend angles and highlighting the limitations of the Shields diagram in accurately predicting sediment movement along a bend. This study provides valuable insights for effectively stabilizing riverbeds and banks, thereby contributing to the success of restoration projects and the health of aquatic ecosystems.

 

Figures should be improved.

Response by the authors:

The figures are enhanced as much as we could.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript contains an experimental study on the prediction of the incipient movement of sediments in curved channels. The experimental study investigates how channel curvature affects the incipient motion of sediment at a 180-degree bend, as well as a comparative analysis regarding the values of the Shields and Reynolds parameters with the existing diagram in the literature.

The study brings new contributions to these types of analyses. The manuscript is relatively well structured (4 Sections), a number of 21 pages, with a documentation including a number of 31 references. I think it would be appropriate to expand this documentation by presenting more details regarding similar studies existing in the literature.

However, I have the following major observations:

1) The analysis, like all investigations in the laboratory, remains a purely theoretical one, the results of which must be verified with results obtained on concrete case studies in the field. Why wasn't a case study chosen to verify (at least partially) these results?

2) The analysis had to be extended using numerical simulations based on the digital model of the land related to a chosen case study with a sinuosity close to the laboratory model. The current programs allow, with minimal effort, the performance of numerical simulations with an extended range of hypotheses.

Reviewer 2 Report

Comments and Suggestions for Authors

 

This paper presents an experimental study of Shields diagram in curved channels. This study attempts to find a more accurate way to evaluate the critical Shields parameter under the curvature effects. Detailed data analysis, including multivariate polynomial regression (MPR), was provided. However, due to the lacks of data, the equations using MLR may not be representative and thus not practical, and they are statistically meaningful but not physically. This paper raised a good question on Shields diagram for curved channels, but failed to provide effective solutions. Considering its current status, this paper is not publishable. The detailed comments and suggestions are listed as follows:

 

1.     Shields diagram is classic and important in sediment transport studies, because it is capable of predicting the sediment incipient motions. It has been widely used in sediment transport modeling in morpho-dynamics, local scours, etc. There are many studies on modifying the original Shields diagram to make it applicable to wider ranges.

a.      In Fig. 3, was the original Shields diagram or the modified one shown?

b.     In Fig. 7, was the original Shields curve compared to the measurements? If yes, please try to compare to some modified Shields diagrams in the literature. If no, please indicate which modified Shields diagram was used.

c.      Please plot the current results against the whole Shields diagram to get a global view of the current study.

2.     Curvature effects in channel bends are generally not negligible. In such case, in practice the direction of bed load movement is corrected by considering the helical flow and gravity effects.

3.      The Shields diagram includes two variables, critical shear number (related to critical shear stress) and critical shear Reynolds number (related to shear velocity). For a given sediment size, iteration is needed to obtain the critical shear stress. However, explicit approximations of Shields diagram using shear number and nondimensional particle size or Reynolds number were proposed by researchers to make it convenient to use in practice to explicitly estimate the critical shear stress. For this study, such approximation is expected rather than the MLR analysis, because it is physically much more meaningful.

4.     The Shields diagram does not include any variable considering curve path and lateral flow effects, so does the proposed equations, although those equations were obtained using the measured data in the bend channel. Those equations are statistically meaningful but not physically.

5.     Others:

(1)   The paragraph from line 255 to 259 is a repetition of the on from 249 to 253. Please remove it.

(2)   At line 266, please remove “(“.