Refined Simulation Study on the Effect of Scour Environments on Local Scour of Tandem Bridge Piers
Armin Tabandeh
Round 1
Reviewer 1 Report
This paper presents numerical simulations of scoring of tandem combination of piers under two different conditions: open-flow and ice-covered based environments. Throughout the simulations, it is shown that for the ice-covered case local scouring contributes to the total scouring of the submerged pier. The latter has been found to increases the depth and range of the local scouring hole. Also, it is concluded that interactions of turbulent eddies and shear stress on the pier side is the main dynamic mechanism of the scouring generated around the pier. The paper is interesting, well written, and the research is novel. The take-home message of the paper and its application are well described in the abstract. I recommend this paper for publication after a minor revision is done. My comments are listed below.
1- A statement addressing the present gap should be added to last paragraph of Introduction.
2- The structure of the paper needs to be added to the end of Intro Section.
3- One or two statements describing the fluid flow assumptions are welcome. E.g. fluid is assumed to be Newtonian, incopressible, etc.
4- The use of turbulence models in different problems dealing with energetic water flow is highly important and has been the topic of a great number of studies and has received attention of researchers over last decade, as discussed by Tavakoli et al. (2023). I would like to ask authors to add this reference (Tavakoli et al. (2023)) to sub-section 2.1.2 as it provides a strong relevant for their work.
Tavakoli S, Khojasteh D, Haghani M, Hirdaris S, A review on the progress and research directions of ocean engineering, Ocean Engineering, 272, 113617
5- The reason for choosing the dimension of the numerical domain needs to be explained.
6- Figure 13 presents one of the most interesting parts of this paper. Has such behavior been observed by any researcher before? If yet, you can mention it.
7- One statement deserting the application of the present research in environmental and engineering aspects can be added to conclusions (like what is explained in Abstract).
8- Please add the future to the paper.
Author Response
Response to Reviewer 1 Comments
Point 1: A statement addressing the present gap should be added to last paragraph of Introduction.
Response 1: Thank you very much for your recognition of our manuscript. We have added a statement to address the present gap in line 77 of the introduction based on your suggestion, which reads "There is a lack of numerical simulation studies on bridge pier scour applicable to ice cover environment, and the simulation results of this paper are good and can supplement the research gaps in related fields".
Point 2: The structure of the paper needs to be added to the end of Intro Section.
Response 2: Based on your suggestion, we have added the structure of the paper at the end of the introduction section, which reads "The remainder of this article is structured as follows: Section 2 presents the types of architectures of the studied numerical model; Section 3 presents the validation of the applicability of the model; Section 4 presents the analysis of the studied characteristic quantities, which are further discussed in Section 5. Finally, the conclusions stemming from this study are presented". Thank you again for your valuable suggestion, which has improved the quality of our manuscript.
Point 3: One or two statements describing the fluid flow assumptions are welcome. E.g. fluid is assumed to be Newtonian, incompressible, etc.
Response 3: Thanks to your kind suggestion, we have revised the manuscript accordingly by describing the statement of fluid flow assumptions in Section 2.1.1, line 99, as "The hydrodynamic calculations use the continuity equations for incompressible Newtonian fluids based on the Sabbagh-Yazdi assumptions as well as the equations of motion, both of which confine the flow motion".
Point 4: The use of turbulence models in different problems dealing with energetic water flow is highly important and has been the topic of a great number of studies and has received attention of researchers over last decade, as discussed by Tavakoli et al. (2023). I would like to ask authors to add this reference (Tavakoli et al. (2023)) to sub-section 2.1.2 as it provides a strong relevant for their work.
Response 4: As you mentioned, the use of turbulence models in different problems dealing with energetic water flow is highly important and has been the topic of a great number of studies, and the work of Tavakoli et al. provides strong relevance for our manuscript, and we have added the reference (Tavakoli et al. (2023)) to subsection 2.1.2, line 132, citation number 22. Thank you for your suggestion.
Point 5: The reason for choosing the dimension of the numerical domain needs to be explained.
Response 5: The numerical model in this paper is constructed according to the same dimensions as the physical model, drawing on the modeling method of Farooq [36] (line 284), considering that the maximum possible scour depth of the bridge pier is 2.4 times the diameter of the pier, so the height of the bed sand domain is set to 21 cm; in order to avoid the influence of the water depth on the local scour depth, the ratio of the pier diameter to the water depth should be less than 0.7, so the height of water domain is set to 21 cm; ice cover domain is set to 3 cm according to the average thickness of actual ice cover in the field; the final overall geometric model was divided into computational domains based on the hierarchical architecture, where the bed sand domain z = -21~0 cm, the water domain z = 0~21 cm, the air domain (open-flow conditions) z = 34~44 cm and the ice-cover domain (ice-cover conditions) z =31~34 cm. We hope you are satisfied with our reply.
Point 6: Figure 13 presents one of the most interesting parts of this paper. Has such behavior been observed by any researcher before? If yet, you can mention it.
Response 6: Thank you very much for your acknowledgement of our manuscript. We are currently not aware of any researcher observing this behavior, and in accordance with your suggestion, we have made a statement in line 496, which reads "Since most studies focus on the effect of vorticity or bed shear stress on scouring, this paper addresses the relationship between these two characteristic quantities". Due to the addition of the new figure earlier, the numbering of Figure 13 has become Figure 14.
Point 7: One statement deserving the application of the present research in environmental and engineering aspects can be added to conclusions (like what is explained in Abstract).
Response 7: Thanks to your kind suggestion, we have added a statement in line 680 of the conclusion that it deserving the application of the present research in environmental and engineering aspects, and the suggestion you mentioned is helpful to improve the quality of our manuscript.
Point 8: Please add the future to the paper.
Response 8: Thank you very much for your approval of our manuscript. We have added the future in line 698 of the conclusion of the paper, which reads "This paper only simulated and analyzed the local scour of bridge piers under flat-bed conditions, and more numerical simulations may be conducted in the future to provide more solutions for the sustainable development of engineering environment", and we have learned a lot from the suggestions you have given us.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This manuscript develops a computational model to simulate local scouring around bridge piers under open-flow and ice-cover conditions and compares the results with a down-scaled lab experiment (i.e., a flume test). The goal is to understand the effects of scouring environments and sand bed morphology on local scouring.
*** novel contributions ***
The manuscript reviews some relevant methods for the research problem but falls short of discussing the limitations that motivated the present work. The manuscript seems to implement off-the-shelf methods for a case study (i.e., Yellow River Special Bridge in Tuoketuo County, Inner Mongolia) and tries to generalize the insights. If so, it lacks novel contributions for a research paper. It also remains unclear how the insights from the present work can be extended beyond the conditions considered in the specific case. As a suggestion, the authors may consider using their calibrated model to explore the space of input data (e.g., bridge geometry, flow conditions, or sediments) for other realistic situations beyond those of the experiment. In this way, they can extend the applicability range of regression analysis discussed toward the end of the manuscript.
*** content organization ***
The amount of information in some sections should be tailored to be self-contained, allowing the readership to grasp the key ideas. In particular, reading through Section 2 and understanding the connection between different subsections is not straightforward. For example, consider Sections 2.1.1 and 2.1.2. Introducing the Reynold decomposition of the velocity and pressure fields in Section 2.1.1 or hinting at the need for closure equations can help clarify the purpose of Section 2.1.2. The authors should balance the amount of information based on the target readerships of the journal. Also, the lack of consistency in notations or accuracy in language and terminology makes it even more challenging to understand the flow of content. Some examples are as follows:
1- Equation 1, Using Ax, Ay, and Az in the continuity equation is unclear. For incompressible flows, the continuity equation is div(V)=0, where V is the velocity field.
2- Equation 2 does not seem correct. If using indicial notation, the second term should read Dj dDi/dxj
3- Line 98, u, v, and w are not velocity vectors, but the coordinates of the velocity vector (field)
4- Line 99, If Di shows the coordinate of the velocity vector, what is the need to introduce two different notations (e.g., u=D1 or Dx)?
5- Line 106, The statement that "N-S" equations are closed" is incorrect in this context, where turbulent Navier-Stokes equations are not closed
6- Line 120, “compared with other models, the RNG model can fully consider …” is incorrect. Indeed, direct numerical simulation is a more refined approach but comes at a higher computational cost.
7- Equation 5, Make it clear if rs-rf, g, and ds are all in the denominator
8- Equation 6, Could you clarify how you determine the correction factor r?
9- Equation 7, how is the particle size non-dimensionalized? The same notation ds was used earlier for particle size with dimension in Equation 5
10- What does “gravitational acceleration parameterization” mean?
11- Equation 11, Make sure all the variables or terms in the equation are defined. Herein, qi, d*, d50, and r are not defined
12- Line 424, u is defined as the flow approach velocity. Aside from its unclear English writing, velocity is a vector field, and if it is meant some flow speed, it should be defined accurately
Besides the above points, I suggest the authors add a flowchart or pseudo algorithm to explain the simulation process in Section 2.
*** specific comments ***
1- While the ice-cover condition is a main theme of the manuscript, its treatment or implementation detail is not discussed in Section 2.
2- The work is motivated by the effects of scouring on bridges. However, the content remained focused on the scouring mechanism, and the ultimate impact on the bridge behavior is left out. It is worth discussing this aspect in the revised manuscript.
3- This comment is concerned with the scaling effects and boundary conditions. What are the considerations in the down-scaling to ensure the experiment represents the actual scouring behavior? How do you define the boundary conditions? In particular, the boundary condition of the pier’s top surface detached from the bridge superstructure.
4- Equations 3-5, 7, 9, cite relevant references for each equation
5- Line 201, How or where do you account for this “strong stochasticity”?
6- Figure 7, It would be nice to see the same contour levels for the results from the numerical model and experiment
*** English writing ***
Overall, the English writing is fine but requires careful proofreading as there are some issues with composition, typos, and grammatical errors. I just point out a few here.
1- Introduce the short forms or acronyms like RNG, RANS, and CFD before using them
2- Line 42, "Most domestic and foreign scholars" Change this if the audience is not from a specific country.
3- Line 69, what is “combination-shaped”?
4- Line 69, What is “research object”?
5- Line 94, Continuous equation à Continuity equation
6- Equation 1, “y” in "Dy" should be a subscript?
7- Line 113, “to calculating the accuracy of the scour depth” is not correct
8- Line 346, What are "model methods" and "physical test model"?
9- Line 424, What is "flow approach velocity"?
Author Response
Response to Reviewer 2 Comments
*** novel contributions ***
Point 1: The manuscript reviews some relevant methods for the research problem but falls short of discussing the limitations that motivated the present work. The manuscript seems to implement off-the-shelf methods for a case study (i.e., Yellow River Special Bridge in Tuoketuo County, Inner Mongolia) and tries to generalize the insights. If so, it lacks novel contributions for a research paper. It also remains unclear how the insights from the present work can be extended beyond the conditions considered in the specific case. As a suggestion, the authors may consider using their calibrated model to explore the space of input data (e.g., bridge geometry, flow conditions, or sediments) for other realistic situations beyond those of the experiment. In this way, they can extend the applicability range of regression analysis discussed toward the end of the manuscript.
Response 1: We appreciate your professional comments on our manuscript, which focuses on simulating the effect of scour on bridge piers in an ice-covered environment, as few numerical models are available to model local scour of bridge piers in an ice-covered environment. We have considered your suggestion to use the calibrated model to explore realistic situations other than experiments (different flow conditions, i.e., coherence between clear water scour and dynamic bed scour) and have revisited the applicability of the regression analysis at the end of the manuscript (in line 693). Thank you again for your suggestions, which are very helpful for our research work.
*** content organization ***
Point 0: The amount of information in some sections should be tailored to be self-contained, allowing the readership to grasp the key ideas. In particular, reading through Section 2 and understanding the connection between different subsections is not straightforward. For example, consider Sections 2.1.1 and 2.1.2. Introducing the Reynold decomposition of the velocity and pressure fields in Section 2.1.1 or hinting at the need for closure equations can help clarify the purpose of Section 2.1.2. The authors should balance the amount of information based on the target readerships of the journal. Also, the lack of consistency in notations or accuracy in language and terminology makes it even more challenging to understand the flow of content. Some examples are as follows.
Response 0: Based on your suggestion, in order to clarify the purpose of Section 2.1.2, we introduce the Reynold decomposition of the velocity and pressure fields in Section 2.1.1. In order to make the content easier to understand, we have made extensive corrections to the manuscript for lack of consistency in notations or accuracy in language and terminology, and we thank you for your careful reading of our manuscript.
Point 1: Equation 1, Using Ax, Ay, and Az in the continuity equation is unclear. For incompressible flows, the continuity equation is div(V)=0, where V is the velocity field.
Response 1: Based on your suggestions, we have corrected equation 1.
Point 2: Equation 2 does not seem correct. If using indicial notation, the second term should read
Response 2: We checked equation 2 and have corrected it to equations 2-4.
Point 3: Line 98, u, v, and w are not velocity vectors, but the coordinates of the velocity vector (field).
Response 3: We have corrected the “velocity vectors” into “the coordinates of the velocity vector (field)” in line 114.
Point 4: Line 99, If Di shows the coordinate of the velocity vector, what is the need to introduce two different notations (e.g., u=D1 or Dx)?
Response 4: Based on your suggestions, we have corrected it to equations 2-4.
Point 5: Line 106, The statement that "N-S" equations are closed" is incorrect in this context, where turbulent Navier-Stokes equations are not closed.
Response 5: We checked the statement "N-S equations are closed" and corrected it to "N-S equations are not closed" in line 123.
Point 6: Line 120, “compared with other models, the RNG model can fully consider …” is incorrect. Indeed, direct numerical simulation is a more refined approach but comes at a higher computational cost.
Response 6: We checked the statement “compared with other models, the RNG model can fully consider …” and corrected this sentence to “compared with other models, the RNG model has lower computational cost and higher computational efficiency” in line 140 based on your suggestion.
Point 7: Equation 5, Make it clear if rs-rf, g, and ds are all in the denominator.
Response 7: The terms you pointed out are all in the denominator, and we have adjusted the form of Equation 5 to ensure it is more clearly expressed, and the numbering of equation 5 became equation 7 due to the new equation added earlier.
Point 8: Equation 6, Could you clarify how you determine the correction factor r?
Response 8: We determine the correction factor r for the slope in equation 6 for any angle case by using equation 9 derived by researcher Dey, and due to the new formula added earlier, the numbering of Equation 6 becomes Equation 8.
Point 9: Equation 7, how is the particle size non-dimensionalized? The same notation ds was used earlier for particle size with dimension in Equation 5.
Response 9: ds is sediment particle size, d*,s is dimensionless size of the sediment, which can be computed by Equation 7, and the numbering of equation 7 became equation 10 due to the new equation added earlier.
Point 10: What does “gravitational acceleration parameterization” mean?
Response 10: We have corrected the line 176 “gravitational acceleration parameterization” into “magnitude of the acceleration of gravity” and apologize for the semantic confusion caused. Thank you for your correction.
Point 11: Equation 11, Make sure all the variables or terms in the equation are defined. Herein, qi, d*, d50, and r are not defined.
Response 11: We carefully checked all the variables and terms in equation 11 and made sure they were defined, added definitions for all the missing variables and terms in line 222, and the numbering of equation 11 became equation 14 due to the new equation added earlier.
Point 12: Line 424, u is defined as the flow approach velocity. Aside from its unclear English writing, velocity is a vector field, and if it is meant some flow speed, it should be defined accurately.
Response 12: We have corrected this English writing and changed the terms "flow approach velocity" to "mean flow velocity" in line 458. We apologize for our carelessness and thank you for the correction.
Point 13: Besides the above points, I suggest the authors add a flowchart or pseudo algorithm to explain the simulation process in Section 2.
Response 13: According to your suggestion, we have added a flow chart to explain the simulation process of local scouring of bridge piers in Section 2.2.3, which is very helpful to understand the numerical simulation method. Thank you again for your valuable suggestion.
*** specific comments ***
Point 1: While the ice-cover condition is a main theme of the manuscript, its treatment or implementation detail is not discussed in Section 2.
Response 1: Thank you for reading our manuscript carefully, we indeed did not discuss the implementation details of ice cover conditions in Section 2, and since ice cover is used as a scour environmental variable, we have "under ice-cover conditions, polystyrene foam sheets (thickness of 3 cm) were used at the top of the test section to simulate the fixed ice cover" in line 274 in Section 3.1 and "the ice-cover domain (ice-cover conditions) z =31~34cm" in line 289 in Section 3.2 are illustrated, and we thank you again for your suggestions.
Point 2: The work is motivated by the effects of scouring on bridges. However, the content remained focused on the scouring mechanism, and the ultimate impact on the bridge behavior is left out. It is worth discussing this aspect in the revised manuscript.
Response 2: As your concern, much of our research has focused on the scouring mechanism; based on your suggestion, we discuss the effect of scour on the bridge behavior at the end of Section 5.1, and hope that the revised content will be accepted.
(Section 5.1, line 574, added content "As the bridge pier foundation and substructure are influenced by the scouring environment, the ice cover environment contributes to the durability damage (e.g., increased erosion) and force damage (e.g., shear stress) caused by the bridge pier foundation. The research in this paper can further improve the safety assurance and evaluation technology system for the bridge pier foundation across the river, which can provide technical sup-port and theoretical experience for the design and construction of the bridge across the river.")
Point 3: This comment is concerned with the scaling effects and boundary conditions. What are the considerations in the down-scaling to ensure the experiment represents the actual scouring behavior? How do you define the boundary conditions? In particular, the boundary condition of the pier’s top surface detached from the bridge superstructure.
Response 3: Thank you for your comments on our manuscript, and here are the answers to your questions:
1) Scaling effect: In order to ensure that the experiment can represent the actual scouring behavior, the factors considered when scaling down are the geometric similarity of bridge piers, the similarity of water flow movement, and the similarity of sediment initiation; the geometric similarity is the precondition for the similarity of initiation, and the similarity of initiation is the dominant factor for the similarity of movement.
2) Boundary conditions: Reasonable boundary conditions determine the accuracy of the simulation results. In this paper, inlet boundary was the grid-covered boundary, the outlet boundary was the free outflow boundary, and side wall boundary was the no-slip boundary (in line 337); as shown in Figure 4, the top surface of the bridge pier and the bridge superstructure are far from the water surface, the top boundary of the simulation in this paper is only set at the junction of the bridge pier foundation and the water surface, which is defined as the pressure boundary.
Point 4: Equations 3-5, 7, 9, cite relevant references for each equation.
Response 4: Thank you for your reminder that we have cited the relevant references for equations 3-5, 7, and 9. Due to the new equations added earlier, the numbering of equations 3-5, 7, and 9 has changed to equations 5-7, 10, and 12.
Point 5: Line 201, How or where do you account for this “strong stochasticity”?
Response 5: We explain the strong stochasticity of the bed-load transport process in Section 5.1, line 567, its content is "which is caused by the ice-covered river section reducing the scour resistance of the sediment particles at the bottom of the bed, resulting in the loss of bed sediment stability and making it more prone to start, as well as leading to the intermittent collapse of sediment in the scour hole, resulting in a larger fluctuation of the scour hole", which indicates that the force of water flow on the bed-load is a random variable with uncertainty, and thus proves that the study in this paper can reflect the stochasticity of sediment transport in the scour hole.
Point 6: Figure 7, It would be nice to see the same contour levels for the results from the numerical model and experiment.
Response 6: Based on your suggestion, we unified the resultant contours levels of the numerical model and experiments to make their values consistent in terms of the number of bits retained; the development of scour holes in front of the upstream pier being limited by the simulation results, which is a difficult problem faced by the current simulation scour field (in line 359), so that the contours at the same depth are distributed in different locations; and the numbering of Figure 7 became Figure 8 due to the new Figure added earlier.
*** English writing ***
Point 0: Overall, the English writing is fine but requires careful proofreading as there are some issues with composition, typos, and grammatical errors. I just point out a few here.
Response 0: Thank you for your approval of our manuscript. We have carefully proofread the entire text for composition, typos and grammatical errors, and thank you again for your corrections.
Point 1: Introduce the short forms or acronyms like RNG, RANS, and CFD before using them.
Response 1: Thank you for your suggestion, we have introduced the full names of the above terms in line 49, line 13, and line 91 respectively.
Point 2: Line 42, "Most domestic and foreign scholars" Change this if the audience is not from a specific country.
Response 2: Thank you for your correction, we have corrected the "Most domestic and foreign scholars" to "Numerous scholars".
Point 3: Line 69, what is “combination-shaped”?
Response 3: Thank you for your correction. The expression "combination-shaped" may be misleading, so we have removed it.
Point 4: Line 69, What is “research object”?
Response 4: Thank you for your correction, we have corrected the "research object" to "prototype".
Point 5: Line 94, Continuous equation à Continuity equation.
Response 5: Thank you for your correction, we have corrected the "Continuous equation" to "Continuity equation".
Point 6: Equation 1, “y” in "Ay" should be a subscript?
Response 6: The "y" in "Ay" is a subscript. We are very sorry for our careless mistake and thank you for the reminder.
Point 7: Line 113, “to calculating the accuracy of the scour depth” is not correct.
Response 7: Thank you for your correction, we have corrected the "to calculating the accuracy of the scour depth" to "to calculating the scour depth" in line 133.
Point 8: Line 346, What are "model methods" and "physical test model"?
Response 8: Thank you for your correction. We have corrected "model method" to "model calculation" in line 380 and "physical test model" to "physical model" in line 381.
Point 9: Line 424, What is "flow approach velocity"?
Response 9: Thank you for your correction, we have corrected the "flow approach velocity" to "mean flow velocity" in line 458.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The authors addressed my comments.
