Investigating Ice Loads on Subsea Pipelines with Cohesive Zone Model in Abaqus

Round 1

Reviewer 1 Report

This study employs the cohesive zone model to examine the fracture characteristics of ice samples. The simulations are conducted in a 2D environment using the Abaqus explicit solver. The interaction forces resulting from numerous simulations are meticulously recorded and subsequently compared to discern the influence of sample geometry on fracture behavior. To gain deeper insights, repeated interactions with distinct grain configurations are carried out to explore the variability in fracture patterns and applied loads. The statistical analysis, specifically T-tests, reveal that both the angle of force application and the position of the indenter wield a significant impact on the fracture force. This is a very solid work and provides some new insights.  Here are my concerns:

1.      The Related Work section lacks specific details about prior research, including the specific aspects studied and how the current work differs from previous investigations. Providing such details would enhance the contextual understanding of the paper's novelty.

2.      The Mathematical Model section, a crucial component for simulation-related papers, is conspicuously absent. It is imperative to include this section to comprehensively elucidate the mathematical framework underpinning your simulations.

3.      Consider separating the Discussion and Conclusion sections to enhance the clarity and structure of the article. The Discussion section, in particular, requires substantial improvement to enhance its substantive content.

4.      To enhance the readability of the figures, ensuring that the numbers and scales are clearly visible is essential. Consider utilizing professional software for plotting, such as Origin, to generate figures with improved clarity and legibility.

Author Response

Hello,

Thank you for spending the time to review our manuscript. After giving it another careful look, the authors completely agreed with all your remarks. The related work section, while containing several references, did not provide any information about previous work. To address this situation, three paragraphs were added to the section that describe previous cohesive zone publications in more detail. 

Initially, the details of the mathematical model were omitted, because Abaqus is used for computation, which is a closed-source tool. The inner workings of Abaqus are published in its user’s manual. After careful consideration (and looking through the user’s manual) we added a discussion of cohesive zone formulation and its parameter selection in Abaqus. We believe that this addition is valuable, because our selected cohesive zone parameters are different from several previous works. The corresponding subsection is renamed to  “Mathematical framework and parameter selection”.

The Discussion and Conclusion are now separate sections. We completely rewrote the conclusion and added two paragraphs to the discussion. The focus of this work – to tell how fracture forces would change if the geometry changed – is being discussed in the corresponding section. However, the authors are hesitant to draw any additional conclusions, since the real-life scenarios are not well-studied, and may be substantially different from what was simulated. 

All figures were reworked - plots were converted to vector form, unnecessary text in the simulation images was removed, and the size of the remaining text was increased. If there are issues with any particular figure, please let us know. We appreciate the suggestion to use Origin, which we will consider in the future. 

Once again, we thank you for the effort and time in reviewing the manuscript. The authors hope to have addressed the current issues.

Regards,

Igor Gribanov, Mark Fuglem, Rocky Taylor, and Jan Thijssen

Reviewer 2 Report

Based on numerical simulation, this paper reveals the interaction law between submarine pipelines and icebergs by studying the effect of changes in the height of ice samples, indenter position and angle of force application on the magnitude of reaction force of rigid indenter, which provides a reference basis for the protection of Subsea pipelines and cables in the cold regions of high latitudes, but there are still some deficiencies, and it is recommended to receive it after modification, the modifications are as follows:

1、How is the contact area of the rigid indenter with the ice and the height of the raised portion of the ice determined?

2、It is mentioned in the paper that "Pressures of up to 70 MPa were measured on the individual sensels." However, the scale of the stress cloud in the accompanying figure "Fig 3" only shows up to 50 MPa, please add relevant content or pictures.

3、How do you determine the size of the grid size for experimental delineation? What are the differences or advantages of the meshing approach in this article over that of other articles?

4、Please describe in detail how the loading conditions are applied to the rigid indenter.

5、Please describe the effect on the test results of using ice particle sizes in "2.1 Mesh generation" that are much larger than the typical size of natural ice particles.

6、Please keep the format of the figures in table 8 consistent and retain all figures to one decimal place.

7、The following literature maybe useful for improving your quality:

① Yin Q, Wu JY, Zhu C*, He MC, Meng QX, Jing HW. Shear mechanical responses of sandstone exposed to high temperature under constant normal stiffness boundary conditions. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 2021, 7:35.

② Tang SB*, Yu CY, Heap MJ, Chen PZ, Ren YG. The Influence of Water Saturation on the Short- and Long-Term Mechanical Behavior of Red Sandstone, Rock Mechanics and Rock Engineering, 2018, 51(9): 2669-2687.

Based on numerical simulation, this paper reveals the interaction law between submarine pipelines and icebergs by studying the effect of changes in the height of ice samples, indenter position and angle of force application on the magnitude of reaction force of rigid indenter, which provides a reference basis for the protection of Subsea pipelines and cables in the cold regions of high latitudes, but there are still some deficiencies, and it is recommended to receive it after modification, the modifications are as follows:

1、How is the contact area of the rigid indenter with the ice and the height of the raised portion of the ice determined?

2、It is mentioned in the paper that "Pressures of up to 70 MPa were measured on the individual sensels." However, the scale of the stress cloud in the accompanying figure "Fig 3" only shows up to 50 MPa, please add relevant content or pictures.

3、How do you determine the size of the grid size for experimental delineation? What are the differences or advantages of the meshing approach in this article over that of other articles?

4、Please describe in detail how the loading conditions are applied to the rigid indenter.

5、Please describe the effect on the test results of using ice particle sizes in "2.1 Mesh generation" that are much larger than the typical size of natural ice particles.

6、Please keep the format of the figures in table 8 consistent and retain all figures to one decimal place.

7、The following literature maybe useful for improving your quality:

① Yin Q, Wu JY, Zhu C*, He MC, Meng QX, Jing HW. Shear mechanical responses of sandstone exposed to high temperature under constant normal stiffness boundary conditions. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 2021, 7:35.

② Tang SB*, Yu CY, Heap MJ, Chen PZ, Ren YG. The Influence of Water Saturation on the Short- and Long-Term Mechanical Behavior of Red Sandstone, Rock Mechanics and Rock Engineering, 2018, 51(9): 2669-2687.

Author Response

Hello, 

Thank you for spending the time to review our manuscript. After giving it another careful look, the authors agreed with your remarks and made several changes to address them.

The first question was “How is the contact area of the rigid indenter with the ice and the height of the raised portion of the ice determined?” To answer briefly, once the indenter starts moving, most of its exposed surface is in constant contact with the ice - either the intact block or crushed particles. In the experiment, only surface pressure is recorded by using the Tekscan sensor (details are available in the cited publication [8], titled “SIIBED: Investigation of Ice Loads on Subsea Pipelines and Cables using RHITA”). The interaction process and the contact area are captured on video, but the area is not being tracked explicitly. In the experiments, the raised portion of the blocks, i.e., indentation depth is controlled by the height of the ice block itself, as the testing apparatus has a fixed height. For the simulation, the selected indentation depth is 10.1 cm. The indenter itself is not modeled in the simulation. Instead, the forces are applied to the surface of the ice sample directly. To clarify these questions, changes were made to the section “Experimental data for calibration”(lines 99-104).

Pressures of up to 70 MPa were measured on Tekscan sensor (details are available in publication [8]). These are the maximal recorded pressures, which are not representative of the process in the average sense. Current work uses the Tekscan plot (Figure 3) to illustrate that pressures are not distributed uniformly on the indenter. Instead, it is more likely that the pressure will be applied as case ‘H’ or ‘V’ (Figure 6), but not both. Since the value of 70 MPa is not used for model calibration, we removed this statement, but added clarification to the last paragraph of section “Experimental data for calibration”(lines 113-115).

“How do you determine the size of the grid size for experimental delineation? What are the differences or advantages of the meshing approach in this article over that of other articles?”

To answer these questions, two paragraphs were added to the section “Mesh generation”. In brief, we try to make the mesh size as small as the computation resources allow. If the mesh resolution is too high, computation becomes extremely slow. The advantage of using granular tessellation (versus inserting cohesive zones between all elements) is the more natural crack paths at arbitrary angles, rather than 60-degree mesh angles. This results in a more accurate representation of the experimentally-observed fracture events (lines 143-158).

“Please describe in detail how the loading conditions are applied to the rigid indenter.”
The answer was added to section “Experimental data for calibration” (lines 91,92). In the testing apparatus, the indenter is driven at constant velocity by hydraulics. In the simulation, the boundary conditions are applied directly to the ice sample as shown in Figure 6.

“Please describe the effect on the test results of using ice particle sizes in "2.1 Mesh generation" that are much larger than the typical size of natural ice particles.”
The discussion of the influence of grain size on the simulation parameters is provided in the section “Mathematical framework and parameter selection” (lines 218-223). Since the simulated grains are larger than the actual ice grains, their fracture energy accounts for larger volumes of material. Consequently, the parameter “fracture energy” in the simulation is set higher than the experimentally-measured energy of surface decohesion for ice. 

“Please keep the format of the figures in table 8 consistent and retain all figures to one decimal place.”
Significant figures are made consistent in Tables 4-8.

Once again, we thank you for the effort and time in reviewing the manuscript. The authors hope to have addressed the current issues. Two authors, who are native English speakers - Rocky Taylor and Mark Fuglem - have proofread the text for style and grammar. If there are specific parts of the text where the language is unclear, please point them out. 

Regards,

Igor Gribanov, Mark Fuglem, Rocky Taylor, and Jan Thijssen

Reviewer 3 Report

Dear Authors,

Thank you for submitting your paper to Modelling. Your article presents your approach to modeling the fracture of ice. I like the way you approach the problem. I have only two small questions.

You wrote that you apply forces directly to nodes and why do not you use the contact problem?

Do you have any comparison of your algorithm for detecting the fracture with the moment of removing the first cohesive element?

 

Best regards,

Author Response

Hello,

Thank you for taking the time to read our manuscript and for your feedback. To answer your questions: 

“You wrote that you apply forces directly to nodes and why do not you use the contact problem?”

At earlier stages of this work, we attempted simulations with ice-indenter contact that ran for the entire duration of the experiment of 10 seconds (https://www.youtube.com/watch?v=Av23JH0DZ-U). There were several downsides: (1) Since the simulation does not reproduce crushing, the contact surface is always a polygon, and the contact with the indenter occurs at 1-2 points. Instead, we wanted to model the contact similar to the Tekscan readings in the experiment, i.e., covering a 10-degree angle. (2) In a full simulation, the contact occurs at various spots on the indenter, but we wanted to check how the fracture force is affected by the angle in a controlled way. (3) At mesh resolutions of about 300K elements, simulating 0.1 seconds of the test takes about one hour. That is, simulating the full 10 seconds would take ~100 hours. With a contact constraint, the simulation runs even slower. It is possible to run a semi-static (0.1 second) simulation with the contact condition, but we opted to apply the force directly for better control of the force application angle.

“Do you have any comparison of your algorithm for detecting the fracture with the moment of removing the first cohesive element?”

Unfortunately, removal of individual cohesive elements did not reliably detect the fracture. The reliable algorithm had to consider two factors - removal of cohesive zones and the reaction force drop.

Once again, we thank you for the effort and time in reviewing the manuscript.

Regards,

Igor Gribanov, Mark Fuglem, Rocky Taylor, and Jan Thijssen

Reviewer 4 Report

The authors presented an interesting work on simulating indentation fracture of ice with a CZM-based polycrystalline fracture modeling technique. The implementation was based on ABAQUS and was focused on two dimensional cases. Below are some of my questions and comments.

1. The engineering background of this study is ice-induced damage of subsea pipelines and cables in the arctic and subarctic regions. My question is, in engineering, are there generally more concerns about the destruction and fracture of submarine structures or ice?

2. What is the importance of accurately simulating the trajectory of ice cracks to correctly predict ice loading of subsea infrastructures? Can a reasonable ice load be predicted with a rigid indenter?

3. The authors note in lines 35-37 that this work places more emphasis on “to predict the precise trajectory of every crack” and “the fracture process rather than predict the exact loads”. However, “investigating ice loads” is the main content of this article in the title and Abstract. In Section 3, only the numerical results of the fracture forces are compared with the experimental results. The numerical results of the crack path have not been verified.

4. We know that the fracture behavior of ice is strongly related to its microstructure. This characteristic makes the correspondence between numerical results and experimental results very weak. Although the author attempts to use the average numerical results of multiple models for comparison, unfortunately, the validation is still very limited.

Author Response

Hello, 

Thank you for reviewing our manuscript. We will try to answer the questions and address the issues one-by-one below:

1. The engineering background of this study is ice-induced damage of subsea pipelines and cables in the arctic and subarctic regions. My question is, in engineering, are there generally more concerns about the destruction and fracture of submarine structures or ice?

There is definitely more concern about the durability and safety of the man-made structures, such as subsea pipelines and cables than the ice. In some cases, these two problems may be related, e.g., river ice breakup and accumulation causing a flood. 

2. What is the importance of accurately simulating the trajectory of ice cracks to correctly predict ice loading of subsea infrastructures? Can a reasonable ice load be predicted with a rigid indenter?

In certain extreme cases, the location of fractures can be predicted. In the current work, the repeatable “end spall” was detected for some simulated batches, and such spall was observed in the experiments. However, in nature, ice contains inclusions and imperfections, such as air bubbles, internal stresses, and existing damage, which make it impossible to predict the exact crack paths. In the current work, the randomized grain geometries are studied from the statistical perspective, to investigate the influence of sample shapes and indenter locations on the fracture forces.
Rigid indenter, which is assumed both in the experiment and in the simulations, is a representation of a subsea cable or pipeline. Strictly speaking, such cables and pipelines are not rigid, but experiments showed that their deformation is small at the typical forces of ice indentation. So, for the purpose of medium-scale experimental studies and simulations, rigid indenter is an acceptable approximation of the actual pipe or cable.

3. The authors note in lines 35-37 that this work places more emphasis on “to predict the precise trajectory of every crack” and “the fracture process rather than predict the exact loads”. However, “investigating ice loads” is the main content of this article in the title and Abstract. In Section 3, only the numerical results of the fracture forces are compared with the experimental results. The numerical results of the crack path have not been verified.

The manuscript states “the random nature of fracture introduces significant uncertainties, making it impossible to predict the precise trajectory of every crack.” and “objective of this work is to investigate the influence of geometric factors on the fracture process rather than predict the exact loads.” While we are interested in repeatable patterns, such as end spalls, the goal is to understand how the changes in block sizes, shapes, and indenter positions affect the fracture forces. This information helps to understand how the experimental data would scale to real-world scenarios, i.e., seabed gouging by ice.

4. We know that the fracture behavior of ice is strongly related to its microstructure. This characteristic makes the correspondence between numerical results and experimental results very weak. Although the author attempts to use the average numerical results of multiple models for comparison, unfortunately, the validation is still very limited.

We agree that many factors affect the fracture processes, including the composition of the material. Numerical simulations still have a long way to go before they can become a reliable tool in ice mechanics. However, there are cases where certain physical phenomena are dominant and can be modeled. In the current study we attempt to understand whether the medium-scale RHITA tests are sufficient for drawing conclusions about the actual seabed gouging events. Thus, we investigate how the change in sample sizes and shapes affect the fracture forces in the simulation. Of course, the results of numerical simulations must be interpreted with caution, and the limitations of the presented approach are discussed in the “Conclusion” section of the manuscript.

Once again, we thank you for the effort and time in reviewing the manuscript.

Regards,

Igor Gribanov, Mark Fuglem, Rocky Taylor, and Jan Thijssen

Round 2

Reviewer 2 Report

it can be accepted for publication

it can be accepted for publication