A New Semi-Analytical Method for the Calculation of Multi-Crack Stress-Intensity Factors under Hydro-Mechanical Coupling
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsDear Authors,
The topic of the article is interesting. The manuscript has certainly potential to improve. To help improve the quality of this manuscript, I have added more comments bellow:
General Comments:
1. Abbreviate "Abstract" with concrete results expressed in numbers.
2. Please check all citations in the text and correct according to the MDPI standard.
3. Define the "Results" chapter within the paper. Please add.
4. Please change the word "study" in the sentences to "paper”.
5. Write mathematical formulas in the appropriate format. Also, when specifying individual marks, separate and specify the unit of measurement. Check the full text.
6. Please check the space between the unit of measurement and the number in the entire text.
7. Expand the conclusion with specific (numbered) results.
8. "Conflicts of Interest" is missing, please add it to the paper.
Line-by-line comments:
L214 Improve quality of Figure 4. a) Structural model (too small).
L233 Improve quality of Figure 4. a) Structural model (too small).
L245 The introductory text for “4. Discussion" is missing. Please add.
Kind regards,
Reviewer
Author Response
Please see the attachment.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsGeneral thoughts
Figure 1 and 2 are very similar. Please consider removing Figure 1, because Figure 2 is its extension.
Table 1 and 3. Since the existing models were compared, it is difficult to clearly state which one is more realistic. The computational model would have to be verified experimentally, which is a big challenge. At present, it is a more advanced model than those available in the literature.
Do the authors foresee verification in real conditions or on a test bench?
There are 2 Tables marked with number 4: line 259 and 277.
The following parts of the paper are considered original and relevant to the field of geotechnical engineering and fracture mechanics:
Introduction of a new semi-analytical method: This paper presents a novel semi-analytical method for calculating stress intensity factors (SIF) under hydro-mechanical coupling. This approach addresses the limitations of existing methods, in particular in accurately modeling the behavior of cracks under varying hydraulic pressure and mechanical loads—the normal stress at the crack surface is zero, not the hydraulic pressure Ph.
The paper addresses several specific gaps in the field of geotechnical engineering and fracture mechanics, in particular regarding the calculation of stress intensity factors (SIF) under hydro-mechanical coupling:
Complexity of existing methods: Many current methods for calculating multi-crack SIFs are complex and become increasingly difficult to apply with the increasing number of cracks. This paper proposes a new semi-analytical method that simplifies the calculation process, making it more accessible for practical applications.
Inadequate stress field representation: Traditional methods often assume that the normal stress at the crack surface is zero, which does not accurately reflect the real conditions under which hydraulic pressure (Ph) occurs.
The proposed method takes into account the real hydraulic pressure acting on the crack surface, which leads to a more realistic representation of the stress field around cracks. Limited focus on hydromechanical coupling: Previous studies have mainly focused on mechanical loading without adequately considering the effect of hydraulic pressure on crack behavior. This paper highlights the importance of hydromechanical coupling in the analysis of crack initiation and propagation, filling a critical gap in understanding how these factors interact.
The paper adds several important contributions to the field of geotechnical engineering and fracture mechanics compared to other published materials:
New semi-analytical method: The introduction of a new semi-analytical method for calculating stress intensity factors (SIFs) under hydromechanical coupling conditions represents a significant advance. Unlike existing methods that can be overly complex or limited to specific scenarios, this method simplifies the computational process while maintaining accuracy, making it more practical for engineers.
Consideration of hydraulic pressure: The study highlights the importance of accurately modeling the effect of hydraulic pressure on crack behavior. By proposing a method that considers the non-zero normal stress at the crack surface, it provides a more realistic framework for analyzing crack propagation under hydromechanical loading, which is often neglected in traditional approaches.
Unified approach to multiple crack analysis: The paper’s method is designed to be independent of the number of cracks, enabling a unified approach to multiple crack analysis. This is in contrast to many existing methods that become increasingly complex with the appearance of additional cracks, which increases the usefulness of the proposed method in practical applications.
The authors could consider several specific improvements to the methodology and further checks to increase the robustness and applicability of their study:
Sensitivity analysis: Conducting a sensitivity analysis to assess how changes in key parameters (e.g., hydraulic pressure, crack spacing, and material properties) affect the calculated SIF and stress fields could provide deeper insight into the robustness of the method. This analysis would help identify critical parameters that significantly affect the results and guide future applications.
Consideration of time-dependent effects: The methodology could be improved by considering time-dependent effects, such as creep or stress relaxation, that may occur in geotechnical materials under constant loading conditions. Consideration of these factors could lead to a more comprehensive understanding of the crack behavior over time.
Experimental validation: To further strengthen the methodology, the authors could consider conducting experimental studies to directly measure SIF and stress fields under controlled laboratory conditions. These empirical data would provide additional validation of the proposed method and increase its reliability.
Consideration of environmental factors: The methodology can be extended to include the influence of environmental factors such as temperature changes or chemical interactions that can affect the mechanical properties of materials and fracture behavior. Consideration of these factors would increase the applicability of the method in real-world conditions.
The conclusions drawn in the paper appear to be consistent with the evidence and arguments presented throughout the study. Here is a breakdown of how the conclusions are consistent with the evidence, as well as an assessment of whether all the main questions raised are addressed:
The authors propose a new semi-analytical method for calculating stress intensity factors (SIFs) under hydromechanical coupling. The conclusions highlight the advantages of this method, such as its simplicity and effectiveness in representing the stress field at the fracture surface, which is supported by the theoretical framework and derivations presented in the paper.
The paper asks several key questions regarding the calculation of multi-crack SIFs under hydromechanical coupling, including the effectiveness of the proposed method compared to existing approaches and the effect of hydraulic pressure on the fracture behavior.
The authors address these questions with two specific examples that confirm the effectiveness of the extended semi-weight function method. They analyze the effects of integral paths and loading conditions, providing evidence that the proposed method can accurately capture the behavior of SIFs under different conditions.
Furthermore, the discussion on how the stress field changes under different values ​​of hydraulic pressure and far-field stress further addresses the issue of the interaction of these factors, showing that the proposed method is more consistent with real-world conditions than traditional methods.
Tables and figures presented in the paper play a key role in illustrating the methodology, results, and comparisons made by the authors. Here are some comments regarding their quality and effectiveness:
Figures, such as those depicting structural and finite element models, are essential for visualizing the scenarios analyzed. Clear labeling and appropriate scales improve the reader's understanding of the experimental setups and results.
Tables summarizing the results, such as SIFs for different setups and comparisons with existing literature, provide a concise way to present complex data. The organization of these tables allows for easy comparison of results, which is beneficial for readers who want to assess the validity of the proposed method.
The data presented in the tables appear to be well organized and relevant to the study's objectives. The inclusion of comparative results from existing literature adds credibility to the findings and demonstrates the effectiveness of the proposed method.
Figures illustrating stress fields under different loading conditions effectively convey the differences in stress distributions, supporting the authors' claims about the advantages of their method. Graphical representation of data helps to understand the impact of different parameters on SIF.
Author Response
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Author Response File: Author Response.docx
Reviewer 3 Report
Comments and Suggestions for AuthorsThe abstract should be restricted to the current topic of this paper. Authors must present good results in the abstract section to engage the readers.
The author highlights the novelty of the present work at the end of the introduction.
The quality of some figures is low. It is necessary to enhance the quality of the images.
The introduction should include more details on how SIF calculation works in the safety evaluation of geotechnical engineering.
The author should add more details about hydro-mechanical coupling and its usefulness in the safety evaluation of geotechnical engineering.
Comments on the Quality of English LanguageSome editing for the English language is required throughout the manuscript due to numerous mistakes.
Author Response
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Author Response File: Author Response.docx
Reviewer 4 Report
Comments and Suggestions for AuthorsThe present paper provides a semi-analytical method to calculate the stress intensity factor of cracks in hydromechanical works in geotechnics. This is a very specific topic and of which, in this work, the application to reality is scarce. The loading conditions are analyzed considering the stress field. The authors mention the independence of the number of cracks and the ease of their expression as advantages.
The proposed calculation is based on a complex mathematical development, which is widely exposed in the work and requires special attention for its monitoring, for this reason it is recommended to simplify the presentation of the mathematical development (29 equations!) and some more specific applications to the topic.
The work must be rewritten. The writing is poorly maintained, there are numerous grammatical and translation errors. Reading by an English expert is also recommended.
The new writing of the ENTIRE work also implies the change of the title: Eliminate acronyms from the title.
Author Response
Please see the attachment.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsDear authors,
The corrections I requested for the paper " A new semi-analytical method for the calculation of multi-crack SIFs under hydro-mechanical coupling" were successfully made. The quality and clarity of the text and results has been significantly improved. The scientific contribution is visible and applicable and, following the proposed corrections, future research on this topic can be compared and developed. I wish successful further research.
Best regards,
Reviewer
Reviewer 4 Report
Comments and Suggestions for AuthorsWith the changes introduced in the text, the work can be accepted in the present form
