Research on the Influence Mechanism of Foam Slurry Wall Formation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article contains interesting analyses related to the influence of factors on foam slurry wall formation. The presented numerical calculations and laboratory tests focused on determining foam concentration and flow rate in various configurations are important from the point of view of expanding knowledge for membrane formation. Below are a few minor comments and suggestions: 
1. In the introduction, please expand the information on the main factors affecting slurry wall formation: first of all, please add information on geochemical factors; 
2. In the subsection 2.2, please add two/three sentences indicating the agents that increase foam concentration: mainly referring to agents commonly used in in situ conditions; 
3. In chapter 3, for Figure 3, only for stage 3, please write what the amplitude is: in other words, what is the maximum lift and maximum depression above and below the 70 particles line; 
4. In chapter four, please also add a few sentences regarding the influence of the numerically modeled permeability coefficient; 
5. In Chapter Five, please summarize the results of numerical modeling and laboratory tests of permeability in a table or figure; 
6. In the conclusions, please add two conclusions with numerical values ​​obtained from numerical tests: foam concentration and water absorption and from numerical modeling: flow rate.

Author Response

Comments 1: In the introduction, please expand the information on the main factors affecting slurry wall formation: first of all, please add information on geochemical factors; 
Response 1: Thank you for your suggestion. In response, we have added a brief discussion on geochemical factors—such as pH, ionic strength, and mineral composition—and their potential influence on slurry behavior and wall integrity. This addition is now included in the Introduction section, while clarifying that the present study focuses primarily on the dominant physical characteristics of the soil. We hope this revision better contextualizes our research scope while addressing your recommendation.

Comments 2:  In the subsection 2.2, please add two/three sentences indicating the agents that increase foam concentration: mainly referring to agents commonly used in in situ conditions; 
Response 2: Thank you for the suggestion. As Section 2.2 focuses on numerical simulation rather than experimental formulation, foam concentration is treated as an input parameter without reference to specific field agents. Therefore, we respectfully did not include detailed information on in situ chemical agents in this section.

Comments 3:  In chapter 3, for Figure 3, only for stage 3, please write what the amplitude is: in other words, what is the maximum lift and maximum depression above and below the 70 particles line; 
Response 3: Thank you for your suggestion. In response, we have revised the corresponding paragraph in Chapter 3 to clarify the amplitude of particle fluctuation during stage 3 in Figure 3. Specifically, for Scheme 22, the number of bentonite particles fluctuates around 70, with a maximum of 76 and a minimum of 60. This information has been added in the second paragraph of Chapter 3 (line 148 in the revised manuscript) to improve the clarity of the discussion and address your comment.

Comments 4:  In chapter four, please also add a few sentences regarding the influence of the numerically modeled permeability coefficient; 
Response 4: Thank you for your suggestion. In our study, the permeability coefficient is not directly assigned but is instead determined by the inherent soil properties in each numerical model. Specifically, parameters such as particle size (or maximum particle size), porosity, and gradation parameters b and m collectively influence the soil structure and thus indirectly determine the permeability. By varying these parameters individually, we effectively examine how changes in soil characteristics—and consequently the permeability coefficient—affect the foam slurry membrane formation process.

Comments 5: In Chapter Five, please summarize the results of numerical modeling and laboratory tests of permeability in a table or figure; 
Response 5: We sincerely thank the reviewer for the insightful suggestion. In response, we have added a paragraph at the end of Chapter 5 to clarify the scope and purpose of our experimental validation. Due to limitations in experimental conditions and workload, we did not conduct experimental validation for every numerical simulation scenario. Instead, we selected representative parameters—such as foam concentration, bentonite swelling ratio, and infiltration pressure—for preliminary experimental validation. The experimental results demonstrated trends consistent with those observed in the numerical simulations, thereby confirming the effectiveness of the simulations in predicting the trend of filter cake formation. It is important to note that the primary purpose of the experimental validation was to assess the reliability of the numerical simulations in trend prediction, rather than to achieve precise quantitative validation for each simulation parameter.​

Comments 6: In the conclusions, please add two conclusions with numerical values ​​obtained from numerical tests: foam concentration and water absorption and from numerical modeling: flow rate.
Response 6: Thank you for your valuable suggestion. In response, we have revised the conclusion section to include practical recommendations for engineering applications. Specifically, we now provide parameter thresholds such as a recommended foam concentration of approximately 20%, a swelling ratio of around 5%, and a maximum soil particle size less than 1 mm to promote effective membrane formation. These additions aim to enhance the applicability of our findings to real-world slurry wall construction practices.

Reviewer 2 Report

Comments and Suggestions for Authors

The strength of the paper lies in its multiscale approach, its detailed parameter studies, and clear identification of influencing mechanisms. I have following comments:

1. The manuscript can be significantly improved through stronger structure, improved clarity of figures and modeling steps, and better alignment of numerical results. In total, they should be improved.
2. Add real-world consequences of poor slurry wall formation (e.g., collapse risks, construction delays) and current limitations in predictive modeling to highlight the novelty of using CFD-DEM.
3. Include a simplified explanation of how PFC3D models particle-bubble interactions.
4. Move some of the tabular data and parameter combinations (Tables 1–4) to an appendix, and instead provide a high-level summary table of the experimental design strategy in the main text.
5. Elaborate briefly on the physical implications of the two types e.g., whether Type 2 is more desirable in tunneling or pile excavation, and why??.
6. Connect the numerical soil gradation parameters (b, m, porosity) with common soil types (e.g., sand, silt, gravel) to make the conclusions more applicable.
7. Add comparison plots and tables showing simulation vs. experimental flow/membrane formation time, with percentage error metrics provided in 10.1007/s11831-024-10143-1 to demonstrate model accuracy.
8. Suggest practical conclusions e.g., recommended foam concentration range, particle size thresholds that engineers can use it.

Author Response

Comments 1:The manuscript can be significantly improved through stronger structure, improved clarity of figures and modeling steps, and better alignment of numerical results. In total, they should be improved.

Response 1: Thank you for your suggestion. In response, we have supplemented the relevant sections of the manuscript and revised the figures as you recommended. These changes aim to improve the overall structure, clarity, and presentation of the modeling steps and numerical results.

Comments 2:Add real-world consequences of poor slurry wall formation (e.g., collapse risks, construction delays) and current limitations in predictive modeling to highlight the novelty of using CFD-DEM.

Response 2: Thank you for your insightful comment. In response, we have added a sentence at line 50 in the Introduction to emphasize the real-world consequences of poor slurry wall formation, such as excavation collapse, groundwater infiltration, construction delays, and associated safety and economic risks. Furthermore, the advantages of using the DEM approach—especially its ability to simulate discrete particle behavior and capture complex infiltration mechanisms—are discussed in Chapter 2 (line 69) to highlight the novelty and suitability of the CFD-DEM method adopted in this study.

Comments 3:Include a simplified explanation of how PFC3D models particle-bubble interactions.

Response 3: We appreciate the reviewer’s insightful suggestion to include a simplified explanation of how PFC3D models particle-bubble interactions. In response, we have added a detailed description inSChapter 2of our manuscript. In our study, both soil particles and foam bubbles are represented as spherical particles (balls) within the PFC3D framework. Soil particles are modeled as rigid, non-deformable entities, while foam bubbles are assigned lower stiffness values to allow for deformation. The interactions between particles are governed by the built-in linear contact model provided by PFC3D . This model simulates the mechanical behavior of an infinitesimal, linear elastic, and frictional interface that carries a point force, allowing for particle overlaps to represent deformation. As a foam bubble encounters a constriction between soil particles, it deforms to navigate through the pore space and subsequently regains its original shape upon exiting the constriction. This modeling approach effectively captures the dynamic processes involved in mud cake formation.​

We hope this addition provides clarity on our modeling approach and adequately addresses your comment.

Comments 4:Move some of the tabular data and parameter combinations (Tables 1–4) to an appendix, and instead provide a high-level summary table of the experimental design strategy in the main text.

Response 4: Thank you for your constructive suggestion. In response, we have moved the detailed tabular data and parameter combinations (original Tables 1–4) to the appendix for improved clarity and conciseness in the main text. A high-level summary table of the experimental design strategy is now provided in the main body as the revised Table 4, which outlines the classification of influence factors and parameter ranges.

Comments 5:Elaborate briefly on the physical implications of the two types e.g., whether Type 2 is more desirable in tunneling or pile excavation, and why??.

Response 5: Thank you for the valuable comment. We have added a brief explanation in the manuscript to clarify the physical implications of the two types. Specifically, Type 1 indicates inefficient clogging, as the number of infiltrated particles continues fluctuating around 70 by the end of the simulation, suggesting that membrane formation has not yet occurred. In contrast, Type 2 represents effective clogging, with the number of infiltrated particles gradually decreasing to near zero, indicating successful mud cake formation. This behavior is more desirable in practical applications such as tunneling or pile excavation, where rapid and stable membrane formation is essential to prevent slurry loss and ensure excavation stability.

Comments 6:Connect the numerical soil gradation parameters (b, m, porosity) with common soil types (e.g., sand, silt, gravel) to make the conclusions more applicable.

Response 6: Thank you for your valuable suggestion. In response, we carefully reviewed and classified the numerical soil models based on key gradation parameters (b, m, and porosity), along with particle size and permeability characteristics. Following the standard classification criteria outlined in GB 50021–2021, each model has now been associated with a corresponding common soil type. This classification has been added to the updated table (see Table 1 and Table 2) to enhance the practical relevance and engineering applicability of our results.

Comments 7:Add comparison plots and tables showing simulation vs. experimental flow/membrane formation time, with percentage error metrics provided in 10.1007/s11831-024-10143-1 to demonstrate model accuracy.

Response 7: We sincerely thank the reviewer for the insightful suggestion. In response, we have added a paragraph at the end of Chapter 5 to clarify the scope and purpose of our experimental validation. Due to limitations in experimental conditions and workload, we did not conduct experimental validation for every numerical simulation scenario. Instead, we selected representative parameters—such as foam concentration, bentonite swelling ratio, and infiltration pressure—for preliminary experimental validation. The experimental results demonstrated trends consistent with those observed in the numerical simulations, thereby confirming the effectiveness of the simulations in predicting the trend of filter cake formation. It is important to note that the primary purpose of the experimental validation was to assess the reliability of the numerical simulations in trend prediction, rather than to achieve precise quantitative validation for each simulation parameter.​

Comments 8:Suggest practical conclusions e.g., recommended foam concentration range, particle size thresholds that engineers can use it.

Response 8: Thank you for your valuable suggestion. In response, we have revised the conclusion section to include practical recommendations for engineering applications. Specifically, we now provide parameter thresholds such as a recommended foam concentration of approximately 20%, a swelling ratio of around 5%, and a maximum soil particle size less than 1 mm to promote effective membrane formation. These additions aim to enhance the applicability of our findings to real-world slurry wall construction practices.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

According to response 7, I am unsure about the modeling validity and can't check whether it is justified or not. Please check the comment and improve the paper as requested.

Author Response

Comments：According to response 7, I am unsure about the modeling validity and can't check whether it is justified or not. Please check the comment and improve the paper as requested.

Response：Thank you for your follow-up comment regarding the modeling validity. In response, we have revised the final part of Chapter 5 to more clearly articulate the purpose and scope of the experimental validation. Due to practical constraints, it was not feasible to replicate every numerical simulation scenario in the laboratory. Instead, we selected representative parameters (such as foam concentration, bentonite swelling ratio, and infiltration pressure) for preliminary experimental testing. While some discrepancies in absolute values were observed—owing to the inherent differences between idealized simulation and practical experiment—the overall trends in infiltration and mud film formation were found to be consistent. This confirms that the numerical model reliably captures the essential mechanisms and is effective in predicting the qualitative influence of key factors. The revised paragraph (now integrated at the end of Chapter 5) clarifies this point and directly addresses your concern.

Author Response File: Author Response.pdf