Physics-Informed Ensemble Machine Learning Framework for Improved Prediction of Tunneling-Induced Short- and Long-Term Ground Settlement

Round 1

Reviewer 1 Report

This study presents a physics-informed ensemble machine learning method for prediction of ground settlement. Relatively better results can be obtained compared with traditional ML algorithms. The arrangement of the manuscript is straightforward and easy to follow. The study can provide some reference for ground settlement prediction under similar engineering conditions. However, this manuscript requires major revisions before possible publication. I have made some comments below:

1、  The innovation point of this work is not clearly presented.

2、  Session 2.3. The description on PIML model is too general. Detailed theoretical derivation should be presented. Especially how physical model is imbedded, and how ensemble model is established.

3、  Line302-347. These descriptions are too basic and should be simplified.

4、  Session 4.2. How feature importance is analyzed and determined? The adopted methodology is missing and should be present.

Can be improved.

Author Response

We want to express our gratitude for the reviewer's constructive comments/questions, and suggestions. The feedback from the reviewer has helped a great deal in improving the quality of the manuscript.

(1) The innovation point of this work is not clearly presented.

Response: Thank you for the comment. One of the scientific contributions of this research is that the PIML models are established for short-term and long-term ground settlements separately due to their different physical mechanisms. This research also focuses on extending the applications of ML in predicting tunneling-induced ground settlement by Physics-Informed ensemble Machine Learning (PIML) to utilize the physical meaning of parameters and ensure the continuum between physics mechanisms and ML models. We have emphasized more on the contributions of this research in the "Abstract" and added a paragraph in the “Introduction” section (Lines 21-24, 77-83 in the revised version).

(2) Session 2.3. The description on PIML model is too general. Detailed theoretical derivation should be presented. Especially how physical model is imbedded, and how ensemble model is established.

Response: Thanks for the comment. This study applies the physics-informed model initialization and framework design, combining ML and physics-based models to predict ground subsidence due to tunneling. Section 2.3 illustrates the overall PIML procedure based on sections 2.1 and 2.2. Section 2.1 addresses the theoretical mechanisms of tunneling-induced short-term and long-term ground movements, which guides the PIML model to determine input variables. Furthermore, section 2.2 describes the detailed implementation of the ensemble model from base algorithm selection to hyperparameter design. The architecture of three algorithms has been implemented by Scikit-learn (Sklearn) library in Python. We have uploaded and shared Python code via GitHub (https://github.com/wzhough/PIML.git).

(3) Line302-347. These descriptions are too basic and should be simplified.

Response: Thanks for your excellent suggestion. Lines 302-347 in the original version described the PIML framework implemented via 5 steps based on sections 2.1 & 2.2. We have consolidated this part and only used a few sentences to preset the necessary contents. From our point of view, some “basic” ML frameworks should be mentioned to ensure readability for readers with various scientific backgrounds.

(4) Session 4.2. How feature importance is analyzed and determined? The adopted methodology is missing and should be present.

Response: Thank you for the suggestion. We have added Section 2.4 (Lines 350~366 in the revised manuscript) to present the Permutation Feature Importance method procedure to determine the feature importance.

 

Reviewer 2 Report

Study has merits. Readers can benefits. Some comments are;

1. Last paragraph of INTRODUCTION must be design of your study.

2. Why authors selected Terzaghi’s consolidation theory? There are some new theories.

3. Can this model use for long-term settlement calculation? if not, then why?

4. For which type of ground (soft or hard) it is more appropriate? 

5. Before case study, check model accuracy.

6. Discussion part is less for such important study. It must be increased.

7. Overall write-up must be improved and linked with objectives.

8. Reduce the length of conclusions. 

 

 

Need to improve.

Author Response

We want to express our gratitude for the reviewer's constructive comments/questions, and suggestions. The feedback from the reviewer has helped a great deal in improving the quality of the manuscript.

 

Study has merits. Readers can benefits. Some comments are;

(1)  Last paragraph of INTRODUCTION must be design of your study.

Response: Thanks for the excellent suggestion. We have rewritten the Introduction accordingly (Lines 84-98 in the revised manuscript).

(2) Why authors selected Terzaghi’s consolidation theory? There are some new theories.

Response: Thank you for the comment. Physics-informed model in this study aims to guide ML in selecting the appropriate input parameters. Since ML models are created from data-driven analyses, Terzaghi’s consolidation theory serves the purpose of a better understanding of causative factors for ground deformation. The actual mathematical equation of Terzaghi’s consolidation theory is not used for ML. If new theories use similar parameters as Terzaghi’s consolidation theory, then it is not significant to use a different theory.

(3) Can this model use for long-term settlement calculation? if not, then why?

Response: Thank you for the question. The proposed PIML framework uses past field observation data to train the model for predicting ground behavior in the future. Thus, it can be used to calculate/predict long-term settlement.

(4) For which type of ground (soft or hard) it is more appropriate?

Response: Thank you for the comment. The tunnel in this case study is excavated using shield TBM in soft-ground urban settings. Hence, soft ground would be more appropriate.  Please refer to Lines 369~377 in the revised version for more information about the project background.

(5) Before case study, check model accuracy.

Response: Thank you for the excellent suggestion. Models have been trained 1000 times in the pilot experiment to test their accuracy and stability. Corresponding results have been published and cited in this manuscript (Lines 236~255 in the revised version).

(6) Discussion part is less for such important study. It must be increased.

Response: Thank you for the suggestion. We have added one more paragraph in the Discussion section to discuss the proposed PIML framework (Lines 487~496 in the revision version).

(7) Overall write-up must be improved and linked with objectives.

Response: Thank you for the excellent suggestion. We have paid extra attention to the “Introduction,” “Methodology,” “Discussion,” and “Conclusion” parts to improve this manuscript’s quality.

(8) Reduce the length of conclusions.

Response: Thank you for the suggestion. We have eliminated redundancy and shortened the Conclusion section (Lines 536~553 in the revised version)

Reviewer 3 Report

Manuscript ID: sustainability-2448248

 

 

Title: Physics-informed ensemble machine learning framework for improved

prediction of tunneling-induced short- and long-term ground settlement

 

 

Sustainability

The paper presents an interesting subject related to short and long-term settlement induced by tunneling. The following notes were outlined:

1.     The “Introduction” must start with definitions related to tunneling in soft ground and problem of settlement.

2.     Page 2 – line 71: What do you mean by “this study” ? Why do you refer to a reference ?

3.     Page 2: The following studies may be beneficial. You can also refer to them:

·        Fattah, M. Y., Shlash, K. T., Salim, N. M., (2011), “Effect of Reduced Ko Zone on Time Dependent Analysis of Tunnels”, Advances in Civil Engineering, Vol. 2011, Article ID 963502, 12 pages, 2011. doi:10.1155/2011/963502, Hindawi Publishing Corporation. https://doi.org/10.1155/2011/963502.

·        Fattah, M. Y., Shlash, K. T., Salim, N. M., (2011), “Settlement Trough Due to Tunneling in Cohesive Ground”, Indian Geotechnical Journal, 41(2), 2011, 64-75.

 

4.     Sec. 2.1. is talking about literature review. You can move it to the “Introduction”.

5.     Define units of eq. (1).

6.     How can you determine the gap parameter ?.

7.     Page 5: Are the values of the stress release ratio less than 1 ?

8.     Is H in eq. (6) affected by the drainage conditions ?

9.     In Figure 7, what type of monitoring was conducted ?.

10.  Some details can be removed from the “Conclusions”.

Author Response

We want to express our gratitude for the reviewer's constructive comments/questions, and suggestions. The feedback from the reviewer has helped a great deal in improving the quality of the manuscript.

 

The paper presents an interesting subject related to short and long-term settlement induced by tunneling. The following notes were outlined:

(1)  The “Introduction” must start with definitions related to tunneling in soft ground and problem of settlement.

Response: Thank you for the excellent suggestion. We have rewritten the beginning paragraph of the Introduction section with the definition and importance regarding tunneling-induced ground movements in soft ground (Lines 37~43 in the revised version).

(2)  Page 2 – line 71: What do you mean by “this study”? Why do you refer to a reference?

Response: Thank you for catching this problem. We deleted sentences that were not necessary and rewritten this part of the manuscript to aid in bringing clarifications (Line 84 in the revised version).

(3) Page 2: The following studies may be beneficial. You can also refer to them:

• Fattah, M. Y., Shlash, K. T., Salim, N. M., (2011), “Effect of Reduced Ko Zone on Time Dependent Analysis of Tunnels”, Advances in Civil Engineering, Vol. 2011, Article ID 963502, 12 pages, 2011. doi:10.1155/2011/963502, Hindawi Publishing Corporation. https://doi.org/10.1155/2011/963502.
• Fattah, M. Y., Shlash, K. T., Salim, N. M., (2011), “Settlement Trough Due to Tunneling in Cohesive Ground”, Indian Geotechnical Journal, 41(2), 2011, 64-75.

Response: Thank you for the suggestion. We have carefully studied these two papers and cited both in our manuscript (Lines 611~614 in the revised version).

(4)  Sec. 2.1. is talking about literature review. You can move it to the “Introduction”.

Response: Thank you for the suggestion. Section 2.1 aims to illustrate the physical theory of tunneling-induced ground settlements followed by two specific physics-based models. We have reorganized section 2.1 for clarity and rewritten the Introduction section correspondingly (Lines 37~43 in the revised version).

(5) Define units of eq. (1).

Response: Thank you for catching this problem. We have added the unit (mm) of Equation 1 (Lines 139~141 in the revised version).

(6) How can you determine the gap parameter?

Response: Thank you for the question. The gap parameter is the sum of deformation (mm) due to the tail void of the shield machine, equivalent 3D elastoplastic deformation (mm) at the tunnel face, and radial deformation (mm) at the tunnel face. We added a definition of the gap parameter in the revised manuscript (Lines 131 -133).

(7) Page 5: Are the values of the stress release ratio less than 1?

Response: Thank you for the question. That’s correct - the value of the stress release ratio ranges from 0 to 1, which can be calculated from in situ measurements or derived using empirical methods and numerical modeling.

 

(8) Is H in eq. (6) affected by the drainage conditions?

Response: Thank you for the question. The parameter H represents tunnel depth in Equation (6), which is determined by construction design rather than drainage conditions.

(9) In Figure 7, what type of monitoring was conducted?

Response: Thank you for the question. Ground surface displacement was monitored by precise leveling of transverse profiles. We have added clarification of this to Lines 380~381 in the revised version.

(10) Some details can be removed from the “Conclusions”.

Response: Thank you for the excellent suggestion. We have refined, simplified, and re-written the Conclusion section for clarity (Lines 536~553 in the revised version).

Reviewer 4 Report

This paper presents a physically informed machine learning algorithm for the application of long-term settlement and short-term settlement in tunnels. The article calculates short-term settlement using an equivalent ground loss model and long-term settlement using the Terzaghi’s theory. An integrated machine learning model is selected to predict tunnel surface settlement and the accuracy and stability of the model is tested. The article considers the influence of the input of different tunnel characteristic parameters on the settlement output, and the structure of the article is relatively complete. However, to further improve the quality of the paper, I suggest the following changes.

1. The readability and linguistic quality of the manuscript should be further enhanced by careful review of the whole paper to avoid typos, grammar and spelling mistakes.

2.The Introduction section needs a revision in terms of providing more accurate and informative literature review and the pros and cons of the available approaches and how the proposed method is different comparatively. Also, the motivation and contribution should be stated more clearly.

3. The paper uses RF, GB and DT to form a VR model, how were these algorithms selected? If a combined model of SVM, GB and DT is used will the effect be different. In addition, the paper needs to add a description of the intrinsic connection and implementation steps of the three algorithms included in the integration method. It is too simple to illustrate only with Figure 4.

4. There are some figures in the paper whose clarity needs to be improved and some figures whose font size needs to be adjusted to improve the readability of the paper. For example, please see Figure 11 and Figure 12.

5. The figure numbers need to be labeled in order. For example, Figure 12 followed by a figure number of Figure 2, please check the revision.

 

6. The conclusion section of the paper can be appropriately refined and simplified by stating the main conclusions of the paper in points.

The readability and linguistic quality of the manuscript should be further enhanced by careful review of the whole paper to avoid typos, grammar and spelling mistakes.

Author Response

We want to express our gratitude for the reviewer's constructive comments/questions, and suggestions. The feedback from the reviewer has helped a great deal in improving the quality of the manuscript.

 

This paper presents a physically informed machine learning algorithm for the application of long-term settlement and short-term settlement in tunnels. The article calculates short-term settlement using an equivalent ground loss model and long-term settlement using the Terzaghi’s theory. An integrated machine learning model is selected to predict tunnel surface settlement and the accuracy and stability of the model is tested. The article considers the influence of the input of different tunnel characteristic parameters on the settlement output, and the structure of the article is relatively complete. However, to further improve the quality of the paper, I suggest the following changes.

(1) The readability and linguistic quality of the manuscript should be further enhanced by careful review of the whole paper to avoid typos, grammar and spelling mistakes.

Response: Thank you for the comment. We have gone through the manuscript carefully and paid special attention to English expressions during the manuscript revision.

(2) The Introduction section needs a revision in terms of providing more accurate and informative literature review and the pros and cons of the available approaches and how the proposed method is different comparatively. Also, the motivation and contribution should be stated more clearly.

Response: Thank you for the excellent suggestion. We have reorganized and rewritten the Introduction section to highlight reviewing ML, physics-based, and physics-informed ML models (Lines 60~76 in the revised version). In addition, we added a paragraph to emphasize the rationale and contributions of this research (Lines 77~83 in the revised version).

(3) The paper uses RF, GB and DT to form a VR model, how were these algorithms selected? If a combined model of SVM, GB and DT is used will the effect be different. In addition, the paper needs to add a description of the intrinsic connection and implementation steps of the three algorithms included in the integration method. It is too simple to illustrate only with Figure 4.

Response: Thank you for the question and suggestions.

(1) Theoretically, base models with performances on par can be selected to form the ensemble model and provide an average prediction. By combining multiple algorithms, the random errors of a single model can be compensated by other models, leading to a better overall model performance than a single ML model. Thus, a pilot experiment on six machine learning models has been conducted to select the base algorithm, including Random Forest (RF), Gradient Boosting (GB), Decision Tree (DT), Support Vector Machine (SVM), multiple linear regression and Back-Propagation Neural Network (BPNN). More detailed information can be found in a published paper (Liu et al., 2022) by the same authors. As a result, three models with top performance on par are selected, i.e., RF, GB, and DT. We refined the description regarding this part in the revised manuscript (Lines 236~242).

• Liu, L.; Zhou, W.; Gutierrez, M. Effectiveness of predicting tunneling-induced ground settlements using machine learning methods with small datasets. Journal of Rock Mechanics and Geotechnical Engineering. 2022, 14(4), 1028-1041.

(2) Figure 4 presents a general procedure of the ensemble regressor. All the necessary hyperparameters involved in the three models are provided in Table 1.

The architecture of three algorithms has been implemented by Scikit-learn (Sklearn) library in Python. We have uploaded and shared Python code via GitHub (https://github.com/wzhough/PIML.git).

(4) There are some figures in the paper whose clarity needs to be improved and some figures whose font size needs to be adjusted to improve the readability of the paper. For example, please see Figure 11 and Figure 12.

Response: Thank you for the suggestion. We have redrawn and updated Figures 11 and 12 in the revised version. We are happy to improve the figures’ resolution further but are cautious about increasing the overall file size of the manuscript (currently 215.4 MB).

(5) The figure numbers need to be labeled in order. For example, Figure 12 followed by a figure number of Figure 2, please check the revision.

Response: Thank you for catching this mistake. We have corrected the Figure numbers (Line 519 in the revised version).

(6) The conclusion section of the paper can be appropriately refined and simplified by stating the main conclusions of the paper in points.

Response: Thank you for the excellent suggestion. We have refined the Conclusion section for clarity and simplicity (Lines 536~553 in the revised version).

Round 2

Reviewer 1 Report

All my concerns have been reasonably addressed. 

I suggest acceptance of this manuscript.

Reviewer 2 Report

Acceptable