Review Reports - Face Lag Distance of Large-Section Excavation in Shallow-Buried Closely Spaced Tunnels Under Bias Loading

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript addresses an important engineering problem related to the stability of shallow-buried, closely spaced tunnels under bias loading conditions. The combination of numerical modeling and field monitoring is valuable, and the topic is relevant to the readership of Applied Sciences.

The clarity and readability of the figures need improvement. Several graphs (e.g., Figures 5–12) are difficult to interpret due to low resolution, small labels, and crowded legends.
Please enhance the quality, font size, and contrast of all figures to ensure they are fully legible in print and digital formats.

A dedicated Discussion section should be added. Currently, the paper presents results but lacks a deeper comparison and critical reflection. The discussion should explicitly compare the numerical and field results with findings from other studies, highlight agreements and discrepancies, and explain the implications for tunnel engineering practice.

The literature review should be expanded, particularly to include more references from the last 5 years. Recent international studies on excavation sequence, lagging distance, and tunnel interaction effects (beyond the mainly Chinese context) should be considered. The comparison of the obtained results with published findings will strengthen the scientific positioning of the study.

The selection of material parameters (Table 2) is presented only briefly. More detailed justification of parameter values is required, including the sources (laboratory tests, field measurements, empirical correlations, or code recommendations). Sensitivity of the results to parameter variation should be at least qualitatively discussed.

The paper should explicitly address the limitations of the numerical modeling approach, such as assumptions of isotropy, simplified boundary conditions, or neglect of groundwater influence. A short discussion on the applicability and limitations of the method to other geological and construction conditions would be very beneficial.

The manuscript is generally understandable but would benefit from careful proofreading for grammar, sentence clarity, and consistency in terminology (e.g., “lag distance” vs. “lagging distance”). Ensure that all abbreviations are clearly defined at first use.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

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Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The abstract is generally clear, but several sentences are overly long and contain multiple ideas, which may reduce readability. To break these into shorter it would focus sentences and would enhance clarity.
The introduction is good preparation, but there is one point of improvement with the research gap. The mechanism of lagging distance in large-section, shallow-buried, biased tunnels is unclear. It could be stated more explicitly. Additionally, several sentences are very long and combine multiple ideas. This makes the argument harder to follow.
Symbol in Equation (1) is not correct; the abbreviation should be the international symbol.
The parameter in table 2 present the geotechnical and support tunnel, but there are not source of information. How did the authors obtain the parameter values?
The section concludes that the 2.0D scheme is safe, but does not discuss whether these findings are generalizable beyond the Georgia No. 1 Tunnel. Did the authors apply the validation approach to other shallow-buried, biased tunnels?
The result section is long and has many details; it should be separated into the result and discussion parts for understanding.
Section 4.1, the settlement differences are low in absolute magnitude on Line 190 - 196. The authors should discuss how this reduction is practically significant in the context of tunnel safety and deformation control.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I accept the corrections made and recommend the article for publication in its current form.

Author Response

Thanks again to the reviewers' and editors’ help in improving the quality of the paper. We tried our best to correct the paper and made some changes to the manuscript. We earnestly appreciate the Editors/Reviewers' warm work and hope that the correction will be approved.

Reviewer 2 Report

Comments and Suggestions for Authors

Reviewer Report for revised version manuscript

Manuscript Title: Face Lag Distance of Large-Section Excavation in Shallow-Buried Closely Spaced Tunnels under Bias Loading

General Evaluation

The authors have thoroughly revised the paper in response to the previous review including the clarification of model parameters, expansion of literature review, addition of quantitative validation metrics, refinement of figures/tables, and improved discussion of groundwater, support stiffness, and simulation schemes. The current version is significantly improved in clarity, completeness, and technical credibility. Only a few minor issues remain, which presented below:

Abstract

The authors have incorporated quantitative results (example:11.9% reduction in surface settlement and maximum settlement values up to 3.48 mm). The recommendation of 2.0D lag distance is now explicitly framed as case-specific to the Georgia No.1 project.
The abstract now highlights the engineering implications. The revised abstract is concise, quantitative, and contextually clear.

Introduction

The literature review has been expanded to include multiple recent studies addressing face lag, bias loading, and twin-tunnel interaction. The authors clearly identified the knowledge gap (“unclear interaction mechanism of large-section shallow-buried biased tunnels with varying lag distance”) and presented specific objectives.
A paragraph describing the novelty of this study (real project validation, comprehensive range of lag distances, large-section NATM tunnel) has been added.

Project Overview

2.1 Project Description

The definition of D is now clearly stated as the equivalent excavation diameter based on tunnel width, with D = 12 m. The correspondence between 0.5D, 1.0D, and 2.0D (6 m, 12 m, 24 m) is presented.

2.2 Geological and Hydrological Conditions

Table 2 now includes full geotechnical parameters (unit weight, E, ν, φ, c) with units and typical magnitudes. The origin of parameters is clarified (lab tests, code-based adjustments, and literature calibration). Groundwater justification is strengthened: the water table is located approximately 30 m below the tunnel, and the low permeability was confirmed by field testing, justifying omission of seepage.
It would still be beneficial to include the measured permeability or hydraulic conductivity (if available) to fully support the claim.

2.3 Tunnel Support System Description

The modeling sequence is now explicitly described: excavation and immediate activation of the primary lining; secondary lining after stabilization. Time-dependent stiffness of shotcrete is acknowledged as a simplification, justified by calibration to field results.
Can you please add one sentence noting how this simplification may slightly underestimate initial deformation but not affect long-term equilibrium results.

Finite Element Model

3.1 Model Dimensions and Boundary Conditions

The boundary conditions and domain size (112 m × 60 m × 35 m) are described with reference to Saint-Venant’s principle and prior literature. The justification for the base and lateral extents is given qualitatively (3-4 times tunnel width).
While the reasoning is improved, the authors did not perform or show a boundary-sensitivity check. It remains unclear whether the model covers the deepest overburden zone (up to 94 m). Therefore, I recommend one of the followings conditions: Either (a) include a brief sensitivity analysis showing negligible effect of increasing model depth/width, or (b) explicitly state that the modeled section corresponds to the shallower (portal) zone with overburden <35 m.

3.2 Material Parameter Selection (Table 2)

The table now lists complete data with consistent units (MPa, kPa, kN/m³). The previous confusion about the high E-values for primary (68,000 MPa) and secondary (31,500 MPa) supports has been clarified. The authors explain that these are equivalent composite stiffness calculated from steel arch and shotcrete materials. Parameter sources and calibration are referenced to TB 10003-2016 and JTG 3370.1-2018.
Can you please add a short footnote under Table 2 confirming E values are in MPa.
Can you please present the detailed calculation of the composite stiffness (showing component moduli and section properties) in an appendix or supplementary note for transparency.

3.3 Numerical Simulation Scheme Design

The excavation steps are now expressed numerically (6 m, 12 m, 24 m corresponding to 0.5D, 1.0D, 2.0D). The modeling process (activation/deactivation method, sequential excavation, immediate primary support) is clearly described.
The omission of shotcrete hardening is acknowledged and justified.

Analysis of Numerical Simulation Results

4.1 Displacement Analysis

Settlement reduction and displacements are now quantitatively presented with percent differences. Mechanistic explanation (arch effect stabilization beyond 2.0D) is added.

4.2 Stress Analysis

The explanation of principal stress distribution and stress recovery behind the excavation face has been improved. The fixed value of -0.33 MPa is explained as a consequence of stress field symmetry and boundary equilibrium rather than imposed constraint. Relation between the 15 m threshold and D (approximately 1.25D) is clarified.

4.3 Analysis of Surrounding Rock Plastic Zones

The Mohr-Coulomb yield criterion and equivalent plastic strain threshold (0.002) are defined. Figures are now clearer and include color scales with units. Authors confirm that the maximum plastic strain (approximately 0.008) is an emergent result, not a set limit.

Monitoring Data Analysis

5.1 Monitoring Scheme

Table 4 now details monitoring instruments (Total Station TCR702, convergence meter), and the measurement schedule is presented. Monitoring layout and frequency are explained. The instrument accuracy is listed as “1” without units. Please clarify (for example: ±1 mm for settlement or ±1 arc-second angular precision).

5.2 Monitoring Results

The measurement frequency and spatial layout are clearly shown.

5.3 Comparison between Field and Numerical Results

The comparison table now includes RMSE, MAE, and MAPE, with MAPE in the range of 20-40%, which considered as acceptable for tunneling in heterogeneous ground. The discussion explains underestimation due to idealized rock stiffness and homogeneous assumption.
Can you please add a short note that future calibration could reduce MAPE by adjusting local stiffness or joint parameters.

Conclusions

The revised Conclusions section now satisfies all major requirements from your previous version. It contains quantified results, clearly framed site-specific recommendations, acknowledges modeling and methodological limitations, and communicates practical guidance for engineering application.
Can you please add a single line acknowledging that the boundary condition sensitivity and heterogeneous rock behavior remain areas for future research.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript has been improved as the reviewer's suggestion. Therefore, I would like to accept this manuscript with this revision.

Author Response