Life-Cycle Safety Evaluation of Arch Dam Abutments: A Comprehensive Framework Considering Spatiotemporal Variation in Fault Mechanical Parameters
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper proposes a comprehensive, multi-index framework for evaluating the long-term safety of arch dam abutments situated on faulted foundations. The authors develop an enhanced constitutive model implemented via an ABAQUS UMAT subroutine that couples three mechanisms: the confining pressure strengthening effect with depth, the local reinforcement from discrete random intact rock blocks, and fatigue damage accumulation under cyclic water level fluctuations.
- Firstly the author should use the journal template which has lines number.
- In the abstract I see that "shallow fractured zones deteriorating 2–3 times faster than deep high-confining-pressure regions" is slightly ambiguous. It is recommended to clarify the baseline of this comparison
- The abstract states that the "abutment safety factor decreases from 2.43 to 1.24 after 40,000 days." However, according to Table 7, the strength reduction index (Fs​) at 40,000 days is 1.17. Please ensure all numerical claims are perfectly consistent between the abstract and the results section.
- In the final paragraph of the introduction, the authors state that the paper "makes four significant extensions and methodological improvements" over their previous work. However, the text only explicitly lists the "First" and "Second" extensions. The third and fourth extensions are completely missing. The authors must either list all four extensions or correct the text to reflect the actual number of improvements discussed.
- instead of ∗ use ×
- In Equation (9), the term σamax normaly it the product of stress and strain amplitudes (σmax​ ×εa​).
- In Equations (15) through (17), the variable EK​ is used. It is assumed this represents the coupled elastic modulus derived from Equations (7) and (8), but it is not explicitly defined in the text. Please clarify the subscript "K" or use a more descriptive variable name.
- In equation 19 , THE authors should briefly justify why the energy equivalence approach (exponent of 2) is preferred, more accurate, or physically justified for this specific fault material compared to traditional empirical S-N approaches.
- In 3.1 Project Overview (Page 10) there is a broken cross-reference in the text just before the figure “Error! Reference source not found”.
- There is a significant contradiction between Equations (23, 24, 25 ) and the actual calculations presented in Table 7. i wrote all used values in blod
In Section 2.5, the authors correctly state a fundamental rule of their evaluation framework:
"for adverse indexes such as relative stress magnitude, the normalized value decreases with the original index." This means that if a dam has a low proportion of over-limit, its normalized score (Sn​) should be high (close to 1.0). Conversely, if the dam has a high proportion of over-limit stress, the score should drop toward 0. In other hand Equation (23) defines the normalized stress index as: Sn​=VS​ (Where S is the number of over-limit elements and V is the total elements).
This formula calculates the raw proportion of defective elements. If you use this formula, a dam with only 0.25% over-limit stress gets a score of 0.0025. This is a terribly low score for a perfectly safe dam, which completely violates the authors own rule that adverse indices should yield high scores when the defect rate is low.
We can mathematically prove that the authors did not use Equation (23) to generate Table 7. Let's look at the data for Day 0 in Table 7 and calculate the Comprehensive Stability Index (K) ourselves.
The Given Data for Day 0:
- Proportion of over-limit stress (S/V) = 25% (or 0.0025)
- Strength Reduction Index (Fs​) = 2.36
- According to Equation (24), since Fs​≥1.5, the normalized stability index Fn​ = 1.0
- The weights coefficients are explicitly stated in the text (in page 20) the second line after table 6 as ω1​=0.1 (for stress) and ω2​=0.9 (for stability).
The Formula for K (Equation 25): K=ω1​×Sn​+ω2​×Fn​
If we use the author written Equation (23) If we plug in the raw proportion (Sn​=0.0025): K=0.1×(0.0025)+0.9×(1.0) so K=0.00025+0.9=0.90025
What Table 7 actually reports for Day 0, the Comprehensive Stability Index K is 0.99.
There is a massive gap between the calculated result (0.90) and the reported result (0.99).
- The same for Conclusion:
The conclusion states that "under 28000 days of water level cycling, the strength reduction index decreases by 58%." However, based on the data provided in Table 7 (initial Fs​≈2.36 at 0 days, and Fs​≈1.22 at 28,000 days), the actual decrease is approximately 48.3%.
Author Response
Please see the attachment
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe article " Life-Cycle Safety Evaluation of Arch Dam Abutments: A Comprehensive Framework Considering Spatiotemporal Variation of Fault Mechanical Parameters” utilizing the UMAT subroutine in ABAQUS software to simulate the three-dimensional spatiotemporal evolution of the arch dam's mechanical and structural properties, thereby enabling an assessment of the geological faults. Investigating the spatiotemporal variation of these properties is of great importance to the scientific community. Some suggestions are recommended for publication in the Applied Sciences.
1 - In the application of the finite element model, what are the boundary conditions for the upper, lateral, and lower limits of the rock blocks?
2 - By applying the ABAQUS UMAT model, would it be possible to analyze stresses associated with geological faults as well as water loads on arch dams?
3 - Can the spatiotemporal variation of fault mechanical parameters, estimated by the ABAQUS UMAT model, be confirmed through experimental analyses based on laboratory rock mechanics test results?
4 - If possible, include images of rock blocks showing the temporal evolution of fault-induced damage in shallow and deep regions.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsWhile the authors successfully addressed several formatting and minor textual issues, they made a classic and severe mistake: they updated the formula in the text, but completely forgot to update the data in the main results table to match the new formula. Furthermore, they left a new typo and forgot to add a promised theoretical justification to the manuscript text.
- In Response 8, I asked them to justify why the energy equivalence approach (exponent of 2) is used in Equation (19) instead of traditional S-N curves. The authors wrote a very good explanation in their Response Letter ("Traditional empirical S-N formulations merely establish... The energy equivalence approach with an exponent of 2 enables..."). But they did not insert this justification into the revised manuscript.
- In Response 6, the authors attempted to fix the typo in Equation (9) by replacing the asterisk * with a multiplication sign × . In doing so, they accidentally deleted the stress symbol (σ). It must be corrected to ΔW = 1/2 σmax × εa
- The authors correctly updated Equation (23) in the text to Sn​=1−S/V (Line 340). They also correctly updated the conclusion to state a 48% decrease (Lines 773-774). However, they completely failed to update Table 7 in the manuscript. Not updated it but :
For Day 0: Fs​=2.36→Fn​=1.0. The true K should be 0.1 × (0.9975) + 0.9× (1.0)= 0.99975. However, Table 7 still reports K = 0.99, which is incorrect. Please report K = 0.99975 and present numerical values with five decimal places to avoid rounding errors and ensure consistency throughout the manuscript.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe corrections were made by the authors. The article is recommended for publication in the journal Applied Sciences.
Author Response
We sincerely appreciate the careful review and constructive suggestions from the reviewer, which have greatly helped us improve the quality and rigor of this manuscript. We are grateful for the positive evaluation and the recommendation for publication in Applied Sciences.
Round 3
Reviewer 1 Report
Comments and Suggestions for AuthorsI confirm that all of my comments have been addressed appropriately in the revised version of the manuscript.
