Hybrid AI–FEA Framework for Seismic Assessment of Confined Masonry Walls Using Crack Image-Based Material Property Inference
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper presents an AI–FEA hybrid framework combining MobileNetV20 CNN for estimation of mechanical properties with DIANA FEA analysis for seismic response assessment of confined masonry wall. The idea is interesting and potentially impactful for post-earthquake diagnostics. However, several methodological, structural, and presentation issues must be addressed before publication.
- Similar studies exist in literature. The novelty compared to previous studies should be highlighted. The research gap should be clearly identified and a short paragraph summarizing the novelty and hypothesis should be included.
- Previous studies are presented as a long list, including some unrelated work. Grouping the literature section by topic would be more helpful for the reader.
- Information such as the model's training time, learning rate, and convergence graphs are not included.
- Considerable abbreviations are used in the study. The expanded form of abbreviations used in the text should be given where they are first used (BLR, BMR, BHR, …).
- Figures 1–3 are repeated. Inconsistent numbering between text and captions. Fix figure numbering inconsistencies.
- Include a table summarizing all CNN parameters.
- No comparison between model-predicted and real parameters for test data. Include a plot or table comparing predicted vs. reference parameters.
- Reporting only MAE and “78% accuracy” is sufficient? Otherwise, other index as R², RMSE, or correlation plots should be included?
- Figure 6-8: Inconsistencies in axis labels must be corrected. Different languages are used.
Author Response
Comment 1:
Similar studies exist in literature. The novelty compared to previous studies should be highlighted. The research gap should be clearly identified and a short paragraph summarizing the novelty and hypothesis should be included.
Response 1:
We appreciate the reviewer’s insightful comment. To clarify the novelty and research gap, the Introduction section was reorganized. Sections 1.2 and 1.3 now explicitly differentiate this work from existing literature that focuses only on qualitative crack detection or independent FEA modeling. The revised Section 1.3 introduces a short paragraph summarizing the hypothesis that crack morphology encodes sufficient information to estimate mechanical parameters of confined masonry, enabling their direct integration into nonlinear FEA analysis. This addition highlights the originality of the hybrid AI–FEA framework and its relevance for non-destructive post-earthquake evaluation.
Comment 2:
Previous studies are presented as a long list, including some unrelated work. Grouping the literature section by topic would be more helpful for the reader.
Response 2:
We thank the reviewer for this helpful suggestion. The literature review was reorganized to present prior research by topic instead of a single continuous list. The revised Introduction now contains three subsections: 1.1 Vision-Based Crack Detection and Quantification, 1.2 Seismic Behavior and Finite Element Modeling of Masonry Walls, and 1.3 Hybrid AI–FEA Frameworks for Structural Assessment. This structure groups references thematically, removes unrelated citations, and improves the logical flow from computer-vision studies to seismic modeling and finally to hybrid AI–FEA approaches. The new organization provides a clearer context for the proposed framework and strengthens the connection between existing work and this study’s contribution.
Comment 3:
Information such as the model's training time, learning rate, and convergence graphs are not included.
Response 3:
We appreciate the reviewer’s comment. The Deep Learning Model section (2.2) was updated to include all relevant training details. The model was trained using the Adam optimizer with an initial learning rate of 1 × 10⁻⁴, batch size 16, and 100 epochs on an NVIDIA RTX 3060 GPU (12 GB VRAM). The training process required approximately 5 hours for convergence. In addition, a new Figure 4 was added to show the training and validation loss curves, confirming stable convergence without overfitting. These additions provide the necessary transparency on training configuration and model behavior.
Comment 4:
Considerable abbreviations are used in the study. The expanded form of abbreviations used in the text should be given where they are first used (BLR, BMR, BHR, …).
Response 4:
We appreciate the reviewer’s observation. During the revision process, several abbreviations that appeared in earlier drafts (such as BLR, BMR, and BHR) were removed to improve clarity and consistency. All abbreviations that remain in the final version (e.g., CNN, FEA, UHS, and AI) are now defined at their first appearance in the text. This ensures clarity for readers and maintains a uniform technical style throughout the manuscript.
Comment 5:
Figures 1–3 are repeated. Inconsistent numbering between text and captions. Fix figure numbering inconsistencies.
Response 5:
We thank the reviewer for pointing out this issue. All figures were carefully reviewed, corrected, and renumbered to ensure consistency between their order of appearance in the text and their corresponding captions. The duplicated content previously associated with Figures 1–3 was removed, and each figure now appears only once with a unique caption.
Specifically, Figure 4 now presents the model’s training and validation convergence curves, table 1 summarizes the CNN architecture and training configuration, and Figure 3 shows the updated methodological flowchart of the proposed hybrid AI–FEA framework. The numbering of subsequent figures was also revised accordingly throughout the manuscript. These adjustments ensure logical continuity, eliminate redundancy, and improve visual coherence across all graphical elements.
Comment 6:
Include a table summarizing all CNN parameters.
Response 6:
We appreciate the reviewer’s suggestion. In the revised manuscript, a new table (Table 1) has been added to summarize the main configuration parameters and hyperparameters of the convolutional neural network (CNN) employed in this study. The inclusion of this table ensures transparency and reproducibility of the deep learning model used for mechanical property estimation.
Specifically, Table 1 now details the CNN architecture (MobileNetV2), image input size, optimizer, learning rate, batch size, number of epochs, loss function, activation function, and output type. These values correspond to the configuration adopted during the model training phase, which was implemented using the Adam optimizer, a learning rate of 1 × 10⁻⁴, batch size of 16, and 100 training epochs. The loss function was defined as the Mean Absolute Error (MAE), and the ReLU activation function was employed across convolutional layers.
Comment 7:
No comparison between model-predicted and real parameters for test data. Include a plot or table comparing predicted vs. reference parameters.
Response 7:
We thank the reviewer for this insightful suggestion. In response, a new section has been included within the Results and Discussion to provide a quantitative and graphical comparison between the CNN-predicted mechanical parameters and the corresponding reference values obtained from experimental and numerical data.
Figure 13 now presents the lateral load–displacement curves derived from the finite element model (using AI-estimated parameters) and from the experimental reference envelope. The comparison demonstrates strong agreement, with less than 10% deviation in peak strength and approximately 12% difference in displacement at maximum load. This close correlation confirms that the AI–FEA hybrid framework can accurately replicate stiffness degradation and nonlinear response behavior typical of confined masonry walls.
Additionally, the section discusses that the predicted property set—comprising elastic modulus, tensile and compressive strengths, shear modulus, and fracture energies—achieved a coefficient of determination (R²) of 0.87 and a mean absolute error (MAE) of 0.22 on the test dataset. These metrics further validate the model’s predictive reliability.
By incorporating this comparison, the revised manuscript now provides both a visual validation (Figure 13) and quantitative metrics demonstrating the consistency between the CNN predictions and empirical reference data, addressing the reviewer’s comment and reinforcing the technical soundness of the proposed method.
Comment 8:
Reporting only MAE and “78% accuracy” is sufficient? Otherwise, other index as R², RMSE, or correlation plots should be included?
Response 8:
Thank you for the valuable suggestion. The performance evaluation of the CNN has been expanded accordingly. In addition to the previously reported MAE and accuracy, the revised manuscript now includes the coefficient of determination (R²) and the root mean squared error (RMSE) on the test dataset. The model achieved R² = 0.87, MAE = 0.22 (normalized), and RMSE = 0.28 (normalized), indicating strong agreement between predicted and reference mechanical parameters.
Furthermore, Figure 13 provides a structural validation by comparing the lateral load–displacement curve generated using the AI-estimated parameters with an experimental reference envelope, showing less than 10% difference in peak capacity and approximately 12% in drift at maximum load. These additions provide a more complete and rigorous assessment of the model’s predictive performance.
Comment 9:
Figure 6-8: Inconsistencies in axis labels must be corrected. Different languages are used.
Response 9:
We thank the reviewer for noting this issue. Figures 6–8 were reviewed, and all axis labels, legends, and annotations have been standardized to English for consistency. In addition, font size and unit formatting were harmonized to ensure visual uniformity across the figures. These revisions improve clarity and align the graphical presentation with the journal’s formatting guidelines.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsI have reviewed the paper titled "Analysis and Prediction of Failures in Mansory Walls Using
Neural Networks and FEA simulation in the Lima Tambo Urbanization". Here are my general comments for the authors:
Note typo in the title.
Affiliations are 1,2,3 but 3 is missing. Recommend to only use 1 if all affiliations are the same, and * only for the corresponding author, especially since the other two authors seem to provide temporary addresses.
there are many english mistakes that should be addressed. Some sentences do not even have a verb, for example: "On the other hand, the effects of seismic movements of the pulse-type near the fault on seismically isolated buildings."
The literature review is unclear. Sometimes it reads like it is about the present paper but it is referring a quoted study. Most of these paragraphs need to be rephrased and the link between the reviewed study and the present paper should be established clearly.
I am familiar with many of the quoted works and their description is often inaccurate, and again, the links to the current study are unclear.
A flowchart of what is being done must be added to the paper. Figure 3 schematic, but raises several questions fundamental to the methodology:
How can pushover curves for a complex geometry of *confined* masonry shown in the photo be constructed based on material properties derived by computer vision of zoomed-in crack photographs? Confined masonry is characterised by concrete tie beams and columns of which the reinforcement seems unknown. If assumptions are made regarding the presence and location of ties and the minimum RF is speculated, this was not made clear.
"A computer-vision pipeline with a MobileNetV2-based CNN infers key mechanical properties of cracked walls directly from images" How? It seems it only infers properties for the specific section, not the entire wall.
Figures have labels/annotations in Spanish. This reviewer understands but these need to be in English.
Pushover curves will not only be affected by material properties of URM but by geometry, openings, tie beams and columns. This is a major limitation and should be discussed.
If the case study buildings are just used to collect photographs for the example of using the CNN to derive material properties for URM (which the buildings are not, according to the authors), why is this mentioned in the title?
If the buildings, which look to have complex geometries, are not being modelled, why do they appear in the paper so prominently?
Are different buildings or different example walls with different crack intensity being assigned different material vectors? are the pushover results different? How many calculations were performed?
Would heavily cracked walls have a much lower capacity in terms of force and displacement? How many walls failed to lack of force capacity and how many due to lack of displacement capacity? Were pools of heavily cracked walls more prone to one or the other? Were performance levels different between these types of walls?
Were, depending on the material properties assigned, shear sliding, shear diagonal, rocking, etc. failures observed?
A list of assumptions should be included in the paper.
Are the UHS spectra site specific?
Does the cause of the existing damage affect the material properties or capacity of the walls? Is it from settlements, previous earthquakes, construction/design issues?
I recommend to focus on the premise that the authors want to highlight, which seems to be that cracked pictures can be used to generate material properties, which can be linked to NLFEM to generate ADRS evaluations. But several simplifications, assumptions, and limitations arise and are not discussed in depth.
Moreover, there seems to be no validation possible since: how is the capacity or performance of walls with material properties as in the cracked pictures, being compared against known performance data?
The title and abstract suggest that an assessment for the building population in Limatambo would be conducted. This would entail models of the specific buildings, which could be derived from photographs, and material properties, which are being derived from photographs but for entire walls and not specifically cracked sections.
Specifically, the incompatibility of the modelled URM and the observed Confined M is not discussed.
The influence of cracking is not being assessed but this seems an important point for the authors.
I recommend the authors give a critical look at their methodology, the goal of the paper, and the message that they want to convey and can also support with their work. The paper can be rewritten to focus on the work that was actually carried out.
Author Response
Comment 1:
Affiliations are 1,2,3 but 3 is missing. Recommend to only use 1 if all affiliations are the same, and * only for the corresponding author, especially since the other two authors seem to provide temporary addresses.
Response 1:
We thank the reviewer for this clarification. In the revised manuscript, the affiliation structure has been corrected to ensure consistency and accuracy. Since all authors are affiliated with the same institution, the numbering has been simplified to a single affiliation, and only the corresponding author is marked with an asterisk, as recommended.
This modification removes the previously unused third affiliation and avoids unnecessary complexity in the author information. The updated author and affiliation section now follows standard journal formatting conventions and accurately reflects the authors’ institutional association.
Comment 2:
there are many english mistakes that should be addressed. Some sentences do not even have a verb, for example: "On the other hand, the effects of seismic movements of the pulse-type near the fault on seismically isolated buildings."
Response 2:
We thank the reviewer for this observation. The manuscript has undergone a thorough language review to correct grammatical issues, sentence structure, and clarity throughout the text. The sentence referenced by the reviewer, along with other similar constructions, has been fully rewritten to ensure proper verb structure and academic clarity.
In particular, the sentence cited has been removed, as it was part of a previous draft that is no longer relevant to the current version of the Introduction. Additionally, the revised manuscript now uses concise and direct English, and paragraph transitions were improved for readability.
These edits enhance the fluency, technical precision, and clarity of the manuscript while maintaining its scientific content.
Comment 3:
The literature review is unclear. Sometimes it reads like it is about the present paper but it is referring a quoted study. Most of these paragraphs need to be rephrased and the link between the reviewed study and the present paper should be established clearly.
I am familiar with many of the quoted works and their description is often inaccurate, and again, the links to the current study are unclear.
Response 3:
We appreciate the reviewer’s detailed observation. The Introduction has been substantially rewritten to address this concern. The literature review was reorganized into three structured subsections 1.1 Vision-Based Crack Detection and Quantification, 1.2 Seismic Behavior and Finite Element Modeling of Masonry Walls, and 1.3 Hybrid AI–FEA Frameworks for Structural Assessment. This restructuring clarifies the progression from prior work to the contribution of the present research.
Descriptions of previously cited studies were rephrased for accuracy, and unnecessary or tangential references were removed. In each subsection, we now explicitly explain how the referenced works relate to this study, highlighting the gap that remains unaddressed: the lack of a method that quantitatively infers mechanical properties from crack morphology and integrates them into nonlinear FEA for seismic assessment.
These revisions ensure that the literature review is both accurate and directly linked to the novelty and hypothesis of the proposed framework, improving clarity and coherence for the reader.
Comment 4:
A flowchart of what is being done must be added to the paper. Figure 3 schematic, but raises several questions fundamental to the methodology:
How can pushover curves for a complex geometry of *confined* masonry shown in the photo be constructed based on material properties derived by computer vision of zoomed-in crack photographs? Confined masonry is characterised by concrete tie beams and columns of which the reinforcement seems unknown. If assumptions are made regarding the presence and location of ties and the minimum RF is speculated, this was not made clear.
Response 4:
We thank the reviewer for this important observation. To address this, Figure 3 has been replaced with a detailed flowchart that clearly illustrates the full hybrid AI–FEA workflow, from visual data acquisition to nonlinear simulation and performance evaluation.
Additionally, the concerns regarding the structural modeling assumptions have been explicitly addressed in a new section titled 2.3 Assumptions and Limitations. In this section, we clarify that the CNN estimates representative mechanical properties at the wall-panel scale, derived from crack morphology patterns, and not reinforcement detailing. The confinement elements (tie columns and beams) were modeled in DIANA FEA using standard confinement detailing recommended in existing experimental literature for confined masonry with similar typologies, since reinforcement was not directly measurable from photographs.
These assumptions are now stated transparently, and their effect is discussed. The objective of the FEA is not to reproduce the exact reinforcement layout of a specific building, but to evaluate whether the AI-inferred material property set produces a consistent nonlinear seismic response aligned with observed confined masonry behavior.
This clarification, together with the revised flowchart and modeling explanation in Section 2.4.4, ensures full methodological transparency and resolves the ambiguity noted by the reviewer.
Comment 5:
"A computer-vision pipeline with a MobileNetV2-based CNN infers key mechanical properties of cracked walls directly from images" How? It seems it only infers properties for the specific section, not the entire wall.
Response 5:
We thank the reviewer for raising this clarification. In the revised manuscript, Section 2.4.2 now explains that the CNN does not infer localized material properties for a single crack region. Instead, it predicts a representative set of mechanical parameters for the wall panel as a whole, derived from the global crack morphology patterns visible in the image.
Crack geometry (orientation, length, branching, texture, and distribution) is governed by the wall’s overall stiffness degradation state, not by isolated localized defects. Therefore, the CNN learns to map macroscopic crack morphology to equivalent homogenized mechanical properties, such as elastic modulus, shear modulus, cohesion, and fracture energies.
Additionally, Section 2.3 Assumptions and Limitations explicitly states that the output parameters correspond to the panel-level constitutive behavior used in the FEA model—not detailed reinforcement or localized damage zoning. The method does not attempt to reconstruct exact reinforcement layouts; instead, it provides non-destructive parameter estimation suitable for structural modeling and performance evaluation.
This clarification strengthens the conceptual consistency of the proposed hybrid AI–FEA framework and aligns the scale of inference with the scale of numerical simulation.
Comment 6:
Figures have labels/annotations in Spanish. This reviewer understands but these need to be in English.
Response 6:
We thank the reviewer for this remark. All figures have been revised to ensure that axis labels, annotations, legends, and descriptive text are consistently presented in English. The updated figures now use standardized terminology aligned with the manuscript vocabulary (e.g., lateral displacement, shear cracking, compressive toe crushing, etc.).
Additionally, font size and alignment were standardized across Figures 3 through 11 to improve visual clarity and consistency with journal formatting guidelines. These revisions enhance readability for the international research community and ensure full linguistic consistency throughout the manuscript.
Comment 7:
Pushover curves will not only be affected by material properties of URM but by geometry, openings, tie beams and columns. This is a major limitation and should be discussed.
Response 7:
We thank the reviewer for this important observation. This limitation has now been explicitly addressed in the manuscript. A new subsection titled 2.3 Assumptions and Limitations has been added, clarifying that the proposed method estimates panel-level homogenized mechanical properties, and the pushover analysis is performed on a representative confined masonry wall configuration, not on building-specific geometries with individualized reinforcement layouts or opening distributions.
We state clearly that geometry, openings, confinement detailing, and reinforcement patterns are significant factors influencing actual structural capacity. Since these details cannot be inferred directly from crack images, the FEA model adopts standardized confinement configurations based on validated experimental studies. The objective of the analysis, therefore, is not to reproduce the exact capacity of a specific wall, but to evaluate whether the AI-inferred material parameters lead to a realistic nonlinear response consistent with known confined masonry behavior.
This limitation is now explicitly acknowledged and discussed in Section 4 (Discussion), where we indicate that future work should integrate geometric and reinforcement inference to extend the framework toward full-building seismic assessment.
Comment 8:
If the case study buildings are just used to collect photographs for the example of using the CNN to derive material properties for URM (which the buildings are not, according to the authors), why is this mentioned in the title?
Response 8:
Thank you for this observation. The role of the case study has been clarified and the title has been corrected accordingly. The buildings from the Limatambo urbanization are not modeled structurally in this study; they are used only as a source of field crack imagery to demonstrate the visual inference stage of the CNN. Therefore, the previous reference to Limatambo in the title has been removed to avoid implying that the buildings were analyzed in full structural detail.
In the revised manuscript, Section 2.4.1 now explains that the case study provides photographic evidence representative of typical crack patterns in confined masonry, which is used to validate the image-based parameter estimation process, while the nonlinear simulation is performed on a generic but experimentally consistent wall model.
This adjustment ensures that the scope and contribution of the case study are accurately represented and avoids misinterpretation of the research objectives.
Comment 9:
If the buildings, which look to have complex geometries, are not being modelled, why do they appear in the paper so prominently?
Response 9:
Thank you for this important clarification request. The buildings shown in the figures are not modeled structurally. Their purpose in the manuscript is to illustrate real-world crack patterns from confined masonry housing in a high-seismic urban context. These photographs are used only in the visual inference stage, where the CNN extracts crack morphology features to predict representative mechanical properties.
To avoid implying that the buildings themselves were modeled, the manuscript has been revised so that these images now appear only in Section 2.4.1 (Field Image Acquisition), where their role is explicitly described as visual data input, and not as structural case studies. Meanwhile, the nonlinear FEA simulations are performed on a standardized confined masonry wall model consistent with published experimental typologies, as stated in Section 2.4.4.
Comment 10:
Are different buildings or different example walls with different crack intensity being assigned different material vectors? are the pushover results different? How many calculations were performed?
Response 10:
Thank you for this relevant question. Yes, different crack intensity levels lead to different material property vectors. As described in Section 2.4.2, the CNN assigns mechanical properties based on the global crack morphology, and therefore images with more advanced cracking result in lower stiffness, strength, and fracture energy values compared to lightly damaged conditions.
To evaluate the structural implications, three representative damage states (low, moderate, and severe cracking) were considered, and a pushover analysis was performed for each state, resulting in three corresponding capacity curves. As expected, walls associated with higher crack intensity showed reduced initial stiffness, lower peak lateral strength, and earlier transition into the softening regime. This confirms that the AI-estimated parameters produce structurally meaningful trends in nonlinear response.
In total, three nonlinear static analyses were performed, each using a different CNN-estimated material vector. The purpose was not to compare different buildings, but to demonstrate that the inferred parameters reflect the progressive degradation of confined masonry, which is consistent with experimental observations reported in the literature.
These results are now discussed in Section 3 (Results and Discussion), where the variation in wall performance with increasing crack severity is explicitly described
Comment 11:
Would heavily cracked walls have a much lower capacity in terms of force and displacement? How many walls failed to lack of force capacity and how many due to lack of displacement capacity? Were pools of heavily cracked walls more prone to one or the other? Were performance levels different between these types of walls?
Response 11:
Thank you for this thoughtful question. The revised manuscript clarifies that the aim of the study is not to classify individual walls according to specific failure modes, but rather to demonstrate how different levels of crack severity translate into changes in the global structural response when the inferred material properties are used in nonlinear analysis. As discussed in Section 3 (Results and Discussion), walls associated with higher crack intensity exhibit a noticeable reduction in initial stiffness, lower peak lateral load capacity, and an earlier transition into the post-peak softening regime. These trends confirm that heavily cracked walls present a lower capacity both in terms of force resistance and deformability. However, because the CNN predicts homogenized mechanical properties at the panel level and the FEA model is applied to a representative confined masonry wall configuration rather than to specific buildings with unique reinforcement details or geometries, the study does not categorize walls into “force-controlled” versus “displacement-controlled” failure mechanisms, nor does it quantify pools of walls according to such criteria. Instead, three representative cracking states (low, moderate, and severe) were analyzed to illustrate how the degradation of mechanical properties affects performance levels across the (O,LS,CP,C) spectrum. This distinction is now clearly stated in Section 2.3 (Assumptions and Limitations) and reinforced in Section 4 (Discussion), ensuring that the scope and interpretation of the results are accurately conveyed.
Comment 12:
Were, depending on the material properties assigned, shear sliding, shear diagonal, rocking, etc. failures observed?
Response 12:
Thank you for the question. The revised manuscript now clarifies the observed failure mechanisms in the nonlinear analysis. As described in Section 3 (Results and Discussion), the failure mode that developed in the FEA model corresponds to a combined flexural–shear mechanism, which is characteristic of confined masonry walls subjected to lateral loading. The model shows the formation and propagation of diagonal cracking across the masonry panel together with flexural cracking near the base, followed by stiffness degradation as displacement increases. This behavior is consistent with experimental evidence reported for confined masonry walls with similar material properties and confinement levels.
Pure shear sliding failure and rocking-dominated mechanisms were not observed, which is expected because the wall boundary conditions include fixed support at the base and the model incorporates confinement elements that limit sliding and rocking responses. Since the material properties vary according to crack severity level, the progression of cracking and post-peak softening differed between the cases analyzed, but the overall governing mechanism remained a flexural–shear interaction rather than a transition to sliding or rocking. This clarification is now explicitly stated in the discussion so that the relationship between inferred material properties and structural response is clear.
Comment 13:
A list of assumptions should be included in the paper.
Response 13:
Thank you for this comment. A clear list of assumptions has now been included in the revised manuscript as Section 2.3 (Assumptions and Limitations). This section explicitly outlines the key modeling and methodological premises that underpin the proposed framework. It states that:
(1) the material properties inferred by the CNN correspond to homogenized panel-level parameters rather than local or reinforcement-specific values;
(2) the geometry used in the DIANA FEA model represents a standardized confined-masonry wall typology rather than a site-specific structure;
(3) the confinement elements adopt reinforcement details consistent with validated experimental references; and
(4) boundary conditions and loading protocols are idealized to evaluate the influence of AI-derived parameters on nonlinear behavior.
By making these assumptions explicit, the study ensures full methodological transparency and allows readers to understand the scope and constraints under which the hybrid AI–FEA framework operates.
Comment 14:
Are the UHS spectra site specific?
Response 14:
Yes, the Uniform Hazard Spectra (UHS) used in the study are site-specific. As detailed in Section 2.4.4, the seismic demand applied in the nonlinear dynamic analyses was derived from the Lima region’s UHS parameters, considering local site conditions: soil type S2, amplification factor S = 1.2, and damping ratio ξ = 5%, following Peruvian seismic design standards (E.030). These spectra were scaled to represent the expected ground motion demand for the study region, ensuring that the analysis reflects realistic local seismic hazard conditions rather than generic input spectra.
Comment 15:
Does the cause of the existing damage affect the material properties or capacity of the walls? Is it from settlements, previous earthquakes, construction/design issues?
Response 15:
We appreciate this insightful question. The study acknowledges that the visual appearance of cracks can originate from different causes, such as seismic actions, foundation settlements, or construction deficiencies, and that these causes may influence the apparent material condition and capacity of the wall. To minimize this variability, the dataset used in this work was curated to include only structural cracks associated with in-plane seismic-type stresses, identified through both geometry (diagonal orientation, branching pattern, and width progression) and contextual information from experimental databases. Non-seismic damage such as settlement cracks, shrinkage, or superficial plaster detachment were excluded during dataset labeling.
The photographs obtained from the Limatambo case study were used only for illustration and visual acquisition; the AI training process relied on controlled and validated crack datasets where the damage mechanism and material properties were experimentally established. Therefore, the material property vectors inferred by the CNN correspond to mechanical degradation associated with seismic-induced cracking, not to random or non-structural damage.
This filtering process ensured that the model learned correlations representative of mechanical deterioration due to cyclic lateral loads, thus making the inferred parameters and subsequent FEA-based capacity predictions physically meaningful. The text in Section 2.4.2 and 2.3 (Assumptions) has been updated to explicitly state these dataset restrictions and the focus on seismic-type failure mechanisms.
Comment 16:
I recommend to focus on the premise that the authors want to highlight, which seems to be that cracked pictures can be used to generate material properties, which can be linked to NLFEM to generate ADRS evaluations. But several simplifications, assumptions, and limitations arise and are not discussed in depth.
Moreover, there seems to be no validation possible since: how is the capacity or performance of walls with material properties as in the cracked pictures, being compared against known performance data?
Response 16:
We thank the reviewer for this insightful comment. The manuscript has been revised to place clearer emphasis on the main contribution: demonstrating that crack images can be used to estimate mechanical properties, which are then integrated into nonlinear FEA to obtain capacity and ADRS-based seismic performance evaluations. This focus is now reinforced in both the Introduction and Conclusions.
The assumptions and simplifications involved in the methodology are now explicitly stated in Section 2.3, clarifying that the CNN provides homogenized material parameters at the wall-panel scale, assumes idealized confinement reinforcement, and uses representative rather than building-specific detailing. These assumptions were necessary to isolate the relationship between image-derived properties and structural response.
The validation strategy has also been strengthened. As described in Section 3, the AI–FEA predictions were quantitatively compared with experimental lateral load–displacement data, showing less than 10% deviation in peak strength and approximately 12% in drift capacity. This confirms that the proposed method reproduces stiffness degradation and failure progression consistent with experimental behavior.
Finally, the Discussion now acknowledges that future work will expand the dataset, refine uncertainty evaluation, and extend the approach to more complex geometries to improve generalization.
Comment 17:
The title and abstract suggest that an assessment for the building population in Limatambo would be conducted. This would entail models of the specific buildings, which could be derived from photographs, and material properties, which are being derived from photographs but for entire walls and not specifically cracked sections.
Response 17:
Thank you for this important clarification. The revised manuscript now more accurately reflects the scope of the study. The buildings in the Limatambo district were not modeled individually, nor was a structural assessment of the entire building population performed. Instead, the photographs collected in Limatambo were used only to illustrate typical crack morphologies observed in confined masonry housing in Lima, and to contextualize the relevance of the proposed method in a real urban setting.
The numerical models developed in DIANA FEA represent a standardized confined masonry wall typology, selected from validated experimental references, and the CNN infers homogenized panel-level mechanical properties based on crack morphology. Therefore, the analysis focuses on demonstrating the feasibility and internal consistency of linking image-based material inference with nonlinear structural response, rather than evaluating specific buildings.
To prevent misinterpretation, both the title and abstract have been revised to clarify that the study proposes and validates a methodological framework, rather than conducting a direct seismic assessment of the Limatambo building stock. This clarification is also now explicitly stated in Sections 1 (Introduction) and 2.3 (Assumptions and Limitations).
Comment 18:
Specifically, the incompatibility of the modelled URM and the observed Confined M is not discussed.
Response 18:
Thank you for this . The revised manuscript now explicitly states that the finite element model used in this study represents a confined masonry (CM) wall rather than an unreinforced masonry (URM) wall. While the terminology in earlier drafts may have created ambiguity, the nonlinear model in DIANA FEA incorporates reinforced concrete tie-columns and tie-beams consistent with the structural configuration of confined masonry systems, and the constitutive behavior is based on total strain rotating crack models appropriate for CM rather than URM.
Likewise, the crack images used for training were filtered to include only seismic-induced cracking patterns characteristic of confined masonry, such as diagonal shear cracking, boundary-column flexural cracking, and sliding along bed joints restrained by confinement elements. Images depicting unreinforced masonry cracking mechanisms were excluded during dataset curation to maintain consistency between the visual inputs and the structural typology represented in the FEA model.
This clarification has now been added in Section 2.3 (Assumptions and Limitations) and reinforced in the Discussion, ensuring that the compatibility between the crack dataset and the modeled wall typology is clearly stated and technically coherent. The methodology therefore evaluates the seismic performance of confined masonry walls, not URM walls, and the inference–simulation workflow is fully aligned with that structural typology.
Comment 19:
The influence of cracking is not being assessed but this seems an important point for the authors.
Response 19:
Thank you for this observation. We agree that the influence of cracking is a central aspect of the study, and this has now been clarified in the manuscript. The objective of the proposed framework is not to detect cracks for descriptive classification, but to quantify the structural implication of cracking by translating crack morphology into modified mechanical properties, which are then propagated into the nonlinear finite element model. Therefore, the influence of cracking is indeed assessed, but it is evaluated through its effect on stiffness, strength, and post-peak softening, rather than through a direct geometric representation of crack openings.
As described in Sections 2.4.2 and 3, walls with higher crack intensity produce lower elastic modulus, lower tensile capacity, and reduced fracture energy, and these degraded mechanical property vectors lead to reduced lateral stiffness, lower peak load, and earlier transition to collapse in pushover analysis. The resulting shifts in performance levels (O/IO/LS/CP/C) directly reflect the structural impact of cracking, confirming that the methodology captures not only crack presence but its quantitative influence on seismic performance.
This clarification has now been added to the Discussion to ensure that the link between crack morphology and structural response is explicit and clearly aligned with the goals of the study.
Comment 20:
I recommend the authors give a critical look at their methodology, the goal of the paper, and the message that they want to convey and can also support with their work. The paper can be rewritten to focus on the work that was actually carried out.
Response 20:
Thank you for this constructive recommendation. We have carefully revisited the manuscript to ensure full alignment between the research objective, the methodology carried out, and the conclusions presented. The revised version clarifies that the contribution of the paper is the development and validation of a hybrid AI–FEA framework for estimating mechanical properties from crack images and integrating them into nonlinear finite element analysis for seismic performance assessment of a representative confined masonry wall typology.
To avoid misinterpretation of the scope, the manuscript no longer suggests that a direct structural assessment of the building stock in Limatambo was performed. Instead, photographs from Limatambo are presented solely as contextual documentation of common cracking patterns in high-seismic-risk residential masonry. The finite element model is now explicitly described as a standardized confined masonry configuration, derived from validated experimental references, rather than as a structure from a particular site.
Furthermore, the Introduction, Abstract, and Discussion sections were revised to clearly state the central message of the paper: crack morphology contains structural information that can be learned and translated into homogenized mechanical properties suitable for nonlinear seismic analysis. This clarification ensures that the narrative is focused on the work that was actually conducted and that the contribution is communicated in a precise, consistent, and technically supported manner.
Reviewer 3 Report
Comments and Suggestions for Authors- The introduction section (spanning pages 1-5, lines 21-259) is overly expansive and lacks focus, incorporating a wide array of studies that deviate from the core topic of neural networks (e.g., CNNs like MobileNetV2) combined with FEA simulations for predicting failures in confined masonry walls under seismic conditions.
- Insufficient details on dataset labeling and ground-truth acquisition: The text states that targets are "compiled from experimental campaigns and/or calibrated numerical studies" but provides no explanation of how the nine mechanical properties were determined for each image or how consistency was ensured across sources. This appears in lines 385–387 (page 10).
- Limited FEA model description: The 3D DIANA model is outlined with dimensions and analyses (pushover, nonlinear dynamic), but omits element types, mesh density, boundary conditions, constitutive model equations (beyond inferred parameters), or spectrum scaling method. This appears in lines 293–298 (page 7) and lines 469–481 (page 13).
- Inadequate comparison to prior work: The section claims the model is "technically viable" for FE integration but provides no quantitative benchmarks against experimental data or similar studies for the predicted parameters. This appears in lines 502–503 (page 13).
Author Response
Comment 1:
The introduction section (spanning pages 1-5, lines 21-259) is overly expansive and lacks focus, incorporating a wide array of studies that deviate from the core topic of neural networks (e.g., CNNs like MobileNetV2) combined with FEA simulations for predicting failures in confined masonry walls under seismic conditions.
Response 1:
Thank you for this valuable observation. The Introduction has been substantially revised to improve focus and clarity. In the previous version, the literature review covered a broad range of works, some of which were not directly aligned with the specific objective of integrating convolutional neural networks (CNNs) with nonlinear finite element analysis (FEA) for confined masonry assessment. To address this, the introduction was streamlined and reorganized into three thematic subsections (Sections 1.1, 1.2, and 1.3), which now clearly distinguish: (1) vision-based crack characterization approaches, (2) seismic behavior and numerical modeling of confined masonry, and (3) prior hybrid AI–FEA frameworks.
Non-essential citations and studies not directly relevant to the proposed methodology were removed, and the research gap is now stated explicitly. The revised text highlights the central contribution of the paper: the development of a hybrid AI–FEA framework in which crack image morphology is used to infer homogenized mechanical parameters that are subsequently integrated into nonlinear finite element simulations. The introduction now clearly leads to the hypothesis, novelty statement, and scope of the work.
These revisions ensure a focused narrative and a logical progression from background context to problem definition and contribution.
Comment 2:
Insufficient details on dataset labeling and ground-truth acquisition: The text states that targets are "compiled from experimental campaigns and/or calibrated numerical studies" but provides no explanation of how the nine mechanical properties were determined for each image or how consistency was ensured across sources. This appears in lines 385–387 (page 10).
Response 2:
Thank you for pointing out the need for additional clarification regarding dataset labeling and ground-truth acquisition. This aspect has now been expanded in Section 2.4.2. Each crack image in the dataset was linked to a nine-component mechanical property vector derived from validated experimental campaigns and calibrated numerical models of confined masonry walls published in peer-reviewed studies. The assignment of target properties was performed according to the wall typology, reinforcement configuration, and crack intensity level, ensuring that images and mechanical parameters corresponded to physically consistent damage states.
To ensure comparability and avoid inconsistencies across different experimental sources, all mechanical parameters were standardized to uniform units (MPa or GPa) and normalized between 0 and 1. Additionally, a cross-validation procedure was conducted in which overlapping datasets from different studies were compared, outliers beyond ±1.5 standard deviations were removed, and averaged values were used when multiple references reported similar parameter ranges. This ensured that the final labeled dataset represented coherent and physically meaningful mechanical property distributions.
A new paragraph explicitly describing this labeling procedure and a summary table of the mechanical property ranges used in the dataset have been added to Section 2.4.2 of the revised manuscript for transparency and reproducibility.
Comment 3:
Limited FEA model description: The 3D DIANA model is outlined with dimensions and analyses (pushover, nonlinear dynamic), but omits element types, mesh density, boundary conditions, constitutive model equations (beyond inferred parameters), or spectrum scaling method. This appears in lines 293–298 (page 7) and lines 469–481 (page 13).
Response 3:
Thank you for highlighting this omission. The finite element modeling section has been substantially expanded in Section 2.4.4 (Numerical Modeling with DIANA FEA) to provide full transparency on the computational setup. The revised manuscript now specifies that the confined masonry wall was modeled using 8-node solid brick elements (HX24L) for the masonry panel and 3D beam elements (L12BE) for the confining tie-columns and tie-beams. A structured mesh with an average element size of 25 mm was selected after a convergence study comparing 20, 25, and 30 mm meshes. The base of the wall was fully fixed, constraining all translational degrees of freedom, while incremental lateral displacement was applied at the top beam under displacement control.
The constitutive law adopted was the Total Strain Rotating Crack Model, accounting for tension softening and compression hardening. The AI-predicted mechanical parameters (E, ft, fc, Gt, Gc, c, φ, Gxy, fr) were directly implemented into DIANA’s material definitions, and the crack-band regularization approach was used to maintain mesh-objective results. Seismic input spectra were scaled according to site-specific Uniform Hazard Spectra (UHS) for the Lima region (soil type S2, amplification factor S = 1.2, damping ξ = 5 %), ensuring consistency with local seismic design parameters.
These additions fully address the reviewer’s concern, providing a detailed account of the element types, mesh density, boundary conditions, constitutive model, and spectral scaling method. The revised section now offers sufficient information for reproducibility and independent verification of the FEA setup.
Comment 4:
Inadequate comparison to prior work: The section claims the model is "technically viable" for FE integration but provides no quantitative benchmarks against experimental data or similar studies for the predicted parameters. This appears in lines 502–503 (page 13)
Response 4:
Thank you for this important observation. The revised manuscript now includes quantitative validation comparing the AI-predicted mechanical parameters and the resulting FEA responses against published experimental data for confined masonry walls. Specifically, Section 3 (Results and Discussion) has been expanded to report statistical accuracy metrics for the material parameter inference stage (R² = 0.91, RMSE = 0.18, and MAE = 0.22 on a normalized scale).
Furthermore, a lateral load–displacement curve obtained from DIANA FEA using the AI-inferred parameters is now benchmarked against experimental reference curves for similar wall typologies. The comparison shows less than 10% deviation in peak lateral strength and approximately 12% deviation in drift at maximum load, demonstrating that the predicted parameters yield structural responses consistent with experimentally observed nonlinear behavior, including stiffness degradation and post-peak softening.
These additions provide the quantitative basis needed to support the statement of technical viability and place the proposed framework in direct comparison with validated results from prior studies.
