Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper presents a novel and well-executed study that will be of interest to researchers in rock mechanics, hydraulic fracturing, and geomechanics. The suggested revisions are intended to further clarify the methodology, deepen the interpretation of key mechanisms, and enhance the overall readability.

1. Provide a more detailed discussion of the mechanical competition mechanism between fractures. Section 4.2 and 5 describe how early growth of one fracture suppresses the other due to stress redistribution. This is a key finding. However, the explanation could be expanded: for example, by showing stress or energy fields around the competing crack tips at critical time steps, or by quantifying the reduction in the driving force (e.g., energy release rate) for the delayed fracture. A more mechanistic description would enhance the scientific depth.

2. Discuss the potential limitations of the homogeneous model comparison. The homogeneous model in Section 5 is used to contrast with heterogeneous cases. While this is useful, the homogeneous model assumes isotropic material properties and may not represent any real rock. The authors should briefly acknowledge that the homogeneous case is an idealized end-member and that real rocks always possess some degree of heterogeneity. This would contextualize the comparison and avoid overgeneralization.

3. Strengthen the statistical interpretation of peak pressure variability. In Section 4.2, the mean and standard deviation of peak pressure are reported for 18 specimens under two axial stress levels. It would be valuable to include a simple statistical test (e.g., t-test) to assess whether the difference between the two loading conditions is significant. This would support the claim that axial compression has a "limited" effect compared to mineral distribution.

4. This study conducted interesting research based on the background of hydraulic fracturing. As the author stated, hydraulic fracturing is crucial for unconventional energy and geothermal extraction. Therefore, I encourage authors to broaden their perspectives and enrich the contributions of existing work in different fields. The following literature can be reviewed, but not limited to：

（a）Distinct element modeling of hydraulic fracture propagation with discrete fracture network at Gonghe enhanced geothermal system site, northwest China. Journal of Rock Mechanics and Geotechnical Engineering. 2025. 

（b）Evaluating In-Situ Stress State and Stress Heterogeneity by Hydraulic Fracturing and Image Logging in Changcun Coalbed Methane Area, North China. Rock Mechanics and Rock Engineering. 2024.

（c）Mechanisms of stress-and fluid-pressure-driven fault reactivation in Gonghe granite: Implications for injection-induced earthquakes. International Journal of Rock Mechanics and Mining Sciences. 2024. 

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have extended some of the author's previous work (Ref. No. 49) into a much needed comprehensive analysis on the influence of mineral distribution on the complex crack growth within rocks during hydraulic fracturing. Some comments are below:

1) Lines 128-134: Seems like the introduction paragraph to section 2 is missing.

2) Line 168 is repeated from Line 167.

3) Were the simulations conducted in COMSOL? It would be better to mention what software and modules were used for the simulations.

4)Line 239: Not sure what the initial time step of 0.25 l_o means here.

5) It would be useful for the readers to have an idea about the numerical implementation methodology adopted within the current study. The authors may provide or direct the readers to relevant literature while discussing how they used the models in Figure 3 while simulating the BC's depicted in Figure 1(a).

5) Lines 470-471: Although the statement by the authors regarding the fundamental mechanism is correct, It is still not clear as to why the crack1 would progress at a faster rate compared to crack2 under 10 MPa if conditions were similar as the homogenous nature of the rock should provide same crack growth, does the mesh sensitivity cause this?

 

 

 

Author Response

Please see the attachment.

Author Response File: Author Response.docx