Research on the Dynamic Response Patterns of Layered Slopes Considering Non-Homogeneity Under Blast-Induced Vibration Effects

Comments 1: The article should include a more detailed description of the forcing as well as the applied signal filtering and calibration. References to the literature are also lacking in this regard.

Response 1: Thank you very much for the comments from the reviewer. We agree with this comment. Therefore, We have added relevant content in the second paragraph of section 2.2 of the article: A large number of monitoring results indicate that the degree of harm caused by blasting vibration effects is closely related to the peak acceleration of particle vibration. Therefore, in actual monitoring, the peak acceleration of particle vibration is used as the standard to measure the intensity of vibration. Corresponding measurement points were arranged according to the experimental blasting conditions. Figure 2 shows the waveform processing flow. Performing high pass filtering on the waveform can obtain the true three-dimensional waveform of blasting vibration, as shown in Figure 2 (a); Synthesize the waveforms in the X, Y, and Z directions into vectors to obtain the particle velocity, as shown in Figure 2 (b); Taking the Z direction as an example, frequency spectrum analysis is performed on the velocity in that direction to obtain the longitudinal frequency spectrum analysis diagram of particle vibration, as shown in Figure 2 (c). The waveform diagram in the Z direction is first integrated to obtain the displacement diagram of the particle vibration in the Z direction, as shown in Figure 2 (d). Perform first-order differentiation on the waveform in the Z direction to obtain the variation of particle vibration acceleration with time, as shown in Figure 2 (e). The waveform, after filtering and calibration, can meet the accuracy required for dynamic calculations. The revised content, as shown in lines 158-184, has been highlighted in red.

Comments 2: Also, the statement that measurement points were arranged based on the experimental blasting conditions is too vague.

Response 2: Thank you for pointing this out. We have added relevant content in the first paragraph of section 2.2 of the article: The blasting vibration monitoring adopts the Blast UM type blasting vibration monitoring instrument, including vibration sensors, converters, amplifiers, data processors, recorders and other equipment. The system can simultaneously record the original wave-form of blasting vibration in the X, Y, and Z directions. The range of the instrument is: vibration speed of 0.001-35cm/s; Frequency range: 5-300Hz. According to the testing requirements, set the sampling rate to trigger an electrical frequency of 0.035cm/s and record for 2 seconds. The measuring point is located along the west bank of Yanshan Iron Mine's highway. The blasting level (X) measured by the west bank has particle vibration velocities ranging from 0.1645 to 1.7489cm/s, and the main frequency of vibration is distributed between 5.3 and 29.3Hz; The Y-direction vibration velocity of the particle is between 0.1336-1.4509cm/s, and the main frequency distribution is between 5.8-29.3Hz; The vertical vibration velocity of the particle ranges from 0.0903 to 1.5523cm/s, and the main frequency distribution is between 5.0 and 29.8Hz; The combined velocity of particle vectors mainly ranges from 0.1471 to 2.1185 cm/s. The revised content, as shown in lines 144-157, has been highlighted in red.

Comments 3: The section on the description of the numerical model from Section 2.2 should be moved to where the entire numerical model is described.

Response 3: Thank you very much for the comments from the reviewer. Section 2.2 provides a description of blasting vibration data, without any content on numerical models.

Comments 4: What is the relationship between the notations 1'1', 2'2', ..., and x', y', z'?

Response 4: Thank you for your valuable feedback. We supplemented Figure 4 in Section 3.1.1 by stating that in the local coordinate system, x 'represents the inclination direction of the weak plane, y' represents the strike direction of the weak plane, and z 'represents the normal direction of the weak plane. The revised content, as shown in lines 206-208, has been highlighted in red.

We provided additional explanations for formula 2 in section 3.1.1: The generalized stress vector describing the failure of a weak surface has four components, namely ,,,。 Among them, ,,are the normal stresses in the normal direction (,,) of the weak plane local coordinate system.  is the shear stress in the weak plane local coordinate system. The generalized strain vector describing the failure of weak surfaces has four components, namely ,,,, Among them, ,, are the normal strain in the normal direction in the weak plane local coordinate system, and  is the shear strain in the weak plane local coordinate system . The revised content, as shown in lines 213-219, has been highlighted in red.

We provided additional explanations for formula 3 in section 3.1.1: In the formula, ,,are the increments of normal stress in the weak plane local coordinate system. is the increment of shear stress in the weak plane local coordinate system. ,,are the elastic increments of normal strain in the weak plane local coordinate system.  is the elastic increment of shear strain in the weak plane local coordinate system. ,​ are the correlation coefficient of elastic modulus, G is the shear modulus of the weak plane, describing the elastic stiffness of the material in the shear direction. The revised content, as shown in lines 228-234 has been highlighted in red.

Comments 5: The authors should rethink the designations used in the article, e.g., s (l.190) is referred to as “load on the rock”, while in line 194 it is referred to as stress, which makes the article significantly more difficult to understand. Also, “E” (l. 190) stands for “initial elastic modulus,” while in line 217 it stands for modulus of elasticity.

Response 5: Thank you for your valuable feedback. Modified  to stress; Modify E to E₀ in formulas (5) to (9). This represents the initial elastic modulus.

Comments 6: Where were the parameters shown in Table 2 taken from?

Response 6: Agree. Considering the length of the article, we have added a brief explanation before Table 2 in Section 4.1: This study processed the collected rock mass on site and obtained cylindrical specimens of layered biotite granulite. Uniaxial compressive strength tests and acoustic emission monitoring were conducted on the specimens to obtain parameters such as rock density, uniaxial compressive strength, and elastic modulus. At the same time, a digital drilling camera was used to measure, interpret, and analyze the structural planes of mining engineering geological drilling holes, obtaining parameter information such as the orientation, dip angle, number of structural planes, linear density, and bulk density of the structural planes. Based on the ‌Hoek-Brown criterion, the rock mechanics parameters that are more in line with engineering practice were obtained through reduction, as shown in Table 2. The revised content, as shown in lines 347-356, has been highlighted in red.

Comments 7: Please let me know what the authors mean by “viscous boundary” (l. 287) and what is the difference between “viscous boundary” and “free-field boundaries”?

Response 7: Viscous boundary is an artificial boundary condition used to reduce the influence of boundary reflection waves in a model. Its main purpose is to absorb seismic waves or moving carriers passing through the boundary, thereby simulating the energy dispersion characteristics of an infinite field. Viscous boundaries absorb seismic wave energy that propagates vertically and horizontally by applying resistive forces (or velocity dependent viscous forces) on the boundaries of the model. It is based on the velocity field of waves, achieved by setting damping coefficients at the boundaries that are related to material properties and wave propagation speed. Generally, viscous boundaries are set at the bottom of the model or away from the boundary of the load to prevent seismic waves (or blasting load waves) from reflecting back into the model at the boundary and interfering with the internal wavefield distribution. Free Field Boundary is a more complex boundary condition used to simulate an infinitely extended geological environment (or an infinitely extended solid slope), in order to more realistically reproduce the propagation and attenuation behavior of waves.

Comments 8: Considering the influence of boundary conditions, shouldn't the forcing point more in the center of the model?

Response 8: Boundary conditions do play an important role in blasting and model analysis, but in the actual mining process, the blasting point is often not located at the center of the model, but is limited by various factors such as terrain, blasting depth, and slope excavation design. Due to the different depths of blasting, the blasting point needs to be close to the slope or boundary in order to achieve more efficient blasting effects and meet the requirements of slope stability and excavation design. Therefore, from the perspective of the actual operation and design of the mine studied in this article, it is reasonable and necessary to have the blasting action point at the edge position, which may be different from the "center position" in the idealized model, but this offset is an optimized choice under actual engineering conditions.

Comments 9: Inadequate description of the model in relation to the results presented prevents further review of the article, e.g. Figure 9 “the rock hardness decreasing model” and Figure 10 “the rock hardness increasing model” - which models are in question? Where in the article is specified, defined “the rock hardness decreasing model” and “the rock hardness increasing model”?

Response 9: Thank you very much for the comments from the reviewer. We explained in lines 390-395：Figure 9(a) and (b) respectively illustrate the variation of PGA at different monitoring points on slopes without joints and with joint angles of 0°, 15°, 30°, 45°, 60°, 75°, and 90°, where the corresponding rock mass mechanical parameters decrease from the bottom to the top of the slope, indicating a decrease in rock hardness from the toe to the crest of the slope. Figure 10(a) and (b) show the variation of PGA with elevation on slopes where rock hardness increases from the toe to the crest.

Comments 10: Moreover :Equation (1) no definition or description of stress tensors；l.156 - 157 and others - inadequate fonts to describe parameters and variables；No sentence that “'” means variables and parameters in the local coordinate system；No definition of a number of variables and parameters appearing in Equation 3；Equation (8) parameter Emax is not defined；Figs. 5 and 6 are common knowledge and should be removed；Fig. 8 incorrect description of layers； Figs. 9 and 10 no information as to why the designation “None” in the figures corresponds to.

Response 10: We appreciate the valuable feedback from the reviewers. Equations (1) to (3) provide additional explanations（Lines 213-234）.The supplementary parameter E_max in equation (8) is defined as the maximum elastic modulus corresponding to the stress-strain relationship of the material. （Line 275）Merge Figure 5 and Figure 6 into Figure 6. Figures 9 and 10 'none' correspond to jointed slopes without joints.

Comments 1: Could you please explain how Eq. (8) derived from Eq. (7)? Also, I cannot reproduce Eq. (7) from Eq. (6). Please clarify. I believe Eq. (7) has a mistake.

Response 1: Thank you for your valuable feedback. Eq. (8) is derived from Eq. (6). And we have re derived Eq. (7) from Eq. (6).

Comments 2: β in Eq. (11) is missing. Please modify.

Response 2: Thank you very much for the comments from the reviewer. I also admire your diligent research attitude. We have revised the Eq. (11).

Comments 3: Figs. 5 and 6 can be combined.

Response 3: Thank you for your valuable feedback. We have merged Figure 5 and Figure 6 into Figure 6.

Comments 4: In line 246, what do “A” values mean? Similarly, in line 257, what does “B” parameter mean?

Response 4: Thank you for pointing this out. A has been modified to a scale parameter , and B has been modified to a shape parameter β. The revised content, as shown in lines 328-334, has been highlighted in red.

Comments 5: In Figs. 9 to 14, the units of PGA are missing. Why certain lines are smooth (Figs. 9 to 12), while others are non-smooth (Figs. 13 and 14)?

Response 5: Thank you very much for the comments from the reviewer. The article explains in line 386 that: The PGA units throughout the text are all in cm/s². The reason why the lines analyzing the variation of PGA with relative height in this article are smooth (Figs. 9 to 12) is that PGA is an absolute indicator that reflects the maximum acceleration at a certain point on the slope surface under earthquake or blasting action. Its changing trend is more controlled by the overall structure (such as slope geometry and input wave characteristics), and usually shows a relatively continuous trend with changes in height. The lines analyzing the variation of M_PGA with relative height are not smooth (Figs. 13 and 14) because M_PGA is a relative indicator, representing the ratio of PGA at a certain point to PGA at the foot of the slope. It not only depends on the PGA at a certain point on the slope surface, but also is influenced by the PGA at the foot of the slope.

Comments 6: There is a mistake in labeling equation number. For example, on page 17, it should be “(13)” instead of “(133)”.

Response 6: Thank you very much for the comments from the reviewer. I also admire your diligent research attitude. We have modified (133) to (13).

Comments 7: Please avoid using the same symbols to represent different physical meanings. For example, the authors use “F” in Eq. (13) and (11) to denote different meanings.

Response 7: Thank you very much for the comments, and we also appreciate any feedback you may have on our paper work. Eq. (11) is Formula F (x), and Eq. (13) is the safety factor F .They are not the same.

Comments 8: Why Figs. 10(a) and 10(b) are identical to each other?

Response 8: Thank you very much for the comments from the reviewer. I also admire your diligent research attitude. We will replace Figs. 10(a) with the correct image

Comments 9: The References styles are very inconsistent. Please modify.

Response 9: Thank you for pointing this out. We have modified the citation format to be the same.

Comments 10: The literature review is very insufficient. There are many important works about the dynamic response of slopes under blast loads are missing.

Response 10: Thank you to the reviewers for their valuable feedback. We have revised the introduction, adding new references in Section 1. The revised content, as shown in lines 32-103, has been highlighted in red.

Comments 11: On page 20, it should be Table 3, not Table 1. Also, it should not be “Capacity”. Please use proper terminology (similar problem occurs in Table 2).

Response 11: We appreciate the valuable feedback from the reviewers. We will modify the capacity in Tables 1 and 2 to Natural unit weight.

Comments 12: The authors repeatedly define “PGA” for peak ground accelerations, which is unnecessary and redundant. They just need to define it once.

Response 12: We appreciate the valuable feedback from the reviewers. We have removed duplicate content.

Comments 13: There are no sufficient insightful discussions in the paper. The whole analysis is like a numerical game. The authors should substantially improve this part.

Response 13: We sincerely appreciate the valuable feedback from the reviewers and acknowledge the importance of engaging in insightful discussions to enhance the impact of our analysis. This study mainly proposes a method of introducing Weibull distribution into the heterogeneity description of layered slopes, and characterizes the spatial variation characteristics of rock parameters such as elastic modulus and strength from a statistical perspective. This method can more accurately reflect the material properties of complex rock masses and avoid the result bias that may be caused by traditional uniform models. Although the original manuscript mainly focused on presenting numerical results, the research findings indicate that non-uniformity significantly affects the wave propagation path and energy distribution of slopes, especially in areas with dense joints where wave reflection and scattering effects are more significant, leading to enhanced local amplification effects. This can provide a new perspective for understanding the dynamic response of heterogeneous rock masses.

Comments 1: the correct size of the font defining the variables

Response 1: Thank you for your suggestion. We have made revisions to this section and addressed similar issues throughout the text. All formulas are uniformly set to 10pt size during editing. Thank you for your meticulous review.

Comments 2: no indication of what ‘None’ means in Figures 9 and 10

Response 2: Thank you for pointing this out. None indicates a slope without joints. In order to provide readers with a clearer understanding, we have changed 'None' to 'Without joints' in Figures 9, 10, and related images throughout the text. The revised content is highlighted in red.

Comments 3: how were the signals calibrated?

Response 3: Thank you to the reviewer for providing valuable feedback on our work. In order to avoid misinterpretation of signal characteristics, eliminate the influence of filtering differentiation, and ensure the accuracy of frequency domain analysis, the NUBOX-8016 intelligent vibration monitor's built-in scheme is used to calibrate the blasting waveform. The main steps include removing DC offset, amplitude calibration, timeline calibration, and filtering noise reduction. The calibrated waveform can truly reflect the intensity, frequency, and time characteristics of blasting. Considering the length of the paper and not the main research content, we did not elaborate on it in the main text.

Comments 4: too many meanings e.g. in the paragraph contained in lines 390-395 there is a description that ‘mechanical parameters decrease from the bottom to the top of the slope, indicating a decrease in rock hardness from the toe to the crest of the slope ...’ etc. However, no description of this model is available. What numerical values of the parameters were adopted in this case and why?

Response 4: Thank you for your valuable feedback. Thank you for pointing it out. We have supplemented the lithology and numbering of 12 rock masses in Figure 7, and provided 12 lithology parameters in Table 1. The elastic modulus increases from No.1 to No. 12, indicating that their hardness also increases accordingly. When assigning parameters to the calculation model from top to bottom according to No.1~ No.12, it is considered that the model is a "rock hardness decreasing model" where the rock hardness gradually decreases from the foot to the top of the slope. We have removed the relevant results of the rock hardness increasing model and changed the title from "rock hardness decreasing model" to "multi lithology model". As shown in l.338~l.343, the revised content is highlighted in red.

Comments 5: Also the description of ‘slope surface’ and ‘slope interior’ (Figures 9 and 10) is too laconic. These descriptions denote any of a number of possible points.

Response 5: Thank you for your valuable feedback. According to Figure 8 (Layout of Monitoring Points) and Table 1 (Coordinates of Monitoring Point Layout), N1-N17 are closer to the slope surface and are defined as slope surface monitoring points, while N18-N34 are located inside the slope and are defined as slope monitoring points. In order to express more clearly, we have modified Figure 8 by representing the slope surface monitoring points with red circles and the slope interior monitoring points with blue circles.

Comments 6: In numerical analyses, there is no perfect method that reflects the boundary conditions. Placing the forcing too close to one of the boundaries causes a disturbance in the propagation of waves (energy) in the considered system, which may result in bad or strongly distorted results of numerical analyses. Taking the above into account, have numerical analyses been carried out on the effect of the distance between the place of application of the forcing and the closer boundary of the system under consideration, and how does this affect the results?

Response 6: We agree with this viewpoint. The position of the force in numerical simulation is set according to the real mining situation. Since the monitoring points are not located on the side close to the boundary, current research has not considered the influence of the distance between the closer boundaries on the action points. This will serve as our subsequent research content. In the conclusion of the article, we have added relevant explanations, as shown in l.777~l.783, and the revised content is highlighted in red.

Comments 7: The authors wrote: ‘Based on the expression of damage parameters...’, however, no information is given as to which parameter they are referring to.

Response 7: Thank you for pointing this out. We have added the damage parameter D in Eq. (5) and (6) , hoping this can solve your doubts.

Comments 8: There is no information on what filtering cut-off frequency was adopted and on what basis (l.163). There is also no information on how the differentiation of the measurement signal was realised.

Response 8: Thank you for your question. We obtained the frequency distribution range of the blasting vibration signal through spectrum analysis of multiple test signals, and found that the main frequency components of the effective signal are concentrated between 0-60 Hz. Based on the main frequency characteristics of blasting vibration propagation and engineering requirements, a low-pass filter with a cutoff frequency of 60 Hz was selected. When differentiating, MATLAB's built-in function diff is used to quickly perform differential operations, achieving rapid analysis and dynamic feature extraction of blasting vibration signals. As shown in l.l58~l.168, the supplementary content is highlighted in red. I hope the above supplementary information can answer the reviewer's questions.

Comments 9: The authors wrote: ‘By analysing the variation of the Peak Ground Acceleration (PGA, measured in cm/s2) at various monitoring points on the slope, we can study the characteristics of the propagation of blasting vibration waves in rocky jointed slopes.’ (l.388) However, it is not clear where the monitoring points were located.

Response 9: Thank you for your question. Figure 8 shows the layout of monitoring points, and Table 2 shows the coordinates of monitoring point layout In order to express more clearly, we have modified Figure 8 by representing the slope surface monitoring points with red circles and the slope interior monitoring points with blue circles.

Comments 10: The description of E0max as ‘maximum elastic modulus’ is incorrect.

Response 10: Thank you for your question. We will define E_0max as the elastic modulus corresponding to the ε_max. As shown in l.260, the revised content is highlighted in red.

Comments 11: The authors wrote: ‘Figures 12(a) and (b) illustrate the variation of PGA with elevation for the hard rock model (No.12).’ (l. 414) Which rock model was used?

Response 11: Thank you for your question. After using a multi lithology model for analysis, representative No. 1 (softest rock) and No. 12 (hardest rock) were selected based on rock strength and rock mass distribution, and the entire model was compared and analyzed by assigning parameters. Relevant explanations have been added in l.344~l.347 of the text, and the revised content is highlighted in red.

Comments 12: Moreover:  Fig. 2 No description of vertical axes, font too small；Fig. 3 Previously axes were marked with capital letters；l. 260 - 261 and equation (5) No derivation of the relationship shown or reference to literature；Equation (7) Please check subscripts；l. 503 no definition of MPGA；l. 601 why were such values of the parameter adopted?

Response 12: Thank you for your question. We have redrawn Figure 2 and adjusted the font and format to be consistent throughout the entire text. We also modified the format of Figure 3 to a unified style for the entire text. We have added the damage parameter D to Eq. (5). We have modified ε in Eq.(7) to ε₀.  Additional explanations have been provided for M_PGA, as shown in l.484~l.485, with the revised content highlighted in red.

Comments 13: l. 601 why were such values of the parameter adopted?

Response 13: Thank you for your question. Setting different Weibull distribution shape parameters can analyze the impact of different distribution characteristics on the results. As β increases, the distribution shape gradually shifts towards a bell shape, and the peak values of the distribution become more concentrated, indicating an increase in the uniformity of the system. By selecting β=1,3,5,7,9, a series of situations ranging from exponential distribution to near deterministic distribution can be covered, thus comprehensively studying the influence of shape parameters on system behavior. This selection of increasing values can capture the trend of shape parameters changing from low to high, while also avoiding overly lengthy analysis. Provides sufficient comparison of shape characteristics while avoiding the computational burden caused by excessive parameter selection. Relevant explanations have been added to the text, as shown in l.583~ l.586, and the revised content is highlighted in red.

Comments 1: Eq. (7) has an error. It should be …The authors should also explain how ? relates to ? in Eq. (5).

Response 1: Thank you for your valuable feedback. We have modified ε in Eq. (7) to ε₀. Eq. (5) uses the mean and variance of microelements to represent the distribution of strength parameters, while Eq. (7) uses the shape factor ? to determine the distribution form of strength parameters. There is no quantitative relationship between ? and s. s reflects the degree of data dispersion, while ? can reflect the quantity and degree of data dispersion. I hope our explanation can answer your doubts.

Comments 2: Figure 2 is problematic. For example, the labels of the vertical axes of Figures 2(b), (c), (d), and (e) are missing. The captions for Figures 2(d) and (e) are also inaccurate. They are not response spectra. The authors should use the terminologies appropriately. In Figure 2(a), there are even Chinese characters in the labels of vertical axes. The font sizes are also too small.

Response 2: Thank you very much for the comments from the reviewer. I also admire your diligent research attitude. We have redrawn Figure 2 and changed its name, supplemented the detailed information of the coordinate axes, and applied the unified format throughout the text.

Comments 3: In Figure 4, the ?′ axis should be perpendicular to the ?′?′ plane.

Response 3: Thank you for your valuable feedback. We want to express that the ? 'axis should be perpendicular to the ?′ ?' plane. To avoid misunderstandings, we have modified the direction of ? 'and added a vertical symbol.

Comments 4: Please add units of cm/s² to Figures 9 to 14. All figures should be self-explanatory, even though in the main text, the authors mentioned that PGA are in cm/s². Similar problems occur in Figures 19 to 23.

Response 4: Thank you for pointing this out. We have added explanations about the units to the vertical axis PGA of all relevant images.

Comments 5: The authors should change the symbol of ? in Eq. (13). It is very confusing. I have raised this concern in the previous review, but the authors simply overlook it.

Response 5: Thank you very much for the comments from the reviewer. We have re-understood your suggestion and changed the symbol F in equation (13) to K.

Comments 6: It is puzzling that I have expressed concerns about the insufficiency of the literature review. The authors address this issue by merely highlighting certain texts, as if that adequately resolves my concerns.

Response 6: Thank you very much for the comments from the reviewer. I also admire your diligent research attitude. We have revised the relevant content of the first section on research status again, reorganized the overall logic, and supplemented the research methods.

Comments 7: The authors argue that their method can “more accurately reflect the material properties of complex rock masses and avoid the result bias that may be caused by traditional uniform models.” However, many existing methods from different studies make similar claims. The authors should perform quantitative comparisons between different methods to substantiate overclaiming their works. Overall, in my opinion, the analyses are simply numerical exercises that do not contribute enough to the field.

Response 7: Thank you very much for the comments, and we also appreciate any feedback you may have on our paper work. This article only discusses the response law of slopes under blasting dynamic action from two aspects: joint dip angle and heterogeneity. There are indeed similar methods in current research, and a comparison of research methods is still needed, which will be a direction for our future work.

Comments 8: The referencing styles remain inconsistent. Please compare references [16], [18], and [25]. Again, it shows that the authors did not pay attention to details.

Response 8: Thank you for your careful review. We have reorganized the format of all references according to the template provided by the journal.

Comments 9: I just realize that the authors choose “local damping” in line 379 without giving details related to the parameters of the local damping. This part should be improved and justified.

Response 9: Thank you for pointing this out. In dynamic analysis, it is usually necessary to set local damping control for vibration and energy dissipation in numerical simulations to ensure the stability and accuracy of the simulation. The default value for setting local damping in the calculation is 0.8. As shown in l.363~l.364, the supplementary content is highlighted in red.

Comments 10: In lines 840 and 842, the authors mention about ? and ?. These symbols are inaccurate.

Response 10: Thank you to the reviewers for their valuable feedback. We have changed ? to β, deleted ?, and checked for similar issues in the revised article.

Comments 11: The units for the properties in Figure 17 should be given.

Response 11: We appreciate the valuable feedback from the reviewers. We have modified the subheading of Figure 17 and added corresponding units for each attribute.

Comments 1: The unit for Fig. 2(a) appears to be incorrect. The unit for a velocity response spectrum is not cm/s.

Response 1: Thank you very much for the comments, and we also appreciate any feedback you may have on our paper work. Fig.2 (a)shows the relationship between particle vibration velocity and frequency, with the y-axis representing the particle vibration velocity and the unit in cm/s being correct.

Comments 2: In addition, please make sure that figure captions include those of sub-figures. For instance, the captions of Figures 2, 5, 9-11, and 15-18 should be modified.

Response 2: Thank you for pointing this out. These insightful comments have strong guiding significance for our future scientific research work. We have modified all image names containing subheadings in the article to the style shown in the journal template.

Comments 3: In line 364, the authors mentioned that they use the default damping "coefficient" of 0.8 (I am not sure if it is a damping ratio or a damping coefficient. If it is a damping coefficient, it should have a unit.). Is this number realistic? Will the choice of this number affect the results (in other words, are the results sensitive to this parameter)? The authors select the "default" values. Some empirical evidence from the literature should be given to justify this choice.

Response 3: Thank you to the reviewer for providing valuable feedback on our work. Local damping in FLAC^3D calculations is one of the damping forms used, which is frequency independent and does not require estimating the natural frequency of the modeled system. The local damping coefficient is mainly used to help dissipate excess energy in the system and ensure stability in the simulation. For dynamic or nonlinear analysis, appropriate damping coefficients can help accelerate convergence. FLAC^3D defaults to a preset damping coefficient value of 0.8, which usually does not require user modification. The selection of default values is based on experience, with the aim of providing a reasonable balance in most cases, ensuring computational stability without having a significant impact on physical results. I hope our explanation can answer your doubts.

Comments 4: In line 440, the unit is not cm/s2. It should be cm/s².

Response 4: Thank you for your valuable feedback. We also admire your diligent research attitude. We have made revisions to this section and addressed similar issues throughout the entire text.

Comments 5: In line 584, it should be "It provides sufficient ...", instead of "Provides sufficient ...".

Response 5: Thank you for pointing it out. Your feedback has played an important role in improving the quality of the paper. We have made revisions to this section and addressed similar issues throughout the entire text.

Comments 1: In the pdf version of the article I downloaded from the publisher's website, I do not see the changes in lines 262-263 (Comments 3).

Response 1: Thank you for pointing this out. We have re uploaded the latest revised version of the manuscript. We have revised the interpretation of E_0max, which represents the reciprocal of the ratio of strain to corresponding stress at the peak strength of the element. As shown in l.262~l.263, the revised content is highlighted in red.