Simulating the Failure Mechanism of High-Slope Angles Under Rainfall-Mining Coupling Using MatDEM
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors utilized the MatDEM numerical simulation software to analyze slope failure at high slope angles (45°, 55°, and 65°) under the coupled effects of rainfall and excavation. Moreover, they simulated the stress distribution, failure characteristics, and energy conversion in the models under different slope angles and analyzed the failure mechanisms at each stage.
From a practical engineering point of view, I think this study aligns well with the issues encountered on site, especially in southern China. Therefore, I believe that both the research methodology and the depth of analysis are innovative.
However, there are still some issues in the manuscript that require further explanation or correction.
Overall, I think this paper can be published in Water after minor revisions.
Herein the specific review comments are as follows:
1) Abstract section: Further improvement is needed to highlight the influence of high slope angle on the deformation mechanism of the rock masses.
2) Why the failure mode of the slope model with a 55° slope angle is smaller than that of the 45° and 65° models requires further explanation by the authors.
3) Please review the entire manuscript and add the units of letters or symbols below each equation.
4) In this study, how you control the size of the rainfall should be briefly described.
5) The important findings in the conclusions need to be supported by valid simulation data. Therefore, I recommend supplementing this data to support the conclusions drawn.
6) To facilitate further thinking for readers regarding this research, please briefly outline the direction of future research.
Author Response
Authors’ responses to the comments of Reviewer #1:
1, Abstract section: Further improvement is needed to highlight the influence of high slope angle on the deformation mechanism of the rock masses.
>Response: Thank you for your valuable advice. We have optimized the abstract to further highlight the influence of high slope angles on rock deformation mechanisms.
>Implemented: As shown in Lines 27-36. Herein the stress distribution, failure characteristics, and energy conversion of the model were simulated under different slope angles to analyze the failure mechanism at each stage. The simulation results show that the damage scale is smallest at 55° and largest at 65°. This indicates that setting the slope angle to 55° can reduce the risk of slope instability. Moreover, the reduction of elastic potential energy during the mine room mining stage is similar to that of mechanical energy. During the pillar mining stage, stress is concentrated in each goaf, result- ing in a greater reduction in mechanical energy compared to elastic potential energy. Finally, after the completion of the continuous pillar mining stage, stress becomes concentrated in the failure area, and the effect of the slope angle on mechanical energy reduction becomes evident after the complete collapse of the model.
2, Why the failure mode of the slope model with a 55° slope angle is smaller than that of the 45° and 65° models requires further explanation by the authors.
>Response: Thank you for your valuable advice. We have further explained in this manuscript that the failure modes of the 55° slope angle model are smaller than those of the 45° and 65° models.
>Implemented: As shown in Lines 295-300. By comparing the stress distr- ibution at different stages and under various slope angles, it can be found that the slope angle has little influence on the stress distribution during the mining stage of the mine room. Nevertheless, the stress concentration area in each failure area differs during the continuous pillar mining stage. Herein the 55° model has the smallest area, while the 65° model has the largest. As shown in Lines 330-340. Compared with the stress variations at different high slope angles, the overall stress variation pattern is similar. The difference lies in the varying reduction values of stress. In the mining stage, the reduction value for the 65° model is higher than that of the 45° and 55° models. Furthermore, during the mining stage of the pillar, the change in the 55° model is minimal, with changes remaining roughly consistent throughout the continu- ous pillar mining stage. Among them, the overall maximum stress difference for the 65° model is 51.5 kPa, for the 55° model it is 43.3 kPa, and for the 45° model it is 48.61 kPa. Accordingly, this fully demonstrates that the 65° slope angle model exhibits a greater conversion of mechanical energy into other forms during the numerical simulation of transitioning from open-pit to underground mining under the coupled effect of rainfall and mining activities, resulting in the highest degree of damage. As shown in Lines 361-369. After the end of the continuous pillar mining stage, the displacement areas under different slope angles are clearly distinct. Herein, the displacement area of the 45° slope angle model has extended to the edge of the upper surface; the 65° model has the most significant impact on the overlying rock displacement, as well as the 55° model primarily affects the upper part of the goaf. This shows once again that different slope angle models have different influences on the subsidence of overlying rock under numerical simulation. A 55° slope angle has the least influence, followed by a 45° slope angle, and a 65° slope angle has the most influence on the stability of overlying rock. As shown in Lines 390-393. Among them, the maximum displacement is at the 65° slope angle, measuring point No. 13 (above mine rooms 2# and 3#), which is -0.605 mm. The minimum displacement is -0.41 mm at measuring point No. 17 (in the continuous pillar 2# area), with a 55° slope angle. As shown in Lines 430-433. Here, the difference in energy between a 45° and a 55° slope angle is 1.16 J, and between a 45° and a 65° slope angle is 1.4277 J. In the mining stage, the energy reduction values of different slope angles vary; at 45°, it is 0.602 J more than at 55°, and 0.2801 J less than at 65°. As shown in Lines 436-438. The overall rule is that the mechanical energy reduction value for the 65° model is the greatest, followed by the 45° model, and the least is the 55° model.
3, Please review the entire manuscript and add the units of letters or symbols below each equation.
>Response: Thank you for your valuable advice. We have read the full text and have supplemented the relevant units in letters below each equation.
>Implemented: As shown in Lines 178-179. where Fsmax is the maximum shear force, MPa; Fs0 is the adhesion between particles, MPa; μ is the friction coefficient; and Fn is the normal pressure, MPa. As shown in Lines 180-181. where Kn is the normal elastic modulus, MPa; Ks is the tangential stiffness, N/m3; as well as k1 and kn are the properties of the two particles themselves. As shown in Lines 185-186. where Fv is the global damping force, N; η is the damping coefficient, N/(m/s); and x is the particle velocity, m/s. As shown in Lines 188-190. where Ee is the elastic potential energy, J; Eg is the gravitational potential energy, J; Xn is the normal displacement, m; Xs is the tangential displacement, m; m is the particle mass, kg; g is the gravitational acceleration, m/s2; and h is the relative height of the plane, m. As shown in Lines 195-196. where E is Young's modulus, MPa; d is the particle radius, m; and v is Poisson's ratio, MPa. As shown in Line 197. where Xb is the fracture displacement, m; and Tu is the tensile strength, MPa. As shown in Line 198. where μi is the coefficient of internal friction; and Cu is the compressive strength, MPa. As shown in Lines 207-210. where K is the hydraulic conductivity coefficient corresponding to saturation, m2/d; Ks is the saturated hydraulic conductivity, cm/s; S is the saturation; θs and θr are the saturated water content and initial water content, respectively; Hp is the pressure head, m; and α and n are fitting parameters. As shown in Lines 215-216. where θi is the water content at the current time, %; as well as Ii is the distance from the particle center to the contact point, m. As shown in Line 219. where Lij is the particle spacing based on the particle centers, m. As shown in Lines 258-260. where Qi is the discharge rate of particle i at the boundary, m3/s; S is the surface area of the boundary region, m2; B is the number of particles in the boundary region, and Ci is the cross-sectional area of particle i, m2.
4, In this study, how you control the size of the rainfall should be briefly described.
>Response: Thank you for your valuable advice. We have briefly described in the manuscript how to control the amount of rainfall.
>Implemented: As shown in Lines 277-278. Herein the rainfall infiltration process is simulated by setting the parameters of rainfall intensity and duration in the VGM model.
5, The important findings in the conclusions need to be supported by valid simulation data. Therefore, I recommend supplementing this data to support the conclusions drawn.
>Response: Thank you for your valuable advice. We have added relevant data from numerical simulations into our conclusions to support our findings.
>Implemented: As shown in Lines 468-480. The numerical simulation results show that the vertical displacement in the mining stage appears over the mine room, forming a small arc-shaped area. When in the pillar mining stage, different displacement areas show a tendency to interconnect. Here, the 55° slope angle model is relatively stable, with no subsidence occurring in any pillar. Continuous pillar 1# subsidence under the 45° slope angle model. The displacement area of the 65° slope angle model is basically connected, and continuous pillars 1# and 2# both show signs of subsidence. When the continuous pillar mining is completed, a large area of displacement occurs above the goaf, and the roof collapses. The maximum displacement is at the 65° slope angle, measuring point No. 13 (above mine rooms 2# and 3#), which is -0.605 mm. The minimum displacement is -0.41 mm at measuring point No. 17 (in the continuous pillar 2# area), with a 55° slope angle. Hence, the support work for the overlying rock should be done well during the underground mining using the room-and- pillar method, especially in the stage of continuous pillar extraction.
6, To facilitate further thinking for readers regarding this research, please briefly outline the direction of future research.
>Response: Thank you for your valuable advice. We have briefly outlined the direction of future research in the Conclusions.
>Implemented: As shown in Lines 492-495. In the future, based on this research, we will explore the characteristics of fracture evolution in slope rock masses under different slope height conditions. Additionally, we will continue to study the deformation rules of rock masses under the coupling effects of three scenarios: rainfall, excavation, and blasting.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsIn this study, a VGM method is proposed to simulate the deformation characteristics of rock slopes under the coupled effects of rainfall and excavation. I think it's doable. In addition, the evolution process of each stage of underground mining is discussed in detail from the angles of stress distribution, failure characteristics, and energy conversion, and the influence of high slope angles is summarized. I think the workload is quite substantial and has some originality.
The writing details of the paper are not very good, and there are some issues that need further improvement. I think this manuscript can be considered for publication after moderate revisions.
--Why is the slope angle of 45°~65° regarded as a high slope angle? Is there any theoretical basis or evidence for this?
--Line 84: What does "LAB Chrysotile" mean? Can you provide me with the full name?
--Section 2.2.4: What is the basis for the classification of rainfall intensity?
--Lines 285-288: After the mine-room excavation is completed, why is the stress mainly concentrated above 1# and 2# instead of 3# to 6#? Please explain.
--Line 328: Explain how to understand the sentence "The difference lies in the varying reduction values of stress."
--How to link the results of stress distribution, displacement and deformation characteristics, as well as energy conversion analysis together is a problem that needs to be solved at present.
Author Response
Authors’ responses to the comments of Reviewer #2:
1, Why is the slope angle of 45°~65° regarded as a high slope angle? Is there any theoretical basis or evidence for this?
>Response: Thank you for your valuable advice. We have explained in the manuscript why a slope angle of 45° to 65° is considered a high slope angle.
>Implemented: As shown in Lines 113-115. Based on the excavation status of most open-pit mines in China, a considerable proportion of slope angles are relatively high (generally defined as angles greater than 45°).
2, Line 84: What does "LAB Chrysotile" mean? Can you provide me with the full name?
>Response: Thank you for your valuable advice. We have explained the meaning of "LAB Chrysotile"; it is the name of an open-pit mine. See Ref. 24.
>Implemented: As shown in Lines 82-86. Besides, Amoushahi et al. utilized the finite element shear strength reduction method and limit equilibrium method to conduct deterministic and probabilistic analyses of slope stability. The results from all analyses indicate that the current mining slopes at LAB Chrysotile meet the acceptable design criteria limits [24]. As shown in Lines 564-565. Amoushahi, S.; Grenon, M.; Locat, J.; Turmel, D. Deterministic and probabilistic stability analysis of a mining rock slope in the vicinity of a major public road - case study of the LAB Chrysotile mine in Canada. Can. Geotech. J. 2018, 55, 1391-1404.
3, Section 2.2.4: What is the basis for the classification of rainfall intensity?
>Response: Thank you for your valuable advice. We have provided the basis for classifying rainfall intensity. The classification of rainfall intensity is primarily based on the actual rainfall data from Section 2.1 regarding Dexing Copper Mine, and in conjunction with the rainfall gradient, the rainfall intensity levels used in the numerical simulation are categorized as 10 mm/h, 20 mm/h, and 40 mm/h.
>Implemented: As shown in Lines 270-277. Considering the effect of high slope angles, the open-pit slope is divided into three numerical models: 45°, 55°, and 65°. At this stage, the rainfall intensity is 10 mm/h, and the rainfall duration is 1 hour. The mining stage of the underground room and pillar method revolves around the mining sequence of the first mine rooms (1# to 6#), the second pillars (1# to 3#), and the final continuous pillars (1# to 2#). Detailed mining sizes are shown in Figure 5. In this stage, the rainfall intensity (time) in the mine room, pillar, and continuous pillar is 20 mm/h (1 hour), 40 mm/h (0.5 hours), and 40 mm/h (0.5 hours), respectively.
4, Lines 285-288: After the mine-room excavation is completed, why is the stress mainly concentrated above 1# and 2# instead of 3# to 6#? Please explain.
>Response: Thank you for your valuable advice. We have explained this phenomenon.
>Implemented: As shown in Figure 6. After the mine-room excavation is completed, combined with the numerical simulation results in Figure 6, it can be seen that the values and ranges of StressZZ at locations 1# and 2# are significantly higher than those at locations 3# to 6#.
5, Line 328: Explain how to understand the sentence "The difference lies in the varying reduction values of stress."
>Response: Thank you for your valuable advice. There is ambiguity in this sentence. After discussion among all the authors, we decided it is more reasonable to delete this sentence. Therefore, we have deleted it.
6, How to link the results of stress distribution, displacement and deformation characteristics, as well as energy conversion analysis together is a problem that needs to be solved at present.
>Response: Thank you for your valuable advice. We have integrated the results of stress distribution, displacement deformation characteristics, as well as energy conversion analysis, providing relevant explanations.
>Implemented: As shown in Lines 439-444. Overall, according to the simulation results from the MatDEM numerical software, the stress distribution, displacement changes, and energy conversion under room-and-pillar mining with different slope angle models are summarized. Herein the 55° slope angle model is the smallest in terms of stress distribution, displacement change, and mechanical energy reduction. Therefore, we should design the slope cutting angle as 55° where possible to reduce the instability of the slope in practical engineering.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsPlease refer to attached file.
Comments for author File: Comments.pdf
Author Response
Authors’ responses to the comments of Reviewer #3:
1, This manuscript presents modelling scenario of the stress distribution, failure characteristics, and energy conversion under different slope angles for the transition from open-pit to underground mining. The study lacks (1) data to justify the model assumptions such as stress strain relations and failure criterion; (2) modelling explanation from the micro- to the macro-level; and (3) comparison between actual monitoring (experimental) data with model predications.
>Response: Thank you for your valuable advice. We have answered these three questions. First, the model assumes the data that we have already supplemented in Section 2.2.1, which mainly includes the Mohr-Coulomb criterion. Second, we have explained the process of the numerical model from micro to macro in Section 2.2.3. Third, we are carrying out relevant experimental studies and will need to cross-verify these with numerical simulations in subsequent papers. For details on VGM model modeling, please refer to Ref. 11.
>Implemented: As shown in Lines 170-177. In practical engineering, rock mass is influenced by various factors and undergoes different changes. To facilitate the numerical simulation, the establishment of the model needs to be based on some assumptions. Firstly, the model material is considered to be an ideal elastic-plastic body obeying the Mohr-Coulomb criterion. Secondly, the underground geological structure is ignored, so that the rock mass material is homogeneous. Finally, the rainwater infiltration capacity of the rock slope is considered to be uniform [33‒35]. Accordingly, based on the contact model with linear elasticity in MatDEM and according to the Mohr-Coulomb criterion. As shown in Lines 229-244. Herein the mechanical parameters of the rock masses should be determined before numerical simulation. In the MatDEM numerical software, the model is formed by the random accumulation of particles of various sizes, and there is no direct correspondence between the micro-mechanical parameters of the DEM model particles and the macro-mechanical properties of the rock [39]. Besides, the particle micromechanical parameters obtained by MatDEM through macro- and micro-mechanical transformation equations cannot meet practical requirements. Accordingly, it is necessary to calibrate the micro-mechanical parameters of the particles to match the macroscopic mechanical behavior of the model material. In this study, the material training box module of MatDEM software is utilized. The module integrates uniaxial compression, tensile, and other unit tests, and adjusts the microscopic parameters of the model by automatically testing five macro-scopic mechanical properties of the material (Young's modulus, Poisson's ratio, compressive strength, tensile strength, as well as internal friction angle) through continuous modification of the proportionality coefficient, so as to achieve the convergence of each mechanical property to the set value. After four rounds of parameter training, the error in the rock masses parameters can be reduced to 2%. As shown in Lines 536-537. Li, X.S.; Li, Q.H.; Wang, Y.M.; Liu, W.; Hou, D.; Zhu, C. Effect of slope angle on fractured rock masses under combined influence of variable rainfall infiltration and excavation unloading. J. Rock Mech. Geotech. 2024, 16, 4154-4176.
2, Lines 170-172: Model assumptions: "Firstly, the model material is considered to be an ideal elastic-plastic body obeying the Mohr-Coulomb criterion. Secondly, the underground geological structure is ignored, so that the rock mass material is homogeneous." First, you must provide figures showing the stress strain relationships as well as the standard figures that represent the Mohr-Coulomb criterion for the rock mass under investigation to justify the first assumption. Second, ignoring the underground geological structure as well as the fractures in the rock mass, while you are modelling the system as discrete particles is huge over estimation. A detailed justification is needed.
>Response: Thank you for your valuable advice. First of all, our hypothesis has been confirmed in previous studies, which you can refer to in Refs. 10 and 11. Secondly, this study primarily examines the impact of rainfall and excavation on slope rock mass. Future studies will further explore more complex modeling concepts regarding underground geological structures and fractures within rock mass.
>Implemented: As shown in Lines 534-535. Li, X.S.; Li, Q.H.; Wang, Y.M.; Liu, W.; Hou, D.; Zheng, W.B.; Zhang, X. Experimental study on instability mechanism and critical intensity of rainfall of high-steep rock slopes under unsaturated conditions. Int. J. Min. Sci. Techno. 2023, 33, 1243-1260. As shown in Lines 536-537. Li, X.S.; Li, Q.H.; Wang, Y.M.; Liu, W.; Hou, D.; Zhu, C. Effect of slope angle on fractured rock masses under combined influence of variable rainfall infiltration and excavation unloading. J. Rock Mech. Geotech. 2024, 16, 4154-4176.
3, Lines 175-207: Presented equations are for the porous medium at the macroscopic level. Then, line 208, indicates that "Eqs. (13) and (14) can be used to calculate the saturation of each particle in the VGM. " Explain how it can be done and highlight the number of particles used in the VGM?
>Response: Thank you for your valuable advice. We have explained this question and added the number of particles used in the VGM model in the manuscript. Please refer to Refs. 37 and 38 for the detailed calculation procedure.
>Implemented: As shown in Lines 200-206. Based on previous studies on numerical simulation of seepage flow, it is believed that each rock and soil particle can be analyzed as a collection of discrete particles and pores, as well as water flow is transmitted between these particles [36]. In particular, van Genuchten proposed an equation for the soil water content-pressure head curve [37, 38]. The closed-form expression for relative hydraulic conductivity can be derived from this equation, which can be used to accurately predict unsaturated water conductivity. The van Genuchten model (VGM, number of particles is 76,425) is expressed as follows. As shown in Lines 591-592. Hayek, M. Analytical solution for steady vertical flux through unsaturated soils based on van Genuchten- Mualem model. J. Hydrol. 2024, 634, 131066. As shown in Lines 593-594. Younes, A.; Mara, T.; Fahs, M.; Grunberger, O.; Ackerer, P. Hydraulic and transport parameter assessment using column infiltration experiments. Hydrol. Earth Syst. Sc. 2017, 21, 2263-2275.
4, Line 209: Equation 15, is the expansion coefficient of a particle adjacent to a cracked zone the same as that within a continuum of uniform particles? Also, what is the impact of particle size, geometry, and surface texture properties on model calculations using Eq. 15?
>Response: Thank you for your valuable advice. In the MatDEM modeling, we set the expansion coefficient of a particle adjacent to a cracked zone the same as that within a continuum of uniform particles. The particle size will affect the running speed of the model; differences in geometric shape will influence the outcome of the model's running process; and surface texture attributes will impact the stress distribution and plastic zone distribution following rainfall infiltration.
5, Line 244: Table 2. Microscopic mechanical parameters of the model material. Describe how these parameters were calculated and their relationships to the data shown in Table 1. Macroscopic mechanical parameters of the model material.
>Response: Thank you for your valuable advice. We have explained the parameters in Tables 1 and 2.
>Implemented: As shown in Lines 237-245. In this study, the material training box module of MatDEM software is utilized. The module integrates uniaxial compression, tensile, and other unit tests, and adjusts the microscopic parameters of the model by automatically testing five macro- scopic mechanical properties of the material (Young's modulus, Poisson's ratio, compressive strength, tensile strength, as well as internal friction angle) through continuous modification of the propor- tionality coefficient, so as to achieve the convergence of each mechanical property to the set value. After four rounds of parameter training, the error in the rock masses parameters can be reduced to 2%. The macro- and micro-mechanical parameters of the materials after training are presented in Table 1 and Table 2.
6, Lines 250-252: "When the volumetric water content of adjacent particles at the upper boundary forms a hydraulic difference, the seepage channel opens, and the water migrates downward." what is the impact of existing cracks on this kind of assumption?
>Response: Thank you for your valuable advice. Herein the existence of cracks makes it easier for rainwater to seep downward. As a result, these cracks can accelerate the downward movement of rainwater and may increase the width of the seepage channels.
7, Line 257: "By substituting Qi into Eq. (18), the infiltration process of boundary particles under constant rainfall intensity can be realized." since Eq. 18 does not have Qi, explain how the infiltration is calculated.
>Response: Thank you for your valuable advice. Although there is no parameter Qi in Eq. (18), the process of boundary particle infiltration under constant rainfall intensity can be obtained by calculating the parameters in Eq. (20) and then solving it jointly with Eq. (18).
8, Lines 260-262: "After the seepage calculation, the slope's strength parameters are adjusted based on the particle volume water content information." show the equations that relate the strength parameters to the volumetric water content at both the microscopic and macroscopic levels.
>Response: Thank you for your valuable advice. We have added the relationship between strength parameters and volumetric water content at both micro and macro levels. Please refer to Ref. 10 for details.
>Implemented: As shown in Lines 264-265. After the seepage calculation, the slope's strength para- meters are adjusted based on the particle volume water content information [10]. As shown in Lines 534-535. Li, X.S.; Li, Q.H.; Wang, Y.M.; Liu, W.; Hou, D.; Zheng, W.B.; Zhang, X. Experimental study on instability mechanism and critical intensity of rainfall of high-steep rock slopes under unsaturated conditions. Int. J. Min. Sci. Techno. 2023, 33, 1243-1260.
9, How does the model account for the stress-strain distribution during crack initiation as well as after cracks are fully developed?
>Response: Thank you for your valuable advice. In this study, we mainly consider the relationship between stress distribution, displacement changes, and energy conversion in slope rock mass during the excavation of mine-rooms, pillars, and continuous pillars in the transition from open-pit to underground mining. The influence of high slope angles on these factors is emphasized. Here, the stress-strain distribution of the rock mass during crack initiation and after complete development can be clearly seen in Figure 6. This is mainly because the cracks first began to develop during the mining period of mine-rooms 1# and 2#. With the mining of pillars and continuous pillars, when the cracks were finally fully developed, a large area of the roof collapsed in the mining area. Besides, The evolution process of the cracks can be represented by deep yellow particles in the stress concentration region.
10, Line 388: "Figure 11. Displacement values of different monitoring points under different slope angle model." A Comparison between the data shown in Figure 11 for actual field monitoring with model prediction is required.
>Response: Thank you for your valuable advice. At present, we have not carried out any relevant practical engineering research, and the VGM model is a theoretical model proposed by us. In the future, we will further integrate our work with actual and experimental data.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors have revised their manuscript to an appropriate level. Hence, I recommend acceptance as revised.
