The present study aims to elucidate the problem of a rock mass structural plane with a range of damage degrees and the numerical model selection for analysis of a slope with multiple sliding surfaces. Based on the relative displacement between blocks, the dynamic strength reduction-discontinuous deformation analysis (hereinafter referred to as DSR-DDA) method is proposed for studying slopes with multiple sliding surfaces. The slope-slider classic case was used to test the displacement threshold. The model was applied to the stability analysis of multiple sliding surfaces of a high rock slope in the Fushun West Open-Pit Mine. The results show that when the displacement threshold is set to 1 mm, the error between the DSR-DDA results and the theoretical solution is within 0.5%, which satisfies the calculation requirements. The most dangerous slip surface in the Fushun West Open-Pit Mine slope was identified. Based on the numerical slope model after the first landslide, the position of the secondary slip surface was then identified. The failure mode is traction sliding failure, and the middle and lower oil shales play a key role in the slope stability. This study recommends that mining of the remaining oil shale should stop to avoid causing large-scale landslides in the upper part of the slope and landslides at the pit-city boundary.
Large-scale geographical areas have complicated geological and instability conditions. A high slope with an open pit forms large areas prone to secondary instability after initial instability, resulting in a secondary sliding surface. The high rock slope is affected by the bedding structure, which complicates the stability problem of the slope. Therefore, it is necessary to elucidate the stability of rock high slopes with multiple potential sliding surfaces through research [
There are two commonly used calculation methods in slope stability analysis: the limit equilibrium method (LEM) [
Discontinuity is an intrinsic property of a rock mass. The discontinuous deformation analysis (DDA) proposed by Shi [
Shahami et al. [
The key problem in the development of slope stability evaluation is the safety factor and solution of the corresponding slip surface. Previously, the strength reduction method mostly assumes a uniform reduction in a rock mass. In an actual situation, the mechanical properties of the structural plane mainly determine the mechanical properties of the rock mass. However, the structural damage of a rock mass does not exhibit the same degree of damage through time. After the first instability of the slope, the block position and stress redistribute. Therefore, the secondary slip surface should be analyzed using the slope model after the first instability. In the past, the secondary sliding surface of the slope was studied. Few studies have considered the actual situation. To solve this problem, we draw on the advantage of DDA to calculate the displacement and consider the relative displacement between blocks. We proposed a multiple-sliding-surface search based on the DSR-DDA method and evaluated the slope stability. This method is mainly applied to solve rock mass stability problems, especially for large-scale rock masses with numerous structural planes. Moreover, this method can consider the variation in damage along a rock mass structural plane and help with numerical model selection in the analysis of a slope with multiple sliding surfaces. By analyzing a rock mass using this method, we can easily determine the safety factor and corresponding slip surface. Thus, measures can be taken to prevent the instability of a rock mass over time. We used an inclined plane slider to test the displacement threshold and verify the feasibility and accuracy of the proposed method and attempted to apply this approach to the stability analysis of a rock high slope in the Fushun West Open-Pit Mine.
The DDA uses a first-order displacement function to express the motion parameters of each block and assumes that the stress and strain are cconstant [
The overall equilibrium equation of the system based on the principle of minimum potential energy is as follows:
To consider the dissimilarity of the damage along the block structure surface in the real situation, it is proposed that the shear strength of the block structure surface is reduced so that the displacement change does not exceed the threshold value. We used the classic slope slider case to test the displacement threshold of the shear strength reduction. The model is shown in Figure
Model of the sliding block along the slope.
Mechanical properties of the slope model.
Number | Density (kg·m−3) | E (MPa) | Cohesion (MPa) | Friction (°) | Poisson’s ratio | Theoretical safety factor |
---|---|---|---|---|---|---|
01 | 2700 | 1000 | 40 | 50 | 0.35 | 1.192 |
02 | 2700 | 1000 | 40 | 55 | 0.35 | 1.428 |
03 | 2700 | 1000 | 40 | 60 | 0.35 | 1.732 |
04 | 2700 | 1000 | 40 | 65 | 0.35 | 2.145 |
05 | 2700 | 1000 | 40 | 70 | 0.35 | 2.747 |
06 | 2700 | 1000 | 40 | 75 | 0.35 | 3.732 |
07 | 2700 | 1000 | 40 | 80 | 0.35 | 5.671 |
The theoretical safety factor of the simple slope model is as follows:
Figure
Curve of safety factor and its error with the displacement threshold: (a) safety factor; (b) percentage error of safety factor.
Finding the exact solution of the contact force between the blocks is the core step in solving the total equilibrium equation. In each time step, it is necessary to redetermine the application of the spring and position of the spring. It is necessary to repeatedly generate a solution to solve the total stiffness matrix. The process of application and removal of the rigid spring is called an open-close iteration. There are three states of contact: opening, sliding, and locking. The criteria to determine the mode change are shown in Table
Contact status table.
Contact switch | Contact condition | Contact force |
---|---|---|
Open-open |
|
No |
Open-sliding |
|
Yes |
Open-locked |
|
Yes |
Sliding-open |
|
No |
Sliding-sliding |
|
Yes |
Sliding-locked |
|
Yes |
Locked-open |
|
No |
Locked-sliding |
|
Yes |
Locked-locked |
|
Yes |
1
Based on the above analysis, the DSR-DDA method is implemented in the program as shown in Figure
Flow chart of the DDA procedures.
The Fushun West Open-Pit Mine is located in the southeastern part of Fushun City and has a mining history of more than 100 years. It has formed “Asia’s largest pit” with a length of 6.6 km, a width of 2.2 km from north to south, and a depth of 400–500 m, representing a total volume of 1.7 billion cubic kilometers. The northern part of the coal-mining pit is adjacent to the urban area of Fushun City. If a landslide occurs in the northern slope, it will cause a large number of casualties and major property loss, seriously affecting the safety of all nearby construction facilities and endangering the safety of the entire city. The layout of the Fushun West Open-Pit Mine and the northern part of the western slope are shown with a geological section map in Figure
Layout of the Fushun West Open-Pit Mine and the northern part of the western slope in the geological section map: (a) Fushun West Open-Pit Mine; (b) geological section map.
Discontinuous structures such as joints and fissures play a controlling role in the deformation of a rock mass. The accuracy of the information acquisition of the structural plane is critical to the accuracy of the numerical simulation analysis. Using high-precision and high-efficiency unmanned aerial vehicle technology, deterministic structural plane information is accurately acquired to generate a point cloud model [
DJI Phantom 4 Pro and control system.
The definition of inclination requires that the surface structure of the rock mass is known, including the normal vector of the plane where the production is located, assuming that the equation representing the structural plane is as follows:
The least squares method is used to solve (
From the conversion formula, the dip direction is as follows:
The dip angle is as follows:
The point cloud parameters of the structural plane are selected. The plane equation is fitted according to the point cloud information, and the structural surface morphology is determined. The calculation results of some occurrences are shown in Table
Yield calculation results.
Number | Structural plane equation parameter | Structural plane information | ||||
---|---|---|---|---|---|---|
|
|
|
Dip direction (°) | Dip angle (°) | The length of the trace (m) | |
01 | 0.368 | 0.245 | 0.621 | 33.7 | 35.5 | 6.55 |
02 | 0.440 | −1.270 | 0.265 | 109.0 | 78.9 | 6.70 |
03 | 0.337 | 2.824 | 0.324 | 263.2 | 83.5 | 8.53 |
04 | −1.380 | 3,452 | 0.443 | 291.8 | 83.2 | 4.26 |
05 | 0.455 | 2.088 | 0.266 | 282.3 | 82.9 | 2.88 |
06 | −0.100 | 1.480 | 0.185 | 265.9 | 82.9 | 1.20 |
07 | −0.640 | 5.600 | 0.247 | 96.6 | 73.2 | 5.88 |
08 | 0.316 | 0.882 | 0.201 | 250.3 | 77.9 | 1.47 |
09 | 0.447 | 1.703 | 0.247 | 284.7 | 89.0 | 2.06 |
10 | 57.150 | −28.400 | 0.433 | 26.5 | 89.6 | 1.95 |
Statistical cloud chart of the structure surface.
The acquired structural plane information is imported into the DSR-DDA program, and the structural plane mesh cuts the rock mass to form a block unit in the DSR-DDA. Figure
DDA model of the slope in the Fushun West Open-Pit Mine for numerical calculation and analysis.
The natural stress field takes only gravity into account and does not include the regional tectonic stress. According to the geological exploration and test results, the parameters in Table
Mechanical parameters of the slope model.
Lithology | Density (kg·m−3) | E (GPa) | Cohesion (MPa) | Friction (°) |
---|---|---|---|---|
Oil shale | 2100 | 16.5 | 3.5 | 26 |
Coal | 1500 | 12.0 | 4.7 | 25 |
Sandstone | 2300 | 15.2 | 20.0 | 19 |
Mudstone | 2500 | 12.5 | 33.0 | 20 |
Basalt | 2800 | 57.5 | 27.0 | 25 |
Gneiss | 2800 | 38.2 | 32.0 | 29 |
The cumulative displacement values measured at different depths in each inclined hole during two months are shown in Figure
Cumulative displacements of the monitoring point in surveying the inclined hole: (a) surveying inclined hole 69002; (b) surveying inclined hole 55026; (c) surveying inclined hole 74003.
The analysis of Figure
To further determine the potential slip surface position of the slope, according to the DSR-DDA method, the shear strength parameters are dynamically reduced, and the progressive instability of the slope was characterized. The slip surface and corresponding safety factor were measured. The feasibility of the method was verified by identifying the most dangerous slip surface and secondary slip surface in the slope. Figures
First failure process of the northern slope in the Fushun West Open-Pit Mine: (a) step 1.361 × 106; (b) step 1.363 × 106; (c) step 1.365 × 106; (d) step 1.367 × 106.
Second failure process of the northern slope in the Fushun West Open-Pit Mine: (a) step 1.892 × 106; (b) step 1.894 × 106; (c) step 1.896 × 106; (d) step 1.898 × 106.
Before the 1.360 × 106 time step, the displacement of the monitoring points of each block and the overall slope of the block remain basically stable. When the calculation is at step 1.360 × 106, the slope quickly deforms, the reduction factor reaches 1.136, and the displacement of the corresponding block sharply increases. The subsequent deformation also shows a gradual increasing trend. The overall deformation of the slope shows that the lower landslide body slips along the corresponding sliding surface, which indicates that the slope is unstable for the first time. The safety factor corresponding to the most dangerous slip surface was 1.136.
According to the block large deformation data and DSR-DDA program image, the slope slip surface appears at a depth of approximately 100 m in hole 69002. The large deformation of the rock mass occurs above the sliding surface. The position of the deep part of hole 55026 does not significantly change, and only the block in the near-surface position is displaced. There is no obvious deformation of the rock mass in hole 74003. These characteristics are consistent with the on-site monitoring data, which further proves the feasibility of the method.
After the first instability of the slope, the block position and internal stress are redistributed. The slope modeling continued after the first instability process to identify the secondary slip surface.
Before step 1.890 × 106, the slope tends to be stable. When the calculation is completed at step 1.890 × 106, the reduction factor reaches 1.189. The slope again quickly deforms and forms a secondary slip surface. Its corresponding safety factor is 1.189. The slope of the first slope is larger than the first slope instability. The slope strength is slightly reduced after the first instability occurs, which is notably different from the results obtained by the conventional analysis.
The failure mode of the slope of the Fushun West Open-Pit Mine is traction-type sliding failure. The middle and lower oil shales play a key role in the stability of the slope. Therefore, the remaining oil shale cannot be continuously mined to avoid large-scale landslides from initiating in the upper part of the slope and to avoid landslides at the pit-city boundary.
In this paper, we theoretically confirmed the necessity and significance of dynamically reducing the strengths of rock mass structural planes. We further revealed the effects of the problem of different degrees of damage of rock mass structural planes and the problem of numerical model selection for analyzing slopes with multiple sliding surfaces. We determined the displacement threshold to reduce the error between DSR-DDA and the theoretical solution. Then, we used these methods in the stability analysis of the northern slope of the Fushun West Open-Pit Mine.
In addition, the slope strength is slightly reduced after the first instability occurs, which is quite different from the results obtained by conventional analysis [
Although there are advantages in the DSR-DDA method for slope-stability analysis and large-deformation slope-instability analysis, there are still weaknesses in the precision of the method. It is difficult to complete slope failure experiments in the laboratory. The displacement threshold is set by the DSR-DDA numerical simulation test, which makes the accuracy of the results overly dependent on the accuracy of the DSR-DDA program. Therefore, the results suggest that, in the future, different projects will require simulation training to improve their accuracy and that similar laboratory experiments should be attempted. For further study, this method will be improved to solve the problems of tunnel assessment and the failure mechanisms of different rocks [
This study aims to elucidate the problem of different degrees of damage along a rock mass structural plane and numerical model selection for analyzing slopes with multiple sliding surfaces. Furthermore, a series of numerical simulations and on-site monitoring data were used to study the mechanism controlling different degrees of damage along a rock mass structural plane. The following conclusions have been drawn from this study: A DSR-DDA method controlled by the displacement threshold is proposed. The basic process of calculating the safety factor of a slope with multiple sliding surfaces by the DSR-DDA method is provided, contributing a new method for slope-stability analysis. The feasibility and calculation accuracy of the DSR-DDA method are verified by the case of the classic slope slider. The displacement threshold is 1 mm, and the dynamic strength of the rock mass is reduced under different degrees of damage. Furthermore, the heterogeneity of the rock mass structural surface damage was analyzed. Based on the DSR-DDA method, the stability of multiple sliding surfaces of the northern slope of the Fushun West Open-Pit Mine was analyzed. The most dangerous slip surface and secondary slip surface position were determined, proving that the slope is prone to slipping. The results suggest that there is a requirement of dynamic change in the model for accurate slope surface stability analysis. The results indicate that the failure mode of the slope was traction sliding failure. The middle and lower oil shales play a key role in the stability of the slope. Therefore, the remaining oil shale cannot be continuously mined to avoid large-scale landslides and landslides along the pit-city boundary in the upper part of the slope.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare no conflicts of interest.
Shuhong Wang and Chengjin Zhu contributed equally.
The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Nos. 51474050 and U1602232), Fundamental Research Funds for the Central Universities (No. N17010829), Doctoral Scientific Research Foundation of Liaoning Province (Nos. 20170540304 and 20170520341), and Research and Development Project of Guizhou University of Engineering Science (Grant No: G2018016).