Study on Three-Dimensional Dynamic Stability of Open-Pit High Slope under Blasting Vibration

During the production process of the open-pit mine, the blasting vibration effect not only threatens the stability of the slope but also even leads to local or large-scale landslide accidents [1, 2]. Globally, from 1967 to 1979, there were 25 landslide disasters in Daye Iron Mine due to the impact of blasting vibration, and the total amount of landslides reached 1.2303 million m³. Among them, the largest one-time landslide was 876,000 m³ [3]. In 1974, a landslide disaster occurred in Nanfen Iron Mine, and the total amount of landslides reached 6,500 m³ [4]. In November 1980, Baguanhe Limestone Mine was horizontally blasted with 3 tons of 10 holes at an elevation of 1388 m, causing a landslide disaster of 26,000 m³. Later, in June 1981, a cavern blasting was carried out in the western part of the stope (total charge was 1,200 tons), and a large-scale landslide disaster of 4.16 million m³ occurred [5]. These landslide disasters have caused heavy casualties and property losses [6, 7]. Affected by the high temperature and high pressure generated by shock waves and explosive air waves, the rock mass has inelastic effects such as crushing and cracking, and a fracture zone is formed. In addition, the blasting vibration destroyed the integrity of the rock mass, causing the adjacent slopes to lose stability and causing landslide disasters [8]. Therefore, it is necessary to develop blasting technology and blasting vibration for the open-pit of Jianshan Phosphorus Mine, which can ensure the safety of rock slopes and provide guidance for subsequent mining and blasting [9, 10].

With the increase in demand for rock mining by blasting in mines, many scholars have carried out in-depth research in theoretical analysis, field tests, and numerical simulations [11, 12]. Guo et al. analyzed the response of different types of slopes to blasting vibration [13]. Zhang et al. used the field test method of blasting vibration to carry out an experimental study on the propagation law of blasting vibration under the influence of elevation factors [14]. Wang proposed a calculation formula for dynamic time history stability coefficient of bedding high-steep rock slopes driven by underground blasting for the common high-steep bedding rock slopes in engineering [15]. Narayan et al. proposed a novel directional controlled blasting technology for unstable highway slopes, which effectively improved the stability of the slope after blasting [16]. Wu et al. evaluated the stability of high and steep slopes driven by repeated blasting of the fault zone by combining shaking table tests, limit equilibrium theory, and least-squares method [17]. On the basis of previous research results, Deng and Chen comprehensively discussed the blasting excavation and stability control technology of ultrahigh and steep rock slopes in China’s hydropower projects and discussed its research progress and limitations [18]. On the other hand, Ma et al. studied the weakening of slope stability under the dual effects of rainfall infiltration and blasting vibration [19]. However, these methods only conduct experiments and theoretical analysis on the stability of the slope after blasting and have no effective verification and are limited.

In recent years, computer technology has developed rapidly, and numerical simulation technology has gradually been widely used in the stability analysis of rock slopes under blasting vibration [20, 21]. Among them, a series of numerical simulation verification studies have been carried out in the mine blasting process. Xie et al. used SLIDE software to simulate the actual slope model of the open-pit mine and proposed a slope stability criterion based on the safety factor [22]. Gui et al. established a numerical simulation considering the geological characteristics of the site by means of the finite difference method and concluded that the propagation of the explosion wave in the free field is significantly controlled by the geological conditions of the site [23]. Jiang et al. used the dynamic finite element method to analyze the characteristics of the explosive load and produced three-dimensional numerical models of open-pit mines and underground mines [24]. Chen et al. used the tensile and compression damage model to simulate the entire process of blasting and excavation of a typical bedrock slope, through parameter analysis, the stability of the slope under the blasting load was ensured [25]. Li et al. used a comprehensive study method combining theoretical analysis, field testing, and numerical simulation to develop a collaborative blasting technology for high and steep slopes and underground tunnels [26].

In summary, the above methods did not systematically explore and analyze the adjacent high-steep rock slopes after blasting vibration. As well as the magnitude of the shock wave generated by the blasting vibration, the evaluation of slope stability has always been a difficult problem. In addition, for the adjacent rock slopes, the large-aperture mine blasting technology has certain limitations, which will seriously damage the stability of the slope. Against these challenges, a small-aperture shock-absorbing blasting technology with a diagonal line of hole-by-hole initiation was proposed, which can greatly improve production efficiency. In addition, based on engineering geological investigation, field blasting test, blasting vibration monitoring, numerical simulation technology, and theoretical analysis, the three-dimensional dynamic stability of adjacent high slopes was systematically studied. Among them, by establishing four slope geomechanics numerical models, the slope’s own frequency, damping characteristics, and the dynamic response acceleration distribution of the slope under blasting vibration were studied, respectively. Combined with the 8-degree seismic intensity Ei Centro wave on the slope, it shows the high slope near the Jianshan Phosphate Mine maintains overall stability under the action of blasting vibration unloading or seismic waves. Our study can provide theoretical guidance and technical support for the stability analysis of open-pit high slopes under blasting vibration.

The Dianchi Lake area of Yunnan Province is one of the main distribution areas of phosphate deposits in China. These include the Jianshan Phosphate Mine and Kunyang Phosphate Mine. Yunnan Province has a subtropical monsoon climate with hot and rainy summers and an average annual rainfall of about 886.99 mm. As shown in Figure 1, the rainfall in a single month of summer in Yunnan Province is 120~150 mm. In our study, the Jianshan Phosphorus Mine is located near Haikou Town, Xishan District, Kunming City, Yunnan Province, China, adjacent to Dianchi Lake and Fuxian Lake, and the surrounding railway is relatively convenient. The study area is located at 102°06$′$09$″$-102°49$′$56$″$ east longitude and 24°48$′$24$″$-25°05$′$35$″$ north latitude (Figure 1). According to the geological investigation, the Jianshan Phosphate Mine is located in the middle of the Jianshan mining area. It is characterized by a high mountain topography, with the characteristic of being flat on the south and steep on the north. The topography of the foothills is roughly the same as the slope of the rock formations. In Figure 1, the highest peak height of the mining area is 2205.75 m, and the lowest erosion benchmark elevation is 1883.15 m. More than 20 perennial rivers in the surface water system converge into Dianchi Lake, and the river at the exit of Dianchi Lake is Haikou River. It flows from east to west through the northern edge of the mining area. At present, the water level of mining is 1982 m, which is much higher than the groundwater level and the water level of the surface water system.

The mining area is located in the north wing of the Xiangtiao Village anticline. The secondary folds are relatively simple in structure and small in scale. There are mainly two types of folds:

• (1)

  Wide and Gentle Folds. Distributed in the western part of the mining area, the folds are generally between 150 and 200 m in length and width, and less than 10 m in height. It is a short-axis dorsal and syncline with small undulations, which often appear in groups

• (2)

  Traction Folds. Mainly distributed in the eastern part of the mining area, small folds produced by local compression, with a short extension

The fault structure in this mining area is not well developed. In contrast, joints and fracture structures are more developed, especially in the brittle rock and ore layers of the second member (Є1m²) of the Meishucun Stage. Compression fracture zones can be seen locally on reverse faults (main faults, with a vertical fault distance of no more than 30 m), which are mostly a compressive structural surface, but only two ore layers of the fault are broken and small traction folds appear [27]. On the other hand, normal faults are small in scale, mostly tensile structural planes, with small vertical fault distances. In general, when the section cut by the fault is brittle rock formations such as phosphorite and dolomite, the fracture zone structure of normal faults and reverse faults is relatively loose. And when the section cut by the fault is a plastic rock layer such as phosphorous clay rock, whether it is a normal fault or a reverse fault, the fracture zone structure is relatively dense.

After geological survey, the degree of weathering of the phosphorite deposit by the fault is mainly related to the material composition and structure of the fault fracture zone. As shown in Figure 2, the fracture zone with loose material structure is mostly phosphorite and dolomite, with looser structure and higher porosity. In this environment, the water conductivity of the ore bed is strong, and the fault structure greatly improves the weathering degree of the phosphorite [28, 29]. In addition, most of the fracture zone with dense material structure is composed of phosphorus-bearing clay rocks. Porosity and fissure rate are low, which can prevent water from the footwall of the fault [30, 31]. In this case, the degree of weathering of the phosphorite in the hanging wall of the fault is still high, but the degree of weathering of the phosphorite in the foot wall is relatively weak. This is because the penetration and migration of groundwater are blocked, and the lower mine layer is protected from weathering [32, 33]. Therefore, the fault structure plays a certain role in controlling the weathering degree of phosphorite in its affected area.

Based on the results of the geological investigation, using the layered characteristics of layered slopes, the natural fissures between layers are used as prefissures to implement a slope-controlled blasting test similar to presplitting blasting. To reduce the damage to the slope surface by blasting, blasting and excavating are given priority to 15 m away from the adjacent reserved side slope to form a free surface with a height of 10.5 m. Second, carry out piercing operations on the remaining platforms adjacent to the slope and implement controlled blasting [34]. As shown in Figure 3(b), from the reserved side slope 3.5 m away, the second row of buffer holes is 7.5 m deep, and the hole spacing is 4 m. The distance between the first row and the second row is 4 m, the hole spacing is 4 m, and the drilling depth is 10.5 m. The drilling angles of the two rows of holes are 60° and 75°, and the angle of the holes in the third row and outside the main blasting zone is 90°. At the same time, the millisecond network plastic detonator is used to start from the free surface, and the detonation is performed hole by hole with a slight difference between the rows. In the test, we used the diagonal detonation method, with a $8×4m$ hole mesh parameters. The delay time of the detonator was 35 ms between the holes, 65 ms between the rows, and 500 ms within the holes.

Combining the actual perforation needs of the adjacent open-pit slope, and realizing the effects of shock absorption, energy buffering, and slope protection, the buffer blasting control area (the first and second rows of holes adjacent to the slope) choose to drill a straight $D=115mm$ drilling rig. As shown in Figure 3(a), the third row of the blasting buffer zone is imaginary presplit holes (natural fissures in the rock at the excavation line). The second row of buffer holes are $a=4.0m$⁠, $b=3.5m$⁠, the parameters of the first row of buffer holes are $a=4.0m$⁠, $b=4.0m$⁠, and the hole network parameters of the main explosion zone are $a×b=5×5.5$⁠. The inclination angle of the slope rock layer surveyed on site is between 48° and 52°, which is taken as 50°. In order to protect the open-pit slope and reduce the damage to the final slope rock formation, based on the perforation technical performance and construction cost of the drilling rig, the perforation angle of the second row of holes in the blasting buffer zone is determined to be 60° [35]. In Figure 3(c), considering the overall blasting effect, two rows of buffer holes are finally selected to adopt the form of segmented charging. The lower part of the first row of buffer holes is charged 2/3, and the upper part is charged 1/3. In order to avoid overcrushing at the bottom of the second row of buffer holes, which would affect the stability of the slope, a method of charging 2/3 of the upper part and 1/3 of the lower part is adopted. The middle part of the two rows of holes adopts 1.5 m inert filling material, and the main blast hole adopts a centralized charge structure. Finally, a diagonal line is used to detonate the network hole by hole (Figure 4). The blast holes in the same row are connected with the same interhole delay. When the rows are connected, the second blast hole in the first row is connected with the interrow delay detonator to the first blast hole in the second row. The platoon connection method is similar to this. Among them, T1 is the delay between holes (35 ms), T2 is the delay between rows (65 ms), and T0 is the delay of the detonator in the holes (500 ms).

The blasting test completed the task of slope cutting and unloading below the 2160 m level of Jianshan Phosphate Mine. In the process of implementation, the impact and damage of flying rocks on the surroundings can be better controlled, and no blasting casualties occurred. In addition, by accelerating the unloading speed of the slope, the rate of change of the slope is effectively slowed down, which provides a guarantee for the continuous progress of the mining work below. Meanwhile, this technology effectively protects the open-pit slope, and the entire slope is smooth and flat, which improves production efficiency and speeds up the slope cutting progress [36].

Figure 5 shows the wave velocity changes of blasting vibration on the high slope of Jianshan and the slope near Haifeng stope. Among them, the high slope of Jianshan has the strongest wave velocity in the range of 1000 s, and the high slope of Haifeng has the strongest wave velocity in the range of 1700 s to 1900 s. According to the safety allowable vibration speed standard for permanent rock high slopes, the on-site slope vibration speed standard control is determined to be 5 cm/s [31, 33]. However, the peak vibration velocity of the measuring point on the high slope of Jianshan mountain is less than this standard. In order to further study the vibration of mining blasting, we have carried out more than 20 vibration monitoring tasks. And select several groups of measured data on high slopes for comparative analysis. In Table 1, when the maximum single shot charge is the same, the blasting vibration velocity at the same blasting location basically decreases with the increase of the blasting center distance [37]. The reason is that the nature of the rock mass, the integrity of the rock mass, and the slope and the thickness of the slope and the mountain mass are the main factors that affect the elevation effect [38]. In addition, the slope will affect the intensity and frequency of the blasting vibration wave, so different amplification effects will appear.

As shown in Figure 6, to study the seismic effect of blasting vibration on high slopes and to determine whether the high slopes are within the safe allowable range, we have arranged denser measurement points in areas where the slopes are severely deformed. According to the actual situation of blasting in Jianshan Phosphorus Mine, monitoring points are arranged on the high slope of Jianshan stope. Next, the three-dimensional dynamic stability analysis of the high slope after blasting vibration is carried out based on the monitoring points.

In formula (1), $D$ is the burst distance (horizontal distance), m; $k$ is the site condition factor; $Q$ is the maximum amount of blasting charge, kg; $α$ and $β$ are the blasting vibration wave attenuation index; $H$ is the point distance, m.

Among them, $v$ is the peak vertical vibration velocity of blasting vibration, cm/s; $k$ is the site condition factor; $Q$ is the maximum amount of blasting charge, kg; $R$ is the slope distance between measuring point and burst center, m; $α$ is the blasting vibration wave attenuation index.

The propagation law of blasting vibration in Jianshan stope and Haifeng stope is as shown in Figure 7. The propagation acceleration of the blasting vibration on the $x$-axis monitored at the Jianshan stope is the largest, while the average propagation velocity on the $x$-axis monitored at the Haifeng stope is the largest. Blasting in the open-pit does not fully reflect the propagation law from the blasting area to the entire phosphate mining area, but it can effectively predict the impact on the adjacent slope. Due to changes in geological conditions, topographical environment, and other factors, the propagation law of blasting vibration may also be different [41, 42].

The time-history curve of vibration acceleration caused by mining blasting vibration in Jianshan stope and Haifeng stope is as shown in Figure 8. Based on the velocity changes on $x$⁠, $y$⁠, and $z$ in Figure 5, overall, the Jianshan stope blasting vibration wave accelerates in the $x$-direction of the slope and decelerates in the $y$-direction (Figure 8(a)) [43]. On the other hand, the blasting vibration waves make regular variable-velocity motions in the $x$⁠, $y$⁠, and $z$ directions of the side slope of the coastal abundance stope (Figure 8(b)) [44]. Here, the vibration waves in the $x$ and $z$ directions first accelerate and then decelerate in a sequential cycle, and the vibration waves in the y direction first decelerate and then accelerate in a sequential cycle. The rock mass parameters are used in theoretical analysis and calculation as shown in Table 2. In our study, using geotechnical analysis modeling software and some self-compiled preprocessing programs, a three-dimensional model of the topographic contour of the Jianshan open-pit was established [45, 46]. Affected by the difference of terrain, lithology, blasting distance, and maximum charge, the acceleration transmitted by the blast wave will change irregularly. Combining exploration conditions and using geotechnical engineering calculation and analysis software, a preliminary three-dimensional analysis model of blasting vibration of four Jianshan open-pit was established (Figure 9).

To determine the natural vibration characteristics of the four three-dimensional slope models, Midas-GTS (Geotechnical and Tunnel analysis System) software was used to conduct modal analysis on the four three-dimensional slope models [47]. The first 10 frequencies of each model are extracted, the corresponding relationship between the vibration frequency and the period is analyzed, and the natural vibration periods of the four three-dimensional slope models are as shown in Figure 10 [48]. In detail, model II has the largest natural frequency and the shortest period. Model III has the smallest natural frequency and the longest period.

In formula (11), $α$ is the damping constant proportional to the mass; $β$ is the damping constant proportional to the stiffness; $αM$ is the mass component, which is equivalent to the damper connecting each node and the ground; $βK$ is the stiffness component, which is equivalent to the damper between the connected units.

For geotechnical materials, the critical damping ratio generally ranges from 2% to 5%. Combined with the monitoring section of the slope, the natural frequency is used as the center frequency of Rayleigh damping. Figures 11–14 are the maximum total displacement, maximum total velocity, maximum total acceleration, and maximum element stress (Von Mises stress) of the three-dimensional model I-IV under blasting vibration. Comparing models I-IV, the maximum total displacement of model I is the largest, the maximum total velocity and maximum acceleration of model III are the largest, and the maximum element stress of model II is the largest. The reason is that these differences may be related to the blasting location and the geological conditions of the model area [51].

In Figures 11–14, the maximum total acceleration amplification factor during time-history analysis under the action of blasting vibration of the four three-dimensional models can be obtained. As shown in Table 3, the time-history analysis of the four models of blasting vibration has a maximum total acceleration amplification moment of 4.07% to 10.9%, respectively, indicating that the overall acceleration of the slope is basically not amplified. If the slope stability coefficient is reduced according to the acceleration amplification factor [54], blasting has basically no effect on the overall stability of the slope.

A three-dimensional finite element model was established for the current status of slope excavation after unloading at the top of the eastern mining area [55]. The time-history analysis results of the high slope three-dimensional model under the action of blasting vibration after unloading are shown in Figure 15. As shown in Figure 15, the maximum total displacement, total acceleration, and total velocity of the high slope after unloading under the action of blasting vibration are 2.363 cm, 0.776 m/s², and 0.013 m/s, respectively. Therefore, the high slope is overall stable after unloading under the action of blasting vibration.

To verify the dynamic stability of the Jianshan open-pit slope under earthquake loads. In this study, the Ei Centro wave (as shown in Figure 16) with an earthquake intensity of 8-degrees was used to analyze and calculate the dynamic stability of the three-dimensional model I [56, 57]. In Figure 17, when the three-dimensional model I is under the action of the 8-degree seismic intensity Ei Centro wave (⁠$a=0.2g$⁠), the maximum total displacement of the high slope of Jianshan Phosphate Mine is 98 cm, and the maximum total displacement occurs at the top of the high slope (area 1). The maximum unit shear stress generated is 780 Kpa, and the maximum unit shear stress occurs on the slope of Jianshan Phosphorus Mine (area 4). In addition, the maximum total velocity and maximum total acceleration generated by the slope are 1.34 m/s and 2.96 m/s², respectively. Among them, the maximum total velocity and maximum total acceleration both appear at the top of the slope (area 2 and area 3). In summary, when the bottom of the three-dimensional model I encounters an earthquake intensity of 8-degrees, the high slope of Jianshan Phosphate Mine can still maintain overall stability.

Based on the three-dimensional models I-IV of the high slope after unloading, the dynamic stability of the high slope after unloading is calculated and analyzed when it encounters an earthquake intensity of 8-degrees (⁠$a=0.2g$⁠) [58, 59]. After unloading, the three-dimensional model of high slope under the action of 8-degrees seismic intensity Ei Centro wave response acceleration time-history and maximum total displacement analysis results are as shown in Figures 18 and 19. In Figure 18, different blasting areas produce different accelerations, but their function values basically fluctuate very little. The maximum acceleration function value of the four groups of models within 10 s is between 2.2 and 3.3, and the minimum acceleration function value is about 0. Among them, the maximum value is 3.2486 (model I), and the minimum value is 0.0023 (model IV). It can be seen from Figures 18 and 19 that when the three-dimensional model I is under the action of the 8-degree seismic intensity Ei Centro wave, the maximum total displacement of the Jianshan Phosphate Mine slope is 105 cm, and the maximum total displacement occurs at its top. In addition, the maximum total acceleration generated by the slope of Jianshan Phosphorus Mine is 3.2487 m/s², which also occurs at the top of the slope. Thus, the slope of Jianshan Phosphorus Mine can still maintain overall stability [60].

In summary, under the action of the 8-degree seismic intensity Ei Centro wave, the Jianshan Phosphate Mine remains stable near the high slope regardless of whether it is unloaded or not. The simulation results show that the maximum total displacement, maximum total acceleration, maximum total velocity, and maximum total unit stress generated by the seismic waves all occur at the top of the slope. In other words, the top of the slope is the most vulnerable area. Therefore, focusing on the blasting site monitoring of the top of the slope can effectively ensure the safety of the adjacent high slope after the blasting vibration.

In our study, by using the small-diameter buffer shock-absorbing blasting technology of the adjacent slope, the production efficiency is greatly improved and the slope cutting progress is accelerated. Currently, based on numerical simulation technology, the maximum total displacement, velocity, acceleration, and stress values of the four groups of high slope models after blasting vibration are calculated from the time dimension, revealing the dynamic stability of Jianshan Phosphate Mine after blasting vibration. In the future, we will develop a new blasting method from the perspective of economic benefits, which can not only improve the safety and efficiency of blasting but also save raw materials. In addition, new blasting technology is injected into the existing dynamic stability analysis research results, combined with deep learning, Bayesian interpolation, and numerical simulation technology, to explore the stability of the adjacent high slope after blasting vibration in the two dimensions of time and space.

According to the investigation of engineering geology and rock weathering degree of Jianshan Phosphorus Mine, combined with field blasting, vibration propagation monitoring, numerical simulation calculation, and theoretical analysis, the three-dimensional dynamic stability of adjacent high slopes after blasting vibration is systematically studied. By establishing four three-dimensional slope models to simulate the maximum total displacement, velocity, acceleration, and stress changes of Jianshan Phosphate Mine under blasting vibration and unloading, the following conclusions are drawn.

• (1)

  Based on the geological conditions of Jianshan Phosphate Mine, a small-diameter buffer shock-absorbing blasting technique for adjacent slopes is proposed. In the actual engineering application, the production efficiency is improved and the slope cutting progress is accelerated. In addition, the proposed blasting method effectively protects the slope surface and provides a guarantee for the continuous mining work below

• (2)

  Regression analysis is performed on a large number of blasting vibration test data, and the law of blasting vibration propagation in Jianshan stope, Haifeng stope, and adjacent high slopes is obtained

• (3)

  Under the action of blasting vibration, the maximum total acceleration magnification of the four three-dimensional models in the eastern mining area of Jianshan Phosphorus Mine reached 4.07% to 10.9%, respectively. Therefore, the overall acceleration of the slope is basically not amplified. If the slope stability coefficient is reduced according to the acceleration amplification factor, the blasting basically has no effect on the overall stability of the slope. In addition, after blasting vibration is unloaded, the maximum total displacement, total acceleration, and total velocity of the three-dimensional model of the eastern mining area of Jianshan Phosphorus Mine are 2.36 cm, 0.776 m/s², and 0.013 m/s, respectively, and the high slope tends to be stable as a whole

• (4)

  Affected by the 8-degree seismic intensity Ei Centro wave, the maximum total displacement produced by the eastern slope of Jianshan Phosphorus Mine is 105 cm, and the maximum total acceleration is 3.2487 m/s². Among them, the maximum total displacement and maximum total acceleration occur at the top of the slope, but the high slope of Jianshan Phosphorus Mine still maintains overall stability. In the future, focusing on the blasting site monitoring of the top of the slope can effectively ensure the safety of the adjacent high slope after the blasting vibration

The data used to support the findings of this study are included within the article.

The authors declare no conflicts of interest.

This work was supported by National Natural Science Foundation of China (no. 41867033), Postdoctoral Science Foundation of China (no. 2019M650144), and State Key Laboratory of Safety and Health for Metal Mines (zdsys2019-005). The authors wish to acknowledge these supports.