As shown in Figure 1, the Jianshan Phosphate Mine is located near Haikou Town, Xishan District, Kunming City, Yunnan Province, China, with well-developed land and water transportation. The longitude of the study area is 102°06′09″-102°49′56″ and the latitude is 24°08′24″-24°17′35''. In addition, Haikou Town is a heavy industrial zone in Kunming City, with abundant natural resources, convenient transportation and well industrial foundation. The Jianshan Phosphate Mine is located in the middle of the Jianshan mining area.and the northern slope of Jianshan is the exposed part of the bottom rock of the stope. The topography is characterized by alpine topography, with the characteristics of gentle south and steep north. The topography of the foothills is roughly the same as the tilt direction of the rock formations. The peak elevation of the highest peak in the mining area is 2,205.75 m, and the slope has north-south rain fissures and gully cuts, and the lowest erosion base elevation is 1,883.15 m. Over 20 perennial rivers in the surface water system converge into Dianchi Lake, 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, the highest water level is 1,886.86 m, and the lowest water level is 1,883.15 m. The annual average rainfall is 886.99 mm and the evaporation is 1,903.8 mm. In addition, there will be frost from December to February, with an average annual frost period of 64–75 days.

The mining area is located in the eastern section of the north wing of the Xiangtiao Village anticline, and the stratum is inclined to the north, in a monoclinic form, with a relatively simple structure and no faults with a drop of more than 30 m. The eastern strata strikes nearly east-west, with steep dips to upright. There are two reverse faults parallel to the axis of the Xiangtiao Village anticline in the southern part of the middle section of the mining area. It pushes the deep strata upwards and makes the ore strata overlap, and the force to the west is weaker than the east. Correspondingly, there are some small axially along strike and inclined wide and gentle fold groups, and vertical fractures with tensile characteristics and small normal faults.

Common folds in the mining area are generally of two types: one is the wide and gentle folds along the inclined direction and strike in the west of the mining area; the other is the traction folds produced by the strong compression in the east of the mining area. The fault structure in the area is not well developed, with only one strike reverse fault group (F₁) and one strike normal fault group (F₂), which are mainly manifested as duplication or lack of ore layers. In addition, the reverse fault group (F_1-1, F_1-2) has a certain influence on the northern ore body in the east mining area of Jianshan Phosphorus Mine.

1) F_1-1 reverse fault: The F_1-1 reverse fault is the main fault in the mining area. The overall strike is close to east-west, with an inclination of 330°–20°, a length of 1,420 m, and the dip angle of the fault plane is steep from the east to the west. The north plate rises, pushing the deep ore layer to the shallower, causing the ore layer to be repeated, and the repeated fault distance is less than 17 m.

Currently, with the continuous decrease of mining depth, the east mining area of Jianshan Phosphorus Mine has formed a high-steep slope with a step height of 30 m, a slope surface of 42–51°, and a slope height of more than 200 m. Since the Jianshan stope is close to the high and steep slopes of Jianshan, and the production operations are more frequent, it is particularly important to avoid the high and steep slopes from being affected by blasting vibration. The production of Jianshan Phosphate Mine adopts the deep-hole step blasting method, and the designed step height is 10 m. The drilling equipment is the Atlas φ152 drilling rig of Jianshan Phosphate Mine and the Atlas φ145 (φ130, φ120, φ115, φ90) drilling rig of the engineering company. Blasting mainly uses 1# rock emulsion explosive and rock expanded ammonium nitrate explosive (the diameter of the roll is 70 mm, 1.5 kg/cylinder).

In this study, the hole mesh parameters used by the mine (5.5 m × 5 m for φ152 drilling rigs, 5 m × 4.5 m for φ145 drilling rigs) are generally acceptable from the field test results. However, when the isosceles triangle is used to arrange the holes and the blast hole density coefficient m = 1.155, the resistance lines of the blast holes in different directions are the most uniform, which is the most effective for increasing the blasting volume of the blast hole and improving the blasting crushing quality (Li et al., 2021; Li et al., 2021). The blasting parameters are designed as follows:

1) Chassis Resistance Line (The horizontal distance from the center of the bottom of the blast hole to the foot of the step):

In the formula: D-Drilling diameter (0.145 m).

2) Super deep:

In the formula: m-Blast hole density factor (1.155).

5) Row spacing:

In the formula: q 1 -Line charge density (about 10 kg/m).

9) Length of blockage:

Based on the empirical formula L ₂ ≥ (0.7–0.8) W _d ≥ 3.15–3.6m, the designed packing length of 3.6 m is feasible.

As shown in Figure 2, a diagonal hole-by-hole detonation network was used in the field test. Among them, the blasting direction of the blast hole is toward the side of the steps and the steep slope, and the line of the deep holes that are detonated at the same time obliquely intersects the eyebrow line of the steps at an angle (generally 45°) (Geng et al., 2021; Li et al., 2021). The advantage is that the actual distance between the blast holes increases, and the blast hole density coefficient increases, which is beneficial to improve the fragmentation of blasting and reduce the vibration at high and steep slopes. In addition, appropriately increasing the delay interval between holes can increase the frequency of blasting vibration, thereby reducing the impact on adjacent slopes.

To further improve the blasting effect and increase mine production efficiency we optimized the plan, considering the implementation of a wide hole spacing and small resistance line blasting plan. In order to reduce the on-site test workload, a numerical simulation model was established to provide technical guidance for the optimization plan (Li et al., 2021).

The 1# rock emulsion explosive is used for medium-wave mining and blasting of dolomite and sandy dolomite in Jianshan Phosphate Mine. After investigation, it is found that the reasonable delay time between holes in Jianshan Phosphate Mine is 15–50 ms, and the delay time between rows is 40–80 ms. In addition, combined with the surface delay of the existing plastic detonator network detonator series, it is preliminarily determined that the delay time between the holes is 17 ms/42 ms, 35 ms/65 ms, 25 ms/42 ms, 42 ms/65 ms. In order to better complete geometric solid modeling and dynamic response analysis, ANSYS/LS-DYNA software is used to numerically calculate 16 combinations of wide hole spacing and small resistance line blasting schemes (4 kinds of hole mesh parameters and the delay time between four groups of holes and rows) (Peng. 2005).

Through the numerical calculation of 16 groups of blasting plans, the propagation process of the equivalent stress between the holes and the superposition of the equivalent stress of each group of plans are analyzed to determine the optimal blasting plan. The model scheme is as shown in Table 1.

Based on the optimized combination of blasting parameters, blast hole network parameters, and delay interval, an 8 × 4 scheme is selected for field testand the mine’s existing detonator with a combination of 35 and 65 ms delay interval is used. A diagonal hole-by-hole detonation network is adopted. The blastholes in the same row are connected with the same delay between the holes. When the rows are connected, the second blasthole in the first row is connected to the second row with an interrow delay detonator. A blast hole is connected in the same way for each row in the back row.

Compared with the large block rate of the mine before the test, the large block rate of the three tests using the 8 × 4 scheme has been reduced by 10.4, 16.7, and 15.6% respectively, and the maximum size of the block has been reduced. It shows that with the increase of the blast hole density coefficient, the distance between the rows decreases and the stress superposition between the rows increases, which makes the rock fragmentation more uniform (Miao et al., 2021). In the process of blasting, the influence of flying rocks on the surroundings can be better controlled (Li et al., 2021). After the resumption of mining in the east mining area of Jianshan Phosphorus Mine, by accelerating the slope unloading speed, the slope change rate was effectively slowed down, which provided a guarantee for the continuous mining work below (Li et al., 2021). At the same time, the technology effectively protects the slope surface, makes the entire slope surface smooth and flat, improves production efficiency, and speeds up the slope cutting progress.

As shown in Figure 10A, in order 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 measuring points in areas where the slopes are severely deformed. According to the actual situation of blasting in Jianshan Phosphorus Mine, monitoring points were arranged on the high slope of Jianshan stope (Chen et al., 2020). Figure 10B which shows the time history curve of the vibration velocity of the measuring point at the 2,070 m platform on the east side of the Jianshan slope. During the mining blasting process, more than 20 vibration monitoring tasks were carried out. Among them, several groups of data measured on high slopes are selected for comparison and analysis (Table 2). The comparison results show that: 1) 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. However, the peak vibration velocity of the measuring point on the high slope of Jianshan mountain is less than this standard. 2) As shown in Table 2, when the maximum single shot charge is the same, the blasting vibration speed basically decreases with the increase of the blasting center distance. Among them, the elevation amplification effect appeared in 7–12 blasts. This is because the nature of the rock mass, the integrity of the rock mass, the slope and the thickness of the slope and the mountain mass affect the elevation effect. In addition, the slope will affect the intensity and frequency of the blasting vibration wave. Therefore, the degree of elevation magnification effect is different (Chen et al., 2020).

Considering the elevation effect of blasting vibration wave propagation, regression analysis is carried out on the measured data in Table 2. The following formula is used to predict the attenuation law and propagation law of blasting vibration on high slopes (Shi et al., 2015): v = k [ Q 3 D ] α [ Q 3 H ] β . (10)

In the formula: D-Explosion center distance (Horizontal distance, m); Q-Explosive charge; H-Design step height.

The logarithms on both sides of Formula 10 are: lg ν = lg   k + α   lg [ Q 3 D ] + β lg [ Q 3 H ] . (11)

In Formula 11, let Y = lg  v , X 1 = lg [ Q 3 R ] , X 2 = lg [ Q 3 H ] , then: Y = lg  k + α X 1 + β X 2 . (12)

Since Formula 11 can be transformed into a binary linear relationship, use the binary linear regression Matlab program to find the values of k, α, ß.

1) Regression analysis of X-axis vibration data

According to Formula 12, using MATLAB software regression analysis, the result is shown in Figure 11A, the calculation can be: k = 29.7235, a = 1.5243, ß = -0.5152.

Thus, the X-axis propagation law of blasting vibration on the high slope of Jianshan Phosphorus Mine: v = 29.7235 [ Q 3 D ] 1.5243 [ Q 3 H ] − 0.5152 . (13)

Meanwhile, the maximum amount of medicine Q _max for slope safety can be deduced as follows: Q m a x ≤ [ V 29.7235 ] 2.9729 ⋅ D 4.5316 ⋅ H − 1.5316 . (14)

2) Regression analysis of Y-axis vibration data

According to Formula 12, the result is shown in Figure 11B, the calculation can be: k = 19.3108, a = 0.8960, ß = 0.0350.

Thus, the Y-axis propagation law of blasting vibration on the high slope of Jianshan Phosphorus Mine: v = 19.3108 [ Q 3 D ] 0.8960 [ Q 3 H ] 0.0350 . (15)

Meanwhile, the maximum amount of medicine Q _max for slope safety can be deduced as follows: Q m a x ≤ [ V 19.3108 ] 3.2223 ⋅ D 2.8872 ⋅ H 0.1128 . (16)

3) Regression analysis of Z-axis vibration data

According to Formula 12, the result is shown in Figure 11C, the calculation can be: k = 1430.54, a = 1.9255, ß = 0.0701.

Therefore, the Z-axis propagation law of blasting vibration on the high slope of Jianshan Phosphorus Mine: v = 1430.54 [ Q 3 D ] 1.9255 [ Q 3 H ] 0.0701 . (17)

At the same time, the maximum amount of medicine Q _max for slope safety can be deduced as follows: Q m a x ≤ [ V 1430.54 ] 1.5033 ⋅ D 2.8946 ⋅ H 0.1054 . (18)

The sound wave test method before and after blasting is used to judge the quality damage of the slope of Jianshan open-pit mine caused by blasting. Specifically, by testing the post-blast wave velocity Cp2 and the pre-blast wave velocity Cp1 of the rock mass at the same part of the slope of the Jianshan open-pit stope, and calculating the sound wave change rate ΔCp=(1-Cp2/Cp1) of the rock mass at the same part before and after the explosion. If ΔCp is greater than 10%, it is judged that the blasting has destroyed the rock mass. If ΔCp is less than or equal to 10%, it is judged that the blasting is safe and the rock mass is not damaged. In our study, blasting tests were carried out on holes 1#, 2# and 3# respectively, and the wave velocity Cp1 before blasting and the wave velocity Cp2 after blasting of holes 1#-3# were calculated and analyzed. Figures 12A–C are the comparison diagrams of the pre-blast wave velocity Cp1 and post-blast wave velocity Cp2 of the tested holes #1, #2 and #3, respectively.

As shown in Figure 12, the depth of the impact of blasting on the slope of the Jianshan open-pit is in the range of 0–3.6 m. And according to the sonic test results before and after blasting, the blasting has almost no damage to the deeper rock mass (Xu et al., 2012; Zhang et al., 2020). Thus, the blasting will not cause damage to the adjacent high and steep slopes as a whole.

The fatigue damage of a material refers to the ratio of the number of active load cycles that the current material can withstand to the number of active load cycles that the material can withstand when it is destroyed (Xu et al., 2021). Generally speaking, the damage to the rock mass caused by blasting excavation will cause the original joint fissures of the rock mass to open, expand, or generate new fissures, resulting in the decrease of the mechanical parameters of the rock mass. The damage degree of rock mass can be expressed as: D = 1 − E E 0 = 1 − [ v v 0 ] 2 = 1 − K = 1 − ( 1 − η ) 2 . (19)

In Formula 19, D-damage degree of rock mass; E-the elastic modulus of the rock mass before blasting; E ₀-the equivalent elastic modulus of the rock mass after blasting; v-sonic wave velocity before rock blasting; v ₀-sonic wave velocity after rock blasting; K-rock mass integrity factor; η-sonic wave velocity reduction rate.

Rock damage should include two parts: one part is the initial damage D ₀ caused by geological defects such as natural joints, fissures, and micro-cavities in the rock; the other part is the blasting damage ΔD caused by crack propagation caused by blasting stress waves. Therefore, the rock mass damage D after blasting can be expressed as follows: D = D 0 + Δ D . (20)

Simultaneous Formulas 19, 20 can be obtained: D 0 = 1 − [ v m v 0 ] 2 = 1 − [ v 0 − Δ v 0 v 0 ] 2 = 1 − ( 1 − η 0 ) 2 . (21)

In Formula 21, v _m-sonic velocity of the rock mass; v ₀-sonic velocity of the rock mass; Δv ₀-the difference between the sound velocity of the rock mass and the sound velocity of the rock mass; η0-the initial sound velocity reduction rate of the rock mass before blasting.

After the blasting stress wave acts, the rock mass blasting damage appears, and the total damage increases. Based on the change of sound velocity, the damage ΔD of rock mass blasting can be defined as: Δ D = 1 − [ v v m ] 2 = 1 − [ 1 − Δ v v m ] 2 = 1 − ( 1 − η ) 2 . (22)

In Formula 22, v-sonic wave velocity of rock mass after blasting; Δv-sonic wave velocity of rock mass before and after blasting.

Under the influence of blasting for a long period of time, rock mass blasting damage continues to accumulate. Each blasting damage can be expressed by the sonic velocity reduction rate ΔD, therefore: Δ D n = 1 − [ v n v m ] 2 = 1 − [ 1 − Δ v n v m ] 2 = 1 − ( 1 − η n ) 2 . (23)

The formula for cumulative damage of rock mass under blasting action is: D = D 0 + Δ D n = 1 − ( 1 − η 0 ) 2 + 1 − ( 1 − η n ) 2 = 2 ( η 0 + η n ) 2 − η 0 2 − η n 2 , (24) D = A 1 + A 2 n + A 3 n 2 + A 4 n 3 . (25)

In Formula 25, D-damage degree of rock mass; n-the number of blasting; A ₁, A ₂, A ₃ and A ₄-the undetermined constants of the regression curve, respectively.

The cumulative damage expansion model of rock mass blasting characterized by the reference quantity of rock mass sound velocity reduction rate is shown in Formula 24. Under the action of multiple blasting, the damage of the rock mass continues to accumulate. When the accumulation of damage reaches a certain level, it will cause the rock mass instability and destruction. In Figure 13, with the hole depth 2.4 and 4.0 m as the research object of cumulative damage of blasting, a third degree polynomial is used to fit the degree of cumulative damage of rock mass, and the mathematical model of non-linear cumulative damage of rock mass under the action of six blasting is analyzed.

Currently, our method adopts the 8 × 4 m hole network parameters and the slash hole-by-hole initiation method, and the detonator delay time adopts 35 ms between holes, 65 ms between rows, and 500 ms within holes to achieve a better blasting effect. In detail, the blasting fragmentation is relatively uniform, the block rate is reduced, and it will not affect the adjacent high and steep rock slopes. In addition, by establishing a mathematical model of cumulative damage of rock mass blasting, it shows that blasting vibration will not cause damage to the slope as a whole. In the future, we will widely apply this technology in the field of mine blasting. And try to test the blasting methods of 17/42, 25/42, 25/65, 42/65 and other forms of detonators outside the hole with extended time to find a best blasting plan. In addition, since the initial joints and fissures in the rock are not considered in the numerical simulation of blasting in our study, we will consider these factors in the selection of the best blasting plan in future studies. On the other hand, the mathematical model of cumulative damage of rock mass blasting can be used to predict the rock mass damage caused by subsequent blasting, which provides a reference for mine production blasting.