Multilateral Boundary Blasting Theory of High and Steep Slope in Open Pit Mine and Its Application

Abstract

At present, the blasting theory of high and steep rock slope mainly focuses on flat terrain, ignoring the influence of micro-terrain boundary factors on blasting effect, which leads to excessive blasting energy and affects the stability of slope. Therefore, based on the theory of multilateral boundary rock blasting, this paper deduces the calculation formula of blasting charge for high and steep rock slope under multilateral boundary conditions, and verifies it with field test. The results show that: (1) The multilateral boundary charge calculation formula directly includes micro-topography boundary conditions and blasting effect, and the rock blasting theory is based on the interaction of blasting energy provided by explosives and potential energy in medium, which effectively improves the energy utilization rate of explosives. (2) The influence of surplus blasting energy on the surrounding environment under different boundary conditions is controlled, and the explosive explosion effect is effectively controlled, so that a stable high and steep slope of open pit mine is formed after blasting.

1 Introduction

The application and research of engineering blasting technology in national economy and national defense construction has a long history. Since modern open pit mine stripping works are mostly carried out under the condition of high mountains and complex changes of wavy micro-topography, it is very important to establish blasting characteristics and blasting charge calculation theory under multilateral boundary conditions. The multilateral boundary condition refers to the boundary condition of micro-topography, which belongs to the shape geometry condition compared with the horizontal boundary condition [1].

Wang [2] systematically proposed the comprehensive theory of multilateral boundary stone blasting for the first time, and directly introduced the micro-topography into the blasting theory as a main condition. Chen et al. [3] studied quantitatively the influence of geological conditions and physical and mechanical properties of rock on the blasting effect and the effect of blasting on the stability of mountain or slope. Gu [4] proposed that the possibility of amplitude superposition should be considered when the interval time between charge bags is small, and the permissible distance of blasting vibration should be calculated according to equivalent charge. Chen et al. [5] improved the three-multiple blasting method and adopted multi-layer, multi-initiation and multi-face open terrain blasting to make the deep cutting take shape in one blast, which improved the blasting method of deep cutting facing open terrain in multi-boundary blasting theory. Xia et al. [6] made equivalent transformation of blasting vibration speed monitored on site according to Sadoski formula, and used linear regression control method to calculate blasting charge amount for subsequent construction. Huang et al. [7] uses high-speed photography technology and numerical calculation method to carry out research, and obtains that the maximum initial throwing velocity of slope rock increases, stabilizes and decreases in the direction of blasting propagation in the extended blast hole. Hu et al. [8] put forward the concept of equivalent path, which provides a new method for predicting the peak value of particle vibration velocity of bench blasting seismic wave. Gan et al. [9] built a theoretical model of iron ore crushing energy, which provides a theoretical basis for the calculation of ore crushing energy in iron mines. Yang et al. [10] proposed a liquid explosive fracturing technology based on deep-hole blasting of coal and rock, which enhanced the energy utilization rate of explosives in the direction of hard rock fracturing.

The above-mentioned research mainly focuses on the blasting theory and charge calculation of flat terrain. However, the change of boundary conditions of the micro-topography is not considered enough, or only the micro-topography is considered as a factor that has an influence on the blasting effect. Since the charge calculation formula and design, method did not consider the potential energy of the rock mass itself, it caused a waste of explosive charge, easily caused geological diseases, and caused slope instability. Based on the comprehensive blasting theory of multi-boundary stonework, this paper directly introduces the micro-topography boundary conditions into the charge calculation and blasting effect, and conducts deep-hole controlled blasting to study the action law of charge, terrain conditions and blasting effect under multi-boundary conditions.

2 Main Role of Explosive Under Multilateral Boundary Conditions

2.1 Upswing

Upswing is also called sublation action under horizontal boundary condition. The explosive wave generated by the explosive charge explosion and the thrust of the expansion of the explosive product make the medium rise upward and then blow out to form the blasting funnel. It can be seen that the size of the blasting funnel and the quality of the throwing effect depend on the kinetic energy generated by the explosive explosion. The larger the dosage and the higher the throwing, the larger the throwing amount obtained, and the stable blasting effect. Under the condition of horizontal boundary, the drop rate is proportional to the amount of charge.

$$ E \propto Q $$

(1)

Upswing is the basis for determining the volume of the visible blasting funnel and the throwing rate of the two types of boundary conditions, the horizontal and the concave pass.

2.2 Collapse

Under non-horizontal terrain conditions, the medium in the collapse funnel itself contains a certain amount of potential energy, and the blasting surface of the charge receiving bag collapses. It has a great effect on a number of technical indicators of engineering blasting, such as blasting hopper volume, throwing rate and unit consumption, etc. It is also the physical basis of multi-boundary blasting theory. According to the statistics of a large number of engineering practices, in different media, the ratio of the upper and lower damage radius is calculated by Eq. (2):

$$ R_{u} = \left( {1 + \frac{{\alpha^{2} }}{5000\sim 7000}} \right)R_{l} $$

(2)

In Eq. (2), $R_{u}$ is the upper destruction radius of the blasting funnel (m). $R_{l}$ is the lower destruction radius of the blasting funnel (m). $\alpha$ is the ground slope (°).

Under the inclined boundary condition, the reason why the upper destruction radius of the blasting funnel increases with the increase of the ground slope is essentially caused by the collapse. The upper damage radius increases with the slope of the ground, which is 1 to 2.6 times larger than the lower damage radius, and it is larger in soil and rock masses controlled by structural planes. From this, it can be seen that the collapse effect expands the damage range of the cartridge explosion.

2.3 Slump

The high throwing rate in steep terrain is due to the existence of slump. When the medicine packet is only broken, the slump rate of the rock block is Eq. (3):

$$ E_{o} = 1 - \frac{1}{\xi }\left( {{{\frac{\tan \theta }{{1 - \cot \psi \,tan\theta }}} \mathord{\left/ {\vphantom {{\frac{\tan \theta }{{1 - \cot \psi \,tan\theta }}} {\frac{\tan \alpha }{{1 - \cot \psi \,tan\alpha }}}}} \right. \kern-\nulldelimiterspace} {\frac{\tan \alpha }{{1 - \cot \psi \,tan\alpha }}}}} \right) $$

(3)

In Eq. (3), $E_{o}$ is the slump rate of the rock block when the medicine packet is only broken (%). $\xi$ is the looseness coefficient of the rock, generally taken as 1.3. $\theta$ is the average angle of repose of the rock, generally around 35°, not more than 40°. $\psi$ is the angle formed by the designed step slope line and the horizontal plane.

According to Eq. (3), it is obtained that when the cartridge only serves to break the rock mass, the slump rate of the exploded rock mass increases sharply with the steepening of the natural ground slope. Therefore, in the terrain above the steep slope ($\alpha > 50^\circ$), the rock mass only needs to be fully broken, and its slump rate will reach the best throwing rate of the slope terrain using throwing blasting, and it has a good effect on the stability of the steep slope. In cliff topography, the slump rate can exceed 70%. Under steep terrain, no need to use throwing blasting. Because the potential energy contained in the rock mass itself has replaced the explosive energy required to throw the rock block out of the blasting funnel, the potential energy contained in the rock mass itself increases the effective utilization of explosive energy.

2.4 Side Throwing

The effect of side throwing can be expressed by the increment of throwing rate, and the relationship with the natural ground slope is shown in Eq. (4):

$$ \Delta E = - 77.52\lg f\left( \alpha \right) $$

(4)

In Eq. (4), $\Delta E$ is the increment of throwing rate (%). $f\left( \alpha \right)$ is the slump coefficient, and the calculation method is shown in Eq. (5):

$$ f\left( \alpha \right) = \left\{ {\begin{array}{*{20}l} {1 - {{\alpha^{2} } \mathord{\left/ {\vphantom {{\alpha^{2} } {7000}}} \right. \kern-\nulldelimiterspace} {7000}}} \hfill & {\alpha < 30^\circ } \hfill \\ {{{26} \mathord{\left/ {\vphantom {{26} \alpha }} \right. \kern-\nulldelimiterspace} \alpha }} \hfill & {\alpha < 30^\circ } \hfill \\ \end{array} } \right. $$

(5)

Under multiple boundary conditions, the charge volume remains unchanged, and the increase in throwing rate increases with the steepness of the natural ground slope. The essence is that under multiple boundary conditions, the explosive kinetic energy and the potential energy of the rock are the result of the combined effect. The rock mass has a certain potential energy and a favorable throwing angle, so that the rock mass thrown from the side is not easy to fall back into the blasting funnel. Therefore, only a smaller throwing height and throwing distance are required to obtain a higher throwing rate.

3 Calculation Formula of Blasting Charge Under Multilateral Boundary Conditions

3.1 Basic Principles and Assumptions

• (1) Under multiple boundary conditions, the mechanical energy required to slump a certain amount of the same medium is constant. In addition to the kinetic energy provided by the explosion of the cartridge, this mechanical energy also has the potential energy contained in the medium itself. In horizontal and steep terrain, kinetic energy and potential energy respectively play a major role in the blasting effect. The mutual transformation of kinetic energy and potential energy depends on the change of boundary conditions. Under general boundary conditions, the blasting effect is usually the result of the combined action of kinetic energy and potential energy.

• (2) The potential energy of the medium itself is equivalent to an increase in the effective explosive energy of explosives.

• (3) The throwing rate is used as the standard for evaluating the blasting effect. With horizontal boundary conditions, the throwing rate $E = 27\%$ is the standard state.

• (4) In order to achieve a new balance, the rock blocks formed by blasting slid into piles outside the blasting funnel under the action of their potential energy. The slope of the piles is the angle of blasting repose.

3.2 Multilateral Boundary Dose Calculation Formula

• (1) Theoretical calculation formula of multilateral boundary dose

According to the law of conservation of mechanical energy, the principle of functional balance and the above assumptions, the calculation formula for the multilateral boundary drug amount is obtained as follows:

$$ Q = KW^{3} F_{\psi } \left( {E,\alpha } \right) = KW^{3} \frac{{10^{0.0129E} }}{{\left( {\sqrt {0.05\alpha } + 1} \right)\left( {1.11 - \frac{86.133}{E}\lg f\left( \alpha \right)} \right)}} $$

(6)

In Eq. (6), $Q$ is the multi-boundary blasting charge (kg). $K$ is the dosage per cubic meter of standard throwing blasting (kg/m³). $W$ is the minimum resistance line (m). $F_{\psi } \left( {E,\alpha } \right)$ is the theoretical drug packet property index, which can be calculated by Eq. (7):

$$ F_{\psi } \left( {E,\alpha } \right)\,{ = }\,\varphi (E) \cdot f_{\psi } (\alpha ,E) $$

(7)

In Eq. (7), $\varphi (E)$ is the function of the throwing rate, generally $\varphi (E)\,{ = }\,0.45 \times 10^{0.0129E}$, for the collapse blasting, $\varphi (E)\,{ = }\,{1}$. $f_{\psi } (\alpha ,E)$ is the topographic coefficient or the dose attenuation coefficient, which can be calculated by Eq. (8):

$$ f_{\psi } (\alpha ,E)\, = \,V(\alpha ) \cdot E(\alpha ) $$

(8)

In Eq. (8), $V(\alpha )$ is the collapse factor, calculated by Eq. (9). $E(\alpha )$ is the side throwing factor, calculated by Eq. (10):

$$ V(\alpha )\, = \,{2 \mathord{\left/ {\vphantom {2 {(\sqrt {A\alpha } }}} \right. \kern-\nulldelimiterspace} {(\sqrt {A\alpha } }} + 1) $$

(9)

In Eq. (9), $A$ is the collapse coefficient. In the calculation of multi-boundary drug dose, $A = 0.05$, and $A\alpha \ge 1$.

$$ E(\alpha )\, = \,{1 \mathord{\left/ {\vphantom {1 {\left[ {1 - \frac{77.52}{E}\lg f(\alpha )} \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {1 - \frac{77.52}{E}\lg f(\alpha )} \right]}} $$

(10)

In Eq. (10), $f\left( \alpha \right)$ is the slump coefficient, and the calculation method is shown in Eq. (5).

According to Eq. (8)–(10), the topographic coefficient is shown in Eq. (11):

$$ f_{\psi } (\alpha ,E)\, = \,{1 \mathord{\left/ {\vphantom {1 {\left( {\sqrt {0.05\alpha } + 1} \right)\left[ {0.5 - \frac{38.76}{E}\lg f\left( \alpha \right)} \right]}}} \right. \kern-\nulldelimiterspace} {\left( {\sqrt {0.05\alpha } + 1} \right)\left[ {0.5 - \frac{38.76}{E}\lg f\left( \alpha \right)} \right]}} $$

(11)

The Eq. (11) to calculate the theoretical property index of the drug pack is shown in Eq. (12):

$$ F_{\psi } \left( {E,\alpha } \right)\, = \,\frac{{10^{0.0129E} }}{{\left( {\sqrt {0.05\alpha } + 1} \right)\left( {1.11 - \frac{86.133}{E}\lg f\left( \alpha \right)} \right)}} $$

(12)

• (2) Empirical calculation formula of multilateral boundary dose

  $$ Q = KW^{3} F\left( {E,\alpha } \right) $$

  (13)

In Eq. (13), $F\left( {E,\alpha } \right)$ is the property index of the drug package.

$$ F\left( {E,\alpha } \right){ \,=\, }\varphi (E) \cdot f(\alpha ) $$

(14)

3.3 Comparison of Theoretical Formula and Empirical Formula

By comparing theoretical Eq. (6) and empirical Eq. (13), we can see that there are certain differences between the two, which are mainly manifested in the following two aspects:

• (1) The terrain coefficient is different from the slump coefficient

  The theoretical topographic coefficient refers to the slump coefficient when considering the law of lateral tossing, and takes a step forward, so that the topography or slump coefficient has a clear physical and mechanical meaning, that is, the $f_{\psi } (\alpha ,E)$ value reflects the effective utilization rate of blasting energy along with the topographic boundary The law of changing conditions. The terrain is favorable, the effective utilization rate of explosive energy is increased, and the amount of charge needs to be reduced. On the contrary, the terrain is unfavorable, and the utilization rate of explosive energy decreases, and the amount of charge needs to be increased like the terrain of a pass.

• (2) The relationship between slump coefficient and terrain coefficient

  The current empirical formula may produce the following situations in production: when the design-throwing rate E < 60%, the actual effect is higher and safer. When E > 60%$\sim$70%, it is likely to be slightly lower, mainly in steep terrain. At this time, due to the sharp increase in slump, the actual blasting effect will not be affected. Therefore, it can be considered that the calculation Eq. (13) of the multi-boundary charge is consistent with the theoretically derived formula. In the steep terrain, the principle of slump should be obeyed, and slump blasting should be used.

3.4 Calculating Formula of Charge for Multilateral Boundary Deep Hole Blasting

Based on the analysis of the characteristics of rock mass blasting under multi-boundary conditions, especially the rock mass blasting of high and steep slopes, according to the calculation principle of formula (13), the formula for calculating the packing charge of deep-hole blasting columnar charge under multi-boundary conditions is obtained:

$$ Q = KW^{3} F\left( {E,\alpha } \right) = KF\left( {E,\alpha } \right)aWh $$

(15)

In Eq. (15), $a$ is the hole distance (m). $h$ is the drilling depth (m).

The multilateral boundary charge calculation formula directly includes the terrain boundary conditions and the blasting effect. The blasting theory is based on the combination of the explosive energy provided by the explosive and the potential energy in the medium to control the excess blasting energy and excessive explosive consumption under different terrain conditions. Established the functional relationship among the explosive quantity, terrain boundary conditions and blasting effect, which is convenient for practical inspection and application of engineering blasting, and has been widely used in engineering blasting in our country.

4 Project Example

4.1 Project Overview

Xingguang Coal Mine is located in the west wing of Zhuozishan anticline, and its geomorphic features belong to the low mountain and hilly area of the Inner Mongolia Plateau. The terrain is relatively flat, the thickness of the loose cap layer is small, and geological disasters such as landslides and mudslides are rarely occurred. Gray-white medium and coarse sandstone with a small amount of gray-green sandy mudstone are distributed in a large area in the area. The stratum has been extensively weathered and eroded and is in integrated contact with the underlying Shanxi Formation. Sandy mudstone has weak water richness, hardens after losing water, easy to crack, and has little water content. The softening coefficient of various types of rocks varies greatly, ranging from 0.21 to 0.83, with an average of 0.40. Except for coal, all kinds of rocks are basically easy to soften rocks. The mine is a gas mine, and there is no outburst of coal and gas.

4.2 Deep Hole Blasting Design Under Multilateral Boundary Conditions

According to the multilateral boundary blasting theory, the open-pit mine blasting design is carried out. The deep hole loosening millisecond delayed blasting construction is used to control the direction of the minimum resistance line of blasting, avoid facing the direction of residential houses and various buildings, and take safety protection measures. The environmental conditions of the blasting area are good, and the rock is drilled once and blasted to reach the design depth to ensure the construction progress. In order to control the blasting flying rocks, ensure the length of the blockage during construction, press sandbags at the orifices, and cover the wicker if necessary. At the same time, the millisecond delayed detonation technology is used to limit the maximum amount of detonating charge in a period to control the impact of blasting vibration and flying rocks on the surrounding environment. The blasting design parameters are as follows:

• (1) The unit consumption of explosive is q = 0.22 kg/m³, the density of linear charge is q₁ = 5.7 kg/m, and the single hole charge is Q = 44 kg.

• (2) The height of step is H = 16 m, and the slope angle of step is 80°.

• (3) The depth of step hole is L = 16.5 m, the ultra-depth is H = 1 m, and the resistance line of chassis is W = 4 m.

• (4) The distance between rows of holes is a × b = 5 m × 4 m, and the delay time is 50–100 ms between rows and 20–40 ms between holes.

• (5) The drilling type is DTH drilling rig with a drilling diameter of 90 mm.

• (6) The blasting workers measure the actual hole depth when charging, and then charge and plug.

• (7) Charge. ANFO explosives are used for anhydrous holes, and Φ70 mm emulsion explosives are used for water holes.

• (8) Plugging. The plugging is dense, plugging with blasting mud and tamping with blasting stick and the plugging length L₂ = 2.8 m.

4.3 Detonation Network

The network of digital electronic detonator is used in blasting, in which the outermost row near the side slope is firstly detonated, and then detonated hole by hole from outside to inside. Delay time setting: delay time between holes is 25 ms, and delay time between rows is 60 ms. The schematic diagram of initiation network is shown in Fig. 1.

Fig. 1.

Initiation network diagram of bench blasting.

4.4 Blasting Effect and Analysis

In this mining area, the multilateral boundary blasting theory is studied for deep-hole controlled blasting. The blasting of 76848 m³ and 73438 m³ is studied by multi-boundary design method and empirical design method respectively. Combined with the actual situation in the field, groups of measuring points are arranged at the horizontal distance of 70 m, 90 m, 110 m and 130 m respectively. Through the analysis of waveform diagram of vibration time history of four groups of measuring points (Fig. 2), the amplitude of blasting vibration velocity produced by multilateral boundary design method is less than that of empirical design. Under the same conditions, the multi-boundary design method uses less explosives, improves the energy utilization rate of explosives, makes the construction safer, and has less influence on the surrounding disturbance.

Fig. 2.

Vibration monitoring waveform diagram.

Based on the theory of multi-boundary rock blasting and the formula of explosive charge calculation, the design and construction of rock mass blasting on high and steep slope of mine have been fully considered, and the blasting effect has been significantly improved. Field monitoring and camera show that blasting vibration and flying rocks have been effectively controlled; the fragmentation of blasting pile meets the design requirements, and all broken rock mass collapses within the design range (Fig. 3 and Fig. 4).

Fig. 3.

Comparison of blasting fragmentation.

Fig. 4.

High and steep slope formed after blasting.

5 Conclusions

Multi-boundary blasting theory considers the influence of topography and geological conditions on charge blasting. The blasting engineering practice of Xingguang Coal Mine in Inner Mongolia Kinergy Blasting Co., Ltd. shows that based on the analysis of blasting characteristics of charge under multi-boundary conditions, the following conclusions are drawn:

• (1) The multi-boundary charge calculation formula directly includes micro-terrain boundary conditions and blasting effect, the theory of rock blasting is based on the interaction of explosive energy and potential energy in the medium, and controls the influence of surplus explosive energy on the surrounding environment under different boundary conditions, to effectively improve the energy utilization rate of explosives.

• (2) The multi-boundary blasting theory considers the influence of topography and geological conditions on blasting at the same time, the millisecond delay controlled blasting inside and outside the hole is adopted to effectively control the explosive explosion, control the rock breaking effect of blasting and the harm of blasting vibration to the slope. All the broken rock mass collapses within the design range, effectively prevent blasting flying rocks, and stabilize the high and steep bench slope of open-pit mine after blasting.