Design Method for Specific Charge in Deep Mining considering Influence of In Situ Stress

In situ stress has a large influence on blasts in deep mines and should be considered in blasting design. In this study, explosion crater tests were conducted to investigate the variation of specific charges under different stress loading conditions. It was revealed that rock blasting under high stress is different from that under low stress. A correction coefficient for specific charge was defined to consider the influence of in situ stress on blasting. A quantitative relation between the correction coefficient, stress-to-strength ratio, and lateral stress coefficient was presented. Based on the explosion-crater test results, a design method for specific charges was proposed with the consideration of in situ stress. Finally, the design method was applied to a field blasting test at Hongtoushan Copper Mine. The test results indicate that the proposed design method can effectively use the high in situ stress at depth for rock fragmentation. Compared with the original blasting design, the specific charge is reduced by 19.8% and the average block rate is reduced from 6.8% to 2.84%. At the same time, the blasting boundary is well controlled and the ore loss and dilution rates are reduced. This research has important guiding significance to deep mine blasting design.


Introduction
With the decrease of shallow mineral resources, the exploitation of deep mineral resources has gradually become the trend in mining. e mining depth of the deepest mine in the world has extended to nearly 4000 m below the Earth's surface [1]. An important issue in deep engineering projects is the high in situ stress field [2][3][4][5].
e drill-and-blast method is one of the main methods of rock fragmentation [6][7][8][9]. When the drill-and-blast excavation method is used in excavation of deep mineral resources, rocks are fragmented under the coupled effect of high static stress and blastinginduced dynamic stress [8][9][10][11][12]. e in situ stress plays a large role in affecting efficiency and quality of blasting, which should be considered in blast design.
Many investigations on the effects of field stress on rock blasting have been carried out. Kutter and Fairhurst [8] found that blasting-induced cracks propagate preferably in the direction of the applied static stress. Similar results have been reported by several other researchers [9][10][11][12]. In addition, three-dimensional numerical simulation conducted by Yilmaz and Unlu [13] showed that the anisotropy of the tensile failure zone of the blasting crater becomes larger when the differences between two principal stresses increase. Xie et al. [14] investigated the damage evolution process of deep rock during cut blasting, and the results showed that the damage zone decreases with the increase of in situ stresses. Yi et al. [15] studied the effect of levels and states of in situ stresses in rock on blasting damage evolution. Previous studies indicated that in situ stress has a large effect on the propagation of blasting-induced cracks as well as on the shape and size of failure zones. However, the existing studies are mostly limited to laboratory testing and numerical simulation and have seldom been applied in engineering practice. As a result, blasting efficiency can hardly be controlled in deep mining. Specific charges comprise a major index for blast design and assessment. Higher explosive consumption will lead to overbreak, while lower explosive consumption will lead to underbreak [16,17]. Moreover, the specific charge also affects the fragmentation of blasting. Kuznetsov [18] established a quantitative relationship model between the specific charge and fragmentation size distribution. e simulation results of Cho and Kaneko [19] show that higher specific charge leads to smaller fragmentation size. Experiments by Zhou et al. [20] and Li et al. [21] showed that the tensile strength and spall strength of rock decreases with increasing static prestresses, which means that high-stress rock excavation requires fewer explosives. It can be seen that the specific charge is closely related to the scope of the blasting damage zone, the blasting profile, the fragmentation size, and so on. Reasonable specific charges can not only improve blasting quality but can also reduce blasting cost.
In this study, the effect of stress loading on the specific charge is investigated using laboratory tests, and a design method for specific charges with the consideration of field stress is proposed. e design method is then applied to mining at China's Hongtoushan Copper Mine.

Test Condition.
Results from explosion-crater tests are the basis for determining the design parameters of blast holes [22][23][24][25]. In blasting experiments on cement specimens, a qualitative model is mainly used. All model test blocks adopt the same parameters and specifications, and the failure law of the blasting process is studied through the difference analysis of blasting effect under different stress combination conditions. Cement specimens with a dimension of 200 mm × 200 mm × 150 mm were used for the crater blasting tests (Figures 1 and 2). e uniaxial compressive strength and density of the test material are 25.0 MPa and 2143 kg/m 3 , respectively. e blasting parameters and stress loading conditions are shown in Figure 2. Static stresses were applied on the two side faces (200 mm × 150 mm) of the specimen by a hydraulic loading device before detonation, as shown in Figure 2(a). e explosion model is described by the Cartesian coordinate system (x, y, z), where the x, y, and z directions correspond, respectively, to the maximum compressive stress direction, minimum compressive stress direction, and normal direction of the free surface. e stresses on the two side faces of the specimen are expressed as where σ x and σ y are the normal stresses acting on the boundaries, λ is the lateral stress coefficient (0 ≤ λ ≤ 1), and σ 0 is a constant defining the stress magnitude. A normalized variable, i.e., the stress-to-strength ratio, is introduced to represent the stress level, which has the form where σ c is the uniaxial compressive strength.
Using equation (2), equation (1) can be expressed in terms of σ as e blast hole, with a diameter of 8 mm, was located on the center line of the 200 mm × 200 mm surface. e bottom of the hole was 20 mm from the free surface (Figure 2(a)). e charge quantity remained constant at 500 mg for each blast, with a charge height of 8 mm, density of 1.24 mg/mm 3 , and a least-resistance line of w � 24 mm (Figure 2(b)). e explosives were composed of RDX (cyclotrimethylene trinitramine) and detonating explosives at a mixture ratio of 1 : 1 (Figure 3(a)). e blasting equipment included a fuse head and capacitive detonator (Figures 3(b) and 3(c)).

Explosion Crater Shape under Different Stress Loading
Conditions. Taking the cases of λ � 0 and λ � 1 as examples, the effects of stress on the explosion-crater shape and specific charge are discussed. Figure 4 presents the explosion-crater shape under different stress loading conditions. e results indicate that the crater on the free surface is roughly circular when no lateral stress is applied (Figure 4(a)). When confining stresses are applied on the side faces, the explosion crater tends to be elliptical and the direction of the long axis of the crater is in the same direction of the lateral stress (Figures 4(b) and 4(c)). is indicates that the direction of major principal stress is the primary direction of failure propagation. Under an equal biaxial stress state, the failure zone is again circular due to the symmetry of stress loading conditions (Figures 4(d)-4(f )), which is similar to the case without any stress.
To more significantly describe the morphology of the explosion crater under different stress states, the morphology diagram of an explosion crater under different stress states was drawn according to the explosion-crater results in the field. As can be seen from Figure 5, when λ � 0, the elliptical area increases with the increase in σ, and the direction of the long axis increases significantly. When λ � 1, the shape of the explosion crater is round. When σ � 0.2-0.25, the explosion-crater area increases with increasing σ. When σ � 0.3, the boundary of the specimen has been exceeded, indicating that the biaxial static stress has a more significant effect on blasting failure. e results show that the stress state of rock mass is one of the main factors influencing blasting rock fragmentation. e blasting design can be matched with the stress state of rock mass, and then, the blasting rock-breaking effect can be improved.

Variation of Specific Charge with Static Stress.
Specific charge is defined as the amount of explosives required for blasting a unit mass of rock and can be described by the following equation: where q is the specific charge in kg/t, Q e is the amount of explosive consumption in kg, and Q b is the amount of rock blasted in t.
During the blasting tests, the explosive charge was Q e � 500 mg and the amount of rock blasted, Q b , was determined by the following equation: where ρ is the density of cement mortar and V cr is the volume of the explosion crater.
To investigate the variation of specific charge with the lateral stress, the volume of the explosion crater was measured. e amount of rock blasted was calculated by equation (5), and then, the specific charge (in units of mg/g) was determined by equation (4). e variations of specific charge under different stress states were obtained and are shown in Figure 6.
It can be seen that the variations of specific charge are different under the two stress states of λ � 0 and λ � 1. With the same explosive charge and resistance line, uniaxial stress promotes specimen fragmentation under blasting. With increasing stress, the specific charge decreases gradually. However, under equal biaxial stress loading, the specific    Advances in Civil Engineering charge increases first and then decreases as the stresses increase, indicating that the biaxial stress first restrains and then promotes the formation of explosion craters. is role change occurs when the stress-to-strength ratio changes from σ � 0.2 to 0.25. ereafter, the specific charge decreases rapidly, indicating that rock fragmentation by blasting is easier under high equal biaxial stress loading. ese results indicate that the stress-to-strength ratio of σ and the lateral stress coefficient λ are two important parameters that influence specific charge.

Correction Coefficient for Specific
Charge. It is shown from the above analysis that the specific charge can be determined based on the stress-to-strength ratio σ and lateral stress coefficient λ. In this study, a correction coefficient, which is a function of the stress-to-strength ratio σ and lateral stress coefficient λ, is introduced to consider the effect of stress on specific charge. e specific charge after correction can be expressed as where q 0 is the specific charge without stress loading, q(σ, λ) is the specific charge under high stress loading, and δ q (σ, λ) is the correction coefficient, which can be determined from the following equation: e correction coefficient corresponding to λ � 0 and λ � 1 can be calculated using equation (7), and the result is shown in Figure 7.
It can be seen that the variation trend of the unit consumption correction coefficient of explosives under two different stress states is obviously different. It is shown that the lateral pressure coefficient has a great effect on the unit consumption correction coefficient of explosives. In the case of the same charge and resistance line, the unit consumption correction factor will decrease rapidly when the stress value changes from 0 to 0.1, and it will decrease slowly with increasing pressure value after the stress value exceeds 0.1. With increasing biaxial equivalent compressive stress, the unit consumption correction coefficient of explosive first increases and then slowly decreases. After the pressure value exceeds 0.25, there is a period of sharp decline. is phenomenon is in contrast with that shown in Figures 4(d)-4(f ).
In Table 1, λ is in the range 0 to 1 during mining. erefore, a large number of test or numerical simulations are required to obtain δ q (σ, λ) under different stress states. In this paper, δ q (σ, λ) was obtained using interpolation between δ q (σ, 0) and δ q (σ, 1), and the results are shown in Table 1. In the table, the results corresponding to λ � 0 and λ � 1 were obtained from the laboratory tests, and the other values were obtained based on linear interpolation between the test results. When σ > 0.3, δ q (σ, λ) values corresponding to σ � 0.3 are suggested.

Blast Design considering In Situ Stress Field and Its Heterogeneity
e test results from this study and the numerical simulation results from other studies [14,15,26] indicate that the stress state changes the shape and range of blasting-induced failure zones and influences blasting efficiency. In this section, a blast design method considering the in situ stress field and its heterogeneity is proposed for mining in depth; the method is based on the corrected specific charge discussed above. e blasting design method is based on the following basic assumptions: (a) the rock mass is an ideal elastomer and (b) multirow porous blasting is the superposition of single-hole blasting action. e stress distribution in a rock mass is heterogeneous and continuously evolves during mining. e stress field around each blast hole varies, and it is better to design the specific charge for each blast hole according to the stress field to increase blasting efficiency. However, this method involves a large amount of work and can hardly be implemented in practice. To simplify the blast design, an orebody is divided into zones with approximately uniform stress in each zone. e correction coefficient δ q (σ, λ) for a specific charge can then be determined according to the average stress-to-strength ratio σ a and the average lateral stress coefficient λ a from the following equations: where V is the volume of rock in a zone. e design procedures are as follows: (1) e stress distribution in the orebody during mining is obtained by field measurement and back analysis using numerical simulation. e orebody is preliminarily divided into zones with approximately equal stresses.
(2) σ a and λ a for each zone are calculated using equation (8), and the correction coefficient δ q (σ, λ) is determined according to Table 1. (3) e specific charge q(σ a , λ a ) for each zone is calculated using equation (6). (4) e blast design parameters can be determined according to the corrected specific charge.

Test Mine and Mining Area. Fushun Hongtoushan
Copper Mine of the China Nonferrous Metal Mining (Group) Co. Ltd. was selected to test the blast design method considering the influence of stress field. e ore vein extends for more than 2000 m below the ground surface and the mine is one of the deepest metal mines in China with an annual output of 600,000 t. Both horizontal adits and vertical shafts were constructed for mining. e original blast design scheme was established based on past experience, with some adjustments to the conditions encountered at the mine site. A lack of systematic study on improving blasting efficiency has existed in the past, leading to a poor ore dilution rate and loss rate. At the same time, the strong brittleness of rock mass frequently leads to the phenomenon of rockburst [27,28].
In this study, field blasting experiments were conducted based on the corrected specific charge. As shown in Figure 8, the test field was located in a mining area 1077 to 1137 m (−647 to −707 m) below the ground surface; the mining area was 28 m long, 17 m wide, and 60 m high [29]. Sublevel stoping was adopted as the mining method. e thicknesses of the roof and sill pillars were 8 and 10 m, respectively. e medium-length hole caving method was adopted. ree layers of fan-shaped blast holes were drilled with a layer thickness of 14 m. e orebody is copper-zinc ore, the surrounding rock mass is gneiss, and the material parameters are listed in Table 2.

In Situ Stress Field and Correction Coefficient for Specific Charge during Mining.
e magnitudes and directions of the principal stresses in the rock masses were measured using the borehole stress relief method [30,31], and the results are σ 1 , σ 2 , and σ 3 are the maximum principal stress, second principal stress, and minimum principal stress, respectively; l i , m i , and n i are the cosines of σ i to the x, y, and z axis directions in the original coordinate system, respectively. e borehole stress relief method can only give the stresses at the measurement locations, and the back-analysis method was used to obtain the stress distribution in the mining area [32,33]. e blasting zones and sequence are shown in Figure 8. e average stress-to-strength ratio σ a and average lateral stress coefficient λ a in each zone were obtained by equation (8). Finally, the correction coefficients for specific charge in each zone were determined as listed in Table 1 and the results are listed in Table 3.

Results.
During mining, slots were first drilled to provide free surfaces and compensation space for subsequent large-scale blasting. Blasting was then conducted from Zones I to V. Ores and rocks were collected by the bottom structure after each caving zone, which provided compensation space for subsequent blasting. e numbers of blast holes and explosive consumptions in the original and revised designs based on the proposed method are listed in Tables 4 and 5, respectively. It can be seen that, using the proposed blasting scheme, the number of blast holes in the test area decreased It should be noted that the actual specific charge in the test field was only reduced by 19.8%, while the theoretical average specific charge obtained by calculation was reduced by 27.2%. e theoretical correction coefficient for specific     charge was calculated based on the laboratory test results in combination with the in situ stress field. e lithology and blasting conditions were different from those in the test field. erefore, the correction coefficients for specific charge in various zones adopted in the field tests were smaller than the theoretical values.

Conclusions
e conclusions of this study can be summarized as follows. e stress loading condition has a large influence on specific charge. Under the uniaxial stress state, the stress field promotes rock fragmentation, and the specific charge decreases with increasing stress magnitude. Under the equal biaxial stress state, the specific charge first increases and then decreases rapidly as the stress-to-strength ratio increases.
A design method for specific charge, considering the influence of field stress in underground mines, is proposed. e stress distribution in the blasting area is obtained first. e blasting area is preliminarily divided into zones with approximately equal stress in each zone. e average stressto-strength ratio and average lateral stress coefficient are then calculated for each zone. e correction coefficient and specific charge are determined. e corrected specific charge can be applied to the blast design. e blasting test results at Hongtoushan Copper Mine indicate that drilling and blasting workload can be reduced significantly, as the actual specific charge was reduced by 19.8%.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.