Enhancing Sustainable Mining Practices Through Fracture-Informed Blasting Strategies: A Case Study of the Aïn El Kebira Limestone Quarry in Algeria

The ever-increasing global demand for raw materials necessitates efficient utilization of mineral resources, playing a pivotal role in the economic prosperity of nations worldwide [1]. Mining enterprises are tasked with maximizing resource extraction while navigating diverse technical, economic, and human considerations.

The science and art of blasting for rock fragmentation in mining has evolved dramatically. Historically, chemists played a crucial role in developing stable, powerful explosives and tailoring mixtures for specific applications. Recent years have seen intensified research driven by the need to minimize blasting costs and enhance fragmentation quality. This research encompasses advancements in computer modeling, explosive formulation, and high-speed photography [2]. Despite these efforts, achieving precise control over fragmentation variables remains a significant challenge [3].

The advent of high-powered computers has spurred research into continuous, discontinuous, and continuous-discontinuous models to simulate fracturing and fragmentation. Some researchers have adopted a micro-static approach to analyze solid explosive fracturing and fragmentation [4]. Although numerous numerical models exist, they still struggle to provide reliable and accurate predictions of particle size distribution based on rock geometry, mechanical, and physical properties [5].

For example, in the Krivoï-Rog quarries, rocks with a hardness of f=12 or higher typically yield minimal oversized fractions (less than 0.5%), while the -400mm fraction accounts for 75% to 90%. For softer rocks (f<12), the percentage of these fractions can reach 92-97% [6].

Achieving consistently uniform fragmentation through blasting paves the way for implementing cyclic and continuous technologies in quarries. These technologies utilize various transportation methods within the quarry, such as excavators, rail transport, trucks, and conveyors, to move blasted ore to processing sites [7]. To justify the economic viability of combined technology, the blasted ore must contain less than 80% of the -400mm fraction [8]. The maximum economic benefit is achieved with a fraction size of -300mm, constituting 77-85% of the total [9]. Therefore, improving rock fragmentation quality is crucial for the widespread adoption of combined and future continuous technologies in quarries [10].

Several avenues exist for enhancing the technical and economic performance of drilling and blasting operations [11]. These include:

Modernizing methods and techniques for rock destruction through explosives. This includes optimizing drilling and blasting parameters, selecting efficient drilling techniques, tools, and explosives, and exploring new forms of energy-based rock destruction methods.

Developing and introducing new technologies. This encompasses innovative explosives, drill types, and associated components, along with novel drilling and blasting technologies specifically designed for quarries.

Exploring alternative forms of energy for rock destruction.

This article specifically focuses on the future prospects for modernizing drilling and blasting operations. We chose to study the mining conditions at Ain El Kebira, which primarily involves sedimentary limestone. We observe the presence of two fracturing systems and a third, diffuse system with no preferred orientation [12].

In some instances, the occurrence of oversized fractions is remarkably high, reaching up to 40%. This article draws upon meticulously analyzed data provided by CETIM (Center for the Study and Technological Services of the Construction Materials Industry), supplemented by firsthand observations, measurements, determinations, and expert reports [12]. Our blasting methodology relies on geometric modeling and utilizes original, previously unpublished formulas. This article presents a comprehensive analytical summary, incorporating a fresh scientific perspective through digital mapping to provide all essential data for its compilation [13].

This study takes into consideration the following points:

The need to fragment diversity in the practice of discrimination and contribute to strengthening the Algerian community. It also aims to address the current issues faced by Algerian limestone quarries.

The focus is on relevant studies related to fracking, drilling techniques, and sustainability outcomes. This provides a more precise scope for the literature review.

The volume of oversized materials was determined through photogrammetry, as illustrated in Figure 3:

3.png

Figure 3. Diagram of the equipment setup for capturing a photoplane image of the blasted rock slope

The planimetry measurement method is one in which the volume of oversized materials is determined as the ratio of the total surface area of the oversized pieces in the plan to the overall surface area over which the measurement is taken.

In situations where precise measurements are required within a pile of rocks, a favorable spot is photographed, and then the analysis of the photos is carried out at a specific scale. This method is referred to as photoplanimetry [15, 16].

Many referenced authors do not present a clear methodology for rock blasting under Algerian conditions. In this work, using modern digital mapping tools and reliable references from leading institutions, we are addressing the development of an explosive blasting methodology that takes into account the Algerian mining conditions [19].

Upon reviewing the existing research, it is evident that the understanding of the explosive working mechanism remains unresolved due to the lack of precise observation means for all detonation sequences and the rather complex mathematical interpretations that result. Unfortunately, explosives still remain a destructive agent when they could be an effective regulator of fragmentation [20].

5.1 Classification of methods for controlling rock fragmentation with explosives

The known methods for controlling the fragmentation of rock masses with explosives can be classified based on various factors [21]:

Adjustment through the influence of the explosion on the rock mass can be achieved by varying:

a) Specific explosive consumption calculated.

b) Diameter of the charge.

c) Type of explosive used.

d) Charge construction.

e) Orientation of the initiation of continuous charge.

f) The order of initiation of parts of the discontinuous charge.

g) Quality of stemming and its length, and more ...

During the change in the character of the charge's effect in the regulated fragmentation zone, the part of the energy transmitted in the practically unregulated fragmentation zone varies, resulting in changes in the dimensions of these zones and the intensification of fragmentation in the mass.

Adjustment of the explosive effect on the rock mass in the unregulated fragmentation zone can be achieved by the interaction of adjacent charges and groups of charges through the variation of:

a) Hole layout and the number of rows.

b) Delay intervals and the sequence of charge firing, bench height, hole layout patterns on the bench.

Methods for controlling fragmentation can be divided into two classes:

The first class relates to methods that ensure the desired level of fragmentation: specific explosive consumption, calculated diameter, and hole layout.

The second class includes methods that allow for changing the level of fragmentation in limited zones and do not exclude the flow of oversized fractions. This encompasses various methods that may reduce the volume of oversized material by 10-20%, including the use of discontinuous charges (solid, air, water stemming), charges with empty or water-filled intervals in sub-drilling or between the charge and stemming, sequential initiation of different parts, reverse initiation of continuous charges, different types of explosives with varying detonation velocities, densities, and volumetric energy concentrations, paired hole blasting, block blasting from high benches, combination of charges with different diameters and lengths, micro-delay blasting patterns, blasting in confined spaces, pre-splitting, and more.

5.2 Calculation of the blasting plan parameters

5.2.1 Theory for calculating specific explosive consumption

To improve blasting plan design, we propose a framework for choosing specific explosive consumptions and starting directions. This framework prioritizes minimizing oversize material while considering energy expenditure, rock properties, and economic feasibility. We utilize experimental blasts and data analysis to determine optimal q values for different rock types, ensuring efficient and sustainable blasting operations.

For the destruction of rock masses down to a specific particle size, a certain amount of energy needs to be expended (energy capacity, etc.). This dependency is known based on the fundamental laws of fragmentation and remains true for explosive destruction [2].

However, there are several distinguishing features between explosive fragmentation and mechanical fragmentation. Mechanical fragmentation has a two-sided force pattern (Figure 13a), whereas explosive fragmentation (except for oversize reduction and tight-space blasting) exhibits a one-sided force pattern (Figure 13b).

13.png

Figure 13. Force diagram

In mechanical fragmentation, different pieces of rock are involved, while in blasting, fractured rock masses of significant dimensions are encountered. The fissures and heterogeneity during blasting facilitate the division of large rock pieces and reduce the specific energy capacity for destruction. During blasting, fissures act as a barrier to the expansion of energy, reducing the possibility of fragmentation and often increasing the specific explosive consumption required to achieve the desired particle size [22].

The smaller the diameter of the charge, the less likely the energy expansion screen effect is between the charge and the free surface of the bench.

With an increase in specific explosive consumption, the degree of fragmentation in the rock mass increases more intensively over the output (Figure 14). Then comes the so-called state of saturation of the rock mass with blast energy, where it can't absorb a large amount of energy spent unnecessarily on rock dispersion. In this case, the change in fragmentation intensity remains insignificant, and the curve roughly parallels the x-axis. The curve's smoothness is also influenced by the direction of practically unregulated fragmentation [14, 15].

For a small charge diameter (d < 150mm), the curve passes lower, and in some cases, it can even reach the x-axis (in this case, the oversize output is zero). With a large charge diameter (d > 250mm), the curve passes higher, and practically, for any specific explosive consumption (q), it's impossible to achieve a zero-oversize output; in other words, there are minimum values for the oversize output, denoted as Vct and Vtc [21].

The curve intersects the y-axis at a point that represents the content of oversize material in the rock mass before blasting.

14.png

Figure 14. Dependence of the oversize output on q for different charge diameters and their rock breakability. 1-2: Oversize output from the unregulated fragmentation zone, 1_for d1, 2_for d2 [4]

Depending on the rock's fissure category and the permissible fragment size in the operations, this value can vary from 100% to 0.

When calculating explosive consumption, it is practical to replace the curves on the graph with straight lines. In this case, the precision of the results obtained falls within the range of 15-20%, which is generally acceptable. The selection of a rational specific consumption is a techno-economic issue that is resolved based on the cost of extracting valuable minerals for all processes. However, in most cases during blasting, efforts are made to minimize the oversize output, aiming for a value close to 0%.

In the graph (Figure 15) showing the variation of q for a given charge diameter and different rocks based on their workability, the percentage of oversize blocks (dhg > 700mm) in the rock mass before blasting is plotted on the y-axis.

15.png

Figure 15. Dependency of the oversize output rate on q for different rock categories [4]

As the acceptable rock fragment size changes, the content of this fraction in the rock mass also varies. The slope angle of the lines and the flow rate of the large fractions in the non-regulated fragmentation zone change. Therefore, the threshold values for specific explosive consumption change, but the methodological principle of choosing q to ensure the minimal oversize flow remains the same [15-17].

With increasing fragment sizes, all the lines shift downward, meaning the specific explosive consumption decreases. To determine its value, if you know the content of the large fraction in the mass (the point on the line on the ordinate axis), it is necessary to carry out one or, preferably, two experimental blasts with selected different specific consumptions, plot the large fraction flow rate obtained on the graph, and connect the point on the ordinate axis to the point obtained using a straight line. By extending this line to its intersection with the line representing the minimum oversize flow rate, you can find the threshold value of q. Beyond this threshold, it is not rational to go because, in this zone, the curve of the large fractions' flow rate with varying specific consumption already levels off [20].

Most often, it is not practical to apply the specific consumptions determined in this way because they result in a broad rock pile and mining operations that are not feasible according to the technology. When carrying out experimental blasts, you should select rock blocks with similar properties based on hardness and fissuring and use a method for conducting experimental blasts developed by researchers from the Moscow Mining Institute [22].

The practical method for determining specific explosive consumptions for 234 mm diameter holes, taking into account the fissuring of the rock mass and the strength properties of its components, is based on the fundamental work of Academician Rjevsky [6]. The dependence of q on rock strength properties (hardness coefficient f) during the blasting of divisions to fragment sizes less than 100 mm is as follows:

$q=f . e . b . \sigma_c^2 0.73 \times 10^2 \times 0.349$     (1)

where, this formula is analogous to the theoretical formula by Academician Rebinder, encompassing the laws of Patinger, and Kirpitchev [6].

$K w^2=\frac{\sigma_c^2}{2 E}+\frac{S_p P_n}{V}$     (2)

The formula contains the following variables: K: A coefficient for unit conversion into the SI system; w: The specific energy consumption for rock fragmentation in J/m³; σ_c: The uniaxial compressive strength of the rock in Pascals (Pa); E: The rock's modulus of elasticity in Pascals (Pa); P_n: The specific surface energy in J/m²; S_p: The new surface area created in square meters (m²); V: The volume of the rock to be fragmented in cubic meters (m³).

Let us apply the notion of fragmentation coefficient K_frag as the ratio of the surface of the block before the shot (S_n) and the surface after the shot (S_p). Afterwards, the energy expenditure equation, for the case of fragmentation at the explosive, takes the form:

$W=\frac{\sigma_c^2}{2 E}+\theta \mathrm{K}_{\mathrm{frag}}+\varepsilon$     (3)

where, θ: Coefficient taking into account energy expenditure for fragmentation; ε: Coefficient taking into account energy losses.

The processing of the results of the experimental shots made it possible to design the above formula as follows:

$W=\frac{\sigma_c^2}{2 E}+1111,004 K_{\text {frag }}+39.693$     (4)

Taking for the average conditions σc²/(2E)=11.10^-4 and returning to the specific consumption taking into account the mechanical equivalent we will have :

$Q_s=25.10^{-10} \cdot \sigma_c+2.6 K_{\text {frag }}+0.093$      (5)

The dependence of the fragmentation coefficient on the limit of the rock to compression according to experimental data in the form:

$K_{\text {frag }}=20 \times 10^{-10} \sigma_c+0.0965$      (6)

The specific consumption characterizing the fragmentation of the divisions in Kg/m³:

$q_s=0.77 \times 10^{-8} \sigma_c+0.345$      (7)

Taking into account the dependencies obtained previously:

$q=q_s\left(a+b \cdot d_{\text {charg }}+d_c\right)$     (8)

We obtain :

$q=q_s\left(0.6+3.3 \times 10^{-3} \cdot d_{\text {charg }} \cdot d_c\right) \cdot\left(\frac{d_c}{d_k}\right)^{\frac{2}{5}} \cdot e \cdot\left(\frac{\rho}{2.6}\right)$      (9)

And finally:

$q=\left(0.77 \times 10^{-8} \sigma_c+0.345\right) \cdot\left(0.6+3.3 \times 10^{-3} \cdot d_{\text {charg }} \cdot d_c\right) \cdot\left(\frac{d_c}{d_k}\right)^{\frac{2}{5}} \cdot e \cdot\left(\frac{\rho}{2.6}\right)$      (10)

where, q: specific consumption calculated to obtain the required degree of rock fragmentation, Kg/m³; b: coefficient taking into account the degree of cracking of the rock; a: coefficient taking into account the energy expenditure to overcome the connections between the divisions; d_c: average diameter of the division in the massif, m; d_k: admissible (fixed) dimension of the piece, m; e: relative working capacity of the explosive; ρ: density of the rock, t/m³.

Based on the generalization of firing work through experience in quarries and the method proposed by researchers of the Moscow Mining Institute and the Scientific Research Institute of Ferrous Metals, a classification on the firingability of massifs of rocks was established when applying loads of Φ 250 mm and according to which it is recommended to choose the specific consumption of the explosive (Table 2).

Table 2. Rock classification based on drillability for quarries

The distinctive features of the proposed classification include: the introduction of about ten categories that group the various rock formations encountered in quarries, taking into account their main properties, which significantly influence the results of fragmentation, namely, fissuring and mesh hardness. According to this classification, for each quarry, no more than four types of rock are selected, taking into account the required specific consumption. This approach eliminates one of the main drawbacks of existing classifications: in each quarry, there are rocks that are easily, moderately, and difficult to drill, but the specific consumption of explosives for mass blasting for a given category can vary by two times or more. When using the given classification, the corresponding drillability categories are chosen based on the specific consumption of explosives. This approach provides an objective characteristic of the specific rock formation [23].

In the future, within this classification, it is advisable to replace the mesh hardness with impact resistance (resilience), which to a large extent characterizes the destruction of the mesh during blasting. It is necessary to take into account the degree of water saturation in the rock masses to be blasted, as well as the methods of transitioning from the standard blasting conditions of the given classification to other conditions (different bench heights, charge diameters, explosive types, permissible fragment sizes, micro-delay schemes, etc.) [24].

Other authors provide its approximate value, which is determined based on experimental results or industrial blasting, taking into account rock properties. The specific consumption of explosives for multi-row blasting is applied for the first row from the tables provided, but for the second and subsequent rows, it is increased by 5-10% in rocks of fissure categories I-III and by 10-15% in rocks of categories III-X.

5.2.2 Theory of calculating charge diameter

For quarries, the following specific features of boreholes can be formulated [25]:

(1) For rocks in the drillability category I-III, it is advisable to choose the largest possible diameter (250-300 mm).

(2) For rocks in the drillability category IV-VIII, as well as homogeneous category III rocks in the case of the possibility of using multi-row delay blasting, the preferred diameter is (200-250 mm).

(3) For rocks with large meshes in drillability category VIII-X, as well as heterogeneous and often alternating category III rocks, it is advisable to reduce the charge diameter to 150 mm.

Since the output of mined material per meter of borehole is proportional to the square of the charge diameter, in this case, the efficiency of drills increases with the amount of material drilled by large-diameter holes, and the drilling cost per cubic meter decreases. That's why in modern conditions, there is a trend toward using large-diameter holes, especially for high-capacity quarries.

(1) Determination of drillability (standard q): The resistance of rocks to blasting is characterized by the specific standard consumption of explosives (Tables 3-5). It is determined by the following formula:

$q_{\text {ét }}=0.02\left(\sigma_{c o m p}+\sigma_{\text {dép }}+\sigma_{t r}\right) 2 \gamma$      (11)

where, σ_comp: Compressive strength of rocks; kgf/cm²; σ_dép: Displacement strength of rocks; kgf/cm²; σ_tra: Tensile strength of rocks; kgf/cm²; γ: Density; kg/m³.

σ_comp =75.74 MPa= 772.4 kgf/cm² (Medjounes I)

σ_comp =104.15 MPa=1062.03 kgf/cm² (Medjounes II)

σ_dépl: It is the resistance of the rock to displacement; it depends on the compressive stress and can be calculated using the following formula:

$\sigma_{\text {dép }}=(0.13 \div 0.33) \sigma_{\text {comp }}$      (12)

σ_dépl=0.23×772.4 = 177.65 kgf/cm² (Medjounes I);

σ_dépl=0.23×1062.03 = 244.26 kgf/cm² (Medjounes II).

The tensile strength, which is determined by the following empirical formula:

$\sigma_t=(0.08 \div 0.12) \sigma_{\text {comp }}$      (13)

σ_t=0.10x772.4=77.24 kgf/cm² (Medjounes I)

σ_t=0.10x1062.03=106.20 kgf/cm² (Medjounes II).

Table 3. Initial data

q_ét=0.02 (772.4+177.65+77.24) +2* 2.76 = 26.07 g/m³ ... Medjounes I;

q_ét=0.02 (1062.03+244.26+106.2) +2* 2.68 = 33.61 g/m³ ... Medjounes II.

Table 4. Classification of rock by drillability index

Medjounes I → Difficult tirability, Class III, Category 14.

Medjounes II → Very difficult tirability, Class IV, Category 17.

(2) The drillability of rocks can be determined using the empirical formula of Academician Rjevsky.

$D_f=0.007\left(\sigma_{c o m p}+\sigma_{\text {dép }}\right)+0.7 \rho$      (14)

D_f=0.007(772.4+177.65)+0.7*2.76= 8.58; easy drillability, category 8; Medjounes I.

D_f=0.007(1062.03 + 244.26) + 0.7*2.68 = 11.02; moderate drillability, category 11; Medjounes II.

Table 5. Rock classification by drillability index

The permissible particle size of large blocks after blasting is limited by the following conditions:

(a) By the capacity of the loader bucket:

$C \leq 0.8 \sqrt[3]{E}, C \leq 0.8 \sqrt[3]{8} \leq 1.6(\mathrm{~m})$     (15)

where, C: maximum block size, (m); E: loader bucket capacity, m³.

(b) According to the capacity of the truck's bed (or volume). The volume of the truck's bed is 34.2 m³, so the average diameter of the rocks (pieces) will be equal to:

$C \leq 0.5 \sqrt[3]{V}, C \leq 0.5 \sqrt[3]{34.2} \leq 1.62(\mathrm{m})$      (16)

(c) By the size of the crusher's opening:

$C \leq 0.8 \times b$     (17)

where, b: Crusher's feed opening: b= 1300 mm; C≤(0.8*1.3)≤1.04 m , with a threshold value: C≤1.04m.

Based on the obtained results, the acceptable block size is set at 1.04 m. Any block not meeting this dimension will be considered an oversized rock and will require a secondary fragmentation operation (secondary blasting) to reduce its size.

(3) Hole Diameter Determination: We choose a hole diameter based on the initial recommendations proposed in our analytical summary, considering both quantitative and qualitative criteria (based on the categories of fissuring and drillability). For our case, we adopt: D = 150 mm.

$q=q^{\prime} \cdot K_{e x}$     (18)

where, q' is chosen from the table of q selection in this article, equal to 0.45 kg/m³.

$K_{\text {ex }}=A_{\text {ét }} / A_u$     (19)

where, K_ex=1.1; A_ét: Standard Explosive - Ammonite N6GV; A_u: Used explosives (Marmanite III and Anfomil).

q=0.45 × 1.1 = 0.49 kg/m³ (Medjounes II).

Similarly for Medjounes I, where q=0.40 x 1.1=0.44 kg/m³.

Length of the hole:

$L=\frac{H}{\sin \beta}+l_{s f}$     (20)

where, β=75°.

The length of the subdrilling is determined by the following formula:

$l_{s f}=k_s . D$     (21)

Other authors propose the following formula:

$l_b=0.75. w$     (22)

l_b = (20÷30)*D=29*0.15=4.35 m (Medjounes I)

l_b = (20÷30)*D=30*0.15=4.5 m (Medjounes II)

Determination of the line of least resistance:

$W=\frac{\sqrt{p^2+4 m q p H L}-p}{2 m q H}$     (23)

where, m=0.95 for both Medjounes I and II.

This value is the most suitable for cement limestone based on the academic experience of former Soviet trainers who have worked in Algeria. The explosives used are Marmanit III and Anfomil, so the recommended initiation rate is 20%.

$\Delta=0.20 \times 0.95+0.80 \times 0.90=0.91 \mathrm{~kg} / \mathrm{m}^3$

$\mathrm{P}=785 \times d^2 \times \Delta$     (24)

where, P=785×(0.150)²×0.91=16.07 kg/m.

$W=\frac{\sqrt{16.07^2+4 \times 0.95 \times 0.44 \times 16.07 \times 15 \times 17.55}-16.07}{2 \times 0.95 \times 0.44 \times 15}=5.54 m($ Medjounes I)

$W=\frac{\sqrt{16.07^2+4 \times 0.95 \times 0.49 \times 16.07 \times 15 \times 17.62}-16.07}{2 \times 0.95 \times 0.49 \times 15}=5.32 m$ (Medjounes II)

Calculation of W according to safety conditions:

$W \geq H \operatorname{tg} \alpha+c$     (25)

This sentence means: "Htgα+c=15. tg85°+3=4.13m Htgα+c=15×tg85°+3=4.13m; therefore, the conditions are met."

It's confirming that the calculated value of 4.13 meters satisfies the specified conditions.

The distance between the holes in the first row:

$a=m . W$     (26)

$a=m . W=0.95 \times 5.54=5,26 m$ (Medjounes I)

$a=m . W=0.95 \times 5.32=5,05 m$ (Medjounes II)

The distance between rows of holes: staggered pattern due to the shape of the blocks.

$b=0.85 \times a$    (27)

$b=0.85 \times a=0.85 \times 5.26=4.47 m$ (Medjounes I)

$b=0.85 \times a=0.85 \times 5.05=4.29 m$ (Medjounes II)

- Load quantity of a hole:

1^st row:

$Q_{c h_1}=q \cdot W \cdot H \cdot a_1$     (28)

$Q_{c h_1}=q \cdot W \cdot H \cdot a_1=0.44 \times 5.54 \times 15 \times 5.26=192.33 \mathrm{~kg} / \mathrm{tr}$ (Medjounes I)

$Q_{c h_1}=q \cdot W \cdot H \cdot a_1=0.49 \times 5.32 \times 15 \times 5.05=197.46 \mathrm{~kg} / \mathrm{tr}$ (Medjounes II)

2^nd row:

$Q_{c h_2}=q \cdot W \cdot H \cdot b$     (29)

$Q_{c h_2}=q . W . H . b=0,44 \times 15 \times 5.26 \times 4.47=155.18 \mathrm{~kg} / \mathrm{tr}$ (Medjounes I)

$Q_{c h_2}=q . W . H . b=0.49 \times 15 \times 5.05 \times 4.29=159.23 \mathrm{~kg} / \mathrm{tr}$ (Medjounes II)

- Load length:

1^st row:

$l_{c h_1}=\frac{Q_{c h_1}}{P}$     (30)

$l_{c h_1}=\frac{Q_{c h_1}}{P}=\frac{192.33}{16.07}=11.97 \mathrm{~m}$ (Medjounes I)

$l_{c h_1}=\frac{Q_{c h_1}}{P}=\frac{197.46}{16.07}=12.29 \mathrm{~m}$ (Medjounes II)

2^nd row:

$l_{c h_2}=\frac{Q_{c h_2}}{P}$     (31)

$l_{c h_2}=\frac{Q_{c h_2}}{P}=\frac{155.18}{16.07}=9.66 m$ (Medjounes I)

$l_{c h_2}=\frac{Q_{c h_2}}{P}=\frac{159.23}{16.07}=9.91 m$ (Medjounes II)

- Jam length:

1^st row:

$l_{b_1}=L-l_{c h_1}$    (32)

$l_{b_1}=L-l_{c h_1}=17.55-11.97=5.58 m$ (Medjounes I)

$l_{b_1}=L-l_{c h_1}=17.62-12.29=5.33 m$ (Medjounes II)

2^nd row:

$l_{b_2}=L-l_{c h_2}$     (33)

$l_{b_2}=L-l_{c h_2}=17.55-9.66=7.89 m$  (Medjounes I)

$l_{b_2}=L-l_{c h_1}=17.62-9.91=7.71 m$ (Medjounes II)

-Mining mass flow:

$J_m=\frac{Q_{c h_1}+Q_{c h_2}}{2 \times L \times q}$     (34)

$J_m=\frac{Q_{c h_1}+Q_{c h_2}}{2 \times L \times q}=\frac{192.33+155.18}{2 \times 17.77 \times 0.44}=22.50 \mathrm{~m}^3 / \mathrm{m}$ (Medjounes I)

$J_m=\frac{Q_{c h_1}+Q_{c h_2}}{2 \times L \times q}=\frac{197.46+159.28}{2 \times 17.62 \times 0.49}=20.66 \mathrm{~m}^3 / \mathrm{m}$ (Medjounes II)

-Volume of a block:

V = 1988.5 m³  (Medjounes I)

V =14963 m³ (Medjounes II)

-The length of drilled holes required for a block:

$\sum L=\frac{V}{J_m}$     (35)

$\sum L=\frac{V}{J_m}=\frac{11988.5}{22.50}=532.82 m$ (Medjounes I)

$\sum L=\frac{V}{J_m}=\frac{14969}{20.66}=724.25 m$ (Medjounes II)

-Number of holes drilled:

$N_{t r}=\frac{\sum L}{L}$    (36)

$N_{t r}=\frac{\sum L}{L}=\frac{532}{17.55}=30.36 \cong 30$ holes (Medjounes I)

$N_{t r}=\frac{\sum L}{L}=\frac{724.25}{17.62}=41.1 \cong 41$ holes (Medjounes II)

-Number of sounders:

$N_s=\frac{\sum L}{R_s \times n_{p s} \times N_j}$     (37)

$N_s=\frac{532}{224 \times 1 \times 1}=2.357 \cong 03$ sounders 

furukawa (Medjounes I)

$N_s=\frac{532}{160 \times 1 \times 1}=3.325 \cong 04$ sounders

Atlas copco (Medjounes I)

$N_s=\frac{724,25}{224 \times 1 \times 1}=3.23 \cong 04$ sounders

furukawa (Medjounes II)

$N_s=\frac{724,25}{160 \times 1 \times 1}=4.53 \cong 05$ sounders

Atlas copco (Medjounes II)

(RsFurukawa = 224 m/shift), (Rs Atlas Copco = 160 m/shift).