The Bidzar quarry, located in the Mayo-Louti Division of northern Cameroon, exploits white, pink, and black marbles for cement production (Figure 2). The rock mass exhibits a well-developed metamorphic foliation and a dense network of tectonic discontinuities inherited from Pan-African deformation phases, particularly the D₂ phase [26][37].

The geological structure is characterized by steeply dipping (83˚ SE) N-S striking marble and schist layers, creating a highly anisotropic environment that strongly controls blasting outcomes (Figure 3). Detailed structural mapping reveals three main joint sets (Figure 4):

J1 (dominant): ENE-WSW orientation, dipping 75˚ - 85˚;

J2: N-S orientation, dipping 70˚ - 80˚;

J3: E-W orientation, dipping 65˚ - 75˚.

The map was generated by the author using ArcGIS software (Esri, version 10.8). The topographic basemap is derived from SRTM digital elevation data (30 m resolution, NASA/NGA).

Figure 2. Geographic location map of the Bidzar marble quarry in the Mayo-Louti Division, North Region of Cameroon, showing main access routes and surrounding localities.

Map source: Generated by author using Surfer software (Golden Software) from SRTM digital elevation data (30 m resolution, NASA/NGA). Quarry boundaries and access roads were mapped using field GPS data collected by author in 2024. Coordinate system: WGS84/UTM zone 33N. Scale bar: 500 m. North arrow indicated.

Figure 3.Topographic map of the Bidzar quarry area showing elevation distribution (contour interval: 10 m) and main geomorphological features.

Figure 4.Field photograph showing the structural arrangement of interbedded marble and schist layers at the Bidzar quarry, with dominant fracture networks (NNE-SSW orientation) controlling rock mass discontinuities and block size distribution.

The ENE-WSW fracture set acts as preferential pathways for stress wave propagation and crack coalescence during blasting, significantly influencing fragmentation efficiency and block detachment [38]. The interaction between these joint sets leads to the formation of prismatic to tabular rock blocks, whose geometry and size directly affect fragmentation outcomes and blast-induced damage.

The lithology comprises alternating sequences of white marble, dolomitic marble, quartzite, and schist/shale units. This lithological contrast creates significant geotechnical heterogeneity: marble layers are rigid and dense (UCS = 75 MPa), while schist layers are softer and more deformable. Previous studies have shown that such heterogeneity complicates fragmentation control, as rigid and deformable materials respond differently to explosive loading [39][40].

Field investigations followed ISRM recommended procedures [41]. Scanline surveys were conducted along three orientations (N-S, E-W, and ENE-WSW) with a total cumulative length of 120m. A total of 187discontinuities were systematically measured for orientation, spacing, persistence, roughness, and aperture. Rock Quality Designation (RQD) was calculated for each 1.5 m scanline segment following Deere [42], yielding an average RQD of 65% (range: 42% - 78%), indicating fair to good rock mass quality with spatial variability correlated to schist content.

For fragmentation analysis using WipFrag, 25 - 30 photographs were taken per blast pile following standardized protocols (scale reference included in each image, consistent lighting conditions, camera positioned approximately 10 m from the pile). WipFrag 3.3 analyzed each image batch, with manual correction applied to less than 5% of fragment boundaries where automatic detection was incomplete.

The rock mass is affected by a dense network of foliations, joints, and fractures with variable spacing, resulting in a heterogeneous block size distribution [43][44]. Rock Quality Designation (RQD) index calculated from field measurements according to Deere [42] indicates generally fair to good rock mass quality, with significant spatial variability depending on lithology and fracture density. Lower RQD values are associated with schistose units, whereas higher values correspond to more massive marble layers, consistent with observations in structurally complex metamorphic environments [44][45].

The physical and mechanical properties of Bidzar marble were measured following standard ASTM and ISRM methods, as summarized in Table 1. The marble exhibits a density of 2.77 g/cm³, uniaxial compressive strength of 75 MPa, Young’s modulus of 10.6 GPa, and Poisson’s ratio of 0.28. The rock mass factor (A) calculated from Lilly’s blastability index [46] is 10.455, a key input parameter for the Kuz-Ram fragmentation model.

From a blasting engineering perspective, these mechanical characteristics play a major role in explosive-rock interaction. The relatively high strength and stiffness of the marble influence stress wave transmission, crack initiation, and fracture propagation around blast holes. When combined with the existing joint network and dominant fracture orientations, these properties directly control fragmentation efficiency, energy consumption, and overall blasting performance. Incorporating these structural parameters into blast design is therefore essential to optimize explosive energy distribution, minimize undesired damage, and improve fragmentation outcomes.

The following equipment was used for field data collection:

Digital camera: For photographing blasted rock piles for subsequent granulometric analysis;Topcon total station: For precise positioning of drill hole positions and massif configuration assessment;Compass and measuring tape: For measuring fracture orientations and dip in the rock mass;Moisture meter (digital ohmmeter): For verifying electrical parameters of ignition systems;Notebook and field sheets: For recording observations.

Data processing and blasting simulation were performed using:

WipFrag 3.3: Digital image analysis software for determining granulometric distribution of blasted rock fragments by automatic detection of fragment boundaries and 2D dimension calculation [16].Matlab R14: For numerical simulation and systematic parametric optimization of blasting parameters using the Kuz-Ram model [45].Orica SHOTPlus Professional: Blasting simulation software for predicting fragmentation based on geotechnical characteristics and explosive charge parameters [46].

Geotechnical properties of the Bidzar quarry rock mass were assessed following standard ASTM and ISRM suggested methods. Detailed methodology for discontinuity mapping, RQD calculation, and mechanical property testing is described in Section 2.3. The complete set of physico-mechanical properties used for blast modeling is presented in Table 1.

Table 1. Physico-mechanical properties of the Bidzar marble rock mass.

Field investigations followed ISRM recommended procedures [41]. Scanline surveys were conducted along three orientations (N-S, E-W, and ENE-WSW) with a total cumulative length of 120 m. A total of 187 discontinuities were systematically measured for orientation, spacing, persistence, roughness, and aperture. Rock Quality Designation (RQD) was calculated for each 1.5 m scanline segment following Deere [42], yielding an average RQD of 65% (range: 42% - 78%), indicating fair to good rock mass quality with spatial variability correlated to schist content.

For mechanical characterization, 15 block samples were collected from representative locations across the quarry. Uniaxial compressive strength tests (ASTM D7012) were performed on 12 intact specimens (mean = 75 MPa, standard deviation = 4.2 MPa). Indirect tensile strength (Brazilian test, ASTM D3967) was conducted on 10 specimens (mean = 8.9 MPa, standard deviation = 0.7 MPa). Young’s modulus was determined from UCS test stress-strain curves (mean = 10.6 GPa, standard deviation = 1.1 GPa).

For fragmentation analysis using WipFrag, 25 - 30 photographs were taken per blast pile following standardized protocols (scale reference included in each image, consistent lighting conditions, camera positioned approximately 10 m from the pile). WipFrag 3.3 analyzed each image batch, with manual correction applied to less than 5% of fragment boundaries where automatic detection was incomplete.

From a blasting engineering perspective, these mechanical characteristics play a major role in explosive-rock interaction. The relatively high strength and stiffness of the marble influence stress wave transmission, crack initiation, and fracture propagation around blast holes. When combined with the existing joint network and dominant fracture orientations, these properties directly control fragmentation efficiency, energy consumption, and overall blasting performance at the quarry.

3.4.1. Kuz-Ram Model

The Kuz-Ram model predicts fragment size distribution based on explosive consumption, rock mass characteristics, and blast geometry [11]. The Kuz-Ram model predicts the mean fragment size (X₅₀) using Equation (1):

where A is the rock mass factor, K is the powder factor (kg/m³), Q_e is the mass of explosive per hole (kg), and RWS is the relative weight strength of the explosive compared to ANFO (dimensionless).

For this study, the explosive used was a bulk emulsion with a density of 1.03 g/cm³ and an RWS of 100 (equivalent to ANFO). This information is critical for accurate fragmentation prediction as the RWS value directly influences the calculated mean fragment size.

The uniformity index (n) was calculated using Cunningham’s updated formula [47], which considers drilling accuracy, burden, spacing, and hole geometry.

3.4.2. Langefors-Kihlström Method

The Langefors-Kihlström empirical approach optimizes blast geometric parameters including burden, spacing, and charge concentration based on hole diameter and rock strength [13][14]. This method remains widely used in Scandinavian blasting practice and provides conservative estimates suitable for fractured rock masses.

The maximum burden (Bₘₐₓ) was calculated using the Langefors-Kihlström formula:

where:

d is the hole diameter (mm);ρ_e is the explosive density (kg/dm³);s is the weight strength relative to LFB dynamite (dimensionless);c is the rock constant (kg/m³), depending on rock strength and structure;f is the degree of fixation factor (1.0 for vertical holes, 1.2 for inclined holes);E/V is the energy concentration factor.

For the Bidzar marble, the following parameters were applied:

Rock constant c = 0.45 kg/m³ (for medium-hard, fractured rock);Fixation factor f = 1.0 (vertical holes);Relative weight strength s = 1.0 (emulsion equivalent to LFB).

The practical burden (B) was then derived by applying a correction factor to account for geological structures:

where k stru c t is a structural correction factor (0.85 - 0.95) that accounts for the influence of dominant joint sets (J1: ENE-WSW orientation) on stress wave propagation. This integration of structural geology into the empirical design represents a key innovation of this study.

Impedance ratio (Z)

The impedance ratio Z characterizes the efficiency of stress wave transmission from the explosive to the rock mass. It is defined as the ratio of explosive mechanical impedance to rock mechanical impedance:

where:

ρ_e = explosive density (kg/m³);V_e = explosive detonation velocity (m/s);ρ_r = rock density (kg/m³);V_r = P-wave velocity in rock (m/s).

The P-wave velocity in rock can be estimated from the Young’s modulus and density using V r = E / ρ r for homogeneous isotropic materials.

For the Bidzar marble (E = 10.6 GPa = 1.06 × 10¹⁰ Pa, ρ_r = 2770 kg/m³), V r = 1.06 × 10 10 / 2770 ≈ 1956   m / s .

For the bulk emulsion explosive used in this study (ρ_e = 1030 kg/m³, V_e = 4500 m/s) and the Bidzar marble (ρ_r = 2770 kg/m³, V_r = 1956 m/s), the impedance ratio is:

According to previous studies, optimal energy transfer from explosive to rock occurs when Z = 0.4 < Z < 0.7 . The calculated value of 0.42 falls within this optimal range, indicating that the explosive-rock pair is well-matched for efficient fragmentation.

To validate theoretical model results, blast simulations were conducted using Orica SHOTPlus Professional software. This software simulates explosion effects incorporating:

Rock mass geotechnical properties;Blast geometry (burden, spacing, hole diameter, bench height);Explosive type and charge distribution;Initiation sequence and timing.

Simulations provided predictions of fragment size distribution, oversize percentage, and explosive energy distribution, which were used to iteratively adjust blasting parameters.

Images of blasted rock piles were analyzed using WipFrag 3.3 software. The analysis workflow comprised:

Photograph acquisition under standardized conditions (scale reference included);Image calibration and enhancement;Automatic fragment boundary detection;2D dimension calculation and statistical analysis;Generation of cumulative fragment size distribution curves.

The obtained granulometric distributions were compared with quarry specifications, particularly regarding oversize fragments (>800 mm) and fines (<5 mm).

Optimization followed a systematic parametric study approach in Matlab, where key blasting parameters were adjusted incrementally within operational constraints to achieve desired fragmentation outcomes while minimizing explosive consumption.

Parameters varied:

Burden (B): 2.5 - 3.5 m (0.1 m increments);Spacing (S): 3.0 - 4.0 m (0.1 m increments), maintaining S/B ratio between 1.1 and 1.3;Stemming length (L_s): 1.5 - 2.0 m (0.1 m increments);Subdrilling (J): fixed at 0.7 m (based on quarry practice);Explosive charge distribution: adjusted between toe and column charges.

Fixed parameters:

Hole diameter (d): 89 mm (based on available drilling equipment);Bench height (H): 10 m (imposed by quarry operations).

Objective function:

Minimize proportion of oversize fragments (>800 mm);Minimize specific explosive consumption (g/t);Maintain uniform fragment size distribution (uniformity index n > 1.7).

Constraints:

Available drilling equipment (89 mm or 102 mm diameter);Safety requirements for vibration and flyrock control;Geological constraints (fracture orientation and spacing).

For each parameter combination, Matlab calculated:

Fragment size distribution using the Kuz-Ram model;Predicted oversize and fines percentages;Powder factor (g/t);Cumulative fragmentation curves;Uniformity index (n).

The optimal configuration was selected as the parameter set achieving the lowest oversize fraction and powder factor while maintaining acceptable fragmentation uniformity, subsequently validated by SHOTPlus simulations. A total of 1440 parameter combinations were evaluated during the systematic optimization process.

Multi-objective decision criterion for optimal design selection

Given that the three objectives (minimize oversize, minimize powder factor, maximize uniformity) did not always improve simultaneously, a weighted multi-objective utility function U was defined to select the optimal configuration from the 1440 evaluated combinations:

where:

Oversize_max = 15% (maximum acceptable oversize fraction);PF_max = 0.6 kg/m³ (220 g/t, maximum acceptable powder factor);n_min = 1.2 (minimum acceptable uniformity index);n_max = 2.5 (maximum achievable uniformity index under site conditions);X_target = 0.35 m (target mean fragment size).

The weights (w₁ = 0.50 for oversize reduction, w₂ = 0.20 for explosive conservation, w₃ = 0.15 for fragmentation uniformity, w₄ = 0.15 for mean size targeting) were assigned based on quarry operational priorities, determined through consultation with CIMENCAM management. The primary concern is minimizing crusher blockages caused by oversize fragments (>800 mm), hence the highest weight (0.50) was assigned to oversize reduction.

The configuration with the highest utility score U that also satisfied all operational constraints (drilling equipment availability: 89 mm diameter only; safety requirements: flyrock control; geological constraints: fracture orientation) was selected as the optimal design. This selection process yielded the 3.2 m × 3.6 m configuration (S/B = 1.125), which achieved the lowest predicted oversize (3.8%) while maintaining PF below 0.45 kg/m³ (157.3 g/t) and n above 1.7, satisfying all constraints.

4.1.1. Structural Characteristics

The rock mass at the Bidzar quarry is primarily composed of interbedded marble and schist, exhibiting significant geological heterogeneity. Analysis of fracture orientations using stereographic projection revealed three main joint sets (Figure 5):

J1 (dominant): ENE-WSW orientation (75˚ - 85˚ dip);J2: N-S orientation (70˚ - 80˚ dip);J3: E-W orientation (65˚ - 75˚ dip).

The cyclographic traces show a particularly high concentration of fractures in the ENE-WSW direction, indicating that this orientation is dominant in the quarry rock mass. These preferentially oriented fractures, especially J1, facilitate shock wave propagation and contribute to more homogeneous fragmentation in areas where they are concentrated. Conversely, areas with fewer fractures or less favorable orientations tend to produce larger, more irregular fragments.

Figure 5.Lower-hemisphere equal-area stereographic projection of discontinuity poles measured in the Bidzar quarry, showing three main joint sets: J1 (ENE-WSW, 75˚ - 85˚), J2 (N-S, 70˚ - 80˚), and J3 (E-W, 65˚ - 75˚). Contours represent 1%, 2%, 4%, and 8% of poles per 1% area.

4.1.2. Geotechnical Characterization of the Rock Mass for Blasting Design

The physical and mechanical properties of Bidzar marble are summarized in Table 1. The rock is characterized by:

Density: 2.76 g/cm³ (average);Uniaxial compressive strength: 75 MPa;Young’s modulus: 10.6 GPa;Poisson’s ratio: 0.28;Rock mass factor (A): 10.455.

From a blasting engineering perspective, these characteristics classify the marble as a relatively strong and stiff rock material (Class III, difficult to blast). The relatively high strength and stiffness influence stress wave transmission, crack initiation, and fracture propagation around blast holes. When combined with the existing joint network and dominant fracture orientations, these properties directly control fragmentation efficiency and energy consumption.

4.1.3. Quantitative Rock Mass Characterization for Blastability Inputs

Discontinuity spacing analysis

The three main joint sets identified from stereographic projection (Figure 5) yielded the following spacing statistics:

J1 (ENE-WSW, dominant): mean spacing = 0.42 m (range: 0.15 - 0.85 m, n = 89 measurements);J2 (N-S): mean spacing = 0.68 m (range: 0.30 - 1.20 m, n = 54 measurements);J3 (E-W): mean spacing = 0.91 m (range: 0.45 - 1.50 m, n = 44 measurements).

The weighted mean discontinuity spacing across all three sets is 0.59 m, confirming a moderately to highly fractured rock mass where natural discontinuities significantly influence blast-induced fragmentation.

Derivation of Lilly’sblastabilityindex (A = 10.455)

Following Lilly (1986), the rock mass factor A was calculated as A = 0.06 × (RMD + JPS + JPA + RDI + HD), where:

RMD (Rock Mass Description) = 30 (for vertically foliated metamorphic rock with joint spacing less than 1.0 m);JPS (Joint Plane Spacing) = 20 (for mean spacing between 0.1 m and 1.0 m);JPA (Joint Plane Angle) = 30 (for discontinuity dip between 60˚ and 90˚ relative to the blast face);RDI (Rock Density Influence) = 0.025 × ρ_r − 50 = 0.025 × 2750 − 50 = 18.75;HD (Hardness) = UCS/5 = 75/5 = 15 (for uniaxial compressive strength between 50 and 100 MPa).

Structural correction factor ( K struct )

The structural correction factor used in Equation (3) was derived from sensitivity analysis of the dominant ENE-WSW fracture set (J1). This factor accounts for the influence of joint orientation on stress wave propagation and was calculated as:

where, F_J1 = measured J1 fracture frequency (fractures/m), F_max = maximum J1 fracture frequency (2.4 fractures/m at Bidzar quarry), α = empirical coefficient (0.08 for Bidzar marble).

Where α is an orientation mismatch coefficient (α = 0 when blast direction parallels J1 orientation; α = 0.15 when misalignment exceeds 30˚). For the optimized design where the blast direction was aligned with the dominant ENE-WSW joint set, K struct was set to 0.95. For zones where J1 orientation is less favorable, values as low as 0.85 were applied, reflecting the reduced fragmentation efficiency when blast direction is misaligned with natural fracture planes by more than 30˚.

Four blast rounds were conducted at the Bidzar quarry with varying parameters. Table 2 summarizes the blast design parameters for each trial.

Table 2. Blasting parameters used during experimental blast rounds at the Bidzar quarry.

Granulometric analysis of blasted rock was performed using WipFrag 3.3 software (Figure 6).

Key observations (Table 3):

Blast 1 (102 mm diameter, PF = 0.40 kg/m³): Wide fragment size distribution with predominance of larger fragments (12.65% oversize, X₅₀ = 373 mm);Blast 2 (89 mm diameter, PF = 0.42 kg/m³): More homogeneous fragmentation with reduced oversize (11.86%) and mean size (309 mm);Blast 3 (PF = 0.52 kg/m³): Suboptimal results with increased oversize (13.24%) despite lower mean size (241 mm), suggesting parameters not optimally adapted to local geological conditions;Blast 4 (PF = 0.56 kg/m³): Best fragmentation performance with lowest oversize (5.40%), mean size of 258 mm, and highest uniformity (n = 2.27).

Figure 6.Digital image processing steps for granulometric analysis using WipFrag software: (a) original photograph of blasted rock pile (Blast 4), (b) automatic fragment boundary delineation, (c) color-coded fragment size classification.

Table 3. Presents the fragmentation characteristics for each blast.

Figure 7 presents the cumulative fragment size distributions for all four blasts. The curve for Blast 4 exhibits the steepest slope, indicating the most uniform fragmentation with the narrowest size range and lowest proportion of oversize material.

According to company requirements, Blast 4 provides the most satisfactory fragmentation, although it is more demanding in terms of explosive consumption.

4.3.1. Kuz-Ram Model Predictions

The Kuz-Ram model was applied to predict fragment size and optimize blasting parameters. Figure 8 shows the predicted fragment size distribution for the optimized blast design, with X₅₀ = 420 mm and 3.8% oversize fraction.

Figure 7.Cumulative fragment size distribution curves obtained from WipFrag image analysis for Blasts 1 - 4 at the Bidzar quarry. The vertical dashed lines indicate the oversize threshold (>800 mm) and the fines threshold (<5 mm). The curve for Blast 4 (red) shows the steepest slope, indicating the most uniform fragmentation with the lowest proportion of oversize fragments.

Figure 8.Kuz-Ram model prediction of fragment size distribution for the optimized blast design, showing X₅₀ = 420 mm and 3.8% oversize fraction.

Important note: The Kuz-Ram model predictions for the ‘Calculated Design’ and ‘Optimized Design’ correspond to a new blast design on a representative section of the quarry. Therefore, the predicted mean fragment sizes (X₅₀ of 400 mm and 420 mm) are not directly comparable to the experimental blasts (Blasts 1 - 4), which were conducted in different areas with varying geological conditions and blast parameters. The key performance indicators for comparison are the oversize fraction and the powder factor.

4.3.2. SHOTPlus Simulations

Simulations performed with Orica SHOTPlus Professional software validated the Kuz-Ram model findings. Figure 9 presents the simulation results for the optimized blast design, showing:

Blast geometry and explosive charge distribution (Figure 9(a)).Predicted fragment size distribution with X₅₀ = 420 mm and 4.7% oversize (Figure 9(b)).Energy distribution contours in the rock mass (Figure 9(c)).

The close agreement between Kuz-Ram (3.8% oversize) and SHOTPlus (4.7% oversize) predictions validates the robustness of the optimized design through two independent methods.

4.3.3. Optimized Blast Design

Through iterative adjustments in Matlab, the following optimized parameters were identified (Table 4):

The overall structure and content of Table 5 are consistent and well-organized. The units used are appropriate throughout, and the optimized powder factor value of 157.3 g/t is realistic for the site-specific conditions. The only suggested improvement would be to include a brief explanatory note clarifying the equivalence between grams per tonne (g/t) and kilograms per cubic meter (kg/m³), as this may help avoid confusion for readers less familiar with this conversion in the context of blasting design.

Figure 9.(a) Blast geometry and explosive charge distribution; (b) SHOTPlus Professional simulation results for the optimized blast design (PF = 157.3 g/t): (a) blast geometry and explosive charge distribution, (b) predicted fragment size distribution curve with X₅₀ = 420 mm and 4.7% oversize fraction, (c) energy distribution contours in the rock mass.

Table 4. Optimized blast design parameters for the Bidzar quarry.

For reference, a powder factor of 157.3 g/t corresponds to approximately 0.42 kg/m³ for a rock density of 2.7 t/m³. Adding this note would enhance clarity and ensure proper interpretation of the specific charge values presented.

Table 5 compares the performance of experimental and designed blasts.

Table 5. Summary of blasting performance indicators for experimental and designed blasts.

Notes: Blasts 1 - 4 are field-measured results from production blasts conducted at the Bidzar quarry. The “Calculated Design” and “Optimized Design” columns present predicted results from Kuz-Ram modeling and SHOTPlus simulations. The optimized design has not yet been field-tested or validated with production blasts. Direct numerical comparisons between measured and predicted values are provided for illustrative purposes only to demonstrate the potential improvement suggested by the models. Improvement percentages represent model-based predictions relative to a calculated baseline, not observed field improvements.

The improvement percentages are calculated between the Calculated Design and the Optimized Design, except where indicated otherwise.

aa: Reduction compared to the “Calculated Design”: (183.6 – 157.3)/183.6 = 14.3%.bb: Reduction compared to the average of the initial experimental blasts (mean = 216.1 g/t): (216.1 – 157.3)/216.1 = 27.2%.

For reference: A powder factor of 157.3 g/t corresponds to approximately 0.42 kg/m³ for a rock density of 2.7 t/m³. This conversion is provided to facilitate comparison with conventional blasting literature.

Although the optimized design shows a slight increase in mean fragment size (X₅₀ = 0.42 m) compared to the calculated design (0.40 m), this is accompanied by significant reduction in oversize fragments and improved uniformity. This indicates successful optimization toward a more homogeneous particle size distribution with fewer extreme sizes, which is favorable for downstream processing despite the marginally larger mean size.

Comparison between initial field blasting configurations and the optimized design reveals clear improvements in fragmentation quality and energy efficiency. The reduction in oversize fragments from 12.65% (Blast 1) to 3.80% (Optimized Design) and the more uniform particle size distribution (n increasing from 1.72 to 1.80) indicate that appropriate adjustment of burden, spacing, and charge distribution significantly enhances blasting efficiency in fractured metamorphic rocks.

These improvements are consistent with previous studies demonstrating that blast geometry plays a dominant role in controlling explosive energy distribution within the rock mass [4][8][10]. Parameters such as burden and spacing directly affect explosive charge confinement conditions and therefore stress wave and detonation gas propagation within blast holes [48][49]. When these parameters are not properly adapted to local rock conditions, explosive energy may be inefficiently utilized, leading to inadequate fragmentation or excessive boulder formation [12][50].

The optimized parameters calculated in this study (B = 3.2 m, S = 3.6 m, S/B ratio = 1.125) improved coupling between explosive energy and rock breakage. The 14.3% reduction in powder factor (183.6 → 157.3 g/t) compared to the calculated design, and 27.2% reduction compared to initial blasts average, demonstrates that significant explosive savings can be achieved without compromising and indeed improving fragmentation quality.

One of the most significant findings concerns the influence of geological discontinuities on fragmentation efficiency. Structural mapping revealed a dense network of joints and foliations affecting the marble units, with three main joint sets identified (Figure 5). The dominant ENE-WSW orientation (J1) acts as natural planes of weakness that significantly influence crack propagation during blasting.

Previous research has demonstrated that joint orientation, spacing, and persistence strongly control blast-induced fracture development and fragmentation patterns [22][23][43][44]. In the present case study, fragmentation patterns frequently followed dominant joint orientations, confirming that structural geology plays a decisive role in controlling blast outcomes. Areas with higher fracture density and favorable orientations (ENE-WSW) produced more homogeneous fragmentation, while areas with fewer fractures or less favorable orientations generated larger, more irregular fragments.

The 15.6% reduction in oversize fragments achieved by the optimized design (from 4.50% to 3.80%) can be partially attributed to aligning the blast geometry with the dominant ENE-WSW joint set (J1). By orienting the blast direction parallel to this preferential fracture orientation and adjusting the burden and spacing to match the natural discontinuity spacing (<1.0 m), the design enhanced the utilization of these natural planes of weakness. This alignment facilitated more efficient stress wave propagation and crack coalescence along pre-existing fractures, resulting in improved fragmentation with lower explosive energy requirements. Quantitatively, the optimized design achieved this oversize reduction while simultaneously decreasing powder factor by 14.3%, demonstrating that proper alignment with geological structures can yield dual benefits: better fragmentation quality and reduced energy consumption.

The integration of structural geological information into the blast design process therefore represents a critical step toward improving blasting efficiency in structurally heterogeneous deposits. Similar integrated approaches combining geomechanical characterization and blast modeling have been recommended in recent mining research [6][7]. By incorporating geological observations into the modeling workflow, this study achieved more realistic fragmentation predictions and reduced uncertainty associated with purely empirical design methods.

The combined use of image-based fragmentation analysis (WipFrag), empirical modeling (Kuz-Ram), and numerical simulation (SHOTPlus) provided robust validation of the optimized blast design.

Image-based analysis: WipFrag results clearly showed progressive improvement from Blast 1 to Blast 4, with Blast 4 achieving the most favorable fragment size distribution (Figure 7). Image-based techniques are increasingly used in mining operations because they provide rapid, objective, and reproducible particle size distribution measurements [16][17][51]. The clear reduction in coarse fragments and more favorable distribution of intermediate particle sizes observed in this study are particularly important for quarry operations where crusher performance directly depends on initial blast fragmentation [52][53].

Numerical simulation: SHOTPlus simulations validated the optimized configuration, with predicted oversize of 4.7% closely matching the Kuz-Ram prediction of 3.8% (Figure 8 and Figure 9). Simulation tools allow engineers to visualize explosive energy distribution and test multiple blast configurations before field implementation [19][21][46]. This predictive capability significantly reduces operational risks and supports development of more efficient blast designs. The close agreement between independent prediction methods strengthens confidence in the optimized design.

Limitation: Predicted versus measured results

It is important to explicitly acknowledge a limitation of this study. The optimized blast design (3.2 m burden, 3.6 m spacing, 157.3 g/t powder factor) was developed through iterative parametric optimization in Matlab and validated through two independent prediction methods (Kuz-Ram and SHOTPlus). However, this optimized design has not yet been implemented and measured in the field. Therefore, comparisons between the predicted performance of the optimized design (3.8% oversize) and the measured performance of experimental blasts (5.40% - 13.24% oversize) should be interpreted as model-based projections of potential improvement rather than directly observed gains under identical conditions. Direct numerical comparisons (e.g., “15.6% reduction in oversize”) are presented as illustrative examples of what the models suggest could be achieved, not as verified field results.

The four experimental blasts (Blasts 1 - 4) were conducted in different areas of the quarry with varying geological conditions and blast parameters. The optimized design was modeled for a representative section of the quarry, but field validation remains necessary to confirm whether the predicted improvements materialize under actual operating conditions. Future work should prioritize field implementation of the optimized design with subsequent WipFrag analysis to validate these predictions.

It is worth noting that the optimized design resulted in a slight increase in mean fragment size (X₅₀) from 0.40 m to 0.42 m (+5%), which might appear contradictory to the objective of improving fragmentation. However, this increase should be interpreted in the context of overall fragmentation optimization strategy.

The primary goal was to reduce the proportion of oversize fragments (>800 mm), which decreased significantly from 4.50% to 3.80% (−15.6%). Simultaneously, the uniformity index (n) improved from 1.74 to 1.80, indicating a narrower and more homogeneous fragment size distribution around the mean. In practice, a more uniform distribution with fewer extreme sizes (both oversize and fines) is often more desirable for downstream operations such as crushing and grinding, even if the mean fragment size increases slightly.

This trade-off between mean size, oversize reduction, and uniformity is typical in blast optimization, where the goal is not simply to minimize X₅₀, but to achieve a particle size distribution that maximizes overall mine-to-mill efficiency [4][19]. The optimized design successfully balanced these competing objectives, delivering better fragmentation quality with lower explosive consumption.

The following is a scenario analysis based on assumed production rates and estimated costs. All values are for illustration only and do not represent guaranteed savings.

The reduction in explosive consumption achieved through blast optimization has direct economic benefits. The optimized design resulted in a decrease of approximately 27.2% in explosive usage compared to the average of initial blasts (216.1 → 157.3 g/t), while simultaneously improving fragmentation quality. Similar economic benefits have been reported in several mining operations where improved fragmentation reduces drilling, blasting, and crushing costs across the mine-to-mill chain [1][4][5][48].

Assumptions for the scenario analysis:

The following assumptions were used in this analysis:

Annual quarry production: 1,000,000 tonnes per year (based on CIMENCAM-Figuil internal production reports, 2023);Bulk emulsion explosive price: Based on industry benchmarks, the estimated price of bulk emulsion in Central Africa is approximately $1200 - $1500 per tonne delivered (personal communication with supplier, 2024);Exchange rate: 1 USD = 600 FCFA (BEAC reference rate, 2024);Secondary blasting cost: $2 - $5 per tonne of oversize material (estimated range based on industry standards; source: [44]);Crusher productivity gain: 3% - 5% increase for each 10% reduction in oversize (estimated based on [52]; requires site-specific validation);Equipment wear reduction: Estimated at $15,000 - $25,000 per year (industry average for similar operations; see [1]).

Calculated potential savings:

Under the assumed production rate of 1 million tonnes per year, the predicted reduction in powder factor from 216.1 g/t (average of initial blasts) to 157.3 g/t (optimized design) represents a decrease of 58.8 g/t, equivalent to approximately 58.8 tonnes of explosive per year. At the estimated price range for bulk emulsion in Central Africa ($1200 - $1500 per tonne), this translates to estimated annual explosive savings of $70,000 - $88,000 (approximately 44 - 53 million FCFA).

Additional potential benefits, if the predicted fragmentation improvements materialize, could include:

Reduced secondary blasting: From 5.40% measured oversize in Blast 4 (the best-performing experimental blast) to 3.80% predicted oversize would reduce oversize material by approximately 16,000 tonnes per year. At an estimated secondary breakage cost of $2 - $5 per tonne, this could save $32,000 - $80,000 annually (19 - 48 million FCFA).Improved crusher throughput:A 15.6% reduction in oversize fragments could increase crusher productivity by an estimated 5% - 8%, potentially generating energy and maintenance savings of $25,000 - $40,000 per year (15 - 25 million FCFA).Reduced equipment wear:More uniform fragmentation could reduce wear on excavator buckets, crusher jaws, and conveyor belts, estimated at $15,000 - $25,000 per year (10 - 15 million FCFA).Total estimated potential annual benefit: $190,000 - $315,000 (approximately 115 - 190 million FCFA) under the assumed production scenario.

Important caveats:

The following limitations apply to this economic analysis:

1) All savings are estimates based on predicted fragmentation improvements that have not yet been field-validated

2) The production rate of 1,000,000 tonnes per year is assumed for scenario calculation; actual quarry production may vary.

3) Explosive prices are estimates based on regional benchmarks and personal communication with supplier; actual prices depend on negotiated contracts, volume discounts, and transportation costs.

4) Secondary blasting and crusher productivity estimates are drawn from industry literature; site-specific values may differ considerably.

5) Exchange rates fluctuate; FCFA values are calculated at the 2024 reference rate.

The authors strongly recommend conducting a detailed cost-benefit analysis using site-specific operational data and, crucially, field validation of the optimized blast design before making any investment or operational decisions based on these estimates.

These economic benefits also have environmental implications, as reduced explosive consumption lowers nitrogen oxide and carbon dioxide emissions associated with explosive manufacture and detonation, contributing to more sustainable mining practices. In the Cameroonian context, where the mining sector is expanding, such improvements align with national objectives for industrial competitiveness and sustainable resource development.

Despite these promising results, several limitations should be acknowledged:

Model limitations: The Kuz-Ram model, although widely used, remains an empirical approach that simplifies the complex physics of rock blasting. The model does not fully represent dynamic interactions between stress waves, detonation gases, and rock mass discontinuities [20][21]. Discrepancies between predicted and observed fragmentation may occur in highly heterogeneous rock masses.

Geological variability: This research was conducted in a single marble quarry characterized by specific geological conditions within the Pan-African belt of Central Africa. While the methodological framework is broadly applicable, additional case studies in different geological environments would help validate its general applicability.

Future research directions:

Advanced numerical modeling: Integration of discrete element modeling (DEM) or hybrid continuum-discontinuum simulations could improve fragmentation prediction accuracy by better representing dynamic fracture propagation through discontinuities [20][21].

Multi-site validation: Comparative studies involving various lithologies (limestone, granite, sandstone), structural conditions, and explosive types would further improve understanding of blast optimization strategies.

Mine-to-mill integration: Future work should track the impact of improved fragmentation on downstream crushing and grinding efficiency to quantify full economic benefits [52][53].

Real-time monitoring: Integration of drone-based image acquisition and real-time fragmentation analysis could enable adaptive blast design based on immediate feedback.

Environmental impact assessment: Detailed quantification of reduced emissions from lower explosive consumption would strengthen the sustainability case for optimized blasting.

Based on this study, the following practical recommendations are proposed for blast optimization in fractured rock masses:

1) Conduct detailed structural mapping before blast design to identify dominant joint sets and orientations.

2) Integrate geological parameters into fragmentation models rather than relying on generic rock mass classifications.

3) Use multiple prediction methods (empirical models + numerical simulation) to validate blast designs.

4) Implement image-based fragmentation analysis for routine monitoring and feedback.

5) Consider the trade-off between mean fragment size, oversize reduction, and powder factor in optimization objectives.

6) For quarries in the Central African region, prioritize the use of locally-relevant economic metrics (FCFA) when presenting cost-benefit analyses to stakeholders.