OPTIMIZATION OF STOPE DIMENSIONS IN A GEOTECHNICALLY COMPLEX MINE USING AUTOMATED STABILITY ANALYSIS

2.1. Modified Stability Number

The stability analysis method utilized in this study is based on the modified stability number (N') introduced by Potvin (1988), which builds based on the stability number developed by Mathews et al. (1980). This original stability number is derived by adjusting the Q' value to account for factors such as induced stresses, the orientation of geological discontinuities, and the angle of the stope wall. The modified stability number, N', is calculated using Equation 1.

[TeX:] N^{'} = Q' \times A \times B \times C$N^{\prime }=Q\prime \times A\times B\times C$ (1)

The rock stress factor (A) represents the strength of rock and the stress around the stope excavation. The joint orientation factor (B) assesses how the orientation of the primary joint set relates to the excavation surface, and the gravity adjustment factor (C) represents the influence of gravity on the stope wall stability. The values of these factors can be obtained using the chart shown in Figure 1.

Figure 1. Factors A, B, and C by Potvin (1988)

An empirical approach is utilized to evaluate the stability or potential failure of stopes, wherein the hydraulic radius is correlated with the modified stability number (N'). This method is based on an extensive compilation of case histories originally developed by Mathews et al. (1980) and later refined by Potvin (1988). The relationship is graphically represented in Figure 2, which categorizes stope conditions into three zones: stable, transition, and collapse. By plotting the N' value against the hydraulic radius, the chart provides a practical framework for assessing stope stability. This enables engineers to determine safe design dimensions for stope excavation.

Figure 2. Modified stability graph by Potvin (1988)

2.2. Digitizing Graph Data

The linear approximation method will be used in this research to reconstruct several graphs from Potvin (1988) into mathematical functions. Most graphs were piecewise linear functions, making linear interpolation particularly suitable for accurately reproducing the trends without introducing artificial curvature. This method was chosen because the original datasets were only available as graphical plots, and linear interpolation offers simplicity, robustness, and low computational cost compared with higher-order polynomial or spline method, which can overfit local noise or produce unrealistic oscillations (Press et al., 2007). A sufficient number of points were sampled from each graph to ensure fidelity, and functions were constructed using Equation 2 (Salomon, 2006). To determine the value of [TeX:] f(x)$f\left(x\right)$ using the interpolation method, find [TeX:] i$i$ such that [TeX:] x_{i} \leq x \leq x_{i + 1}$x_i\le x\le x_{i+1}$, then interpolate the value using Equation 2.

[TeX:] f(x) = f_{i} + \frac{x - x_{i}}{x_{i + 1} - x_{i}}(f_{i + 1} - f_{i})$f\left(x\right)=f_i+\frac{x-x_i}{x_{i+1}-x_i}(f_{i+1}-f_i)$ (2)

The accuracy of the digitization was evaluated using the Mean Absolute Error (MAE) for each function, summarized in Table 2. MAE values were below 0.5% in all cases, confirming that the reconstructed functions reliably represent the original graphs and are suitable for subsequent analysis. To further increase the accuracy of this method, additional sampling points can be incorporated, particularly in regions where the function changes rapidly (Salomon, 2006). Minor deviations may still occur due to image resolution or scaling effects.

Table 2. Number of Sampled Point and Mean Absolute Error (MAE)

3.1. Stope Shape Determination

Iterations will be conducted to determine the optimum stope shape. The objective of this optimization is to make the stope with the longest possible length, as described in Equation 3.

[TeX:] Objective\ function\ :\ Max\left( L_{s} \right)$Objectivefunction:Max\left(L_s\right)$ (3)

Stope length is constrained by the stability of the stope, as a longer stope is more prone to instability. So, the optimum stope length must be verified as stable through a stability analysis, as described in Equation 4. The stope shape parameters, denoted as [TeX:] Shp_{s}$Sh{p}_s$ comprise a numerical list representing the geometric and geotechnical attributes of the stope wall. The function [TeX:] f_{sta}$f_{sta}$ serves as a binomial indicator of stope stability classification, where [TeX:] f_{sta} = 1$f_{sta}=1$ signifies the stope shape parameters resulted in stable stope, and [TeX:] f_{sta} = 0$f_{sta}=0$ mean stope shape parameters resulted in unstable stope. As previously outlined, the principal constraint in the optimization process is stope stability, necessitating that the resulting stope configuration satisfies [TeX:] f_{sta}(shp_{s}) = 1$f_{sta}\left(sh{p}_s\right)=1$. Details about the stability analysis will be discussed in Section 3.2.

[TeX:] Constrain\ :f_{sta}(shp_{s}) = 1$Constrain:f_{sta}\left(sh{p}_s\right)=1$ (4)

Based on the objective function and constraints, the pseudocode for the iteration is described in Algorithm 1. In the present algorithm, stability analysis is performed at each iteration to rigorously assess stope configurations. The computational complexity of this algorithm is O(N), where N represents the total number of stope slices, indicating a direct relationship between the process count and the number of slices evaluated. This systematic approach provides a robust framework for optimizing stope geometry while upholding structural stability throughout the evaluation process.

The proposed algorithm can be classified as a heuristic, constructive iterative algorithm designed to optimize stope geometry under explicit stability constraints. It operates by progressively merging stope slices and performing stability checks at each step, halting expansion once instability is detected. This rule-based process emphasizes computational efficiency and practical feasibility rather than exhaustive exploration of all possible configurations and therefore does not guarantee a globally optimal solution. Instead, it produces a locally optimal configuration that is inherently dependent on the sequence in which slices are evaluated. Due to the absence of backtracking, enumeration, or global search strategies, the algorithm is best described as greedy-like and heuristic, making it particularly suitable for practical applications in large scale mining scenarios where speed, simplicity, and reliable stability verification are prioritized over theoretical global optimality.

3.2. Stability Evaluation

Based on the generated stope shape [TeX:] (Shp_{s}$(Sh{p}_s$), several parameters will be generated to evaluate the stability of the stope. To determine these parameters, the outline of each stope wall will be generated to determine wall orientation, perimeter, and area. To define the representative rock mass properties for each stope wall, an n-meter boundary extension from the stope wall was applied, corresponding to the expected overbreak depth. Since the resulting stope is expected to be stable, the overbreak is anticipated to be less than 3 m (classified as large overbreak) based on McFadyen et al. (2024). Therefore, the default value of n will be set to 3 m. This value remains consistent with the case study used in this research, considering the influence of stope geometry, stress conditions, and rock mass quality (Cepuritis et al., 2007; Villaescusa, 2014).

Subsequently, using the modelled stress of the stope, the wall orientation, and the rock mass properties of the stope wall, the N' value for each slice wall will be determined. This value is then used to evaluate the stability of each stope wall. The algorithm’s general workflow is presented in the Figure 5, and the details of the stability evaluation will be discussed in this section.

Figure 5. Stope shape stability workflow

As mentioned before, the stability of the stope is the function of several parameters, as described in Equation 5.

[TeX:] sta_{s} = f_{sta}(shp_{s}) = f_{sta}({Wo}_{s}^{w},{Wp}_{s}^{w},{Wa}_{s}^{w},\ Q_{s}^{w},\ UCS_{s}^{w},\ Si_{s}^{w},\ Dd_{s}^{w})$st{a}_s=f_{sta}\left(sh{p}_s\right)=f_{sta}({Wo}_s^w,{Wp}_s^w,{Wa}_s^w,Q_s^w,UC{S}_s^w,S{i}_s^w,D{d}_s^w)$ (5)

[TeX:] {Wo}_{s}^{w},{Wp}_{s}^{w},{Wa}_{s}^{w}${Wo}_s^w,{Wp}_s^w,{Wa}_s^w$ are the geometrical parameters of the stope wall and the other parameter is the geotechnical parameters of the stope wall. The geotechnical parameters were generated from the block models and stress models using Equations 6-9.

[TeX:] Q_{s}^{w} = \frac{\sum_{}^{}{Q_{r} \times tr{\times m}_{r}^{w}}}{\sum_{}^{}{tr{\times m}_{r}^{w}}}$Q_s^w=\frac{{\sum }_{}^{}{Q}_r\times tr{\times m}_r^w}{{\sum }_{}^{}tr{\times m}_r^w}$ (6)

[TeX:] {UCS}_{s}^{w} = \frac{\sum_{}^{}{{UCS}_{r} \times tr{\times m}_{r}^{w}}}{\sum_{}^{}{tr{\times m}_{r}^{w}}}${UCS}_s^w=\frac{{\sum }_{}^{}{UCS}_r\times tr{\times m}_r^w}{{\sum }_{}^{}tr{\times m}_r^w}$ (7)

[TeX:] {Si}_{s}^{w} = \frac{\sum_{}^{}{{Si}_{r} \times tr{\times m}_{r}^{w}}}{\sum_{}^{}{tr{\times m}_{r}^{w}}}${Si}_s^w=\frac{{\sum }_{}^{}{Si}_r\times tr{\times m}_r^w}{{\sum }_{}^{}tr{\times m}_r^w}$ (8)

[TeX:] \mathbf{D}\mathbf{d}_{\mathbf{s}}^{\mathbf{w}} = \left\{ \ a\ \in \ \mathbf{Dd}_{\mathbf{r}}^{\mathbf{w}}\mid\ \frac{\sum_{\mathbf{Dd}_{\mathbf{r}}^{\mathbf{w}} = a}^{}{tr{\times m}_{r}^{w}}}{\sum_{}^{}{tr{\times m}_{r}^{w}}} > 0.1\ \right\}$𝐃{𝐝}_{𝐬}^{𝐰}=\{a\in {𝐃𝐝}_{𝐫}^{𝐰}\mid \frac{{\sum }_{{𝐃𝐝}_{𝐫}^{𝐰}=a}^{}tr{\times m}_r^w}{{\sum }_{}^{}tr{\times m}_r^w}>0.1\}$ (9)

Given that [TeX:] f_{N}(HR)$f_N\left(HR\right)$ is the function of stable boundary of minimum [TeX:] N'$N\prime$ value for each [TeX:] HR$HR$ from Potvin (1988) digitized graph. So, the stope wall stability can be determined using Equations 10-12.

[TeX:] N_{s}^{w} = Q_{s}^{w} \times A_{s}^{w} \times B_{s}^{w} \times C_{s}^{w}$N_s^w=Q_s^w\times A_s^w\times B_s^w\times C_s^w$ (10)

[TeX:] HR_{s}^{w} = \frac{{Wa}_{s}^{w}}{{Wp}_{s}^{w}}$H{R}_s^w=\frac{{Wa}_s^w}{{Wp}_s^w}$ (11)

[TeX:] sta_{s}^{w} = \left\{ \begin{array}{r} 1,\ \ N_{s}^{w} \geq f_{N}(HR_{s}^{w})\ \ \\ 0,\ \ N_{s}^{w} < f_{N}(HR_{s}^{w})\ \ \ \end{array} \right.\ $st{a}_s^w=\{\begin{array}{c}\hfill 1,N_s^w\ge f_N\left(H{R}_s^w\right)\\ \hfill 0,N_s^w<f_N\left(H{R}_s^w\right)\end{array}$ (12)

Equation 13 is then used to assess the stability of the stope.

[TeX:] sta_{s} = \left\{ \begin{array}{r} sta_{s}^{0}\ \times \ sta_{s}^{1} \times \ sta_{s}^{2} \times \ sta_{s}^{3} \times \ sta_{s}^{4},\ \ j = 1\ and\ x = 1 \\ sta_{s}^{1} \times \ sta_{s}^{2} \times \ sta_{s}^{3} \times \ sta_{s}^{4},\ \ j > 1\ and\ x = 1\ \ \ \ \ \\ sta_{s}^{0}\ \times \ sta_{s}^{1} \times \ sta_{s}^{2},\ \ j = 1\ and\ x = 2 \\ \ sta_{s}^{1} \times \ sta_{s}^{2},\ \ j > 1\ and\ x = 2 \end{array} \right.\ $st{a}_s=\{\begin{array}{c}\hfill st{a}_s^0\times st{a}_s^1\times st{a}_s^2\times st{a}_s^3\times st{a}_s^4,j=1andx=1\\ \hfill st{a}_s^1\times st{a}_s^2\times st{a}_s^3\times st{a}_s^4,j>1andx=1\\ \hfill st{a}_s^0\times st{a}_s^1\times st{a}_s^2,j=1andx=2\\ \hfill st{a}_s^1\times st{a}_s^2,j>1andx=2\end{array}$ (13)

3.3. Factor A determination

Given that [TeX:] f_{A}\left( UCS/\sigma_{\max} \right)$f_A\left(UCS/{\sigma }_{max}\right)$ is the function of Rock Stress factor from Potvin (1988) digitized graph, so the Factor A can be determined using Equation 14.

[TeX:] A_{s}^{w} = f_{A}\left( \frac{UCS_{s}^{w}}{{Si}_{s}^{w}} \right)$A_s^w=f_A\left(\frac{UC{S}_s^w}{{Si}_s^w}\right)$ (14)

3.4. Factor B determination

Given that:

So, Factor B can be determined using Equations 15-16.

[TeX:] \alpha_{s,\ jo}^{w} = \cos^{- 1}\left( \frac{\mathbf{Wo}_{s}^{w} \cdot \mathbf{D}\mathbf{d}_{s,jo}^{w}}{\parallel \mathbf{Wo}_{s}^{w} \parallel \parallel \mathbf{D}\mathbf{d}_{s,jo}^{w} \parallel} \right)${\alpha }_{s,jo}^w={cos}^{-1}\left(\frac{{𝐖𝐨}_s^w\cdot 𝐃{𝐝}_{s,jo}^w}{\parallel {𝐖𝐨}_s^w\parallel \parallel 𝐃{𝐝}_{s,jo}^w\parallel }\right)$ (15)

[TeX:] B_{s}^{w} = \min\left( f_{B}\left( \alpha_{s,\ jo}^{w} \right)\ \forall\ jo \in \{ 0,1,2,3,\ldots\}\ \right)\ $B_s^w=min(f_B\left({\alpha }_{s,jo}^w\right)\forall jo\in \{0,1,2,3,\dots \})$ (16)

3.5. Factor C determination

Given that:

So, Factor C can be determined using Equations 17-22.

[TeX:] f_{Cs}(\alpha)\ = 8 - 7 \times cos(\alpha)$f_{Cs}\left(\alpha \right)=8-7\times cos\left(\alpha \right)$ (17)

[TeX:] {\alpha s}_{s}^{w} = \cos^{- 1}\left( \frac{\mathbf{Wo}_{s}^{w} \cdot \mathbf{Vo}}{\parallel \mathbf{Wo}_{s}^{w} \parallel \parallel \mathbf{Vo} \parallel} \right)${\alpha s}_s^w={cos}^{-1}\left(\frac{{𝐖𝐨}_s^w\cdot 𝐕𝐨}{\parallel {𝐖𝐨}_s^w\parallel \parallel 𝐕𝐨\parallel }\right)$ (18)

[TeX:] {\alpha j}_{s,\ jo}^{w} = \cos^{- 1}\left( \frac{\mathbf{Vo} \cdot \mathbf{D}\mathbf{d}_{s,jo}^{w}}{\parallel \mathbf{Vo} \parallel \parallel \mathbf{D}\mathbf{d}_{s,jo}^{w} \parallel} \right)${\alpha j}_{s,jo}^w={cos}^{-1}\left(\frac{𝐕𝐨\cdot 𝐃{𝐝}_{s,jo}^w}{\parallel 𝐕𝐨\parallel \parallel 𝐃{𝐝}_{s,jo}^w\parallel }\right)$ (19)

[TeX:] {Cs}_{s}^{w} = f_{Cs}\left( {\alpha s}_{s}^{w} \right)${Cs}_s^w=f_{Cs}\left({\alpha s}_s^w\right)$ (20)

[TeX:] {Cj}_{s}^{w} = \min\left( f_{Cj}\left( {\alpha j}_{s,\ jo}^{w} \right)\ \ \forall\ jo \in \{ 0,1,2,3,\ldots\},\ \ \alpha_{s,\ jo}^{w} < 30^{0} \right)${Cj}_s^w=min(f_{Cj}\left({\alpha j}_{s,jo}^w\right)\forall jo\in \{0,1,2,3,\dots \},{\alpha }_{s,jo}^w<{30}^0)$ (21)

[TeX:] C_{s}^{w} = Q\min\left( \{{Cs}_{s}^{w},{Cj}_{s}^{w}\} \right)$C_s^w=Qmin(\{{Cs}_s^w,{Cj}_s^w\})$ (22)

4.1. Geotechnical Data

This research utilizes a case study from a copper mine to demonstrate the proposed method. This case study was chosen because it highlights the importance of optimizing stope dimensions in areas where high productivity is required despite relatively poor ground conditions. Several geotechnical parameters were simplified and stored in the block model. The maximum dimensions of a regular block model are 10m × 10m, with parameter values estimated from drill hole data and laboratory test results. The geotechnical parameters considered in this study include:

The major joint orientation parameters are represented as integers that correspond to specific joint set codes. For example, joint set 1 represents a joint set with an orientation of 220°/45° NE. Figure 6 illustrates the section view of the block model.

Figure 6. Block model of geotechnical data

The copper deposit is hosted within a vein geotechnical domain, with 15 to 80 meters of apparent thickness. The vein generally trends about N 50° E and dips between 60° and 80°. The footwall belongs to a marble geotechnical domain, while the hanging wall consists of a diorite geotechnical domain.

The planned stopes are distributed across five levels, with 20 meters of vertical spacing between each level. The surface elevation is approximately 595 meters above sea level, placing the depths of the stope between 395 meters and 295 meters of elevation.

The geotechnical condition is relatively complex, with high variability in rock mass strength as summarized in Table 4. This variability results in significant differences in stope stability conditions, leading to a wide range of optimal stope dimensions.

Table 4. Summary of the rock mass properties

4.2. Mining Method and Stope Sequence

The mining method used in this study is transverse longhole stoping with a primary and secondary stope sequence. This method is typically applied to ore bodies that are tabular and either vertical or steeply dipping. It is most effective when both the ore and the surrounding waste rock have fair to good rock quality (SME, 2011).

In this method, the stope design consists of two types of stopes: primary stopes and secondary stopes. The primary stopes are mined first and then backfilled with cemented backfill, serving as pillars when the secondary stopes are later mined, as presented in the Figure 7. Different sizes of primary and secondary stopes are applied in this study, and their dimensions are presented in Table 5.

Table 5. Stope dimension

Figure 7: Mining method

This method was selected because the ore body thickness exceeds 60 meters, necessitating an efficient, large-scale mining approach. A partial backfill stope approach is implemented in certain areas where the ore body is too thick to be mined in a single stope sequence. In these cases, the stope is divided into multiple sections, and each section must be backfilled before mining the next section.

The stope sequence follows an overhand stoping sequence, meaning that a stope can only be mined once the stope below it has already been mined and backfilled. Additionally, a primary-secondary stoping dependency is enforced, where a secondary stope can only be mined after the primary stopes in the three levels above have been mined and backfilled. The stope sequence used in this case study is illustrated in Figure 8. The sequence is divided into nine phases, with each phase required to be mined in the specified order.

Figure 8. Stopping sequence

4.3. Stress Model Result

To capture the stress changes during the stope extraction and backfilling process, stress modelling was performed using FLAC3D. The analysis was based on the representative properties of the rock mass and backfill materials. The material properties applied in the stress modelling are summarized in Table 6.

Table 6. Material properties of the model

The modelling was performed in eight phases, following the stope mining and backfilling sequence. The maximum and minimum principal stress on each stope wall was then queried. These stress values were subsequently used to represent the stress component in the N' stability number analysis. An example of stress results from several phases is shown in Figure 9.

Figure 9. Stress model result

4.4. Stope Final Result

The analysis shows that the optimized stope design produced a total of 83 individual stopes, consisting of 51 secondary stopes and 32 primary stopes, shown in Figure 10. The stability analysis results show that all walls of each stope were in a stable condition. Several stope walls also reached their critical hydraulic radius.

Figure 10. Final stope geometry (left) and Stability analysis (Right)

The computation of the stope final results required approximately 32 minutes for the algorithm to complete the entire process, corresponding to an average of 3.1 seconds per stope slice. This computation time is deemed feasible for implementation in larger and more complex mining scenarios. The analysis was conducted on a personal computer equipped with an AMD Ryzen 9 270 (8-core) processor, an NVIDIA GeForce RTX 5080 GPU, and 16 GB of GDDR7 memory. Notably, the algorithm’s running time may vary depending on the mine’s complexity, the number of generated stope slices, and the device specifications.

5.1. Stope Dimension Sensitivity Analysis

As described in Section 4.1, the geotechnical conditions are relatively complex, with high variability in rock mass strength. This variability leads to significant differences in stope stability, resulting in a wide range of optimal stope dimensions. To investigate the relationship between rock mass variability and stope geometry, a sensitivity analysis is presented in this section.

The sensitivity analysis was conducted using the calculated N' values for each stope wall orientation, as shown in Figure 11. The results indicate that N' values ranged from 0.5 to 90, reflecting the wide variability in potential stope dimensions. Figure 11 further presents the percentage of samples that resulted in unstable stopes at different stope lengths. The analysis shows that stope lengths should be limited to less than 8 m to ensure that 90% of stopes remain stable. Applying a uniform stope length across all stopes would lead to higher costs and reduced production efficiency. These findings highlight the necessity of further optimization that accounts for the spatial distribution of rock mass strength, allowing stope lengths to vary according to local geotechnical conditions.

Figure 11. N' Values Distribution (left) and Percentage of Stabel Stope (right)

5.2. Stope Geometry Analysis

Based on the Figure 12, the majority of the secondary stopes have reached their maximum dimension at the back. Meanwhile, for the primary stopes, most have reached their maximum dimension due to the mined boundary. The results also show that no stope has reached its maximum dimension at the hanging wall or footwall.

Figure 12. Critical wall of stope

Figure 13 shows that several stopes (13% of the total volume) have a total length of less than 10 meters. Based on this result, further analysis can be conducted to evaluate the economic feasibility of these short stopes. Mining small stopes can be uneconomical due to increased mining costs (Samanta et al., 2024).

Figure 13. Distribution of Stope length

5.3. Result Comparison

To further evaluate the effectiveness of the proposed optimization approach, a series of simulations were conducted in comparison with conventional stope design methods. These simulations incorporated varying stope length scenarios as dictated by standard design practices. The outcomes of this comparative analysis are summarized in Table 7, which details the performance metrics of both the conventional and optimization-based methodologies.

Table 7. Stope stability result

The results show that the new method produces a more stable stope geometry while requiring fewer stopes. In contrast, the conventional methods, which applies a uniform stope length, results in either a more number of stopes or the presence of unstable stopes. The distribution of the unstable stopes is shown in Figure 14. Figure 15 shows that most unstable face walls in regular stope scenarios occur at the back and endwall. In contrast, stopes designed using the optimization method have more adaptable HR based on the N' value, enhancing stope stability.

Figure 14. Distribution of Unstable Stopes

Figure 15. Stope stability analysis

Stope instability frequently leads to overbreak of stope walls (Villaescusa, 2014), resulting in higher mining costs due to increased ore dilution. Consequently, unstable stopes are typically associated with greater dilution percentages. The empirical relationship between the hydraulic radius (HR), the modified stability number (N'), and the anticipated stope dilution is presented in Equation 23 (Roux, 2017).

[TeX:] Stope\ dilution = \left\{ \begin{array}{r} 0.6305\ln(HR) - 0.9575\ ,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ N^{'} < 4 \\ 0.5090\ln(HR) - 0.8596\ ,\ \ \ \ 4 \leq \ N^{'} < 11 \\ 0.4144\ln(HR) - 0.4673\ ,\ \ 11 \leq \ N^{'} < 21 \\ 0.6357\ln(HR) - 1.1934\ ,\ \ \ \ \ \ \ \ \ \ \ \ \ \ N^{'} \geq 21 \end{array} \right.\ $Stopedilution=\{\begin{array}{c}\hfill 0.6305ln\left(HR\right)-0.9575,N^{\prime }<4\\ \hfill 0.5090ln\left(HR\right)-0.8596,4\le N^{\prime }<11\\ \hfill 0.4144ln\left(HR\right)-0.4673,11\le N^{\prime }<21\\ \hfill 0.6357ln\left(HR\right)-1.1934,N^{\prime }\ge 21\end{array}$ (23)

Although longer stopes are generally more susceptible to instability and increased dilution, their use can significantly reduce overall stoping costs and streamline the mining sequence. By employing longer stopes, the total number of individual stopes is minimized, which in turn lowers the requirements for slot raises and filling barricade constructions. This approach not only optimizes operational efficiency but also leads to more cost-effective production. The cost parameters utilized to compare the conventional and optimization methods are presented in Table 8, providing a comprehensive assessment of total stope production costs for each approach.

Table 8. Stope cost parameters

Empirical dilution, as presented in Equation 23 and supported by the cost parameters in Table 8, was utilized to calculate the expected total stope production cost for both conventional and optimization methods. Table 9 offers a direct comparison of ore tonnage, dilution tonnage, and total stope production costs between these approaches. The results indicate that smaller stopes with a regular length of 10 meters more effectively control dilution compared to other stope dimensions, albeit at the expense of an increased number of separate stopes. Conversely, stopes configured with a 20-meter regular length exhibit the highest percentage of expected dilution, yet result in the smallest number of stopes overall. Notably, stopes produced through the optimization method demonstrate a balanced outcome in terms of dilution percentage and number of stopes. The optimized stope shapes yield the lowest total production cost, with a reduction of approximately 1.6 to 2.4 million dollars relative to the conventional method. This finding supports the conclusion that the optimization method produces more cost-efficient stope configurations.

Table 9. Stope dilution and production cost result

Stope production cost calculations, as reflected in Table 9, primarily account for production aspects; however, they often overlook the broader implications arising from unstable stopes. In practice, stope collapse can lead to increased expenses due to necessary rehabilitation, loss of ore reserves, and potential delays in production. Furthermore, the safety risks associated with such collapses are considerable, as they may result in equipment damage or, in extreme cases, serious injury and even fatalities. These consequences underscore the critical importance of ensuring stope stability, a goal that can be effectively achieved through optimization method. Indeed, the application of optimized stope design not only mitigates geotechnical and safety risks but may also deliver greater economic benefits than those indicated solely by the value presented in Table 9.