Advancing mine pillar design: Evaluating traditional methods and integrating AI for enhanced stability of pillars in the Great Dyke, Zimbabwe-深地科学

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Advancing mine pillar design: Evaluating traditional methods and integrating AI for enhanced stability of pillars in the Great Dyke, Zimbabwe

Abstract

Mine pillar design plays a crucial role in ensuring the stability and safety of underground mining operations, particularly in geologically and geotechnically complex settings like the Great Dyke of Zimbabwe. Traditional pillar stress determination methods, such as the tributary area method (TAM) and Coates’ method, have been widely applied in room and pillar mining. However, these approaches rely on simplifying assumptions—such as uniform load distribution, independent pillar behavior, and elastic deformation—which may not accurately capture the heterogeneous and anisotropic geotechnical conditions of the Great Dyke. This study critically revisits these methods, evaluating their limitations and proposing advanced alternatives for a more robust pillar design. The study observes that TAM oversimplifies stress distribution, leading to potential underestimations of stress concentrations in irregular pillar geometries and varying rockmass conditions. While Coates’ method improves on TAM by incorporating geometric parameters, it fails to account for overburden stiffness, seam interactions, and mining-induced stress redistribution. The study highlights the necessity of integrating real-time monitoring systems, site-specific numerical model calibration, and AI-driven predictive frameworks to improve pillar design reliability. The study enhances the understanding of stress redistribution, time-dependent failure mechanisms, and geological discontinuities that significantly impact pillar stability by critically reflecting on these computational approaches. It contributes to a deeper understanding of pillar stress determination on the Great Dyke, contributing to safer and more efficient mining operations. The study recommends a hybrid approach that merges traditional empirical techniques with advanced numerical modeling and machine learning, ensuring resilience against complex geological challenges while optimizing resource extraction and minimizing failure risks.

Highlights

This study assesses the limitations of the tributary area method and Coates’ method in accurately estimating pillar stress under complex geotechnical conditions.
This study identifies oversimplifications in TAM and Coates’ method, including assumptions of uniform load distribution and neglect of mining-induced stress redistribution.
This study emphasizes the need for numerical model calibration and real-time monitoring to account for heterogeneous and anisotropic conditions in the Great Dyke.
This study proposes integrating AI-driven predictive frameworks and hybrid modeling approaches to enhance pillar design reliability.
This study highlights the significance of stress redistribution, time-dependent failure mechanisms, and geological discontinuities in pillar design.
This study advocates combining empirical, numerical, and AI-based methods to optimize resource extraction while minimizing failure risks.

1 INTRODUCTION

Mining operations rely heavily on the stability of rock structures. One critical aspect is the design of pillars, which support the underground workings. Incorrect design can lead to catastrophic failures, endangering lives and equipment (Mark & Gauna, 2017; Zvarivadza & Van der Merwe, 2017; Chinyowa & Zvarivadza, 2015). Pillar design is a key component in the stability of underground mines. Properly designed pillars ensure the safety and efficiency of mining operations. This is particularly important in hardrock mining environments, where the mechanical properties of the rock are highly variable. The Great Dyke is a unique geological feature in Zimbabwe, rich in minerals such as platinum and chromite. It is of great economic significance to Zimbabwe and the world, as it hosts platinum resources, which make Zimbabwe the world's number 3 supplier of platinum (World Population Review, 2024). The platinum-bearing complexes of the Great Dyke are presented in Figure 1.

Details are in the caption following the image — Figure 1
Open in figure viewer PowerPoint

Platinum-bearing complexes of the Great Dyke (Siachingoma et al., 2023).

Its challenging geotechnical conditions present unique challenges for mining operations, making pillar design even more critical. The main objective of this study is to re-evaluate the tributary area method (TAM) and Coates’ method in the context of robust pillar design on the Great Dyke of Zimbabwe. The Great Dyke is characterized by complex geological and geotechnical conditions, as illustrated in Tables 1 and 2 and Figures 2 and 3, necessitating pillar design and pillar stress prediction methods uniquely tailored for these special conditions.

Table 1. Rockmass rating of different locations of a Great Dyke platinum deposit at different locations (Chikande & Zvarivadza, 2016a).

Location	UCS (MPa) rating	RQD rating	Spacing of discontinuity (mm) rating	Conditions of discontinuity (mm) rating	Groundwater rating	Adjustment for orientation rating	RMR	Calculated RMR from Q
66nbg	53	88	100	1–5	Completely dry	Unfavorable	47	44
66nbg	7	17	8	10	15	−10	47	44
65nbg	53	89	52	1–5	Completely dry	Unfavorable	44	43
65nbg	7	17	5	10	15	−10	44	43
64nbg	53	91	48	1–5	Completely dry	Unfavorable	44	40
64nbg	7	17	5	10	15	−10	44	40
64ntg	53	85	98	1–5	Completely dry	Unfavorable	47	37
64ntg	7	17	8	10	15	−10	47	37
63nbg	53	77	79	1–5	Completely dry	Unfavorable	47	45
63nbg	7	17	8	10	15	−10	47	45
63ntg	53	74	100	1–5	Completely dry	Unfavorable	43	40
63ntg	7	13	8	10	15	−10	43	40
62nbg	53	71	100	1–5	Completely dry	Unfavorable	41	40
62nbg	7	11	8	10	15	−10	41	40
62ntg	53	78	89	1–5	Completely dry	Unfavorable	47	48
62ntg	7	17	8	10	15	−10	47	48
61nbg	53	82	200	1–5	Completely dry	Unfavorable	49	52
61nbg	7	17	10	10	15	−10	49	52

Abbreviations: RMR, rock mass rating; RQD, rock quality designation; UCS, uniaxial compressive strength.

Table 2. Example geotechnical log from a database of geotechnical logs showing some of the major structures in the Selukwe Complex of the Great Dyke.

Distance or interval (m)		Structure type		Typical orientation	Brittle structure properties			Water staining	Description
From	To	Code	Class	Alpha	Micro-scale geometry	Infill	Alteration	Water staining	Description
110.32	110.51	J	2	15	8	SP	1	√	1OCJ, faulted with displacement, RIR
110.51	111.42	J	2	15	_	SP	1	√	1OCJ, faulted with displacement, RIR
111.42	112.05	J	2	40	8	SP	1	√	1OCJ, faulted with displacement, RIR
112.05	112.62	_	_	_	_	_	_	_	Wholly intact rock
112.62	112.90	FZ	3		_	SP	3	√	Rockmass weakened by strong fracturing
112.90	113.78	J	2	35	5	SP	1	√	1OCJ, faulted with displacement, RIR
113.78	114.21	J	2	45	8	SP	1	√	1OCJ, faulted with displacement, RIR
114.21	116.09	J	2	45	8	SP	1	√	1OCJ, faulted with displacement, RIR
116.09	116.79	J	2	50	8	SP	1	√	1OCJ, faulted with displacement, RIR
116.79	117.10	_	_	_	_	_	_	_	Wholly intact rock
117.10	118.40	F	2	15	8	SP	3	√	7OCJs, 3CJs, faulted with displacement, RIR
118.40	121.93	J	2	85	8	SP	1	√	1OCJ, faulted with displacement, RIR
121.93	123.85	J	2	30	8	SP	1	√	1OCJ, faulted with displacement, RIR
123.85	128.32	J	2	40	8	SP	1	√	1OCJ, faulted with displacement, RIR
128.32	131.20	J	2	30	2	SP	1	√	1OCJ, faulted with displacement, RIR
131.20	131.32	F	2	30	2	SP	3	√	1OCJ, faulted with displacement, RIR

Logging abbreviations. Structure code: Shear zone (SZ); Fracture zone (FZ); Fault (F); Fracture (Fr); Joint (J); Striation lineation (L); Fold axis (FA); Vein (V); and Dyke (D).
Structure class: Strongly sheared (cataclasite/mylonite) or brecciated (1). Clearly faulted with displacement or striations (2). The rockmass is weakened by alteration or strong fracturing, a nearby major structure is likely (3). The core is completely broken because of poor core recovery. Possibly structure related (4). The core is strongly or completely altered/weathered to residual soil/mud (5). Fill Type: Q, Quartz; G, Gouge; C, Calcite; M, Magnesium; FE, Iron oxide; H, Hematite; CL, Clay; S, Sulfide; B, Breccia; O, Other. Wall Alteration: 1—wall = rock hardness; 2—wall > rock hardness; and 3—wall < rock hardness. Micro/Small-Scale Joint Expression: Rough/Stepped/Irregular—1; Smooth Stepped—2; Slickensided stepped—3; Rough Undulating—4; Smooth Undulating—5; Slickensided Undulating—6; Rough Planar—7; Smooth Planar—8; and Polished—9. Other Descriptions: OCJ, Open cemented joints; RIR, Rest intact rock; Btw, Between; Tot, Total; Nat, Natural; Fol, Foliation; S1, Set 1; S2, Set 2; S3, Set 3; IC/m, Intensity Count per meter; and MTPL, Multiple.

This study critically revisits TAM and Coates’ method for mine pillar stress determination within the complex geological and geotechnical conditions of the Great Dyke of Zimbabwe. It aims to assess the limitations of these conventional methods and explore more advanced and reliable approaches for improving pillar design in hardrock room and pillar mining. The study is driven by the necessity to address the inadequacies of traditional stress determination models that fail to capture the complex interactions of geological discontinuities, heterogeneous rock properties, and stress redistribution mechanisms. A significant research gap exists in the adaptation of empirical and analytical methods to account for the unique geological conditions of the Great Dyke, which features variable rockmass properties, anisotropic stress fields, and complex structural discontinuities. While TAM is widely applied in pillar design due to its simplicity, its fundamental assumptions—such as uniform load distribution, independent pillar behavior, and elastic material response—render it ineffective in environments with significant geotechnical variability. Similarly, Coates’ method, though an improvement over TAM, does not account for critical factors such as overburden stiffness, seam interactions, and time-dependent stress redistribution. This study provides an in-depth exploration of the extent to which these limitations impact accurate pillar stress determination and proposes more accurate predictive methodologies. The study notes that a hybridized approach, which merges traditional empirical methods with advanced computational techniques to improve the precision and adaptability of pillar stress analysis, is suitable for the geological and geotechnical conditions of the Great Dyke of Zimbabwe. The findings of the study show the need for site-specific calibration of numerical models, the importance of incorporating machine learning for stress prediction, and the benefits of transitioning from purely empirical approaches to data-driven decision-making in mining operations. This study enhances the understanding of pillar stability on the Great Dyke and contributes to the broader objective of optimizing underground mine safety and efficiency.

2 REFLECTIONS ON THE TAM

The TAM is a fundamental and widely used approach in mining operations to estimate the stress (or load) acting on mine pillars (Kumar et al., 2023; Salmi et al., 2017). This method is particularly useful in room and pillar mining operations, where understanding the load distribution on pillars is crucial for ensuring the stability and safety of underground structures. The fundamental premise of TAM is that each pillar is responsible for supporting the weight of the overburden rock within its defined tributary area, which includes the vertical column of rock directly above the pillar and extends horizontally halfway to adjacent pillars on all sides. This area represents the portion of the roof load attributed to that specific pillar.

The load distribution is assumed to be evenly spread across the tributary area with the following attributes:

Simplified geometry—the method assumes regular, often square or rectangular, pillar and panel geometries.

Elastic behavior—the surrounding rockmass and pillars are assumed to behave elastically up to failure.

Neglect of pillar interaction—the method typically neglects the interaction between adjacent pillars, treating each pillar as an independent unit.

2.1 Tributary area calculation

To determine the load on a pillar using TAM, it is essential to calculate the tributary area. The tributary area for a pillar can be defined based on the geometry of the mine layout (Figure 4). In Figure 4, B1 is bord width 1, B2 is bord width 2, L is the pillar length, W is the pillar width, red color and letter A represent the pillars, and white color and number 1 represent the excavated areas.

Consider a room and pillar mining layout where the pillars are arranged in a regular grid pattern. In a regular grid, each pillar supports a portion of the overlying strata (the load directly above it and halfway to the surrounding pillars). From the tributary area ( L + B 1)( W + B 2), the extraction ratio, e, which is a key component of the pillar stress formula, can be determined. The formula for e using the convention adopted in Figure 4 is given in Equation ( 1).

𝑒 = ( 𝐿 + 𝐵 1 ) ⁢ ( 𝑊 + 𝐵 2 ) − 𝐿 𝑊 ( 𝐿 + 𝐵 1 ) ⁢ ( 𝑊 + 𝐵 2 ) . (1)

2.2 Load calculation

Once the tributary area is determined, the next step is to calculate the load that this area imposes on the pillar. The weight of the overlying strata is a function of the height of the rock column above the pillar and the density of the rock. Equation ( 2) provides the load (stress) on an individual pillar based on the tributary area that it supports. Note that Equation ( 2) is derived from the first principles of normal stress definition, that is, weight of the overburden rockmass within the pillar tributary zone divided by the pillar plan area.

𝑃 s t r e s s = 𝜎 v 1 − 𝑒 , (2)

𝜎 v = 𝜌 ⁢ 𝑔 ℎ ,

where P stress is the average pillar stress; σ v is the vertical component of the virgin stress, MPa; ρ is the rock density, kg/m 3; g is gravitational acceleration, m/s 2; h is the depth below ground surface, m.

2.3 Design considerations

Pillar spacing and size—adjustment of the spacing and size of pillars is a primary method to manage the stress distribution and ensure stability.

Rock properties—accurate knowledge of the rock properties, such as unit weight and compressive strength, is crucial for reliable calculations.

Safety factors—incorporation of appropriate safety factors is essential to account for uncertainties in geological conditions and loading scenarios.

2.4 Reflections on the limitations of TAM

Figure 5 illustrates some of the limitations of TAM.

2.4.1 Simplified load distribution

The assumption of uniform load distribution is a fundamental simplification within TAM. In ideal conditions, each pillar is considered to support an evenly distributed portion of the overlying strata. However, geological realities often deviate significantly from this idealization. Complex geological settings frequently have heterogeneous rock properties, variable depths, and anisotropic stress fields. These factors can cause substantial deviations from the assumed uniform load distribution. Geological features such as faults, fractures, folds, and varying rock stiffness can lead to highly uneven stress distributions (Amadei & Stephansson, 2012; Garza-Cruz et al., 2019). A fault zone intersecting a pillar might relieve stress from one part of the pillar while concentrating it on another, leading to stress concentrations that TAM does not predict. Differences in rock stiffness can result in uneven load sharing among pillars, with stiffer pillars carrying more load and more compliant ones carrying less. These complexities mean that the stress distribution across a mine cannot be accurately modeled by a simple uniform assumption.

Due to the occurrence of shear stress in pillar–roof and pillar–floor contacts, the major principal stress acting on the mine pillar is located in a direction other than the vertical direction. Stress transformation, as given in Equation ( 3), becomes necessary to determine the state of stress ( 𝜎 𝑥 ′ , 𝜎 𝑦 ′ , 𝜎 𝑧 ′ , 𝜏 𝑥 ′ ⁢ 𝑦 ′ , 𝜏 𝑦 ′ ⁢ 𝑧 ′ , 𝜏 𝑧 ′ ⁢ 𝑥 ′ ) at any orientation ( x , y , z ) (one of which is the principal stresses orientation), from the reference orientation ( x, y, z) state of stress( 𝜎 𝑥 , 𝜎 𝑦 , 𝜎 𝑧 , 𝜏 𝑥 𝑦 , 𝜏 𝑦 𝑧 , 𝜏 𝑧 𝑥 ), using the direction cosines ( ). Direction cosines are crucial, as they relate the orientation of the original coordinate system to the new coordinate system. The direction cosines are determined by the angles between the corresponding axes of the two coordinate systems. The transformation of a 3D stress tensor from the original coordinate system ( x, y, z) into a rotated system ( x′, y′, z′) using direction cosines is given by Equation ( 3).

(3)

where σ t is the transformed stress tensor. L is the direction cosine matrix. σ o is the original stress tensor. L T is the transpose of the direction cosine matrix.

An expanded version of Equation ( 3) is given in Equation ( 4).

(4)

The matrices in Equation ( 4) represent the following:

The first matrix on the left-hand side is the stress tensor in the transformed coordinate system.
The matrix in the middle on the right-hand side is the original stress tensor in the original coordinate system.
The matrices on either side of the original stress tensor are the direction cosine matrices, which relate the orientation of the two coordinate systems.

Expressions for the transformed stress components can be written as given in Equations (5)–(10).

1. Normal stress components (normal stress is stress acting perpendicular to a plane)

–normal stress on the face (a plane [face] is named after the axis perpendicular [normal]) to it

(5)

– normal stress on the face

(6)

- normal stress on the z′ face

(7)

2. Shear stress components (shear stress is stress acting parallel to a plane)

In stress notation, the first subscript represents the name (normal) of the plane (face) and the second subscript represents the direction of action of the stress. One subscript is used for normal stress, since the name of the plane and the direction of action of the normal stress are the same.

–shear stress on the x′ face in the y′ direction.

(8)

–shear stress on the y′ face in the z′ direction

(9)

–shear stress on the z′ face in the x′ direction

(10)

In Equations (4) to (10), the direction cosines are defined as follows:

are cosines between x′ and x, y, z, respectively.

are cosines between y′ and x, y, z, respectively.

are cosines between z′ and x, y, z, respectively.

Ignoring these complexities can lead to inaccurate stress estimates and design flaws in mining operations. Rock engineers might underestimate the stress on some pillars, leading to premature failure, or overestimate it on others, resulting in overly conservative designs that waste resources. More sophisticated methods such as numerical modeling, machine learning, and in situ stress measurements can be used to address these issues. These methods can account for the variable and complex nature of geological settings, providing a more accurate representation of the stress distribution and thus improving the reliability of pillar design.

Table 3 presents some stress transformation calculation results for a Great Dyke deposit, considering the practical mining layout given in Figure 4 (at 200 m depth) and different permutations of shear stress and confinement provided by supporting the pillar with shotcrete and or rockbolts. Note that the vertical direction is y, the horizontal in-plane direction is x, and the horizontal out-of-plane direction is z. σ1, σ2, and σ3 are the major, intermediate, and minor principal stresses, respectively. DA is the direction angle. 1 and 3 are the major and minor principal stress axes, respectively.

Table 3. Practical stress transformation calculations for a Great Dyke Deposit considering different permutations of stress at 200 m depth.

Permutations of stress	Stress (MPa)									Angle (°)
Permutations of stress	σx	σy	σz	τxy	τxz	τyz	σ1	σ2	σ3	DA1x	DA1y	DA1z	DA3x	DA3y	DA3z
Without support on pillar faces	0	37.94	0	0	0	0	37.94	0	0	90.0	0	90.0	90.0	90.0	0
	0	37.94	0	2	0	4	38.46	0	−0.52	87.0	6.6	84.1	63.6	96.6	27.3
	0	37.94	0	4	0	2	38.46	0	−0.52	84.1	6.6	87.0	27.3	96.6	63.6
	0	37.94	0	4	0	4	38.77	0	−0.83	84.1	8.3	84.1	45.6	98.3	45.6
	0	37.94	0	10	0	10	42.63	0	−4.69	77.1	18.4	77.1	47.8	108.4	47.8
	0	37.94	0	10	0	15	45.14	0	−7.20	78.1	21.8	72.0	59.0	111.8	39.4
	0	37.94	0	15	0	10	45.14	0	−7.20	72.0	21.8	78.1	39.4	111.8	59.0
	0	37.94	0	15	0	15	47.43	0	−9.49	73.2	24.1	73.2	49.8	114.1	49.8
	0	37.94	0	15	0	20	50.35	0	−12.41	74.5	26.4	69.2	57.5	116.4	44.2
	0	37.94	0	20	0	15	50.35	0	−12.41	69.2	26.4	74.5	44.2	116.4	57.5
	0	37.94	0	20	0	20	53.03	0	−15.09	70.6	28.1	70.6	51.4	118.1	51.4
With support on pillar faces: 10 MPa confinement	10	37.94	10	0	0	0	37.94	10	10.00	90.0	0	90.0	90.0	90.0	0
	10	37.94	10	2	0	4	38.64	10	9.30	86.0	8.9	82.1	63.8	98.9	27.9
	10	37.94	10	4	0	2	38.64	10	9.30	82.1	8.9	86.0	27.9	98.9	63.8
	10	37.94	10	4	0	4	39.04	10	8.90	82.2	11.0	82.2	46.0	101.0	46.0
	10	37.94	10	10	0	10	43.85	10	4.09	74.2	22.7	74.2	49.3	112.7	49.3
	10	37.94	10	10	0	15	46.78	10	1.16	75.9	26.1	68.5	60.1	116.1	41.7
	10	37.94	10	15	0	10	46.78	10	1.16	68.5	26.1	75.9	41.7	116.1	60.1
	10	37.94	10	15	0	15	49.37	10	−1.43	70.4	28.3	70.4	51.5	118.3	51.5
	10	37.94	10	15	0	20	52.61	10	−4.67	72.3	30.4	66.1	58.8	120.4	46.4
	10	37.94	10	20	0	15	52.61	10	−4.67	66.1	30.4	72.3	46.4	120.4	58.8
	10	37.94	10	20	0	20	55.52	10	−7.58	68.1	31.9	68.1	53.1	121.9	53.1
With support on pillar faces: 20 MPa confinement	20	37.94	20	0	0	0	37.94	20	20.00	90.0	0	90.0	90.0	90.0	0
	20	37.94	20	2	0	4	38.99	20	18.95	84.1	13.2	78.2	64.2	103.2	29.5
	20	37.94	20	4	0	2	38.99	20	18.95	78.2	13.2	84.1	29.5	103.2	64.2
	20	37.94	20	4	0	4	39.57	20	18.37	78.7	16.1	78.7	47.2	106.1	47.2
	20	37.94	20	10	0	10	45.72	20	12.22	70.1	28.8	70.1	51.7	118.8	51.7
	20	37.94	20	10	0	15	49.11	20	8.83	73.0	31.8	64.0	61.9	121.8	45.0
	20	37.94	20	15	0	10	49.11	20	8.83	64.0	31.8	73.0	45.0	121.8	61.9
	20	37.94	20	15	0	15	52.00	20	5.94	67.0	33.5	67.0	53.9	123.5	53.9
	20	37.94	20	15	0	20	55.53	20	2.41	69.8	35.1	62.6	60.6	125.1	49.1
	20	37.94	20	20	0	15	55.53	20	2.41	62.6	35.1	69.8	49.1	125.1	60.6
	20	37.94	20	20	0	20	58.64	20	−0.70	65.3	36.2	65.3	55.2	126.2	55.2

Note: σ2 is positive when confinement is applied. This contributes to the strength of the rockmass. There are instances where σ3 is negative. This contributes to rock failure in tension, causing instability. Some pillar failures on the Great Dyke due to geotechnical complexities are shown in Figure 6.

2.4.2 Neglecting pillar interaction

The interaction between pillars is another critical aspect that TAM does not consider. Pillars do not act as isolated entities in reality but rather influence and are influenced by the stress and deformation of adjacent pillars. This interaction can significantly affect the overall stress distribution in a mine. When one pillar deforms or fails, it can transfer additional load to neighboring pillars, causing a cascading effect where the failure of one pillar leads to the failure of adjacent pillars. This load transfer mechanism is critical in understanding the stability of a pillar system, especially in highly stressed mining environments. The stress redistribution following the failure of a single pillar can lead to unexpected and catastrophic outcomes, which TAM, with its independent pillar assumption, cannot predict (Van der Merwe, 2006). Numerical modeling techniques, such as the finite element method (FEM) or the discrete element method (DEM), can simulate these interactions. Mining practitioners can better understand the load transfers and interactions by modeling the entire pillar system as an interconnected network. These models can account for the mechanical properties of the rock, the geometry of the mine layout, and the in situ stress conditions, providing a more comprehensive assessment of the stability of the pillar system.

2.4.3 Elastic assumptions

The assumption that rockmass behaves elastically up to failure is a simplification that often does not hold in the complex stress environments of underground mines. Real rockmasses show non-linear, plastic, and time-dependent behaviors that significantly influence their response to stress. Highly stressed or fractured rockmasses can behave in ways that deviate considerably from simple elastic models. Elastic behavior assumes that the rock will deform proportionally to the applied load and return to its original shape upon load removal. However, rockmasses often show plastic deformation, where permanent deformation occurs. This plasticity is especially prevalent near failure, where microcracking, slip along fractures, and other irreversible processes dominate. Time-dependent behaviors such as creep (slow deformation over time under constant stress) can significantly impact pillar stability, especially in deep mines, where high stresses persist for extended periods. Ignoring these non-elastic behaviors can lead to significant underestimations of deformation and stress concentrations. Advanced numerical models, incorporating elastoplastic and viscoelastic constitutive laws, are necessary to capture these complex behaviors. These models can simulate the progressive failure of rock and the associated stress redistributions, providing a more realistic prediction of pillar performance under high stress conditions.

2.4.4 Geometric and structural limitations

1. Geometric regularity

TAM assumes a regular geometric layout of pillars and rooms, which is rarely the case in practical mining operations. Irregular geometries arise due to varying ore body shapes, the need to navigate around geological features, and operational constraints. These irregularities can complicate the load distribution and stress patterns in ways that TAM cannot accurately predict. In an idealized, regular layout, each pillar has a well-defined tributary area that is easy to calculate. However, in irregular layouts, the tributary areas are not uniform, and the load that each pillar supports can vary significantly. A pillar at the edge of a mining panel or near a fault zone might have a different stress distribution compared to a centrally located pillar. The presence of inclined seams, uneven floors, or variable pillar heights further complicates the stress analysis. To account for these irregularities, detailed site-specific assessments are necessary. Advanced numerical models that can handle complex geometries are particularly useful (Shapka-Fels & Elmo, 2022). These models can simulate the stress distribution in irregular layouts by accurately representing the geometry and mechanical properties of the rockmass. Field measurements, such as stress monitoring and deformation surveys, also play a crucial role in validating these models and ensuring that the designs are resilient under the actual mining conditions.

2. Ignoring pillar shape effects

TAM generally simplifies pillars to basic geometric shapes, such as squares or rectangles, and assumes uniform stress distribution across these shapes. However, the actual shape of a pillar can significantly influence the stress distribution within it. Pillars with irregular shapes, tapered sides, or non-uniform cross-sections can experience uneven stress concentrations that are not accounted for by TAM. Pillars with sharp corners or edges may have higher stress concentrations at those points, increasing the likelihood of local failure. Tapered pillars might have a different load-bearing capacity compared to pillars with uniform cross-sections. The simplified geometric assumptions of TAM do not capture these complexities, potentially leading to inaccurate stress estimates. More detailed geometric modeling and analysis, such as using three-dimensional finite element models, can better represent the actual shapes of pillars and provide a more accurate assessment of stress distribution.

3. Simplified assumption of pillar uniformity

TAM also assumes that all pillars within the mining layout are uniform in size, shape, and material properties. However, in practice, variations in pillar dimensions and material properties are common due to geological variability, mining practices, and operational constraints. These variations can lead to significant differences in the stress distribution and load-bearing capacity of the pillars. Variations in the mineral composition, grain size, and the presence of microfractures can result in different mechanical properties for each pillar. Variations in the mining process can lead to pillars with different shapes and sizes. Ignoring these variations can result in an oversimplified stress analysis, leading to underdesigned or overstressed pillars. Detailed site-specific investigations and variability analysis are necessary to account for these differences and provide a more accurate assessment of pillar stress and stability. Figure 7 shows a mine pillar observed on the Great Dyke with irregular dimensions due to pillar robbing mining practice.

2.4.5 Limitations in pillar–roof interaction and dynamic load representation

1. Inadequate representation of pillar–roof interaction

The interaction between the pillars and the roof (or back) of the mine is another aspect that TAM oversimplifies. The roof can deform and influence the load distribution on the pillars in reality (Skrzypkowski, 2019; Zhienbayev et al., 2023). The roof–pillar interaction can be particularly significant in weak or highly jointed roof conditions, where the roof may sag or collapse, transferring additional load to the pillars. In a mine with a weak roof, the sagging of the roof can cause uneven load distribution, increasing the stress on certain pillars and leading to localized failure. TAM does not capture these interactions, potentially leading to an underestimation of the stress on the pillars. Detailed roof–pillar interaction analysis, using methods such as coupled numerical modeling, is necessary to accurately predict the stress distribution and ensure the stability of both the pillars and the roof.

2. Assumption of instantaneous load transfer

TAM assumes that load transfer to pillars is both instantaneous and static, implying that any changes in mine geometry or the failure of adjacent pillars immediately result in a new equilibrium state without any time delay. This assumption fails to account for the dynamic and time-dependent nature of load transfer in actual mining conditions. When a pillar fails or deforms, the surrounding rockmass and adjacent pillars require time to adjust and redistribute the load, leading to transient stress states that TAM cannot capture. The gradual collapse of a pillar might lead to progressive failure in nearby pillars as the load is slowly transferred and redistributed. This time-dependent behavior can result in stress waves or delayed failures, which the static nature of TAM cannot predict. Advanced dynamic modeling techniques, such as time-dependent finite element analysis, are better suited to simulate these processes and provide insights into the evolution of stress over time, highlighting the importance of considering the temporal aspects of load transfer for designing robust pillars.

3. Dynamic loading and seismic activity

TAM does not account for dynamic loading conditions such as those caused by seismic activity, blasting operations, or sudden rock bursts. Kaiser et al. (2000) note that, in mining environments, particularly in deep underground mines, dynamic loading can significantly alter stress distribution. Seismic events can induce transient stress waves that propagate through the rockmass, leading to temporary but severe increases in stress on pillars. Such dynamic loads can cause instantaneous failure or weakening of pillars, a scenario that TAM, being a static method, cannot predict or accommodate. Likewise, blasting operations generate shock waves that can temporarily elevate stress levels in the vicinity of the blast, leading to cumulative damage in pillars over time, a phenomenon known as fatigue. Since TAM does not model these dynamic effects, it might underestimate the true stress on pillars, leading to a false sense of security and increasing the risk of sudden pillar collapse under dynamic conditions.

To account for a dynamic load on a mine pillar in hardrock room and pillar mining, several key factors need to be considered, including static load, dynamic load factors, and the interaction between these loads. The stress on a mine pillar, accounting for dynamic loading, can be represented by Equation ( 11). Substitution of Equations ( 12)–( 14) into Equation ( 11) yields the full form of the mine pillar stress, accounting for dynamic loading, as expressed in Equation ( 15).

𝜎 p s t r e s s = 𝜎 s t a t i c × ( 1 + 𝜅 ⋅ 𝐷 𝐿 𝐹 ) , (11)

𝜎 s t a t i c = 𝑊 𝐴 , (12)

𝜅 = 𝑣 p + 𝑣 s 2 × 𝜌 𝐸 , (13)

𝐷 𝐿 𝐹 = Δ ⁢ 𝐹 d y n a m i c 𝐹 s t a t i c , (14)

𝜎 p s t r e s s = 𝑊 𝐴 ⁢ [ 1 + ( 𝑣 p + 𝑣 s ) ⁢ 𝜌 2 ⁢ 𝐸 ⋅ Δ ⁢ 𝐹 d y n a m i c 𝐹 s t a t i c ] , (15)

The parameters in Equations ( 11)–( 15) are as follows:

σpstress is the total stress experienced by the pillar when both static and dynamic loads are considered. This is critical for assessing the stability of the pillar, especially in environments where dynamic events like seismic activity are common.
σstatic is the static stress on the pillar, which is the stress without considering dynamic effects, as also given in Equation (2). It is essential for understanding the fundamental load that the pillar must support under normal conditions.
κ is a factor that accounts for the increase in stress due to dynamic loading, which could be due to events such as seismic activity or blasting.
DLF is the dynamic load factor, which quantifies the increase in load due to dynamic events. It is a multiplier that scales the impact of dynamic events on the pillar. Higher DLF values indicate greater sensitivity to dynamic events, which may necessitate more conservative pillar designs.
W is the weight of the overlying rockmass (N). This represents the gravitational load exerted on the pillar by the overburden.
A is the cross-sectional area of the pillar (m²). This is the area over which the load is distributed.
vp is the primary wave velocity (P-wave velocity) in the rockmass (m/s). P-waves are the fastest seismic waves and are crucial in determining how stress propagates through the rockmass.
vs is the secondary wave velocity (S-wave velocity) in the rockmass (m/s). S-waves are slower but typically have larger amplitudes than P-waves, contributing significantly to dynamic stress.
ρ is the density of the rockmass (kg/m³). Higher density rockmasses transmit more force during dynamic events.
E is the Young's modulus of the rockmass (Pa). This parameter represents the stiffness of the rockmass, with stiffer rockmasses transmitting stress more effectively.
The term ( 𝑣 p + 𝑣 s ) ⁢ 𝜌 / 2 ⁢ 𝐸 represents the dynamic amplification factor, which accounts for how seismic waves (both P- and S-waves) increase stress on the pillar. This factor is crucial in regions with significant seismic activity, as it quantifies the additional stress transmitted through the rockmass.
ΔFdynamic is the change in force (N) due to dynamic events, such as seismic activity or blasting.
Fstatic is the static force exerted on the pillar, which is equivalent to the weight (W) of the overlying rockmass.
DLF is dimensionless and represents the ratio of dynamic force to static force, indicating how much additional load is applied to the mine pillar during dynamic events.

Equation (15) provides a comprehensive framework for evaluating the total stress on a mine pillar, accounting for dynamic stress in room and pillar mining. Each parameter in the equation has a significant impact on the overall stress and, therefore, on the stability of the pillar. Rock engineers can better predict the behavior of pillars under dynamic loading conditions, ultimately leading to safer and more reliable mining operations by understanding and applying these parameters.

2.4.6 Inadequate consideration of stress and hydrological factors in mining operations

1. Effect of groundwater and hydrostatic pressure

Groundwater and the associated hydrostatic pressure significantly affect the stress distribution in a mine, an aspect that TAM does not explicitly consider. Water presence can alter the effective stress within the rockmass and pillars, reducing the strength and increasing the stress. Hydrostatic pressure can lead to increased pore pressure within the rockmass, which in turn reduces the frictional resistance along fractures and faults, making them more prone to movement and failure. Water infiltration can also lead to chemical weathering of rock material, further weakening the pillars. In cases where water pressure is high, it can lead to hydraulic fracturing, causing new fractures to develop or existing ones to propagate, thereby altering the stress distribution. The inability of TAM to incorporate the effects of groundwater and hydrostatic pressure means that the method can significantly underestimate the risk posed by water-related factors, which can be critical for the stability of the pillars.

2. Lack of consideration for mining-induced subsidence

Zvarivadza (2016) notes that mining-induced subsidence (illustrated in Figure 8), the gradual sinking of the ground surface due to underground mining activities, can significantly affect stress distribution in a mine. TAM does not consider the effects of subsidence, which can lead to additional stresses on pillars and changes in the load distribution. Subsidence can cause differential settlement, leading to uneven stress distribution and instability. As the ground surface subsides, the overburden load may shift, causing increased stress on certain pillars while reducing it on others. This shifting load can result in unexpected stress concentrations and failure. Monitoring subsidence and incorporating its effects into stress analysis are crucial for accurate pillar design. Advanced monitoring techniques, such as surface deformation surveys and subsidence modeling, can provide data on subsidence patterns, which can be integrated into stress analysis to account for its impact on pillar stability.

3. Neglecting the role of horizontal stresses

While TAM focuses on the vertical load due to the overlying rockmass, it neglects the role of horizontal stresses, which can be significant in underground mining environments. Horizontal stresses, arising from tectonic forces, residual stress fields, or mining-induced stress changes, can influence the stress distribution and stability of the pillars. In regions with high horizontal stresses, the pillars may experience biaxial or triaxial stress states, which can alter their load-bearing capacity and failure mechanisms. Ignoring these horizontal stresses can lead to an incomplete understanding of the stress conditions and result in inaccurate predictions of pillar stability. Advanced stress analysis techniques can incorporate both vertical and horizontal stresses, providing a comprehensive assessment of the stress state in the pillars.

4. Ignoring the influence of mining-induced stress changes

TAM does not consider the changes in the stress field induced by the mining process itself. As mining progresses, the removal of rock and the creation of voids lead to stress redistribution in the surrounding rockmass, which can significantly affect the stress on the pillars. This mining-induced stress change is dynamic and evolves with the advancement of the mining operations. The initial stress state in the rockmass is altered as new rooms are excavated and pillars are exposed to different loading conditions. The stress concentration around the newly created voids can increase the stress on nearby pillars, leading to unexpected failure. The static approach of TAM does not capture these dynamic changes, leading to potentially inaccurate predictions. Advanced stress modeling techniques, such as sequential excavation analysis and real-time monitoring, are essential to account for mining-induced stress changes and ensure the stability of the pillars throughout the mining process.

5. Insensitivity to stress redistribution from progressive failure

TAM does not account for the progressive failure of pillars and the subsequent stress redistribution that occurs as a result. The failure of one pillar can lead to a redistribution of stress to adjacent pillars in reality, which may then become overstressed and fail in a cascading manner. This progressive failure mechanism is critical to understanding the overall stability of the pillar system, especially in highly stressed mining environments. If a single pillar fails due to excessive load, the load that it was carrying is transferred to nearby pillars, increasing their stress and potentially causing them to fail as well. This chain reaction can lead to large-scale collapse, which TAM cannot predict. Numerical methods can simulate the progressive failure and stress redistribution, providing a more accurate assessment of the overall stability of the pillar system.

6. Temporal variations in stress

TAM does not account for temporal variations in stress, which can arise due to long-term mining activities and geological processes. As mining progresses, the removal of material and the creation of new voids change the stress distribution continuously. Over time, this can lead to stress redistribution, relaxation, or build-up around pillars. The slow, time-dependent deformation of rock, known as creep, can also alter the stress state over extended periods. Seasonal changes, such as freeze–thaw cycles or variations in groundwater levels, can also induce stress changes in the rockmass. These temporal variations can result in progressive weakening or strengthening of the pillars, which TAM, with its static snapshot approach, cannot capture. Therefore, relying solely on TAM can result in a failure to predict long-term stability issues, leading to unexpected pillar failures after extended periods of seemingly stable conditions.

7. Inability to model pillar deterioration over time

Pillar deterioration over time due to weathering, chemical reactions, or fatigue from repeated stress cycles is another factor that TAM does not consider. As pillars age, their strength can decrease, leading to increased stress on the remaining intact material. This time-dependent degradation can significantly impact the long-term stability of the pillars, which TAM, being a static and time-independent method, fails to capture (Li, Li, et al., 2023; Wang et al., 2012; Yu et al., 2017). Exposure to water can lead to chemical weathering or dissolution of minerals within the pillar, weakening its structure. Similarly, cyclic loading from repeated blasting or seismic events can cause fatigue, reducing the load-bearing capacity of the pillar over time. Advanced modeling techniques that incorporate time-dependent deterioration processes, such as creep and fatigue analysis, are essential for predicting the long-term performance of pillars and ensuring their stability throughout the life of the mine.

2.4.7 Limitations in rockmass characterization and geological representation

1. Anisotropic rock properties

Rockmasses often show anisotropic properties, where their strength and deformation characteristics vary depending on the direction of loading. This anisotropy can arise from the inherent fabric of the rock, such as foliation in metamorphic rocks, bedding planes in sedimentary rocks, or joint sets and fractures. TAM assumes isotropic conditions, where rock properties are uniform in all directions, which is rarely the case in natural rock formations. Anisotropic conditions can lead to uneven stress distributions and differential deformation of pillars. A pillar loaded parallel to a weak plane might experience significantly higher stress and deformation compared to one loaded perpendicular to the same plane. This anisotropy can cause unexpected stress concentrations and failure patterns that TAM cannot predict. Advanced methods that account for anisotropic properties are necessary to accurately model and design pillars in such conditions.

2. Non-homogeneous rockmass

The assumption of a homogeneous rockmass in TAM overlooks the natural variability in rock properties within a mining site. Rockmasses are rarely uniform and often consist of different lithologies, varying strengths, and the presence of faults, joints, and other discontinuities. These variations can lead to significant differences in stress distribution and mechanical behavior across the mine. A pillar situated in a stronger rock type (Figure 9a) might bear more load than one in a weaker rock type (Figure 9b), leading to uneven stress distribution and potential failure in the weaker areas. Faults and joints can act as planes of weakness, altering the stress paths and concentrating stresses in ways that TAM cannot predict. Homogenization assumptions might lead to over- or underestimation of pillar stress in different parts of the mine, thereby compromising the overall stability and safety. Advanced geotechnical investigations and modeling techniques that account for heterogeneity are essential for accurate stress assessment and design in non-homogeneous rockmasses.

Appropriate bord (room) support in a room and pillar layout is critical to avoid wedge failures or layered rockmass failure, which can increase the height and/or the bord width, leading to pillar instability due to stress concentrations. Figures 10 and 11 present a practical bord support design for a Great Dyke of Zimbabwe deposit, considering major joint sets and layered rockmass, respectively.

3. Oversimplification of geological structures

TAM assumes a simplified geological setting without accounting for the complexity of geological structures such as faults, folds, dykes, and shear zones. These structures can significantly influence the stress distribution and mechanical behavior of the rockmass, leading to localized stress concentrations or weak zones that are not considered in TAM. The presence of a fault zone intersecting a pillar can reduce its effective load-bearing capacity and alter the stress distribution in the surrounding rockmass. Similarly, shear zones can act as planes of weakness, leading to differential deformation and increased stress on adjacent pillars. Advanced geological modeling and geotechnical investigations are essential to identify and characterize these structures, providing a more accurate representation of the stress conditions in the mine.

2.4.8 Influence of oversimplification of boundary conditions and influence of scale, thermal effects, and unaccounted failure mechanisms

1. Oversimplification of boundary conditions

TAM assumes simple boundary conditions where the load is uniformly distributed and the rockmass surrounding the pillars is continuous and homogeneous. However, actual mining environments often present complex boundary conditions such as varying rock stiffness, discontinuities, and heterogeneities in the surrounding rockmass. These conditions can significantly influence the stress distribution on pillars. A pillar located near a mine boundary, fault, or other geological discontinuity may experience different stress conditions compared to a pillar surrounded by a continuous rockmass. The presence of stiffer or softer layers, voids, or previously mined-out areas can alter the load paths and stress concentrations. Ignoring these complex boundary conditions can lead to erroneous stress predictions. Advanced numerical modeling techniques, such as boundary element methods (BEMs) and FEMs, can incorporate these complex boundary conditions and provide a more realistic assessment of stress distribution.

2. Scale effect and size dependency

The strength and behavior of rockmasses can vary with scale, known as the scale effect (Bandis et al., 1981; Barton, 2013; Edelbro et al., 2007). Laboratory tests on small rock samples often show higher strengths compared to large in situ rockmasses due to the absence of large-scale defects and discontinuities in small samples. TAM does not account for this scale effect, often using rock strength values derived from small-scale tests to predict the behavior of much larger pillars. The size of the pillars relative to the size of the rooms and the entire mine structure also affects the stress distribution. Larger pillars might experience different stress concentrations and failure mechanisms compared to smaller ones. The lack of consideration for scale effects in TAM can lead to inaccurate predictions of stress and stability, particularly in large-scale mining operations where pillar dimensions are substantial. Numerical methods that incorporate scale-dependent properties provide a more realistic assessment of pillar stress and stability.

3. Neglect of thermal effects

Mining operations, particularly deep underground mines, can experience significant temperature variations due to geothermal gradients and mining activities. These thermal effects can induce additional stresses in the rockmass and pillars, which TAM does not consider. Temperature changes can cause the rock to expand or contract, leading to thermal stresses that can add to the mechanical loads on the pillars. In deep mines where the rock temperature is naturally higher, the expansion of rock can exert compressive stresses on the pillars. Conversely, cooling of the rock due to ventilation or water inflow can cause contraction and tensile stresses. These thermal stresses can interact with mechanical stresses, leading to complex stress states that TAM cannot predict. Incorporation of thermal effects into stress analysis requires advanced modeling techniques, such as coupled thermo-mechanical simulations, which can account for the interaction between temperature changes and stress distribution.

4. Failure mechanisms not accounted for

Rock failure is a complex process influenced by multiple factors, including confinement, loading rate, and the presence of pre-existing fractures. TAM does not capture these complexities, leading to inaccurate predictions of pillar failure. Rockmasses show different strengths under varying stress conditions in reality. Rocks under high confining pressure may have higher strength due to the suppression of tensile fractures. Conversely, rocks with pre-existing fractures may fail at lower stress levels. Advanced failure criteria provide a more comprehensive representation of rock behavior by considering these factors. Incorporation of advanced failure criteria into stress analysis can improve the accuracy of failure predictions.

2.4.9 Limitations of TAM in multi-level mining and support design

1. Limited applicability to multi-level mining

TAM is primarily designed for single-level mining operations, where the load on each pillar is determined by the overlying rockmass. However, in multi-level mining operations, where multiple layers of mining occur at different depths, the stress distribution becomes more complex. The load on pillars is influenced not only by the overlying rockmass but also by the activities and pillar layout in the levels above and below. In multi-level mining, stress transfer between levels can result in complex stress interactions that TAM does not account for. The removal of pillars in an upper level can increase the load on pillars in lower levels, leading to instability. Advanced modeling techniques can simulate the stress interactions between different mining levels and provide a more accurate assessment of pillar stability in multi-level operations.

2. Simplistic approach to support design

TAM simplifies the complex interactions between the rockmass and the mine support systems, often neglecting the impact of additional supports such as backfill, rock bolts, and shotcrete. In reality, these support systems significantly influence the stress distribution and the load-bearing capacity of the pillars. The presence of backfill can help distribute the load more evenly and reduce the stress concentration on individual pillars. Rock bolts and shotcrete can also reinforce the rockmass, increasing its overall strength and stability. TAM does not account for these reinforcements, leading to a potentially conservative estimation of the pillar stress. In mining operations where extensive support systems are used, relying solely on TAM can result in overdesigned pillars, leading to unnecessary expenditure. A more comprehensive approach that integrates the effects of these support systems is necessary for an accurate assessment of pillar stability.

2.4.10 Overall observations on TAM limitations

TAM is a useful starting point for estimating pillar stress in room and pillar mining, but falls short in complex environments like the Great Dyke of Zimbabwe. Its simplifying assumptions—such as uniform load distribution, neglect of pillar interactions, and static, elastic behavior—can lead to inaccurate stress predictions and potential stability issues. TAM's limitations, including its inability to account for groundwater effects, temporal stress variations, and complex geological conditions, necessitate the integration of advanced numerical modeling, in situ measurements, and machine learning methods. These approaches offer more accurate and reliable assessments of pillar stress and overall mine stability. The failure of TAM to consider factors such as instantaneous load transfer, pillar shape effects, multi-level mining, and mining-induced stress changes further undermines its effectiveness. To ensure safer and more efficient mining operations, particularly in challenging settings like the Great Dyke, TAM should be complemented with detailed geological investigations, real-time monitoring, and advanced analytical techniques.

3 REFLECTIONS ON COATES’ METHOD

Coates ( 1981) introduced a formula for pillar load calculation, highlighting the limitations of TAM, which fails to incorporate geometric and rock properties (Alencar et al., 2023; George & Maji, 2024; Idris et al., 2015; Li, Cui, et al., 2023; Zvarivadza, 2012). To address this, Coates developed a more comprehensive approach that integrates these critical parameters. He noted that his formula is specifically applicable to the center of the mining area, particularly where there is an undisturbed long rib pillar, and the mine span does not exceed half the depth. The formula devised by Coates for calculating pillar load in deep and extended mining zones is detailed in Equation ( 16) (Zvarivadza, 2012).

𝐴 𝑃 𝑆 = 𝜎 v × [ 1 + 2 ⁢ 𝑒 ⁢ ( 1 + ℎ s ) − 𝑘 ⁢ ℎ s ⁡ ( 1 − 𝑤 + 𝑤 p ⁢ 𝑛 ) ℎ s ⁡ 𝑛 + 2 ⁢ ( 1 − 𝑒 ) ⁢ ( 1 + ℎ s ) + 2 ⁢ 𝑒 𝑏 ⁢ ( 1 − 𝑤 ) π ] , (16)

𝑒 = 𝐵 o 𝐵 o + 𝐵 p , 𝑘 = 𝜎 h 𝜎 v , 𝑤 = 𝑣 1 − 𝑣 , 𝑤 p = 𝑣 p 1 − 𝑣 p , 𝑛 = 𝐸 ⁢ ( 1 − 𝑣 2 p ) 𝐸 p ⁢ ( 1 − 𝑣 2 ) , 𝑏 = 𝐵 p 𝐿 , ℎ s = 𝐻 𝐿 ,

where APS is the average pillar stress. σ v is the vertical component of the virgin stress, MPa. e is the areal extraction ratio. H is the height of the stope, m. σ h is the horizontal component of the virgin stress, MPa. v is Poisson's ratio for abutments. v p is Poisson's ratio for pillars. E is Young's Modulus for abutments. E p is Young's Modulus for pillars. B o is the room width, m. B p is the pillar width, m. L is the width of the extraction span, m.

Coates recognized the need to factor in both the geometrical configuration of the mining area and the inherent properties of the rock, which TAM neglects. This advanced formulation considers the distribution of stress and strain more accurately, providing a reliable method for assessing pillar loads in complex geological settings. Coates ensured that the formula accounts for the stability provided by these structural elements by focusing on the undisturbed long rib pillar, which is crucial in maintaining the integrity of deep mining operations. The specific application to scenarios where the mine span is limited to half the depth ensures that the formula remains relevant to the most critical aspects of underground mining stability.

A derivation by Zvarivadza (2012) shows that Coates’ approach converges to the conventional TAM as the parameter L approaches infinity, as demonstrated in Equation (17).

When L → infinity, B p = 0, b = 0, and h s = 0 such that

𝐴 𝑃 𝑆 = 𝜎 v × [ 1 + 2 ⁢ 𝑒 ⁢ ( 1 + ℎ s ) − 𝑘 ⁢ ℎ s ⁡ ( 1 − 𝑤 + 𝑤 p ⁢ 𝑛 ) ℎ s ⁡ 𝑛 + 2 ⁢ ( 1 − 𝑒 ) ⁢ ( 1 + ℎ s ) + 2 ⁢ 𝑒 𝑏 ⁢ ( 1 − 𝑤 ) π ] ⁢ = 𝜎 v × [ 1 + 2 ⁢ 𝑒 ⁢ ( 1 + 0 ) − 0 0 + 2 ⁢ ( 1 − 𝑒 ) ⁢ ( 1 + 0 ) + 0 ] = 𝜎 v 1 − 𝑒 . (17)

A key observation made by Zvarivadza (2012) is that Coates’ method has a significant omission—it does not account for the stiffness of the overburden and the seam. These factors are critical in accurately determining the load on a pillar. The rigidity of the overburden influences the stress distribution across the mining area, while the seam stiffness impacts how the load is transferred through the pillar. Without incorporating these parameters, the formula may not provide a comprehensive assessment of pillar stability.

Coates acknowledged that although the rock properties for both pillars and abutments should theoretically be identical due to the shared material composition, practical conditions necessitate a distinction between the two. The abutments feature sharp edges, which lead to localized stress concentrations that are not present in the pillars. This stress concentration results in a variation in the stresses experienced by the pillars and the abutments, subsequently influencing their elastic modulus and Poisson's ratio. The stress concentration at the sharp edges of abutments causes a higher localized stress compared to the relatively uniform stress distribution in the pillars. This difference in stress distribution means that the abutments can deform differently under load, altering their elastic properties. The elastic modulus, a measure of the ability of a material to deform elastically (i.e., return to its original shape after the load is removed), is affected by the higher stress concentrations at the abutments. Poisson's ratio, which describes the ratio of lateral strain to axial strain, also differs between the two due to these stress variations. The practical implications of these differences are significant in the design and stability assessment of mining structures. Mining practitioners can more accurately predict the behavior of both pillars and abutments under load by recognizing the varying stress distributions and their effects on material properties, leading to safer and more efficient mining operations. Coates’ differentiation between the elastic modulus and Poisson's ratio for pillars and abutments highlights the importance of considering localized stress effects in engineering calculations, ensuring that theoretical models align more closely with real-world conditions.

3.1 Unique limitations of Coates’ method for determining pillar stress

Some of the unique limitations of Coates’ method are shown in Figure 12.

Coates’ method offers a significant advancement over TAM by incorporating some of the geometric configurations and rock properties into the calculation of pillar stress. However, despite its more comprehensive approach, Coates’ method has its unique limitations that must be considered when applying it to real-world mining operations. These limitations, distinct from those of TAM, include issues related to the specific application conditions, omission of certain critical factors, and practical challenges in distinguishing between properties of pillars and abutments.

3.1.1 Applicability to specific mining conditions

Coates’ method is designed with specific assumptions about the mining environment, particularly its application to the center of the mining area, where there is an undisturbed long rib pillar, and the mine span does not exceed half the depth. This constraint significantly limits the generalizability of the method to other mining scenarios. In mines where the span exceeds half the depth or where the rib pillar is disturbed or not present, the method may not provide accurate stress estimations. This specificity means that the method may not be universally applicable across all mining configurations, and deviations from these conditions can lead to significant errors in stress calculation. In contrast, TAM, with its broader applicability, does not impose such strict conditions, albeit at the cost of greater simplification.

3.1.2 Omission of overburden and seam stiffness

A critical limitation identified by Zvarivadza (2012) is Coates’ method's failure to account for the stiffness of the overburden and the seam. The stiffness of the overburden influences the stress distribution across the mining area, while the seam stiffness affects how the load is transferred through the pillar. These factors are vital for accurately determining the load on a pillar. Without considering these parameters, the formula may not provide a comprehensive assessment of pillar stability, especially in environments where the overburden and seam show significant stiffness variations. This omission can lead to an under- or overestimation of pillar stress, affecting the reliability of the design and safety assessments.

3.1.3 Complexity in differentiating material properties

3.1.4 Sensitivity to geometric variations

Coates’ method explicitly incorporates the geometric configuration of the mining area, including the room width, pillar width, and extraction span. While this enhances the accuracy of stress estimations for specific configurations, it also makes the method highly sensitive to geometric variations. Small inaccuracies in measuring these dimensions can lead to significant errors in the calculated stress. An error in determining the room width or extraction span could result in an incorrect assessment of the areal extraction ratio (e), leading to flawed stress predictions. This sensitivity necessitates precise surveying and measurement practices, which may not always be feasible in complex and variable mining environments.

3.1.5 Assumption of an undisturbed long rib pillar

The method assumes the presence of an undisturbed long rib pillar, which is crucial for maintaining the integrity of deep mining operations. However, in practical mining operations, it is often challenging to ensure that rib pillars remain completely undisturbed. Mining activities, natural geological processes, and human interventions can disturb these pillars, affecting their load-bearing capacity and the stress distribution in the surrounding area. The assumption of an undisturbed rib pillar may not hold true in many real-world scenarios, leading to potential discrepancies between the theoretical predictions of Coates’ method and actual conditions.

3.1.6 Empirical calibration requirements

Coates’ method, like many empirical approaches, relies on calibration with local data to determine the empirical constants and factors used in the equations. This dependence on empirical calibration can be a limitation in areas where such data are sparse or unavailable. The accuracy of the method hinges on the quality and relevance of the empirical data used for calibration. In new or less studied mining areas, the lack of appropriate empirical data can result in significant uncertainties and potential inaccuracies in stress estimations. This requirement for extensive calibration data makes the method less adaptable in areas with limited historical mining information.

3.1.7 Difficulty in accounting for complex geological features

While Coates’ method improves upon TAM by incorporating more detailed geometric and material properties, it still faces challenges in accounting for highly complex geological features such as complex fault systems, varying rock strata, and heterogeneous rockmasses. These geological complexities can significantly influence the stress distribution in a mining area, and their effects may not be fully captured by the method's equations. The presence of multiple intersecting faults can create localized stress concentrations and zones of weakness that are difficult to model accurately using Coates’ approach. Advanced numerical modeling techniques that can handle such complexities are often required to supplement the limitations of empirical methods like Coates’ formula.

3.1.8 Limited validation in diverse mining conditions

Coates’ method has been validated and applied primarily in specific mining contexts, particularly in the environments for which it was originally developed. However, its applicability and accuracy in a wide range of mining conditions, including different types of mineral deposits, varying depths, and diverse geological settings, remain less thoroughly validated. This limited validation can be a drawback when attempting to apply the method to new or significantly different mining conditions. Extensive field testing and validation across a broader spectrum of mining environments are necessary to ensure the method's strength and reliability in diverse contexts.

3.1.9 Inadequate representation of stress redistribution post-failure

While Coates’ method improves upon TAM by considering more detailed geometric and material properties, it does not fully capture the stress redistribution that occurs after a pillar fails. When a pillar fails, the load that it was bearing is redistributed to adjacent pillars and the surrounding rockmass. This dynamic process of stress redistribution can significantly affect the stability of nearby pillars and the overall integrity of the mining area. Coates’ method, being more static in nature, does not account for these post-failure stress redistributions, underestimating the risk of progressive failure and collapse.

3.1.10 Difficulty in modeling complex load paths

In mining environments, the load paths can be highly complex due to variations in rockmass properties, geological structures, and mining-induced changes. Coates’ method simplifies the load paths by assuming a relatively straightforward distribution of stress based on geometric and material properties. However, in reality, the presence of faults, joints, and other discontinuities can create complex load paths that are not easily modeled by Coates’ approach. This limitation means that the method may not fully capture the true stress distribution in highly complex geological settings, leading to potential oversights in stability assessments.

3.2 Overall observations on unique limitations of Coates’ method

While Coates’ method provides a more detailed and variegated approach to determining pillar stress by integrating geometric configurations and rock properties, it has unique limitations that set it apart from simpler methods like TAM. These limitations include its reliance on specific mining conditions, the omission of overburden and seam stiffness, and the complexity of differentiating material properties. Its sensitivity to geometric variations, the assumption of undisturbed long rib pillars, and the need for empirical calibration can impact its accuracy. The method also struggles with accounting for complex geological features and has limited validation across diverse mining conditions. To mitigate these limitations and enhance the reliability of the method, it is essential to use advanced numerical modeling, detailed geological investigations, extensive field validation, and machine learning approaches. Numerical modeling can simulate complex stress distributions and interactions, providing clarity that empirical approaches alone might miss. Detailed geological investigations are crucial for obtaining the accurate data needed for precise calibration and application of the method. Extensive field validation ensures that theoretical models are aligned with actual mining conditions, offering a strong framework for stress assessment. Machine learning approaches can recognize complex patterns in the mining operations data and accurately predict pillar stress and mine stability. Coates’ method can be adapted to provide more accurate and reliable stress predictions by addressing these challenges, ensuring safer and more efficient mining operations. This comprehensive approach not only improves the accuracy of stress assessments but also optimizes resource extraction while minimizing the risk of catastrophic failures. Ultimately, integrating advanced techniques with Coates’ method allows mining practitioners to better navigate the complexities of modern mining environments, ensuring the stability and safety of underground structures.

4 PRACTICAL IMPLEMENTATION OF AI ON THE GREAT DYKE TO ENHANCE PILLAR DESIGN

The implementation of AI approaches in pillar design for the Great Dyke of Zimbabwe is a significant advancement, offering improved accuracy, adaptability, and predictive capability in complex geological conditions. Given that the geotechnical environment of the Great Dyke is highly heterogeneous and structurally complex, featuring anisotropic rockmasses, variable orebody geometries, and discontinuities such as faults and shears that affect load transfer mechanisms, traditional analytical and empirical design methods, such as TAM and Coates’ method, are inadequate and often rely on oversimplified assumptions that inadequately capture the geological complexities, leading to conservative or unsafe pillar designs. Zvarivadza, Grobler, Rajpurohit, et al. (2025) implemented machine learning approaches (GBM, XGBoost, NGBoost, Random Forest, and AdaBoost) using 503 practically observed in situ pillars on the Great Dyke to support effective pillar design. The data set used in the comprehensive study comprises seven input parameters: depth below surface (DBS), actual panel width (APW), pillar length (PL), pillar width (PW), actual pillar area (APA), total area (TA), and actual extraction ratio (AER), with the target output being actual pillar stress (APS). Figure 13 shows the performance metrics of the models.

Among the evaluated models, GBM delivered the highest predictive accuracy, achieving the lowest mean squared error (MSE) of 0.3094 and the highest R2 score of 0.9958, indicating its superior performance in estimating actual pillar stress (APS) in the study. Realizing the critical importance of rockmass quality in pillar design, Zvarivadza, Lawal, et al. (2025) developed a deep learning approach for estimating Q from rock mass rating (RMR) parameters, eliminating the need to use the two rockmass classifications independently, greatly reducing field work. An artificial neural network (ANN) model was developed for this. Two independent optimization algorithms were applied to the ANN, that is, the flow direction optimization algorithm (FDA) and the sine–cosine optimization algorithm (SCA). The Chord diagram shown in Figure 14 facilitated model ranking, while the class activation map (CAM) identified the most influential parameters affecting the RMR output. The achieved overall R2 scores for the ANN, FDA–ANN, and SCA–ANN models were 0.9951, 0.9960, and 0.9955, respectively, with corresponding mean absolute error values of 0.099, 0.096, and 0.085. Among the evaluated models, FDA–ANN demonstrated superior predictive accuracy compared to both ANN and SCA–ANN approaches.

Lawal et al. ( 2025) developed an ANN mathematical model to directly predict Q from its parameters (rock quality designation [RQD], joint set number [ J n], joint roughness number [ J r], joint alteration number [ J a], joint water number [ J w], and stress reduction factor [ SRF]) using practically observed rockmass characterization data from the Great Dyke of Zimbabwe. The developed ANN equation is presented in Equation ( 18) with the Q input parameters normalized to be between −1 and 1 to alleviate overfitting.

𝑄 A N N = 2 . 3 ⁢ t a n h ⁡ ( 𝑛 ∑ 𝑖 = 1 𝑥 𝑖 − 0 . 1 5 8 2 9 8 ) + 2 . 7 , (18)

where x 1 to x 8 are presented below

𝑥 1 = − 2 . 3 3 8 6 ⁢ t a n h ⁡ ( − 0 . 0 3 0 5 4 ⁢ 𝐽 n + 0 . 7 0 3 0 8 ⁢ 𝐽 a + 0 . 9 1 5 9 1 ⁢ 𝑆 𝑅 𝐹 − 0 . 0 5 5 7 2 8 ⁢ 𝐽 r − 0 . 7 0 2 7 9 ⁢ 𝑅 𝑄 𝐷 − 0 . 2 5 1 8 5 ⁢ 𝐽 w − 0 . 6 4 4 9 6 6 ) ,

𝑥 2 = = 2 . 6 5 4 7 9 ⁢ t a n h ⁡ ( 0 . 0 2 4 3 8 ⁢ 𝐽 n + 0 . 8 4 7 9 ⁢ 𝐽 a + 0 . 1 4 0 8 4 9 ⁢ 𝑆 𝑅 𝐹 + 0 . 3 8 1 6 7 4 ⁢ 𝐽 r − 0 . 7 1 6 2 6 2 ⁢ 𝑅 𝑄 𝐷 − 1 . 1 0 5 0 3 ⁢ 𝐽 w − 2 . 4 3 1 7 2 7 ) ,

𝑥 3 = − 3 . 5 8 9 3 4 3 ⁢ t a n h ⁡ ( − 0 . 1 1 1 8 1 ⁢ 𝐽 n + 0 . 6 4 9 3 ⁢ 𝐽 a − 5 . 1 2 5 6 7 ⁢ 𝑆 𝑅 𝐹 + 3 . 4 7 3 4 8 ⁢ 𝐽 r − 1 . 4 1 7 4 2 ⁢ 𝑅 𝑄 𝐷 + 3 . 9 9 7 1 2 ⁢ 𝐽 w + 1 . 0 8 3 7 0 8 ) ,

𝑥 4 = 1 . 6 3 5 6 5 ⁢ t a n h ⁡ ( 0 . 0 1 2 8 1 ⁢ 𝐽 n + 0 . 2 9 7 9 4 ⁢ 𝐽 a + 0 . 0 8 3 6 2 ⁢ 𝑆 𝑅 𝐹 − 0 . 7 0 2 7 4 ⁢ 𝐽 r + 0 . 6 2 1 5 7 ⁢ 𝑅 𝑄 𝐷 + 0 . 3 4 5 0 1 ⁢ 𝐽 w − 0 . 0 3 2 0 4 ) ,

𝑥 5 = 2 . 1 3 8 3 6 ⁢ t a n h ⁡ ( 0 . 0 2 3 6 4 ⁢ 𝐽 n + 1 . 0 9 0 9 2 ⁢ 𝐽 a + 0 . 4 5 3 8 6 ⁢ 𝑆 𝑅 𝐹 + 0 . 0 6 9 9 1 ⁢ 𝐽 r − 2 . 6 4 1 2 8 1 ⁢ 𝑅 𝑄 𝐷 − 0 . 3 2 7 7 7 ⁢ 𝐽 w − 1 . 3 0 9 6 1 ) ,

𝑥 6 = − 2 . 7 4 9 0 5 9 ⁢ t a n h ⁡ ( − 0 . 0 0 5 5 9 ⁢ 𝐽 n + 0 . 9 7 2 2 7 ⁢ 𝐽 a − 0 . 5 1 3 5 5 ⁢ 𝑆 𝑅 𝐹 − 0 . 0 3 8 3 7 ⁢ 𝐽 r − 2 . 2 0 8 8 2 ⁢ 𝑅 𝑄 𝐷 + 0 . 3 1 9 1 7 ⁢ 𝐽 w − 1 . 4 0 2 4 7 8 )

𝑥 7 = − 4 . 9 1 1 0 6 ⁢ t a n h ⁡ ( − 0 . 2 3 7 8 1 ⁢ 𝐽 n − 0 . 4 4 7 1 1 ⁢ 𝐽 a + 0 . 5 7 1 8 4 ⁢ 𝑆 𝑅 𝐹 + 0 . 5 8 7 6 7 ⁢ 𝐽 r + 2 . 7 7 1 3 9 7 ⁢ 𝑅 𝑄 𝐷 − 1 . 0 6 1 0 5 ⁢ 𝐽 w − 1 . 1 3 8 0 6 ) ,

𝑥 8 = 0 . 7 5 5 8 3 ⁢ t a n h ⁡ ( − 0 . 0 7 4 5 8 ⁢ 𝐽 n − 0 . 7 1 2 8 9 9 ⁢ 𝐽 a + 3 . 6 3 4 0 6 ⁢ 𝑆 𝑅 𝐹 − 0 . 6 2 8 5 4 ⁢ 𝐽 r − 0 . 9 8 9 5 1 ⁢ 𝑅 𝑄 𝐷 + 0 . 0 5 3 2 4 ⁢ 𝐽 w + 3 . 3 7 9 6 9 ) .

In the study, a graphical user interface (GUI) (Figure 15) was developed to enable easy use of the developed ANN product by field practitioners who often do not have a deep AI background.

Accurate rockmass classification is fundamental in pillar design. Traditional empirical methods, such as the Q-system and RMR, are widely used but require time-consuming and expert-dependent assessments. AI models capture complex nonlinear relationships between key rockmass attributes (e.g., RQD, joint set number, joint roughness, joint alteration, and groundwater conditions) and the Q or RMR output. The models demonstrate exceptional predictive accuracy and generalizability, as observed from the performance assessment, making them reliable surrogates for field-intensive classification. For pillar design, the automated and high-accuracy approach to Q or RMR estimation allows for rapid, consistent, and scalable integration of geotechnical inputs into numerical models and machine learning algorithms used for stress prediction. Since Q and RMR are directly linked to rock strength, deformability, and failure characteristics, their accurate estimation is crucial for determining pillar load-bearing capacity, factor of safety, and deformation response. AI-powered classification tools also support real-time assessments when integrated with digital data acquisition systems, enabling dynamic updates to pillar design as mining progresses or geological conditions change. For the complex Great Dyke lithological variations and adverse ground conditions, AI models provide a practical solution to enhance geotechnical input reliability. They improve decision-making in pillar dimensioning, sequencing strategies, and support system optimization. The models also lay the foundation for broader AI integration into pillar design workflows, ensuring safer and more efficient underground mining operations.

Artificial Intelligence approaches like machine learning, artificial neural networks, and deep learning models offer the capacity to extract patterns and relationships from large, multi-dimensional geotechnical datasets that would be difficult to uncover using conventional techniques. Models such as Random Forests, gradient boosting machines, and extreme gradient boosting have demonstrated high accuracy in stress classification, regression, and failure prediction tasks. These models are capable of handling non-linear relationships among variables like pillar width-to-height ratio, mining depth, rock strength, and in situ stress conditions. Deep learning architectures, including artificial neural networks, convolutional neural networks, and recurrent neural networks, allow for automatic feature extraction and improved modeling of time-series data such as stress changes during progressive excavation. Artificial intelligence methods, considering the Great Dyke, facilitate the development of predictive frameworks that integrate historical failure cases, numerical modeling outputs, and field instrumentation data to dynamically assess pillar stability. These data-driven systems can be continuously updated with real-time monitoring data, enabling adaptive support design and proactive risk management. The ability to generalize from past data while adapting to new conditions allows for more resilient and efficient pillar systems, thus enhancing safety, reducing operational costs, and improving ore recovery in structurally complex mining environments like the Great Dyke.

5 INTEGRATING ANALYTIC, NUMERICAL, AND MACHINE LEARNING APPROACHES FOR ENHANCED PILLAR STRESS PREDICTION AND REAL-TIME DECISION SUPPORT IN COMPLEX MINING ENVIRONMENTS

The evaluation of TAM and Coates’ method in the context of room and pillar mining on the Great Dyke of Zimbabwe reveals critical knowledge gaps that demand innovative solutions. While both methods offer analytical simplicity and ease of use, qualities desirable for preliminary or emergency design, they inherently rely on significant simplifications. TAM assumes a uniformly distributed vertical load and neglects complex factors such as geological heterogeneity, pillar interaction, and dynamic loading. Coates’ method, although more advanced, still lacks the capacity to account for real-time deformation, anisotropy, and stress transfer under evolving boundary conditions. These limitations have been clearly demonstrated in our study through both theoretical analysis and field-based observations.

While traditional analytic methods remain useful for rapid assessments, their use is increasingly confined to early-stage evaluations and emergency decision-making due to the limitations described. Numerical modeling techniques, such as the FEM and the DEM, on the other hand, are being adopted for detailed stress mapping and design optimization because of their ability to simulate complex stress redistribution, time-dependent deformation, and heterogeneous rock behavior. Despite the relatively longer setup and runtime, these methods offer the accuracy needed for deep-level mining in geologically complex regions like the Great Dyke. Design teams, in practice, often begin with analytic calculations and then validate or refine results using numerical tools, demonstrating a hybridized design philosophy in modern rock engineering.

To bridge the gap between accuracy and responsiveness, our study introduces a forward-looking framework that incorporates machine learning and real-time monitoring into the pillar design process. Unlike static analytic models, ML algorithms such as gradient boosting machines and XGBoost can be trained on historical and real-time geotechnical data, enabling dynamic stress prediction and rapid risk detection. These models can operate in near real time when linked with in situ monitoring systems such as stress meters and convergence sensors. Machine learning models trained on numerical outputs can act as surrogate models, predicting stress states faster without rerunning complex simulations. The integration of kriging or other spatial interpolation techniques further refines predictions, enabling spatially continuous stress mapping between monitored locations. This hybrid framework ensures that analytic simplicity, numerical depth, and predictive adaptability are leveraged holistically. Such integration allows for predictive alerts and rapid redesign actions based on data streams during the operational phase of mining. It can be noted that while analytic methods retain relevance for quick estimation, the incorporation of ML and real-time monitoring offers the agility and precision required for modern underground mine design, such as pillar design. This convergence is vital for managing geotechnical risks and ensuring pillar stability in structurally challenging environments like the Great Dyke.

6 CONCLUSIONS

The study critically revisits TAM and Coates’ method for mine pillar stress determination within the complex geological and geotechnical conditions of the Great Dyke in Zimbabwe. It highlights the significant limitations of these conventional methods, emphasizing their inability to fully account for stress redistribution, geological heterogeneity, and real-time operational conditions. TAM's simplifying assumptions—such as uniform load distribution and independent pillar behavior—make it inadequate for structurally complex mining environments. Coates’ method, while an improvement, remains limited in its applicability due to its reliance on rigid geometric constraints and lack of consideration for dynamic stress interactions. A key contribution of this study is its demonstration that empirical methods alone cannot ensure optimal pillar stability in challenging geological and geotechnical conditions of the Great Dyke of Zimbabwe. The research shows the necessity of integrating advanced numerical modeling techniques to simulate non-linear stress responses and dynamic load variations. The study also highlights the value of machine learning algorithms for improving predictive accuracy in pillar stress determination. The combination of numerical modeling and machine learning provides a hybridized framework that surpasses the predictive capabilities of traditional approaches. The practical importance of this study lies in its recommendations for optimizing pillar design on the Great Dyke, where mining-induced stress redistribution, anisotropic rock properties, and geological discontinuities significantly impact stability. It proposes that future mining operations adopt site-specific calibration of numerical models, integrate real-time monitoring systems, and leverage AI-driven stress prediction models to enhance decision-making in pillar design. The study also suggests that empirical methods should be complemented rather than replaced, ensuring that both traditional rock engineering principles and modern computational advancements are utilized for robust pillar design. This research advances the field of underground mining engineering by presenting a more comprehensive, adaptive, and data-driven approach to mine pillar stress determination. Implementing these methodologies will significantly enhance safety, optimize resource extraction, and minimize the risk of catastrophic failures in complex mining environments like the Great Dyke of Zimbabwe.

AUTHOR CONTRIBUTIONS

Tawanda Zvarivadza: Conceptualization; methodology; software; formal analysis; investigation; data curation; writing—original draft preparation; writing—review and editing; visualization; project administration; funding acquisition. Hendrik Grobler: Methodology; formal analysis; resources; supervision; funding acquisition. Peter Apata Olubambi: Methodology; formal analysis; investigation; supervision; funding acquisition. Moshood Onifade: Validation; formal analysis; resources, writing—review and editing; supervision; funding acquisition. Manoj Khandelwal: Validation; formal analysis; resources; writing—review and editing; supervision; project administration.

ACKNOWLEDGMENTS

The authors express their deep gratitude to the University of Johannesburg, South Africa, for the financial support of this research through the Global Excellence, Fourth Industrial Revolution research award.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

Biographies

Tawanda Zvarivadza is a mining engineer with a wide range of experience in the Rock Mechanics and Rock Engineering field, covering academia, practical hands-on open pit and underground mining, and consultancy. He is extensively published, with over 100 peer-reviewed journal and conference papers published at high-impact platforms in Africa, Asia, Europe, North America, South America, and Australia. Tawanda has held senior academic roles, including having served as a University Senate member in South Africa and Zimbabwe. He is a member of several international professional organisations, including the International Society for Rock Mechanics and Rock Engineering (ISRM—Lifetime member), the American Rock Mechanics Association (ARMA—Lifetime member), the Southern African Institute of Mining and Metallurgy (SAIMM), the South African National Institute of Rock Engineering (SANIRE), the Society of Mining Professors (SOMP), and the Golden Key International Honour Society (GKIHS—Lifetime member). Tawanda is the Lead Rock Engineer of Vimbo Consulting (Pty) Ltd.
Hendrik Grobler is an associate professor and head of the Mining Engineering and Mine Surveying Department at the University of Johannesburg, overseeing 21 staff and 800 students. He is a registered Professional Mine Surveyor with 19 years of mining industry experience, including 15 years as the responsible mine surveyor across various South African mining operations involving gold, uranium, platinum, chrome, nickel, and coal deposits. His industry roles encompassed mine planning, ore reserve valuation, sampling, survey network alignment, ore reconciliation, and forensic surveys. He specializes in gyro-theodolite surveying and sidewall station survey networks, with current research interests in laser scanning for documentation and monitoring, remotely piloted aerial systems (RPAS), and Virtual Reality applications aligned with Industry 4.0 educational standards. Hendrik previously served as President of the Institute of Mine Surveyors of South Africa. He holds National (Protea) colors in Kendo and Target shooting and represented South Africa internationally in both disciplines.
Peter Apata Olubambi obtained BEng (Hons) and MEng degrees in Metallurgical and Materials Engineering from the Federal University of Technology, Akure, Nigeria, and a PhD degree in Metallurgy at the University of the Witwatersrand, Johannesburg, South Africa. He is a research professor of Materials Engineering and currently the director of the Centre for Nanomechanics and Tribocorrosion. His research activities are focused on three key and interrelated fields of advanced materials processing: “Powder Metallurgy and Alloy Development,” “Tribocorrosion and Electrochemical Techniques,” and “Nanomechanics and Materials Characterisation.” His research efforts are centered on the utilization of innovative powder metallurgical techniques for developing nanoengineered materials for automotive, aerospace, microelectronics, mines, energy storage, chemical and allied industries, and for biomedical applications.
Moshood Onifade is an associate professor at the Institute of Innovation, Science and Sustainability, Federation University Australia. He has been recognized as a leading expert in mining engineering and his relevance in mining has been highlighted with support from the Coaltech Research Association of South Africa. Moshood has published over 90 peer-reviewed research papers in high-impact journals. His publishing background reflects his national and international standing and international engagement with a variety of researchers, industry, and stakeholders. Moshood has received several grants and awards, and he is a reviewer of scientific papers for different internationally accredited journals. He is a fellow of the Southern African Institute of Mining and Metallurgy (SAIMM), a registered engineer of the Council for the Regulation of Engineers in Nigeria (COREN), and a member of different professional associations. He has been ranked among the top 2% of scientists globally by Stanford University since 2021.
Manoj Khandelwal is an associate professor and program coordinator of Mining Engineering at Federation University Australia and a distinguished Australian Endeavour Fellow. With over two decades of academic and research experience in Australia and India, he is a leading expert in mining geomechanics and rock blasting. He has authored over 230 research papers, earning more than 9500 citations with an h-index of 54, and has been ranked among the top 2% of scientists globally by Stanford University since 2019. He has also published a technical book and completed several notable research and consultancy projects. His contributions have been recognized with prestigious awards, including the Young Scientist Award from the President of India and accolades from the Mining Engineers’ Association of India. Additionally, he serves on the editorial boards of several esteemed international journals, highlighting his influence and leadership in the field.