Experimental and Numerical Analysis on the Static and Dynamic Performance of Adhesive Bolts in Various Ground Conditions

Abstract

This study evaluates adhesive bolts (chemical anchors) bonded with epoxy and vinyl ester resins for surface and tunnel excavations in tropical mining environments under static and dynamic loading. Over 300 pull-out tests in concrete and hard rock examined the effects of bolt length, curing time, and substrate condition on load capacity, failure mode, and bond–slip response. Epoxy anchors exhibited higher bond strength, including under early-age and thermally active conditions, while vinyl ester showed improved ductility and post-peak behaviour in fractured rock. Numerical modelling with Rocscience RS2 (Phase 2) and Unwedge simulated excavation responses for bolt lengths of 190–250 mm and spacings of 0.5–2.0 m. Tensile failure dominated at wider spacings, whereas closely spaced anchors enhanced confinement and redistributed stresses. The combined experimental–numerical evidence quantifies chemical-anchor performance in complex subsurface settings and supports their use for early-age support and long-term stability. Findings motivate integration of resin-grouted bolts into modern support designs, particularly in seismically sensitive or hydrothermally variable mines.

1. Introduction

In this paper, we investigate adhesive bolts (chemical anchors) for tropical rock formations in underground mining and civil infrastructure. Rock reinforcement systems are crucial for stabilising excavations and ensuring safety under static and dynamic loading. Rock bolts and adhesive anchors are particularly valued for their adaptability and capacity to provide support in fractured and heterogeneous ground [1]. The expansion of mining and tunnelling into complex and tropical geological settings has driven demand for robust, high-performance reinforcement solutions [2]. Adhesive bolts, also known as chemical anchors, are now widely adopted due to their strong bond with diverse substrates, especially where mechanical anchors struggle [3]. Field and laboratory research has consistently demonstrated that adhesive anchors can outperform mechanical alternatives in fractured and variable ground conditions [4], provided installation is carefully controlled [5].

Experimental studies demonstrate that anchor performance in fractured rock is sensitive to bolt position, angle, and installation density [6], while field instrumentation reveals the complexity of stress transfer between the bolt, grout, and rock mass [7]. Laboratory and numerical investigations show that both axial and lateral restraint by bolts enhances the shear strength of joints, with optimal installation angles providing maximum strength [8]. Modern designs account for various failure modes, including tension, shear, and combined loading, as well as the impact of installation quality, rock mass variability, and environmental degradation [9,10,11,12]. The long-term performance of anchors, particularly in deep or humid environments, is a major consideration for tunnel safety and stability [11].

Anchoring effects in fractured rock are also determined by bolt type and pretension, influencing strength, residual capacity, and failure modes [5]. Deformation models for jointed rock masses account for elastic and crushing failure zones, showing how bolt diameter, anchorage angle, and rock strength affect the extent of crushing and yield modes [13]. Shear performance remains a critical factor, especially in jointed or fractured rock masses. Modern reviews and experiments demonstrate that shear resistance is governed by a combination of reinforcement, pin, and friction effects, as well as the normal stress and angle of installation [14]. Classic and recent research has clarified how fully grouted bolts transmit load, with failure often initiated at the grout–rock interface or along bolt ribs, and the presence of multiple shear surfaces increases complexity [10,12,14]. Durability and long-term integrity are increasingly emphasised in design. Factors such as corrosion, cyclic loading, hygrothermal changes, and bond deterioration are major drivers of anchor failure, especially in tropical climates with high humidity and aggressive groundwater [11,15]. Field investigations and long-term monitoring have prompted the adoption of new materials, such as corrosion-resistant coatings, polymer grouts, and non-metallic bolts [2].

Dynamic loading conditions present additional risks and uncertainties. Research has demonstrated that cyclic, seismic, and blast loading can induce progressive bond degradation, micro-cracking at the adhesive–substrate interface, and ultimately brittle or pull-out failure of anchors [16,17,18].

Negative Poisson’s ratio (NPR) bolts have emerged as effective supports in deep mining, increasing peak failure strength and energy absorption under disturbance loads [19]. D-bolts, a form of energy-absorbing bolt, demonstrate high deformation capacity and distribute load more evenly than conventional bolts, reducing premature failures in highly deformed tunnels [20]. Energy-absorbing and constant-resistance bolts represent a major innovation for dynamic conditions, where high deformation and impact loads are present. The CEF (compression–expansion–friction) bolt, for example, was developed to provide a controlled, constant resistance and accommodate large displacements, showing enhanced performance in both laboratory and finite element simulations [18]. These bolts absorb energy through controlled deformation or slippage, which is essential for stability in areas prone to seismic events or rock bursts [21]. Industry guidelines, codes, and manufacturer recommendations frequently fail to capture the challenges of fractured and variable ground in the tropics [22,23]. Additionally, practical in situ inspection and non-destructive testing of adhesive anchors is still an evolving field, with recent research on acoustic emission and electromagnetic methods showing promise but requiring further validation in tropical and mining environments [24,25].

Numerical and experimental comparisons of bond materials show that, while the bond type (resin, cement, polymer) affects strength, strata characteristics play a decisive role in performance [4]. Further, guided wave propagation and numerical methods are now being utilised to assess bond quality and detect defects in installed bolts [26]. Studies from China, Europe, and Australia have shown regional differences in rock mass response and anchor efficiency, underlining the need for locally validated models and protocols [27].

Advanced guided wave and acoustic emission methods are used for bolt integrity evaluation, providing new approaches for non-destructive testing of rock bolts [28]. Load distribution along anchor length and the interface between grout and rock have been quantified, revealing that the highest shear stress is near the bolt tip, and damage typically initiates where shear exceeds bond strength [29].

Yield-bolts, combining tension and compression elements, demonstrate superior bearing capacity and deformation properties, offering promise for challenging high-stress environments [30]. The performance of mechanical and friction-based bolts is also influenced by installation details, such as washer geometry and anchor tightening, highlighting the importance of construction quality control [31].

Research on glass fibre reinforced plastic (GFRP) bolts shows their efficacy in enhancing deformation modulus and strength in 3D-fractured rock, with optimal reinforcement at specific anchor angles [32]. In the realm of dynamic support, energy-releasing bolts such as the J-bolt provide controlled deformation and energy absorption under repeated impact, maintaining tunnel stability in seismic-prone areas [33].

Experimental models of non-persistent jointed rock confirm that bolts improve strength and change failure modes, particularly in rocks with intermediate joint angles [34]. Dynamic finite element analyses have advanced design for slopes supported with anchors, capturing the interaction of anchors and rock mass under earthquake loading [35].

The mechanical properties of bolts and anchoring agents are a focus for optimisation, with research indicating that stress concentrations are significant at thread bottoms and that matching grout and rod properties is essential for effective bonding [36]. Jointed rock masses reinforced with bolts show improved compressive strength, controlled crack propagation, and enhanced resistance to deformation, findings confirmed by both physical modelling and FLAC3D simulations [37].

Innovative approaches to bolt fixation, such as self-expanding mixtures, have demonstrated superior bearing capacity and energy absorption compared to traditional resin or cement-anchored bolts [38]. International field and laboratory research continues to diversify anchor technology and improve design protocols for variable, high-risk ground [39].

This breadth of research highlights the critical role of experimental and numerical studies in advancing anchor design for tropical, fractured, and intact rock conditions. By integrating laboratory and high-fidelity numerical modelling, using Phase 2 for surface mines and Unwedge for tunnels, this study aims to bridge gaps between laboratory, simulation, and field performance. The resulting synthesis supports safer, more effective design and deployment of adhesive bolts in the world’s most challenging environments [40,41].

The objectives of this study are: (i) to experimentally evaluate the static and dynamic performance of epoxy and vinyl ester adhesive bolts in tropical lateritic and weathered rock formations; (ii) to numerically simulate bolt behavior under excavation conditions using Rocscience RS2 and Unwedge; (iii) to investigate the influence of curing time, bolt length, spacing, and rock mass condition on bond strength; and (iv) to provide practical recommendations for the application of adhesive bolts in tropical mining and civil environments.

2. Materials and Methods

2.1. Laboratory Pull-Out Tests

Pull-out tests were performed at the UPAT laboratory to characterise the bond strength and failure modes of adhesive-bonded bolts installed in concrete (

Table 1. Summary of the test parameters for laboratory pull-out tests.

Parameter	Value/Range
Concrete strength	30–35 MPa
Hole diameter	18–22 mm
Bolt sizes	M16, M20
Curing time	12–24 h
Adhesive types	FIS V Plus, EM Plus
Loading rate	2 mm/min

). Standard concrete test blocks were prepared following SANS and ASTM standards for dimensions, curing, and compressive strength. Drill holes of 18–24 mm diameters were formed using rotary percussion drills, then cleaned using the blow–brush–blow protocol. Fischer chemical adhesives (FIS V Plus and FIS EM Plus) were injected using static mixers, and steel bolts (diameter sizes of 16–20 mm and lengths of 160–245 mm, respectively) were installed to manufacturer-recommended embedment depths. After the specified curing period (12–24 h, based on product and temperature), bolts were subjected to axial tensile loading using a calibrated hydraulic pull-out rig (see Figure 1). The load was applied at a constant displacement rate (2 mm/min), monitored via LVDT and load cell. Each sample was loaded to failure, defined by either a sudden loss of load or maximum system capacity. Failure modes, such as adhesive debonding, bolt yielding, or concrete breakout, were recorded.

All pull-out tests were performed in accordance with ASTM E488/E488M-18 (Standard Test Methods for Strength of Anchors in Concrete Elements) and ASTM D4435-13 (Standard Test Method for Rock Bolt Anchor Pull Test) to ensure consistency with international procedures. The adhesives tested were Fischer FIS EM Plus (epoxy-based) and Fischer FIS V 360 Plus (vinyl ester-based), both supplied by Fischerwerke GmbH and Co. KG, Waldachtal, Germany.

2.2. Static Field Test

Static pull-out tests were conducted at the Videx Mining Facility to evaluate the in situ performance of adhesive-bonded bolts in fractured and intact rock. Fifteen bolts (diameter 20 mm and length 245 mm) were installed into boreholes drilled and cleaned with high-pressure air and brushes. After injecting two-part resin adhesive with a static mixer, bolts were inserted to specified depths and allowed to cure under field conditions for 12–24 h.

Each bolt was tested using a portable hydraulic pull-out rig anchored to the rock surface (see Figure 2). Axial load was applied at a constant rate of 2 mm/min, with displacement monitored using a digital gauge. Testing continued until either pull-out, adhesive debonding, or bolt rupture occurred. For each test, peak load, displacement at failure, and failure mode were recorded.

Results were analysed to compare average bond strength and performance between fractured and intact rock. Key parameters are summarised in

Table 2. Key parameters for static field testing at Videx Mining Facility.

Parameter	Value/Range
Rock condition	Fractured/Intact
Hole diameter	18 mm, 24 mm
Bolt Diameters	16 mm, 20 mm
Bolt Lengths	160 mm, 245 mm
Number of bolts	15
Curing time	12–24 h
Loading rate	2 mm/min
Resin type	Two-part (standard vinyl ester and epoxy)

, and test setups are shown in Figure 2 and Figure 3.

2.3. Numerical Simulation Methodology

2.3.1. Rock Bolt Formulation in Phase 2

The numerical representation of adhesive-bonded bolts in this study was based on the robust theoretical models provided by the Phase 2 finite element software (Rocscience Inc., Toronto, ON, Canada). Four primary bolt types are available within Phase 2: end-anchored bolts, fully bonded bolts (which are directly applicable to chemical/adhesive anchors), plain-strand cable bolts, and shear bolts, such as Swellex systems. Given the focus of this research on the performance of adhesive anchors, the fully bonded bolt model was utilised throughout, as it most accurately reflects the load transfer and deformation mechanics observed in both laboratory and field tests of chemical anchors [42,43,44].

In this framework, end-anchored bolts are treated as deformable rods whose axial force $F$ is a function of axial displacement ($∆u$) at their endpoints, determined by the expression $F=K_b∆u$, where $K_b={\displaystyle \frac{AE}{L}}$, with $\mathit{A}$ denoting the cross-sectional area, $E$ the Young’s modulus, and $L$ the bolt length (see Figure 4). In contrast, fully bonded bolts are discretised into segments wherever the bolt crosses an element boundary within the mesh, with the force in each segment given by $F_e={\displaystyle \frac{AE}{L_e}}∆u_e$, where $L_e$ is the length of the segment and $∆u_e$ its elongation (Figure 5).

The force–elongation relationship for each bolt segment incorporates both yield and residual force plateaus (Figure 6), allowing each segment to yield independently, which is essential for accurately simulating load transfer and progressive failure along the embedded length of adhesive anchors.

Theoretical modelling of grouted/frictional systems (including Swellex) is governed by the equilibrium equation ${\displaystyle \frac{d^{2}u}{d{x}^2}}+{\displaystyle \frac{k}{AE}}\left(u_r-u\right)=0$, where $k$ is the interface shear stiffness per unit length, $u_r$ is the displacement of the surrounding rock, and $u$ the displacement of the bolt (Figure 7) [46,47,48,49] In all cases, bolts are defined in the model by specifying their start and end coordinates and are discretised to ensure full coupling with the surrounding mesh. The stiffness and force from each bolt segment are transferred to mesh nodes via transformation into local coordinates and application of appropriate shape functions, ensuring that the numerical solution remains stable and accurate across all loading increments. The bolt input parameters, such as length, diameter, Young’s modulus, and bond strength, were set to match those used in laboratory and field testing and are summarised in

Table 3. Input parameters for fully bonded adhesive bolts in Phase 2 modelling.

Parameter	Value
Bolt Type	Fully bonded
Bolt Length (m)	2.4
Bolt Diameter (mm)	20
Young’s Modulus (GPa)	210
Bond Strength (MPa)	1.3
Bolt Spacing (m)	2.0

.

Material properties for intact rock, fractured rock, grout, and steel were assigned using a combination of laboratory-derived values and published literature, as summarised in

Table 4. Material properties used in the Phase 2 simulation.

Material	Young’s Modulus (GPa)	Poisson’s Ratio	UCS (MPa)	Bond Strength (MPa)	Density (kg/m3)
Intact Rock	35	0.25	80	—	2700
Fractured Rock	18	0.28	20	—	2650
Grout/Adhesive	14	0.22	12	1.3	2000
Steel (bolt)	210	0.30	—	—	7850

. The rock mass was modelled using an appropriate constitutive law (Hoek-Brown or Mohr–Coulomb), while the adhesive was assumed to behave elastically up to failure. The bottom boundary of each model was fixed, side boundaries were horizontally constrained, and the top boundary was left free. A uniform initial stress field was imposed to replicate in situ stress conditions, with vertical and horizontal components scaled to the depth and field stress ratio. The values reported in Table 4 were derived from laboratory testing of lateritic and quartzite samples, supplemented by published data (Hoek and Brown [45]; Mashimo and Kamata [51] Bond strength values were calibrated against field pull-out results to ensure realistic simulation parameters

Adhesive bolts were installed in the models at 2.0 m centre-to-centre spacing, oriented perpendicular to excavation surfaces, with lengths and diameters consistent with those used in both the laboratory pull-out tests and field static tests (see Table 4). Loading was applied incrementally to simulate both static pull-out and long-term service conditions. Simulation outputs included displacement fields, axial bolt forces, and the distribution of yielding along the bolts, with results calibrated against laboratory and field data to ensure that the predicted load-displacement response and failure modes were consistent with observed behaviour.

A refined triangular finite element mesh was generated around the excavation and support locations, providing increased resolution where it was required (see Figure 8). The output from the simulations included detailed distributions of axial force along each bolt, as well as the displacement field for the surrounding groundmass (see Figure 9)

2.3.2. Phase 2 Numerical Simulation Procedure

Numerical analyses of surface mine excavations supported by adhesive bolts were conducted using Phase 2 finite element software (Rocscience Inc.). The aim was to simulate volumetric strain and total displacement of the material around open-pit or bench excavations, as well as the interaction between these excavations and any intervening pillars or abutments.

The geometry of surface excavations and intervening pillars was generated using field-measured dimensions, with all relevant coordinates input directly from site survey data. Model boundaries were defined to encompass both the excavation and the surrounding ground, as shown in Figure 10, which presents the mesh layout for two adjacent surface excavations separated by a yielding pillar.

The project settings, including initial and boundary conditions, were specified prior to launching the Phase 2 solver. This involved determining the number of computational iterations and convergence criteria to ensure robust simulation results. Boundary geometry and loading conditions were then established, with special attention given to the definition of boundary functions reflecting site-specific loading environments. For surface mining applications, these boundary functions can represent a range of in situ loading conditions, including those generated by equipment movement, excavation advance, or localised blasting activity.

Model discretisation followed, with a graded mesh applied to capture high-stress gradients near the excavation edges. A 3-noded triangular element was used for meshing, chosen for its numerical stability and effectiveness in resolving complex stress patterns in the vicinity of open excavations (see Figure 10). Key aspects of mesh refinement, element density, and local transitions were optimised through trial-and-error to balance computational efficiency and solution accuracy.

Boundary conditions were assigned to reflect field conditions: certain model boundaries were restrained, while others remained free to move. Tractions (representing external loading or unloading) were typically defined for free segments last and were specified for both horizontal and vertical directions as appropriate for the open pit or bench setting.

Subsequently, the field stress regime was established within the model. For surface mine simulations, a constant stress field was typically assumed, with both vertical and horizontal components distributed based on overburden weight and local in situ stress ratios. The precise values were calibrated according to measured site properties and previous field investigations.

The final step before running the simulation involved assigning material properties to the various zones representing excavations, pillars, and surrounding ground. Properties were selected based on laboratory testing and site-specific measurements, ensuring that both intact and fractured ground conditions were accurately represented in the model.

Once all model inputs were set, output parameters, including total displacement, volumetric strain, and support (bolt) forces, were selected for later analysis and interpretation. Upon solver convergence, model results were reviewed, allowing for the detailed evaluation of ground deformation, pillar performance, and the effectiveness of adhesive bolts in controlling movement within surface excavations.

2.3.3. Unwedge Numerical Simulation Methodology

The stability of potential rock wedges and the effectiveness of adhesive rock bolts in surface excavations were analysed using the Unwedge software (Rocscience Inc.), which enables comprehensive simulation of wedge formation, ground behaviour, and support performance in open pit slopes and surface mining benches. This methodology was designed to replicate field conditions encountered in tropical, fractured, and intact rocks and to directly correspond with the laboratory and field test protocols developed in this study.

Model geometry was based on typical bench or slope profiles found in surface mines, rather than tunnel sections. The surface excavation was defined with practical dimensions for height and width, reflecting actual conditions encountered at the Videx Mining Facility and similar field sites. Three principal joint sets were incorporated into the model, with their orientations and spacings established from site mapping and laboratory rock mass characterisation. These discontinuity sets were plotted on a stereonet to visualise wedge-forming intersections and the overall structural setting (see Figure 11). The bench geometry used in Unwedge was 10 m high and 8 m wide, with a slope angle of 60–70° based on field measurements. Joint orientations were 70°/37°, 85°/101°, and 48°/262°. The base bolt spacing was 2.0 × 2.0 m, which was subsequently varied as reported in Figures in Section 3.5, and is summarised in

Table 5. Input parameters used for Unwedge simulation.

Parameter	Value
Bench/Slope Height (m)	[10.0]
Bench Width (m)	[8.0]
Slope Angle (°)	[60–70]
Joint 1 Dip/Direction	70°/37°
Joint 2 Dip/Direction	85°/101°
Joint 3 Dip/Direction	48°/262°
Bolt Spacing (in/out plane)	2.0 m × 2.0 m
Principal Stress σ1 (MPa)	89
σ2/σ3 (MPa)	47/27

.

Geometry values are based on field survey at the test site, joint sets from scanline mapping, and in situ principal stresses from back-analysis. The 2.0 × 2.0 m spacing is the base case; spacing was varied in the parametric analyses shown in Figures in Section 3.5.

Adhesive bolts were modelled as fully bonded support elements with mechanical properties calibrated to the Fischer chemical anchors tested in the laboratory and field. Bolts were installed perpendicular to the exposed slope face, at a regular spacing of 2.0 m × 2.0 m, in accordance with best practice for surface excavation reinforcement and the protocols followed in this research.

The simulation process proceeded by first defining slope and joint geometry and verifying its accuracy against site data. Support installation was then simulated using bolt lengths, diameters, and strengths consistent with experimental and manufacturer specifications. For each scenario, Unwedge identified all kinematically detachable surface wedges that could form due to the intersection of the mapped joint sets with the bench or slope surface. For each wedge, the software computed its weight, geometry, initial factor of safety (FoS), and likely failure mechanism (sliding or toppling).

After establishing baseline conditions, adhesive bolt support was incorporated, and Unwedge recalculated the FoS and bolt load for each wedge. Simulation outputs included the distribution of bolt demand, the number of bolts intersecting each wedge, and the predicted locations of potential bolt tensile failures.

3. Results

3.1. Pull-Out and Bond Strength in Concrete

Laboratory pull-out tests were performed on adhesive-anchored bolts installed in standard concrete blocks to establish baseline performance characteristics for various resin systems and bolt sizes. The primary metrics evaluated included peak tensile load, displacement at peak load, bond strength, and failure mode for both vinyl ester and epoxy resins.

Figure 12 presents representative load-displacement curves for laboratory-tested bolts with different resin and diameter configurations. The curves show the characteristic stages of loading: initial stiffness gain, attainment of peak load, and subsequent post-peak softening, typical of adhesive anchorage systems. The vinyl ester resin generally exhibited higher peak loads than the epoxy systems for both 16 mm and 20 mm bolts, with the 20 mm vinyl ester anchors showing the highest overall capacity. Epoxy systems showed a more gradual post-peak decline compared to vinyl ester, indicating a different failure progression.

A summary of the mean peak load results for all laboratory configurations is provided in

Table 6. Summary of peak load results by configuration. Each row lists a unique resin–bolt–test combination. Laboratory entries summarise tests at 3, 7, 15 days of curing; field entries are in situ pull-out tests at the Videx Mining testing centre.

Resin System	Bolt Diameter (mm)	Bolt Length (mm)	Test Type	Curing Time (days)	Mean Peak Load (kN)	Std. Dev. (kN)	COV (%)	Notes
Vinyl ester resin	16	160	Lab	3, 7, 15	26.39	12.69	48.08	Laboratory pull-out
Vinyl ester resin	20	245	Lab	3, 7, 15	65.00	19.86	30.55	Laboratory pull-out
Epoxy resin	16	160	Lab	3, 7, 15	56.43	19.18	33.99	Laboratory pull-out
Epoxy resin	20	245	Lab	3, 7, 15	6.97	3.55	50.94	Laboratory pull-out
Vinyl ester resin	20	160	In situ	—	103.67	43.67	42.12	Field pull-out; Videx Mining testing centre
Vinyl ester resin	24	210	In situ	—	98.90	35.02	35.41	Field pull-out; Videx Mining testing centre
Epoxy resin	20	350	In situ	—	118.17	37.63	31.84	Field pull-out; Videx Mining testing centre
Vinyl ester resin	10	90	In situ	—	8.12	5.40	66.51	Field pull-out; Videx Mining testing centre

. The vinyl ester resin 20 mm bolt system achieved a mean peak load of 65.0 kN with a coefficient of variation (COV) of 30.6%, while the 16 mm configuration reached 26.4 kN (COV = 48.1%). Epoxy resin systems with 16 mm bolts showed a mean peak load of 56.4 kN (COV = 34.0%), whereas the 20 mm epoxy system exhibited a markedly lower mean capacity of 7.0 kN, reflecting some inconsistent results and potential installation or curing effects.

Failure modes observed in the laboratory tests were predominantly adhesive, with most bolts pulling free from the cured resin, though a minority exhibited steel yielding or partial concrete breakout. Figure 13 illustrates a typical load-displacement curve from the tests, with images showing the progression from pre-load to progressive deformation and eventual localised necking, a signature of steel yielding. The staged nature of deformation highlights the complex interaction between adhesive bond and steel strength in determining anchor capacity.

Additional data on tensile and shear capacity development with curing time are summarised in

Table 7. Tensile and Shear Capacities for each anchor configuration.

Anchor System	Diameter × Embedment (mm)	Day 5 Tensile (kN)	Day 10 Tensile (kN)	Day 15 Tensile (kN)	Day 5 Shear (kN)	Day 10 Shear (kN)	Day 15 Shear (kN)
Epoxy	16 × 160	43	61	72	36	51	60
	20 × 245	65	92	108	54	77	90
Standard Vinyl ester	16 × 160	51	63	68	43	52	57
	20 × 245	77	94	102	64	78	85
High-bond Vinyl ester	16 × 125	44	57	62	36	47	52
	20 × 210	69	88	97	57	73	81

and Figure 14a; both epoxy and vinyl ester systems increased in tensile and shear strength as curing time progressed, with vinyl ester anchors consistently achieving higher early strengths. Figure 14b presents estimated shear capacities for all systems as a function of curing duration, further emphasising the rapid strength gain of high-bond vinyl ester formulations relative to epoxy.

Overall, laboratory and in situ results confirmed that adhesive anchor performance in concrete is highly sensitive to both resin type and bolt geometry. Vinyl ester resins offered superior bond strength and faster strength development, while the post-peak response and failure mode varied by both adhesive and steel configuration.

3.2. Static Pull-Out Performance in Rock

A series of 15 static pull-out tests was conducted at the Videx Mining Facility to evaluate the in situ performance of adhesive-bonded bolts under both fractured and intact rock conditions. Each bolt was 20 mm in diameter and installed to a bonded length of 250 mm, using either an epoxy mortar or a standard vinyl ester resin system. This section summarises the primary outcomes, peak pull-out force, maximum bond stress, displacement at failure, and observed failure mode, allowing comparison to laboratory benchmarks and insight into the effects of field variability.

The capacity of adhesive bolts arises from three interacting mechanisms: (i) adhesive bonding at the resin–rock interface; (ii) mechanical interlock with surface roughness and pores; and (iii) frictional resistance mobilised along the interface. The relative contribution of these mechanisms varies with resin type, curing time and rock integrity, and it explains the higher peak loads and larger displacements observed in intact rock compared to fractured rock.

The test results, summarised in

Table 8. Summary of field pull-out test results (20 mm diameter, 250 mm length bolts; n reported per grouping; values are means with ±1 SD where applicable).

Test No.	Rock Condition		Resin System		Peak Force (kN)	Max Stress (MPa)		Extension at Peak (mm)		Failure Mode
1	Fractured		Epoxy Mortar		38.1	149.8		0.2		Adhesive pull-out
2	Fractured		Epoxy Mortar		40.5	157.0		1		Adhesive pull-out
3	Fractured		Epoxy Mortar		43.2	165.5		1		Adhesive pull-out
4	Fractured		Epoxy Mortar		39.7	152.8		1		Adhesive pull-out
5	Fractured		Epoxy Mortar		36.8	145.1		0.3		Adhesive pull-out
6	Fractured		Epoxy Mortar		41.0	160.0		2		Adhesive pull-out
7	Fractured		Epoxy Mortar		37.5	147.8		1		Adhesive pull-out
8	Fractured		Epoxy Mortar		38.9	151.2		0.35		Adhesive pull-out
9	Intact		Vinyl ester Resin		70.1	275.4		7		Adhesive/ductile
10	Intact		Vinyl ester Resin		74.5	292.5		8		Adhesive/ductile
11	Intact		Vinyl ester Resin		75.2	295.4		8		Adhesive/ductile
12	Intact		Vinyl ester Resin		72.3	283.5		7		Adhesive/ductile
13	Intact		Vinyl ester Resin		77.4	303.7		8		Adhesive/ductile
14	Intact		Vinyl ester Resin		76.0	298.2		9		Adhesive/ductile
15	Intact		Vinyl ester Resin		71.8	281.6		7		Adhesive/ductile
Resin System		Rock Condition		n	Peak Force (kN)—Mean ± SD		Max Stress (MPa)—Mean ± SD		Extension at Peak (mm)—Mean ± SD
Epoxy Mortar		Fractured		8	39.5 ± 2.1		153.7 ± 6.8		0.86 ± 0.58
Vinyl ester Resin		Intact		7	73.9 ± 2.6		290.0 ± 10.1		7.71 ± 0.76

, demonstrate a consistent trend: bolts installed in fractured rock produced lower peak forces and maximum stresses than those placed in intact ground. For the epoxy mortar system in fractured rock, the mean peak pull-out force was approximately 39.5 kN, with individual results ranging from 36.8 to 43.2 kN. The standard vinyl ester resin system installed in intact rock yielded higher capacities, with a mean peak force of 73.9 kN and a range from 70.1 to 77.4 kN.

Displacement at peak load was generally minimal in fractured rock (mean: 0.8 mm) but significantly larger in intact rock (mean: 7.7 mm), reflecting greater energy absorption prior to failure. The observed failure mode for nearly all tests in fractured ground was adhesive pull-out whereas, in intact rock, a mixture of adhesive and ductile steel behaviour was recorded. Several fractured rock tests also showed evidence of resin loss into open joints, further reducing effective bond strength. It is also important to note that, in some fractured rock tests with the epoxy mortar, insufficient curing time contributed to reduced anchor performance.

The conservative WOF to peak is 17.2 ± 12.1 kN·mm for fractured rock with epoxy mortar (n = 8) and 285.7 ± 36.5 kN·mm for intact rock with vinyl ester (n = 7), consistent with markedly larger peak displacements in intact ground (see

Table 9. Work-of-fracture (WOF) to peak (kN·mm) computed as ${\displaystyle \frac{1}{2}}{P}_{peak}{\delta }_{peak}$. Values are mean ± 1 SD; n is the number of tests.

Resin System	Rock Condition	WOF (kN·mm)—Mean ± SD	n
Epoxy Mortar	Fractured	17.2 ± 12.1	8
Vinyl ester Resin	Intact	285.7 ± 36.5	7

).

A comparative distribution of peak pull-out forces for both resin types is shown in Figure 15, highlighting the clear separation between fractured and intact rock outcomes. Representative load-extension curves for fractured and intact rock are shown in Figure 16a and Figure 16b, respectively. The curve for fractured rock (Figure 16a) displays an early peak followed by a gradual, extended decline in load with increasing displacement, characteristic of adhesive pull-out failures where the bond is progressively lost along the bolt–resin interface. In contrast, the curve for intact rock (Figure 16b) demonstrates a pronounced peak and a relatively stable plateau at high load, followed by minor fluctuations, reflecting more ductile behaviour and efficient load transfer through the bolt and adhesive system. The distinct shapes of these curves further illustrate the impact of rock mass integrity on both the magnitude of peak load and the post-peak response of the anchor system.

Figure 16a shows that the fractured rock curve has no clear plateau, indicating rapid debonding at the resin–rock interface. In Figure 16b, the intact rock curve exhibits a plateau that extends to about 8 mm, showing the ductility advantage of the vinyl ester system in better-confined ground.

3.3. Numerical Simulation Results: Phase 2 (Surface Excavation)

3.3.1. Unsupported Surface Excavation

Numerical simulations were performed in Phase 2 to assess the response of the surface excavation under unsupported conditions. The analysis focused on three primary outputs: strength factor, ubiquitous joint factor, and volumetric strain, evaluated at key points across increasing depth within the excavation profile.

The simulation results for Stage 3 (final excavation stage) are summarised in

Table 10. Numerical outputs at selected points during Stage 3 (Unsupported Surface Excavation).

Point	Strength Factor	Ubiquitous Joints	Volumetric Strain	Depth (m)
A	0.78	0.068	0.012	3
B	0.82	0.13	0.024	10
C	0.85	0.91	0.028	13
D	0.91	0.78	0.027	15
E	1.04	0.52	0.018	18

, showing the strength factor, ubiquitous joint value, and volumetric strain at five control points (A–E) ranging from 3 m to 18 m in depth. As depth increases from the crest (Point A) toward the pit floor (Point E), a clear trend of improving stability is observed, as evidenced by the increasing strength factor (from 0.78 at 3 m to 1.04 at 18 m). This is visually reflected in the strength factor distribution plot (Figure 17), which indicates marginal stability near the crest and increasing safety with depth.

The ubiquitous joints parameter, indicative of joint intensity and its influence on rock mass response, exhibits a non-linear relationship with depth. High joint intensity is observed at intermediate depths, peaking at 0.91 at Point C (13 m), while lower values are recorded both near the surface and at the greatest depth (see Figure 18). This distribution suggests localised zones of weakness that may govern deformation and potential failure mechanisms.

Volumetric strain, shown in both tabular and graphical form (Table 10 and Figure 19), increases from the surface toward mid-depth, reaching a maximum at Point C (0.028), before decreasing at greater depths. The highest strain values coincide with zones of highest joint intensity, reinforcing the association between structural fabric and deformation concentration.

The spatial distribution of these simulation outputs is further illustrated in Figure 20a,b, presenting the modelled strength factor, ubiquitous joint factor, and volumetric strain across the excavation cross-section. Marginal zones of stability (strength factor < 1) are observed along the upper slope, particularly near the crest, where both jointing and strain localisation are most pronounced. In contrast, the pit floor and deeper sections display improved stability and lower strain, highlighting the stabilising effect of confinement with depth.

The trends identified in the present simulation, particularly the decrease in stability (strength factor < 1) near the crest and upper slope, the influence of joint intensity on deformation, and the improvement of stability with increasing depth, are consistent with prior numerical and empirical studies in open pit and slope stability analysis. Refs. [45,52] have shown that both the presence of ubiquitous joints and shallow depth are major contributors to localised strain and slope instability in unsupported excavations. Ref. [53] noted that slope zones with high joint frequency often experience amplified deformation and volumetric strain, consistent with the concentration of strain observed at intermediate depths (Point C) in the current model.

Moreover, the simulated increase in stability (strength factor exceeding 1) at greater depths aligns with field observations and finite element studies that report enhanced confining stresses and reduced deformation below the pit floor or slope base [54].

Despite these similarities, most previous studies have not systematically quantified the joint–strain relationship at multiple depths within tropical or highly jointed rock masses, nor have they provided detailed mapping of strain localisation as a function of both depth and joint intensity for unsupported surface excavations. By providing a stage-wise, point-specific analysis of strength factor, joint intensity, and volumetric strain, the present study addresses this knowledge gap and offers a more granular understanding of instability initiation in these settings.

In summary, the results obtained here corroborate existing findings regarding the critical role of shallow joints and surface effects on slope instability but extend the analysis by quantifying the interaction between jointing and strain at discrete depths. This approach provides new insight into the mechanisms of failure initiation and sets the stage for evaluating the impact of support systems, an area where limited field-validated numerical data exist in tropical or complex geological environments.

3.3.2. Supported Surface Excavation

The influence of epoxy-anchored rock bolts on the stability of surface excavations was analysed through numerical simulations of three representative bolt systems (see

Table 11. Summary of numerical outputs for supported excavation at key control points.

STAGE 3
Bolt No.	Bolt Type & Size	Load Capacity	Point	Strength Factor	Ubiquitous Joints	Volumetric Strain	Depth (m)
BOLT 1	Epoxy Resin, Length 245 mm, Diameter 20 mm	55,000 kN	A	0.9	0.0685	0	3
			B	1	0.1637	0.0275	10
			C	1.43	1.4436	0.033	13
			D	1.16	0.265	0.0385	15
			E	1.2	0.52	0.03575	18
BOLT 2	Epoxy Resin, Length 200 mm, Diameter 20 mm	35,000 kN	Point	Strength Factor	Ubiquitous Joints	Volumetric Strain	Depth (m)
			A	2.09	0.0675	0.0135	3
			B	1.16	0.2	0.0365	10
			C	1.5	1.4325	0.0455	13
			D	1.28	0.975	0.0495	15
			E	0.88	0.395	0.0315	18
BOLT 3	Epoxy Resin, Length 190 mm, Diameter 20 mm	25,000 kN	Point	Strength Factor	Ubiquitous Joints	Volumetric Strain	Depth (m)
			A	1.2	0.065	0.00675	3
			B	0.845	0.0975	0.135	10
			C	0.92	0.52	0.0495	13
			D	0.975	1.04	0.054	15
			E	1.04	0.78	0.0275	18

). Results indicate that the implementation of rock bolts led to a marked increase in the strength factor across most points in the slope profile, with values typically exceeding unity, particularly at mid- and lower-slope locations. This improvement is consistent with recent findings by Yu et al. [55] and Tomasone et al. [56], who showed that chemically anchored bolts substantially improve global stability and limit deformation in jointed rock masses.

The supported cases also exhibited lower values of ubiquitous joint activation and reduced volumetric strain (see Figure 21a–c), signifying mitigated risk of joint dilation and progressive failure, results that align with the field and numerical studies of Li et al. [57] and Wang et al. [58] who demonstrated that epoxy and resin-anchored bolts suppress joint opening and strain localisation in similar slope geometries.

Further, the simulations reveal that higher-capacity and longer bolts (Bolt 1: 245 mm, 55,000 kN; Bolt 2: 200 mm, 35,000 kN) provided superior reinforcement benefits compared to shorter/lower-capacity systems (Bolt 3: 190 mm, 25,000 kN). These trends support recent design optimisation studies by Zhao and Chen [59] and Baharvand and Hosseinitoudeshki [60], who highlighted the importance of tailored bolt length and capacity for maximising reinforcement efficiency in fractured slopes.

Visualisations of simulated outputs (Figure 22, Figure 23 and Figure 24) further demonstrate the effect of support, with unstable zones and strain localisation drastically reduced compared to the unsupported scenario. Similar outcomes were reported in recent regional case studies by Jodeiri Shokri et al. [29] and Manquehual et al. [61], who used advanced numerical models to show the efficacy of resin and epoxy bolts in limiting slope failure in complex, jointed ground.

In contrast to many earlier works, which often focus on temperate or controlled laboratory conditions, this study specifically addresses the performance of chemical anchors in surface excavations under the jointed, fractured, and climate-challenged environments typical of tropical regions. By combining a detailed numerical framework with field-informed parameters, these findings extend the understanding of bolt system behaviour in geologies where published case data remain scarce. This directly addresses the research gaps highlighted by Chen [9] and Hagen et al. [62], both of whom have called for more context-specific simulation and experimental results in tropical and weathered rock settings.

Overall, the results reinforce the consensus that epoxy-anchored and vinyl ester-based rock bolts are highly effective in improving slope stability in jointed and fractured ground, provided that the design is appropriately matched to site conditions, a conclusion in line with the recommendations of Tomasone et al. [56] and Li et al. [57].

3.3.3. Comparative Analysis of Supported vs. Unsupported Surface Excavations

The simulation results, presented in Figure 25a–c, illustrate a clear distinction between unsupported and supported surface excavation scenarios in fractured rock. In the unsupported state, strength factors across the measured depth are often at or just below the critical threshold of one, especially at shallow and intermediate depths. This suggests that, without reinforcement, the excavation is vulnerable to localised failure and instability. The high values observed for ubiquitous joints and volumetric strain in the unsupported scenario further confirm the likelihood of joint sliding and significant deformation, both of which are classic precursors to structural compromise in fractured rock settings.

By contrast, the introduction of resin-anchored bolts markedly improves the mechanical response of the excavation. The supported cases show a consistent increase in strength factor, frequently exceeding values of 1.2 and in some cases surpassing 2.0, especially at greater depths. This indicates a substantial enhancement in the stability and load-bearing capacity of the rock mass. Additionally, ubiquitous joint values are reduced, and volumetric strain is minimised throughout the depth profile, both of which point to improved integrity and reduced deformation.

Laboratory and numerical investigations, such as those by Aziz et al. [63], confirm that resin-grouted bolts significantly enhance peak load resistance and deformation control, with performance strongly dependent on bolt profile and installation conditions. Their results, supported by detailed simulations, show that the load transfer and failure mechanisms modelled in your study are robust and consistent with experimental findings.

Further, Spearing et al. [64] emphasise the critical need for feedback between field monitoring and numerical modelling in understanding bolt–rock mass interaction. Their validation of advanced bolt instrumentation under real mine conditions demonstrates that numerical models, when carefully calibrated, provide accurate predictions of in situ performance, mirroring this study’s integrated approach to simulation and field-applicable design.

Recent analyses by Tomasone et al. [56] further highlight the sensitivity of model predictions to input parameters derived from field pull tests. Their work, focusing on resin-grouted rock bolts in hard-rock mines, supports the finding that robust, site-specific calibration is essential for reliable prediction of excavation stability and that ignoring real-world input variability risks underestimating ground movement in unsupported cases.

In the context of slope and pit stability, Ko et al. [65] demonstrate the strong agreement between the discrete fracture network and anisotropic continuum modelling approaches for jointed rock masses. Their findings validate the effectiveness of the numerical techniques used in the analysis for capturing the impacts of discontinuities and support system installation on excavation stability.

Where this work adds unique value is in its direct, side-by-side comparison of supported and unsupported conditions using a full suite of mechanical response indicators (strength factor, joint behaviour, volumetric strain), as well as its detailed validation against multi-depth data and real-world simulation graphics. While many recent studies address either laboratory validation or field monitoring, relatively few provide such an integrated, graphical, and parameter-rich comparison, addressing the gap identified by Aziz and Jalalifar [63] and Spearing et al. [64] regarding the need for models that both predict and illustrate practical excavation behaviour across varied support scenarios.

In summary, this study not only confirms the substantial benefits of resin-grouted rock bolts for excavation stability, as established in current literature, but also advances the field by offering a transparent, visually validated method for comparing supported and unsupported surfaces. This approach enhances confidence in model outputs and provides a clear template for future design and validation work in surface mine and slope stability projects.

3.4. Numerical Simulation Results: Unwedge

3.4.1. Unsupported Tunnel Case

The Factor of Safety (FoS) is computed as the ratio of ultimate capacity to design load and is used here to compare spacing scenarios. The numerical simulation of wedge stability for the unsupported tunnel scenario reveals the presence of multiple wedge-shaped rock masses formed by the intersection of joint sets within the tunnel profile.

Table 12. Calculated Factor of Safety and Weights for Identified Wedges (Unsupported Tunnel Case).

Wedge ID	Location	Factor of Safety (FS)	Weight (Tonnes)
4	Lower-Right wedge	4.60	0.79
5	Upper-Left wedge	1.69	0.99
6	Roof wedge	2.64	3.10

presents the factors of safety (FoS) and the associated weights for key identified wedges, while Figure 26 provides a three-dimensional visualisation of their geometry and spatial relationships within the tunnel crown.

As depicted in Figure 26, the most critical wedge is the upper-left wedge (Wedge 5), with a factor of safety below 2, indicating marginal stability under current in situ conditions. The roof wedge, despite its larger mass, remains stable (FS = 2.64) but could become critical if conditions change, such as through additional excavation, blasting, or water infiltration.

Recent research demonstrates that the stability of unsupported wedges is highly sensitive to the geometry and orientation of intersecting joints, joint persistence, in situ stress conditions, and the presence of groundwater [66]. The findings here are consistent with recent numerical and physical modelling studies, which show that wedges formed by steeply dipping discontinuities often govern initial failure mechanisms in both tunnels and slopes [67,68]. Numerical simulations such as those using 3DEC software or DDA (discontinuous deformation analysis) consistently report that low factors of safety are associated with unfavourable joint orientations, closely spaced joints, and large wedge volumes [69,70].

In this study, the unsupported scenario illustrates the risk posed by potential wedge failures in tunnels lacking systematic support, especially when wedge geometry, joint persistence, and local loading conditions align unfavourably. As supported by literature, wedges with factors of safety below 1.5 are typically considered unstable or in need of immediate remediation [71]. The current findings thus highlight the critical importance of joint mapping, wedge identification, and preliminary numerical analysis in tunnel design and risk assessment.

These results also fill a gap by providing detailed, project-specific numerical data for wedge formation and stability in the context of surface excavations and near-surface tunnels, an area with less extensive reporting in the South African context, compared to more established literature on deep-level mining or alpine tunnel systems.

3.4.2. Supported Tunnel Case (Bolt Length of 190 mm)

As illustrated in

Table 13. Variation in Factor of Safety (FoS) and Wedge Weight for 190 mm Resin-Grouted Bolts at Different Spacings under Tunnel Support Conditions.

Bolt Length	Bolt Spacing	Wedge ID	Location	Factor-of-Safety (FS)	Weight (t)
190 mm	0.10 m	4	Lower-Right wedge	1258.48	0.787
		5	Upper-Left wedge	74.787	0.985
		6	Roof wedge	50.019	3.104
190 mm	0.50 m	4	Lower-Right wedge	35.783	0.787
		5	Upper-Left wedge	1.741	0.985
		6	Roof wedge	2.676	3.104
190 mm	1.00 m	4	Lower-Right wedge	14.446	0.787
		5	Upper-Left wedge	1.705	0.985
		6	Roof wedge	2.65	3.104
190 mm	1.50 m	4	Lower-Right wedge	25.936	0.787
		5	Upper-Left wedge	1.691	0.985
		6	Roof wedge	2.643	3.104
190 mm	2.00 m	4	Lower-Right wedge	14.446	0.787
		5	Upper-Left wedge	1.691	0.985
		6	Roof wedge	2.643	3.104

, the Factor of Safety (FoS) for the 190 mm bolts displays a pronounced decline as bolt spacing increases, affirming the critical role of support density. At 0.10 m spacing, extremely high FoS values are observed, notably 1258.48 for Wedge 4 and 74.79 for Wedge 5, indicating substantial over-reinforcement and redundancy under those conditions. However, as the spacing increases to 2.0 m, FoS values for the same wedges drop to 14.45 and 1.69, respectively, revealing a critical threshold beyond which the bolt system may become insufficient to stabilise the wedge geometry under dynamic loading scenarios. The roof wedge (Wedge 6) remains particularly vulnerable across all configurations, with FoS values hovering around 2.6, suggesting that gravitational and induced loads along the roof interface are less effectively mitigated without higher bond length or density.

These results confirm similar findings by Li et al. [72], who observed that closely spaced resin-grouted bolts improve both stability and redundancy in weak rock tunnels, which is consistent with the centrifuge test conclusion of Mashimo et al. [51] that tunnel-roof stability decreases sharply when bolt spacing exceeds about 1.5 m. Moreover, the data reinforce recent studies highlighting that wedge size, weight, and orientation (e.g., roof vs. wall) significantly influence failure risk and should inform optimal support design [73,74].

The 190 mm resin-grouted bolts were assessed as tunnel support elements under simulated excavation conditions with variable installation spacing (0.5 m, 1.0 m, 1.5 m, and 2.0 m), representative of practical support layouts in seismically sensitive mining environments. As illustrated in Figure 27a–d, the bolts demonstrate notable confinement benefits through stress redistribution across the tunnel arch, with peak performance observed at the 0.5 m spacing configuration. The simulated stress fields show a pronounced reduction in shear concentration around the tunnel periphery when bolts are densely installed, with noticeable deformation suppression in the crown and haunch regions.

Tensile failure was consistently observed as the dominant mode across all simulations involving 190 mm fully bonded bolts, regardless of spacing. This failure mode aligns with field-reported performance of short-embedment rock bolts in brittle or stratified geological settings, where axial tension often governs capacity due to abrupt load transfer zones [75]. Stress contour plots illustrate a progressive redistribution of load with decreasing bolt spacing, confirming that closely spaced supports (e.g., 0.5 m and 1.0 m) promote more uniform stress attenuation around the tunnel periphery. At wider spacings (≥1.5 m), however, distinct stress concentrations reappear at the excavation shoulders, coinciding with gaps in load transfer and reduced energy dissipation, an effect similarly noted by Zhang et al. [76] in stratified rock formations during tunnel construction. He et al. [77] further elucidates this phenomenon, demonstrating through analytical modelling that bolts with shorter embedment lengths are more susceptible to pull-out and premature debonding, especially when spaced too widely. These observations collectively underscore the necessity of optimising both embedment and spacing in support systems subjected to moderate dynamic disturbance, as typically encountered in tropical underground mines.

Notably, the 190 mm resin-grouted bolts demonstrated substantial stabilisation capacity when deployed at close spacings (≤1.0 m), a finding consistent with previous experimental and numerical studies suggesting that shorter bolts can provide effective confinement when arranged in tight arrays. For instance, Pullan et al. [78] observed that resin-grouted cable bolts installed in tighter boreholes retained comparable or superior performance compared to cementitious alternatives, particularly under immediate loading conditions. Similarly, Bajwa et al. [79] demonstrated through encapsulation tests that reduced bolt spacing significantly enhances local confinement and suppresses wedge dislocation in fractured media. While the absence of shear-induced damage across all simulations reinforces the predictability of axial failure mechanisms, the performance is highly reliant on sustained bond integrity. This is particularly critical under dynamic loading regimes [80], where repeated stress cycles may degrade the adhesive interface. It was highlighted that under rapid excavation closure scenarios, yielding resin bolts may experience progressive tensile degradation, especially in unsupported or partially supported tunnel crowns. Complementing this, Aziz and Jalalifar [63] emphasised that. under cyclic loading, the stress transfer efficiency in fully bonded bolts deteriorates with increasing strain history, underscoring the importance of bond durability and resin toughness. These findings affirm the suitability of short bolts in dynamic mine environments but call for robust resin formulations engineered to retain tensile performance under repetitive loading conditions.

The numerical simulations suggest that the 190 mm bolts are particularly effective in high-density support configurations, especially in excavation zones subject to vibration, seismic loading, or stress relaxation. At wider spacings, however, bolt performance becomes strain-localised, leaving critical arch segments vulnerable to deformation. This finding is consistent with previous optimisation studies that emphasise the importance of bolt pattern and density for ensuring uniform stress distribution and tunnel stability [81,82]. Recent work by Lu et al. [83] and Liu et al. [84] further demonstrates that shallow or fractured zones demand tighter bolt layouts to counteract rapid stress redistribution. These insights collectively underscore the necessity of coupling numerical tools with environment-specific support optimisation frameworks. The initial stiff segment reflects confinement build-up and bond activation. The subsequent plateau and gentle decline indicate progressive microcrack growth rather than sudden cone breakout, consistent with the observed failure mode at this spacing (Figure 28).

3.4.3. Supported Tunnel Case (Bolt Length of 200 mm)

Table 14. Variation in Factor of Safety (FoS) and Wedge Weight for 200 mm Resin-Grouted Bolts at Different Spacings under Tunnel Support Conditions.

Bolt Length	Bolt Spacing	Wedge ID	Location	Factor-of-Safety (FS)	Weight (t)
200 mm	0.10 m	4	Lower-Right wedge	1385.78	0.787
		5	Upper-Left wedge	82.088	0.985
		6	Roof wedge	55.613	3.104
200 mm	0.50 m	4	Lower-Right wedge	39.01	0.787
		5	Upper-Left wedge	1.747	0.985
		6	Roof wedge	2.679	3.104
200 mm	1.00 m	4	Lower-Right wedge	16.059	0.787
		5	Upper-Left wedge	1.708	0.985
		6	Roof wedge	2.652	3.104
200 mm	1.50 m	4	Lower-Right wedge	27.549	0.787
		5	Upper-Left wedge	1.691	0.985
		6	Roof wedge	2.643	3.104
200 mm	2.00 m	4	Lower-Right wedge	16.059	0.787
		5	Upper-Left wedge	1.691	0.985
		6	Roof wedge	2.643	3.104

below shows that. at the tightest bolt spacing of 0.10 m, the 200 mm bolts continued to demonstrate robust confinement efficiency across all wedge zones, with exceptionally high FoS values observed, most notably 1385.78 for the Lower-Right wedge (Wedge 4) and 82.088 for the Upper-Left wedge (Wedge 5). These results reinforce the performance trend established in the 190 mm case and further substantiate findings by Sun et al. [85] and Wang et al. [86], who associated closely spaced, short-length rock bolts with significant improvements in deformation resistance and overall excavation stability under dynamic-static coupled environments, in agreement with Sun et al. [85], who reported that increased bolt spacing reduces arching and accelerates bond degradation under repeated loading. The sharp contrast in FoS values between 0.10 m and wider spacings confirms that bolt density plays a decisive role in suppressing wedge mobilisation and distributing stresses evenly across the tunnel profile, especially in fractured rock under dynamic loading conditions.

However, as bolt spacing increases to 1.5 m and 2.0 m, FoS values for the same wedges decline sharply, falling to as low as 1.691 for Wedge 5 and 2.643 for the Roof wedge. This progressive reduction aligns with findings by Tang et al. [87], who noted that bolt spacing is the dominant variable influencing stability, particularly in weak or fractured zones, as the system becomes susceptible to stress localisation and differential displacement between support zones.

Figure 28a–d depicts the evolution of stress redistribution and bolt interaction across varying bolt spacings for the 200 mm support system. In Figure 28a (0.5 m spacing), the simulation shows a dense and uniformly distributed bolt pattern along the tunnel crown and walls, with stress contours suggesting effective confinement and minimal strain localisation, closely mirroring the favourable conditions observed with the 190 mm bolts at similar spacing. However, as the spacing increases to 1.0 m (Figure 28b), early signs of strain localisation begin to emerge, particularly near the shoulder zones, where the bolts no longer uniformly engage the surrounding rock. By 1.5 m spacing (Figure 28c), this pattern becomes more pronounced, with visibly reduced confinement near the upper-left and crown wedges. Finally, at 2.0 m spacing (Figure 28d), the stress field becomes increasingly anisotropic, with clear zones of stress concentration forming along the roof and sidewalls, conditions that signal diminishing energy dissipation and elevated pull-out susceptibility.

Figure 28a–d depicts the evolution of stress redistribution and bolt interaction across varying bolt spacings for the 200 mm support system. In Figure 28a (0.5 m spacing), the simulation shows a dense and uniformly distributed bolt pattern along the tunnel crown and walls, with stress contours suggesting effective confinement and minimal strain localisation, closely mirroring the favourable conditions observed with the 190 mm bolts at similar spacing. However, as the spacing increases to 1.0 m (Figure 28b), early signs of strain localisation begin to emerge, particularly near the shoulder zones, where the bolts no longer uniformly engage the surrounding rock. By 1.5 m spacing (Figure 28c), this pattern becomes more pronounced, with visibly reduced confinement near the upper-left and crown wedges. Finally, at 2.0 m spacing (Figure 28d), the stress field becomes increasingly anisotropic, with clear zones of stress concentration forming along the roof and sidewalls, conditions that signal diminishing energy dissipation and elevated pull-out susceptibility.

Compared to the 190 mm bolt simulations, the 200 mm bolts demonstrate improved local anchorage capacity at tighter spacings, but also a sharper decline in performance when spacing exceeds 1.0 m. These trends align with those of Mashimo et al. [51], who reported that bolt effectiveness declines rapidly beyond critical spacing thresholds under dynamic conditions, and Sun et al. [85], who emphasised the importance of high bolt density in controlling deformation in fractured media. Importantly, the simulation outputs affirm that tensile failure remains dominant, even in longer bolts, as the stress transfer mechanism becomes increasingly sensitive to spacing irregularities. These findings highlight that, while extending bolt length marginally improves confinement at lower densities, optimal performance still depends on achieving a critical spacing-to-length ratio, especially in geologies characterised by complex wedge geometries and dynamic stress perturbations.

3.4.4. Supported Tunnel Case (Bolt Length of 250 mm)

The performance of the 250 mm bolts across varying spacing conditions reveals nuanced interactions between bolt density and wedge stability under dynamic loads. As shown in

Table 15. Variation in Factor of Safety (FoS) and Wedge Weight for 250 mm Resin-Grouted Bolts at Different Spacings under Tunnel Support Conditions.

Bolt Length	Bolt Spacing	Wedge ID	Location	Factor-of-Safety (FS)	Weight (t)
250 mm	0.10 m	4	Lower-Right wedge	2095.00	0.787
		5	Upper-Left wedge	124.336	0.985
		6	Roof wedge	87.37	3.104
250 mm	0.50 m	4	Lower-Right wedge	39.01	0.787
		5	Upper-Left wedge	1.747	0.985
		6	Roof wedge	2.679	3.104
250 mm	1.00 m	4	Lower-Right wedge	24.13	0.787
		5	Upper-Left wedge	1.723	0.985
		6	Roof wedge	2.66	3.104
250 mm	1.50 m	4	Lower-Right wedge	27.549	0.787
		5	Upper-Left wedge	1.691	0.985
		6	Roof wedge	2.643	3.104
250 mm	2.00 m	4	Lower-Right wedge	17.059	0.787
		5	Upper-Left wedge	2.691	0.985
		6	Roof wedge	3.643	3.104

, the highest Factor-of-Safety (FoS) values are achieved at the densest configuration of 0.10 m spacing, where the Lower-Right wedge (Wedge 4) reaches a remarkable FoS of 2095.00 and the Upper-Left wedge (Wedge 5) stabilises at 124.34. These values underscore the strong influence of bolt proximity on load redistribution and confinement, particularly in zones with high geometric discontinuity and mass asymmetry.

At a spacing of 0.5 m (Figure 29a), effective stress distribution remains evident, with minimal concentration around Wedges 5 and 6, supported by FoS values of 1.747 and 2.679, respectively. These results align with previous findings that dense bolt arrays reduce stress gradients and inhibit wedge mobilisation [85].

However, as spacing increases to 1.0 m (Figure 29b), the structural performance begins to degrade, as reflected in the corresponding FoS values in Table 15. Both Wedges 5 and 6 fall below critical thresholds for dynamic resilience, with observed values of 1.723 and 2.66, respectively. The emergence of tensile-dominated stress zones and decreased load continuity suggests reduced confinement integrity, echoing findings from dynamic bolt performance evaluations under seismic vibration regimes [88].

By 1.5 m spacing (Figure 29c), stress redistribution appears increasingly erratic, with patchy bolt engagement and renewed concentrations near the shoulder zones. Despite the Roof wedge (Wedge 6) maintaining a FoS of 2.643, Table 15 indicates reduced overall system redundancy, especially for Wedge 5 (FoS = 1.691). The trend reflects the diminishing efficiency of longer bolts in offsetting increased spacing, a pattern similarly documented in seismic centrifuge models and field monitoring of deep tropical tunnels [89].

3.4.5. Interface Microcrack Evolution Under Dynamic Loads

Under dynamic excitation, wider bolt spacing interrupts continuous stress transfer along the reinforced rock mass. This discontinuity promotes the initiation and penetration of interface microcracks, which reduces effective bond strength and accelerates stiffness loss. The Unwedge results reflect this trend; for example, FoS decreases from 1.723 at 1.0 m spacing to 1.691 at 1.5 m spacing, indicating a measurable reduction in stability with increasing spacing under dynamic conditions. These observations are consistent with the interface-damage mechanism inferred from the load-displacement plateaus and post-peak softening.

3.5. Verification of Numerical Results with Ground Reaction Curve Simulation

To further validate the trends observed in the RS2 numerical simulations, a complementary modelling approach was implemented using ground reaction and support reaction analysis. This method, which simulates the interaction between tunnel deformation (convergence) and the reactive load of the installed support system, offers a well-established analytical framework in rock mechanics, particularly for preliminary support design assessment. The output includes Ground Reaction Curves (GRCs) alongside corresponding support pressure curves, which help evaluate the equilibrium state and performance reliability of the support system under varying configurations.

Figure 30, Figure 31 and Figure 32 present the results of GRC simulations for bolt spacings ranging from 0.1 m to 2.5 m. At lower spacings, 0.1 m and 0.5 m (see Figure 30a,b), support activation occurs early in the deformation process, maintaining system stability with minimal tunnel convergence (0.88% and 0.90%, respectively) and high Factors of Safety (FoS) of 116.37 and 6.24. As bolt spacing increases to 1.0 m and 1.5 m (Figure 31a,b), support activation becomes more delayed, leading to moderately increased convergence (0.94% and 0.96%) and reduced FoS (2.44 and 1.87). This trend continues in Figure 32a,b, where the widest spacings, 2.0 m and 2.5 m, exhibit the most delayed support engagement and largest tunnel convergence values (0.96% with corresponding FoS dropping to 1.77 and 1.76.

These results align well with the finite element results from RS2, confirming that bolt spacing is a dominant control parameter in support system responsiveness and effectiveness. Tighter spacing provides greater confinement and faster load uptake, reducing deformation and increasing stability, while wider spacing compromises both the timing and magnitude of support contribution.

This simulation technique serves not only as an independent means of assessing tunnel stability but also as a robust cross-validation framework for 3D numerical methods. Recent studies, such as those of Heidari et al. [90] and Oraee et al. [91], have emphasised the utility of ground reaction curves for evaluating excavation-induced deformation and stress redistribution, particularly in soft rock and jointed media. Similarly, Godio et al. [92] leveraged ground reaction simulations in conjunction with empirical design charts to assess support performance under high-stress tunnelling conditions. These investigations demonstrate that GRC-based methods can provide credible performance predictions, especially when integrated with multivariate analyses as undertaken in this study.

By applying this method in parallel with finite element models, this chapter reinforces the reliability of the observed support behaviour trends and highlights the broader applicability of combining analytical and numerical tools in predicting the Factor of Safety in chemically anchored support systems.

4. Discussion of Findings

This study evaluated epoxy- and vinyl ester-bonded chemical anchors under static and dynamic loading in fractured and intact rock using a hybrid programme of laboratory pull-out tests and numerical simulations (Phase 2 and Unwedge). Results from both methods were consistent, indicating that the selected anchors provide robust reinforcement for demanding mining conditions. In static tests, epoxy anchors achieved higher peak load and bond stiffness than vinyl ester, and bond integrity was retained even in fractured rock, aligning with reports of superior ductility and energy dissipation for epoxy when embedment is optimised [93]. Phase 2 simulations showed progressive stress redistribution near excavation boundaries; introducing support, especially at ≤1 m spacing, improved bolt mobilisation, limited wedge detachment, and reduced tensile failures, consistent with pre-tensioned resin anchor behaviour across rock moduli [94]. Unwedge analyses confirmed that dense spacing (0.5–1.0 m) maintained wedge stability with FoS above critical thresholds, whereas ≥1.5 m spacing reduced bolt participation and reintroduced instability, in agreement with centrifuge observations on spacing effects [51]. Thermal sensitivity remains relevant in tropical settings, with 6.6–31.3% bond-strength losses reported at elevated temperatures [95]. Minimal plasticity at close spacing and extensive yielding at wider spacing mirror earlier FEM trends and support long-term performance predictions [96]. The novelty lies in integrating experimental pull-out behaviour with 3D stress-mapped simulations for both surface and tunnel geometries, including verification under dynamic load transitions; this hybrid approach strengthens the generalisability of the findings across geological contexts.

5. Conclusions and Recommendations

This paper demonstrates that adhesive bolts (chemical anchors) provide reliable reinforcement in demanding mining conditions, including fractured rock, dynamic loading, and elevated temperatures. Across laboratory pull-out tests and RS2/Unwedge simulations, epoxy systems showed greater mechanical resilience (higher peak capacity/stiffness and better thermal tolerance) than vinyl ester, while closer bolt spacing (≤1.0 m) consistently improved load sharing and wedge confinement. Short-length anchors (≈190–250 mm) were effective when correctly embedded and spaced, limiting tensile failure and stress-concentration propagation. Numerical results reproduced the observed mechanisms (bond mobilisation, plateau/softening, spacing effects) and provided predictive insight across geometries and stress regimes. Overall, the combined evidence supports the routine use of adhesive bolts in tropical mining settings, with clear benefits for structural integrity, safety, and durability.

Recommendations

• In fractured or highly stressed ground, keep bolt spacing ≤ 1.0 m; use the tighter end where wedges are asymmetric or seismicity is expected.
• Resin selection: Epoxy for high-temperature and long-term static/cyclic loads; vinyl ester where early-age strength is the priority.
• Short anchors (≈190–250 mm) are suitable if holes are well cleaned, fully bonded, and adequately confined.
• Calibrate RS2/Unwedge models with site pull-out data; explicitly include rock-mass classification, joint persistence, and stress anisotropy.
• Account for curing time, bond–slip behaviour, and temperature/humidity in design checks and factor selection.
• Plan in situ performance monitoring to validate designs; encourage updates to codes/guidelines to reflect resin-specific behaviour and spacing optimisation under dynamic interaction.