Behavior Of Pillars Research Articles

Role of viscoelasticity in the adhesion of mushroom-shaped pillars

The contact behaviour of mushroom-shaped pillars has been extensively studied for their superior adhesive properties, often inspired by natural attachment systems observed in insects. Typically, pillars are modeled with linear elastic materials in the literature; in reality, the soft materials used for their fabrication exhibit a rate-dependent constitutive behaviour. Additionally, conventional models focus solely on the detachment phase of the pillar, overlooking the analysis of the attachment phase. As a result, they are unable to estimate the energy loss during a complete loading-unloading cycle.
This study investigates the role of viscoelasticity in the adhesion between a mushroom-shaped pillar and a rigid flat countersurface. Interactions at the interface are assumed to be governed by van der Waals forces, and the material is modeled using a standard linear solid model. Normal push and release contact cycles are simulated
at different approaching and retracting speeds.
Results reveal that, in the presence of an interfacial defect, a monotonically increasing trend in the pull-off force with pulling speed is observed. The corresponding change in the contact pressure distribution suggests a transition from short-range to long-range adhesion, corroborating recent experimental and theoretical investigations.
Moreover, the pull-off force remains invariant to the loading history due to our assumption of a flat-flat contact interface. Conversely, in the absence of defects and under the parameters used in this study, detachment occurs after reaching the theoretical contact strength, and the corresponding pull-off force is found to be rate
independent. Notably, the hysteretic loss exhibits a peak at intermediate detachment speeds, where viscous dissipation occurs, which holds true in both the presence and absence of a defect. However, the presence of a defect shifts the region where the majority of viscous dissipation takes place.

Determination of strength of UG2 chromitite pillars at Impala Platinum from laboratory tests and FLAC3D

The results of FLAC3D modelling on chromitite Upper Group 2 Reef pillars from the Bushveld Complex of South Africa are described. The model input parameters were determined from laboratory triaxial tests with post-failure measurements. These geomechanical tests were performed on rock materials within the pillars and the immediate pillar foundations. In the models, post-failure behaviour was simulated using the concept of cohesion softening. Models were built to determine the strength and behaviour of pillars with a width-to-height ratio of approximately two. The original research aimed to find a suitable depth below the surface where Impala Platinum Ltd could safely introduce crush pillars; however, the paper only describes the model results: the ideal depth of the crush pillar introduction is not discussed. The results of the modelling are compared with the PlatMine formula for peak pillar strength and with an underground instrumented pillar located elsewhere on the same reef. Some insight into the effects of grid size on strength is also provided. Further underground measurements are recommended to verify the model results.

Beyond the empirical pillar design method: The strain criterion and the pillar load inversion concepts

Pillar design is a crucial aspect of underground mining engineering, as it directly impacts the safety, stability, and overall effectiveness of mining operations. In this paper we present a method to calculate pillar stability based on the strain criterion and pillar load inversion concept, which complements the empirical pillar strength formulae. Those formulae do not account for certain parameters that can affect the stability of the pillars, e.g. weak layers, changes in stress orientations due to mining, orebody dip, mining layout complexity, and the influence of regional stabilizing pillars. The approach presented here is not intended to replace the empirical method; rather, we suggest using it as the initial step in the pillar design process. This should be followed by iterative numerical modelling to study pillar behaviour, define pillar stability, and optimize the pillar design by considering site-specific and representative rock mass properties and criteria.

Numerical Investigation for Estimation of Behaviour of Barrier Pillars, Gateroads and Face of a Deep Longwall Mine: a Case Study

Numerical Investigation for Estimation of Behaviour of Barrier Pillars, Gateroads and Face of a Deep Longwall Mine: a Case Study

Study of the Impact of Hard Rock Pillar Behavior on the Raise Caving Mining System

Raise caving is a novel mining method with an active stress control approach, which is suitable for deep mining environments. The application of raise caving is investigated for LKAB’s Kiruna mine. This mining method consists of two different phases. In the de-stressing phase, inclined de-stressing slots are created with a minimum amount of infrastructure and long-raise bore holes. The de-stressing slots provide stress shadows for subsequent large scale mining activities. These slots are separated by massive pillars, with width to height ratios of up to 10 and a length of several hundreds of meters, which are required to control stresses and seismicity and prevent hangingwall caving. Due to the stress redistribution in the mine, pillars and abutment areas become highly stressed. In the so-called “production phase”, which follows the de-stressing phase, large scale mineral extraction is conducted. As pillars are highly stressed after the de-stressing phase, it is important to de-stress them in the production phase to be able to extract them in a safe manner. Overall, pillars play a decisive role for the success of the raise caving mining method. Hence, studies on pillars and their impact on the raise caving mining method are of great importance. The first part of the contribution outlines the importance of pillars in the raise caving mining method on a conceptual basis. Numerical simulations for different mine layouts and different pillar behavior are then conducted to study the impact of pillar behavior on the system. The stress redistribution in the mining system and the infrastructure stability, with the help of the RCF-value, are analyzed. For this purpose, simulations with a linear elastic material behavior are a well-suited method. Consequently, the de-stressing of the pillar due to crushing cannot be analyzed with a linear elastic model. To do so, a method for de-stressing the pillar has to be implemented into the simulation. The behavior for pillars with a different width to height ratio is implemented with the help of pre-calculated stress-strain curves from available knowledge on pillar strength and behavior. Since mining is a progressive process, the sequence of mining plays an important role for the stress development in pillars and abutment areas and is also included in the simulations. Different ways for pillar de-stressing are outlined and discussed. Furthermore, the influence of stoping in the production phase is discussed in this contribution.

Methodology to predict mechanical properties of PA-12 lattice structures manufactured by powder bed fusion

Topology optimization for weight reduction of additive manufacturing parts is commonly achieved throughout the creation of lattice structures, typically generated with beams of small size cross-section. In order to carry out accurate simulations of these lattice structures, knowing the mechanical behavior of pillars is required. In this paper, a methodology for determining the mechanical properties of small size pillars printed in PA-12 material, using polymer powder bed fusion (PBF) and in particular the Selective Laser Sintering (SLS) technology, is presented. The effect of defects originated during the manufacturing process on the macroscopic mechanical properties is studied and the mechanisms which influence these properties are analyzed. A methodology for the determination of these properties is proposed, based on a successive correction of the printed nominal diameters according to two approaches; one due to the outer skin of unmelted material and the other due to internal melting defects. Once the material properties are determined, as a function of the cross-section of the lattice pillars, the numerical simulation of lattice-type structures has been carried out and the degree of adjustment of the proposed methodology has been experimentally verified, obtaining good results. This validation provides a reliable method for the simulation of the macroscopic behavior of lattice-type structures with reduced sizes, taking into account the intrinsic defects generated during the printing process.

Stability analysis of crown pillar under the zone of relaxation around sub-level open stopes using numerical modelling

The stability of stopes and pillars is a critical concern in deep underground metal mining due to the potential for stress concentration and relaxation that can cause the dynamic failure of pillars. This study employs a finite element approach to investigate the behaviour of crown pillars to various stress and geo-mining parameters. The analysis includes examining stresses, deformations, and yielding zones around the crown pillars using variations in rock mass parameters. The study involves 240 non-linear numerical models with the Mohr–Coulomb elastoplastic failure criteria under plane strain conditions. The results indicate that increasing the crown pillar thickness from 5 to 8 m reduces maximum vertical deformation by 55.8% and the maximum extent of yielding zones from 2.2 to 0 m. The study suggests a 6 m crown pillar for depths up to 670.56 m and thicker pillars of 7 m or more for greater depths.

Superelastic ferroelectric micropillar with large hysteresis and super-durability

Hysteresis and durability are generally on the opposite sides of a trade-off for superelastic materials. We herein break this trade-off and report that BaTiO3 (BT) micropillars present size-dependent superelasticity and possess simultaneous large hysteresis and super-durability, sustaining up to 108 superelastic cycles without functional degradation and structural failure. TEM results reveal that the as-fabricated BT pillars are composed of inner BT crystal part and surface BT amorphous layer. In addition, it is found that after high temperature annealing, the BT pillar with cross sectional side length d of 2 µm loses superelasticity. Based on these results, a model was developed to explain the size dependent behavior of BT pillars by considering the constitutive behavior difference of BT crystal and BT in amorphous phase, and their interaction during compressive stress loading and unloading. The super-durability was attributed to the small ferroelastic switching stress, which are much smaller than the dislocation nucleation activation stress and the compression strength of BT pillars, and the moderate mismatch stress between different ferroelectric variants as well as the stress relaxation by the high surface area of the small volume BT pillar. These discoveries enable ferroelectric micropillars many promising applications such as microdampers, and also provide significant insight into developing superelastic materials with enhanced durability.

ANALYSIS OF WALLS AND PILLARS OF THE HYPOSTYLE HALL AT THE QH31 TOMB (ASWAN, EGYPT) BASED ON 3D MODELS

Abstract. This study describes the methodology developed and the results obtained about the geometric behaviour of walls and pillars of one of the most prominent rock-cut funerary structures of the Middle Kingdom period located in the Necropolis of Qubbet el-Hawa. More specifically, we selected the hypostyle hall of the QH31 hypogeum, one of the greatest in the Necropolis, to apply this methodology. The main objective is related to obtaining geometrical aspects of walls and pillars in order to understand the constructive procedure carried out almost four millennia ago. The methodology was based on photogrammetric and TLS surveys that allowed us to obtain a complete combined 3D model of the structure, geometrically contrasted and with real texture. From this product we obtained a high density point cloud, where some planes were fitted considering the walls and pillars that defined the structure. These planes were characterized by their normal vectors, which were used to analyse several geometric aspects such as inclinations, parallelism and perpendicularity. As results, we have obtained important information about the level of accuracy of the constructive procedure carried out by the ancient Egyptians. In this sense, the values obtained allow us to suggest and confirm several hypotheses about the construction of this hypogeum. The proposed methodology has demonstrated its feasibility for determining these geometric aspects of funerary structures through the analysis of the fitted planes obtained from the 3D model.

Mechanical behaviors of deep pillar sandwiched between strong and weak layers

A variety of coal room and pillar mining methods have been efficiently practiced at depths of up to 500 m with least strata mechanics issues. However, for the first time, this method was trialled at depths of 850–900 m in CSM mine of Czech Republic. The rhomboid-shaped coal pillars with acute corners of 70°, surrounded with 5.2 m wide and 3.5–4.5 m high mine roadways, were used. Pillars were developed in a staggered manner with their size variation in the Panel II from 83 m × 25 m–24 m × 20 m (corner to corner) and Panel V from 35 m × 30 m–26 m × 16 m. Coal seam inclined at 12° was affected by the unusual slippery slickenside roof bands and sometimes in the floor levels with high vertical stress below strong and massive sandstone roof. In order to ensure safety, pillars in both the panels were continuously monitored using various geotechnical instruments measuring the induced stresses, side spalling and roof sagging. Both panels suffered high amounts of mining induced stress and pillar failure with side-spalling up to 5 m from all sides. Heavy fracturing of coal pillar sides was controlled by fully encapsulated steel bolts. Mining induced stress kept increasing with the progress of development of pillars and galleries. Instruments installed in the pillar failed to monitor actual induced stress due to fracturing of coal mass around it which created an apprehension of pillar failure up to its core due to high vertical mining induced stress. This risk was reduced by carrying out scientific studies including the three-dimensional numerical models calibrated with data from the instrumented pillar. An attempt has been made to study the behavior of coal pillars and their yielding characteristics at deeper cover based on field and simulation results.

Unconventional dislocation starvation behavior of medium-entropy alloy single crystal pillars containing pre-existing dislocations

The excellent dislocation storage ability of bulk multi-principal element alloys (MPEAs) has been widely reported. To date, however, the underlying mechanisms of dislocation escape behavior in small-size face-centered cubic (FCC) MPEAs have rarely been studied. Here, we quantitatively control the initial dislocation densities (∼1015 m–2 and ∼1016 m–2) by large-scale molecular dynamics (MD) simulations and perform uniaxial compression simulations to compare the dislocation starvation behavior of CrCoNi with pure Cu single crystal pillars (SCPs). The analysis reveals that the CrCoNi SCPs with low initial dislocation density (∼1015 m–2) can continuously accommodate mobile dislocations, and the critical dimension for dislocation starvation is about 30 nm. In particular, the CrCoNi SCPs with chemical short-range ordering (SRO) exhibit better dislocation storage and multiplication abilities than the random solid solution (RSS) samples even when the initial dislocation density is low. However, the presence of a large number of pre-existing dislocation locks governs the strong dislocation multiplication ability of the small-size RSS CrCoNi SCPs, in obvious contrast to the deformation of all pure Cu SCPs which is completely dominated by intermittent mobile dislocation starvation. Most importantly, we reveal the fundamental physics for the good dislocation storage of CrCoNi SCPs at small sizes from the perspective of chemical heterogeneity. The new phenomena reported in this work provide a unique atomic-scale perspective for understanding the microscopic physical origin of the mechanical behavior of MPEAs and the discovery of extremely slow dislocation escape behavior in small-scaled pillars, providing a reliable basis for the development of the dislocation starvation model.

Pseudo-discontinuum model to simulate hard-rock mine pillars

In this study, the pseudo-discontinuum modeling technique, called continuum Voronoi block model (CVBM), was applied to represent the behavior of hard-rock pillars from underground mines subjected to high field stresses. The CVBM’s ability to produce numerical results consistent with the observed behavior of pillars is demonstrated through the numerical analysis of a hypothetical case and a back analysis of the Creighton mine pillar. The results show that the model can capture convergence displacements and explicitly show the formation of macro-fractures parallel to excavation walls, intact rock slabs, and V-shaped notches. These components are characteristics of brittle failure induced by highly stressed ground conditions. The studies presented in this work confirm the CVBM as a convenient tool for the numerical modeling of intact rock pillars excavated in deep underground mines.

Modeling and Characterization of Annealing-Induced Cu Protrusion of TSVs With Polyimide Liner Considering Diffusion Creep Behavior

Polymer liner has been used in through-silicon-vias (TSVs) for smaller parasitic capacitance and better thermo-mechanical performance. For the application in heterogeneous integrated systems, it is critical to study the thermal reliability of such TSVs in both theoretical modeling and experimental characterization. Among the numerous reliability challenges, the Cu protrusion phenomenon of TSVs is one of the most severe issues, which can lead to cracks and delamination in integrated systems. In this article, the annealing-induced Cu protrusion of polyimide (PI) liner TSVs is studied by experiments and simulations. PI-TSVs are fabricated and the Cu protrusion at various annealing conditions is characterized. Finite element analysis (FEA) is carefully carried out taking into account the diffusion creep rate model, and the deviations between FEA and experiment results of protrusion heights are less than 3%. Besides, the deformation procedure and the creep behavior of Cu pillars during annealing are analyzed. Based on the proposed FEA model, comprehensive parametric analyses are conducted to study the effects of different annealing conditions on the Cu protrusion heights, which are helpful to understand and improve the thermal reliability of PI-TSVs.

Improving Rock Pillar Stability Guidelines Through Detailed Numerical Investigation

Pillar stability guidelines have been presented by numerous authors in the past, based on a combination of empirical observations (mostly visual) from mining applications and simple numerical (elastic or simple continuum plasticity) models. In many cases, the resulting design limits for pillar dimensioning are presented as universal for all rockmass conditions and stress regimes. There have been numerous developments in the past decades in mechanistic classification (brittle spalling, effective continuum rockmass, structural control) and mechanism-appropriate modelling and design metrics. These new tools and paradigms for rockmass behaviour allow for a modelling-based revision of the empirical guidelines from the past century that still form the basis of many performance critical designs. This paper includes the consideration of rockmass deformation and yield (rockmass strength approach), brittle strength, and damage behaviour where appropriate. This paper presents correlations for residual GSI and the effects of Hoek-Brown dilation on pillar behaviour. The investigation includes generating 3D FEM synthetic pillar models with equivalent elastic and plastic continuum.

Stress-deformation monitoring and modelling of an underground marble quarry

Geotechnical instruments have been installed in a marble quarry that are dedicated for the monitoring of the mechanical behavior of rooms and pillars during the successive stages of concurrent surface and underground excavations. To facilitate fast and easy monitoring of stress and relative displacement changes with time, a web-driven platform was created for the collection, processing and presentation of monitoring data on the computer or mobile phone screen on an everyday basis. Since the collected data are local in character they are combined with the full-field three-dimensional solution of a Distinct Element Model. This combination of ground behavior monitoring with 3D numerical modeling data is proposed for the application of the observational or “experimental” method for the proper design and monitoring of safe underground marble quarries.

Study on failure mechanism of room and pillar with different shapes and configurations under uniaxial compression using experimental test and numerical simulation

Experimental and discrete element methods were used to investigate the failure behavior of room and pillar with different configurations under uniaxial loading. Concrete samples with dimension of 15 cm × 15 cm × 5 cm were prepared. Within the specimens, rooms and pillars with different configurations were provided. The room dimension was 1 cm × 1 cm, and the pillar dimension was according to the room configuration. Twelve different configurations were chosen for rooms and pillars. The axial load was applied to the model by rate of 0.05 mm/min. The results show that the failure process was mostly governed by both the non-persistent joint angle and joint number. The compressive strength of the specimens was related to the fracture pattern and failure mechanism of the pillars. It was shown that the shear behaviour of pillars was related to the number of the induced tensile cracks, which increased by increasing the room angle. The compressive strength of samples increased with the increase of the room angle. The failure pattern and failure strength are similar in both methods, i.e., the experimental testing and the numerical simulation.

Study on the Bending Effect and Rock Burst Mechanism of Middle Rock Pillars in Extremely Thick Subvertical Coal Seams

Rock bursts occur in nearly vertical coal seam mines at shallow to moderate burial depths, which endangers safe mining. To study the rock burst mechanisms of nearly vertical and extremely thick coal seams, the characteristics of rock bursts were studied via on-site investigation, and a field test of in situ stress was carried out. The mechanical behavior of rock pillars in the middle of the B1+2 and B3+6 coal seams was analyzed using theoretical and numerical simulation methods. The results show that the horizontal maximum principal stress orientation and the nearly vertical coal seam strike were both 82°. The bending of the rock pillars occurred due to the horizontal unbalanced force, and a large amount of bending energy was accumulated within 50 m above the mining level. Rock pillars were bent toward the B1+2 mining goaf and exerted a reverse bending and squeezing effect on the B3+6 coal seam below the mining levels. In addition to the inclination and compression of the B3+6 coal seam roof, stress concentration zones formed in the B3+6 coal seam, where a large amount of elastic energy had accumulated in the coal-rock mass. Consequently, both the rock pillars and the B3+6 coal body at the mining level are in an unstable state undue to mining disturbance. Rock burst energy theory and numerical calculation results showed that in the stress concentration zones of the B3+6 coal seam, the energy density of the coal mass reached or exceeded its critical value before rock burst occurred, and rock bursts were prone to occur under mining disturbances. The in situ microseismic results showed that high-energy microseismic events were mainly concentrated in middle rock pillars around the mining levels and the coal mass in high-stress concentration zones.

Influence of Moisture Content on Creep Mechanical Characteristic and Mic-Fracture Behavior of Water-Bearing Coal Specimen

The most challenging aspect of constructing an underground reservoir is ensuring that the safety coal pillar has long-term stability. It is of great significance to study the creep mechanical behavior of coal pillars under water-rock interaction for the construction of underground reservoirs. Five kinds of coal specimens with different moisture contents (dry, 2.42%, 5.53%, 7.55%, and saturated) were prepared. The effect of moisture content on the creep mechanical behavior of coal specimens was studied by graded loading, and the acoustic emission signals during the creep loading of coal specimens were monitored. The results showed that with the increase in moisture content, the instantaneous strain and creep strain of coal specimens gradually increase, and the total time of the creep test, creep failure stress, and long-term strength generally decreases. The creep failure stress to peak strength and the ratio of long-term strength to peak strength were 73%~85% and 57%~65%, respectively, which are basically independent of water content. As the water content of the coal increased, the cumulative acoustic emission energy decreased, and the failure form of the coal specimen gradually shifted from tension failure ( ω = 0 % and 2.42%), tension shear composite failure ( ω = 5.53 % ) to shear failure ( ω = 7.55 % and 10.08%). The research results can be used as a reference for the design and strength evaluation of coal pillars for underground reservoirs in coal mines.

Simulation of hard rock pillar failure using 2D continuum-based Voronoi tessellated models: The case of Quirke Mine, Canada

The Quirke Mine, ON, Canada, is a typical example of a mine that experienced a chain reaction of pillar failure. In this mine, the rib pillars were initially laid out with their long axis parallel to the dip direction of the orebody. In the central part of the mine, the pillars were re-aligned at 45° to the orebody true dip. This realignment resulted in adverse shear loading conditions that led to their failure. In this study, a two-dimensional finite element program was used to simulate the failure of Quirke Mine pillars under compressive and shear loading conditions. The pillars were simulated as a heterogeneous material, consisting of randomly generated Voronoi blocks. The calibration of this model, referred to as a Voronoi Tessellated Model (VTM), was conducted against the rock mass strength estimated based on a tri-linear, brittle failure criterion. The calibrated VTM was then employed to investigate the pillar behavior during drift development and stope excavation. It was found that the pillar under shear loading experiences higher confinement loss and tensile stress at its core and, therefore, fails at a lower stress level than that under compression. The simulated pillar failure process was found to agree with documented field observations.

The Role of Pillars in Raise Caving

Mining advances to greater depth, where the control of rock pressure is central for a successful operation. To handle the increasing rock pressure at LKAB’s Kiruna iron ore mine, LKAB and Montanuniversität Leoben develop a novel mining method called “raise caving”. Raise caving is based on an active stress management approach. De-stressing slots, which are separated by substantial pillars, are developed first and provide stress shadows for stope development and subsequent large-scale mineral extraction. At an advanced stage of extraction, these pillars are extracted, too. The pillars are decisive for the success of the raise caving method. They are responsible for the control of stresses, the stability of the hanging wall, and the control of seismic energy release. Hence, studies on pillars have a high importance. This contribution investigates the effect of pillar behavior on the overall extraction system by means of numerical simulations. Two different types for pillar behavior are examined, namely infinitely strong pillars and pillars which yield or crush in the process of extraction. In the second case, pillar stress strain curves are created and replicated numerically. The investigated behavior of pillars is based on available studies on the pillar stress strain behavior. Results show the importance of intact (not overloaded) pillars in the initial de-stressing phase in raise caving. These pillars are essential for controlling the stress levels at the position of the raise bore holes for the initial slot development. Pillar overloading results not only in an increase of the spatial extent of the stress shadow but also in a growth of stresses in the abutment areas and neighboring not yet overloaded pillars. It has been found that this instance can endanger the mining activities in the de-stressing phase. Furthermore, it has been found that the layout of the slot-pillar system together with the extraction sequence is decisive for ensuring that pillars are not overloaded in the de-stressing phase.