Slender Pillars Research Articles

A study of the effect of pillar shape on pillar strength

Pillar strength is affected by pillar shape, but this has largely been ignored in past research studies. Bord-and-pillar layouts are typically designed using empirical strength equations developed for square pillars. Owing to the poor quality of pillar cutting, many hard-rock pillars have an irregular shape and it is not clear how this affects pillar strength. Furthermore, the strength of rectangular pillars in comparison with square pillars is also difficult to quantify. The 'perimeter rule' is widely adopted for rectangular pillars, but its applicability for pillars with irregular shapes has never been tested. We used numerical modelling in this study to investigate the effect of pillar shape on strength. An analytical limit equilibrium model of a square and a strip pillar also provided useful insights. For slender pillars, the strength of a long rib pillar is essentially similar to that of a square pillar. In contrast, for rib pillars with a large width to height ratio, there is a substantial increase in strength. The study found that the perimeter rule should not be used for irregularly shaped pillars. Displacement discontinuity modelling, using a limit equilibrium approach, is proposed as an alternative to determine the strength of these pillars.

Elastomeric Pillar Cages Modulate Actomyosin Contractility of Epithelial Microtissues by Substrate Stiffness and Topography.

Cell contractility regulates epithelial tissue geometry development and homeostasis. The underlying mechanobiological regulation circuits are poorly understood and experimentally challenging. We developed an elastomeric pillar cage (EPC) array to quantify cell contractility as a mechanoresponse of epithelial microtissues to substrate stiffness and topography. The spatially confined EPC geometry consisted of 24 circularly arranged slender pillars (1.2 MPa, height: 50 µm; diameter: 10 µm, distance: 5 µm). These high-aspect-ratio pillars were confined at both ends by planar substrates with different stiffness (0.15-1.2 MPa). Analytical modeling and finite elements simulation retrieved cell forces from pillar displacements. For evaluation, highly contractile myofibroblasts and cardiomyocytes were assessed to demonstrate that the EPC device can resolve static and dynamic cellular force modes. Human breast (MCF10A) and skin (HaCaT) cells grew as adherence junction-stabilized 3D microtissues within the EPC geometry. Planar substrate areas triggered the spread of monolayered clusters with substrate stiffness-dependent actin stress fiber (SF)-formation and substantial single-cell actomyosin contractility (150-200 nN). Within the same continuous microtissues, the pillar-ring topography induced the growth of bilayered cell tubes. The low effective pillar stiffness overwrote cellular sensing of the high substrate stiffness and induced SF-lacking roundish cell shapes with extremely low cortical actin tension (11-15 nN). This work introduced a versatile biophysical tool to explore mechanobiological regulation circuits driving low- and high-tensional states during microtissue development and homeostasis. EPC arrays facilitate simultaneously analyzing the impact of planar substrate stiffness and topography on microtissue contractility, hence microtissue geometry and function.

A matter of morphology: The role of asperity characteristics in hydrogel friction

Hydrogels can be easily modified to have a particular surface roughness. This modularity in hydrogels is an important feature, as roughness affects friction. Here, we systematically vary the surface morphology by separately altering the height, diameter and distance between surface asperities shaped as cylindrical pillars. Using a custom- made 3D-printed tribometer, we show that slender pillars conjure a higher friction coefficient, which we attribute to their bending and hence larger exposed contact area. In contrast, we measure low friction coefficients when the small diameter of asperities or their sparse presence on the surfaces reduces the total effective sliding contact area. We investigate two surface patterns with different spatial symmetry and demonstrate that the mechanisms behind probe-pillar friction depend on the spatial location of the pillars on the surface with respect to the sliding path. Our findings provide a path towards optimization of frictional properties of soft hydrogel surfaces.

Failure Modes of Masonry Pillars Strengthened with PBO Fibres

The paper presents compression tests of stocky and slender masonry pillars strengthened in bed joints with PBO fibres and an inorganic matrix. Five stocky pillars and four slender pillars were tested under static loading. Physical models were prepared using lime mortar similar to that used in historical structures. Fibres were applied in the grooves that were made after the mortar setting period in order to recreate real-world conditions. One of the models was subjected to preloading before the strengthening was applied. The failure modes, load-bearing capacity, cracking stresses, stiffness and deformations (longitudinal and transverse) were all determined through experimental testing. Strengthening effectiveness in terms of the increase in load-bearing capacity and stiffness, as well as anti-cracking was determined on the basis of the experimental results. The results obtained for the stocky and slender pillars were also compared, indicating the influence of slenderness on strengthening effectiveness. Special attention was also paid to failure modes and the interaction of the PBO fibres with the bed joint. Methods that strengthen pillars in their bed joints using PBO fibres increase their load-bearing capacity, stiffness and cracking resistance, while maintaining a satisfactory visual appearance which is especially important in heritage structures.

Numerical modeling of time-dependent spalling of rock pillars

Time-dependent deformation of brittle rock pillars is investigated using laboratory-scale pillar models using the grain-based time-to-failure model (GBM-TtoF). First, time-dependent deformations of rock pillars are analyzed and the results are compared qualitatively with field observations. Second, the influence of the boundary profile of pillar walls on time-dependent strength and deformation of rock pillars is investigated. Two factors, pillar shape and loading ratio, which influence the time-dependent strength and deformation of rock pillars, are studied by conducting a series of creep simulations using four pillar models with width to height ratios of W/H = 0.5, 1.0, 1.5 and 2.0. Finally, long-term strengths and deformation features of slender and squat pillars are analyzed. It is found that time-dependent strengths and deformation of rock pillars can be simulated using the GBM-TtoF creep model properly. Gradual spalling on the pillar walls can be captured using pillar models with rough boundary profiles. Creep deformations of slender and squat pillars could be quite different. Slender pillars are more likely to fail as time passes but squat pillars can tolerate more spalling on the walls without losing their stability. It is demonstrated that the GBM-TtoF creep model can simulate time-dependent strength and deformation of hard rock pillars well under creep loading conditions.

An Investigation of the Factors Controlling the Mechanical Behaviour of Slender Naturally Fractured Pillars

Previous studies on the strength and deformability of pillars in hard-rock mines have demonstrated that the influence of natural fractures diminishes with increasing pillar width. Jointing conditions and fracture intensity/intersections play a critical role in the behaviour of slender pillars (width-to-height ratio less than 0.5). An important challenge is the characterization of rock mass damage as a function of the natural fracture network and loading conditions. In this paper, we present advanced pre-processing methodologies to measure fracture intensity and fracture density prior to loading and relate those measures to the evolution of damage (intensity and density) with increasing pillar load. A hybrid finite-discrete element method (FDEM) with fracture mechanics capabilities is used to simulate the mechanical behaviour of synthetic pillar models with different embedded discrete fracture traces of similar total length. Newly developed post-processing methodologies are used to capture the location of damage events, track rock mass damage intensity and density as the simulation progresses and relate those changes to the modelled pillar strength. We believe the results of this study provide useful insights on rock mass damage evolution.

Both slender pillars and hierarchical structures achieving superhydrophobicity and the comparison of their properties

In this paper, both slender pillars and hierarchical structures on steel substrate including slender pillar ZnO structures on Zn coating, flower-like CuO structures on Cu coating and dandelion-like CuO structures on Cu-Zn coating were obtained. After low-energy modification, contact angles of these three coatings are 157.59°, 160.69° and 157.94°, respectively, and slide angles of them are ~6°, ~3° and ~3°, respectively. Based on classical Wenzel and Cassie theories, by fabricating microstructure models, we theoretically prove that both slender pillars and hierarchical structures can achieve superhydrophobicity. Furthermore, we systematically study the stability of these three superhydrophobic coatings with slender pillars or hierarchical structures using different methods and compare their applications in the field of self-cleaning, oleophobicity, anti-corrosion, and anti-scaling. We discover that these three superhydrophobic coatings with slender pillars or hierarchical structures all show excellent stability and self-cleaning property. The slender pillared superhydrophobic Zn coating presents excellent superhydrophobic property after sandpaper abrasion compared with hierarchical structured superhydrophobic Cu and Cu-Zn coatings. Whereas, the hierarchical structured superhydrophobic Cu coating with flower-like structures shows the best oleophobicity and anti-corrosion property, as well as the hierarchical structured superhydrophobic Cu-Zn coating with dandelion-like structures promises good anti-scaling property.

A Case Study of the Collapse of Slender Pillars Affected by Through-Going Discontinuities at a Limestone Mine in Pennsylvania

The sudden collapse of approximately 3 Ha of room-and-pillar workings at a limestone mine in southwestern Pennsylvania in 2015 resulted in an air blast that injured three mine workers. Subsequent investigations showed that an area encompassing 35 pillars had collapsed. The pillars were 9-10 m wide and up to 18 m high. A notable geologic feature is the through-going joints that dip at 50-80° and can extend from the roof to the floor of the pillars. These structures are thought to have weakened the pillars well below the strength that is predicted by empirical equations for hard-rock pillar design. This paper presents the relevant geotechnical data related to the collapsed area and numerical model results that were used to estimate the pillar loading underneath the variable topography, and compares the pillar loads to some established hard-rock pillar strength equations. The outcome is also compared to a strength equation that was developed specifically for limestone mines in which the negative impact of large angular discontinuities is explicitly accounted for. The results show that established hard-rock pillar strength equations do not adequately account for the impact of large through-going discontinuities on the strength of slender pillars. The equations would have significantly overestimated the strength of the pillars at the case study mine. The critical state of the workings would have been predicted correctly by the limestone pillar strength equation that accounts for the large discontinuities.

Deflecting flexural wave with high transmission by using pillared elastic metasurface

This paper proposes an innovative and simple elastic metasurface, which is one kind of ultrathin metamaterial, to abnormally deflect normally and obliquely incident flexural waves. In particular, negative refraction of flexural wave is also realized. The proposed metasurface can support high transmission and full phase control for transmitted waves. The metasurface is composed of three-dimensional (3D) functional units which are combined with multiple slender pillars for phase shift accumulation. The slots are filled in the 3D functional units to avoid coupling between adjacent functional units. Firstly, based on the generalized Snell’s law, the metasurface in the sub-wavelength regime is theoretically designed. Secondly, the deflecting functionality of the metasurface for incident flexural waves is numerically demonstrated. Finally, the deflecting functionality is verified by the corresponding experiments. The proposed metasurface has a great application potential in many fields, such as ultrasonic detection, energy harvesting, and vibration control.

A neutron diffraction and imaging study of ancient iron tie rods

Milan Cathedral is one of the biggest and widest churches ever built among the other coeval architectures. It had a very long and complex construction history, which started in 1386 and lasted more than four centuries. The dominant style is the European gothic but the lombard tradition has strongly influenced the composition. Gothic cathedrals were diffusely built in Europe during the Middle Age, and each region developed its own local interpretation. However, a common feature of the style was the presence of slender pillars and of many elements able to reduce the horizontal thrusts of the vaults, such as spires, buttresesses, flying buttresesses and tie rods. In Milan Cathedral, tie rods have a fundamental role due to the specific characteristics of the structural system and its complex history. In 2012, a broken tie rod was found and it was substituted with a new one. Therefore, a multidisciplinary research on these elements started, aiming at a deeper material characterization and an in-situ identification of local defects. Among non-destructive techniques, several neutron analyses were performed on different samples. We will report on neutron diffraction measurements and neutron resonant capture analysis on part of the original broken tie rod. Moreover, neutron imaging was recorded on other iron tie rods (from an external spire). Results will be useful for an independent assessment and validation of models and of new on-site monitoring techniques, since no other conventional non-destructive technique will allow the same characterization.

Numerical study of pillar stresses and interaction effects for twin rock caverns

SummaryLarge underground caverns are increasingly being considered for the construction of industrial facilities and transportation infrastructure in order to optimize the use of surface land in large urban cities. Due to the geological constraints underground, it is sometimes necessary to construct a cavern close to an existing cavern. Pillars serve as an underground support element in twin caverns, without which it is difficult to sustain the weight of the overburden materials. If the strength of a pillar is exceeded, it will fail, and the load that it carried will be transferred and thereby contribute to the collapse of the twin caverns. The lack of confinement in slender pillars also contributes to the complete collapse of pillars at relatively low stress magnitudes. From a design point of view, understanding the pillar failure mechanism and the interaction effect between twin caverns is essential. This paper presents a numerical investigation on the influence of various design parameters on twin cavern interaction. Pillar performances with respect to the changes to the maximum principal stress in the pillar, the peak vertical stress, and the peak principal stress difference in the pillar core are studied in order to examine the failure mechanisms and to identify situations in which there is significant cavern interaction and overlap of the plastic zones. Copyright © 2014 John Wiley & Sons, Ltd.

Web pillar design approach for Highwall Mining extraction

“Highwall Mining” is practised when the open pit coal mines reach their pit limits due to the presence of surface dwellings or uneconomical stripping ratios. It involves driving a series of parallel entries separated by web pillars using a remotely operated continuous miner into a coal seam exposed at the highwall. The design of web pillar is crucial to the overall stability and safety of the Highwall Mining operations. In multiple seam extractions it is also necessary to protect the overlying workable seams and minimise surface subsidence. Hybrid empirical and numerical modelling techniques adopted for web pillar design in Indian conditions are described in this paper. Web pillar vertical stress was estimated for both up dipping and down dipping coal seams using numerical modelling tool, which accounts for highwall slope and abutment stresses caused by the open-pit excavation and the “end-effect” of the highwall excavations facing the solid boundary. Using numerical modelling tools, a correction factor is suggested in the empirical pillar strength equation for slender pillars having width to height ratio less than unity. Numerical strain-softening models, representing various possible configurations for multiple seams in close proximity and multi-pass extraction within a thick coal seam, are run and the peak stress is calibrated against pillar strength determined by the empirical equation. Finally a case example of successful design of web pillars for Highwall Mining extractions is presented.

Numerical modelling of longwall mining and stability analysis of the gates in a coal mine

This paper presents a novel numerical approach to simulate the longwall mining in detail, aiming to investigate the stability of gates and the loading process to rock bolts. The study site is the Svea Nord coalmine in Svalbard. In the proposed approach, progressive cave-in and fracturing of the roof strata, consolidation of the cave-in materials and stress changes are simulated in detail. The results of the simulations are used to analyse the loading process of the rock bolts in the gates. The numerical model is calibrated with the measurement data. The simulations reveal that the stability of the gates and the loading to the rock bolts are closely related to the width of the chain pillars. With slender pillars, shear displacements along weak interlayers and bedding planes results in heavy loading to the rock bolts. Therefore, the locations of weakness zones should be taken into account for rock bolt design. The proposed numerical approach can be used to find an optimal combination of the dimension of the chain pillars and the rock reinforcement in the gates.

An Integrated Numerical Modelling–Discrete Fracture Network Approach Applied to the Characterisation of Rock Mass Strength of Naturally Fractured Pillars

Naturally fractured mine pillars provide an excellent example of the importance of accurately determining rock mass strength. Failure in slender pillars is predominantly controlled by naturally occurring discontinuities, their influence diminishing with increasing pillar width, with wider pillars failing through a combination of brittle and shearing processes. To accurately simulate this behaviour by numerical modelling, the current analysis incorporates a more realistic representation of the mechanical behaviour of discrete fracture systems. This involves realistic simulation and representation of fracture networks, either as individual entities or as a collective system of fracture sets, or a combination of both. By using an integrated finite element/discrete element–discrete fracture network approach it is possible to study the failure of rock masses in tension and compression, along both existing pre-existing fractures and through intact rock bridges, and incorporating complex kinematic mechanisms. The proposed modelling approach fully captures the anisotropic and inhomogeneous effects of natural jointing and is considered to be more realistic than methods relying solely on continuum or discontinuum representation. The paper concludes with a discussion on the development of synthetic rock mass properties, with the intention of providing a more robust link between rock mass strength and rock mass classification systems.

Structural Behaviour of the Flying-Buttresses of the OL-Cathedral of Tournai (Belgium)

Nowadays, a great number of heritage buildings are affected by structural defects. This paper presents the particular case of the Our Lady Cathedral of Tournai (World Heritage – UNESCO). According to historians and archeologists, the gothic choir of this building shows signs of weaknesses (problems affecting the flying-buttresses, the buttresses and the very slender pillars) since its erection. Over the centuries, several teams of engineers and architects have studied the problem, trying to understand the behaviour of the structure in order to propose a solution to preserve it. Unfortunately, using contemporary theories and calculations (graphostatic approach and limit analysis) these experts have not succeed in finding a convenient solution and the structural problems still exist today. A few years ago, a team from the Polytechnic Faculty of Mons began to study the building using Finite Element Models. From very simplified models, they began to understand the particular behaviour of the flying-buttresses. Then, by coupling their work with a team of archeologists and historians, they advanced their understanding of the building, making models more complicated and more precise. The analysis is based on “2D1/2” models taking into account the superstructure itself. All the materials involved in the study are assumed to be linear elastic. Some non linearities are introduced with a discrete iterative approach to simulate crack propagation. The results obtained confirm the result of preliminary studies but the observed pathologies are much more understood than with previous simplified models. By using FEM the behaviour of the building can be studied at each step of its life and the mistakes made by the engineers of the past can be better understood. Now, the effective behaviour of the flying-buttresses is better known and an effective solution for the future can be planned.

Superhydrophobicity and Superhydrophilicity of Regular Nanopatterns

The hydrophilicity, hydrophobicity, and sliding behavior of water droplets on nanoasperities of controlled dimensions were investigated experimentally. We show that the "hemi-wicking" theory for hydrophilic SiO(2) samples successfully predicts the experimental advancing angles and that the same patterns, after silanization, become superhydrophobic in agreement with the Cassie-Baxter and Wenzel theories. Our model topographies have the same dimensional scale of some naturally occurring structures that exhibit similar wetting properties. Our results confirm that a forest of hydrophilic/hydrophobic slender pillars is the most effective superwettable/water-repellent configuration. It is shown that the shape and curvature of the edges of the asperities play an important role in determining the advancing angles.

A batch fabricated biomimetic dry adhesive

The fine hair adhesive system found in nature is capable of reversibly adhering tojust about any surface. This dry adhesive, best demonstrated in the pad of thegecko, makes use of a multilevel conformal structure to greatly increase inelasticsurface contact, enhancing short range interactions and producing significantamounts of attractive forces. Recent work has attempted to reproduce and testthe terminal submicrometre ‘hairs’ of the system. Here we report the first batchfabricated multi-scale conformal system to mimic nature’s dry adhesive. Theapproach makes use of massively parallel MEMS processing technology to produce20–150 µm platforms, supported by single slender pillars, and coated with∼2 µm long, ∼200 nm diameter, organic looking polymer nanorods, or ‘organorods’. To characterize thestructures a new mesoscale nanoindenter adhesion test technique has been developed.Experiments indicate significantly improved adhesion with the multiscale system.Additional processing caused a hydrophilic to hydrophobic transformation of the surfaceand testing indicated further improvement in adhesion.

Mimicking the Lotus Effect: Influence of Double Roughness Structures and Slender Pillars

Surface roughness is known to amplify hydrophobicity. The apparent contact angle of a drop on a rough surface is often modeled using either Wenzel's or Cassie's formulas. These formulas, along with an appropriate energy analysis, are critical in designing superhydrophobic substrates for applications in microscale devices. In this paper we propose that double (or multiple) roughness structures or slender pillars are appropriate surface geometries to develop "self-cleaning" surfaces. The key motivation behind the double structured roughness is to mimic the microstructure of superhydrophobic leaves (such as lotus). Theoretical analysis similar to that presented in the paper can be used to obtain optimal geometric parameters for the rough surface. The calculation procedure should result in surface geometries with excellent water repellent properties.

The Effect of Mining Geometry on Stability of Rock Mass Around Underground Excavations

Stability of underground excavations depends on mining geometry defined by extraction ratio and pillar shape. Laboratory studies were carried out to determine the relationship between mining geometry and the behaviour of rock samples in high stress conditions. It was observed that for slender pillars and high extraction ratio (total extraction of a deposit), rock instability was local, manifested as pillar rupture and spalling. Stability was controlled by pre-failure brittle behaviour of rock. For squat pillars and low extraction ratio (selective extraction of a deposit), instability of the rock mass was on a global scale, manifested as shear movement or large scale collapse. Stability was controlled by post-failure ductile behaviour. For standard pillars and typical extraction ratio (partial extraction of a deposit), instability was manifested as pillar punching into the hangingwall and footwall accompanied by shear fracturing of the rock mass. Instability developed progressively and rock behaviour exhibited some post-failure strength.

Geology and mining practice in relation to shallow subsidence in the Northern Coalfield, New South Wales

The former Northern Coalfield, comprising much of the Newcastle‐Maitland‐Cessnock‐Lake Macquarie region, has now been mined for two hundred years. Most of the twenty‐odd seams in the Newcastle, Tomago and Greta Coal Measures have been worked, but the bulk of production has been drawn from just four coalbeds: the Borehole, Greta, Homeville and Great Northern Seams. Literally hundreds of mine names are on record for the coalfield, the great majority working these seams at depths of less than 30 m. This paper reviews regional subsidence problems in the context of mining history, past mining practices and coal measures geology. Subsidence over shallow bord‐and‐pillar workings may result in highly disturbed ground, open fissures, cratering, seam fires and ‘creeps’ (slow surface movements caused by gradual closure of mine cavities). This form of subsidence differs from that over modern longwall mines in being less predictable, affecting much smaller areas, and occurring sometimes decades after mine abandonment. The geological factors contributing to this subsidence hazard include the multiplicity of seams, the strong roof sandstones, stiff coal and relatively soft floors, and the presence of faults and dykes. The working of thick seams like the Borehole Coal in up to three phases, leaving high, slender pillars, also contributed to later ground instability. Contrary to expectation, the main problem areas are not over haphazardly laid‐out convict‐era pits, but rather above small hand‐worked scavenger mines (‘ratholes’) which operated as late as the 1950s. Many of these short‐lived collieries still contain large voids at shallow depth, sometimes only a few metres, which must eventually collapse or be backfilled.