Source Radius Research Articles

Temperature and density effects on the two-nucleon momentum correlation function from excited single nuclei

Two-nucleon momentum correlation functions are investigated for different single thermal sources at given initial temperature $(T)$ and density $(\rho)$. To this end, the space-time evolutions of various single excited nuclei at $T$ $= 1 - 20$ $MeV$ and $\rho$ = 0.2 - 1.2 $\rho_0$ are simulated by using the thermal isospin-dependent quantum molecular dynamics $(ThIQMD)$ model. Momentum correlation functions of identical proton-pairs ($C_{pp}(q)$) or neutron-pairs ($C_{nn}(q)$) at small relative momenta are calculated by $Lednick\acute{y}$ and $Lyuboshitz$ analytical method. The results illustrate that $C_{pp}(q)$ and $C_{nn}(q)$ are sensitive to the source size ($A$) at lower $T$ or higher $\rho$, but almost not at higher $T$ or lower $\rho$. And the sensitivities become stronger for smaller source. Moreover, the $T$, $\rho$ and $A$ dependencies of the Gaussian source radii are also extracted by fitting the two-proton momentum correlation functions, and the results are consistent with the above conclusions.

The wave beating produced by circular plane pistons

The physics textbooks presents the fundamental concepts of wave beating from an interference process of two plane waves at the time domain. In this work, we propose a teaching practice, based on computational simulation, at undergraduate level, combining the beating caused by waves transmitted from two plane circular pistons vibrating on thickness mode with the resulting acoustic field. The proposal leads to the perception of the beating at the spatial domain. The results show that the pressure amplitude generated from the beating has periodic variations along the central axis from a boundary location. This boundary is determined by the number of extreme values and the ratio between source radius and wavelength.

A quantum bound on the compactness

We present a simple quantum description of the gravitational collapse of a ball of dust which excludes those states whose width is arbitrarily smaller than the gravitational radius of the matter source and supports the conclusion that black holes are macroscopic extended objects. We also comment briefly on the relevance of this result for the ultraviolet self-completion of gravity and the connection with the corpuscular picture of black holes.

Production of light (anti)nuclei in pp collisions at sqrt{s} = 13 TeV

Understanding the production mechanism of light (anti)nuclei is one of the key challenges of nuclear physics and has important consequences for astrophysics, since it provides an input for indirect dark-matter searches in space. In this paper, the latest results about the production of light (anti)nuclei in pp collisions at sqrt{s} = 13 TeV are presented, focusing on the comparison with the predictions of coalescence and thermal models. For the first time, the coalescence parameters B2 for deuterons and B3 for helions are compared with parameter-free theoretical predictions that are directly constrained by the femtoscopic measurement of the source radius in the same event class. A fair description of the data with a Gaussian wave function is observed for both deuteron and helion, supporting the coalescence mechanism for the production of light (anti)nuclei in pp collisions. This method paves the way for future investigations of the internal structure of more complex nuclear clusters, including the hypertriton.

Rupture properties and safety assessment of raw coal specimen rupture process under true triaxial hydraulic fracturing based on the source parameters and magnitude

To realize the safety assessment and risk management of the raw coal specimen rupture process under true triaxial hydraulic fracturing, the AE parameters and source parameters were obtained based on the AE monitoring of raw coal specimen rupture under true triaxial hydraulic fracturing. Throughout the process of hydraulic fracturing, the variation rule of AE parameters and the spatio-temporal distribution of the AE events induced by hydraulic fracturing of raw coal under true triaxial stress were studied. Then, based on the Brune model and grid search method, the source parameters and moment magnitude of raw coal specimens rupture under true triaxial hydraulic fracturing were obtained, and the relationship between the seismic moment and the other source parameters was analyzed. Finally, the source parameters relating AE events in raw coal specimens rupture under true triaxial hydraulic fracturing and micro-earthquakes induced by hydraulic fracturing were compared and investigated; the relationship between Mw (moment magnitude) and ML (local magnitude) of AE events of raw coal specimens rupture under true triaxial hydraulic fracturing was revealed. The results show that: the AE locating results are generally consistent with the actual rupturing of raw coal specimens. The source displacement spectrum of raw coal specimens rupture under true triaxial hydraulic fracturing is in good accordance with predictions made using the Brune model. By calculating the source parameters and moment magnitude, the source scale of hydraulic fracturing of raw coal specimens under true triaxial stress can be evaluated accurately. Source parameters such as corner frequency and apparent stress of raw coal specimen decrease linearly with the increase of seismic moment, and the source radius and source energy increase linearly with the increase of seismic moment; the stress drop tends to fluctuate around a certain value. The source properties of hydraulic fracturing of raw coal specimens under true triaxial stress can be evaluated. The seismic source properties relating AE events in raw coal specimens rupture under true triaxial hydraulic fracturing and micro-earthquakes induced by hydraulic fracturing are different. Considering Mw, ML1 can be better used to calculate the magnitude of AE events of raw coal specimens rupture during true triaxial hydraulic fracturing. These results can reveal the source properties throughout the rupturing of raw coal specimens during true triaxial hydraulic fracturing, and evaluate the safety of rupture process.

A Study on Welding Deformation in Fiber Laser Welding of 9% Nickel Steel through Finite Element Analysis Part I: Implementation of Welding Heat Source Model

Due to various environmental regulations, the demand for natural gas, i.e., a clean energy, is expected to increase continuously. In terms of efficient storage and transportation of natural gas, liquefied natural gas has an advantageous volume of 1/600 compared to natural gas, but the materials that can be used at a cryogenic temperature of −163 °C are limited. A 9% nickel steel is a material recommended by IMO through IGC. It has excellent mechanical properties compared to other cryogenic materials, but its use has been limited due to its disadvantages in arc welding. Therefore, the main topic of this study is the automatic welding of 9% nickel steel using fiber laser and its purpose is to predict the welding deformation during fiber laser welding. First, an investigation was conducted to find the fiber laser welding heat source. A model that can cover all the models in prior studies such as curve, exponential, conical, conical-conical combination, and conical-cylinder combination models was proposed and the heat source model was constructed in a multi-layer format. Heat transfer analysis was performed using the ratio of a heat source radius and heat energy of each layer as a variable and the pass or failure of a heat source was determined by comparing the analysis results to the experimental results. By changing the variables in conjunction with the optimization algorithm, the main parameters of a passed heat source model were verified in a short period of time. In addition, the tendency of parameters according to the welding speed was checked.

Source parameters and scaling relations for small to moderate earthquakes in theIndo‐BurmaRanges,North‐east India, and its seismotectonic implications

The Indo‐Burma Ranges (IBRs) and its surrounding North‐east India is one of the seismotectonically active subduction systems in the world, where the Indian Plate is subducting beneath the Sunda Plate. This has resulted in major earthquakes in the past. In this study, spectral analysis of S‐wave has been used to investigate the source parameters for local earthquakes (3.3 ≤ MD ≤ 5.8) exclusively in the Indo‐Burma region fusing a network of six stations by adopting the Brune model. The corner frequencies (fc) of the events are varied from 0.6 to 3.2 Hz. The estimated source parameters lie in the range from 9 × 1013–3.7 × 1017 N m, 0.2–35.1 MPa, 410–1,956.4 m, 0.002–1.196 m, and 2.9–13.5 Hz for seismic momentM0, stress drop (Δσ), source radius, source dislocation, and maximum cut‐off frequency (fmax), respectively. The scaling relation betweenM0andfchas been derived asM0 = 1.622 × 1016 fc−5.298. The scaling relations ofM0withfmaxand stress drop have also been derived. The high‐stress drops (>10 MPa) were at a depth zone of ~40–60 km, while the stress drops were less than 4.0 MPa beyond this depth, indicating the shallow and deeper portion of the lithosphere to be relatively brittle. We postulate that this could occur due to a complex detachment process as a result of slab tearing in the region. The upper boundary of stress drop was found to have an increasing trend with the focal depth of the earthquakes. The empirical relations betweenM0 − MDandMW − MDhave also been derived for the IBRs. The estimated source parameters and scaling relations will be useful in estimations of lithospheric strength, simulation of strong ground motion in the IBRs, and calibrating the coefficient of the local earthquakes in the IBR and its surrounding region.

Magma source region size controls along axis variations in crustal thickness, axial depth and relief at plate spreading centers

The amplitude of variations in axial depth and across-axis relief that define spreading center segmentation vary systematically with spreading rate. Seismic and gravity data show that crustal thickness also varies along segments. We derive a highly idealized model to relate axial lithospheric thickness, crustal thickness, and effective magma source region size to segment-scale variation in axial depth and across-axis relief. All magma to build the crust is assumed to pool in a segment-centered magma source region and is distributed along the spreading axis by flow in dikes. The magma source and dike are regarded as a closed system and the magma pressure is taken to decrease linearly with the volume of magma going into dikes. The pressure-volume relation driving lateral magma flow is taken to be proportional to the along-axis gradient of depth. Axial depth variations depend on: (1) local isostatic compensation from crustal thickness variations; and (2) across-axis relief or axial valley depth. The axial valley depth is related to crustal and lithospheric thickness using the recently published model of Liu and Buck (2018). Excellent fits to bathymetric data for 12 segments from intermediate to ultra-slow spreading ridges are found by varying three model parameters (HC0, HL and ΔP/ΔV). The dependence of pressure drop on volume withdrawn is parameterized in terms of an effective radius for a spherical source region in an elastic half-space. A key result is that the effective magma source radius increases with spreading rate.

Observability of zero-angular-momentum sources near Kerr black holes

We revisit monochromatic and isotropic photon emissions from the zero-angular-momentum sources (ZAMSs) near a Kerr black hole. We investigate the escape probability of the photons that can reach to infinity and study the energy shifts of these escaping photons, which could be expressed as the functions of the source radius and the black hole spin. We study the cases for generic source radius and black hole spin, but we pay special attention to the near-horizon (near-)extremal Kerr ((near-)NHEK) cases. We reproduce the relevant numerical results using a more efficient method and get new analytical results for (near-)extremal cases. The main non-trivial results are: in the NHEK region of a (near-)extremal Kerr black hole, the escape probability for a ZAMS tends to frac{7}{24}approx 29.17%, independent of the NHEK radius; at the innermost of the photon shell (IPS) in the near-NHEK region, the escape probability for a ZAMS tends to 512-17+27πarctan17≈12.57%.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\frac{5}{12} -\\frac{1}{\\sqrt{7}} + \\frac{2}{\\sqrt{7}\\pi }\\arctan \\frac{1}{\\sqrt{7}}\\approx 12.57\\% . \\end{aligned}$$\\end{document}

Making the most of the Mogi model: Size matters

Magma movements are almost universally associated with volcanic deformation. The Mogi (1958) and McTigue (1987) models link observed surface displacements to behaviour within inaccessible magmatic plumbing systems. Mogi and McTigue models are well-used due to their computational simplicity and ease of application, but both models are limited by their assumptions about the deformation source and its embedding domain. Domain assumptions, including elasticity, homogeneity, and flat topography, have been previously described and corrected for. Whilst recognising the limits of these models, their frequent use in the literature requires an objective assessment of their utility against more sophisticated Finite Element (FE) models, their operational limits (radius-to-depth ratio, ε) and their relative merits in the light of limited field data. Here, we relax the source assumption of a small ε. We simulate volcanic deformation using Mogi, McTigue and FE models - the latter unrestricted by ε - to validate the maximum ε for which the analytical models can be applied, and to compare analytical and FE interpretations of deformation data from Kīlauea Volcano, Hawai'i. We find that analytical and FE models correspond for deformation sources with a range of ε that is wider than previously suggested limits. The differences between simulated surface displacements (forward modelling) and estimated deformation source parameters (inverse modelling) are less than 5% when ε < 0.37 (Mogi) or ε < 0.59 (McTigue). Misfits between analytical and FE models depend on whether radial or vertical displacements are considered simultaneously or independently, and on the values of source radius and depth - not only their ratio, as was assumed previously. There is little or no difference between best-fitting source parameters inferred using Mogi, McTigue and FE models at Kīlauea Volcano, despite the high ε of the system geometry, but sometimes poor correspondences between model results and GNSS observations. Our results demonstrate that Mogi and McTigue models can be applied to volcanoes with a wider range of magma reservoir radii and depths than was hitherto supposed, but previously-established corrections for domain simplifications are necessary to accurately interpret volcanic deformation.

Deuteron-deuteron correlation function in nucleus-nucleus collisions

A formula of the $D$-$D$ correlation function is derived. The deuterons are treated either as elementary particles or as neutron-proton bound states. In the first case the deuterons are directly emitted from a source and in the second one the deuteron formation is a final-state process simultaneous with a generation of $D$-$D$ correlation. The source radius of deuterons formed due to final-state interactions is bigger by the factor of $\sqrt{2}$ than that of directly emitted deuterons. To check how sizable is the effect we compute the $D$-$D$ correlation function taking into the Bose-Einstein statistics of deuterons, the $s$-wave scattering due to strong interaction and the Coulomb repulsion. The correlation function is shown to be sensitive to the source radius for sources which are sufficiently small with RMS radii smaller than 3.5 fm. Otherwise the correlation function is dominated by the Coulomb repulsion and weakly depends on the source radius. Measurements which can make use of our finding are discussed.

Automatic identification model of micro-earthquakes and blasting events in Laohutai coal mine based on the measurement of source parameter difference

The micro-seismic signal of coal mine is obviously affected by blasting signal, which seriously affects the identification accuracy of micro-seismic signal. For this purpose, automated identification and discrimination methods exist to monitor seismicity occurrence. In this study, seismic source properties of blasting events and micro-earthquakes in the Laohutai coal mine are quantified to more accurately distinguish between these two types of events and to investigate potential physical differences between them. Besides examining the space–time evolution of micro-earthquakes in the Laohutai coal mine, source parameters of blasting events and micro-earthquakes (corner frequency f0; spectral level Ω0; seismic moment M0; moment magnitude Mw; source radius R; stress drop △σ; apparent stress σa, radiated seismic energy E) are determined and scaling relationships between them are investigated. Our results show that the number of micro-earthquakes is closely related to the mining activity. Source-spectral characteristics of blasting events are well described by the Brune omega-square model and follow in general the classical scaling relations (i.e. increasing seismic moment with decreasing corner frequency), like the source-spectral characteristics of micro-earthquakes. Importantly, for events of same magnitude, corner frequency and stress drop of blasting events are larger than for micro-earthquakes. This observation helps to improve automatic identification and discrimination of micro-seismic and blast events, thereby providing important information for (real-time) seismic hazard monitoring and risk management.

Source parameters and focal mechanism of ruptures in coal and sandstone specimens under uniaxial loading based on acoustic emission signals

To investigate the source properties and focal mechanism of coal and sandstone specimen rupture under uniaxial loading, acoustic emission (AE) testing of sandstone and coal specimen rupture under uniaxial loading was conducted. The spatio-temporal evolution of AE parameters in the rupture process was determined through the AE testing of coal and sandstone specimen rupture under uniaxial loading. The source parameters of sandstone and coal specimen rupture were then calculated and analyzed using the Brune model and grid-search method. Finally, the focal mechanism of sandstone and coal specimen rupture was deduced by inversion and compared based on source parameters and moment tensor inversion. The results show that: the rupture morphology of sandstone specimens differs from that of coal specimens; the source displacement spectra of sandstone and coal specimens under uniaxial loading are in good agreement with the Brune model. The corner frequency of coal and sandstone specimens decreases linearly with the increase of seismic moment; source radius and energy increase linearly with increasing seismic moment; the stress-drop fluctuates around a certain value. For events of the same magnitude, the corner frequency, energy, and source radius of sandstone specimens at rupture are greater than those of coal specimens at rupture, but the stress-drop in sandstone specimens (at rupture) is smaller than that occurring in coal specimens. In the middle and early stages of rupture, the coal and sandstone specimens mainly undergo shear failure. Shear-tension and shear-compression failures occur in the later stage of rupture. These results can be used to quantify and evaluate the source properties and focal mechanism of small-scale specimens at rupture.

INVESTIGATION OF GMAW BY SIMULATION MODELLING

The thermal and deformation cycle during welding is directly reflected on the formation of the welded joint and the imperfections that can occur in any specific case. The simulation modelling of the heating and cooling processes makes it possible to determine the temporary and residual stresses in the welded joint. When solving the thermal and deformation tasks, it is essential to use data on the characteristics of the material in the entire temperature range in which the studied processes take place. At the same time, these data are often not available. In order to be able to use simulation solutions in practice, the standard EN ISO 18166 provides for calibration of thermal and deformation models before they are applied to the welded structure. In this study, the calibration of a thermal model applicable to MIG / MAG welding is considered. The heat source is superficial and axisymmetric. The calibration parameters are efficiency, effective radius of the heat source and coefficient determining the deviation from the normal central Gaussian distribution. Experimental data on the bead shape were used for the calibration process. The obtained simulation results for the temperature field are compared with the experimental ones. Sensitivity analysis of the solution with respect to the material characteristics was performed.

Numerical studies on minimum ignition energies in methane/air and iso-octane/air mixtures

In this study, the dependence of minimum ignition energies (MIE) on ignition geometry, ignition source radius and mixture composition is investigated numerically for methane/air and iso-octane/air mixtures. Methane and iso-octane are both important hydrocarbon fuels, but differ strongly with respect to their Lewis numbers. Lean iso-octane air mixtures have particularly large Lewis numbers. The results show that within the flammability limits, the MIE for both mixtures stays almost constant, and increases rapidly at the limits. The MIEs for both fuels are also similar within the flammability limits. Furthermore, the MIEs of iso-octane/air mixtures with a small spherical ignition source increase rapidly for lean mixtures. Here the Lewis number is above unity, and thus, the flame may quench because of flame curvature effects. The observations show a distinct difference between ignition and flame propagation for iso-octane. The minimum energy required for initiating a successful flame propagation can be considerably higher than that required for initiating an ignition in the ignition volume. For iso-octane with a small spherical ignition source, this effect was observed at all equivalence ratios. For iso-octane with cylindrical ignition sources, the phenomenon appeared at lower equivalence ratios only, where the mixture's Lewis number is large. For methane fuel, the effect was negligible. The results highlight the significance of molecular transport properties on the decision whether or not an ignitable mixture can evolve into a propagating flame.

Analytical solutions for rapid prediction of transient temperature field in powder-fed laser directed energy deposition based on different heat source models

The present paper aims to develop an effective analytical solution for laser directed energy deposition through powder feeding (LDED-PF). Three heat source models are introduced and compared to analytically describe the transient temperature field in the process. These models are known as point (1D) heat source, circular (2D) heat source, and semi-spherical (3D) heat source. For the validation tests, single-track deposition of Ti-5Al-5 V-5Mo-3Cr powder on Ti-6Al-4 V substrate is conducted at different laser powers, scanning speeds, and powder feed rates. The temperature field is validated using the measurement of melt-pool/deposit geometry. In order to improve the model fidelity, the enhanced thermal diffusivity and heat source radius are calibrated in terms of linear functions. It is found that the 2D Gaussian heat source model, which is in agreement with the underlying physics of the process, establishes a better match between the predicted and experimental data. The developed model only needs the basic information from the LDED-PF setup and material thermal properties to predict the thermal history and melt-pool geometry at different processing parameters.

ΛK femtoscopy in Pb-Pb collisions at sNN=2.76 TeV

The first measurements of the scattering parameters of ΛK pairs in all three charge combinations (ΛK+, ΛK−, and ΛKS0) are presented. The results are achieved through a femtoscopic analysis of ΛK correlations in Pb-Pb collisions at sNN=2.76 TeV recorded by ALICE at the Large Hadron Collider. The femtoscopic correlations result from strong final-state interactions and are fit with a parametrization allowing for both the characterization of the pair emission source and the measurement of the scattering parameters for the particle pairs. Extensive studies with the THERMINATOR 2 event generator provide a good description of the nonfemtoscopic background, which results mainly from collective effects, with unprecedented precision. Furthermore, together with HIJING simulations, this model is used to account for contributions from residual correlations induced by feed-down from particle decays. The extracted scattering parameters indicate that the strong force is repulsive in the ΛK+ interaction and attractive in the ΛK− interaction. The data hint that the ΛKS0 interaction is attractive; however, the uncertainty of the result does not permit such a decisive conclusion. The results suggest an effect arising either from different quark-antiquark interactions between the pairs (ss¯ in ΛK+ and uu¯ in ΛK−) or from different net strangeness for each system (S=0 for ΛK+, and S=−2 for ΛK−). Finally, the ΛK systems exhibit source radii larger than expected from extrapolation from identical particle femtoscopic studies. This effect is interpreted as resulting from the separation in space-time of the single-particle Λ and K source distributions.3 MoreReceived 5 June 2020Accepted 30 March 2021DOI:https://doi.org/10.1103/PhysRevC.103.055201Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.©2021 CERN, for the ALICE CollaborationPhysics Subject Headings (PhySH)Research AreasParticle & resonance productionParticle correlations & fluctuationsParticle interactionsRelativistic heavy-ion collisionsNuclear Physics

Study on the rupture properties and automatic identification model of micro-earthquakes and blasting events in a coal mine

Source location is the key step of microseismic monitoring. The monitored microseismic signals are often mixed with unrecognized blasting interference signals, which affect the results of microseismic monitoring and location. Therefore, it is very important to extract the characteristic parameter information to identify the microseismic signal and blasting signal. The rupture processes during micro-earthquakes and blasting events in a coal mine are complicated and have different characteristics, which seriously affects the safety of coal mine. To quantify the seismic source properties of micro-earthquakes and blasting events in coal mines, and further distinguish between micro-earthquakes and blasting events, the source parameters of micro-earthquakes and blasting events in coal mine were obtained, and the differences between micro-earthquakes and blasting events were investigated by comparing the characteristics of their respective source parameters. Firstly, the corner frequency f0, spectral level Ω0, seismic moment M0, source energy E, source radius R, stress drop △σ, apparent stress σa, and magnitude (Mw and ML) of micro-earthquakes and blasting events in Qianqiu coal mine were calculated using the Brune model and grid-search method; then, the relationship between seismic moment and the other source parameters was analysed, the differences between micro-earthquakes and blasting events were studied based on the above source parameters, and the automatic identification model of micro-seismic and blast signals thus established; finally, the local magnitude was calculated and the relationship between moment magnitude and local magnitude analysed. The magnitudes of micro-earthquakes and blasting events are determined based on the calculated Mw and ML. The above analysis can be used to determine and quantify the seismic source properties and scale of micro-earthquakes and blasting events, and further distinguish micro-earthquakes from blasting events effectively to ensure the accuracy of source location and allow implementation of effective control measures.

Spatiotemporal Clustering of Seismicity During the 2018 Kilauea Volcanic Eruption

AbstractThe intense volcanic and seismic activity at Kilauea volcano, Hawaii in 2018 provides an opportunity to understand the characteristics and driving forces of volcano earthquake clusters. Nearest neighbor distance analysis of a high‐resolution earthquake catalog reveals two modes of clustering: M1 and M2. M1 clusters focus on events within short space and time windows, and are concentrated within isolated fault patches. Examination of three structures shows a gradual increase of source radius (assuming a constant stress drop) and spatial migration of seismicity, likely representing aseismic growth of peripheral faults. M2 clusters focus on temporal clustering of all seismicity within the caldera and most clusters represent complete seismicity cycles between major collapse events. Beginning in late June, the M2 cluster duration gradually increased. The event numbers show a strong linear relationship with the tilt rates on the transverse component, suggesting earthquake rates are controlled by the deformation rate within the caldera.

Complexities of underground mining seismic sources.

This paper presents a numerical investigation on the influence of the mining environment on seismic sources, with a focus on pillar failure mechanisms in tabular mining. We investigate the influence of the mining stope (underground excavation or void) on seismic inversions for the scalar moment, corner frequency, source radius, stress drop and moment tensor using synthetic events created within elastodynamic numerical modelling software, WAVE3D. The main objective is to determine whether the source parameters calculated from the recorded waveforms are due to a combination of the stope source and the pillar sources, rather than being related only to crushing of the pillar or shearing in the pillar footwall. The main finding is that the presence of stopes, and types of pillars, have a significant impact on the seismic moment and other source parameters. This is important since the moment is viewed as a robust parameter on which seismic magnitude is often based; however, this study indicates that moments calculated for pillar failure in a tabular stoping environments are less representative of the shearing or crushing source than originally thought. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.