Effect Of Particle Shape Research Articles

Heat transfer studies in a rotating drum containing non-spherical particles

In chemical and pharmaceutical industries, rotating drums are commonly used as mixers, dryers, granulators, and reactors for processing particulate materials (Rutgers, 1965). Most of the earlier studies are limited to the spherical particles and have focused on understanding granular flow in drums operating under a rolling regime. However, there are numerous industrial operations in which non-spherical particles are heated in a rotating drum operating in the cascading regime. In the present work, we attempt to understand the heat transfer process between hot air and non-spherical particles in a rotating drum. Non-spherical particles, considered for the simulations, mimic pharmaceutical tablets having standard round convex (SRC) and oblong shapes. The multi-sphere approach is used to model the tablet shapes. Collisions between the tablets are captured through the interaction between candidate spheres of non-spherical particles. The focus here is to study the heat transfer between hot air and particles and the heat conduction between the particles. The effects of drum speed, particle shape, and air inlet temperature on the bed temperature distribution are investigated. Analysis of average bed temperature profiles shows that the bed temperature remains constant regardless of the drum speed but is influenced by the temperature of the incoming air. The logarithmic mean temperature is not impacted by the incoming air temperature but is influenced by particle shape. The logarithmic mean curve shows a steeper slope for SRC particles due to higher surface area-to-volume ratio and better radial mixing compared to Oblong particles

Effect of sand particle shape on micromechanical modeling in direct shear testing

Soil representation in discrete element method (DEM) simulations is a complex process due to the intrinsic variability in grain shape. Many methods have been proposed to include shape effects in DEM, from rolling friction to aspherical particle representations such as ellipsoids or polyhedra. In this paper the micromechanical differences between two commonly used methods of shape representation, rolling friction applied to spherical particles and ellipsoids, are investigated for direct shear testing. This simulation study is supported by dry direct shear tests in the laboratory using a poorly graded sand and three vertical confining pressures: 50, 100 and 200 kPa. While the bulk behavior observed in the laboratory can be matched using both shape representation approaches, the micromechanics show significant differences. The average cumulative rotation of the ellipsoidal particles is an order of magnitude lower than for the spheres with rolling friction. The addition of rolling friction significantly affects the mechanical redundancy of the system, making the spherical-particle samples more hyperstatic than their ellipsoidal equivalents. Although using ellipsoids enables a better representation of the micromechanical behavior, this increases the computational cost five-fold compared to using rolling friction and spheres.

Numerical study of the volume fraction and thermophysical properties of nanofluids in a porous medium

PurposeThe purpose of the paper is to conduct a numerical and experimental investigation into the properties of nanofluids containing spherical nanoparticles of random sizes flowing through a porous medium. The study aims to understand how the thermophysical properties of the nanofluid are affected by factors such as nanoparticle volume fraction, permeability of the porous medium, and pore size. The paper provides insights into the behavior of nanofluids in complex environments and explores the impact of varying conditions on key properties such as thermal conductivity, density, viscosity, and specific heat. Ultimately, the research contributes to the broader understanding of nanofluid dynamics and has potential implications for engineering and industrial applications in porous media.Design/methodology/approachThis paper investigates nanofluids with spherical nanoparticles in a porous medium, exploring thermal conductivity, density, specific heat, and dynamic viscosity. Studying three compositions, the analysis employs the classical Maxwell model and Koo and Kleinstreuer’s approach for thermal conductivity, considering particle shape and temperature effects. Density and specific heat are defined based on mass and volume ratios. Dynamic viscosity models, including Brinkman’s and Gherasim et al.'s, are discussed. Numerical simulations, implemented in Python using the Langevin model, yield results processed in Origin Pro. This research enhances understanding of nanofluid behavior, contributing valuable insights to porous media applications.FindingsThis study involves a numerical examination of nanofluid properties, featuring spherical nanoparticles of varying sizes suspended in a base fluid with known density, flowing through a porous medium. Experimental findings reveal a notable increase in thermal conductivity, density, and viscosity as the volume fraction of particles rises. Conversely, specific heat experiences a decrease with higher particle volume concentration.xD; xA; The influence of permeability and pore size on particle volume fraction variation is a key focus. Interestingly, while the permeability of the medium has a significant effect, it is observed that it increases with permeability. This underscores the role of the medium’s nature in altering the thermophysical properties of nanofluids.Originality/valueThis paper presents a novel numerical study on nanofluids with randomly sized spherical nanoparticles flowing in a porous medium. It explores the impact of porous medium properties on nanofluid thermophysical characteristics, emphasizing the significance of permeability and pore size. The inclusion of random nanoparticle sizes adds practical relevance. Contrasting trends are observed, where thermal conductivity, density, and viscosity increase with particle volume fraction, while specific heat decreases. These findings offer valuable insights for engineering applications, providing a deeper understanding of nanofluid behavior in porous environments and guiding the design of efficient systems in various industrial contexts.

Effect of Particle Shape on Contact Network and Shear-Induced Anisotropy of Granular Assemblies: A DEM Perspective

Effect of Particle Shape on Contact Network and Shear-Induced Anisotropy of Granular Assemblies: A DEM Perspective

Particle shape and clogging in fluid-driven flow: A coupled CFD-DEM study

Clogging is a critical issue in the flow of particulate matter. This study uses the computational fluid dynamics coupled with discrete element method (CFD-DEM) to investigate how particle shape affects clogging behavior. Settling tests were conducted to confirm the dynamic behavior of irregular particles, modeled using the bonded-sphere method, in flow. The particle shape features were classified into form, roundness, and surface texture. The results demonstrate that sieving mechanisms, particle locking, and friction effects resulting from particle shape significantly impact microscopic clogging behavior. Irregular particles also increase the filter cake’s porosity, resulting in a higher flow rate at the orifice and an elevated probability of macroscopic clogging. This study enhances our understanding of the effect of particle shape on clogging with both microscopic and macroscopic evidence.

Particle size analysis: A comparison of laboratory-based techniques and their application to geoscience

In sedimentary geoscience, the particle size distribution (PSD) of a sediment has a fundamental effect on a sediment's ability to be entrained, eroded, and deposited. Therefore, it is crucial to accurately measure the PSD of sediments. Several laboratory-based methods of particle size analysis are commonly employed in geoscience; however, each method is based on different principles and the comparison of data from one technique to another is challenging. In this study, we have compared the output of four commonly-used laboratory-based techniques: Laser Particle Size Analysis (LPSA), optical point counting, 2D automated image analysis, and X-ray Computed Tomography (XCT). Each technique has been used to measure eight samples of spherical silica particles, all prepared with known particle size ranges. Spherical particles have been used to minimise the effects of variable sorting and particle shape on data output. Here we have compared the differences between the measured PSD and descriptors of each PSD, showing that, at small particle diameters (<150 μm), all techniques agree. However, at particle diameters >150 μm, LPSA overestimates the size of particles, due to limitations in the way that particle diameter is calculated by this technique. In contrast, 2D automated image analysis and optical point counting underestimate the diameters of particles, due to stereology (e.g., the effect of slicing particles during thin section preparation). Results from XCT analyses have the lowest values of sorting (range of measured particle diameters) and are therefore the most tightly constrained. In addition, XCT is the only 3D analysis method, allowing particle shape, orientation, and intraparticle porosity to be measured for a volume of material. We therefore conclude that XCT is the most accurate way to determine a grain size distribution in sediments.

Parameters affecting plug characteristics in dense phase pneumatic conveying of ellipsoidal particles

Even though particle shape tends to have a major influence on the bulk behaviour of a granular system, perfectly spherical particles are often used in numerical simulations. In this study, we examine the plug flow of ellipsoidal particles in dense phase horizontal pneumatic conveying within a rigid and cylindrical pipe with periodic boundaries in the axial direction. We use coupled Computational Fluid Dynamics (CFD) – Discrete Element Method (DEM) simulations to investigate the effect of particle shape on four plug characteristics: velocity, length, porosity, and particle exchange rate with the stationary bed. Both ellipsoidal and spherical particles are used, and the parameters varied are the particle size, aspect ratio, pressure gradient, particle–particle and particle–wall sliding and rolling friction coefficients, and coefficients of restitution. The steady state characteristics of plugs composed of spherical particles are distinctly different from those composed of ellipsoidal particles. Certain parameters, including the particle–wall rolling friction and restitution coefficients, have minimal impact on the steady state plug characteristics. The present study also suggests that introducing interparticle rolling friction for perfectly spherical particles can achieve the velocity and length appropriate for plugs composed of ellipsoidal particles, although differences in dynamics may persist. Overall, this comprehensive analysis offers valuable insights into plug flow behaviour with non-spherical particles, aiding in the efficient modelling and design of pneumatic conveying systems.

Effect of particle shapes on diffusion and mixing in a cylindrical mixer with rotating paddles

Effect of particle shapes on diffusion and mixing in a cylindrical mixer with rotating paddles

Investigation of micro-scale shear response of sand–rubber granule mixture in terms of particle shape and grain scale deformability effects

In this study, the effects of particle shape of rigid sand and soft rubber materials on macro-scale shear response were reasoned based on micro-scale parameters. For this purpose, first, the shape properties of three different sand and two different rubber samples were quantified using image processing techniques, and the contact model parameters were calibrated through physical experiments. The direct shear test was simulated in a two-dimensional discrete element software with realistic particle forms. The soft nature of rubber particles was reflected using body-centered cubic packing with a linear-parallel bond contact model. As a result, coordination number, distribution of contact forces (i.e., strong contact, and fabric anisotropy), and contact sliding were derived by the numerical analyses. It has been observed that the particle shape leads to distinctive micro-scale responses due to the variations in the stiffness of the contacts.

Experimental investigation into segregation behavior of spherical/non-spherical granular mixtures in a thin rotating drum

This paper uses physical experiments to investigate the segregation behavior of binary granular mixtures in a quasi-two-dimensional rotating drum. Spherical polyformaldehyde (POM) beads and cylindrical red beans constitute the granular mixtures. The effects of particle size, particle density, and particle shape interplay during the segregation process in the spherical/non-spherical particulate system. A long-axis ratio (LAR), the ratio of the spherical POM beads' diameter to the red beans' primary dimension, was defined to explore the particle shape effect. The experimental results show that the long-axis ratio and the rotation speed play substantial roles in the granular segregation behavior. As the long-axis ratio increases, the steady-state segregation intensity decreases. An increase in the rotation speed enhances the segregation of the binary granular mixtures for each long-axis ratio studied here. In addition, the average velocity and granular temperature of spherical POM beads increase as the long-axis ratio increases. Both properties also increase as the rotation speed increases. The dynamic angle of repose for the binary mixtures increases with the increase in the long-axis ratio. Most interestingly, reverse granular segregation does occur at a long-axis ratio of 0.70 with the cylindrical red beans in the core and the spherical POM beads at the periphery for each rotation speed studied here. This reverse segregation has not been observed in previous studies. This highlights the substantial impact of particle shape on the granular segregation in binary granular mixtures.

Segregation of binary particles in pulsed gas-solid fluidized bed

Pulsating airflow-driven gas-solid fluidization is an effective method to segregate particles of different densities. The current article presents an elaborate computational study on the development of simulation methodology, and parametric trend identification of pulsating airflow-driven granular segregation for the first time using computational fluid dynamics (CFD), discrete element modeling (DEM) coupled analysis. The rigorous validation of the computational prediction has been produced against the experimental result reported by Li et al. (2021) and an excellent agreement has been observed. Segregation behavior for different density ratios of particles, different patterns of pulsation, and different particle shapes is presented in the current article. The segregation index improves with the density ratio of the binary mixture of particles, but the rate of increment of the segregation index is highly dependent on the airflow rate. Near the optimal value of airflow rate, the rate of increment of the segregation index reduces with the density ratio. Keeping the bed height and material property constant, different patterns of pulsation namely—sinusoidal, triangular, and exponential have been adopted. The segregation index is higher for sinusoidal patterns, whereas it reduces when the pattern is changed to triangular and exponential. Particles of constant volume with different shapes are also considered to understand the effect of particle shape on segregation. The segregation index deteriorates with the increasing surface area of the particle at constant volume.

Effect of particle shape on cyclic liquefaction resistance of granular materials

Effect of particle shape on cyclic liquefaction resistance of granular materials

Synergetic effect of particle shape and multi-layer coating on the magnetic properties of FeSiAl-based soft magnetic composites

Gas atomization and multi-layer coating are widely used powder fabrication techniques to prepare soft magnetic composites (SMCs) utilized in high-power low-loss power electronics. However, the diverse morphologies of gas-atomized powders significantly impact coating effectiveness, subsequently influencing the soft magnetic properties of SMCs. Herein, FeSiAl-based SMCs with different particle shapes and a multi-layer coating of phosphate and heat-resistant silicone resin are prepared to explore the synergetic effects of particle shape and coating on magnetic performances. Compared with dumbbell-shaped powder, the spherical powder has a regular shape and strong flowability, resulting in a close-packing structure of the magnetic core. The spherical particle with a large specific surface area promotes efficient insulation coating effects. The dumbbell-shaped particles are potentially prone to cause pores and defects during the high-pressure compaction process, leading to poor dense packing and magnetic loss performance. With a similar average particle size, the magnetic core prepared by spherical powders exhibits a larger interface area, resulting in a greater demagnetizing field after phosphating passivation, thus significantly improving the DC-bias performance. The FeSiAl-based magnetic core prepared by spherical powders with 1.5 wt% phosphoric acid passivation has better magnetic loss and DC-bias properties than that by dumbbell-shaped powders, showing a stable permeability of 60.4, core loss of 286.2 mW/cm3 at 100 mT, 100 kHz, and DC bias characteristic of 49.1 % at a DC superposition field of 100 Oe.

3D printing-aided numerical study of particle shape effect on behaviours of dry granular flows interacting with rigid barriers

Particle shape plays a crucial role in determining the mobility and impact characteristics of granular flows, yet analyses of the effects of particle shape are rare. In this study, three-dimensional (3D) printing technology is used to create rock-like materials with varying shapes. This approach enables the precise control of mechanical properties other than particle shape, eliminating potential confounding factors. Then, we construct particle flow samples with distinct shape characteristics, quantitatively assessing their shape variations according to their overall regularity (OR). Flume experiments are conducted, with the findings used to calibrate a discrete element numerical model. By integrating the numerical simulations and experimental data, we systematically investigate the flow, impact, and deposition behaviours of granular flows under diverse flume inclinations considering the influence of particle shape. The results demonstrate that the mobility and destructiveness of granular flows increases with higher OR values and steeper flume inclinations. The transition from pile-up to runup deposition is primarily controlled by the flume inclination, while within specific inclination ranges, changes in OR can also induce deposition mechanism transition. This study provides substantial insights into interactions between granular flows and protection structures, emphasizing the significance of particle shape and terrain characteristics within a source area.

Effect of passive particle shape on effective force in active bath

&lt;sec&gt;In active matter, the effective force between passive objects is crucial for their structure and dynamics, which is the basis for understanding the complex behaviors within active systems. Unlike equilibrium states, the factors such as the surface configuration, size, and confinement strength significantly influence the effective forces between passive particles. Previous studies have shown that the shapes of passive particles affect the aggregation of active particles, leading to different forces experienced by passive particles with different shapes. However, recently, a long-range attractive force between passive platelike particles, caused by the bacterial flow field instead of the direct bacterium-plate collisions in active bacterial suspensions, has been found. This raises an intriguing question: how does hydrodynamics affect the forces on passive particles of different shapes in different ways?&lt;/sec&gt;&lt;sec&gt;In this work, we investigate the effective forces exerted on passive spherical and plate-like particles immersed in bacterial suspensions by optical-tweezers experiments. The effective force between passive particles can be calculated from the formula, &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ {F_{{\text{eff}}}} = {\text{ }}k\left\langle {\Delta d} \right\rangle /2 $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M1.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, where &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ \left\langle {\Delta d} \right\rangle $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M2.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; represents the difference in distance between the passive particles in the bacterial bath and those in the solution without bacteria, &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ k $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M3.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; is the effective stiffness of optical traps. The &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ {{{F}}}_{{\mathrm{e}}{\mathrm{f}}{\mathrm{f}}} &gt; 0 $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M5.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M5.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; indicates a repulsive force between passive particles, and the &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$ {F_{{\text{eff}}}} \lt {\text{ }}0 $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M6.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M6.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; represents an effective attractive force between passive particles. Our results demonstrate that the passive spherical particles experience short-range repulsion, while plate-like particles are subjected to long-range attraction. This highlights the substantial effect of particle shape on their effective forces.&lt;/sec&gt;&lt;sec&gt;The forces on passive particles are mainly attributed to two factors: direct bacterium-particle collisions and the bacterial flow field. The analysis of the bacterial concentration and orientation distribution around passive particles reveals that for spherical particles, the concentration of bacteria between particles is higher than that outside the particles, but there is almost no difference in the orientation order between bacteria inside and outside the particles. This suggests that the effective repulsion between spherical particles is mainly due to the direct bacterial collisions. Conversely, for plate-like particles, the long-range attraction is primarily influenced by the bacterial flow field rather than their direct collisions, which is evidenced by the higher bacterial density and orientation order inside the two plates compared with those outside the two plates. This study provides strong evidence that the effective force between passive particles is shape dependent in active bath, and offers new insights into controlling active-directed assembly.&lt;/sec&gt;

Super-quadric CFD-DEM study of spout deflection behaviour of non-spherical particles in a spout fluidized bed

Non-spherical particles are commonly encountered in chemical engineering processes including fluidization processes, yet their instability phenomena still lack understanding. In this study, the spout deflection – a typical instability phenomenon of non-spherical particles in a pseudo-two-dimensional (pseudo-2D) spout fluidized bed is first studied by a super-quadric computational fluid dynamics-discrete element method (super-quadric CFD-DEM) model. The intensity of spout deflection is quantified by the spout deflection angle concept. The effect of particle shape (i.e., sphere, cubic, ellipsoid, and cylinder) on the flow in terms of flow pattern, spout deflection, pressure drop, particle orientation, and normal contact force is systematically studied and compared by the time- and frequency-domain analysis. It shows that the spout channel becomes narrower for cubic, ellipsoid and cylinder particles where the particle aspect ratio increases. With the increase of spouting gas velocity, the median value of the spout deflection angle decreases and increases for cubic and ellipsoid particles, respectively. Furthermore, the pressure drops in the vertical and horizontal directions of the cubic, ellipsoid, and cylinder particles are different from each other. At last, In the bed of cubic particles, the ordered arrangements appear close to the wall region and random arrangements occur in the other regions. This work reveals the influences of non-spherical particles on spout deflection and offers insights into practical applications through optimal operation.

Effect of ceramic particle shape on wear resistance mechanism of zirconia toughened alumina ceramic reinforced high chromium cast iron architectural composite

Zirconia toughened alumina (ZTA)/high chromium cast iron (HCCI) architectural composites are widely used in many fields, and several factors can affect their wear resistance. The objective of this study was to examine the three-body abrasive wear characteristics of an irregularly shaped ZTA/HCCI composite in comparison with conventional HCCI and crushing ZTA/HCCI composites. Irregularly shaped ZTA was prepared in this study, and ZTA/HCCI composites were fabricated with different ZTA shapes. The mass loss rates of crushed and irregularly shaped ZTA/HCCI composites were observed 0.29 % and 0.26 %, respectively, when subjected to the three-body abrasive wear process. These results indicated the improved wear resistance of the ZTA/HCCI composite. Because the irregularly shaped ZTA ceramic particles did not have sharp edges, which suppressed the tendency for stress concentration, the internal stress was significantly reduced. Therefore, the likelihood of crack formation was substantially reduced, reducing the probability of failure and increasing the wear resistance. In this study, this approach provided a new idea to enhance the wear resistance.

Geometrical shape and self-shielding effect of burnable poison particles on pin-in block type HTGR neutronic performance

In our previous works, two different spherical burnable poison particles (BPPs) as B4C and Gd2O3 in pin-in block type HTGR core had utilized to suppress the excess reactivity and to control long-term reactivity during the burnup period. In the present work, we performed the neutronic analysis of a prismatic HTGR operating at 850 °C with thermal power of 100 MW containing spherical and cylindrical BPPs and then studied the self-shielding effect of BPPs and shape effect. The calculations were performed when the surface area (1) or volume (2) of cylindrical BPPs equals to that of the spherical BPPs. The calculations showed that the neutronic parameters were slightly better for the second case than the first one, such as the excess reactivity of the reactor core at the beginning of the cycle were more suppressed, the core lifetime were more extended, and the fuel-burning were more efficiently. The neutron spectrum in each region of the cylindrical BBPs slightly differs than that of the spherical BPPs. Therefore, the self-shielding effect of BPPs on reactor core performance depends on the particle's geometrical shape.

Particle shape anisotropy in pickering interfacial catalysis for Knoevenagel condensation

Dispersions of two immiscible liquids stabilized by solid particles are termed as Pickering emulsions. Stability of such emulsions is affected by various parameters such as amount of solid particle, method of emulsification, size, and shape of particles, etc. In this study, MgO samples prepared by different methods and characterized by XRD, FESEM, HRTEM, DLS, and CO2-TPD techniques were utilized for stabilizing o/w Pickering emulsions. The effect of particle shape on Pickering Interfacial Catalysis (PIC) for Knoevenagel condensation was investigated. It was found that in the case of rod and plate shaped particles, emulsion stability and catalytic activity were higher as compared to those obtained with other MgO samples prepared. The applicability of the MgO-PIC system is also successfully demonstrated for gram scale synthesis (85 % yield in 30 min). The MgO-PIC system was found to be reusable for at least five cycles without substantial loss in activity.

Laboratory investigation on the single particle crushing strength of carbonate gravel incorporating size and shape effects

Particle strength is one of the critical factors that causes the degradation of the mechanical behaviour of crushable soil. Because of the complexity of particle shape, its effect on particle strength has not been completely understood. In this study, single particle crushing tests were performed on carbonate gravel particles with three size fractions (i.e. 5–10 mm, 10–15 mm and 15–20 mm) and three shapes (i.e. blocky, rodlike and flaky), using a PartAn3D Maxi large particle size and shape analyser to obtain the shape characteristics of the particles. The determination of crushing strength for particles with complex shapes was discussed, and it was found that it is appropriate to use the area equivalent circle diameter to obtain the crushing strength. The influence of particle size and shape parameters, including the elongation index, flatness index, intercept sphericity, circularity and convexity, on the crushing strength were identified, and an index termed the form factor considering dimensions in three directions was proposed to describe the effect of particle shape. Based on this form factor, a probabilistic model was established to predict the distribution of crushing strength of carbonate gravel particles with various sizes and shapes. The proposed model could be used in the discrete-element method to consider the influence of shape in addition when evaluating particle breakage.