Influence of Irregular Particle Shape on Volumetric Behaviour of DEM Materials in Rotational Shear Testing

Influence of Irregular Particle Shape on Volumetric Behaviour of DEM Materials in Rotational Shear Testing | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Influence of Irregular Particle Shape on Volumetric Behaviour of DEM Materials in Rotational Shear Testing Jiří ROZBROJ, Jakub HLOSTA, Jan DIVIŠ, Jan NEČAS, Diego BARLETTA, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5298776/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The study investigates the effect of particle shape representation with various contact models on the calibration procedure via shear test. Experimental shear tests were performed using a Schulze Ring Shear Tester RST-01 using spherical and cubic particles. Pre-shear stress and vertical lid position were used for calibration. Hertz-Mindlin and Linear Spring contact models behaviour trends for preshear, vertical lid position, coordination number, porosity and particle shift angle were observed. The changes of the shear zone for different input parameters are show. The findings confirmed the necessity to observe not only the shear force but also the compression behaviour of the particles in the shear test calibration. The results clearly indicate that the position of the shear lid provides DEM users with an overview of the fundamental deformation behaviour during the shear process. The results highlighted fundamental differences between particle models, considering the changes in kinematics due to increased shear rate. The research is intended to provide DEM modellers with general information on which parameters are affected by changing the input data for each contact model and particle shape. These insights can enhance calibration procedures in both industrial and academic settings, serving as a foundation for optimizing DEM models and improving their accuracy. Physical sciences/Mathematics and computing/Computational science Physical sciences/Engineering Physical sciences/Materials science/Theory and computation/Computational methods Hertz-Mindlin contact model Linear Spring cube particle sphere particle DEM calibration Discrete Element Method Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 1 Introduction With the development of the Discrete element method (DEM) [ 1 ] its capabilities and predictive are continually evolving [ 2 , 3 ]. Among the first calibration procedures was the angle of repose test [ 4 ]. It has a sufficient predictive value in terms of static material behaviour, but it has also been well accepted in applications with specific dynamic effects [ 5 ]. Furthermore, there are several other possible ways in which the set behaviour of DEM particulate materials are verified [ 6 , 7 , 8 ]. These methods include shear test of the material [ 9 , 10 , 11 , 12 ]. A shear test measures the deformation of a material under a certain compressive normal stress. Once the desired normal (vertical) load is set on the specimen, the shear strength (shear or horizontal stress) is determined. The ratio of these two stresses indicates the ability of the material to transfer vertical forces between particles of matter to forces between particles in the horizontal direction. The general theory is used in the design applications of bulk material handling and storage equipment, especially with regard to the magnitudes and ratios of the applied pressures [ 13 , 14 ]. These ratios generally characterize the vertical ("gravitational") throughput of the particulate material through the geometry (e.g., the structure of the hopper) [ 15 ]. In terms of the shear deformation of the particulate material, attention must also be paid to the change in volume of the tested sample. For these reasons, the position of the lid during the shear test is also monitored, as the vertical sample deformation (compression/expansion) may also be related to the change in the magnitude of the shear stress [ 16 ]. This relationship can be observed for various shear stress influences such as shear rate [ 17 ]. If the shear stress increases due to a change in the kinematics of the shear process or due to the particle arrangement, the vertical compression of the sample decreases and vice versa. The particles which do not disintegrate due to compressive stress undergo changes in their spatial distribution as the volume of the particle sample changes [ 18 ]. The particle arrangement can affect the ultimate strength of the particulate material with respect to the deformation and the flow capabilities on a macro scale. There may also be associations with changes in material porosity [ 19 ]. Another parameter that influences the volumetric deformation of the sample during shear test is the shape of the particles. The irregular shape of the particles can increase the shear stress values at low normal loads. This is due to an increase in the coordination number, which expresses the number of contacts between particles in a particular volume of the sample. Spherical particles tend to have lower coordination numbers than non-spherical or irregularly shaped particles, and a higher tendency towards isotropic behaviour [ 20 ]. The DEM software generally assumes a certain stiffness of the individual particle contacts [ 1 ]. This stiffness can be set by input parameters such as Young's modulus, Poisson's constant, or shear modulus [ 21 ]. DEM software users use the Shear Modulus values to reduce the computation time. When the number of particles is high, the computation time is reduced by decreasing the shear modulus value. However, it is necessary to maintain a certain degree of stiffness of the particles or the whole sample so that the conditions of the ratios and magnitudes of the vertical pressure values are met [ 16 , 22 ]. There are a number of DEM models, and each is specific in its deformation behaviour [ 23 ]. Whether the deformation is elastic or plastic, there is always a correlation between the input parameters or measured quantities. In order to achieve similar behaviour of different DEM models, different input parameters need to be used [ 16 ]. There is a gap in scientific knowledge regarding the use of shear tests for calibrating and validating virtual particulate materials in DEM simulations. Despite their widespread use, DEM simulation models are not often compared with each other. Additionally, the use of shear tests as a calibration tool is often inappropriate because multiple parameters are not compared, typically focusing on just one selected parameter. Users may not fully understand the implications of changes in input parameters and tend to focus only on a single parameter for calibrating virtual particulate materials. This can lead to inaccuracies and incorrect DEM simulations. The focus of this study is partly aimed at identifying possible ways leading to similar behaviour of different DEM models during shear test of particulate materials with different particle shapes. In this work, spherical particles were used to represent spherical geometries, while multispherical particles were applied to simulate cubic particles. These particle configurations illustrate the variety of DEM models and their potential when simulating shear tests for bulk materials. The aim of the study is to investigate the effect of particle shape on the changes of properties during shear process such as shear stress values or deformation parameters expressed by the vertical position of the shear cap during the shear test. Furthermore, the implications of internal friction with the ability of particle movement and changes in their relative positions in the shear cell layers were addressed. Some relationships are supported by other parameters such as coordination numbers and porosity of the sample volume. The summary of the study's findings should then serve to support academic and commercial DEM modellers to gain a general understanding of the processes, processes and laws for more efficient and accurate calibration of DEM materials using rotational shear test. 2 Methods 2.1 Shear test The basic principle of the shear test is to find the ratio of these values of the normal stress σ pre at preshear stress and shear stress at the end of preshear (steady-state flow) τ pre . The Angle of Internal Friction AIF can be determined by using these two values. More precisely, it is the determination of the AIF at steady-state flow φ sf (1). The determination of these values is based on methods for determining the flow function using a ring shear tester RST-01.pc (RST) [ 24 ]. Default vertical load input value for all measurements σ pre was 20 kPa. Fifteen repeated measurements were performed on the RST, each time with the same sample newly added to the shear cell type S (small v1.2). The inner and outer radii of the shear ring were 60 mm and 30 mm, respectively. The active shear cell height was 24 mm and therefore the cell volume was 2.04·10 − 4 m 3 . The shear cap through which the normal stress value σ pre was applied to the specimen had active area radii of 59 and 31 mm. A real-time recording of the shear stress values τ pre was taken from each measurement with normal stress σ pre setting. Furthermore, the vertical lid position (VLP) values were recorded to reflect the volume change (compression/expansion) of the material sample during the shear test. These VLP or sample volume values could be used to determine the porosity ε. The shear rate was set to a fixed value 1.51 mm·min − 1 . The angular velocity is assumed over the length of the arm 46.45 mm S-type shear cell that rotates 0.031 deg·s − 1 [ 25 ]. $$\:{\phi\:}_{sf}=arctg\frac{{\tau\:}_{pre}}{{\sigma\:}_{pre}}$$ 1 The measured samples were spherical and cubic particles (Fig. 1 ) made of 3D printing material Prusament PLA with a density of 1240 kg·m − 3 according to ISO 1183. The printing was performed on a Prusa i3 MKS3 printer (Prague, Czech Republic), PrusaSlicer version 2.3.0, setup with a layer height of 0.07 mm and 100% fill. The measured outer diameter of the spherical particles was 5.99 ± 0.05 mm (with standard deviation 0.8%) and the number of these spherical particles used in the shear cell was 911 ± 16 (with standard deviation 1.8%). The number of the spherical particles was determined as a part of the change in total sample mass from fifteen repetitions of measurements. The cubic particles had an average edge length value of 3.87 ± 0.08 mm (with standard deviation 1.96%) and the number of particles used in the shear cell was 1935 ± 26 (with standard deviation 1.4%). The number of cubic particles was also determined as a part of the change in the total mass of the sample from fifteen repetitions of measurements. 2.2 DEM simulation Altair® EDEM™ version 2021.0 was used for DEM simulations. Four main physical DEM models were used. For the spheres and multi-spheres, they were Hertz-Mindlin (no slip) and Linear Spring. The Hertz-Mindlin (HM) model is often the fundamental and default contact model of particle interactions. It is used in a various areas of DEM research. The HM model has been published many times in its default or modified form in shear test applications [ 12 , 26 , 27 , 28 , 29 , 30 , 31 ]. Both, the normal and tangential components of the force, usually use damping that is closely tied to the restitution coefficient. Tangential friction forces are based on Coulomb's friction law. Rolling friction model can be implemented in various modifications [ 32 , 33 ]. The Linear Spring (LIN) model is not applied for shear tests as often as the HM model but its usefulness is very similar [ 34 , 35 , 36 , 37 ]. The LIN model uses coefficients such as the Linear Spring Stiffness. The Linear Spring Stiffness is based on mechanical-physical parameters such as Young's Modulus, Radius of the particle, Equivalent Mass, but mainly Typical Impact Velocity. The Typical Impact Velocity can affect the overall stiffness of the sample volume at the macroscale [ 16 ]. Another coefficient of the LIN model is the Dashpot Coefficient, which is influenced by the coefficient of restitution, the equivalent mass and the linear spring stiffness. 2.3 DEM model – input Three particle shapes were used for the study. A regular sphere SP particles (Fig. 2 a) with a radius of 2.99 mm, and two types of multi-spheres representing a cube (Fig. 2 b and Fig. 2 c). The first type of multi-sphere MS-26 particles (Fig. 2 b) was made of 26 spheres with their radius of 0.65 mm. The arrangement was 3x3x3 spheres, with one sphere missing in the middle of the whole particle and each wall consisted of nine particles. The second type of multi-sphere MS-21 particles (Fig. 2 c) was made of 20 spheres with their radius of 0.65 mm and one sphere with a radius of 1.95 mm placed in the centre of the particle. The arrangement was 3x3x3 spheres with each wall consisting of eight particles. A sphere with a radius of 0.65 mm was missing in the middle of each wall because the space was filled by the volume of the central sphere with a radius of 1.95 mm. The number of the SP particles used was 911 ± 16 particles. (Fig. 2 a). The number of particles used for both particle types representing a cube (MS-26 and MS-21) was 1935 ± 26 particles. (Fig. 2 b and Fig. 2 c). Table 1 and Table 2 show the material and interaction parameters of these particles. Timestep was automatically set according to Euler at 1e-06 s. Table 1 Material properties Material property Particle Geometry Poisson's Ratio, ν (−) 0.25 0.25 Solids Density, ρ s (kg·m − 3 ) 1240 7800 Shear Modulus, G e (Pa) 2.4e + 07 7.93e + 10 Table 2 Interaction parameters Interaction Particle/Particle Particle/Geometry Coefficient of Restitution, e (−) 0.5 0.6 Coefficient of Static Friction, µ s (−) 0.4, 0.6, 0.8, 1.0 0.2 Coefficient of Rolling Friction, µ r (−) 0 0 The particles in the shear cell were generated in 2 seconds. The particles were generated randomly with a Generation Rate with Target per number of 2500 per seconds. Then a lid with a vertical load σ = 20 kPa was placed on the shear cell, which was automatically held at a constant value throughout the shear process. The shear lid had a degree of freedom in the vertical Z axis and rotational freedom in the X and Y axes. A more detailed setting of the kinematic and physical properties of a shear cell with a lid in EDEM is given in the publication [ 16 ]. Simulations of the shear process were performed for two shear cell rotation settings at 0.005173683 rpm and 0.02069473 rpm. The change in the rotation is reflected in a change of the shear rate SV. The change of the shear rate was from the SV = 1x to the SV = 4x. The length of the shear process was for the SV = 1x approximately 245 seconds and for SV = 4x approximately 60 seconds. The Inter-Particle Friction µ s was set to values 0.8 and 1.0 for SP particles. The MS particles had the Inter-Particle Friction set to 0.4 and 0.6. Given all 24 combinations of the input parameters (particle shape, physical contact model, Inter-Particle Friction µ s , and shear rate SV), it gives total of 72 number of simulations performer and evaluated. 2.4 DEM model – output According to the procedure presented in [ 16 ] the total shear stress τ, the normal stress σ, the Vertical Lid Position VLP and the Angle of Internal Friction AIF were expressed from the simulations at a time step of 0.5 second. Furthermore, the Coordination Number CN and the data of the actual XYZ particle positions for the Angle of Particle Shifts ϕ S were expressed from the simulations over time with a time step of 1 second. The average horizontal particle velocity (Average Particle Velocity X and Y) (AVXY) and initial ε start and final ε end porosity of the material in the shear cell were also expressed. The Coordination Number CN of a particle is defined in EDEM as the number of contacts that a particle has with another particle. If one particle is composed of several sub-particles (multi-spheres), the contacts of the individual sub-particles with each other are also counted. For this reason, particles consisting of a larger number of sub-particles have a higher CN. The predictive value from comparisons within the CNs themselves is limited to the identical particle shape. It is not possible to directly compare CN Single-Particle and Multi-Spheres particle, but it is possible to compare the change of CN due to the change of e.g. the Inter-Particle Friction µ s . In general, the higher the Inter-Particle Friction µ s , the lower the particle embedment and hence the lower the CN. The CN is influenced by the particle embedment which affects the overall elasticity/stiffness of the particle material during the loading or shear process. The porosity of the bed (spacing) of the particulate material is also related to these properties and behaviour. The CN can be a guide to the correct setting of the mutual embedding of the particles into each other, or to the setting of the correct stiffness and initial porosity of the particle material. The average CN was recorded over time during the shear process for each simulation with a time step of 1 second. Three simulations with the same settings were then used to generate one average CN waveform over time. A single mean value was then expressed from this waveform along with the standard deviation. The effect of the static coefficient of friction µ s between particles on the CN values of the individual models was investigated. Differences in CN values for different µ s were expressed as relative average deviations (RAD) in units of [%]. The RADs were solved for the Inter-Particle Friction µ s 0.8-1.0 for the SP particle model and for the Inter-Particle Friction µ s 0.4–0.6 for the MS21 and MS26 particle model. The XYZ particle positions were exported according to [ 16 ]. In general, a single particle shift S i (t i ) was defined as a change of position in 3D space (Fig. 3 a) from the initial to the final position at time step t i . The coordinates X and Y define the horizontal plane. The Angle of Particle Shifts ϕ Si of each particle P j at time step t i was expressed from the exported data. The Angle of Particle Shifts can be understood as a measure of the resistance to change the particle position in the shear cell. Each subsequent shift S i+1 (t i+1 ) was defined such that the final position from the previous time step t n becomes the new starting position of the next shift. The resulting angle ϕ Sj (9) of the 3D shift S i (t i ) of the particle P j at time step t i was expressed from the tangent of the ratio Δz i to the resulted motion R i (8) in the horizontal XY plane. Based on the initial coordinates z t0 of the particles at time t 0 all particles were assigned an emergence layer (Fig. 3 b). Four layers were created in the shear cell for all particle types (SP, MS-26, and MS-21). The height of one layer was 6 mm. In each layer, for each time step from t i to t n , one value of the average Angle of Particle Shifts ϕ S (t i ) was determined from all angles of particle shifts ϕ Sj (10). \(\:{R}_{i}=\sqrt{\varDelta\:{x}_{i}^{2}+\varDelta\:{y}_{i}^{2}}\) (8) \(\:\left|{\varnothing\:}_{Sj}\left({t}_{i}\right)\right|=arctg\left(\frac{{\varDelta\:z}_{i}}{{R}_{i}}\right)=arctg\left(\frac{{z}_{{t}_{n}}-{z}_{{t}_{n-1}}}{\sqrt{{\left({x}_{{t}_{n}}-{x}_{{t}_{n-1}}\right)}^{2}+{\left({y}_{{t}_{n}}-{y}_{{t}_{n-1}}\right)}^{2}}}\right)\) (9) \(\:\left|{\stackrel{-}{\varnothing\:}}_{S}\left({t}_{i}\right)\right|=\frac{1}{j}\bullet\:{\sum\:}_{i=1}^{j}\left|{\varnothing\:}_{Sj}\left({t}_{i}\right)\right|\) (10) Average Particle Velocity X and Y AVXY was investigated in individual layers which followed the distribution for XYZ shifts. Each layer L1 to L4 consisted of four separate quadrants. In each quadrant, one overall average AVXY value from the shear process was separately determined with a time step of 0.05 seconds. One final AVXY value of one whole layer was created by averaging the four values of all quadrants. The identification of the main (dominant) shear region was a prerequisite for the AVXY solution. The largest difference in the resulting horizontal AVXY between the layers could characterize the dominant shear region. Graphs of the velocities of the individual layers and tables of the values of the line segment directives were created. The graphs characterize the specific magnitude of the velocity difference between two adjacent layers by a single number. The porosity ε [-] was expressed by the Eq. ( 11 ). The mean value and standard deviation for the Porosity ε was obtained from three simulations with the same settings. The objects of interest were the average values for the initial porosity value ε start and the final porosity value ε end of the shear process. The effects of changes in the Inter-Particle Friction µ s and shear rate (SV) on the average values of ε start and ε end were also investigated. The detailed evaluation procedure is given in the article [ 16 ]. $$\:{\epsilon\:}_{start,\:\:end}=\frac{{V}_{Voids}}{{V}_{Total}}$$ 11 3 Results 3.1 Preshear (PS) The resulting shear processes obtained by the Preshear (PS) simulation were compared. This comparison is for all the DEM particle models investigated. The variables were the Inter-Particle Friction µ s and the shear rate (SV). Each individual PS curve for different contact models and Inter-Particle Friction µ s values are expressed by the average values obtained from three repeated simulations. Figure 4 shows the Preshear PS for the SP particles. The change in the Inter-Particle Friction µ s did not significantly affect the final PS values for the shear rate SV = 1x. Towards the end of the PS process, higher Inter-Particle Friction µ s values resulted in a slight decrease in the PS values for both the HM and LIN models. Also, the change in the Inter-Particle Friction µ s did not significantly affect the final PS values for the SV = 4x. Rather, the increase in µ s resulted in a slight decrease in PS values, which is the opposite of the expected pattern. The increase in the SV was reflected by a slight decrease in the PS values. With higher shear rate, there are probably more kinematic effects between particles and the resistance between particles decreases. Particles may have a greater tendency to be oriented to move in the direction of flow, which can reduce this resistance. At higher shear rates, the frequency of particle collisions can increase. This reduces the persistence of particles in mutual contact over time, the effect of kinematic friction. The change in the µ s values was apparently small considering the small changes in the PS for the SP particles. The PS for the MS-26 particle is shown in Fig. 5 The increase in the µ s is significant only for the HM model towards the end of the PS process for the shear rate SV = 1x. The HM model had slightly higher PS values in the first half of the shear process (up to 120 s) than the LIN model. Towards the end of the process, the difference between HM and LIN evened out. For the SV = 4x, a very similar overall PS for the HM and LIN models was obtained. Towards the end of the process, slight differences became apparent. The increase in µ s was reflected more for the SV = 4x than the SV = 1x by an increase in the PS values for the HM model towards the end of the PS process. There is a significant difference in the Preshear PS values (10 kPa vs. 12 kPa) when compared to the SP particles. The increase in PS can be attributed to the particle shape because the Inter-Particle Friction µ s was lower for MS particles compared to SP particles. Cube-shaped particles exhibit a larger particle contact area. Furthermore, uneven distribution of contact forces between the particles may occur due to different rotation of the cubic particles. This phenomenon does not occur for the SP particles as they are spherical and have the same shape at any rotation in 3D space. An increase in the Inter-Particle Friction µ s only had a major impact on the HM model This impact was magnified with higher shear rate. At higher shear rates, cubic particles can orient themselves to more energetically demanding positions for shear stress. This can lead to more energy intensive contacts and resistance between particles. The LIN model shows low sensitivity to a change in the µ s . The LIN model represents a uniform distribution of forces throughout the shear process with a low impact change in the µ s . Figure 6 shows the PS for MS-21 particles. The increase in the Inter-Particle Friction µ s is reflected by an increase in PS for both the HM and LIN models towards the end of the shear process for the shear rate SV = 1x This difference was lower for the SV = 4x. The differences of the PS values between the HM and LIN were lower towards the end of the PS process for the SV = 4x model than for the SV = 1x. The PS values for MS-26 particles were less dispersed towards the end of the PS process for the shear rate SV = 1x than for MS-21 particles. In contrast, the PS values for the MS-26 particles were for shear rate SV = 4x more scattered towards the end of the PS event than for MS-21 particles. The LIN model was less stable for MS-21 particles than MS-26 particles due to the change in µ s . Probably due to the composition of multispheres with a larger central particle The LIN model for SP particles was also less stable than for MS-26 particles. The central multisphere tends to have a point of contact as in the case of SP particles. This is related to the rather lower PS values for the higher shear rate for the MS-21 particle model. Figure 4 to Fig. 6 show several possible outputs from different DEM settings of the shear stress process, which are in the range of experimentally measured values using RST. In terms of the PS measurement approach, these calibrations would be considered sufficient. However, individual differences in the behaviour of the shear stress outputs are not sufficiently informative. The information sufficiency should further investigate particle motion or deformation properties of the models during shear stress. For this reason, the following chapter discusses the description of shear processes in connection with deformation behaviour. 3.2 Vertical lid position (VLP) The curves of the vertical lid position (VLP) were compared for all DEM particle models. Each displayed VLP curve from EDEM was generated from three simulation iterations with specific contact model settings and input parameters. The variable parameters were the Inter-Particle Friction µ s and the shear rate SV. Figure 7 shows the VLP for the SP particles. The increase in the Inter-Particle Friction µ s resulted in a larger change in VLP (bigger compression) for shear rate SV = 1x using HM model Tt was the other way around (lower compression) for the LIN model. The increase in µ s in for shear rate SV = 4x using the HM model was of the same nature (bigger compression). The LIN model also showed an increase in compression for SV = 4x. In cases with higher compression due to an increase in the Inter-Particle Friction µ s , compaction occurred with a decrease in strength or the PS values during the shear process. Due to particles motion, the bonds or the internal structure of the static arrangement of the particles were disturbed. The particles motion overcame critical values of an inter-particle friction. Figure 8 shows the VLP for the MS-26 particles. The increase in Inter-Particle Friction µ s for SV = 1x resulted in a smaller change in VLP (lower compression) for both, the HM model and LIN model. The increase in µ s for SV = 4x was similar (lower compression) for the HM and LIN models. Lower maximum VLP values were obtained for SV = 4x using HM model. The LIN model had a greater tendency to increase compression at higher SV. The HM model decreased compression for higher shear rate SV. The cubic shape of MS-26 particles showed lower deformation strength (resistance over deformation) compared to SP particles. Compression during the shear process was higher for MS-26 particles than that of SP particles. The shape of the MS-26 particles was affected by the initial embedding of the particles, which was lower during and after the shear process compared to the SP particles. Contrary, the combination of shape and higher Inter-Particle Friction µ s values had an effect on compaction with an increase in deformation strength and PS values. Processes that are less clear and not easily identifiable solely by PS curves become more recognizable with VLP curves. In the LIN model, for instance, there is a noticeable decrease in deformation strength and an increase in compression caused by the higher shear rate SV affecting the kinematics and frictional properties of the particles. Figure 9 shows the Vertical lid position VLP for the MS-21 particles. Using the LIN model for the SV = 1x and SV = 4x, the increase in the Inter-Particle Friction µ s resulted in a smaller change in VLP (lower maximum compression). Less compression was achieved for the HM model with an increase in µ s only in terms of the final values. The HM model achieved lower VLP values for the SV = 4x than for the SV = 1x. The opposite was true for the LIN model. The LIN model had a greater tendency to increase compression at higher SV. The HM model reduced compression at higher SV. The same effect was achieved with the MS-26 particles. The HM model was more sensitive to shear rate. Due to the more complex contact-deformation model used by the HM model, there was a faster increase in strength due to higher shear rates. Overall, lower compression was achieved than for the MS-26 particles. The central spherical multi-sphere changes the shape factor affecting the strength contacts before and during the shear process. The MS-26 and MS-21 particles responded similarly to changes in the shear rate SV and the Inter-Particle Friction µ s . The MS-26 particles showed higher maximum compression values than MS-21 particles. The nature of the impact of increased µs in LIN models was identical for both shear rates, SV = 1x and SV = 4x. With higher µ s , the maximum compression during PS decreased. The nature of the effect of the µ s for the MS-21 and MS-26 particles using HM model was identical in terms of the final (in t = 240s) VLP values. The VLP curves changes with the change in the µ s were smaller for the MS-21 particles than for the MS-26 particles using HM and LIN models. Although the PS curves may have seemed applicable, this was not the case for VLP. It was confirmed that output parameters other than shear stresses need to be verified and the VLP values are very suitable for this assessment. The deformation of the sample during the shear test is an important aspect of the global behaviour assessment. 3.3 Coordination Number CN Table 3 to Table 5 show the average Coordination Number CN values for each DEM particle shape from three repeated runs of the shear process. The average values show the effect of an increase in Inter-Particle Friction µ s leading to a decrease in CN values. The smallest effect of the increase in the µ s on the decrease in the CN values was observed for the SP particles (Table 3 ). In general, the spherical particle shape has the best ability of the most compact arrangement. The change in compact arrangement was negligible for SP particles using the µ s values from 0.8 to 1.0. Table 3 Average values and standard deviation of the Coordination Number CN for the SP particles. SP µ s = 0.8, SV = 1x µ s = 1.0, SV = 1x µ s = 0.8, SV = 4x µ s = 1.0, SV = 4x HM 3.99 ± 0.04 3.94 ± 0.05 3.96 ± 0.03 3.96 ± 0.03 LIN 4.28 ± 0.02 4.27 ± 0.03 4.30 ± 0.03 4.28 ± 0.02 Table 4 Average values and standard deviation of the Coordination Number CN for the MS21 particles MS21 µ s = 0.4, SV = 1x µ s = 0.6, SV = 1x µ s = 0.4, SV = 4x µ s = 0.6, SV = 4x HM 9.23 ± 0.05 8.15 ± 0.09 9.15 ± 0.05 8.12 ± 0.05 LIN 12.31 ± 0.31 11.15 ± 0.27 12.37 ± 0.26 11.18 ± 0.25 Table 5 Average values and standard deviation of the Coordination Number CN for the MS26 particles MS26 µ s = 0.4, SV = 1x µ s = 0.6, SV = 1x µ s = 0.4, SV = 4x µ s = 0.6, SV = 4x HM 10.63 ± 0.26 9.04 ± 0.14 10.40 ± 0.21 9.08 ± 0.17 LIN 13.91 ± 0.33 12.28 ± 0.30 13.75 ± 0.36 12.16 ± 0.30 Other particle shapes had the effect of changing Inter-Particle Friction µ s on the Coordination Number CN much more significant than SP particles. The increase in the µ s values was amplified with the greater influence of the particle shape. The cubic particle shape generally reduces the compactness of the arrangement in the volume. This effect was even more noticeable for the MS-26 particles. The Coordination Number CN value increased due to the higher shear rate SV for the SP and MS-21 particles using LIN model. Higher interlocking of the particles increased the number of contacts. The CN value decreased with the higher SV for the MS-26 particles using the LIN model. This is inconsistent with the assumption of sample volume expansion implied by the results in Fig. 8 . There was no significant loosening of the particles from each other or increase in sample volume at higher SV. Rather, there was only a rotation of the particles into positions with fewer contacts. The MS-26 particles have the highest CN because of the largest number of particles that make up a single multi-sphere. The number of these sub-particles increases the number of CN contacts considered. Changes in the kinematics of the particle ensemble due to the higher shear rate SV were predicted to reduce the high CN values. The central particle in the MS-21 particles reversed the effect of the increase in the SV on the CN, which brought the MS-21 particles closer in behaviour to the SP particles. SP, MS-21 and MS-26 particles using the HM model with lower µ s values due to higher SV resulted in lower CN values. The trends of CN values with the use of HM models for higher µ s values were mixed for higher SV. In the future, it is possible to calibrate the typical Impact Velocity V [ 16 ] with the Coordination Number CN values for accurate calibration of the LIN model. The contact velocity V affects the overall stiffness of the particle sample in the volume. With a higher value of V, the CN should theoretically decrease to reach values more similar to the LIN model as with the HM model. The results show basic differences between the particle models also with respect to the change in kinematics due to the increase in shear rate SV. The observed changes in the CN values can support to some extent the ideas about the processes occurring during the shear test with respect to the compactness of the particle arrangement. For example, a lower CN indicates a looser arrangement, which can lead to greater deformation or changes in the shear strength of the material. The influence of parameters and kinematics on CN and material properties is complex and depends on the specific particle model and its application. Detailed analysis of data and models is required for a deeper understanding. 3.4 Porosity The average initial porotsity ε start values for all individual DEM models did not change significantly by changing of the Inter-Particle Friction µ s . The effect of increasing the shear rate SV and the µ s on the final porosity ε end value of the sample was also minimal. For these reasons, final average values of the ε fstart and ε fend were generated based on all ε start or ε end values of an individual particle (shown in Table 6 ). The average value of ε fstart or ε fend was constructed from the ε values of the other µ s , using the HM and LIN models for the SP, MS21, and MS26 particles. The final values shown in Table 6 are only for the SV = 1x, because they were almost identical for the SV = 4x. Further, Table 7 shows the porosity values from the RST experiments. Table 6 Porosity ε fstart and ε fend type of model and particle SP particles (HM and LIN) MS21 particles (HM and LIN) MS26 particles (HM and LIN) ε fstart , [-] 0.50 ± 0.01 0.55 ± 0.01 0.70 ± 0.01 ε fend , [-] 0.49 ± 0.01 0.54 ± 0.01 0.69 ± 0.01 Table 6 shows the minimal difference between ε fstart and ε fend for all particle models. The highest values were measured for the MS-26 and MS-21 particles. In this case, a higher number of subparticles (multispheres) leads to an increase in the porosity ε values. The minimum ε values were measured for the SP particles. Table 7 Average initial ε fstart and final ε fend values experimentally obtained on the Ring Shear Tester RST. Sample Spheres Cubes ε start , [-] 0.51 ± 0.004 0.56 ± 0.004 ε end , [-] 0.51 ± 0.004 0.56 ± 0.004 The values presented in Table 7 confirm that the initial ε start and final ε end porosity values do not change significantly even for the measurements obtained from the RST experiments. For spherical particles, the simulation and experimental values were almost identical. However, there are differences for cubic particles. These discrepancies are attributed to variations in the shape of the cubic particles. The shape variations characterize the multispheres (MS) cubes. The results indicate that the porosity values did not change significantly during the shear process in the cases investigated in this work. Only the shape and size of the particle in specific cases influence the porosity value. This effect is related to the particle volume within the shear cell. The SP particles had the highest particle volume value of 0.00010200 m 3 , following the MS-21 particles with a value of 0.00008696 m 3 , and the MS-26 particles with a value of 0.00005786 m 3 . According to Eq. ( 11 ), it is the particle volume that impacts the magnitude of the final porosity ε. These findings correspond to the results shown in Table 6 . In terms of the vertical lid position, the average value of the shear lid for the RST experiment for spherical particles was 26.39 ± 0.43 mm at the start of the shear process and 26.14 ± 0.39 mm at the end of the process. For cubic particles, the values were 25.86 ± 0.42 mm at the start and 25.50 ± 0.26 mm at the end of the shear process. Table 8 to Table 13 show the shear Vertical Lid Position VLP values for each particle model and the Inter-Particle Friction µ s values. From the results, it can be generally summarized that the VLP increased with increasing the µs value. The VLP was also always lower in the end position than in the start position. However, there were minor exceptions for the SP particles using the LIN model with lower shear rate SV. Increasing the µ s values resulted in a decrease in the compactness of the particles and increased the loosening of the particles, with a very slight expansion of the particle sample volume represented by the higher VLP. Porosity and VLP are affected by particle shape, size, and µ s . During the shear, the porosity does not change significantly; rather, the particle arrangement changes, leading to loosening with slight expansion. Table 8 Vertical lid positions VLP for the SP particles, shear rate SV = 1x HM µ s = 0.8 HM µ s = 1.0 LIN µ s = 0.8 LIN µ s = 1.0 start 26.4 ± 0.14 26.6 ± 0.07 25.7 ± 0.46 25.4 ± 0.12 end 26.1 ± 0.08 26.2 ± 0.06 25.1 ± 0.60 25.0 ± 0.10 Table 9 Vertical lid positions VLP for the SP particles, shear rate SV = 4x HM µ s = 0.8 HM µ s = 1.0 LIN µ s = 0.8 LIN µ s = 1.0 start 26.3 ± 0.01 26.8 ± 0.20 25.4 ± 0.13 25.5 ± 0.18 end 26.1 ± 0.05 26.2 ± 0.09 24.9 ± 0.17 24.9 ± 0.07 Table 10 Vertical lid positions VLP for the MS21 particles, shear rate SV = 1x HM µ s = 0.4 HM µ s = 0.6 LIN µ s = 0.4 LIN µ s = 0.6 start 24.9 ± 0.09 25.8 ± 0.05 23.8 ± 0.11 24.6 ± 0.07 end 24.4 ± 0.04 25.3 ± 0.07 23.4 ± 0.13 24.2 ± 0.16 Table 11 Vertical lid positions VLP for the MS21 particles, shear rate SV = 4x HM µ s = 0.4 HM µ s = 0.6 LIN µ s = 0.4 LIN µ s = 0.6 start 24.8 ± 0.04 25.7 ± 0.18 23.9 ± 0.12 24.6 ± 0.15 end 24.4 ± 0.10 25.4 ± 0.07 23.3 ± 0.01 24.2 ± 0.04 Table 12 Vertical lid positions VLP for the MS26 particles, shear rate SV = 1x HM µ s = 0.4 HM µ s = 0.6 LIN µ s = 0.4 LIN µ s = 0.6 start 24.7 ± 0.15 25.6 ± 0.12 23.6 ± 0.02 24.3 ± 0.06 end 24.1 ± 0.05 25.1 ± 0.11 23.1 ± 0.05 23.8 ± 0.03 Table 13 Vertical lid positions VLP for the MS26 particles, shear rate SV = 4x HM µ s = 0.4 HM µ s = 0.6 LIN µ s = 0.4 LIN µ s = 0.6 start 24.8 ± 0.11 25.7 ± 0.24 23.6 ± 0.17 24.3 ± 0.04 end 24.2 ± 0.11 25.2 ± 0.03 23.0 ± 0.13 23.9 ± 0.02 3.5 Particle shifts The shift of a particle in the shear test process was defined by DEM from the change of position in 3D space (Fig. 3 a) from the initial to the final position (Chap. 2.4). The final average Angle of Particle Shifts ϕ S was calculated using the XYZ coordinates of the particles at each time step across layers L1 to L4 of the shear cell (Fig. 3 b). The evaluation time step was 12 seconds for the lower shear rate SV and 3 seconds for the higher shear rate SV. The ϕ S values of each layer progress upwards in the plots. Layer L1 is the lowest and L4 is the highest layer in the shear cell, with their respective heights depicted in the plots. Each layer's graphs consistently show four runs of layers L1-L4. In each layer, there are two versions of the Inter-Particle Friction µ s and physical DEM model for the SP and MS particles. The value of AIF in the shear test process was defined using the DEM as an arctangent function of the ratio of shear stress to normal stress (1) (Chap. 2.1). The average Angle of Internal Friction AIF values were calculated with a time step of 0.5 seconds. Both the AIF and ϕS values are in angular units, allowing them to be plotted together in common graphs (Fig. 10 to Fig. 12 ). Figure 10 shows the SP particle shifts for two shear rates SV values. There is little effect of SV on the Angle of Particle Shifts ϕ S and Angle of Internal Friction AIF values. For the SV = 4x, a slightly larger scatter of HM vs. LIN models values appeared in the L1 and L2 layers compared to SV = 1x, along with slightly lower AIF values at the end of the shear process due to increased particle kinematics. The AIF values were between the ϕ S values of L3 and L4 layers in both cases. The fourfold increase in the SV in the simulation did not significantly impact the final results. Figure 11 illustrates the shifts of the MS-21 particles for two different shear rate SV values. It is evident that the SV has a minor influence on the final Angle of Particle Shifts ϕ S values during the shear process. Lower SV values resulted in slightly higher ϕ S values using the HM and LIN models in the uppermost layer. The Angle of Internal Friction AIF values were positioned between the ϕ S values of the third and fourth layers in both cases. A fourfold increase in the SV had a minor impact on the final results. However, the AIF values slightly decreased with the higher SV at the end of the shear process. Initially, the ϕ S values in the L4 were higher at the beginning of the shear process. With the higher SV, the ϕ S using HM model values for µ s = 0.8 were greater than those for µ s = 1.0. Compared to the SP particles, the difference in ϕ S values between layers L2 and L3 was much larger. Figure 12 shows the shifts of the MS-26 particles for two shear rate SV values, similar to the case in Fig. 11 . With the lower SV value, slightly higher Angle of Particle Shifts ϕ S values using the HM and LIN models were achieved in the uppermost layer (L4). The greatest variance between the HM and LIN model values gradually increased with layer height for both SV = 1x and SV = 4x. The Angle of Internal Friction AIF values were positioned between the ϕ S values of the third and fourth layers for the lower SV. For the SV = 4x, the AIF values extended more into the fourth layer ϕ S compared to the SV = 1x. Higher SV resulted in the lower ϕ S in the final L4 layer, likely due to the dominance of horizontal velocity components in L4. Final AIF values were more dispersed with the higher SV. With lower SV, ϕ S values showed a more increasing trend than with higher SV. The difference between the MS-21 and MS-26 particles in terms of the ϕ S values was most noticeable in L3 and L4 layers for the higher SV. Higher SV resulted in greater instability in L3 and L4 layers, more so than with the MS-21 particles. The HM model with lower µ s generally showed higher µ s values, but this trend decreased with higher SV. Compared to the SP particles, the difference in the ϕ S values between L2 and L3 layers was much larger. The impact of changing the Inter-Particle Friction µ s coefficient on the Angle of Particle Shifts ϕ S was generally small, but when it did occur, it was more noticeable in the higher layers, L3 and L4. This is due to the increased freedom of particle movement, which is greater in L3 and the greatest in L4. Given the design of the shear lid and the height of the shear bars (4 mm), the main shear process between particles should occur between L3 and L4 layers. Ideally, if the entire L4 layer is driven by the shear bars, it will shear over the L3 layers. Particles can transition between L3 and L4 layers during the shear process, and this transition ability is represented by the geometric value ϕ S . The size of ϕ S correlates with the ability to deform. The higher ϕ S may indicate greater vertical particle movement. This ability can be understood as vertical particle flow, which reduces local strength and increases local flowability in the sample. In contrast, the AIF represents the force or stress conditions on particles, also expressed geometrically by an angle. From this perspective, the geometric representation of the AIF between L3 and L4 layers confirms the main shear region. 3.6 Average Particle Velocity AVXY in layers Figure 13 to Fig. 15 illustrate the Average Particle Velocities AVXY during the shear process in each layer of the shear cell. The method for obtaining values in each layer using quadrants is described in section 2.4. Layer L1 is at the bottom of the rotational shear cell, and layer L4 is in the region affected by the shear lid's vanes. At higher shear rate SV, there is a clear numerical fourfold increase in the AVXY and, in most cases, a similar trend in the curve progression. Table 14 to Table 16 include characteristic values of velocity changes between adjacent layers, represented by the slopes of the line segments. Higher values indicate greater changes in the AVXY between layers and correspond to a more pronounced downward trend in the curves between layers during the shear process, as shown in Fig. 13 to Fig. 15 . Figure 13 and Table 14 presents the results for the SP particles. The values indicating the greatest change in the Average Particle Velocity AVXY between layers for the SP particles were mostly found between layers L3 and L4. The exception was the HM model with Inter-Particle Friction µ s = 1.0 and the shear rate SV = 1x, where this was not the case. It is likely that the higher µ s of the HM model increases the shear strength between layers L4 and L3, causing the shear region to shift lower, between L3 and L2. This effect of increased µ s was not observed for the higher SV. Assuming that the greatest difference in velocities between layers characterizes the shear region, the shear region for SP particles would be located between layers L3 and L4. The highest the Average Particle Velocity AVXY values were achieved using the HM model with Inter-Particle Friction µ s = 1.0, and the lowest using the LIN model with µ s = 0.8 for both shear rate SV values (Fig. 13 ). The change in the AVXY across layers L1-L4 was almost linear. Table 14 Values representing the change in the Average Particle Velocities AVXY between individual layers for the SP particles. SP Velocity with SV = 1x SP Velocity with SV = 4x Layer HM µ s = 0.8 LIN µ s = 0.8 HM µ s = 1.0 LIN µ s = 1.0 Layer HM µ s = 0.8 LIN µ s = 0.8 HM µ s = 1.0 LIN µ s = 1.0 1–2 -0.0028 -0.0036 -0.0024 -0.0029 1–2 -0.0099 -0.0125 -0.0112 -0.0086 2–3 -0.0050 -0.0047 -0.0054 -0.0044 2–3 -0.0166 -0.0191 -0.0138 -0.0182 3–4 -0.0057 -0.0065 -0.0049 -0.0071 3–4 -0.0259 -0.0236 -0.0252 -0.0242 According to Fig. 14 and Table 15 , for the MS-21 particles, the greatest difference in the Average Particle Velocities AVXY was generally observed between layers L2 and L3. Assuming that the greatest velocity difference between layers characterizes the shear region, the shear region for the MS-21 particles would be located between layers L2 and L3, approximately in the middle of the shear cell. The highest AVXY values were achieved using the LIN model for the Inter-Particle Friction µ s = 0.6 and shear rate SV = 1x and using the HM model for the µ s = 0.6 and the SV = 4x. The changes in the AVXY across layers were almost linear. The AVXY values were very similar across the different models, especially for the lower SV values. The cubic shape of the particles exhibited greater shear strength, as shown on Fig. 6 , than the SP particles. This higher overall shear strength also manifested as greater strength between layers L1-L2 and L3-L4. This increased shear strength likely resulted in the weakest point being between layers L2-L3, approximately halfway up the shear cell. The assumption of the main shear region based on the Angle of Particle Shifts φs, Angle of Internal Friction AIF, and AVXY values is not applicable for the MS-21 particles. During the shear test, the MS particles can form mechanical bonds and structures that are more stable than those formed by the SP particles. The MS particles can interlock and create solid clusters that are harder to break during shear stress. Table 15 Values representing the change in the Average Particle Velocities AVXY between individual layers for the MS21 particles MS 21 Velocity MS 21 4x Velocity Layer HM µ s = 0.4 LIN µ s = 0.4 HM µ s = 0.6 LIN µ s = 0.6 Layer HM µ s = 0.4 LIN µ s = 0.4 HM µ s = 0.6 LIN µ s = 0.6 1–2 -0.0046 -0.0042 -0.0043 -0.0035 1–2 -0.0168 -0.0167 -0.0151 -0.0153 2–3 -0.0060 -0.0067 -0.0059 -0.0066 2–3 -0.0254 -0.0271 -0.0240 -0.0224 3–4 -0.0041 -0.0041 -0.0052 -0.0034 3–4 -0.0176 -0.0198 -0.0230 -0.0214 According to Fig. 15 and Table 16 , for the MS-26 particles, the greatest velocity difference was generally between layers L2 and L3. Based on the before mentioned assumption, the shear region for the MS-26 particles would also be between layers L2 and L3, similar to the MS-21 particles. The difference in Average Particle Velocity AVXY values among the different models and Inter-Particle Friction µ s values with changing shear rate SV was mostly consistent, except for the unexpected AVXY values for the HM model with the µ s = 0.4. This change in trend between layers L3 and L4 likely resulted from the reactive effects of particle deformation stress. Increased particle compression can lead to the release of this compression in time pulses. When compression is released, particles accelerate against the direction of shear. As with the MS-21, the MS-26 particles can interlock and form stable clusters that are more difficult to break during shear stress. The AVXY values for the different models and µ s values were more varied for the MS-26 particles compared to the MS-21 particles. Table 16 Values representing the change in the Average Particle Velocities AVXY between individual layers for the MS26 particles MS 26 Velocity MS 26 4x Velocity Layer HM µ s = 0.4 LIN µ s = 0.4 HM µ s = 0.6 LIN µ s = 0.6 Layer HM µ s = 0.4 LIN µ s = 0.4 HM µ s = 0.6 LIN µ s = 0.6 1–2 -0.0023 -0.0054 -0.0038 -0.0043 1–2 -0.0053 -0.0218 -0.0113 -0.0151 2–3 -0.0054 -0.0065 -0.0061 -0.0061 2–3 -0.0338 -0.0272 -0.0194 -0.0278 3–4 0.0081 -0.0032 -0.0034 -0.0045 3–4 -0.0138 -0.0118 -0.0141 -0.0163 For the MS particles, the differences between Angle of Particle Shifts φs values in layers L2 and L3 were greater compared to the SP particles (Fig. 12 ). A larger increase in the φs values indicates a greater ability for vertical particle movement. Since cubic particles have larger contact surfaces and sharp edges, which can facilitate interlocking and forming stable clusters, this increased movement is likely due to these characteristics. With higher Inter-Particle Friction µ s with lower shear rate SV, the main shear region shifts more towards the centre of the rotational shear cell. At the lower SV, the kinetic energy is lower, and therefore, higher friction prevents particles from moving upwards, causing the shear region to move downwards. For this reason, the MS particles likely have their main shear region in layers L2 and L3, as the particle surfaces are composed of sub-particles, and their mechanical interactions increase shear strength. With higher shear rate SV and Inter-Particle Friction µ s , the main shear region, as indicated by the greatest velocity differences, shifts more towards the shear lid. For the highest µ s , the main shear region is located in layers L3 and L4. Between lower and higher shear rate SV, an opposite effect of increasing Inter-Particle Friction µ s can be observed. At the lower SV, the shear region with the higher µ s shifts towards the bottom of the shear cell, whereas at the higher SV, it moves towards the shear lid. The higher Average Particle Velocity AVXY values due to increased Inter-Particle Friction µ s were likely caused by the pulsed release of particle clusters, leading to peaks in the individual velocity components of the particles. With the higher µ s , more kinetic energy can accumulate. Once the accumulated kinetic energy overcomes the friction forces, particle clusters are suddenly released and move more quickly. This process causes spikes in the particle velocities, recorded as the increased AVXY values. The pulsed nature of the movement is due to particles being repeatedly trapped and released, leading to fluctuating velocities and thus pulsed movement. For spherical particles, the greatest differences in the Average Particle Velocity AVXY were predominantly found between layers L3 and L4. For cubic particles, this was not as clear-cut. For the MS particles, the main shear region was identified between layers L2 and L3 due to their shape. Non-spherical particle shapes can create an unexpected discontinuous behaviour, leading to different positions of the main shear region for cubic particles. 4 Discussion For the SP particles using the HM model, achieving higher final compression of the sample during the shear process was accomplished through using higher Inter-Particle Friction µ s values. These initial bonds, which had a certain effect in the static state, were eliminated during the shear process. For other particles using HM model, changes in compression could also be related to shape and the combination of Inter-Particle Friction µ s with kinematics influenced by the shear rate SV. During the shear process under load, the interaction bonds between particles changed due to rearrangement, leading to either higher or lower compression. In the LIN model, higher µ s values generally led to a reduction of the sample compression. Only for the SP particles at high SV resulted higher µ s values into reduced compression. In this case, the SP particles could not withstand the higher kinematic load combined with higher µ s . For cubic particles, all influences and trend changes were reinforced by their shape. The assumption of a relationship between the Preshear PS values and the Vertical Lid Position VLP mentioned in [ 16 ], that higher PS values correspond to the lower VLP values, was met for all cases of extreme PS values. The highest PS value for the SP particles for shear rate SV = 4x corresponded to the lowest VLP compression. For the MS-26 particle, the highest PS value for the SV = 4x was for the HM model with the Inter-Particle Friction µ s = 0.6, and in this setting, the VLP was generally among the lowest values. For the MS-21, the PS to the VLP relationship was more evident in the LIN model than in the HM model. The obtained PS trends were within the expected range of experimentally obtained values, but this was not entirely the case for the VLP. This confirms that it is necessary to verify other output parameters besides the PS. The MS particles had higher Coordination Number CN values, which also correlated with higher shear strength. This higher shear strength impacted the kinematic and movement behaviour of the particles during the shear process, particularly in identifying the main shear plane. Assuming that higher Angle of Particle Shifts ϕ S characterizes greater vertical particle throughput, it is likely that these changes in particle positions also increase the horizontal shear resistance of the tested sample. This effect may be due to the densification of the structure, increased inter-particle forces, greater material heterogeneity, and possible anisotropy resulting from the vertical movement of particles. For the SP particles, the Angles of Internal Friction AIF were between the angles of particle shifts ϕ S of layers L3 and L4. The main shear region for the SP particles was also identified between layers L3 and L4 based on the Average Particle Velocity AVXY values of these layers. For cubic particles, this was not as clear-cut, although the AIF and ϕ S results showed similar characteristics as the SP particles. For the MS particles, the main shear region was identified between layers L2 and L3 using the AVXY, corresponding to approximately half the height of the shear cell. The assumption that the AIF values would occur between the ϕ S values of layers L3 and L4 and that the shear region would be between L3 and L4 using AVXY was not met. For the MS particles, there was a larger step change between the ϕ S values of L2 and L3. This significant change indicated an increase in the ϕ S values, representing a greater ability for vertical particle movement. This effect was most characteristic of the non-spherical MS particles. The shear region extended more throughout the sample volume due to higher interlocking between particles. Rather than individual particles sliding past each other, clusters of particles were shearing together. The AIF values for the MS particles extended more into L3 layer compared to the SP particles. The occurrence of the AIF values more in layer L3 for the MS particles than between layers L3 and L4 suggested that the main shear region would likely shift more towards the lower layers of the shear cell. With the lower Inter-Particle Friction µ s values using the HM model, there was instability or critical particle movement behaviour, reflected in changes in the Average Particle Velocity AVXY values (Fig. 15 ). The sudden release of interlocked particles can generate peak velocity values in a short time step, affecting the overall average AVXY value. The wavy surface of the MS-26 particles makes them more prone to this behaviour compared to the MS-21 particles. Higher shear rate SV combined with higher Inter-Particle Friction µ s values generally resulted in higher slope values for layers L3-L4. The higher SV and µ s helped to better overcome the particle resistance, positioning the main shear region closer to the shear lid. Conversely, the lower SV did not allow the transfer of rotational moments through the particles up to the shear lid, causing the shear process to occur mainly in the lower layers of the shear cell. It appears that the higher SV values could be beneficial in cases where the tested sample is not completely homogeneous, as inhomogeneities could significantly affect the transfer of rotational moments through the layers of the measured sample. The higher SV promotes better particle movement throughout the sample volume over time, which can positively impact the steady flow in some cases. The higher SV can help overcome these inhomogeneities, leading to a more uniform distribution of mechanical properties and more accurate measurement of rotational moment transfer. This approach minimizes the impact of local inhomogeneities on the overall behaviour of the sample. 5 Conclusion The results of this study aim to support users of DEM simulations in calibrating shear tests. Some findings confirmed the need for an individualized approach for each examined property, while also clarifying potential dependencies and dominant parameters. The particles were intentionally made larger relative to the shear cell. This was partly due to the limitations of the 3D printing resolution and also to reduce computational time for repeated simulations. 5.1 Preshear PS For the SP particles, the Preshear PS values were generally on the lower end of the experimentally measured range. Increasing the shear rate SV resulted in a slight decrease in the PS values towards the end of the shear process. For spherical particles, higher Inter-Particle Friction µ s values in DEM simulations were needed compared to other particle shapes to achieve the expected Preshear values from experiments. This was due to the imperfectly smooth surface of the 3D-printed particles. The layering process of 3D printing had a greater impact on the surface of spherical particles than on cubic particles. For the MS particles, the Preshear PS values were generally on the higher end of the experimentally measured range. For the MS-26 particles, an increase in the shear rate SV significantly raised the PS value for the HM model with Inter-Particle Friction µ s 0.6. Conversely, for the MS-21 particles, the PS values decreased with an increase in the SV. The wavy surface texture of the MS-26 particles was much more influential than changes in the µ s values. Compared to spherical particles, lower µ s values were applied, yet the PS values remained higher. Regarding the impact of the changing shear rate SV values on the Preshear PS values, the results were within acceptable ranges of experimental results. Thus, saving time in simulating the shear process by increasing the shear rate is feasible, but it requires an analysis of the fundamental deformation behaviour of the sample during the shear process, as emphasized in this study. 5.2 Vertical Lid Position VLP The results clearly indicate that the position of the shear lid provides DEM users with an overview of the fundamental deformation behaviour during the shear process. For better control and improvement of DEM outputs, shear-induced stress should always be supported by this experiment. Various effects of changing the Inter-Particle Friction µ s on the sample's deformation (compression) ability were observed. Generally, the strength of the particle bulk can be increased by raising the Inter-Particle Friction µ s values. However, this strength is most effective in a static stress state and has its limits during the shear process. Therefore, an apparent static increase in strength by increasing Inter-Particle Friction µ s can reduce the overall shear strength, causing significant increases in compression. This effect was observed more frequently for the SP particles using the HM model compared to the LIN model. The static increase in strength due to friction and the resulting increased compression did not apply to the MS particles with a wavy surface. The surface shape had a more significant impact on strength and shear behaviour than changes in friction. Regarding the change in the shear rate SV, the results were within acceptable experimental ranges. This confirms the need for a highly individualized approach for each model and combination of input values. 5.3 Coordination Number CN The average Coordination Number CN values revealed a clear impact of increasing Inter-Particle Friction µ s on reducing the CN values. Higher µ s values decreased the interlocking and contact capabilities between particles. This reduction in the CN did not always affect the deformation ability of the sample. The smallest changes in the CN values caused by the change of the µ s were observed for the SP particles. Generally, the SP particles have the best ability to achieve the most compact arrangement. For other particle shapes, the impact of the µ s on reducing the CN was much more pronounced. Increasing the µ s values amplified the change in the CN for particles with a more significant influence of shape. Cubic particle shapes generally reduce the compactness of the arrangement within the volume, and this effect was even more pronounced for the MS-26 particles. For precise calibration of the LIN model, there is a future possibility to calibrate the typical Impact Velocity V [ 16 ] using the CN values. The results highlighted fundamental differences between particle models, considering the changes in kinematics due to increased shear rate SV. The observed changes in the Coordination Number CN values can somewhat support the understanding of processes during the shear test concerning particle arrangement compactness. For instance, the lower CN indicates a looser arrangement, which can lead to greater deformation or changes in the shear strength of the material. The influence of parameters and kinematics on the CN and material properties is complex and depends on the specific particle model and its application. A detailed analysis of data and models is necessary for a deeper understanding. 5.4 Porosity From the experimental and DEM results, it was evident that porosity remained a stable parameter, not changing significantly across different models during the shear process. However, the porosity varied for different particle types, primarily determined by particle shape or surface texture. The results generally indicated that an increase in the Inter-Particle Friction µ s corresponded with a higher vertical lid position VLP. The lid's end position was always lower than its start position, with minor exceptions for the SP particles using the LIN model with lower shear rate SV. Changes in the SV did not significantly affect the start and end positions of the lid. Porosity and the position of the shear lid were influenced by the particle shape, size, and µ s . 5.5 Angel of particle shifts ϕ S and Average Particle Velocity AVXY An analogy was discovered between the Angle of Internal Friction AIF and Angle of Particle Shifts ϕ S concerning the main shear region, regardless of particle shape. For the SP particles, this was clear. Although the values from the shear test and the vertical position of the shear lid in simulations were within the range of experimentally measured values, questions remain about particle behaviour concerning their positional changes. Higher Angle of Particle Shifts ϕ S values may indicate a greater ability for vertical particle movement, understood as vertical particle flow, which reduces local strength and increases local flowability within the sample. Conversely, the Angle of Internal Friction AIF represents the force or stress conditions on particles, also expressed geometrically by an angle. From this perspective, the geometric representation of the AIF angle between L3 and L4 layers confirms the main shear region. The impact of the shear rate SV on the Angle of Particle Shifts ϕ S and Angle of Internal Friction AIF values in simulations was generally minor. Considering the effect of particle shape on the AIF values, the MS particles showed slightly higher final AIF values then the SP particles. These differences were due to the wavy surface texture of the MS particles, composed of multiple particles. For the SP particles, the Angle of Internal Friction AIF values were between the Angle of Particle Shifts ϕ S values of layers L3 and L4. The main shear region for the SP particles was also identified between layers L3 and L4 based on the Average Particle Velocity AVXY values of these layers. For the MS particles, the main shear region was identified between layers L2 and L3 using AVXY, which corresponded to approximately half the height of the shear cell. The assumption that the AIF values would occur between the ϕ S values of layers L3 and L4 and that the shear region would be between L3 and L4 using AVXY was not met. Instead, the shear region extended more throughout the sample volume due to higher interlocking between particles. The occurrence of the AIF values in the MS particles more within layer L3 rather than between layers L3 and L4 indicated that the main shear region likely shifts to the lower layers of the shear cell. Declarations COMPETING INTERESTS . The authors declare no competing interests. FUNDING: This paper was created as part of the project No. CZ.02.01.01/00/22_008/0004631 Materials and technologies for sustainable development within the Jan Amos Komensky Operational Program financed by the European Union and from the state budget of the Czech Republic, and project The European Just Transition Fund supported this work within the Operational Programme Just Transition under the aegis of the Ministry of the Environment of the Czech Republic, project CirkArena, number CZ.10.03.01/00/22_003/0000045. Author Contribution Conceptualization, Rozbroj J., Hlosta J., Diviš J., Barletta D., Nečas J.; methodology, Diviš J., Hlosta J., and Rozbroj J.; formal analysis, Hlosta J., Rozbroj J., Pokorná K., and Žurovec D.; investigation, Hlosta J., Rozbroj J., Žurovec D., Poletto M., Nečas J., Zegzulka J.; data curation, Barletta D., Hlosta J., Diviš J. and Rozbroj J.; writing—original draft preparation, Rozbroj J, Hlosta J., Diviš J., and Barletta D., ; writing—review and editing, Poletto M., Žurovec D., Pokorná K., Nečas J., Zegzulka J.; visualization, Rozbroj J., and Hlosta J.; supervision, Poletto M., Nečas J., and Zegzulka J.; project administration, Hlosta J, Žurovec D., Pokorná K., Diviš J., Nečas J., Zegzulka J.; funding acquisition, Rozbroj J., Nečas J., and Zegzulka J. Data Availability DATA AVAILABILITY: The data used in this study is available at: Rozbroj, J. (2024). Evaluation of DEM simulations measuring internal friction and particle movement (Verze 1) [Data set]. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5298776","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":378770219,"identity":"210d76c7-6bf0-44ce-b0b9-ce175bf46b28","order_by":0,"name":"Jiří ROZBROJ","email":"","orcid":"","institution":"VSB-TU Ostrava","correspondingAuthor":false,"prefix":"","firstName":"Jiří","middleName":"","lastName":"ROZBROJ","suffix":""},{"id":378770220,"identity":"1eb0d6ed-0dea-4735-af2e-a5c00cd948c2","order_by":1,"name":"Jakub HLOSTA","email":"","orcid":"","institution":"VSB-TU Ostrava","correspondingAuthor":false,"prefix":"","firstName":"Jakub","middleName":"","lastName":"HLOSTA","suffix":""},{"id":378770221,"identity":"53a233b8-ce8c-4c23-a5af-8e9197b18d32","order_by":2,"name":"Jan DIVIŠ","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAw0lEQVRIiWNgGAWjYBACxgYgwWPAwMPA3sDATKIWngNEagEDHhAhkUCkFub2swcY3hQclpGf+cb4cwGDnT1hh/XkJTDOMTjMY3A7x0x6BkMyYZsYG3IMmHkM0ngMpNPSmHkYDrAR1tL/BqJFfuax5M9ALTyEtcwA22LDw3CD+YA0UIsEEVreGBycA9RicCb5mPQMg2QDgloM+3MMH7z5I2Ev336w+XNBBREhZtjAwHAAwSVsBwODPBFqRsEoGAWjYKQDAJMOMPXJXHIyAAAAAElFTkSuQmCC","orcid":"","institution":"VSB-TU Ostrava","correspondingAuthor":true,"prefix":"","firstName":"Jan","middleName":"","lastName":"DIVIŠ","suffix":""},{"id":378770222,"identity":"f3ee633a-7fa9-46d2-bbd1-7b40822fa14b","order_by":3,"name":"Jan NEČAS","email":"","orcid":"","institution":"VSB-TU Ostrava","correspondingAuthor":false,"prefix":"","firstName":"Jan","middleName":"","lastName":"NEČAS","suffix":""},{"id":378770224,"identity":"1b937690-c2c5-416b-a51b-2cfb78716f31","order_by":4,"name":"Diego BARLETTA","email":"","orcid":"","institution":"University of Salerno","correspondingAuthor":false,"prefix":"","firstName":"Diego","middleName":"","lastName":"BARLETTA","suffix":""},{"id":378770227,"identity":"c59ba063-5be7-409b-912c-ddfb34e105c4","order_by":5,"name":"Massimo POLETTO","email":"","orcid":"","institution":"University of Salerno","correspondingAuthor":false,"prefix":"","firstName":"Massimo","middleName":"","lastName":"POLETTO","suffix":""},{"id":378770229,"identity":"3571df87-30fb-4c27-bbf1-1d51b1e3f81f","order_by":6,"name":"David ŽUROVEC","email":"","orcid":"","institution":"VSB-TU Ostrava","correspondingAuthor":false,"prefix":"","firstName":"David","middleName":"","lastName":"ŽUROVEC","suffix":""},{"id":378770231,"identity":"7785dd36-e5aa-48e4-a123-e05cac1a6980","order_by":7,"name":"Kamila POKORNÁ","email":"","orcid":"","institution":"VSB-TU Ostrava","correspondingAuthor":false,"prefix":"","firstName":"Kamila","middleName":"","lastName":"POKORNÁ","suffix":""},{"id":378770233,"identity":"04f61598-d6da-4232-a0c6-9e0c3aa91534","order_by":8,"name":"Jiří ZEGZULKA","email":"","orcid":"","institution":"VSB-TU Ostrava","correspondingAuthor":false,"prefix":"","firstName":"Jiří","middleName":"","lastName":"ZEGZULKA","suffix":""}],"badges":[],"createdAt":"2024-10-20 14:08:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5298776/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5298776/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":69199572,"identity":"18561828-cc39-4a75-b2ce-4a768dfdadd3","added_by":"auto","created_at":"2024-11-18 02:24:06","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2588303,"visible":true,"origin":"","legend":"\u003cp\u003eThe spherical and cubic particles made by 3D printing material PLA; a) spheres, b) cubes\u003c/p\u003e","description":"","filename":"Fig1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/1a332415c4f19586d7f7e5ee.jpg"},{"id":69199956,"identity":"4962a5c4-e0b5-40d9-aeae-7677c44e60a9","added_by":"auto","created_at":"2024-11-18 02:32:06","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1170316,"visible":true,"origin":"","legend":"\u003cp\u003eParticle shape and the filling of the shear cell; a) SP particle, b) MS-26 particle, c) MS-21 particle.\u003c/p\u003e","description":"","filename":"Fig2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/ff30bf35a8028cc9bf469d70.jpg"},{"id":69198956,"identity":"2c4b81f0-73df-4ebb-a54b-c84f8c10918f","added_by":"auto","created_at":"2024-11-18 02:16:06","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1210789,"visible":true,"origin":"","legend":"\u003cp\u003ea) Change of the particle position in 3D space from the initial to the final position, b) Layers in a shear cell\u003c/p\u003e","description":"","filename":"Fig3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/f7dc29d631ffcac8d8fa7478.jpg"},{"id":69199570,"identity":"5f025ee7-1557-4bcc-8c1e-26979d7a7118","added_by":"auto","created_at":"2024-11-18 02:24:06","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":258658,"visible":true,"origin":"","legend":"\u003cp\u003ePreshear for the SP particles; a) shear rate SV=1x, b) shear rate SV=4x\u003c/p\u003e","description":"","filename":"Fig4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/4746b16f5f008d5a5fbd5c5f.jpg"},{"id":69198958,"identity":"7ed65f38-06ad-45c5-9d51-67d4d220b519","added_by":"auto","created_at":"2024-11-18 02:16:06","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":277492,"visible":true,"origin":"","legend":"\u003cp\u003ePreshear for the MS-26 particles; a) shear rate SV=1x, b) shear rate SV=4x\u003c/p\u003e","description":"","filename":"Fig5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/4fed5c49ccd607dad51e12a9.jpg"},{"id":69199957,"identity":"79954044-d545-4406-bf17-8fe7425fe2d8","added_by":"auto","created_at":"2024-11-18 02:32:06","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":279868,"visible":true,"origin":"","legend":"\u003cp\u003ePreshear for the MS-21 particles; 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a) shear rate SV=1x, b) shear rate SV=4x\u003c/p\u003e","description":"","filename":"Fig8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/9731e61ce85fc98b63cf5ee5.jpg"},{"id":69198959,"identity":"0aaf0f2a-6dbc-43dc-8977-4a80bf2452c5","added_by":"auto","created_at":"2024-11-18 02:16:06","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":256932,"visible":true,"origin":"","legend":"\u003cp\u003eVertical lid position VLP for the MS-21 particles; a) shear rate SV=1x, b) shear rate SV=4x\u003c/p\u003e","description":"","filename":"Fig9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/d9e268fb440874f8b96ca856.jpg"},{"id":69198967,"identity":"a4ba6829-7a49-41b2-8430-115930ff6eae","added_by":"auto","created_at":"2024-11-18 02:16:06","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":318720,"visible":true,"origin":"","legend":"\u003cp\u003eParticle shifts of the SP particles; a) shear rate SV=1x, b) shear rate SV=4x\u003c/p\u003e","description":"","filename":"Fig10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/162e1a45b25ece1d61990e64.jpg"},{"id":69199573,"identity":"a0f4415d-304b-49f6-9880-01b72dc951b8","added_by":"auto","created_at":"2024-11-18 02:24:06","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":331270,"visible":true,"origin":"","legend":"\u003cp\u003eParticle shifts for the MS 21 particles; a) shear rate SV=1x, b) shear rate SV=4x\u003c/p\u003e","description":"","filename":"Fig11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/e0c08b44afa732a0e9145cd9.jpg"},{"id":69198964,"identity":"92092aca-ad0e-4b8f-9279-253e441b655c","added_by":"auto","created_at":"2024-11-18 02:16:06","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":334792,"visible":true,"origin":"","legend":"\u003cp\u003eParticle shifts of the MS 26 particles; a) shear rate SV=1x, b) shear rate SV=4x\u003c/p\u003e","description":"","filename":"Fig12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/610b1b5a3c3a9559777948d7.jpg"},{"id":69199574,"identity":"8b34faca-67eb-452a-9237-9cc996e255d0","added_by":"auto","created_at":"2024-11-18 02:24:06","extension":"jpg","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":160977,"visible":true,"origin":"","legend":"\u003cp\u003eAverage Particle Velocity AVXY in layers for the SP particles; a) shear rate SV=1x, b) shear rate SV=4x\u003c/p\u003e","description":"","filename":"Fig13.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/4d5ff8ff999ac540032a84ad.jpg"},{"id":69199958,"identity":"8a73422a-b156-474a-8bcf-22dcc55b1985","added_by":"auto","created_at":"2024-11-18 02:32:06","extension":"jpg","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":171655,"visible":true,"origin":"","legend":"\u003cp\u003eAverage Particle Velocity AVXY in layers for the MS-21 particles; a) shear rate SV=1x, b) shear rate SV=4x\u003c/p\u003e","description":"","filename":"Fig14.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/9c4cf95106b8ee4847e12fbe.jpg"},{"id":69198968,"identity":"3428bad7-3bb0-4fab-9278-b7e95c224989","added_by":"auto","created_at":"2024-11-18 02:16:06","extension":"jpg","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":181254,"visible":true,"origin":"","legend":"\u003cp\u003eAverage Particle Velocity AVXY in layers for the MS-26 particles; a) shear rate SV=1x, b) shear rate SV=4x\u003c/p\u003e","description":"","filename":"Fig15.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/2c3b58fd573003d4abe6444d.jpg"},{"id":72149360,"identity":"1fa5c2f3-bc69-4e32-ab44-b4ed67a793f4","added_by":"auto","created_at":"2024-12-23 07:54:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9248416,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5298776/v1/55442e77-56ae-4538-873e-d77ad5a6c7c3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Influence of Irregular Particle Shape on Volumetric Behaviour of DEM Materials in Rotational Shear Testing","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eWith the development of the Discrete element method (DEM) [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] its capabilities and predictive are continually evolving [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Among the first calibration procedures was the angle of repose test [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. It has a sufficient predictive value in terms of static material behaviour, but it has also been well accepted in applications with specific dynamic effects [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Furthermore, there are several other possible ways in which the set behaviour of DEM particulate materials are verified [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. These methods include shear test of the material [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. A shear test measures the deformation of a material under a certain compressive normal stress. Once the desired normal (vertical) load is set on the specimen, the shear strength (shear or horizontal stress) is determined. The ratio of these two stresses indicates the ability of the material to transfer vertical forces between particles of matter to forces between particles in the horizontal direction. The general theory is used in the design applications of bulk material handling and storage equipment, especially with regard to the magnitudes and ratios of the applied pressures [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. These ratios generally characterize the vertical (\"gravitational\") throughput of the particulate material through the geometry (e.g., the structure of the hopper) [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn terms of the shear deformation of the particulate material, attention must also be paid to the change in volume of the tested sample. For these reasons, the position of the lid during the shear test is also monitored, as the vertical sample deformation (compression/expansion) may also be related to the change in the magnitude of the shear stress [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. This relationship can be observed for various shear stress influences such as shear rate [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. If the shear stress increases due to a change in the kinematics of the shear process or due to the particle arrangement, the vertical compression of the sample decreases and vice versa.\u003c/p\u003e \u003cp\u003eThe particles which do not disintegrate due to compressive stress undergo changes in their spatial distribution as the volume of the particle sample changes [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. The particle arrangement can affect the ultimate strength of the particulate material with respect to the deformation and the flow capabilities on a macro scale. There may also be associations with changes in material porosity [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAnother parameter that influences the volumetric deformation of the sample during shear test is the shape of the particles. The irregular shape of the particles can increase the shear stress values at low normal loads. This is due to an increase in the coordination number, which expresses the number of contacts between particles in a particular volume of the sample. Spherical particles tend to have lower coordination numbers than non-spherical or irregularly shaped particles, and a higher tendency towards isotropic behaviour [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe DEM software generally assumes a certain stiffness of the individual particle contacts [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. This stiffness can be set by input parameters such as Young's modulus, Poisson's constant, or shear modulus [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. DEM software users use the Shear Modulus values to reduce the computation time. When the number of particles is high, the computation time is reduced by decreasing the shear modulus value. However, it is necessary to maintain a certain degree of stiffness of the particles or the whole sample so that the conditions of the ratios and magnitudes of the vertical pressure values are met [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThere are a number of DEM models, and each is specific in its deformation behaviour [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Whether the deformation is elastic or plastic, there is always a correlation between the input parameters or measured quantities. In order to achieve similar behaviour of different DEM models, different input parameters need to be used [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. There is a gap in scientific knowledge regarding the use of shear tests for calibrating and validating virtual particulate materials in DEM simulations. Despite their widespread use, DEM simulation models are not often compared with each other. Additionally, the use of shear tests as a calibration tool is often inappropriate because multiple parameters are not compared, typically focusing on just one selected parameter. Users may not fully understand the implications of changes in input parameters and tend to focus only on a single parameter for calibrating virtual particulate materials. This can lead to inaccuracies and incorrect DEM simulations. The focus of this study is partly aimed at identifying possible ways leading to similar behaviour of different DEM models during shear test of particulate materials with different particle shapes. In this work, spherical particles were used to represent spherical geometries, while multispherical particles were applied to simulate cubic particles. These particle configurations illustrate the variety of DEM models and their potential when simulating shear tests for bulk materials.\u003c/p\u003e \u003cp\u003eThe aim of the study is to investigate the effect of particle shape on the changes of properties during shear process such as shear stress values or deformation parameters expressed by the vertical position of the shear cap during the shear test. Furthermore, the implications of internal friction with the ability of particle movement and changes in their relative positions in the shear cell layers were addressed. Some relationships are supported by other parameters such as coordination numbers and porosity of the sample volume. The summary of the study's findings should then serve to support academic and commercial DEM modellers to gain a general understanding of the processes, processes and laws for more efficient and accurate calibration of DEM materials using rotational shear test.\u003c/p\u003e"},{"header":"2 Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Shear test\u003c/h2\u003e \u003cp\u003eThe basic principle of the shear test is to find the ratio of these values of the normal stress σ\u003csub\u003epre\u003c/sub\u003e at preshear stress and shear stress at the end of preshear (steady-state flow) τ\u003csub\u003epre\u003c/sub\u003e. The Angle of Internal Friction AIF can be determined by using these two values. More precisely, it is the determination of the AIF at steady-state flow φ\u003csub\u003esf\u003c/sub\u003e (1). The determination of these values is based on methods for determining the flow function using a ring shear tester RST-01.pc (RST) [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Default vertical load input value for all measurements σ\u003csub\u003epre\u003c/sub\u003e was 20 kPa. Fifteen repeated measurements were performed on the RST, each time with the same sample newly added to the shear cell type S (small v1.2). The inner and outer radii of the shear ring were 60 mm and 30 mm, respectively. The active shear cell height was 24 mm and therefore the cell volume was 2.04\u0026middot;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e m\u003csup\u003e3\u003c/sup\u003e. The shear cap through which the normal stress value σ\u003csub\u003epre\u003c/sub\u003e was applied to the specimen had active area radii of 59 and 31 mm. A real-time recording of the shear stress values τ\u003csub\u003epre\u003c/sub\u003e was taken from each measurement with normal stress σ\u003csub\u003epre\u003c/sub\u003e setting. Furthermore, the vertical lid position (VLP) values were recorded to reflect the volume change (compression/expansion) of the material sample during the shear test. These VLP or sample volume values could be used to determine the porosity ε. The shear rate was set to a fixed value 1.51 mm\u0026middot;min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. The angular velocity is assumed over the length of the arm 46.45 mm S-type shear cell that rotates 0.031 deg\u0026middot;s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\phi\\:}_{sf}=arctg\\frac{{\\tau\\:}_{pre}}{{\\sigma\\:}_{pre}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe measured samples were spherical and cubic particles (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) made of 3D printing material Prusament PLA with a density of 1240 kg\u0026middot;m\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e according to ISO 1183. The printing was performed on a Prusa i3 MKS3 printer (Prague, Czech Republic), PrusaSlicer version 2.3.0, setup with a layer height of 0.07 mm and 100% fill. The measured outer diameter of the spherical particles was 5.99\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05 mm (with standard deviation 0.8%) and the number of these spherical particles used in the shear cell was 911\u0026thinsp;\u0026plusmn;\u0026thinsp;16 (with standard deviation 1.8%). The number of the spherical particles was determined as a part of the change in total sample mass from fifteen repetitions of measurements. The cubic particles had an average edge length value of 3.87\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08 mm (with standard deviation 1.96%) and the number of particles used in the shear cell was 1935\u0026thinsp;\u0026plusmn;\u0026thinsp;26 (with standard deviation 1.4%). The number of cubic particles was also determined as a part of the change in the total mass of the sample from fifteen repetitions of measurements.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 DEM simulation\u003c/h2\u003e \u003cp\u003eAltair\u0026reg; EDEM\u0026trade; version 2021.0 was used for DEM simulations. Four main physical DEM models were used. For the spheres and multi-spheres, they were Hertz-Mindlin (no slip) and Linear Spring.\u003c/p\u003e \u003cp\u003eThe Hertz-Mindlin (HM) model is often the fundamental and default contact model of particle interactions. It is used in a various areas of DEM research. The HM model has been published many times in its default or modified form in shear test applications [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Both, the normal and tangential components of the force, usually use damping that is closely tied to the restitution coefficient. Tangential friction forces are based on Coulomb's friction law. Rolling friction model can be implemented in various modifications [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe Linear Spring (LIN) model is not applied for shear tests as often as the HM model but its usefulness is very similar [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. The LIN model uses coefficients such as the Linear Spring Stiffness. The Linear Spring Stiffness is based on mechanical-physical parameters such as Young's Modulus, Radius of the particle, Equivalent Mass, but mainly Typical Impact Velocity. The Typical Impact Velocity can affect the overall stiffness of the sample volume at the macroscale [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Another coefficient of the LIN model is the Dashpot Coefficient, which is influenced by the coefficient of restitution, the equivalent mass and the linear spring stiffness.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 DEM model \u0026ndash; input\u003c/h2\u003e \u003cp\u003eThree particle shapes were used for the study. A regular sphere SP particles (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea) with a radius of 2.99 mm, and two types of multi-spheres representing a cube (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec). The first type of multi-sphere MS-26 particles (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb) was made of 26 spheres with their radius of 0.65 mm. The arrangement was 3x3x3 spheres, with one sphere missing in the middle of the whole particle and each wall consisted of nine particles. The second type of multi-sphere MS-21 particles (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec) was made of 20 spheres with their radius of 0.65 mm and one sphere with a radius of 1.95 mm placed in the centre of the particle. The arrangement was 3x3x3 spheres with each wall consisting of eight particles. A sphere with a radius of 0.65 mm was missing in the middle of each wall because the space was filled by the volume of the central sphere with a radius of 1.95 mm. The number of the SP particles used was 911\u0026thinsp;\u0026plusmn;\u0026thinsp;16 particles. (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). The number of particles used for both particle types representing a cube (MS-26 and MS-21) was 1935\u0026thinsp;\u0026plusmn;\u0026thinsp;26 particles. (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec). Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e show the material and interaction parameters of these particles. Timestep was automatically set according to Euler at 1e-06 s.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMaterial properties\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterial property\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParticle\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGeometry\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePoisson's Ratio, ν (\u0026minus;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSolids Density, ρ\u003csub\u003es\u003c/sub\u003e (kg\u0026middot;m\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7800\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShear Modulus, G\u003csub\u003ee\u003c/sub\u003e (Pa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.4e\u0026thinsp;+\u0026thinsp;07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.93e\u0026thinsp;+\u0026thinsp;10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eInteraction parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInteraction\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParticle/Particle\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eParticle/Geometry\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCoefficient of Restitution, e (\u0026minus;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCoefficient of Static Friction, \u0026micro;\u003csub\u003es\u003c/sub\u003e (\u0026minus;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.4, 0.6, 0.8, 1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCoefficient of Rolling Friction, \u0026micro;\u003csub\u003er\u003c/sub\u003e (\u0026minus;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe particles in the shear cell were generated in 2 seconds. The particles were generated randomly with a Generation Rate with Target per number of 2500 per seconds. Then a lid with a vertical load σ\u0026thinsp;=\u0026thinsp;20 kPa was placed on the shear cell, which was automatically held at a constant value throughout the shear process. The shear lid had a degree of freedom in the vertical Z axis and rotational freedom in the X and Y axes. A more detailed setting of the kinematic and physical properties of a shear cell with a lid in EDEM is given in the publication [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSimulations of the shear process were performed for two shear cell rotation settings at 0.005173683 rpm and 0.02069473 rpm. The change in the rotation is reflected in a change of the shear rate SV. The change of the shear rate was from the SV\u0026thinsp;=\u0026thinsp;1x to the SV\u0026thinsp;=\u0026thinsp;4x. The length of the shear process was for the SV\u0026thinsp;=\u0026thinsp;1x approximately 245 seconds and for SV\u0026thinsp;=\u0026thinsp;4x approximately 60 seconds. The Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e was set to values 0.8 and 1.0 for SP particles. The MS particles had the Inter-Particle Friction set to 0.4 and 0.6. Given all 24 combinations of the input parameters (particle shape, physical contact model, Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e, and shear rate SV), it gives total of 72 number of simulations performer and evaluated.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 DEM model \u0026ndash; output\u003c/h2\u003e \u003cp\u003eAccording to the procedure presented in [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] the total shear stress τ, the normal stress σ, the Vertical Lid Position VLP and the Angle of Internal Friction AIF were expressed from the simulations at a time step of 0.5 second. Furthermore, the Coordination Number CN and the data of the actual XYZ particle positions for the Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e were expressed from the simulations over time with a time step of 1 second. The average horizontal particle velocity (Average Particle Velocity X and Y) (AVXY) and initial ε\u003csub\u003estart\u003c/sub\u003e and final ε\u003csub\u003eend\u003c/sub\u003e porosity of the material in the shear cell were also expressed.\u003c/p\u003e \u003cp\u003eThe Coordination Number CN of a particle is defined in EDEM as the number of contacts that a particle has with another particle. If one particle is composed of several sub-particles (multi-spheres), the contacts of the individual sub-particles with each other are also counted. For this reason, particles consisting of a larger number of sub-particles have a higher CN. The predictive value from comparisons within the CNs themselves is limited to the identical particle shape. It is not possible to directly compare CN Single-Particle and Multi-Spheres particle, but it is possible to compare the change of CN due to the change of e.g. the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e. In general, the higher the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e, the lower the particle embedment and hence the lower the CN. The CN is influenced by the particle embedment which affects the overall elasticity/stiffness of the particle material during the loading or shear process. The porosity of the bed (spacing) of the particulate material is also related to these properties and behaviour. The CN can be a guide to the correct setting of the mutual embedding of the particles into each other, or to the setting of the correct stiffness and initial porosity of the particle material. The average CN was recorded over time during the shear process for each simulation with a time step of 1 second. Three simulations with the same settings were then used to generate one average CN waveform over time. A single mean value was then expressed from this waveform along with the standard deviation. The effect of the static coefficient of friction \u0026micro;\u003csub\u003es\u003c/sub\u003e between particles on the CN values of the individual models was investigated. Differences in CN values for different \u0026micro;\u003csub\u003es\u003c/sub\u003e were expressed as relative average deviations (RAD) in units of [%]. The RADs were solved for the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e 0.8-1.0 for the SP particle model and for the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e 0.4\u0026ndash;0.6 for the MS21 and MS26 particle model.\u003c/p\u003e \u003cp\u003eThe XYZ particle positions were exported according to [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. In general, a single particle shift S\u003csub\u003ei\u003c/sub\u003e (t\u003csub\u003ei\u003c/sub\u003e) was defined as a change of position in 3D space (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea) from the initial to the final position at time step t\u003csub\u003ei\u003c/sub\u003e. The coordinates X and Y define the horizontal plane. The Angle of Particle Shifts ϕ\u003csub\u003eSi\u003c/sub\u003e of each particle P\u003csub\u003ej\u003c/sub\u003e at time step t\u003csub\u003ei\u003c/sub\u003e was expressed from the exported data. The Angle of Particle Shifts can be understood as a measure of the resistance to change the particle position in the shear cell. Each subsequent shift S\u003csub\u003ei+1\u003c/sub\u003e (t\u003csub\u003ei+1\u003c/sub\u003e) was defined such that the final position from the previous time step t\u003csub\u003en\u003c/sub\u003e becomes the new starting position of the next shift. The resulting angle ϕ\u003csub\u003eSj\u003c/sub\u003e (9) of the 3D shift S\u003csub\u003ei\u003c/sub\u003e (t\u003csub\u003ei\u003c/sub\u003e) of the particle P\u003csub\u003ej\u003c/sub\u003e at time step t\u003csub\u003ei\u003c/sub\u003e was expressed from the tangent of the ratio Δz\u003csub\u003ei\u003c/sub\u003e to the resulted motion R\u003csub\u003ei\u003c/sub\u003e (8) in the horizontal XY plane. Based on the initial coordinates z\u003csub\u003et0\u003c/sub\u003e of the particles at time t\u003csub\u003e0\u003c/sub\u003e all particles were assigned an emergence layer (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). Four layers were created in the shear cell for all particle types (SP, MS-26, and MS-21). The height of one layer was 6 mm. In each layer, for each time step from t\u003csub\u003ei\u003c/sub\u003e to t\u003csub\u003en\u003c/sub\u003e, one value of the average Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e(t\u003csub\u003ei\u003c/sub\u003e) was determined from all angles of particle shifts ϕ\u003csub\u003eSj\u003c/sub\u003e (10).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{i}=\\sqrt{\\varDelta\\:{x}_{i}^{2}+\\varDelta\\:{y}_{i}^{2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(8)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|{\\varnothing\\:}_{Sj}\\left({t}_{i}\\right)\\right|=arctg\\left(\\frac{{\\varDelta\\:z}_{i}}{{R}_{i}}\\right)=arctg\\left(\\frac{{z}_{{t}_{n}}-{z}_{{t}_{n-1}}}{\\sqrt{{\\left({x}_{{t}_{n}}-{x}_{{t}_{n-1}}\\right)}^{2}+{\\left({y}_{{t}_{n}}-{y}_{{t}_{n-1}}\\right)}^{2}}}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(9)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|{\\stackrel{-}{\\varnothing\\:}}_{S}\\left({t}_{i}\\right)\\right|=\\frac{1}{j}\\bullet\\:{\\sum\\:}_{i=1}^{j}\\left|{\\varnothing\\:}_{Sj}\\left({t}_{i}\\right)\\right|\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(10)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAverage Particle Velocity X and Y AVXY was investigated in individual layers which followed the distribution for XYZ shifts. Each layer L1 to L4 consisted of four separate quadrants. In each quadrant, one overall average AVXY value from the shear process was separately determined with a time step of 0.05 seconds. One final AVXY value of one whole layer was created by averaging the four values of all quadrants. The identification of the main (dominant) shear region was a prerequisite for the AVXY solution. The largest difference in the resulting horizontal AVXY between the layers could characterize the dominant shear region. Graphs of the velocities of the individual layers and tables of the values of the line segment directives were created. The graphs characterize the specific magnitude of the velocity difference between two adjacent layers by a single number.\u003c/p\u003e \u003cp\u003eThe porosity ε [-] was expressed by the Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e11\u003c/span\u003e). The mean value and standard deviation for the Porosity ε was obtained from three simulations with the same settings. The objects of interest were the average values for the initial porosity value ε\u003csub\u003estart\u003c/sub\u003e and the final porosity value ε\u003csub\u003eend\u003c/sub\u003e of the shear process. The effects of changes in the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e and shear rate (SV) on the average values of ε\u003csub\u003estart\u003c/sub\u003e and ε\u003csub\u003eend\u003c/sub\u003e were also investigated. The detailed evaluation procedure is given in the article [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\epsilon\\:}_{start,\\:\\:end}=\\frac{{V}_{Voids}}{{V}_{Total}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Preshear (PS)\u003c/h2\u003e \u003cp\u003eThe resulting shear processes obtained by the Preshear (PS) simulation were compared. This comparison is for all the DEM particle models investigated. The variables were the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e and the shear rate (SV). Each individual PS curve for different contact models and Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e values are expressed by the average values obtained from three repeated simulations.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the Preshear PS for the SP particles. The change in the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e did not significantly affect the final PS values for the shear rate SV\u0026thinsp;=\u0026thinsp;1x. Towards the end of the PS process, higher Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e values resulted in a slight decrease in the PS values for both the HM and LIN models. Also, the change in the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e did not significantly affect the final PS values for the SV\u0026thinsp;=\u0026thinsp;4x. Rather, the increase in \u0026micro;\u003csub\u003es\u003c/sub\u003e resulted in a slight decrease in PS values, which is the opposite of the expected pattern. The increase in the SV was reflected by a slight decrease in the PS values. With higher shear rate, there are probably more kinematic effects between particles and the resistance between particles decreases. Particles may have a greater tendency to be oriented to move in the direction of flow, which can reduce this resistance. At higher shear rates, the frequency of particle collisions can increase. This reduces the persistence of particles in mutual contact over time, the effect of kinematic friction. The change in the \u0026micro;\u003csub\u003es\u003c/sub\u003e values was apparently small considering the small changes in the PS for the SP particles.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe PS for the MS-26 particle is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e The increase in the \u0026micro;\u003csub\u003es\u003c/sub\u003e is significant only for the HM model towards the end of the PS process for the shear rate SV\u0026thinsp;=\u0026thinsp;1x. The HM model had slightly higher PS values in the first half of the shear process (up to 120 s) than the LIN model. Towards the end of the process, the difference between HM and LIN evened out. For the SV\u0026thinsp;=\u0026thinsp;4x, a very similar overall PS for the HM and LIN models was obtained. Towards the end of the process, slight differences became apparent. The increase in \u0026micro;\u003csub\u003es\u003c/sub\u003e was reflected more for the SV\u0026thinsp;=\u0026thinsp;4x than the SV\u0026thinsp;=\u0026thinsp;1x by an increase in the PS values for the HM model towards the end of the PS process.\u003c/p\u003e \u003cp\u003eThere is a significant difference in the Preshear PS values (10 kPa vs. 12 kPa) when compared to the SP particles. The increase in PS can be attributed to the particle shape because the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e was lower for MS particles compared to SP particles. Cube-shaped particles exhibit a larger particle contact area. Furthermore, uneven distribution of contact forces between the particles may occur due to different rotation of the cubic particles. This phenomenon does not occur for the SP particles as they are spherical and have the same shape at any rotation in 3D space. An increase in the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e only had a major impact on the HM model This impact was magnified with higher shear rate. At higher shear rates, cubic particles can orient themselves to more energetically demanding positions for shear stress. This can lead to more energy intensive contacts and resistance between particles. The LIN model shows low sensitivity to a change in the \u0026micro;\u003csub\u003es\u003c/sub\u003e. The LIN model represents a uniform distribution of forces throughout the shear process with a low impact change in the \u0026micro;\u003csub\u003es\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the PS for MS-21 particles. The increase in the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e is reflected by an increase in PS for both the HM and LIN models towards the end of the shear process for the shear rate SV\u0026thinsp;=\u0026thinsp;1x This difference was lower for the SV\u0026thinsp;=\u0026thinsp;4x. The differences of the PS values between the HM and LIN were lower towards the end of the PS process for the SV\u0026thinsp;=\u0026thinsp;4x model than for the SV\u0026thinsp;=\u0026thinsp;1x.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe PS values for MS-26 particles were less dispersed towards the end of the PS process for the shear rate SV\u0026thinsp;=\u0026thinsp;1x than for MS-21 particles. In contrast, the PS values for the MS-26 particles were for shear rate SV\u0026thinsp;=\u0026thinsp;4x more scattered towards the end of the PS event than for MS-21 particles.\u003c/p\u003e \u003cp\u003eThe LIN model was less stable for MS-21 particles than MS-26 particles due to the change in \u0026micro;\u003csub\u003es\u003c/sub\u003e. Probably due to the composition of multispheres with a larger central particle The LIN model for SP particles was also less stable than for MS-26 particles. The central multisphere tends to have a point of contact as in the case of SP particles. This is related to the rather lower PS values for the higher shear rate for the MS-21 particle model.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e to Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e show several possible outputs from different DEM settings of the shear stress process, which are in the range of experimentally measured values using RST. In terms of the PS measurement approach, these calibrations would be considered sufficient. However, individual differences in the behaviour of the shear stress outputs are not sufficiently informative. The information sufficiency should further investigate particle motion or deformation properties of the models during shear stress. For this reason, the following chapter discusses the description of shear processes in connection with deformation behaviour.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Vertical lid position (VLP)\u003c/h2\u003e \u003cp\u003eThe curves of the vertical lid position (VLP) were compared for all DEM particle models. Each displayed VLP curve from EDEM was generated from three simulation iterations with specific contact model settings and input parameters. The variable parameters were the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e and the shear rate SV.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the VLP for the SP particles. The increase in the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e resulted in a larger change in VLP (bigger compression) for shear rate SV\u0026thinsp;=\u0026thinsp;1x using HM model Tt was the other way around (lower compression) for the LIN model. The increase in \u0026micro;\u003csub\u003es\u003c/sub\u003e in for shear rate SV\u0026thinsp;=\u0026thinsp;4x using the HM model was of the same nature (bigger compression). The LIN model also showed an increase in compression for SV\u0026thinsp;=\u0026thinsp;4x.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn cases with higher compression due to an increase in the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e, compaction occurred with a decrease in strength or the PS values during the shear process. Due to particles motion, the bonds or the internal structure of the static arrangement of the particles were disturbed. The particles motion overcame critical values of an inter-particle friction.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the VLP for the MS-26 particles. The increase in Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e for SV\u0026thinsp;=\u0026thinsp;1x resulted in a smaller change in VLP (lower compression) for both, the HM model and LIN model. The increase in \u0026micro;\u003csub\u003es\u003c/sub\u003e for SV\u0026thinsp;=\u0026thinsp;4x was similar (lower compression) for the HM and LIN models. Lower maximum VLP values were obtained for SV\u0026thinsp;=\u0026thinsp;4x using HM model. The LIN model had a greater tendency to increase compression at higher SV. The HM model decreased compression for higher shear rate SV.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe cubic shape of MS-26 particles showed lower deformation strength (resistance over deformation) compared to SP particles. Compression during the shear process was higher for MS-26 particles than that of SP particles. The shape of the MS-26 particles was affected by the initial embedding of the particles, which was lower during and after the shear process compared to the SP particles. Contrary, the combination of shape and higher Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e values had an effect on compaction with an increase in deformation strength and PS values. Processes that are less clear and not easily identifiable solely by PS curves become more recognizable with VLP curves. In the LIN model, for instance, there is a noticeable decrease in deformation strength and an increase in compression caused by the higher shear rate SV affecting the kinematics and frictional properties of the particles.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the Vertical lid position VLP for the MS-21 particles. Using the LIN model for the SV\u0026thinsp;=\u0026thinsp;1x and SV\u0026thinsp;=\u0026thinsp;4x, the increase in the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e resulted in a smaller change in VLP (lower maximum compression). Less compression was achieved for the HM model with an increase in \u0026micro;\u003csub\u003es\u003c/sub\u003e only in terms of the final values. The HM model achieved lower VLP values for the SV\u0026thinsp;=\u0026thinsp;4x than for the SV\u0026thinsp;=\u0026thinsp;1x. The opposite was true for the LIN model.\u003c/p\u003e \u003cp\u003eThe LIN model had a greater tendency to increase compression at higher SV. The HM model reduced compression at higher SV. The same effect was achieved with the MS-26 particles. The HM model was more sensitive to shear rate. Due to the more complex contact-deformation model used by the HM model, there was a faster increase in strength due to higher shear rates. Overall, lower compression was achieved than for the MS-26 particles. The central spherical multi-sphere changes the shape factor affecting the strength contacts before and during the shear process.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe MS-26 and MS-21 particles responded similarly to changes in the shear rate SV and the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e. The MS-26 particles showed higher maximum compression values than MS-21 particles. The nature of the impact of increased \u0026micro;s in LIN models was identical for both shear rates, SV\u0026thinsp;=\u0026thinsp;1x and SV\u0026thinsp;=\u0026thinsp;4x. With higher \u0026micro;\u003csub\u003es\u003c/sub\u003e, the maximum compression during PS decreased. The nature of the effect of the \u0026micro;\u003csub\u003es\u003c/sub\u003e for the MS-21 and MS-26 particles using HM model was identical in terms of the final (in t\u0026thinsp;=\u0026thinsp;240s) VLP values. The VLP curves changes with the change in the \u0026micro;\u003csub\u003es\u003c/sub\u003e were smaller for the MS-21 particles than for the MS-26 particles using HM and LIN models.\u003c/p\u003e \u003cp\u003eAlthough the PS curves may have seemed applicable, this was not the case for VLP. It was confirmed that output parameters other than shear stresses need to be verified and the VLP values are very suitable for this assessment. The deformation of the sample during the shear test is an important aspect of the global behaviour assessment.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Coordination Number CN\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e to Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e show the average Coordination Number CN values for each DEM particle shape from three repeated runs of the shear process. The average values show the effect of an increase in Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e leading to a decrease in CN values. The smallest effect of the increase in the \u0026micro;\u003csub\u003es\u003c/sub\u003e on the decrease in the CN values was observed for the SP particles (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). In general, the spherical particle shape has the best ability of the most compact arrangement. The change in compact arrangement was negligible for SP particles using the \u0026micro;\u003csub\u003es\u003c/sub\u003e values from 0.8 to 1.0.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage values and standard deviation of the Coordination Number CN for the SP particles.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8, SV\u0026thinsp;=\u0026thinsp;1x\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0, SV\u0026thinsp;=\u0026thinsp;1x\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8, SV\u0026thinsp;=\u0026thinsp;4x\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0, SV\u0026thinsp;=\u0026thinsp;4x\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eHM\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e3.99\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e3.94\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e3.96\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e3.96\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLIN\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e4.28\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e4.27\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e4.30\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e4.28\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage values and standard deviation of the Coordination Number CN for the MS21 particles\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMS21\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4, SV\u0026thinsp;=\u0026thinsp;1x\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6, SV\u0026thinsp;=\u0026thinsp;1x\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4, SV\u0026thinsp;=\u0026thinsp;4x\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6, SV\u0026thinsp;=\u0026thinsp;4x\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eHM\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e9.23\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e8.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e9.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e8.12\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLIN\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e12.31\u0026thinsp;\u0026plusmn;\u0026thinsp;0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e11.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e12.37\u0026thinsp;\u0026plusmn;\u0026thinsp;0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e11.18\u0026thinsp;\u0026plusmn;\u0026thinsp;0.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage values and standard deviation of the Coordination Number CN for the MS26 particles\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMS26\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4, SV\u0026thinsp;=\u0026thinsp;1x\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6, SV\u0026thinsp;=\u0026thinsp;1x\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4, SV\u0026thinsp;=\u0026thinsp;4x\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6, SV\u0026thinsp;=\u0026thinsp;4x\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eHM\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e10.63\u0026thinsp;\u0026plusmn;\u0026thinsp;0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e9.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e10.40\u0026thinsp;\u0026plusmn;\u0026thinsp;0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e9.08\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLIN\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e13.91\u0026thinsp;\u0026plusmn;\u0026thinsp;0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e12.28\u0026thinsp;\u0026plusmn;\u0026thinsp;0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e13.75\u0026thinsp;\u0026plusmn;\u0026thinsp;0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e12.16\u0026thinsp;\u0026plusmn;\u0026thinsp;0.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eOther particle shapes had the effect of changing Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e on the Coordination Number CN much more significant than SP particles. The increase in the \u0026micro;\u003csub\u003es\u003c/sub\u003e values was amplified with the greater influence of the particle shape. The cubic particle shape generally reduces the compactness of the arrangement in the volume. This effect was even more noticeable for the MS-26 particles.\u003c/p\u003e \u003cp\u003eThe Coordination Number CN value increased due to the higher shear rate SV for the SP and MS-21 particles using LIN model. Higher interlocking of the particles increased the number of contacts. The CN value decreased with the higher SV for the MS-26 particles using the LIN model. This is inconsistent with the assumption of sample volume expansion implied by the results in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. There was no significant loosening of the particles from each other or increase in sample volume at higher SV. Rather, there was only a rotation of the particles into positions with fewer contacts. The MS-26 particles have the highest CN because of the largest number of particles that make up a single multi-sphere. The number of these sub-particles increases the number of CN contacts considered. Changes in the kinematics of the particle ensemble due to the higher shear rate SV were predicted to reduce the high CN values. The central particle in the MS-21 particles reversed the effect of the increase in the SV on the CN, which brought the MS-21 particles closer in behaviour to the SP particles. SP, MS-21 and MS-26 particles using the HM model with lower \u0026micro;\u003csub\u003es\u003c/sub\u003e values due to higher SV resulted in lower CN values. The trends of CN values with the use of HM models for higher \u0026micro;\u003csub\u003es\u003c/sub\u003e values were mixed for higher SV.\u003c/p\u003e \u003cp\u003eIn the future, it is possible to calibrate the typical Impact Velocity V [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] with the Coordination Number CN values for accurate calibration of the LIN model. The contact velocity V affects the overall stiffness of the particle sample in the volume. With a higher value of V, the CN should theoretically decrease to reach values more similar to the LIN model as with the HM model.\u003c/p\u003e \u003cp\u003eThe results show basic differences between the particle models also with respect to the change in kinematics due to the increase in shear rate SV. The observed changes in the CN values can support to some extent the ideas about the processes occurring during the shear test with respect to the compactness of the particle arrangement. For example, a lower CN indicates a looser arrangement, which can lead to greater deformation or changes in the shear strength of the material. The influence of parameters and kinematics on CN and material properties is complex and depends on the specific particle model and its application. Detailed analysis of data and models is required for a deeper understanding.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Porosity\u003c/h2\u003e \u003cp\u003eThe average initial porotsity ε\u003csub\u003estart\u003c/sub\u003e values for all individual DEM models did not change significantly by changing of the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e. The effect of increasing the shear rate SV and the \u0026micro;\u003csub\u003es\u003c/sub\u003e on the final porosity ε\u003csub\u003eend\u003c/sub\u003e value of the sample was also minimal. For these reasons, final average values of the ε\u003csub\u003efstart\u003c/sub\u003e and ε\u003csub\u003efend\u003c/sub\u003e were generated based on all ε\u003csub\u003estart\u003c/sub\u003e or ε\u003csub\u003eend\u003c/sub\u003e values of an individual particle (shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). The average value of ε\u003csub\u003efstart\u003c/sub\u003e or ε\u003csub\u003efend\u003c/sub\u003e was constructed from the ε values of the other \u0026micro;\u003csub\u003es\u003c/sub\u003e, using the HM and LIN models for the SP, MS21, and MS26 particles. The final values shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e are only for the SV\u0026thinsp;=\u0026thinsp;1x, because they were almost identical for the SV\u0026thinsp;=\u0026thinsp;4x. Further, Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the porosity values from the RST experiments.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePorosity ε\u003csub\u003efstart\u003c/sub\u003e and ε\u003csub\u003efend\u003c/sub\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003etype of model and particle\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSP particles (HM and LIN)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMS21 particles (HM and LIN)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMS26 particles (HM and LIN)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eε\u003c/b\u003e\u003csub\u003e\u003cb\u003efstart\u003c/b\u003e\u003c/sub\u003e, \u003cb\u003e[-]\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.50\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.55\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e0.70\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eε\u003c/b\u003e\u003csub\u003e\u003cb\u003efend\u003c/b\u003e\u003c/sub\u003e, \u003cb\u003e[-]\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.49\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.54\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e0.69\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the minimal difference between ε\u003csub\u003efstart\u003c/sub\u003e and ε\u003csub\u003efend\u003c/sub\u003e for all particle models. The highest values were measured for the MS-26 and MS-21 particles. In this case, a higher number of subparticles (multispheres) leads to an increase in the porosity ε values. The minimum ε values were measured for the SP particles.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage initial ε\u003csub\u003efstart\u003c/sub\u003e and final ε\u003csub\u003efend\u003c/sub\u003e values experimentally obtained on the Ring Shear Tester RST.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpheres\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCubes\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eε\u003c/b\u003e\u003csub\u003e\u003cb\u003estart\u003c/b\u003e\u003c/sub\u003e, \u003cb\u003e[-]\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.51\u0026thinsp;\u0026plusmn;\u0026thinsp;0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.56\u0026thinsp;\u0026plusmn;\u0026thinsp;0.004\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eε\u003c/b\u003e\u003csub\u003e\u003cb\u003eend\u003c/b\u003e\u003c/sub\u003e, \u003cb\u003e[-]\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.51\u0026thinsp;\u0026plusmn;\u0026thinsp;0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.56\u0026thinsp;\u0026plusmn;\u0026thinsp;0.004\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe values presented in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e confirm that the initial ε\u003csub\u003estart\u003c/sub\u003e and final ε\u003csub\u003eend\u003c/sub\u003e porosity values do not change significantly even for the measurements obtained from the RST experiments. For spherical particles, the simulation and experimental values were almost identical. However, there are differences for cubic particles. These discrepancies are attributed to variations in the shape of the cubic particles. The shape variations characterize the multispheres (MS) cubes. The results indicate that the porosity values did not change significantly during the shear process in the cases investigated in this work. Only the shape and size of the particle in specific cases influence the porosity value. This effect is related to the particle volume within the shear cell. The SP particles had the highest particle volume value of 0.00010200 m\u003csup\u003e3\u003c/sup\u003e, following the MS-21 particles with a value of 0.00008696 m\u003csup\u003e3\u003c/sup\u003e, and the MS-26 particles with a value of 0.00005786 m\u003csup\u003e3\u003c/sup\u003e. According to Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e11\u003c/span\u003e), it is the particle volume that impacts the magnitude of the final porosity ε. These findings correspond to the results shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eIn terms of the vertical lid position, the average value of the shear lid for the RST experiment for spherical particles was 26.39\u0026thinsp;\u0026plusmn;\u0026thinsp;0.43 mm at the start of the shear process and 26.14\u0026thinsp;\u0026plusmn;\u0026thinsp;0.39 mm at the end of the process. For cubic particles, the values were 25.86\u0026thinsp;\u0026plusmn;\u0026thinsp;0.42 mm at the start and 25.50\u0026thinsp;\u0026plusmn;\u0026thinsp;0.26 mm at the end of the shear process.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e to Table\u0026nbsp;\u003cspan refid=\"Tab13\" class=\"InternalRef\"\u003e13\u003c/span\u003e show the shear Vertical Lid Position VLP values for each particle model and the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e values. From the results, it can be generally summarized that the VLP increased with increasing the \u0026micro;s value. The VLP was also always lower in the end position than in the start position. However, there were minor exceptions for the SP particles using the LIN model with lower shear rate SV. Increasing the \u0026micro;\u003csub\u003es\u003c/sub\u003e values resulted in a decrease in the compactness of the particles and increased the loosening of the particles, with a very slight expansion of the particle sample volume represented by the higher VLP. Porosity and VLP are affected by particle shape, size, and \u0026micro;\u003csub\u003es\u003c/sub\u003e. During the shear, the porosity does not change significantly; rather, the particle arrangement changes, leading to loosening with slight expansion.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVertical lid positions VLP for the SP particles, shear rate SV\u0026thinsp;=\u0026thinsp;1x\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003estart\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e26.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e26.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e25.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e25.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eend\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e26.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e26.2\u0026thinsp;\u0026plusmn;\u0026thinsp;0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e25.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e25.0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVertical lid positions VLP for the SP particles, shear rate SV\u0026thinsp;=\u0026thinsp;4x\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003estart\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e26.3\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e26.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e25.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e25.5\u0026thinsp;\u0026plusmn;\u0026thinsp;0.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eend\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e26.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e26.2\u0026thinsp;\u0026plusmn;\u0026thinsp;0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e24.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e24.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVertical lid positions VLP for the MS21 particles, shear rate SV\u0026thinsp;=\u0026thinsp;1x\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003estart\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e25.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e23.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e24.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eend\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e25.3\u0026thinsp;\u0026plusmn;\u0026thinsp;0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e23.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e24.2\u0026thinsp;\u0026plusmn;\u0026thinsp;0.16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab11\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVertical lid positions VLP for the MS21 particles, shear rate SV\u0026thinsp;=\u0026thinsp;4x\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003estart\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e25.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e23.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e24.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eend\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e25.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e23.3\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e24.2\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab12\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 12\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVertical lid positions VLP for the MS26 particles, shear rate SV\u0026thinsp;=\u0026thinsp;1x\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003estart\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e25.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e23.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e24.3\u0026thinsp;\u0026plusmn;\u0026thinsp;0.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eend\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e25.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e23.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e23.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab13\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 13\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVertical lid positions VLP for the MS26 particles, shear rate SV\u0026thinsp;=\u0026thinsp;4x\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHM \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLIN \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003estart\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e25.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e23.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e24.3\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eend\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24.2\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e25.2\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e23.0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e23.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Particle shifts\u003c/h2\u003e \u003cp\u003eThe shift of a particle in the shear test process was defined by DEM from the change of position in 3D space (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea) from the initial to the final position (Chap.\u0026nbsp;2.4). The final average Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e was calculated using the XYZ coordinates of the particles at each time step across layers L1 to L4 of the shear cell (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). The evaluation time step was 12 seconds for the lower shear rate SV and 3 seconds for the higher shear rate SV. The ϕ\u003csub\u003eS\u003c/sub\u003e values of each layer progress upwards in the plots. Layer L1 is the lowest and L4 is the highest layer in the shear cell, with their respective heights depicted in the plots. Each layer's graphs consistently show four runs of layers L1-L4. In each layer, there are two versions of the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e and physical DEM model for the SP and MS particles. The value of AIF in the shear test process was defined using the DEM as an arctangent function of the ratio of shear stress to normal stress (1) (Chap.\u0026nbsp;2.1). The average Angle of Internal Friction AIF values were calculated with a time step of 0.5 seconds. Both the AIF and ϕS values are in angular units, allowing them to be plotted together in common graphs (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e to Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the SP particle shifts for two shear rates SV values. There is little effect of SV on the Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e and Angle of Internal Friction AIF values. For the SV\u0026thinsp;=\u0026thinsp;4x, a slightly larger scatter of HM vs. LIN models values appeared in the L1 and L2 layers compared to SV\u0026thinsp;=\u0026thinsp;1x, along with slightly lower AIF values at the end of the shear process due to increased particle kinematics. The AIF values were between the ϕ\u003csub\u003eS\u003c/sub\u003e values of L3 and L4 layers in both cases. The fourfold increase in the SV in the simulation did not significantly impact the final results.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e illustrates the shifts of the MS-21 particles for two different shear rate SV values. It is evident that the SV has a minor influence on the final Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e values during the shear process. Lower SV values resulted in slightly higher ϕ\u003csub\u003eS\u003c/sub\u003e values using the HM and LIN models in the uppermost layer. The Angle of Internal Friction AIF values were positioned between the ϕ\u003csub\u003eS\u003c/sub\u003e values of the third and fourth layers in both cases. A fourfold increase in the SV had a minor impact on the final results. However, the AIF values slightly decreased with the higher SV at the end of the shear process. Initially, the ϕ\u003csub\u003eS\u003c/sub\u003e values in the L4 were higher at the beginning of the shear process. With the higher SV, the ϕ\u003csub\u003eS\u003c/sub\u003e using HM model values for \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8 were greater than those for \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0. Compared to the SP particles, the difference in ϕ\u003csub\u003eS\u003c/sub\u003e values between layers L2 and L3 was much larger.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the shifts of the MS-26 particles for two shear rate SV values, similar to the case in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e. With the lower SV value, slightly higher Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e values using the HM and LIN models were achieved in the uppermost layer (L4). The greatest variance between the HM and LIN model values gradually increased with layer height for both SV\u0026thinsp;=\u0026thinsp;1x and SV\u0026thinsp;=\u0026thinsp;4x. The Angle of Internal Friction AIF values were positioned between the ϕ\u003csub\u003eS\u003c/sub\u003e values of the third and fourth layers for the lower SV. For the SV\u0026thinsp;=\u0026thinsp;4x, the AIF values extended more into the fourth layer ϕ\u003csub\u003eS\u003c/sub\u003e compared to the SV\u0026thinsp;=\u0026thinsp;1x. Higher SV resulted in the lower ϕ\u003csub\u003eS\u003c/sub\u003e in the final L4 layer, likely due to the dominance of horizontal velocity components in L4. Final AIF values were more dispersed with the higher SV. With lower SV, ϕ\u003csub\u003eS\u003c/sub\u003e values showed a more increasing trend than with higher SV. The difference between the MS-21 and MS-26 particles in terms of the ϕ\u003csub\u003eS\u003c/sub\u003e values was most noticeable in L3 and L4 layers for the higher SV. Higher SV resulted in greater instability in L3 and L4 layers, more so than with the MS-21 particles. The HM model with lower \u0026micro;\u003csub\u003es\u003c/sub\u003e generally showed higher \u0026micro;\u003csub\u003es\u003c/sub\u003e values, but this trend decreased with higher SV. Compared to the SP particles, the difference in the ϕ\u003csub\u003eS\u003c/sub\u003e values between L2 and L3 layers was much larger.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe impact of changing the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e coefficient on the Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e was generally small, but when it did occur, it was more noticeable in the higher layers, L3 and L4. This is due to the increased freedom of particle movement, which is greater in L3 and the greatest in L4. Given the design of the shear lid and the height of the shear bars (4 mm), the main shear process between particles should occur between L3 and L4 layers. Ideally, if the entire L4 layer is driven by the shear bars, it will shear over the L3 layers. Particles can transition between L3 and L4 layers during the shear process, and this transition ability is represented by the geometric value ϕ\u003csub\u003eS\u003c/sub\u003e. The size of ϕ\u003csub\u003eS\u003c/sub\u003e correlates with the ability to deform. The higher ϕ\u003csub\u003eS\u003c/sub\u003e may indicate greater vertical particle movement. This ability can be understood as vertical particle flow, which reduces local strength and increases local flowability in the sample. In contrast, the AIF represents the force or stress conditions on particles, also expressed geometrically by an angle. From this perspective, the geometric representation of the AIF between L3 and L4 layers confirms the main shear region.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.6 Average Particle Velocity AVXY in layers\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e to Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e illustrate the Average Particle Velocities AVXY during the shear process in each layer of the shear cell. The method for obtaining values in each layer using quadrants is described in section 2.4. Layer L1 is at the bottom of the rotational shear cell, and layer L4 is in the region affected by the shear lid's vanes. At higher shear rate SV, there is a clear numerical fourfold increase in the AVXY and, in most cases, a similar trend in the curve progression. Table\u0026nbsp;\u003cspan refid=\"Tab14\" class=\"InternalRef\"\u003e14\u003c/span\u003e to Table\u0026nbsp;\u003cspan refid=\"Tab16\" class=\"InternalRef\"\u003e16\u003c/span\u003e include characteristic values of velocity changes between adjacent layers, represented by the slopes of the line segments. Higher values indicate greater changes in the AVXY between layers and correspond to a more pronounced downward trend in the curves between layers during the shear process, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e to Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab14\" class=\"InternalRef\"\u003e14\u003c/span\u003e presents the results for the SP particles. The values indicating the greatest change in the Average Particle Velocity AVXY between layers for the SP particles were mostly found between layers L3 and L4. The exception was the HM model with Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0 and the shear rate SV\u0026thinsp;=\u0026thinsp;1x, where this was not the case. It is likely that the higher \u0026micro;\u003csub\u003es\u003c/sub\u003e of the HM model increases the shear strength between layers L4 and L3, causing the shear region to shift lower, between L3 and L2. This effect of increased \u0026micro;\u003csub\u003es\u003c/sub\u003e was not observed for the higher SV.\u003c/p\u003e \u003cp\u003eAssuming that the greatest difference in velocities between layers characterizes the shear region, the shear region for SP particles would be located between layers L3 and L4. The highest the Average Particle Velocity AVXY values were achieved using the HM model with Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0, and the lowest using the LIN model with \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8 for both shear rate SV values (Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e). The change in the AVXY across layers L1-L4 was almost linear.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab14\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 14\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValues representing the change in the Average Particle Velocities AVXY between individual layers for the SP particles.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eSP Velocity with SV\u0026thinsp;=\u0026thinsp;1x\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c10\" namest=\"c6\"\u003e \u003cp\u003eSP Velocity with SV\u0026thinsp;=\u0026thinsp;4x\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLayer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLayer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e1\u0026ndash;2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0028\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.0036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.0024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.0029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1\u0026ndash;2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-0.0099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.0125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.0112\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.0086\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2\u0026ndash;3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0050\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.0047\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.0054\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.0044\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2\u0026ndash;3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-0.0166\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.0191\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.0138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.0182\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e3\u0026ndash;4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.0065\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.0049\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.0071\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e3\u0026ndash;4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-0.0259\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.0236\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.0252\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.0242\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAccording to Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab15\" class=\"InternalRef\"\u003e15\u003c/span\u003e, for the MS-21 particles, the greatest difference in the Average Particle Velocities AVXY was generally observed between layers L2 and L3. Assuming that the greatest velocity difference between layers characterizes the shear region, the shear region for the MS-21 particles would be located between layers L2 and L3, approximately in the middle of the shear cell. The highest AVXY values were achieved using the LIN model for the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6 and shear rate SV\u0026thinsp;=\u0026thinsp;1x and using the HM model for the \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6 and the SV\u0026thinsp;=\u0026thinsp;4x. The changes in the AVXY across layers were almost linear. The AVXY values were very similar across the different models, especially for the lower SV values. The cubic shape of the particles exhibited greater shear strength, as shown on Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, than the SP particles. This higher overall shear strength also manifested as greater strength between layers L1-L2 and L3-L4. This increased shear strength likely resulted in the weakest point being between layers L2-L3, approximately halfway up the shear cell. The assumption of the main shear region based on the Angle of Particle Shifts φs, Angle of Internal Friction AIF, and AVXY values is not applicable for the MS-21 particles. During the shear test, the MS particles can form mechanical bonds and structures that are more stable than those formed by the SP particles. The MS particles can interlock and create solid clusters that are harder to break during shear stress.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab15\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 15\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValues representing the change in the Average Particle Velocities AVXY between individual layers for the MS21 particles\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eMS 21 Velocity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c10\" namest=\"c6\"\u003e \u003cp\u003eMS 21 4x Velocity\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLayer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLayer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e1\u0026ndash;2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.0042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.0043\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.0035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1\u0026ndash;2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-0.0168\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.0167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.0151\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.0153\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2\u0026ndash;3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.0067\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.0059\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.0066\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2\u0026ndash;3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-0.0254\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.0271\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.0240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.0224\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e3\u0026ndash;4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.0041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.0052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.0034\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e3\u0026ndash;4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-0.0176\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.0198\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.0230\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.0214\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAccording to Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab16\" class=\"InternalRef\"\u003e16\u003c/span\u003e, for the MS-26 particles, the greatest velocity difference was generally between layers L2 and L3. Based on the before mentioned assumption, the shear region for the MS-26 particles would also be between layers L2 and L3, similar to the MS-21 particles. The difference in Average Particle Velocity AVXY values among the different models and Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e values with changing shear rate SV was mostly consistent, except for the unexpected AVXY values for the HM model with the \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4. This change in trend between layers L3 and L4 likely resulted from the reactive effects of particle deformation stress. Increased particle compression can lead to the release of this compression in time pulses. When compression is released, particles accelerate against the direction of shear. As with the MS-21, the MS-26 particles can interlock and form stable clusters that are more difficult to break during shear stress. The AVXY values for the different models and \u0026micro;\u003csub\u003es\u003c/sub\u003e values were more varied for the MS-26 particles compared to the MS-21 particles.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab16\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 16\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValues representing the change in the Average Particle Velocities AVXY between individual layers for the MS26 particles\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eMS 26 Velocity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c10\" namest=\"c6\"\u003e \u003cp\u003eMS 26 4x Velocity\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLayer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLayer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eHM\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eLIN\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e1\u0026ndash;2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.0054\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.0038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.0043\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1\u0026ndash;2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-0.0053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.0218\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.0113\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.0151\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2\u0026ndash;3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0054\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.0065\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.0061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.0061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2\u0026ndash;3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-0.0338\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.0272\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.0194\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.0278\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e3\u0026ndash;4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.0032\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.0034\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.0045\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e3\u0026ndash;4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-0.0138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.0118\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.0141\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e-0.0163\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor the MS particles, the differences between Angle of Particle Shifts φs values in layers L2 and L3 were greater compared to the SP particles (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e). A larger increase in the φs values indicates a greater ability for vertical particle movement. Since cubic particles have larger contact surfaces and sharp edges, which can facilitate interlocking and forming stable clusters, this increased movement is likely due to these characteristics.\u003c/p\u003e \u003cp\u003eWith higher Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e with lower shear rate SV, the main shear region shifts more towards the centre of the rotational shear cell. At the lower SV, the kinetic energy is lower, and therefore, higher friction prevents particles from moving upwards, causing the shear region to move downwards. For this reason, the MS particles likely have their main shear region in layers L2 and L3, as the particle surfaces are composed of sub-particles, and their mechanical interactions increase shear strength.\u003c/p\u003e \u003cp\u003eWith higher shear rate SV and Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e, the main shear region, as indicated by the greatest velocity differences, shifts more towards the shear lid. For the highest \u0026micro;\u003csub\u003es\u003c/sub\u003e, the main shear region is located in layers L3 and L4.\u003c/p\u003e \u003cp\u003eBetween lower and higher shear rate SV, an opposite effect of increasing Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e can be observed. At the lower SV, the shear region with the higher \u0026micro;\u003csub\u003es\u003c/sub\u003e shifts towards the bottom of the shear cell, whereas at the higher SV, it moves towards the shear lid.\u003c/p\u003e \u003cp\u003eThe higher Average Particle Velocity AVXY values due to increased Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e were likely caused by the pulsed release of particle clusters, leading to peaks in the individual velocity components of the particles. With the higher \u0026micro;\u003csub\u003es\u003c/sub\u003e, more kinetic energy can accumulate. Once the accumulated kinetic energy overcomes the friction forces, particle clusters are suddenly released and move more quickly. This process causes spikes in the particle velocities, recorded as the increased AVXY values. The pulsed nature of the movement is due to particles being repeatedly trapped and released, leading to fluctuating velocities and thus pulsed movement.\u003c/p\u003e \u003cp\u003eFor spherical particles, the greatest differences in the Average Particle Velocity AVXY were predominantly found between layers L3 and L4. For cubic particles, this was not as clear-cut. For the MS particles, the main shear region was identified between layers L2 and L3 due to their shape. Non-spherical particle shapes can create an unexpected discontinuous behaviour, leading to different positions of the main shear region for cubic particles.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eFor the SP particles using the HM model, achieving higher final compression of the sample during the shear process was accomplished through using higher Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e values. These initial bonds, which had a certain effect in the static state, were eliminated during the shear process. For other particles using HM model, changes in compression could also be related to shape and the combination of Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e with kinematics influenced by the shear rate SV. During the shear process under load, the interaction bonds between particles changed due to rearrangement, leading to either higher or lower compression. In the LIN model, higher \u0026micro;\u003csub\u003es\u003c/sub\u003e values generally led to a reduction of the sample compression. Only for the SP particles at high SV resulted higher \u0026micro;\u003csub\u003es\u003c/sub\u003e values into reduced compression. In this case, the SP particles could not withstand the higher kinematic load combined with higher \u0026micro;\u003csub\u003es\u003c/sub\u003e. For cubic particles, all influences and trend changes were reinforced by their shape.\u003c/p\u003e \u003cp\u003eThe assumption of a relationship between the Preshear PS values and the Vertical Lid Position VLP mentioned in [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], that higher PS values correspond to the lower VLP values, was met for all cases of extreme PS values. The highest PS value for the SP particles for shear rate SV\u0026thinsp;=\u0026thinsp;4x corresponded to the lowest VLP compression. For the MS-26 particle, the highest PS value for the SV\u0026thinsp;=\u0026thinsp;4x was for the HM model with the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6, and in this setting, the VLP was generally among the lowest values. For the MS-21, the PS to the VLP relationship was more evident in the LIN model than in the HM model. The obtained PS trends were within the expected range of experimentally obtained values, but this was not entirely the case for the VLP. This confirms that it is necessary to verify other output parameters besides the PS.\u003c/p\u003e \u003cp\u003eThe MS particles had higher Coordination Number CN values, which also correlated with higher shear strength. This higher shear strength impacted the kinematic and movement behaviour of the particles during the shear process, particularly in identifying the main shear plane.\u003c/p\u003e \u003cp\u003eAssuming that higher Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e characterizes greater vertical particle throughput, it is likely that these changes in particle positions also increase the horizontal shear resistance of the tested sample. This effect may be due to the densification of the structure, increased inter-particle forces, greater material heterogeneity, and possible anisotropy resulting from the vertical movement of particles.\u003c/p\u003e \u003cp\u003eFor the SP particles, the Angles of Internal Friction AIF were between the angles of particle shifts ϕ\u003csub\u003eS\u003c/sub\u003e of layers L3 and L4. The main shear region for the SP particles was also identified between layers L3 and L4 based on the Average Particle Velocity AVXY values of these layers. For cubic particles, this was not as clear-cut, although the AIF and ϕ\u003csub\u003eS\u003c/sub\u003e results showed similar characteristics as the SP particles. For the MS particles, the main shear region was identified between layers L2 and L3 using the AVXY, corresponding to approximately half the height of the shear cell. The assumption that the AIF values would occur between the ϕ\u003csub\u003eS\u003c/sub\u003e values of layers L3 and L4 and that the shear region would be between L3 and L4 using AVXY was not met. For the MS particles, there was a larger step change between the ϕ\u003csub\u003eS\u003c/sub\u003e values of L2 and L3. This significant change indicated an increase in the ϕ\u003csub\u003eS\u003c/sub\u003e values, representing a greater ability for vertical particle movement. This effect was most characteristic of the non-spherical MS particles. The shear region extended more throughout the sample volume due to higher interlocking between particles. Rather than individual particles sliding past each other, clusters of particles were shearing together. The AIF values for the MS particles extended more into L3 layer compared to the SP particles. The occurrence of the AIF values more in layer L3 for the MS particles than between layers L3 and L4 suggested that the main shear region would likely shift more towards the lower layers of the shear cell.\u003c/p\u003e \u003cp\u003eWith the lower Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e values using the HM model, there was instability or critical particle movement behaviour, reflected in changes in the Average Particle Velocity AVXY values (Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e). The sudden release of interlocked particles can generate peak velocity values in a short time step, affecting the overall average AVXY value. The wavy surface of the MS-26 particles makes them more prone to this behaviour compared to the MS-21 particles.\u003c/p\u003e \u003cp\u003eHigher shear rate SV combined with higher Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e values generally resulted in higher slope values for layers L3-L4. The higher SV and \u0026micro;\u003csub\u003es\u003c/sub\u003e helped to better overcome the particle resistance, positioning the main shear region closer to the shear lid. Conversely, the lower SV did not allow the transfer of rotational moments through the particles up to the shear lid, causing the shear process to occur mainly in the lower layers of the shear cell. It appears that the higher SV values could be beneficial in cases where the tested sample is not completely homogeneous, as inhomogeneities could significantly affect the transfer of rotational moments through the layers of the measured sample. The higher SV promotes better particle movement throughout the sample volume over time, which can positively impact the steady flow in some cases. The higher SV can help overcome these inhomogeneities, leading to a more uniform distribution of mechanical properties and more accurate measurement of rotational moment transfer. This approach minimizes the impact of local inhomogeneities on the overall behaviour of the sample.\u003c/p\u003e"},{"header":"5 Conclusion","content":"\u003cp\u003eThe results of this study aim to support users of DEM simulations in calibrating shear tests. Some findings confirmed the need for an individualized approach for each examined property, while also clarifying potential dependencies and dominant parameters. The particles were intentionally made larger relative to the shear cell. This was partly due to the limitations of the 3D printing resolution and also to reduce computational time for repeated simulations.\u003c/p\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Preshear PS\u003c/h2\u003e \u003cp\u003eFor the SP particles, the Preshear PS values were generally on the lower end of the experimentally measured range. Increasing the shear rate SV resulted in a slight decrease in the PS values towards the end of the shear process. For spherical particles, higher Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e values in DEM simulations were needed compared to other particle shapes to achieve the expected Preshear values from experiments. This was due to the imperfectly smooth surface of the 3D-printed particles. The layering process of 3D printing had a greater impact on the surface of spherical particles than on cubic particles.\u003c/p\u003e \u003cp\u003eFor the MS particles, the Preshear PS values were generally on the higher end of the experimentally measured range. For the MS-26 particles, an increase in the shear rate SV significantly raised the PS value for the HM model with Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e 0.6. Conversely, for the MS-21 particles, the PS values decreased with an increase in the SV. The wavy surface texture of the MS-26 particles was much more influential than changes in the \u0026micro;\u003csub\u003es\u003c/sub\u003e values. Compared to spherical particles, lower \u0026micro;\u003csub\u003es\u003c/sub\u003e values were applied, yet the PS values remained higher.\u003c/p\u003e \u003cp\u003eRegarding the impact of the changing shear rate SV values on the Preshear PS values, the results were within acceptable ranges of experimental results. Thus, saving time in simulating the shear process by increasing the shear rate is feasible, but it requires an analysis of the fundamental deformation behaviour of the sample during the shear process, as emphasized in this study.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Vertical Lid Position VLP\u003c/h2\u003e \u003cp\u003eThe results clearly indicate that the position of the shear lid provides DEM users with an overview of the fundamental deformation behaviour during the shear process. For better control and improvement of DEM outputs, shear-induced stress should always be supported by this experiment. Various effects of changing the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e on the sample's deformation (compression) ability were observed. Generally, the strength of the particle bulk can be increased by raising the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e values. However, this strength is most effective in a static stress state and has its limits during the shear process. Therefore, an apparent static increase in strength by increasing Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e can reduce the overall shear strength, causing significant increases in compression. This effect was observed more frequently for the SP particles using the HM model compared to the LIN model. The static increase in strength due to friction and the resulting increased compression did not apply to the MS particles with a wavy surface. The surface shape had a more significant impact on strength and shear behaviour than changes in friction.\u003c/p\u003e \u003cp\u003eRegarding the change in the shear rate SV, the results were within acceptable experimental ranges. This confirms the need for a highly individualized approach for each model and combination of input values.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Coordination Number CN\u003c/h2\u003e \u003cp\u003eThe average Coordination Number CN values revealed a clear impact of increasing Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e on reducing the CN values. Higher \u0026micro;\u003csub\u003es\u003c/sub\u003e values decreased the interlocking and contact capabilities between particles. This reduction in the CN did not always affect the deformation ability of the sample. The smallest changes in the CN values caused by the change of the \u0026micro;\u003csub\u003es\u003c/sub\u003e were observed for the SP particles. Generally, the SP particles have the best ability to achieve the most compact arrangement. For other particle shapes, the impact of the \u0026micro;\u003csub\u003es\u003c/sub\u003e on reducing the CN was much more pronounced. Increasing the \u0026micro;\u003csub\u003es\u003c/sub\u003e values amplified the change in the CN for particles with a more significant influence of shape. Cubic particle shapes generally reduce the compactness of the arrangement within the volume, and this effect was even more pronounced for the MS-26 particles. For precise calibration of the LIN model, there is a future possibility to calibrate the typical Impact Velocity V [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] using the CN values.\u003c/p\u003e \u003cp\u003eThe results highlighted fundamental differences between particle models, considering the changes in kinematics due to increased shear rate SV. The observed changes in the Coordination Number CN values can somewhat support the understanding of processes during the shear test concerning particle arrangement compactness. For instance, the lower CN indicates a looser arrangement, which can lead to greater deformation or changes in the shear strength of the material. The influence of parameters and kinematics on the CN and material properties is complex and depends on the specific particle model and its application. A detailed analysis of data and models is necessary for a deeper understanding.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e5.4 Porosity\u003c/h2\u003e \u003cp\u003eFrom the experimental and DEM results, it was evident that porosity remained a stable parameter, not changing significantly across different models during the shear process. However, the porosity varied for different particle types, primarily determined by particle shape or surface texture. The results generally indicated that an increase in the Inter-Particle Friction \u0026micro;\u003csub\u003es\u003c/sub\u003e corresponded with a higher vertical lid position VLP. The lid's end position was always lower than its start position, with minor exceptions for the SP particles using the LIN model with lower shear rate SV. Changes in the SV did not significantly affect the start and end positions of the lid. Porosity and the position of the shear lid were influenced by the particle shape, size, and \u0026micro;\u003csub\u003es\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e5.5 Angel of particle shifts ϕ\u003csub\u003eS\u003c/sub\u003e and Average Particle Velocity AVXY\u003c/h2\u003e \u003cp\u003eAn analogy was discovered between the Angle of Internal Friction AIF and Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e concerning the main shear region, regardless of particle shape. For the SP particles, this was clear. Although the values from the shear test and the vertical position of the shear lid in simulations were within the range of experimentally measured values, questions remain about particle behaviour concerning their positional changes.\u003c/p\u003e \u003cp\u003eHigher Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e values may indicate a greater ability for vertical particle movement, understood as vertical particle flow, which reduces local strength and increases local flowability within the sample. Conversely, the Angle of Internal Friction AIF represents the force or stress conditions on particles, also expressed geometrically by an angle. From this perspective, the geometric representation of the AIF angle between L3 and L4 layers confirms the main shear region.\u003c/p\u003e \u003cp\u003eThe impact of the shear rate SV on the Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e and Angle of Internal Friction AIF values in simulations was generally minor. Considering the effect of particle shape on the AIF values, the MS particles showed slightly higher final AIF values then the SP particles. These differences were due to the wavy surface texture of the MS particles, composed of multiple particles.\u003c/p\u003e \u003cp\u003eFor the SP particles, the Angle of Internal Friction AIF values were between the Angle of Particle Shifts ϕ\u003csub\u003eS\u003c/sub\u003e values of layers L3 and L4. The main shear region for the SP particles was also identified between layers L3 and L4 based on the Average Particle Velocity AVXY values of these layers. For the MS particles, the main shear region was identified between layers L2 and L3 using AVXY, which corresponded to approximately half the height of the shear cell. The assumption that the AIF values would occur between the ϕ\u003csub\u003eS\u003c/sub\u003e values of layers L3 and L4 and that the shear region would be between L3 and L4 using AVXY was not met. Instead, the shear region extended more throughout the sample volume due to higher interlocking between particles. The occurrence of the AIF values in the MS particles more within layer L3 rather than between layers L3 and L4 indicated that the main shear region likely shifts to the lower layers of the shear cell.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003e \u003cb\u003eCOMPETING INTERESTS\u003c/b\u003e.\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFUNDING:\u003c/h2\u003e \u003cp\u003eThis paper was created as part of the project No. CZ.02.01.01/00/22_008/0004631 Materials and technologies for sustainable development within the Jan Amos Komensky Operational Program financed by the European Union and from the state budget of the Czech Republic, and project The European Just Transition Fund supported this work within the Operational Programme Just Transition under the aegis of the Ministry of the Environment of the Czech Republic, project CirkArena, number CZ.10.03.01/00/22_003/0000045.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualization, Rozbroj J., Hlosta J., Diviš J., Barletta D., Nečas J.; methodology, Diviš J., Hlosta J., and Rozbroj J.; formal analysis, Hlosta J., Rozbroj J., Pokorn\u0026aacute; K., and Žurovec D.; investigation, Hlosta J., Rozbroj J., Žurovec D., Poletto M., Nečas J., Zegzulka J.; data curation, Barletta D., Hlosta J., Diviš J. and Rozbroj J.; writing\u0026mdash;original draft preparation, Rozbroj J, Hlosta J., Diviš J., and Barletta D., ; writing\u0026mdash;review and editing, Poletto M., Žurovec D., Pokorn\u0026aacute; K., Nečas J., Zegzulka J.; visualization, Rozbroj J., and Hlosta J.; supervision, Poletto M., Nečas J., and Zegzulka J.; project administration, Hlosta J, Žurovec D., Pokorn\u0026aacute; K., Diviš J., Nečas J., Zegzulka J.; funding acquisition, Rozbroj J., Nečas J., and Zegzulka J.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eDATA AVAILABILITY: The data used in this study is available at: Rozbroj, J. (2024). Evaluation of DEM simulations measuring internal friction and particle movement (Verze 1) [Data set]. Zenodo. https://doi.org/10.5281/zenodo.13959330\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eCUNDALL, Peter, A. \u0026amp; STRACK, Otto, D. L. A discrete numerical model for granular assemblies. \u003cem\u003egeotechnique\u003c/em\u003e. \u003cb\u003e29\u003c/b\u003e (1), 47\u0026ndash;65 (1979).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKetterhagen, W. \u0026amp; Wassgren, C. A perspective on calibration and application of DEM models for simulation of industrial bulk powder processes. \u003cem\u003ePowder Technol.\u003c/em\u003e \u003cb\u003e402\u003c/b\u003e, 117301 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRichter, C., R\u0026ouml;\u0026szlig;ler, T., Kunze, G., Katterfeld, A. \u0026amp; Will, F. 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Calibration of the discrete element method and the effect of particle shape. \u003cem\u003ePowder Technol.\u003c/em\u003e \u003cb\u003e297\u003c/b\u003e, 50\u0026ndash;70 (2016).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Hertz-Mindlin, contact model, Linear Spring, cube particle, sphere particle, DEM calibration, Discrete Element Method","lastPublishedDoi":"10.21203/rs.3.rs-5298776/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5298776/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe study investigates the effect of particle shape representation with various contact models on the calibration procedure via shear test. Experimental shear tests were performed using a Schulze Ring Shear Tester RST-01 using spherical and cubic particles. Pre-shear stress and vertical lid position were used for calibration. Hertz-Mindlin and Linear Spring contact models behaviour trends for preshear, vertical lid position, coordination number, porosity and particle shift angle were observed. The changes of the shear zone for different input parameters are show. The findings confirmed the necessity to observe not only the shear force but also the compression behaviour of the particles in the shear test calibration. The results clearly indicate that the position of the shear lid provides DEM users with an overview of the fundamental deformation behaviour during the shear process. The results highlighted fundamental differences between particle models, considering the changes in kinematics due to increased shear rate. The research is intended to provide DEM modellers with general information on which parameters are affected by changing the input data for each contact model and particle shape. These insights can enhance calibration procedures in both industrial and academic settings, serving as a foundation for optimizing DEM models and improving their accuracy.\u003c/p\u003e","manuscriptTitle":"Influence of Irregular Particle Shape on Volumetric Behaviour of DEM Materials in Rotational Shear Testing","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-18 02:16:01","doi":"10.21203/rs.3.rs-5298776/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"beba9906-0ac5-4f18-931d-ff04ed26c790","owner":[],"postedDate":"November 18th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":40339452,"name":"Physical sciences/Mathematics and computing/Computational science"},{"id":40339453,"name":"Physical sciences/Engineering"},{"id":40339454,"name":"Physical sciences/Materials science/Theory and computation/Computational methods"}],"tags":[],"updatedAt":"2024-12-23T07:53:40+00:00","versionOfRecord":[],"versionCreatedAt":"2024-11-18 02:16:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5298776","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5298776","identity":"rs-5298776","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}