Discrete element analysis of powder spreading in binder jetting of raw Earth sediments

Powder morphology significantly affects spreading behavior. Mussatto et al. [16] showed that powders with high sphericity and smooth surfaces achieved superior flowability and packing in L-PBF, while elongated particles caused mechanical interlocking and heterogeneous layers. Zhang et al. [13] used DEM to examine BJT spreading of Al₂O₃ and found that traverse speed reduces powder bed density (PBD), with layer thickness being the dominant parameter. Nan et al. [17] and Haeri [18] reported similar findings, showing that roller-based systems outperform blades at low speeds but that certain blade designs can achieve competitive uniformity at high speeds.

Particle shape is a key factor: Zhang et al. [19] found that non-spherical PA6 particles formed arches and cavities, reducing PBD. Muñiz-Lerma et al. [20] confirmed that spherical, narrow-PSD powders pack more efficiently than irregular, broad-PSD powders.

DEM accuracy depends on realistic input parameters. Ge and Monroe [21] reported COR values of 0.88–0.98 for dry sands. Rorato et al. [22] linked rolling friction to particle sphericity, with angular Hostun sand exhibiting values near 0.75. Senetakis et al. [23] measured static friction values of 0.23–0.24 for quartz sands, while Brumund and Leonards [24] observed higher friction for angular sands against polished steel. Additional studies [25‐27] support rolling friction values of 0.45–0.65 for natural granular materials.

Segregation is another challenge in powder-bed AM. Percolation effects cause fine particles to settle while coarse ones remain elevated, reducing homogeneity [3, 17]. Adjusting traverse speed and layer thickness can mitigate—but not fully eliminate—segregation [10].

This manuscript extends an earlier feasibility study by the authors [28] by incorporating a full set of DEM simulations with reconstructed particle shapes, a more detailed evaluation of spreading parameters, and a strengthened validation section. These additions allow for benchmarking the behavior of unrefined silt against idealized spherical particles and to contextualize the chosen model inputs using recent literature. Overall, the current study clarifies how grain morphology and processing conditions influence powder bed formation when using raw earth sediments in binder jetting.

Using locally available, unrefined sediments supports sustainable AM and highlights the potential of BJT for construction in remote regions [30]. The targeted feedstock was an unrefined sandy silt from the Gypsum Hills in Kansas, consisting mainly of quartz, red shales, gypsum, and mica (Fig. 2).

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Particle morphology strongly influences flow behavior in powder-bed AM [31, 32], and BJT is especially sensitive because spreading quality directly affects packing density and binder penetration. While spherical powders exhibit favorable flowability [3], natural sediments contain grains ranging from rounded to angular [33]. Understanding their behavior is therefore essential for evaluating the feasibility of raw powders in BJT.

Particle size and shape were characterized using the Morphologi G3 system, which provides high-resolution 2D imaging [34, 35]. Measured diameters ranged from 2.18 to 270.32 μm (mean 15.34 μm), with D₁₀, D₅₀, and D₉₀ equal to 3.45, 9.37, and 34.70 μm, respectively (Fig. 3).

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Representative grain morphologies based on circularity, convexity, and elongation are shown in Fig. 4. These categories illustrate the range of shapes present in the sediment, from nearly spherical to highly angular or elongated particles.

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Although spherical particles simplify DEM contact detection, modeling natural sediments requires irregular geometries. The Altair EDEM multi-sphere method approximates each grain using overlapping spheres, enabling reasonable geometric fidelity at manageable computational cost [29].

To capture the diversity of the measured sediment, 25 particle shapes were selected after reviewing several thousand Morphologi G3 images. The selected shapes span the standard morphology classes—angular, sub-angular, sub-rounded, well-rounded, and elongated—following sedimentological schemes [33]. Each particle was manually reconstructed in EDEM based on its measured dimensions, preserving realistic size characteristics. Table 1 summarizes the morphology metrics for the 25 reconstructed shapes. The sandy silt is classified as a USCS sandy silt, consisting of a dominant silt fraction (< 63 μm) and a significant portion of coarser sand grains.

The selection of twenty-five representative particles was not arbitrary. The full Morphologi G3 dataset contained several thousand grains spanning wide ranges of circularity, convexity, and elongation. To ensure that the DEM particle library captured this measured variability, the dataset was first grouped into the five commonly used morphology classes—well-rounded, sub-rounded, sub-angular, angular, and elongated—following standard sedimentological classification schemes [33, 36]. Five representative grains were then selected from each class, providing proportional coverage of the observed morphology distribution while keeping the total number of multi-sphere reconstructions computationally manageable. Prior particle-scale DEM studies have shown that shape libraries of approximately 20–30 particles are sufficient to capture morphological variability in granular flow while maintaining computational feasibility [19, 37]. Accordingly, the chosen 25 shapes provide statistically meaningful morphological diversity for simulating the spreading behavior of the unrefined sediment.

As shown in Fig. 5, the 25 selected particles shown in Table 1 were divided into five shape categories: (a) angular, (b) sub-angular, (c) sub-rounded, (d) well-rounded, and (e) elongated. The far left of each column displays the 2D images of the selected particles, while the middle column highlights their basic structure, representing the major sphere or spheres forming the particle’s main body. The final column presents the multi-sphere reconstructed versions of the particles used in the EDEM software.

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A randomized PSD scaling range of 1.0–1.1 was applied to the reconstructed particles to maintain realistic size variability while avoiding extremely fine or overly large grains. Because only a subset of the sediment could be reconstructed, assigning the measured PSD directly to this library would bias the distribution toward the chosen shapes. The randomized PSD avoids this bias and better reflects the natural stochastic variation of the unrefined sediment, ensuring representative spreading behavior and packing patterns in DEM simulations.

All simulations incorporated a cylindrical counter-roller, powder bed, and build platform, as shown in Fig. 6, while Table 2 outlines the process parameters used for each EDEM simulation. These DEM parameters investigated are known to directly influence the physical behavior of the powder during spreading, governing adhesion, frictional resistance, and rolling constraints that ultimately affect packing efficiency, layer smoothness, and particle segregation. The gap height was set for all simulations, as the build platform lowers by the layer thickness after each layer deposition. The build platform and the powder bed region used in the simulations each measured 10 mm × 2 mm, corresponding to the active area involved in a single spreading pass. The counter-roller spreads powder by rotating counterclockwise at rotational speed ω while moving linearly at speed V_s, transferring particles to form a uniform layer on the platform. The selected values for V_s, ω, and layer thickness H align with typical ranges used in BJT experiments and commercial systems [3, 4]. Reported studies indicate that traverse speeds between 20 and 200 mm/s cover both high-density, low-speed spreading and faster processing conditions, while rotational speeds of 100–280 rpm ensure effective powder dispersion with minimal interparticle friction. Similarly, layer thicknesses ranging from 40 to 220 μm are commonly used in BJT to balance resolution, uniformity, and process efficiency [3]. Roller dimensions correspond to a scaled-down recoater, which is commonly used in DEM powder-spreading simulations to reduce computational size while keeping the local spreading behavior realistic [3, 4, 7, 13, 15, 17, 38]). As in most DEM powder-spreading studies, only a single-layer spreading event is simulated here, since the recoating mechanics repeat uniformly during each printing cycle and the first-layer behavior is representative of subsequent layers.

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The DEM parameters used in this study represent dry powder behavior because the analysis focuses solely on the spreading stage, which occurs prior to binder deposition. Binder-related effects such as droplet impact, capillary infiltration, and solvent evaporation therefore do not influence the input parameters used here. The material properties used in the simulations were gathered from various sources in the literature and are summarized in Table 3. The density of the sandy silt was set to 1650 kg/m³ [39]. The Young’s modulus and Poisson’s ratio were assigned values of 90.1 GPa [40] and 0.32 [41], respectively. For particle-particle interactions, the coefficient of restitution was set to 0.88 [21], the coefficient of static friction to 0.24 [23], and the coefficient of rolling friction to 0.75 [22]. For particle-wall interactions, the coefficient of restitution was set to 0.68 [26], the coefficient of static friction to 0.50 [24], and the coefficient of rolling friction to 0.65 [25].

The DEM simulations use standard assumptions for dry granular spreading. Particles are modeled as rigid multi-sphere clumps interacting through the Hertz–Mindlin contact law with JKR adhesion. No particle deformation, wear, or moisture-related cohesion is considered, and material properties remain constant during spreading. Controlled environments, and electrostatic effects are neglected. Roller and boundary geometries are treated as rigid with the frictional parameters listed in Table 3. Only a single spreading pass is simulated, as the recoating mechanics repeat uniformly for each layer.

The DEM simulation domain, periodic boundaries, and gravity force were all included in the simulation environment. The simulation domain, shown as a red box in Fig. 6, defines the space where particles reside and interact during processing. Only objects within this domain are used for calculations. The domain was 40 mm in length, 2 mm in width, and 5 mm in height. Acceleration due to gravity was set to 9.81 m/s² in the negative z direction (downwards). The counter-roller was modeled as a rigid geometry with artificially-reduced mechanical properties to improve computational efficiency. Although rollers in physical systems are typically made from stiff and dense materials, assigning such properties in EDEM simulations would lead to extremely small time steps and prolonged computation. Therefore, the roller was assigned lower density and stiffness values, a standard and validated simplification in DEM modeling [14, 29]. This reduced stiffness is a standard DEM simplification used in spreading simulations and does not affect the results because the roller behaves as a rigid boundary, not a deformable body. The utilized roller properties are summarized in Table 4.

Employed contact models for particle-particle and particle-geometry interactions are crucial, as they define how particles behave upon contact. This study employed the Hertz-Mindlin (no slip) model and assumed dry sand conditions. For two spherical bodies in contact, the normal contact force is expressed as [42, 43]:

where \(\:{E}^{*}\) and \(\:{R}^{*}\) are the equivalent Young’s modulus and radius, respectively, which are defined as [42, 43]:

where \(\:{E}_{\text{i}}\), \(\:{v}_{\text{i}}\), \(\:{R}_{\text{i}}\), and \(\:{E}_{\text{j}}\), \(\:{v}_{\text{j}}\), \(\:{R}_{\text{j}}\) are the Young’s modulus, Poisson’s ratio, and radius of each sphere in contact, respectively. In addition, the normal damping force is defined as [42, 43]:

where\(\:{S}_{\text{N}}\) is the normal stiffness, \(\:{v}_{\text{N}}^{\text{r}\text{e}\text{l}}\) is the normal component of the relative velocity, and \(\:{m}^{*}\) is the equivalent mass. The damping coefficient is given by \(\:\beta\:=\:\) \(\:\frac{\text{ln}e}{\sqrt{{\text{l}\text{n}}^{2}e+\:{\pi\:}^{2}}}\), where \(\:e\) is the coefficient of restitution. The normal stiffness \(\:{S}_{N}\) and equivalent mass \(\:{m}^{*}\)are found using Eqs. (7)-(8), respectively:

The tangential force depends on the tangential overlap \(\:{\delta\:}_{\text{T}}\) and the tangential stiffness \(\:{S}_{\text{T}}\):

where \(\:{G}^{*}\) is the equivalent shear modulus, which is expressed as:

Finally, tangential damping is defined as [42, 43]:

The tangential force is limited by Coulomb friction \(\:{\mu\:}_{\text{S}}{F}_{\text{N}}\), where \(\:{\mu\:}_{\text{s}}\) is the static friction coefficient [42, 43].

In BJT, adequate layer spreading results in a dense, uniform layer with consistent PSD and minimal void spaces [17]. The amount of powder supplied for spreading directly affects the green density of printed objects [44]. To ensure optimal binding, the PBD of the dispensed layer is thoroughly assessed by examining multiple locations across the powder bed to evaluate density uniformity [8]. For the current study, the PBD of each grid, \(\varnothing_i\), was calculated by measuring the material density within defined enclosures, quantifying the amount of material per unit volume, typically expressed as [45]:

where \(\:{m}_{\text{i}}\) is the particle mass of grid i, \(\:\rho\:\) is the sand density, and \(\:{V}_{\text{i}}\) is the volume of grid i. Values for \(\:{m}_{\text{i}}\) were directly pulled from the EDEM simulation results. The overall average PBD was determined by dividing the sum of the PBD for each grid by the total number of grids (N):

To quantify segregation, the fraction standard deviation (FSD) is used, with a low FSD indicating a more homogeneous PSD. The formula for calculating the standard deviation of the PBD across the spread layer can be found in [10, 17].

where \(\overline\varnothing\) is the average PBD.

To apply Eqs. (14)–(15), the powder bed was divided into forty equally-sized grids, with ten stretching along the length and four along the width of the substrate. The thickness of the grids corresponds to the layers thickness, which is along the z axis.

To assess the accuracy of the DEM approach, a validation study was embarked using the parameters and results from Zhang et al. [13]. This comparison served to validate not only the simulation setup but also the data processing method used in this study to calculate PBD. In Zhang et al.’s study, the spreading behavior of Al₂O₃ ceramic powder was simulated using DEM to evaluate the effects of roller traverse speed Vs, roller’s rotational speed ω, roller’s diameter D, and powder layer thickness H, on PBD. Their material system used Al₂O₃ particles with particle size distribution values of D₁₀, D₅₀, and D₉₀ were reported as 24, 48, and 72 μm, respectively, with a particle density of 3820 kg/m³. In the present work, Zhang et al.’s conditions were replicated using the same Hertz–Mindlin with JKR contact model and material properties. However, a distinct method was used to calculate PBD: here, the powder bed was divided into grids to compute local and average PBD values, rather than adopting Zhang et al.’s original approach. Despite this difference, the re-simulated results showed close agreement with Zhang et al.’s findings, as shown in Fig. 7.

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The relative error between the re-simulated data and Zhang et al.’s results was calculated:

The computed percent relative errors are summarized in Table 5. The mean relative error (MRE) was found to be 5.6, confirming that the implemented DEM model and grid-based PBD evaluation method accurately capture powder spreading behavior.

To further assess the robustness of the DEM framework under a different process condition, an additional benchmark validation was performed using the blade-velocity analysis reported by Si et al. [38]. Their study investigated the relationship between packing density and blade velocity for PA6 powder across spreading speeds of 5–100 mm/s using a JKR-based DEM model calibrated through angle-of-repose experiments. The present model was used to replicate these conditions, and the resulting packing densities were compared directly with the published values. The simulated results reproduced the same decreasing trend with increasing blade velocity and showed reasonable quantitative agreement, with a mean relative error of approximately 10.8% and deviations of below 2% in the high-velocity regime (50–100 mm/s). This second benchmark, together with the Zhang et al. comparison, demonstrates that the implemented DEM framework accurately reproduces known spreading behavior across multiple independent studies and varying process parameters (Table 6).

Figure 8 illustrates the dynamic flow behavior of the sandy silt particles as the roller moves from left to right across the powder bed. Particles are color-coded by size: yellow for small, blue for medium, and red for large, helping visualize the particle size distribution (PSD).

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A distinct avalanching effect is seen at the roller’s leading edge, where particles climb the roller surface and cascade down the backside. This cascading motion continuously facilitates uniform layer formation/spreading.

Simultaneously, percolation is observed, where smaller particles sift downward through voids between larger ones, concentrating at the base of the layer. Coarser particles accumulate near the surface, creating vertical size segregation. This behavior is common in wide PSD systems and can influence part density and uniformity. The observed angle of repose also reflects powder flowability, which in turn affects layer formation.

These results confirm that gravity-driven percolation—enhanced by the avalanching flow—leads to segregation during spreading, with finer particles settling and coarser ones rising, similar to the “Brazil Nut Effect” [3, 46‐49].

As shown in Fig. 9, finer particles tend to settle near the start of the layer (leading edge), while coarser grains accumulate toward the end (trailing edge). This gradient mirrors the spreading direction and reflects combined effects of gravity and roller momentum. The leading edge appears smoother and denser due to fine particle fill-in, while the trailing edge is rougher with more voids. These variations can affect powder bed density and binder infiltration, potentially compromising part strength and dimensional accuracy [3, 16, 46]. This depth-dependent pattern is characteristic of percolation-driven segregation, where more rounded grains migrate downward under disturbances while angular grains remain closer to the surface.

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Layer thickness affects packing density and binder saturation, influencing part strength and surface quality [50]. As shown in Fig. 10a, FSD reaches its lowest point at 120 μm, indicating maximum uniformity. PBD (Fig. 10b) increases significantly up to 120 μm, then rises only marginally, remaining between 0.48 and 0.51 through 220 μm. Thus, 120 μm represents a practical optimum, balancing high uniformity with near-maximal density. In thinner layers, particle jamming reduces PBD, while irregular shapes cause interlocking and voids that disrupt consistent spreading [51, 52].

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Traverse speed ranged from 20 to 200 mm/s in 20 mm/s increments. As shown in Fig. 11, PBD decreases and FSD increases with higher speeds. Optimal spreading occurs below 40 mm/s, consistent with prior studies [45]. PBD peaks just below 0.5 at 20 mm/s and drops to ~ 0.3 at 200 mm/s. FSD is lowest (~ 0.08) at 20 mm/s and highest at the maximum speed. These trends confirm traverse speed as a critical parameter affecting both density and uniformity during layer deposition. These results highlight that traverse speed governs the time available for particles to rearrange under gravity and roller-induced shear. At higher speeds, insufficient relaxation time prevents fine–coarse percolation from stabilizing, leading to stratified layers and larger voids. This mechanism explains the strong deterioration in both PBD and FSD at V_s > 40 mm/s.

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As shown in Fig. 12, roller diameter had minimal influence on PBD, which varied narrowly between 0.45 and 0.49. FSD ranged from 0.07 to 0.10, showing a slightly greater sensitivity. Among tested cases, the 4 mm roller yielded both the highest PBD and highest FSD. According to Zhang et al. [13], diameters above 6 mm can enhance PBD due to increased compression and particle rearrangement. While all examined diameters produced comparable PBD, FSD exhibited greater variability, suggesting the 2 mm roller may be preferable when minimizing segregation. Overall, roller diameter is less critical than other parameters such as layer thickness or traverse speed.

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As shown in Fig. 13, rotational speed has minimal impact on PBD and FSD. PBD is stable with a slight drop above 220 rpm. FSD fluctuates between 0.060 and 0.100 without a clear trend. A speed of 140 rpm yields low FSD and high PBD. These FSD variations are likely due to particle circulation from roller-induced shear forces. A comparison between the unrefined sediment and an idealized spherical powder is presented in Sect. 3.6, where the influence of particle shape on flowability and packing response is analyzed.

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To establish a benchmark for evaluating the challenges associated with spreading non-spherical particles, it is crucial to compare the PBD of the investigated sample with that of a sample composed solely of spherical particles with a narrow PSD. This comparison also serves to validate the results, ensuring alignment with existing findings in literature, where spherical particles are known to exhibit superior spreadability due to their uniform geometry and lower frictional resistance. Since the layer thickness and traverse speed have been identified as the most influential factors on both PBD and FSD, with 20mm/s being the optimum traverse speed, the focus is placed on comparing results at varying layer thicknesses while maintaining the optimum traverse speed of 20 mm/s.

According to the comparison data in Fig. 14, represented by the orange dotted line for raw earth sample (non-spherical) and the blue dotted line for spherical particles, samples with spherical particles achieved a higher PBD and significantly lower FSD, indicating improved layer uniformity. Specifically, the PBD for spherical particles reached 0.59 at layer thicknesses above 120 μm, while non-spherical particles had a peak PBD of 0.51 at a layer thickness of 220 μm. The PBD for spherical particles gradually increased from 60 to 120 μm, then remained constant from 120 to 220 μm. In contrast, the PBD for non-spherical particles rose sharply from 40 to 120 μm before stabilizing up to 220 μm.

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The FSD was notably lower for spherical particles compared to non-spherical particles, which exhibited a broader PSD. The FSD for spherical particles decreased consistently as layer thickness increased, remaining significantly lower than the FSD of non-spherical particles across all layer thicknesses. Non-spherical particles displayed a variable FSD, fluctuating considerably with different layer thicknesses. These findings demonstrate that spherical particles, with a narrower PSD, result in more consistent and uniform layers, underscoring their advantage in achieving higher packing density and layer uniformity compared to non-spherical particles with a broader PSD. For non-spherical particles, small changes in layer thickness alter how irregular grains interlock, rotate, and settle, which leads to the observed fluctuations in FSD. This sensitivity does not occur for spherical particles, whose geometry produces more consistent flow behavior across different layer heights.