Settling velocity of sediment grains, Part 1: Natural sediment particles are not ellipsoids
DOI:
https://doi.org/10.57035/journals/sdk.2026.e41.1937Keywords:
settling velocity, grain size, particle shape, Reynolds number, drag coefficientAbstract
Particle settling velocity has wide application in sedimentology and engineering. The ability to predict settling velocity based on fluid and particle properties is essential for realistic sediment transport models. It is common practice to describe the size and shape of natural sediment grains with an ellipsoidal model. This paper tests the validity of the ellipsoidal model for predicting particle settling velocity for siliciclastic and carbonate sediments. The parameters associated with this model are the ellipsoidal nominal diameter (Dn = (DsDiDl)1/3) and Corey shape factor (CSF=Ds/(DiDl)1/2), calculated from the short (Ds), intermediate (Di), and long (Dl) axial diameters. An equation for the drag coefficient (i.e., nondimensional friction) expressed as a function of particle Reynolds number (i.e., nondimensional particle size) and Corey shape factor (i.e., ellipsoidity) was reconstructed for siliciclastic and carbonate grains separately, based on the largest available compilations of existing datasets (639 siliciclastic and 3 666 carbonate grains). The ellipsoidal approximation of grain size yields significant errors in settling velocity predictions, yet the equation is more accurate for siliciclastic particles (mean absolute error = 14 %) than for carbonate grains (mean absolute error = 21 %). This difference is explained by the enlarged irregularity of particles in carbonate compared to siliciclastic sediments, due to enhanced angularity and surface roughness of skeletal remains. Thus, the ellipsoidal model, using the nominal diameter and Corey shape factor, is not suitable for describing natural sediments or predicting their settling velocity, despite its widespread use. A companion paper (Part 2, Slootman et al., 2026) investigates alternative particle size and shape descriptors.
Downloads
References
Alcérreca, J. C., Silva, R., & Mendoza, E. (2013). Simple settling velocity formula for calcareous sand. Journal of Hydraulic Research, 51(2), 215–219. https://doi.org/10.1080/00221686.2012.753645 DOI: https://doi.org/10.1080/00221686.2012.753645
Alger, G. R. (1964). Terminal fall velocity of particles of irregular shapes as affected by surface area [Doctoral dissertation, Colorado State University]. https://doi.org/10.25675/3.025083
Allen, J. R. L. (Ed.). (1982). Sedimentary Structures—Their Character and Physical Basis Volume I: Developments in Sedimentology: 30A. Elsevier.
Allen, J. R. L. (1984). Experiments on the settling, overturning and entrainment of bivalve shells and related models. Sedimentology, 31(2), 227–250. https://doi.org/10.1111/j.1365-3091.1984.tb01961.x DOI: https://doi.org/10.1111/j.1365-3091.1984.tb01961.x
Baba, J., & Komar, P. D. (1981). Settling Velocities of Irregular Grains at Low Reynolds Numbers. Journal of Sedimentary Research, 51(1), 121–128. https://doi.org/10.1306/212f7c25-2b24-11d7-8648000102c1865d DOI: https://doi.org/10.1306/212F7C25-2B24-11D7-8648000102C1865D
Bagheri, G. H., & Bonadonna, C. (2016). On the drag of freely falling non-spherical particles. Powder Technology, 301, 526–544. https://doi.org/10.1016/j.powtec.2016.06.015 DOI: https://doi.org/10.1016/j.powtec.2016.06.015
Barrett, P. J. (1980). The shape of rock particle, a critical review. Sedimentology, 27, 291–303. https://doi.org/10.1111/j.1365-3091.1980.tb01179.x DOI: https://doi.org/10.1111/j.1365-3091.1980.tb01179.x
Blott, S. J., & Pye, K. (2008). Particle shape: A review and new methods of characterization and classification. Sedimentology, 55(1), 31–63. https://doi.org/10.1111/j.1365-3091.2007.00892.x DOI: https://doi.org/10.1111/j.1365-3091.2007.00892.x
Braithwaite, C. J. R. (1973). Settling behaviour related to sieve analysis of skeletal sands. Sedimentology, 20(2), 251–262. https://doi.org/10.1111/j.1365-3091.1973.tb02048.x DOI: https://doi.org/10.1111/j.1365-3091.1973.tb02048.x
Briggs, L. I., McCulloch, D. S., & Moser, F. (1962). The hydraulic shape of sand particles. Journal of Sedimentary Research, 32(4), 645–656. https://doi.org/10.1306/74D70D44-2B21-11D7-8648000102C1865D DOI: https://doi.org/10.1306/74D70D44-2B21-11D7-8648000102C1865D
Camenen, B., Bayram, A., & Larson, M. (2006). Equivalent Roughness Height for Plane Bed under Steady Flow. Journal of Hydraulic Engineering, 132(11), 1146–1158. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:11(1146) DOI: https://doi.org/10.1061/(ASCE)0733-9429(2006)132:11(1146)
Caromel, A. G. M., Schmidt, D. N., Phillips, J. C., & Rayfield, E. J. (2014). Hydrodynamic constraints on the evolution and ecology of planktic foraminifera. Marine Micropaleontology, 106, 69–78. https://doi.org/10.1016/j.marmicro.2014.01.002 DOI: https://doi.org/10.1016/j.marmicro.2014.01.002
Cassel, M., Lavé, J., Recking, A., Malavoi, J. R., & Piégay, H. (2021). Bedload transport in rivers, size matters but so does shape. Scientific Reports, 11(1), 1–11. https://doi.org/10.1038/s41598-020-79930-7 DOI: https://doi.org/10.1038/s41598-020-79930-7
Cheng, K. Y., Wang, P. K., & Wang, C. K. (2014). A numerical study on the ventilation coefficients of falling hailstones. Journal of the Atmospheric Sciences, 71(7), 2625–2634. https://doi.org/10.1175/JAS-D-13-0229.1 DOI: https://doi.org/10.1175/JAS-D-13-0229.1
Clift, R., & Gauvin, W. H. (1971). Motion of entrained particles in gas streams. Canadian Journal of Chemical Engineering, 49(4), 439–448. https://doi.org/10.1002/cjce.5450490403 DOI: https://doi.org/10.1002/cjce.5450490403
Clift, R., Grace, J. R., & Weber, M. E. (1978). Bubbles, drops, and particles. Academic Press.
Collins, M. B., & Rigler, J. K. (1982). The use of settling velocity in defining the initiation of motion of heavy mineral grains, under unidirectional flow. Sedimentology, 29(3), 419–426. https://doi.org/10.1111/j.1365-3091.1982.tb01804.x DOI: https://doi.org/10.1111/j.1365-3091.1982.tb01804.x
Corey, A. T. (1949). Influence of shape on the fall velocity of sand grains [Master thesis, Colorado Agricultural and Mechanical College]. https://doi.org/10.25675/3.025499
De Kruijf, M., Slootman, A., De Boer, R. A., & Reijmer, J. J. G. (2021). On the settling of marine carbonate grains: Review and challenges. Earth-Science Reviews, (January), 103532–103532. https://doi.org/10.1016/j.earscirev.2021.103532 DOI: https://doi.org/10.1016/j.earscirev.2021.103532
Dey, S., & Ali, S. Z. (2019). Bed sediment entrainment by streamflow: State of the science. Sedimentology, 66(5), 1449–1485. https://doi.org/10.1111/sed.12566 DOI: https://doi.org/10.1111/sed.12566
Dey, S., Ali, S. Z., & Padhi, E. (2019). Terminal fall velocity: The legacy of Stokes from the perspective of fluvial hydraulics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2228), 20190277. https://doi.org/10.1098/rspa.2019.0277 DOI: https://doi.org/10.1098/rspa.2019.0277
Dietrich, W. E. (1982). Settling velocity of natural particles. Water Resources Research, 18(6), 1615–1626. https://doi.org/10.1029/WR018i006p01615 DOI: https://doi.org/10.1029/WR018i006p01615
Egiazaroff, I. V. (1965). Calculation of Nonuniform Sediment Concentrations. Journal of the Hydraulics Division, 91(4), 225–247. https://doi.org/10.1061/JYCEAJ.0001277 DOI: https://doi.org/10.1061/JYCEAJ.0001277
Fan, M., Su, D., & Yang, L. (2022). Development of a benchmark for drag correlations of nonspherical particles based on settling experiments of super-ellipsoidal particles. Powder Technology, 409. https://doi.org/10.1016/j.powtec.2022.117811 DOI: https://doi.org/10.1016/j.powtec.2022.117811
Ferguson, R. I., & Church, M. (2004). A simple universal equasion for grain settling velosity. Journal of Sedimentary Research, 74(6), 933–937. https://doi.org/10.1306/051204740933 DOI: https://doi.org/10.1306/051204740933
Fornberg, B. (1988). Steady viscous flow past a sphere at high Reynolds numbers. Journal of Fluid Mechanics, 190, 471–489. https://doi.org/10.1017/S0022112088001417 DOI: https://doi.org/10.1017/S0022112088001417
Francalanci, S., Paris, E., & Solari, L. (2021). On the prediction of settling velocity for plastic particles of different shapes. Environmental Pollution, 290(August), 118068–118068. https://doi.org/10.1016/j.envpol.2021.118068 DOI: https://doi.org/10.1016/j.envpol.2021.118068
Ganti, V., Lamb, M. P., & McElroy, B. (2014). Quantitative bounds on morphodynamics and implications for reading the sedimentary record. Nature Communications, 5, 1–7. https://doi.org/10.1038/ncomms4298 DOI: https://doi.org/10.1038/ncomms4298
Ghoddousi, P., Shirzadi Javid, A. A., & Sobhani, J. (2014). Effects of particle packing density on the stability and rheology of self-consolidating concrete containing mineral admixtures. Construction and Building Materials, 53, 102–109. https://doi.org/10.1016/j.conbuildmat.2013.11.076 DOI: https://doi.org/10.1016/j.conbuildmat.2013.11.076
Goossens, D. (1987a). A drag coefficient equation for natural, irregularly shaped particles. Catena, 14(1–3), 73–99. https://doi.org/10.1016/S0341-8162(87)80007-3 DOI: https://doi.org/10.1016/S0341-8162(87)80007-3
Goossens, D. (1987b). Interference phenomena between particle flattening and particle rounding in free vertical sedimentation processes. Sedimentology, 34(1), 155–167. https://doi.org/10.1111/j.1365-3091.1987.tb00567.x DOI: https://doi.org/10.1111/j.1365-3091.1987.tb00567.x
Griffiths, J. C. (1967). Scientific Method in Analysis of Sediments. McGraw-Hill.
Hjulström, F. (1935). Studies in the morphological activity of rivers as illustrated by the river Fyris. Bulletin Geological Institute Uppsala, XXV, 221–527.
Joshi, S., Duffy, G. P., & Brown, C. (2014). Settling velocity and grain shape of maërl biogenic gravel. Journal of Sedimentary Research, 84(8), 718–727. https://doi.org/10.2110/jsr.2014.51 DOI: https://doi.org/10.2110/jsr.2014.51
Komar, P. D. (1980). Settling velocities of circular cylinders at low Reynolds numbers. Journal of Geology, 88(3), 327–336. https://doi.org/10.1086/628510 DOI: https://doi.org/10.1086/628510
Komar, P. D., & Reimers, C. E. (1978). Grain Shape Effects on Settling Rates. Journal of Geology, 86(2), 193–209. https://doi.org/10.1086/649674 DOI: https://doi.org/10.1086/649674
Krumbein, W. C. (1938). Size Frequency Distributions of Sediments and the Normal Phi Curve. Journal of Sedimentary Research, 8. https://doi.org/10.1306/D4269008-2B26-11D7-8648000102C1865D DOI: https://doi.org/10.1306/D4269008-2B26-11D7-8648000102C1865D
Krumbein, W. C. (1941). The Effects of Abrasion on the Size, Shape and Roundness of Rock Fragments. Journal of Geology, 49(5), 482–520. https://doi.org/10.1086/624985 DOI: https://doi.org/10.1086/624985
Lamb, M. P., McElroy, B., Kopriva, B., Shaw, J., & Mohrig, D. (2010). Linking river-flood dynamics to hyperpycnal-plume deposits: Experiments, theory, and geological implications. Bulletin of the Geological Society of America, 122(9–10), 1389–1400. https://doi.org/10.1130/B30125.1 DOI: https://doi.org/10.1130/B30125.1
Le Roux, J. P. (2005). Grains in motion: A review. Sedimentary Geology, 178(3–4), 285–313. https://doi.org/10.1016/j.sedgeo.2005.05.009 DOI: https://doi.org/10.1016/j.sedgeo.2005.05.009
Li, Y., Yu, Q., Gao, S., & Flemming, B. W. (2020). Settling velocity and drag coefficient of platy shell fragments. Sedimentology, 67(4), 2095–2110. https://doi.org/10.1111/sed.12696 DOI: https://doi.org/10.1111/sed.12696
Maiklem, W. R. (1968). Some Hydraulic Properties of Bioclastic Carbonate Grains. Sedimentology, 10(2), 101–109. https://doi.org/10.1111/j.1365-3091.1968.tb01102.x DOI: https://doi.org/10.1111/j.1365-3091.1968.tb01102.x
Mao, L., Li, J., Shimozono, T., & Tajima, Y. (2023). Impacts of Particle Shape, Skeletal Porosity and Density on the Settling Velocity of Gravel‐Size Coral Debris. Journal of Geophysical Research: Earth Surface, 128(5), e2022JF006996. https://doi.org/10.1029/2022JF006996 DOI: https://doi.org/10.1029/2022JF006996
Martin, D., & Nokes, R. (1988). Crystal settling in a vigorously convecting magma chamber. Nature, 332(7), 534–536. https://doi.org/10.1038/332534a0 DOI: https://doi.org/10.1038/332534a0
McKay, G., Murphy, W. R., & Jodieri-Dabbaghzadeh, S. (1989). Settling and Fluidisation Characteristics of Carrot Particles in Water. Irish Journal of Food Science and Technology, 13(1), 51–69.
Middleton, G. V., & Southard, J. B. (Eds.). (1984). Mechanics of Sediment Movement: SEPM Short Course Notes: 3. SEPM Society for Sedimentary Geology. https://doi.org/10.2110/scn.84.03 DOI: https://doi.org/10.2110/scn.84.03
Miedema, S. A. (2010). Constructing the shields curve, a new theoretical approach and its applications. In J. Dobson (Ed.), Proceedings of the 19th world dredging congress (pp. 732–750). Chida. https://www.researchgate.net/publication/228750218
Mulder, T., & Alexander, J. (2001). The physical character of subaqueous sedimentary density flows and their deposits. Sedimentology, 48(2), 269–299. https://doi.org/10.1046/j.1365-3091.2001.00360.x DOI: https://doi.org/10.1046/j.1365-3091.2001.00360.x
Musso, M. S., Slootman, A., Wood, L. J., & Jobe, Z. R. (2025). Stalked crinoids: From skeleton to sediment. Journal of Sedimentary Research, 95(6), 1056–1062. https://doi.org/10.2110/jsr.2025.099 DOI: https://doi.org/10.2110/jsr.2025.099
Olivera, A. M., & Wood, W. L. (1997). Hydrodynamics of bivalve shell entrainment and transport. Journal of Sedimentary Research, 67(3), 514–526. https://doi.org/10.1306/D42685B8-2B26-11D7-8648000102C1865D DOI: https://doi.org/10.1306/D42685B8-2B26-11D7-8648000102C1865D
Polorigni, C. L., Ikumi, D. S., & Ekama, G. A. (2021). Primary sedimentation modelling with characterized setting velocity groups. Water Research, 189, 116621. https://doi.org/10.1016/j.watres.2020.116621 DOI: https://doi.org/10.1016/j.watres.2020.116621
Poulidis, A. P., Biass, S., Bagheri, G., Takemi, T., & Iguchi, M. (2021). Atmospheric vertical velocity—A crucial component in understanding proximal deposition of volcanic ash. Earth and Planetary Science Letters, 566. https://doi.org/10.1016/j.epsl.2021.116980 DOI: https://doi.org/10.1016/j.epsl.2021.116980
Powers, M. C. (1953). A new roundness scale for sedimentary particles. Journal of Sedimentary Research, 23(2), 117–119. https://doi.org/10.1306/d4269567-2b26-11d7-8648000102c1865d DOI: https://doi.org/10.1306/D4269567-2B26-11D7-8648000102C1865D
Reijmer, J. J. G. (2021). Marine carbonate factories: Review and update. Sedimentology, 68(5), 1729–1796. https://doi.org/10.1111/sed.12878 DOI: https://doi.org/10.1111/sed.12878
Riazi, A., & Türker, U. (2019). The drag coefficient and settling velocity of natural sediment particles. Computational Particle Mechanics, 6(3), 427–437. https://doi.org/10.1007/s40571-019-00223-6 DOI: https://doi.org/10.1007/s40571-019-00223-6
Romanovskii, V. V. (1972). Experimental investigation of settling velocity of sediments. Gosudarstvennyy Gidrologicheskiy Institut, 191, 111–136.
Rouse, H. (1949). Elementary Mechanics of Fluids. Wiley.
Schlager, W. (2003). Benthic carbonate factories of the Phanerozoic. International Journal of Earth Sciences, 92(4), 445–464. https://doi.org/10.1007/s00531-003-0327-x DOI: https://doi.org/10.1007/s00531-003-0327-x
Schulz, E. F. (1954). Effect of shape on the fall velocity of sand particles [Master thesis]. Colorado Agricultural and Mechanical College.
Schulz, E. F., Wilde, R. H., & Albertson, M. L. (1954). Influence of shape on the fall velocity of sedimentary particles (MRD Sediment Series No. 5). Colorado Agricultural and Mechanical College & The Missouri River Division Corps of Engineers, U.S. Army. Mountain Scholar. https://hdl.handle.net/10217/184172
Slootman, A., de Kruijf, M., Glatz, G., Eggenhuisen, J. T., Jobe, Z. R., & Reijmer, J. J. G. (2026). Settling velocity of sediment grains, Part 2: Volume/Area ratio as descriptor of particle size and shape in sediment hydrodynamics. Sedimentologika, 4(1). https://doi.org/10.57035/journals/sdk.2026.e41.2307 DOI: https://doi.org/10.57035/journals/sdk.2026.e41.2307
Slootman, A., de Kruijf, M., Glatz, G., Eggenhuisen, J. T., Zühlke, R., & Reijmer, J. J. G. (2023). Shape-dependent settling velocity of skeletal carbonate grains: Implications for calciturbidites. Sedimentology, 70(6), 1683–1722. https://doi.org/10.1111/sed.13103 DOI: https://doi.org/10.1111/sed.13103
Smith, D. A., & Cheung, K. F. (2003). Settling Characteristics of Calcareous Sand. Journal of Hydraulic Engineering, 129(6), 479–483. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:6(479) DOI: https://doi.org/10.1061/(ASCE)0733-9429(2003)129:6(479)
Southard, J. (Ed.). (2006). Course Number 12.090: Introduction to Fluid Motions, Sediment Transport, and Current-Generated Sedimentary Structures. Massachusetts Institute of Technology. OpenCourseWare. https://ocw.mit.edu/courses/12-090-introduction-to-fluid-motions-sediment-transport-and-current-generated-sedimentary-structures-fall-2006/
Stokes, G. G. (1850). On the Effect of the Internal Friction of Fluids on the Motion of Pendulums. Transactions of the Cambridge Philosophical Society, IX(II). https://ia600305.us.archive.org/20/items/b22464074/b22464074.pdf
Stringham, G. E., Simons, D. B., & Guy, H. P. (1969). The behavior of large particles falling in quiescent liquids (Professional Paper No. 562C). United States Geological Survey. USGS Publications Warehouse. https://doi.org/10.3133/pp562C DOI: https://doi.org/10.3133/pp562C
Swamee, P. K., & Ojha, C. S. P. (1991). Drag Coefficient and Fall Velocity of nonspherical particles. Journal of Hydraulic Engineering, 117(5), 661–667. https://doi.org/10.1061/(ASCE)0733-9429(1991)117:5(660) DOI: https://doi.org/10.1061/(ASCE)0733-9429(1991)117:5(660)
Vaz, M. F., & Fortes, M. A. (1988). Grain size distribution: The lognormal and the gamma distribution functions. Scripta Metallurgica, 22(1), 35–40. https://doi.org/10.1016/S0036-9748(88)80302-8 DOI: https://doi.org/10.1016/S0036-9748(88)80302-8
Wadell, H. (1932). Volume, Shape, and Roundness of Rock Particles. Journal of Geology, 40(5), 443–451. https://doi.org/10.1086/623964 DOI: https://doi.org/10.1086/623964
Wadell, H. (1934). Some New Sedimentation Formulas. Physics, 5(10), 281–291. https://doi.org/10.1063/1.1745211 DOI: https://doi.org/10.1063/1.1745211
Walsh, D. E., & Rao, P. D. (1988). A study of factors suspected of influencing the settling velocity of fine gold particles (Industry Research Laboratory Report No. 76; p. 43). University of Alaska Mineral Industry Research Laboratory. http://hdl.handle.net/11122/1133
Wang, Y., Zhou, L., Wu, Y., & Yang, Q. (2018). New simple correlation formula for the drag coefficient of calcareous sand particles of highly irregular shape. Powder Technology, 326, 379–392. https://doi.org/10.1016/j.powtec.2017.12.004 DOI: https://doi.org/10.1016/j.powtec.2017.12.004
Wentworth, C. K. (1922). A Scale of Grade and Class Terms for Clastic Sediments. Journal of Geology, 30(5), 377–392. https://doi.org/10.1086/622910 DOI: https://doi.org/10.1086/622910
Wilde, R. H. (1952). Effects of shape on the fall-velocity of gravel-sized particles [Master thesis, Colorado Agricultural and Mechanical College]. https://hdl.handle.net/10217/195976
Wu, W., & Wang, S. S. Y. (2006). Formulas for Sediment Porosity and Settling Velocity. Journal of Hydraulic Engineering, 132(8), 858–862. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:8(858) DOI: https://doi.org/10.1061/(ASCE)0733-9429(2006)132:8(858)
Yordanova, E. K., & Hohenegger, J. (2007). Studies on settling, traction and entrainment of larger benthic foraminiferal tests: Implications for accumulation in shallow marine sediments. Sedimentology, 54(6), 1273–1306. https://doi.org/10.1111/j.1365-3091.2007.00881.x DOI: https://doi.org/10.1111/j.1365-3091.2007.00881.x
Zhu, X., Zeng, Y., & Huai, W. (2017). Settling velocity of non-spherical hydrochorous seeds. Advances in Water Resources, 103, 99–107. https://doi.org/10.1016/j.advwatres.2017.03.001 DOI: https://doi.org/10.1016/j.advwatres.2017.03.001
Zingg, T. (1935). Beitrag zur Schotteranalyse: Die Schotteranalyse und ihre Anwendung auf die Glattalschotter. Schweizerische Mineralogische Und Petrographische Mitteilungen, 15(1), 39–140. https://doi.org/10.5169/seals-15330
Downloads
Additional Files
How to Cite
License
Some rights reserved 2026 Arnoud Slootman, Max De Kruijf, Guenther Glatz, Joris Eggenhuisen, Zane Jobe, John Reijmer
This work is licensed under a Creative Commons Attribution 4.0 International License.
