Review: Experiments showing dilatancy, a property of granular material, possibly connected with gravitation (Reynolds, 1887)

By Michael Bennett, P.E., M.ASCE (Gannett Fleming, Inc., Audubon, PA)

 

Scientific exploration often leads to breakthroughs that differ dramatically from what researchers expect.  One striking example began innocuously in the 1880s, when most scientists hypothesized that light traveled through an invisible medium known as luminiferous ether.  Researchers such as Prof. Albert Michelson in Cleveland, OH, raced to define and describe the ether’s properties.  In 1887, he and Prof. Edward Morley, also a Clevelander, collaborated on a project to measure how much the ether slowed down light traversing it.  The professors were initially puzzled when their data indicated that the ether had a negligible impact on light’s speed.  Yet they soon realized their results might point toward a more startling truth – the ether not existing!  Michelson and Morley’s findings ultimately led to new research which, in 1905, culminated in Swiss patent clerk Albert Einstein setting forth the special theory of relativity.  The theory, which has permanently altered how humanity understands and uses physics, includes the speed of light being constant and immutable as one of its main tenets (APS 2024).

 

 

Images 1A and 1B: Profs. Albert Michelson (L) and Edward Morley (R), pioneering physics researchers.
Sources: AIP (2015), PSD Trailblazers (2022).

 

Similarly, research on luminiferous ether in the UK by engineer Osborne Reynolds (1842-1912) in the 1880s led to the discovery of the dilatant behavior of granular materials.  Reynolds, whose name is well-known to generations of his successors, spent 37 years as a professor at the University of Manchester.  During his career, he contributed significantly to many subdisciplines of civil and mechanical engineering, including heat transfer, fluid mechanics, and tribology (the study of friction, wear, lubrication, and bearing design).  Every civil or mechanical engineering undergraduate learns to use the Reynolds number to determine whether a fluid is undergoing laminar or turbulent flow.  Reynolds’s contribution to soil mechanics is less widely appreciated than his work in fluid mechanics but remains equally important to modern civil engineering (Elger et al. 2013, Jackson 1995 A, Skempton 1985).

 

 

Osborne Reynolds began investigating the properties of luminiferous ether by assuming it was atomic in nature and could be represented with “a mass of rigid granules in contact with each other.”  Whether Reynolds was familiar with George Darwin’s closely related work a few years earlier on the frictional behavior of sands [see entry for Darwin (1883)] remains unclear.  However, it seems likely since Reynolds and Darwin were contemporaries in British scientific research circles.  It was in fact Darwin who had noted during his experiments that a dense sand under loading had to “unsettle” into a looser state before a failure surface could form within it.  Reynolds quantified this “unsettling” by calculating the volume of spheres and voids for two layers of identical spheres arranged in either their densest or loosest possible configurations.  He found that the “the interstices [occupied] a space about one-third that occupied by the spheres themselves” in the dense pattern – the corresponding void ratio, e, works out to 0.35 – and “about nine-tenths of the volume of the spheres” in the loose one, corresponding to an e of 0.91 (Darwin 1883, Reynolds 1887).

 

 

 

Reynolds, as adept an empiricist as he was a theoretician, then devised a simple solution to model granular materials of infinite extent.  His technique, which he demonstrated before his peers in the Royal Society of Great Britain in February 1886, involved first filling a rubber balloon with buckshot to create a contained system of purely granular material.  Reynolds next filled the voids within the balloon with water, placed a glass coupler inside its neck, and connected a water-filled glass tube to the balloon.  The buckshot-filled balloon in such a set-up can freely expel or take in water, so modern geo-professionals would describe it as analogous to a drained soil condition.  Finally, Reynolds squeezed the balloon as his audience watched.  The buckshot initially rearranged itself into a looser configuration, which increased the volume of its voids, drew water into the balloon, and decreased the water level within the glass tube.  Eventually, the buckshot reached its maximum dilatancy and began densifying again and expelling water (Reynolds 1887, Skempton 1985).

 

 

 

Reynolds concluded his investigation with another test on the buckshot’s dilatancy.  The modified test involved replacing the water-filled glass tube with a mercury manometer so the buckshot-laden balloon could neither take in nor expel water.  Current geo-professionals will recognize this scenario as analogous to an undrained soil condition.  When Reynolds attempted to squeeze the balloon, the mercury in the manometer rose, and the balloon quickly became so rigid that Reynolds could squeeze it no further.  In modern geotechnical parlance, incipient dilatancy within the dense, undrained buckshot was causing the pore water pressure within the balloon to drop.  The effective stress on, and shear strength of, the buckshot thus increased. (The same phenomenon occurs in wet beach sand under the heels of visitors.) While Reynolds apparently didn’t record the pore water pressure at which he could no longer squeeze the bag, it may well have been near the -14.7 psi limit at which cavitation occurs – i.e., when the gases in pore water expand out of solution (Reynolds 1887, Skempton 1985).

 

 

 

 

 

 

Unfortunately, neither Osborne Reynolds nor any of his contemporaries sought to expand upon his research on the dilatancy of granular materials.  Three decades would pass before Karl Terzaghi, then a young engineering professor at Robert College in Istanbul, would rediscover and articulate the principle at play in Reynolds’s second experiment, demonstrate its full applicability, and christen it effective stress [see entry for Terzaghi (1925)].  Yet Reynolds’s paper on dilatancy, together with his contemporary George Darwin’s work on the frictional behavior of sands, offer an excellent introduction to the mechanics of granular soil.  The two works collectively establish the subtle distinction between angle of repose and friction angle, the influence of relative density on friction angle, and dilatancy under both drained and undrained conditions – all concepts which remain critical in present-day geotechnical engineering.  Reynolds had no more intention of contributing to an improved understanding of soil mechanics with his work than his American counterparts Michelson and Morley did of opening the Pandora’s box of special relativity with theirs; all three sought only to better understand the behavior of luminiferous ether.  Yet, by chance, their research has had dramatically different impacts from those they anticipated.  Such unexpected breakthroughs are, of course, a crucial part of what makes scientific research so invaluable.

 

Acknowledgments

Sebastian Lobo-Guerrero, Ph.D., P.E., BC.GE., M.ASCE (A.G.E.S., Inc.: Canonsburg, PA), the author’s former colleague, reviewed the entry’s geotechnical content.  Kevin Delano, Ph.D. (Goddard Space Flight Center: Greenbelt, MD), a practicing astrophysicist and the author’s Lafayette College roommate, provided input on how the Michelson-Morley experiment helped lead to the special theory of relativity.  Thomas Kennedy (Geopier: Davidson, NC), the author’s Virginia Tech classmate, co-authored a 2021 version of the entry posted on an independent webpage.

 

References

AIP (American Institute of Physics). 2015. “Portrait of Edward Morley.” American Institute of Physics. Accessed May 11, 2024. https://repository.aip.org/islandora/object/nbla:305555

APS (American Physical Society). 2024. “Case Western Reserve University, Cleveland, Ohio.” American Physical Society. Accessed May 11, 2024. https://aps.org/programs/honors/history/historicsites/michelson-morley.cfm

Darwin, G.H. 1883. “On the horizontal thrust of a mass of sand.”  Min. Proc. Inst. Civ. Eng., 71, 350-378. Reprinted in A century of soil mechanics: Classic papers on soil mechanics published by the Institution of Civil Engineers, 1844-1946, L.F. Cooling, A.W. Skempton, and A.L. Little (eds.), 1969. London, UK: William Clowes and Sons, Ltd.

Elger, D.F., B.C. Williams, C.T. Crowe, and J.A. Roberson, 2013. Engineering Fluid Mechanics, 10th Ed. New York, NY, USA: John Wiley and Sons.

Jackson, J.D. 1995. “Osborne Reynolds: Scientist, engineer, and pioneer.” Proc. R. Soc. London, Ser. A., 451, 49-86. Accessed May 12, 2024. https://personalpages.manchester.ac.uk/staff/jdjackson/Osborne%20Reynolds/oreyna.htm

Jackson, J.D. 1995. “Reynolds the scientist.” Centre for the History of Science, Technology & Medicine, Faculty of Life Sciences, University of Manchester. Accessed May 12, 2024. https://personalpages.manchester.ac.uk/staff/jdjackson/Osborne%20Reynolds/oreynB.htm#BC

Meerman, R. 2013. “The Surfing Scientist: Dry feet on wet sand.” Australian Broadcasting Corporation. Accessed May 12, 2024. https://aps.org/programs/honors/history/historicsites/michelson-morley.cfm

Michigan Metrology. 2024. “The work of Osborne Reynolds.” Michigan Metrology, LLC. Accessed May 12, 2024. https://michmet.com/osborne-reynolds/

PSD Trailblazers. 2022. “Albert A. Michelson (1852-1931).” University of Chicago Physical Sciences Division. Accessed May 11, 2024. https://www.trailblazers.psd.uchicago.edu/albert-michelson

Reynolds, O. 1887. “Experiments showing dilatancy, a property of granular material, possibly connected with gravitation.” Proc. R. Inst. G.B., 11, 217-227.

Skempton, A.W. 1985. “A history of soil properties, 1717-1927.”  In Proc. 11th Int. Conf. Soil Mech. Found. Eng., San Francisco, CA, USA: ISSMFE, Golden Jubilee Vol., 95-121.