"On the Angle of Repose"

I gave a version of this paper at the Maintainers II Conference on April 5, 2017, at Stevens Institute of Technology.

The “angle of repose” is a technical term used to describe the slope at which loose material forms when piled. It’s a material property: sand, gravel, loam, etc., all form cones of varying squatness—some slumping and sliding more than others. The determination of their base angle or slope has been the cause of much empirical investigation and theorizing since the Enlightenment. As an abstract concept, the angle of repose represents a baseline of entropy in the absence of structure. This slow movement toward slumping and spreading was the subject of the artist Robert Smithson’s early work, who filmed dumptruck loads of asphalt oozing down a Roman hillside as a way of getting at a universal tendency toward chaos and dissolution. Today I am going to speak about resisting the slumping of the earth in the context of the military engineering where it was first mathematically conceptualized, and describe its importance in civil engineering derived from it’s military context. These are nineteenth-century earthworks at Fort McHenry in Baltimore Harbor; examples of engineered dirt-piles that were standard city defense in the gunpowder age. These primordial forms resist betraying the amount of applied mathematics that underlie their construction; on the other hand their mass and volume make the labor involved in building them immediately apparent. It is in this dual context that I wish to speak about the theoretical and practical impact of the concept of the angle of repose. To the engineer, it is a concept that requires action: it is an indication of a “natural” dissolution into near-flatness, it’s very existence is an invitation to apply structure in order to supersede the natural lie of the earth. On the other hand, to the people that must build and maintain the landscape above its natural disposition, it is an exercise in Sisyphean futility, and a concept that asks for resistance. 

The first formulation of the angle of repose I could find was in an early-modern construction manual, where the disposition naturelle of a pile of earth could be imagined as similar to the behavior of a pile of cannonballs. [1] Bullet’s text also includes a standard diagram, showing the portion of earth above the 45 degree angle of repose gained by structuring the ground with a retaining wall. Prosaic civilian landform construction drew on a highly-developed corpus of work on military construction practices—the systematization of ballistics and organization of landforms synonymous with Louis XIV’s famed engineer, Vauban. Early-modern French practice strove for a sophisticated application of high mathematics to landform, and the purview of the engineer extended to the logistics of construction and maintenance of the landscape pressed into prismatic form. [2] As a result of the amount of attention the state paid to technical questions, the écoles militaires became sites of intense investigation by some of the era’s most luminous mathematical minds. Charles-Augustin Coulomb, of the eponymous electrical unit fame, developed his application of calculus to soil mechanics while on military duty in Martinique, after graduating from the école du genie at Mézières. His conclusions about the use of infinitesimal calculus to describe the tenacité of planes of soil in any given configuration prefigured later advances in fluid dynamics and description of the behavior of aggregates. [3] 

​Jean-Victor Poncelet, famous for his ability to translate the abstruse mathematics of his faculty colleagues into accessible manuals, produced a number of reference works to be used by field engineers. In this volume, translated for use by the U.S. Army, he provides a graphic method of sizing a retaining wall, making the theory accessible to an engineer armed only with a compass, ruler, and a smattering of Euclid, while providing the underlying algebraic analysis on the right. [4]

However, piling dirt was inevitably a pragmatic, field-based operation, and the projected geometries always necessarily built of less-than-cooperative materials and in non-geometric environments. This photo shows the extensive structure of gabions--woven, basket-like cylinders--which structured the earthwork defenses outside Petersburg during the American Civil War. Intense manual labor characterized this technology, and the techniques to weave and pile the earth hadn’t changed much since the Punic Wars.

In the plates of the 18th century treatises on both military and civil engineering and construction, one finds a tension between the planar geometry described by the design system, and the assembly of labor and material marshaled to fulfill that geometric outline. Bossut’s treatise on dikes, shown here, portrays the geometric parameters that define a dike’s prism. Subsequent plates describe a variety of levee profiles, and the progressively hardened structures needed to achieve the prescribed prismatic form. As the angle the design called for approached the angle of repose, the practice Bossut found most effective (and probably cheapest) was a woven, embankment-scale textile of saplings and river reeds. Based on the ancient form of the fascine, or bundle of sticks or rods, Bossut described a practice of giving tensile strength to the loose material of embankments, a built revetment that wove together the sides of entire rivers with only the use of marshland materials and some hand tools. [5]

Weaving was part of the curriculum the U.S. Military Academy at West Point throughout the mid-19th century, where, as part of their training in practical military engineering, cadets were taught to make gabions and fascines as part of their education as soldiers. This work was done in the landscape at West Point, in a place called the “Engineers’ Garden.” After spending time weaving, the cadets set up profiles of fortifications, learning the difficult task of projecting idealized landforms across varying topography, and reconciling an array of planes in space. A contingent of common soldiers then built the earthworks, and the cadets returned periodically to gain a sense of how long it took x amount of men to build an earthwork to y height. The fortifications were then demolished, and work begun again, continuing throughout the year. [6]

The effects of this education can be read across the United States, where the corps of engineers sought to embed tensile strength into the landscape, shaping river and bayou and laying in, with a boggling sense of laboriousness, an attempt to make permanent the designed configuration of river and ground. The quest for a permanent binding structure, one that can give integrity to landform even under extreme environmental stress, animates much of the corps’ work well into the 20th century. Note here the brush mattress, which resists the granite blocks of the jetty’s tendency to disintegrate and sink into the mud. I would also add that the notion of the fascine as a binding agent could color an interpretation of that ancient republican symbol of the fasces, prominent in U.S. civic iconography.

But to return to the people who built these structures, and especially the soldiers at West Point whose job it was to build, destroy, and rebuild, over and over again, year after year. From what I can reconstruct, most of the work was done on day labor hired directly by the army. Contractors found it difficult to maintain the vast crews needed, or often went bankrupt after a storm or flood would wipe out months of work overnight.  We of course have precious few sources that can give us insight into what was obviously a tedious and dangerous day’s work. 19th century photographers were notoriously reticent of photographing African Americans, but most of this work, both before and after Emancipation, was done by black laborers. “Mud work” was notorious and avoided, and scholarship has shown that the dissolution of the rice plantations in South Carolina during Reconstruction was largely due to a vast undervaluing of how much it cost, at fair labor prices, to maintain the network of levees and canals. In refusing to do mud work, unless it was well-paid, the freed people expressed resistance to the regime landscape maintenance they had suffered under. [7]

In the West Point archives, however, I found the account of Walter Bartholemew, who had entered the army as a young man and had spent five years building “French works” in the Engineers’ Garden in the 1850s. “On the whole,” Bartholemew recalled, “we had an easy time,” work only about four hours a day and the rest of the time spent drinking at Benny Havens’ Tavern down the hill.  He did recall one dreaded Lieutenant Donaldson, whose maniacal pursuit of ever higher false works, “seven gabions high,” prompted Bartholemew and his compatriots one evening to consider a pile of unused fascines and gabions nearby. “When we had it all done after dark we set it on fire and hurried to our quarters. We had not been long home when a mysterious light began to show over towards [the] valley…The whole post was in an uproar; every one, officers, men, cadets, all rushing to see what it was. It soon burnt out leaving a huge pile of dirt.—Donaldson would have given a hundred to have known who did it but he never found out—and it saved us a lot of work." [8]

​Symbolism is rarely this easy to interpret, and I think the fascine, standing on one hand as binding agent and representative of a desire for control and permanence, can on the other hand connote well, in its multitude of strands and inherent fragility, the embodiment of immense tedium and resentment on the part of those who worked the regime of futility.

I would also like to point out the overlooked role of this kind of mud work in the pre-history of reinforced concrete. A material of infinite plasticity of form and unprecedented structural integrity in both tension and compression, I believe that there is work to be done to understand how resistance from labor to constructing above the angle of repose indeed made this material even more attractive to the engineer in the modern engineered landscape-and how these structures might be interpreted not as heroic, but as describing the remaining desires of older time, when work above the angle of repose, no matter how arduous, could never expect permanence or stability.

​

1. Pierre Bullet, L’Architecture pratique (Paris: Libraires associés, 1768).
2. Anne Blanchard, Les ingénieurs du “roy” de Louis XIV a Louis XVI: Étude du corps des fortifications (Montpellier: Université Paul-Valéry (Montpellier III), 1979); André Guillerme, “La cervelle de la terre: la méchanique des sols et les fondations d’ouvrage de 1750 à 1830,” History and Technology 7, no. 3–4 (1991): 211–54.
3. Jacques Heyman, Coulomb’s Memoir on Statics: An Essay in the History of Civil Engineering (Cambridge: Cambridge University Press, 1972).
4. Jean-Victor Poncelet, Substaining Walls: Geometrical Constructions to Determine Their Thickness under Various Circumstances (Washington, D.C., n.d.).
5. Charles Bossut and Guillaume Viallet, Recherches sur la construction la plus avantageuse des digues: ouvrage qui a remporté le Prix quadruple proposé par l’Académie Royale des Science, Inscriptions & Belles-Lettres de Toulouse, pour l’année 1762 (Paris: Jombert, 1762).
6. John Dean Davis, “‘A Continental Laboratory’: The Landscape of the U.S. Military Academy at West Point,” in Landscape and the Academy, ed. Daniel Bluestone and John Beardsley (Washington, D.C.: Dumbarton Oaks Research Library and Collection, forthcoming).
7. John Scott Strickland, “‘No More Mud Work’: The Struggle for the Control of Labor and Production in Low Country South Carolina, 1863-1880,” in The Southern Enigma: Essays on Race, Class, and Folk Culture, ed. Walter J. Fraser, Jr. and Winfred B. Moore, Jr. (Westport, Conn.: Greenwood, 1983), 43–63.
8. ​Walter G. Bartholemew, “Reminiscence of Enlisted Life at West Point,” 1849, Walter G. Bartholemew Papers, Special Collections and Archives, United States Military Academy Library, West Point, New York.