EJGE/Magazine Feature

Deep Dark Secrets of Geotechnical Engineering

M. Oner, 1997

## Coulomb, Rankine, Terzaghi...

• Charles Augustin Coulomb (1736-1806) is known to have written the oldest text in soil mechanics. Due to this, the shear strength equation for soils is still called the "Coulomb-Mohr" equation. But Coulomb actually refers to one Monsieur Amontons for the origin of his "assumption that strength due to friction is proportional to compressive force," and he adds, "although for large bodies friction does not follow exactly this law."
• "The charming little engraving" (Golder 1948) that marks the end of Coulomb's "essay" is reproduced on the cover of every issue of Geotechnique. It is not clear if Coulomb had anything to do with that figure, but this is an indication of how much Coulomb is revered by modern geotechnical engineering community. Because of his "essay" Coulomb is still quoted as the founder of shear strength and earth pressure theories, though sometimes in a misleading way.

• Coulomb did consider cohesion, though modern textbooks claim otherwise. He never did write the shear strength equation itself explicitly, but he used it as we know it today. He did sketch the failure surfaces as curved (but used planes for simplicity--he says so!), and he derived formulas for the resultant forces and moments (the latter involves the differentiation of the force expression along the wall which indicates a triangular stress distribution). He also derived the formula for the critical height of a vertical cut. Incidentally, the "essay" even stressed the importance of testing the materials used (though in relation to masonry), and the importance of drainage of the backfill of a retaining wall!
• What Coulomb did not do is to derive "Coulomb's lateral earth pressure coefficients" (those with lots of sines and cosines) which are given in all modern soil mechanics books as "the equations derived by Coulomb who ignored cohesion." According to Tschebotarioff's famous textbook (1951) those formulas were derived by Muller-Breslau in 1906. I don't know if we should take this seriously, because--see next item:
• Tschebotarioff's statement that trigonometric functions were not used during Coulomb's time is not correct. Coulomb did use them in the "essay" in relation to his study of stability of arches, but simply chose to use ratios instead in formulating the earth pressure problem. According to Caquot and Kerisel (1956) the formula for the active case was given by General Poncelet in 1840 and "the passive case could be derived easily from that." Feld (1923) also refers to a "Poncelet theory." Terzaghi consistently refers to these formulas as Coulomb's in his papers and books.
• After writing his "essay" Coulomb was admitted to the Academy, which, a few short years later, was closed down because it was seen as a bourgeois institution by the revolutionaries! Fortunately he was well off (after all, he was the Ingenieur du Roi); he retired to a country farm house and got interested in other subjects such as electricity and magnetism. Yes, he is the same man!
• William John Maquorn Rankine (1820-1872) was the Chair of Engineering of Glasgow University (Cook, 1950-51). He studied the state of stress at a point at failure in a semi-infinite, cohesionless medium, and related the principal stresses at failure (1857), as opposed to studying the resultant forces on a wall. He rejected Coulomb theory, on grounds that he did not care to explain clearly, making statements such as "unsatisfactory in a scientific point of view." Well, do you think Maquorn could publish a paper today with such unfounded statements?
• The lateral earth pressure calculation in terms of stress ratios that involves a cohesion term is usually attributed to Rankine. Rankine not only disregarded cohesion, but also advocated that it should not be considered at all, arguing that cohesion is a temporary condition "liable to destruction by atmospheric effects." Not exactly so, maybe, but this shows his incredible insight.
• Both Coulomb and Rankine used the terms "active" and "passive" but not the way they are used today. Coulomb named gravity as an "active force" and friction and cohesion as "passive forces." Rankine modified this slightly, and called the lateral forces as "passive" forces. They were both talking about the forces of nature philosophically!!
• Rankine assumed that the limit equilibrium states would be reached "by the slightest deformation of the soil." This seems to be the reason behind Terzaghi's 1936 statement that "the fundamental assumptions of Rankine's earth pressure theory are incompatible with the known relation between stress and strain in soils, including sand. Therefore the use of this theory should be discontinued." Tschebotarioff (1951) believed that "this recommendation is sound," and decided to follow it, though Terzaghi had changed his mind earlier! (1943).
• Karl von Terzaghi (1883-1963), everyone knows, has not only established the field, but also made major contributions to every area of soil mechanics by experiments and theory, and introduced the fundamental concepts such as effective stress. To follow his development is very interesting. His first paper on the earth pressure topic (1920) ends with the statement: "The earth pressure against a perfectly rigid wall seems to be fairly independent of the density of the backfilling. For sand its value is H = 1/2 (0.42) w h2, implying that K0 is always 0.42. Incidentally, the way Terzaghi measures K0 by primitive means of that time is extemely ingeneous - this should be an inspiration to modern experimentalists. Terzaghi disovers that there is a "striking difference" between a loose and a dense sand in 1934. Until then, like all others, he had been trying to measure the "actual" lateral earth pressure coefficient.
• It appears that the "angle of repose" concept existed before even Coulomb's essay. Coulomb gives an example earth pressure calculation where he uses the angle of repose for phi angle without any explanation. Terzaghi, who himself used the same concept for some time, is the first to find the truth about the angle of repose: "it is always about 34 degrees, but phi can assume any value between the angle of repose and an angle greater than 40 degrees, depending on the degree of compactness of the sand." He was resisted strongly when he presented this finding; he explains his difficulty he has had in convincing others in a 1939 publication, as: "I was accused of to be inadequately grounded in theory." Years later, he was apparently still bitter about his frustration.
• The free earth support method is usually attributed to Krey (1910?, 1932), and the fixed earth support to Lohmeyer (1930) and to Blum (1931, 1933). The first US publication on sheet piles, (Pennoyer, 1933), discusses both cases but gives the equations for the free earth support case only. The concentrated force simplification (that some modern textbooks refer to as Terzaghi's) seems to have been done originally by Blum (1931).
• It should be useful to remember (quoting Lambe and Whitman, 1968) that "foundation engineers 50 years ago were taught that sands were cohesionless and that phi=0 for saturated clays, with intermediate values for intermediate materials [...] Today it is realized that the main difference between sands and clays rests with their relative permeabilities [...]" Not everybody has got the point yet, see next item!
• Sullivan (1972) presented a detailed study of an anchored sheet pile wall failure and the paper recommended that design in a stiff, overconsolidated clay should be based on an effective stress analysis using the drained shear strength parameters. A decade later Daniel and Olson (1982) described the failure of another anchored bulkhead failure at a nearby location, in the same soil, and the paper ended with essentially the same conclusion! (note: both papers were published by ASCE/Geotech Journal!)
• Terzaghi (1936) reports that "less than 10 years ago the Foundations Committee of a well-known engineering society decided that the word "settlement" should be avoided in public discussions, because it might disturb the peace of mind of those who are to be served by engineering profession."

Acknowledgements
Some of the material presented on this page have been a by-product of a study, performed by the writer, for Waterways Experiment Station, Vicksburg, MS
I appreciate the corrections and input I receive from the readers; I would especially thank for the input provided by Dr Trevor Davies of Glasgow University.

e-Mail your complaints, suggestions, corrections, and praise to:

Posted 8/27/97