Tensile Strength of Granular Materials

Abstract

Smalley and Smalley¹ have commented on a theoretical expression for the tensile strength of an ideal granular material (in the pendular stage of moisture distribution), due to Rumpf², and have proposed an alternative approach. Their final equation 10a, namely, (where B is the interparticle force per contact, D is the diameter of the particles, and t is the thickness of the fracture zone), includes in the constant term the value of the co-ordination number, k. The authors quote a value k = 8.5, taken from data published by Bernal and Mason³; my re-examination of these data (given in Table 1, ref. 3) indicates that the value should be k = 8.0, which makes a proportionate change in the constant of equation 10a. While equation 10a is dimensionally consistent, the authors' intuitive reasoning in their final paragraph¹ would seem to require that σ be inversely proportional to D² and not D³, as the number of bonds in a section of constant size is inversely proportional to particle cross-section, and not volume; in this respect, Rumpf's equation σ ≊ 2B/D² is more plausible, though of rather academic interest. Rumpf² measured the tensile strengths of limestone pellets, and found that as moisture content decreased, so also did the strength, contrary to his theoretical expectations for the pendular state. I have determined the tensile strengths of various size fractions of a fine coal, using a split cylinder method. Fig. 1 illustrates some typical results, which show a trend similar to that found by Rumpf for limestone.