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.