Triaxial Testing’s 1/6th Rule: Particle-Continuum Analysis of Granular Stability during Compression

Abstract

The 1/6th Rule of Triaxial Testing says that particles larger than 1/6th the diameter of the specimen will skew test results when not discarded. Although this rule is documented in the procedures of government laboratories, its origin is obscure. In this paper, the rule is derived as a corollary of granular stability. The stability derivation involves particle-continuum analysis. However, instead of a discrete element formulation or Cosserat mechanics, this paper uses the classical solution of Sokolovskii that is the modern basis of Terzaghi bearing capacity theory. Stability of a soil particle is addressed within the continuum by matching leading terms of series expansions, which is also known as the singular perturbation method. This finding is similar to previous derivations involving deformation of geosynthetic reinforced soil.