Formation mechanism of hexagonal structure of basalt columnar joints based on Mechanics of Materials and infinitesimal method

Abstract

The perfect hexagon showed by columnar jointed basalt gets great public appeal. However, the accurate illustration was not given. A new explanation, which has rigid calculation, is proposed here for their origin. With the cooling of basalt, the distribution of stress changes while the normal stress equal to the tensile strength of basalt. Using an equation as τθ=τf, where τθ is the force tangentially acting on the unit shear boundaries and τf represents the shear strength of basalt, to indicate the condition of the shear fracture. The result of numerical calculation shows that cleavages appear at angles of ±59.53° with the σ1, which effectively illustrate why the columnar jointed occur in conjugate pairs with ~120° angle between cleavages. The angle depends on the internal friction angle, the cohesive force, the tensile strength and Poisson’s ratio of basalt. Other factors on the sides and diameter of columnar jointed, such as the velocity of cooling and components of magma, will be deeply researched in our future work.