The Coefficient of Earth Pressure at Rest by Means of the Granular Mechanics

There is abundant evidence that the coefficient of earth pressure at rest, K₀, is somehow related to the internal friction angle of soils. Jaky’s semi-empirical formula is considered to be a sufficiently precise relationship for practical purposes, although its derivation includes some arbitrary approximations. Alternatively, granular mechanics may be used to obtain a rational relationship between these two quantities, based on the assumption that stresses are transmitted as conjugated chains of forces along the edges of an octahedral lattice. Two experimental extreme conditions of an infinite soil slope are considered: the state at rest, when its inclination is zero, and the plastic state, when its inclination equals the friction angle. Eliminating the angle of the assemblage of grains, a relationship between K₀ and the angle of friction is directly achieved in a very simple way. As shear stresses are forbidden in the direction of the ground level lines, there are only two admissible positions of the base of the octahedral lattice: the diagonal and the parallel to the slope, which are related to the triaxial and biaxial compression tests, respectively. The relationships thus obtained are supported by the experimental data reported by several authors.