Discontinuum Mechanics of the One-Dimensional Consolidation of Soils

This paper deals with the one-dimensional primary consolidation of saturated fine-grained soils, described as a discontinuum process. The theory is based on two foundations: the ideal discrete space-time structure of matter, and the principle of the mean value. Discontinuous matter is described by the influence domain of a point or node. Since this domain is a statistical sample of the whole discontinuous body, any associated quantity may be described properly as a point estimator, which is determined by averaging the neighboring values within the influence domain. As a consequence, a parabolic differential equation is attained. When this estimator is linear and logarithmically related to the excess porewater pressure, the settlement, or the vertical strain of a fine-grained soil subjected to the consolidometer test, the theories proposed by Terzaghi, Davis and Raymond, and Mikasa can be weighed, and the abundant reported experimental data may be used to develop deductive relationships between the consolidation parameters.