Deviations from the Theis Solution in aquifers undergoing three‐dimensional consolidation

Abstract

Previously, a new mathematical model based on the ‘tension center’ or ‘strain nucleus’ concept was proposed by the author for the response characterizing flow in a confined aquifer undergoing three‐dimensional consolidation. The new approach differs from Bio's [1941] in that it leads to the development of a unique integrodifferential equation for the pressure head decline occurring within the porous system. The consideration of the horizontal strain components results in a conceptually simple modification of the classical diffusion equation to which a further integrodifferential term accounting for the three‐dimensional effect is added. In the present paper the new equation of flow is solved in a pumped artesian aquifer enclosed in a half space by an iterative finite element technique. It is shown that in shallow and relatively thick units (with W ≃ 0.5, where W is the ratio between the average depth and the thickness of the aquifer), downward vertical components of flow develop and that the average drawdown deviates moderately from the Theis solution and is no longer uniquely represented against the dimensionless time. The three‐dimensional effect produces an additional soil compression which retards the piezometric decline. At large values of time the horizontal strain components vanish, the diffusion equation holds, and the solution becomes parallel to the Theis profile. As a major consequence the traditional aquifer tests can still be applied to assess the formation permeability, but they yield a 40% overestimate of the elastic storage coefficient. In deeper units (W > 0.5) the importance of the three‐dimensional effect diminishes, is already small when W = 1, and becomes negligible for W ≥ 2. In this case the diffusion equation and its solutions are sufficiently accurate. From a practical standpoint the quantitative results given herein are limited by the condition that a mechanically homogeneous and isotropic half space is required.