| Abstract: | Persistent pumping of groundwater is known to cause subsidence of the ground surface. When the soil is composed of alternating layers of sand and clay, subsidence is, in general, a consequence of pressure change in and deformation of all layers. Even with various simplifications, the mathematical task for the mechanics of a layered soil is complex and, in the past, many idealizations have been introduced in the literature. Among the existing approximations, a well-known approximation by Hantush1 for well-hydraulics in leaky aquifers is intuitively attractive. He used the fact known to be strictly true for simple flows in a soil system with horizontal layers, that the flow must be mainly horizontal in a relatively porous aquifer and mainly vertical in a highly impervious aquitard, and invoked the same approximation for transient flows induced by well-pumping. In this paper we shall apply a perturbation analysis to give a mathematical confirmation of the hydrological approximation and to show its degree of accuracy. In particular, we treat a three-layered system, where the middle layer is a relatively soft aquitard, and the well withdraws water from the artesian aquifer at the bottom. The upper aquifer has a phreatic surface. Physically, we examine the often ignored effects of self-weight which is important for thick aquitards. The perturbation theory is worked out for sufficiently weak pumping rates and small soil deformation. Subsidence in the vertical direction due mainly to the deformation of the soft aquitard is studied. Results show that the common assumption of constant total stress with respect to depth is valid only when the storage coefficient is very small. |
