Mathematical simulation of the subsidence of Venice: 1. Theory

A review of land subsidence theory and an outline of the justification for our choice of a model to simulate the subsidence at Venice are provided. The review is essentially a search for a mathematical model that can be used to link realistically the occurrence of land subsidence to the groundwater withdrawals that are its cause. The Biot system of equations for three‐dimensional consolidation offers the best approach at the theoretical level, but the large number of required parameters precludes application of the approach in practice. Approaches based on the independent solution of the diffusion equation provide a practical alternative, as long as the conditions underlying the development of the equation are recognized, and, if necessary, monitored. At Venice, we have chosen a two‐step procedure to analyze the subsidence in the complex aquifer‐aquitard system that exists there. First, the regional hydraulic head drawdowns are calculated in a two‐dimensional vertical cross section in radial coordinates, using an idealized 10‐layer representation of the geology. The computations are carried out with a model based on the diffusion equation and solved with a numerical finite element technique. The calculated head values in the aquifers are then used as time dependent boundary conditions in a set of one‐dimensional vertical consolidation models solved with a finite difference technkme and applied to a more refined representation of each aquitard. This approach appears to offer the best trade off between theoretical elegance, data availability, and computer limitation. Its main disadvantage lies in the limitations imposed by the requirements of radial symmetry.