MATHEMATICAL SIMULATION OF SUBSIDENCE OF VENICE .1. THEORY
MATHEMATICAL SIMULATION OF SUBSIDENCE OF VENICE .1. THEORY
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DOI：
10.1029/wr009i003p00721
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发表时间：
1973-01-01
影响因子：
5.4
通讯作者：
FREEZE, RA
中科院分区：
文献类型：
--
作者：
GAMBOLATI, G;FREEZE, RA
地面沉降理论的审查和轮廓的理由，我们选择的模型来模拟在威尼斯的沉降。该审查实质上是一个数学模型，可以用来现实地联系地面沉降的发生地下水抽取，是其原因的搜索。三维固结的毕奥方程组在理论上提供了最佳方法，但所需参数众多，妨碍了该方法在实践中的应用。基于扩散方程的独立解的方法提供了一种实用的替代方案，只要方程发展的基本条件得到承认，并在必要时得到监测。在威尼斯，我们选择了一个两步程序来分析那里存在的复杂含水层-弱透水层系统的沉降。首先，在径向坐标系下的二维垂直截面中，使用理想化的10层地质表示法计算区域水头下降。计算进行了扩散方程的基础上的模型和数值有限元技术解决。然后将含水层中计算的水头值用作一组一维垂直固结模型中的时间相关边界条件，该模型采用有限差分技术求解，并应用于每个弱透水层的更精确表示。这种方法似乎提供了理论上的优雅，数据可用性和计算机限制之间的最佳权衡。它的主要缺点在于径向对称要求所带来的限制。
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.