Three Dimensional Analytical Study of Landsubsidence
Date Issued
2012
Date
2012
Author(s)
Hsu, Hsiu-Ching
Abstract
On landsubsidence analysis, application of numerical model is more than analystical model, and the study of landsubsidence due to loding is less disscussion. Therefore, according to the complete uncoupled equation using only pore pressure and soil displacement of Tseng’s(2009), we construct the landsubsidence governing equation due to groundwater overpumping and loding, then find the appropriate analytical solution and illustrate the result with cases.
Because the three-dimensional uncoupled equation is very similar to Stokes’ flow, it seems that we can use boundary integral element method to slove equation. However, the order of pore water pressure is more than soil displacement, hence that will cause computational instability.
In the landsubsidence due to overpumping problem, water being pumped underground is a point sink, and the pressure singularity is mass source, hence it can sloved by the image method of singularity method. But the displacement can not use image method. Consequently, we combine image method with separation of variables method which sloved three-dimensional Stokes’ flow in cylindrical coordinates by Happel and Brenner(1983) to successfully solve the governing equation, and it’s called multiple method.
In the landsubsidence due to loading problem, the load strength is a point force, hence the displacement singularity is a stokeslet and pressure singularity is a dipole, so it is sloved by the image method of singularity method. Besides, in this study we can apply the result of image system for a stokeslet in a no-slip boundary of Blake(1971).
We illustrate result with the two cases of finite depth unconfined aquifer and finite depth confined aquifer. From thres result, in the landsubsidence due to groundwater overpumping and loading problem, we understand the amount of order of pressure and displacement and vertical displacement and horizontal displacement. Therefore, it is a useful reference for numerical model.
Subjects
three-dimensional landsubsidence
analytical method
pumping
loading
singularity method
image method
Type
thesis
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