Abstract
This study deals with fluid pressure variations caused by pumping of water and by changes in atmospheric pressure for a semi-infinite body consisting of many horizontal layers and a substratum each of which is homogeneous, porous elastic, and water-saturated. The Thomson-Haskell matrix method is employed for axisymmetric geometry with cylindrical coordinates (r, z). Continuation is considered at the boundary of each layer with respect to 6 quantities, i.e., displacement components ur, uz; stress components σzr, σzz; pore pressure p, and fluid flow rate qz in the z-direction. A variant of the Sommerfeld integral in the wave theory is devised for pumping at a point with time dependence of exp(-iωt). On the campus of the University of Tokyo, an interesting phenomenon was found by Yamaguchi and has since been observed, that is, the groundwater level in a well about 380 m deep rises when pumping begins in another well. The fluid pressure responses to this pumping as well as to changes in atmospheric pressure are simulated numerically by the present model, with good agreement between theory and observation. By way of the same procedure, displacements, tilts or stresses can also be calculated at any point in the medium.
