含水层水平二维弹性形变下的位移与水流方程

DISPLACEMENT AND FLOW EQUATIONS OF AQUIFER UNDER HORIZONTAL 2-D ELASTIC DEFORMATION ASSUMPTIONS

在垂直方向零应变与垂直方向总荷载不变、忽略骨架颗粒本身的压缩性及骨架颗粒与水分别为均质的假定条件下,推导出均质各向同性多孔介质水平面弹性位移方程及水流方程。它们与传统假定(Jacob假定)下的位移及水流方程在形式上没有区别,只是方程中的系数定义式有所不同。新水流方程中的储水率比旧水流方程中的储水率偏大,但仍可按常数对待。新位移方程的系数也比传统假定下的位移方程的系数大,但也仍为常数。如果采用野外抽水试验来确定储水率,则传统假定下水流方程与新水流方程等价,但利用抽水试验确定的骨架弹性储水率计算地面沉降,则计算值偏大。

The horizontal displacement equation and flow equation in homogenic and isotropic porous medium have been derived under assumptions that matrix material is perfectly elastic, that skeletal particles and water are homogenic and can＇t be compressed, and that changes of pore pressure in the aquifer lead only to horizontal displacements of the solid skeleton of the formation with constant vertical mechanical loading, but not to vertical displacements. Compared with the equations derived under traditional assumptions （Jacob assumptions）, the new equations have the same structural forms but with different coefficients. The new-defined specific storage and new-defined skeletal elastic specific storage, although still constants, are greater than traditional ones respectively. The new flow equations should be distinguished from their traditional ones unless the specific storages in them are gotten by site tests in the fields or model calibration. The calculated value of land subsidence will be bigger than that if the skeletal elastic specific storage in the subsidence model is also obtained from pumping test.