地下水动力学1.5讲述.ppt

第一章 渗流理论基础 §1.5 渗流连续方程 1.5.1 含水层的状态方程 含水层的状态方程主要包括地下水的状态方程和多孔介质的状态方程。 (1)地下水的状态方程 Hooke定律： 式中：E——体积弹性系数（体积弹性模量），20℃时， E=2.1×105N/cm2。其倒数为压缩系数。 等温条件下，水的压缩系数(coef. of compressibility)为 Compressibility of Water Fluids are compressible, e.g., an increase in pressure dp will lead to a decrease in the volume of a given mass of water (Vw). The compressibility of water (β) is defined as: where dVw is the change in the volume of the water; Vw is the original volume of the water, and dp is the change in pressure. The negative sign is necessary to ensure a positive 积分（p→p0，V→V0）改写得： 体积： 密度： 按Taylor级数展开，得到近似方程： 和 因 （质量守恒），故有 (2)多孔介质的状态方程 多孔介质压缩系数（Coefficient of compressibility）表示多孔介质在压强变化时的压缩性的指标，用?表示。 多孔介质压缩系数(?)的表达式为： 式中，Vb＝Vs+Vv——多孔介质中所取单元体的总体积； Vs——单元体中固体骨架（solid matrix）体积； Vv——其中的孔隙（voids）体积。 ? ?——介质表面压强。 Compressibility of a Porous Medium The compressibility of a porous medium, α, is defined as where VT is the total volume of the porous medium, dVT is the change in the volume of the porous medium, and dσe is the change in effective stress. Recall that VT = Vs + Vv, where Vs is the volume of the solids and Vv is the volume of the water-saturated voids. An increase in effective stress dσe leads to a reduction dVT in the total volume of the porous medium. In granular materials the reduction in the total volume of the porous medium is almost entirely due to grain rearrangement. The volume change for individual grains due to the change in effective stress is negligible (in other words, individual grains are almost incompressible). Vv＝nVb；Vs＝(1-n)Vb 式中 ——多孔介质固体颗粒压缩系数，表示多 孔介质中固体颗粒本身的压缩性的指标； ——多孔介质中孔隙压缩系数 （Compressibility of the pores of a porous medium），表示多孔介质中孔隙的压缩性的指标，?s?p 。 n——多孔介质的孔隙度。 因 ，故 。 (3) 贮水率和贮