循环抽水越流承压含水层水位变化与变形分析

Drawdown of Underground Water and Compact of the Leakage Confined Aquifer due to Cyclic Pumping

建立了越流承压含水层在循环抽水的地下水运动数学模型,用Heaviside函数性质及Laplace变换求解得该数学模型关于承压含水层水位变化的解析表达式,进而求得承压层压缩变形。通过数学软件Mahtematica对算例进行了计算和分析,结果表明:承压含水层水位恢复存在滞后性,阻越流系数B越小水位恢复的滞后性越小,并且抽水引起的承压含水层水位下降量也越小,因而引起的承压含水层弹性压缩变形也越小;承压含水层以幅值Q0的循环抽水对应的水位降-时间曲线围绕恒定抽水t1Q0/T曲线上下波动,并呈上升趋势;距抽水井越远处的水位受到抽水循环反复作用的影响越不明显,较远处循环抽水水位降深-时间曲线与t1Q0/T曲线重合。

The mathematical models of groundwater movement in leakage confined aquifer due to cyclic water pumping are presented, and the analytical solutions of the models are obtained by making use of the properties of Heaviside ＇ s unit function and Laplace Transformation. By software Mathematica, the computational samples are given to analyze the change of water drawdown of the confined aquifer and its influential factors under cyclic pumping. The results show that ： the recovery of hydraulic head has hysteretic characteristics, i. e. , smaller leakage factor B leads to smaller hysteresis of water recovery and smaller magnitude of drawdown and compact of confined aquifer, and the drawdown-time curve by cyclic water pumping with Q0 amplitude oscillates around the curve of constant-rate water pumping tlQo/T, and the distance away from the pumping well has an influence on the oscillation of water drawdown, two curves coincide there where far away from pumping well.