求直线供水边界抽水试验水文地质参数的解析法

Analytical Method for Obtaining Hydrogeological Parameters Through Pumping Test with Straight Recharge Boundary

直线供水边界条件下非稳定流抽水试验求解水文地质参数的超越方程涉及3个(在已知供水边界方向,未知位置的条件下)或4个(在供水边界方向和位置均未知的条件下)未知数,常规的解析法无法直接求解。现有的特定标准曲线比对法、图解拐点法、简化算法、非线性最小二乘法及二元线性回归法要么依赖图表、计算过程繁复,要么应用范围受限、计算结果误差较大,不便实际工程应用。采用优化拟合方法,在工程适用参数范围内,用较为简单的函数实现了对泰斯非稳定流井函数的替代,并利用水位降深比值关系式,经整理获得了可直接完成参数求解的简化解析式,计算过程简捷,便于实际工程应用。

Under the condition of non-steady flow, the obtaining of hydrogeological parameters through pumping test with straight recharge boundary involves the transcendental equation of 3 （boundary direction known, position un- known） or 4 （ both boundary direction and position unknown） unknowns, which could not be solved by convention- al analytical methods. The existing methods, including method of specific standard curve comparison, method of in- flection point, simplified algorithm, nonlinear least square method and binary linear regression method, are incon- venient for practical engineering as they are dependent on graph with complicated calculation process, limited appli- cation range and big calculation error. In this article, optimization fitting method was employed to adapt to the engi- neering parameter range, and the substitution of simple function for the Theis well function of non-steady flow was carried out. Furthermore, a simplified analytic expression for the parameters was obtained by summarizing the draw- down ratio formulas. The calculation process is simple and convenient for practical use.