摘 要 早期推求均勻降雨條件下，斜坡上地下水滲流之解析解時，為了解決非線性之問題，常須限制其邊界條件，故只能應用於特殊之案例。本文以Childs之理論為基礎，假設流線平行坡面，並沿斜坡計算勢能梯度，推導過程中利用變數轉換，並結合牛頓-羅弗森之疊代方法，可求得自由水面之座標為水面斜率之參數式。利用此解之特性，可直接求得最大正向水深及其發生位置，結果與前人之實驗結果相當符合。本研究之理論解不僅不受邊界條件之限制，亦可用來求解mixed邊界值問題。 本研究著重於非線性地下水方程式之理論解析，並將利用所得之理論解，分析入滲強度因子與坡度因子對斜坡上地下水滲流之影響。此外，針對地下水面可能對斜坡造成之破壞，也將透過土石流發生之案例加以討論。 Abstract The major purpose of this study is to obtain a new approximation for seepage flow over a sloping bed. This study is based on Childs’ theory. The streamlines are assumed to be nearly pararell to the sloping bed, and coordinate s pararell to the bed is used to calculate the hydraulic gradient. In the process, variables translation and the Newton-Raphson interation method are applied to obtain the solution of phreatic surface, which is in form of the function of the derivative of free surface, P. The maximum water table height hmax and its location smax could be easily obtained, and are well coincident with previous published studies. The solution developed here could not only deal with problems with various upstream and downstream depths, but also could be used to explore mixed boundary value problems. The analytical results can be used to evaluate the effects of slope, replenishment, and hydraulic conductivity on the preatic surface. The solution is applied to a case study of a debris flow event.
