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標題: 滯洪水理演算模式之特性解析與試驗驗證
Characteristic Analysis and Experimental Verification of Detention Hydrological Model
作者: 鄭雅珍
Cheng, Ya-Chen
關鍵字: detention pond
Runge-Kutta numerical method
detention pond volume
出版社: 土木工程學系
摘要: 摘 要 台灣地區地狹人稠,對平地使用已趨飽和使得山坡地開發案日漸增多,土地過度的開發與利用將使雨水入滲率減少、逕流量增加,暴雨時因其自然環境坡陡流急而產生坡地災害,滯洪設施設置之目的在於降低因開發山坡地而增加下游地區洪峰流量之危害。本文以水文連續方程式為基礎,利用數值方法發展滯洪水理演算模式,並進行滯洪渠槽試驗以驗證數值演算模式,探討洪水流經滯洪設施之滯洪水理特性,獲致以下成果: 1.經理論分析與實驗結果,本研究提出整合矩形孔口與溢流口之流量公式為Q0=k1(H**1.5*(1-(1-hc/H)**1.5*U(H-hc))-h0**1.5*(1-(1-hc/h0)**1.5*U(h0-hc))) ,式中Q0 為出流口流量、k1=2/3*Cd*bc*(2*g)**0.5 為流量歷線特性參數、Cd為流量係數、g為重力加速度bc、hc分別為出流口開口寬度與高度、H 為出流口水深、h0 為基流水深、U(H-hc) 與U(h0-hc) 為單位階梯函數。 2.利用藍吉-庫塔(Runge-Kutta)數值方法配合渠槽試驗加以模擬驗證,針對不同入流歷線及不同出流開口大小而言,皆可得到良好的模擬結果,證明藍吉-庫塔數值方法之適用性,可用來推求洪水流經滯洪設施後之出流量。 3.配合(5-1)與(5-3)迴歸式可推得三角形、梯形入流歷線作用下矩形出流口之無因次洪峰消減κ。就洪峰稽延而言,當三角形入流歷線特性參數βe愈大即退水時間除以洪峰到達時間之比值愈大,稽延時間較長,而梯形入流歷線特性參數γe愈大即洪峰持續時間愈長,可得較長之稽延時間。 4.有關滯洪設施設計最小滯洪容積sf 之推算,當入流歷線呈三角形時以(3-30)理論式或(5-2)經驗式在設計上皆可應用;呈梯形者於無因次洪峰出流量Qop* =0.5~0.9之間顯示(3-31)理論式較(5-4)經驗式高估約15%~75%之無因次滯洪容積。
Abstract As the local land area is small and the density of population is high, the use of level ground become saturated thus increases the amount of hillside land''s developments. Excessive development could lead to a decrease of the ground infiltration rate and an increase of the surface run-off. When a heavy rainfall occurs in an area with a steep slope, the resulting rapid stream causes a disaster at the hillside. Accordingly, a detention pond is practically set to alleviate the amount of excess flood due to the hill development. In the study, a numerical hydrological routing model, base on the continuity equation, is proposed to investigate the characteristics of flood detention. Additional detention pond experiments are carried out in parallel to verify the results of the numerical model. The conclusions are as follows: 1.According to the theoretical and experimental results, the discharge formula for a rectangular orifice and a spillway outlets is suggested as Q0=k1(H**1.5*(1-(1-hc/H)**1.5*U(H-hc))-h0**1.5*(1-(1-hc/h0)**1.5*U(h0-hc))) , where Q0 is the outlet discharge; k1=2/3*Cd*bc*(2*g)**0.5 , being the discharge hydrograph characteristic parameter; Cd is the discharge coefficient; g is the acceleration of gravity; bc is the width of outlet; hc is the height of outlet; H is the outlet water height; h0 is the base flow water height; U(H-hc) and U(h0-hc) are the unit step functions. 2.By using the Runge-Kutta numerical method together with the verification of the results from the detention pond experiments, the numerical model provides a way for flow predictions with various inflow hydrographs and different sizes of outlets. The good agreement between the predicted and experimental result shows the applicability of the proposed numerical method, which allows for accurate evaluation of flow discharge as a flood passes through a detention pond. 3.Based on the regressed equations (5-1) and (5-3), a normalized peak reduction factor (κ), associated with a rectangular discharge outlet, is obtained for cases with a triangular and a trapezoidal inflow hydrograph. In terms of the peak lag time, when the characteristic parameter (βe) of the triangular inflow hydrograph increases (or when the ratio between the recession time and the peak time of the triangular inflow increases), the lag time increases. On the other hand, as the characteristic parameter (γe) of trapezoidal inflow hydrograph becomes large, it results in a longer lag time due to an increase of the peak sustained inflow time. 4.Regarding the design of the minimum volume of the detention pond, the theoretical formula (3-30) and the empirical formula (5-2) are valid for cases with a triangular inflow hydrograph. For cases with a trapezoidal inflow hydrograph, on the other hand, the resulting dimensionless detention volume based on the theoretical equation (3-31) is about 15 to 75% larger than that from the empirical formula (5-4).
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