第四章 沖刷機制探討與敏感度分析
4.2 遷急點沖刷機制探討
4.2.1 模擬條件
本研究之遷急點沖刷機制（式 3-14），係根據各計算點之縱坡度
（S）與臨界坡度（Scr）關係，修正因遷急點後退所造成之額外沖刷 量，以反映遷急點後退過程。式中 Scr為決定遷急點沖刷是否啟動之 門檻坡度，因此該臨界坡度之大小將影響模擬結果。本研究以一具有 突降高程落差之規則矩形渠道進行模擬測試，藉由改變 Scr瞭解遷急 點沖刷發生時，遷急段底床之變化關係，以供後續模式應用參考。
假設一規則矩形渠道，長 50 m、寬 4 m，初始底床遷急段之上下 游高程差為 0.21 m、遷急段之初始坡度（S）為 0.03，入流量固定為 1 m3/s，為清水沖刷，下游水位為均勻流流況，底床假設全為可沖刷 之軟岩河床，遷急點後退臨界坡度（Scr）設定範圍自 0.1 ~ 0.001，開 啟遷急點沖刷模組進行模擬，模擬時間為 1,500 秒。
4.2.2 模擬成果
圖 4-31(a)為不同時間之模擬底床縱剖面比較圖（Scr = 0.1），由於 模擬過程遷急段底床之坡度 S < Scr，不滿足遷急點沖刷啟動條件，隨 著模擬時間增加，軟岩底床有均勻沖刷情形，無遷急點後退加速沖 刷，沖刷量較不明顯。圖 4-31(b)為設定 Scr = 0.01 之底床縱剖面模擬 結果，模擬過程遷急段之底床坡度達啟動條件，隨著時間增加有遷急 點沖刷情形產生，由於本案例假設底床全為均質可沖刷，模擬底床符 合 Gardner（1983）所提出之替換型（replacement）遷急點變化形式，
如圖 1-6 所示。以同樣模擬時間 T = 500s 觀察，考慮一般沖刷機制時，
於遷急點與初始底床縱方向之後退距離 Lk約為 2 m，有遷急點機制者 Lk將增加為 7 m。
當底床為極易發生遷急點沖刷材質，假設 Scr = 0.001，模擬底床 縱剖面變化如圖 4-31(c)所示。由於遷急點沖刷發生之門檻較低，因 此當遷急段坡度略大於 Scr時，底床即發生遷急點沖刷，產生傾角型
（inclination）遷急點變化形式，導致模擬終了之整體沖刷量大增。
該結果說明本研究所採用之臨界坡度判斷理論，可反映不同坡度特徵 之遷急點沖刷過程。
表 4-1 run24 案例格網密度敏感度分析格網尺寸表 Cases Mesh number Mesh size (m)
Length Width Length Wide Case1 (loose mesh) 29 17 0.61 0.0375 Case2 (normal mesh) 57 17 0.305 0.0375 Case3 (fine mesh) 113 17 0.152 0.0375
0.1
Distance from downstream boundary (m)
initial bed_t=0 hr measured bed_t=1 hr simulated bed_t=1hr measured water level_t=1hr simulated water level_t=1hr
圖 4-1 輸砂模組模擬底床高程縱剖面比較圖(t=1hr)
Distance from downstream boundary (m)
initial bed_t=0 hr measured bed_t=4.5 hr simulated bed_t=4.5hr
Distance from downstreamboundary (m)
initial bed_t=0 hr measured bed_t=10 hr simulated bed_t=10hr
圖 4-3 輸砂模組模擬底床高程縱剖面比較圖(t=10hr)
-0.08 -0.06 -0.03 -0.01 0.02
2 4 6 8 10 12 14 16
Bed change(m)
Distance from downstream boundary (m)
measured dz_t=1hr simulated dz_t=1hr
圖 4-4 輸砂模組模擬底床沖淤變化縱剖面比較圖(t=1hr)
-0.08 -0.06 -0.03 -0.01 0.02
2 4 6 8 10 12 14 16
Bed change(m)
Distance from downstream boundary (m)
measured dz_t=4.5hr simulated dz_t=4.5hr
圖 4-5 輸砂模組模擬底床沖淤變化縱剖面比較圖(t=4.5hr)
-0.08 -0.06 -0.03 -0.01 0.02
2 4 6 8 10 12 14 16
Bed change(m)
Distance from downstream boundary (m)
measured dz_t=10hr simulated dz_t=10hr
圖 4-6 輸砂模組模擬底床沖淤變化縱剖面比較圖(t=10hr)
-0.10 -0.05 0.00 0.05
-0.10 -0.05 0.00 0.05
Measured bed changes (m)
Simulated bed changes (m)
t=1hr t=4.5hr t=10hr
圖 4-7 輸砂模組模擬與實測底床變化誤差分析比較圖
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.2 0.3 0.4 0.5
2 4 6 8 10 12 14 16
V el oc ity (m )
B ed e le va tio n (E L. m )
Distance from downstream boundary (m)
initial bed_t=0 hr
measured bed_t=10 hr simulated bed_t=10hr simulated velocity_t=1hr simulated velocity_t=2hr simulated velocity_t=3hr simulated velocity_t=4.5hr simulated velocity_t=10hr
圖 4-8 輸砂模組不同時刻流速與底床高程縱剖面圖
0.20 0.22 0.24 0.26 0.28 0.30 0.32
2 4 6 8 10 12 14 16
B ed e le va tio n (E L. m )
Distance from downstream boundary (m)
initial bed_t=0 hr simulated bed_t=1hr simulated bed_t=4.5hr simulated bed_t=10hr
圖 4-9 岩床模組模擬底床高程縱剖面比較圖
0
Cumulative erosion depth(m)
Time (hr)
Erosion depth and velocity vary with time at CS11
Erosion depth (alluvial module) Erosion depth (bedrock module) Velocity
Cumulative erosion depth(m)
Time (hr)
Erosion depth and velocity vary with time at CS21
Erosion depth (alluvial module) Erosion depth (bedrock module) Velocity
Cumulative erosion depth(m)
Time (hr)
Erosion depth and velocity vary with time at CS41
Erosion depth (alluvial module) Erosion depth (bedrock module) Velocity
圖 4-12 底床累積沖刷深度與流速逐時變化圖(CS41 位置)
0.15
Distance from downstream boundary (m) initial bed_t=0 hr
measured bed_t=1 hr
simulated bed_t=1hr (Em=0.000625m) simulated bed_t=1hr (Em=0.00125m) simulated bed_t=1hr (Em=0.0025m)
圖 4-13 輸砂模組作用層厚度敏感度分析比較圖(t=1hr)
Distance from downstream boundary (m) initial bed_t=0 hr
measured bed_t=4.5 hr
simulated bed_t=4.5hr (Em=0.000625m) simulated bed_t=4.5hr (Em=0.00125m) simulated bed_t=4.5hr (Em=0.0025m)
圖 4-14 輸砂模組作用層厚度敏感度分析比較圖(t=4.5hr)
Distance from upstream to downstream (m) initial bed_t=0 hr
measured bed_t=10 hr
simulated bed_t=10hr (Em=0.000625m) simulated bed_t=10hr (Em=0.00125m) simulated bed_t=10hr (Em=0.0025m)
-0.10 -0.05 0.00 0.05
2 4 6 8 10 12 14 16
Bed change(m)
Distance from downstream boundary (m) measured dz_t=1hr
simulated dz_t=1hr (Em=0.000625m) simulated dz_t=1hr (Em=0.00125m) simulated dz_t=1hr (Em=0.0025m)
圖 4-16 輸砂模組作用層厚度敏感度分析比較圖(t=1hr)
-0.10 -0.05 0.00 0.05
2 4 6 8 10 12 14 16
Bed change(m)
Distance from downstreamboundary (m)
measured dz_t=4.5hr
simulated dz_t=4.5hr (Em=0.000625m) simulated dz_t=4.5hr (Em=0.00125m) simulated dz_t=4.5hr (Em=0.0025m)
圖 4-17 輸砂模組作用層厚度敏感度分析比較圖(t=4.5hr)
-0.10 -0.05 0.00 0.05
2 4 6 8 10 12 14 16
Bed change(m)
Distance from downstream boundary (m) measured dz_t=10hr
simulated dz_t=10hr (Em=0.000625m) simulated dz_t=10hr (Em=0.00125m) simulated dz_t=10hr (Em=0.0025m)
圖 4-18 輸砂模組作用層厚度敏感度分析比較圖(t=10hr)
0.20 0.22 0.24 0.26 0.28 0.30 0.32
2 4 6 8 10 12 14 16
B ed e le va tio n (E L. m )
Distance from downstream boundary (m)
initial bed_t=0 hr
simulated bed_t=1hr (Kp=0.5e-6) simulated bed_t=1hr (Kp=1.0e-6) simulated bed_t=1hr (Kp=2.5e-6) simulated bed_t=1hr (Kp=5.0e-6) simulated bed_t=10hr (Kp=0.5e-6)
圖 4-19 岩床模組無因次沖蝕係數(Kp)敏感度分析比較圖
0.20 0.22 0.24 0.26 0.28 0.30 0.32
2 4 6 8 10 12 14 16
B ed e le va tio n (E L. m )
Distance from downstreamboundary (m)
initial bed_t=0 hr
simulated bed_t=1hr (Kh=5.3764e-6) simulated bed_t=1hr (Kh=5.3764e-7) simulated bed_t=1hr (Kh=5.3764e-8) simulated bed_t=1hr (Kh=5.3764e-9)
圖 4-20 岩床模組沖蝕指數(Kh)敏感度分析比較圖
0.12
Bed elevation varies with time at CS21 (Kh=5.3764e-9)
Kp=0.5e-6
Bed elevation varies with time at CS21 (Kp=2.5e-6)
Kh=5.3764e-6 Kh=5.3764e-7 Kh=5.3764e-8 Kh=5.3764e-9
圖 4-22 沖蝕指數 Kh敏感度分析底床高程逐時變化圖
-0.08
Distance from downstream boundary (m) measured dz_t=1hr
simulated dz_t=1hr (normal mesh) simulated dz_t=1hr (fine mesh) simulated dz_t=1hr (loose mesh)
圖 4-23 不同格網密度模擬底床沖淤變化縱剖面比較圖(t=1hr)
Distance from downstream boundary (m)
measured dz_t=4.5hr
simulated dz_t=4.5hr (normal mesh) simulated dz_t=4.5hr (fine mesh) simulated dz_t=4.5hr (loose mesh)
圖 4-24 不同格網密度模擬底床沖淤變化縱剖面比較圖(t=4.5hr)
Distance from downstream boundary (m)
measured dz_t=10hr
simulated dz_t=10hr (normal mesh) simulated dz_t=10hr (fine mesh) simulated dz_t=10hr (loose mesh)
圖 4-25 不同格網密度模擬底床沖淤變化縱剖面比較圖(t=10hr)
-0.10 -0.05 0.00 0.05
-0.10 -0.05 0.00 0.05
Measured bed changes (m)
Simulated bed changes (m) loose mesh (29x17)
圖 4-26 疏格網模擬與實測底床變化誤差分析比較圖
-0.10 -0.05 0.00 0.05
-0.10 -0.05 0.00 0.05
Measured bed changes (m)
Simulated bed changes (m) normal mesh (57x17)
圖 4-27 一般格網模擬與實測底床變化誤差分析比較圖
-0.10 -0.05 0.00 0.05
-0.10 -0.05 0.00 0.05
Measured bed changes (m)
Simulated bed changes (m) fine mesh (113x17)
圖 4-28 密格網模擬與實測底床變化誤差分析比較圖
0.20 0.22 0.24 0.26 0.28 0.30 0.32
2 4 6 8 10 12 14 16
Bed elevation(EL.m)
Distance from downstream boundary (m)
initial bed_t=0hr
simulated bed_t=1hr (loose mesh) simulated bed_t=4.5hr (loose mesh) simulated bed_t=10hr (loose mesh) simulated bed_t=1hr (normal mesh) simulated bed_t=4.5hr (normal mesh) simulated bed_t=10hr (normal mesh)
圖 4-29 岩床模組以不同格網密度模擬底床高程縱剖面比較圖 1
0.20 0.22 0.24 0.26 0.28 0.30 0.32
2 4 6 8 10 12 14 16
Bed elevation(EL.m)
Distance from downstream boundary (m)
initial bed_t=0hr
simulated bed_t=1hr (fine mesh) simulated bed_t=4.5hr (fine mesh) simulated bed_t=10hr (fine mesh) simulated bed_t=1hr (normal mesh) simulated bed_t=4.5hr (normal mesh) simulated bed_t=10hr (normal mesh)
圖 4-30 岩床模組以不同格網密度模擬底床高程縱剖面比較圖 2
0.35
Bed elevation (m)
Initial bed
Bed elevation (m)
(b) Scr= 0.01
Bed elevation (m)
Distance from downstream (m)
(c) Scr= 0.001
Lk = 4 m, Ld = 0.0888 m
圖 4-31 遷急點沖刷案例模擬底床縱剖面圖(Lk為遷急點後退距離、