第七章 結論與建議
7.2 建議
1. 本研究分析結果土層內部側向水流動具有明顯影響崩塌發生，目前模式 尚未考量地表側向(y 方向)與地下水側向(y 方向)水理模擬，未來可朝向 地表二維結合地下水三維模式邁進。
2. 由敏感度分析可知，參數之不確定性因素對坡地崩塌影響甚大，如單純 以安全係數做為坡地崩塌判釋，可能因不確定因素造成判釋誤差，未來 可對崩塌模式進行可靠度分析，藉以使判釋標準整合參數不確定性因 素。
3. 模式目前未對坡面上張力裂縫納入分析，未來可嘗試將該因素納入崩塌 模式分析。
4. 模式尚未計算土體間施加應力後形變之問題，未來可朝整合應力應變方 程式納入崩塌模式分析。
5. 對於局部破壞機制，地下水滲流攜出土壤顆粒造成之管湧現象，未來可 嘗試探討其生成力學機制，將此現象納入模式運算。
6. 目前模式未納入植物根系對土壤強度之效應，以及坡面或坡址上之保護 工程與擋土牆所增加抗滑能力，未來可納入分析考量，期使模式更接近 實際情況。
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附錄 A 降雨引致淺崩塌分析模式(一維飽和模式)
Tsai and Yang (2006)所發展之降雨引致淺崩塌分析模式，可做為預測坡地在 降雨過程中是否發生崩塌之分析工具，該模式亦已成功應用於石門水庫集水區坡 地淺崩塌之模擬(楊錦釧等 2008)。模式係利用莫爾庫侖理論所發展之無限邊坡穩
定分析，配合時變壓力水頭之計算即可估計降雨入滲是否引發崩塌，圖A.1 為其
示意圖。安全係數計算方式可表示如下：
( , ) tan tan
tan sin cos sin cos
w
sat sat
Z t c
FS Z Z
(A.1)其中
FS 為安全係數，FS < 1 表示坡地將發生崩塌，反之則表示坡地處於穩
定狀態。t 為時間(T)；Z 為垂向深度(L)；(Z,t)為第 t 時刻位於地表下方 Z 公尺處 之壓力水頭(pressure head)(L)；為土壤摩擦角度(friction angle)；c 為土壤凝聚力 (cohesion)；為坡度(slope angle)；γw與γ
sat則分別代表地下水與飽和土壤之單位 重(unit weight)。圖 A.1 降雨入滲引發淺崩塌示意圖
在式(A.1)中壓力水頭之計算方面，假設土壤趨於飽和，坡地因降雨而產生入
滲之控制方程式(Iverson, 2000)可表示為
其中
I
Z為降雨強度(rainfall intensity) (LT-1)；Td為降雨延時(rainfall duration) (T)。在數值方法上，Tsai and Yang (2006)利用有限元素法求解式(A.2)。先假設降
雨完全入滲，也就是入滲能力大於降雨強度，利用式(A.5)計算壓力水頭分佈，若 地表面之壓力水頭小於或等於零(
(0, ) 0 t
)，表示完全入滲之假設正確並計算下 一個時距；然而若地表面之壓力水頭大於零( (0, ) 0 t
)，表示產生窪蓄現象 (ponding)，即入滲能力小於降雨強度，在不考慮窪蓄造成漫地流(overland flow) 水深影響下，改變地表邊界條件，令地表面之壓力水頭為零，如式(A.6)所示，再 進行壓力水頭分佈之計算。附錄 B 降雨引致未飽和坡地淺崩塌一維模式
Tsai et. al. (2008)利用有限差分法建立坡地降雨入滲模擬方法，並考量 地表窪蓄效應之影響，再將各時刻模擬結果之孔隙壓力分佈，引入無限邊 坡穩定分析之用，計算坡地是否崩塌，模式整體計算流程如圖B.1。
圖B.1 模式計算流程圖 坡地降雨入滲模擬
根據Richards 方程式，三維坡地地下水流之控制方程式(Hurley and Pantelis, 1985)可表示為
式中，
為含水量(moisture content)； 為壓力水頭(pressure head)；
為坡地之坡度；t 表示時間；x、y 及 z 表示空間座標；
K
L與K
z分別表示在 x、y 及 z 方向之水力傳導係數，且為壓力水頭之函數。
在降雨引發淺崩塌(shallow landslide)之假設下，若坡地可能發生崩塌之 深度遠小於坡地之長度與寬度，且降雨延時遠小於孔隙水在
x y
方向之傳輸 時間(Iverson, 2000)，(B.1))式可進一步簡化為( ) cos( )
求 解(B.2) 式 需 要 適 當 之 初 始 條 件 (initial condition) 以 及 邊 界 條 件 (boundary condition)。如圖 B.2 所示，初始時，坡地之穩態水流平行坡面，
且地下水位距離坡面下
z d
處，則初始之壓力水頭可表示為降雨過後，坡面再無水流入滲，所以坡面之邊界條件變為零流邊界
也就是保水曲線(water retention curve)。本研究採用 Van Genuchten (1980)所 提出之飽和度與壓力水頭和水力傳導係數間的關係式，如下所示
其中，s為飽和含水量(saturated moisture content)，r為殘餘含水量(residual moisture content)，
K
s為飽和水力傳導係數(saturated hydraulic conductivity)， 為進氣潛能因子(empirical parameter of air entry value)，
N
為孔徑指數(pore index)，M
為曲線密合因子(curve fitting parameter)，M
、N
之關係為1, 1 1, 1 1, 1
m m
MAXERROR
(B.15)此外，邊界條件與初始條件，可離散化如下: