一維未飽和坡地淺崩塌模式之整體敏感度分析

Abstract

本論文目的在針對Tsai and Chen (2010)所發展之「一維未飽和坡地淺崩塌模式」進行整體敏感度分析，以探討模式各項輸入條件在其變異範圍內變動時對邊坡安全係數之影響程度。研究中所考慮之模式輸入條件包含保水曲線參數、初始地下水位、坡度、土層厚度、有效凝聚力、有效摩擦角以及土壤比重等，其中坡度之變異係肇因於數值高程量測之隨機誤差，此隨機誤差除了與數值高程模型(Digital Elevation Model, DEM)之解析度有關外，亦受量測地點之地形影響，因此本研究考慮兩種台灣常見之DEM解析度(5 m與40 m)，並分別考慮在緩、中與陡等三種地形下總計六個案例。待獲得前述各項參數之統計資料分析後，本研究以艾利颱風48小時之降雨事件針對前述六個案例進行模擬，並利用變異數法與取樣法對模式輸出之孔隙水壓與安全係數做整體敏感度分析。六個案例之一階與全域敏感度指數分析結果皆顯示，參數彼此間之交互作用對模式輸出具有一定程度影響。孔隙水壓敏感度分析結果顯示，保水曲線參數變異性對孔隙水壓之影響隨累積降雨之增加而增加，而初始地下水位之變異性對孔隙水壓之影響隨累積降雨之增加而降低。另外在安全係數敏感度分析方面，保水曲線參數與初始地下水位對安全係數之影響皆隨累積雨量之增加而增加。此外，以5 m 以及40 m DEM解析度所計算之坡度其變異性對安全係數之影響以前者較高；而在相同DEM解析度下，地形越緩則坡度變異性對安全係數之影響越高。土層越深處之安全係數其受土層厚度變異性之影響越大，但土層越深處之安全係數其受凝聚力變異性之影響則越小。兩種整體敏感度分析之方法以及所有案例之分析結果皆顯示有效摩擦角之變異對安全係數之影響最大，而土壤比重之變異對安全係數之影響極小。

In this study, the global sensitivity analysis was performed to estimate the effect of model input variability on the output (pore pressure and safety factor, FS) of a one-dimensional unsaturated shallow landslide model. Seven model inputs, including the parameters in the water retention curve, initial groundwater level, slope angle, soil thickness, effective cohesion, effective friction angle, and specific weight of soil were considered and the sensitivity indexes between the model output and individual input variable were calculated based on the variance-based and sampling-based methods. The variability of slope angle results from the random error of the digital elevation model (DEM) which is influenced by the grid space of DEM and terrain surface characteristic. Thus, two DEMs with different grid space (5 m and 40 m) and three slopes with different characteristics (gentle, medium, and steep) were considered. The combination of the considered DEMs and terrain surface characteristics renders six cases to be analyzed in this study. For the sensitivity feature in pore water pressure, the analysis results showed that the importance of water retention curve parameters and initial groundwater level are increased and decreased, respectively, with the increase in accumulative rainfall depth. However, for the sensitivity feature in safety factor, the importance of water retention curve parameters and initial groundwater level are simultaneously increased with the increase in accumulative rainfall depth. The influence of slope angle variability on the safety factor in the case with 5 m grid space DEM is higher than that in the case with 40 m grid space DEM. For the cases with the same grid space of DEM, the importance of slope angle in gentle slope is always higher than that in steep slope. The analysis results among the six cases showed that the safety factor near the ground surface is significantly influenced by the effective cohesion variability. Besides, the effective friction angle is the most important input for rainfall triggered landslide modeling while the variability of specific weight of soil could be neglected