數種不確定性分析方法於降雨引發坡地淺崩塌模式之比較研究

Abstract

降雨引發之坡地淺崩塌常造成大規模之天然災害，以無限邊坡理論建立之數值模式已廣泛地應用於評估坡地是否會因降雨而發生崩塌，然全面而完整之參數資料獲得不易導致參數具有不確定性(uncertainty)，其不確定性可能會影響崩塌模式模擬結果。本論文以Tsai and Yang (2006)所發展之「降雨引發坡地淺崩塌模式」為基礎，將飽和水力傳導係數(Ksat)、土壤內摩擦角(□)、土壤凝聚力(c)、初始地下水位(dZ)、土壤厚度(dLZ)與坡度(α)等六項輸入條件視為具不確定性之隨機變數，並利用石門水庫集水區砂崙仔崩塌地之實際案例，以一階二次矩法(first-order second-moment method, FOSM)、Rosenblueth’s點估計法(Rosenblueth point estimation method, R-PE)、Li’s點估計法(Li point estimation method, LI-PE)等近似法進行不確定性分析以獲得模式輸出(安全係數值)之統計特性以及艾利颱風期間坡地之崩塌機率，並將近似法結果與蒙地卡羅模擬(Monte Carlo Simulation, MCS)結果進行比較，予以探討各種方法之適用性。為了解近似法在不同輸入條件不確定性程度下，與蒙地卡羅模擬之差異，本論文共設計了六個不同輸入條件不確定性程度之案例，此六個案例涵蓋了坡地緩陡與DEM解析度差異等因素。分析結果顯示各種近似法應用於降雨引發坡地淺崩塌之不確定性分析時，皆有其優點與缺點，就崩塌機率推估之準確性而言，Rosenblueth’s與Li’s點估計法所推估之崩塌機率在六個案例中皆與蒙地卡羅模擬法無明顯差異，而在輸入條件不確定性程度較高之案例中，一階二次矩法則有顯著之誤差，惟其所推估之崩塌機率在六個案例中皆較蒙地卡羅模擬法高，以管理之角度而言，一階二次矩法之計算結果較為保守；另外就計算效率而言，一階二次矩法具有最高之計算效率，估算單一格網崩塌機率時僅需執行崩塌模式9次，而Rosenblueth’s與Li’s點估計法則分別須執行崩塌模式16次與15次；最後就不確定性分析事前所需資料而言，一階二次矩法僅需具備輸入條件之前二階動差，而Rosenblueth’s與Li’s點估計法則分別需要輸入條件之前三階與前四階動差。綜合上述分析結果可知，各種不確定性近似分析方法有其適用條件，對於大範圍集水區坡地崩塌機率分布之推估而言，通常無法獲得全面之輸入條件調查資料，且範圍較大計算格網數多，因此資料需求少、計算快速且分析結果較保守之一階二次矩法較為適用；而對於小範圍特定坡地之崩塌機率分析而言，較可能進行詳細之輸入條件調查工作，且計算格網少較無計算時間之考量，因此適用崩塌機率計算結果較為準確之Rosenblueth’s或Li’s點估計法。

Rainfall-triggered shallow landslide is one of the major natural disasters over the world which may immediately cause large numbers of casualties and huge economic losses. To mitigate the landslide disasters, the numerical model simulations based on the infinite slope theory have been widely applied to predict the slope stability during a rainfall event. However, due to the inherent heterogeneity and lack of complete information about model input variables, uncertainties exist in specifying the values of these variables in the numerical model rendering potential failure to obtain the authentic model output (safety factor, FS) for the slope under consideration. In this study, three approximated uncertainty analysis methods, including the first-order second-moment (FOSM), Rosenblueth’s point estimation (R-PE), and Li’s point estimation (LI-PE) were utilized with the developed rainfall triggered shallow landslide model (Tsai and Yang, 2006) to obtain the statistical properties of FS and the landslide probability (Pf) at the Salunzai slope during typhoon Aere. Besides, the relative errors of computed Pf with respect to Monte Carlo simulation (MCS) result were compared. Six stochastic model input variables, including the saturated hydraulic conductivity (Ksat), friction angle (□), cohesion (c), initial groundwater depth (dZ), soil thickness (dLZ), and slope (α) were considered. Moreover, six cases involving different uncertainty levels of slope angle and soil thickness were considered. The results showed that each of the three approximated methods has its own advantages and drawbacks for the uncertainty analysis of rainfall triggered shallow landslide model. The performances of the approximated uncertainty analysis methods were evaluated through three criteria including: (1) accuracy; (2) efficiency; and (3) prior information requirements. For the accuracy of the approximated methods, the differences in obtained landslide probability between the point estimation (Rosenblueth’s and Li’s) and MCS are minimal in all of the six cases. However, the FOSM method tends to significantly overestimate the landslide probability especially in the case with higher model inputs uncertainties. In contrast to accuracy, the FOSM method has highest computational efficiency because the required number of numerical model evaluation in one simulation grid is 9, while the Rosenblueth’s and Li’s point estimation methods require 16 and 15 model evaluations, respectively. In view of the prior information requirement, the FOSM method only requires the first two moments of the stochastic model input variables while the Rosenblueth’s and Li’s point estimation methods require the first three and four moments of model inputs, respectively. In summary, the applicability of the three approximated uncertainty analysis methods for rainfall-triggered shallow landslide model depend on the space scale of the application. For the estimation of the distributions of the landslide probabilities within a watershed, the third and fourth moments of stochastic model inputs might not be reliably obtained, besides, the amounts of simulation grids might be huge, thus the FOSM method is more applicable than the Rosenblueth’s and Li’s point estimation methods. In contrast, for the estimation of landslide probability at a specified slope, the third and fourth moments of stochastic model inputs might be reliably through a more comprehensive field investigation, thus the Rosenblueth’s and Li’s point estimation methods are more applicable due to the higher accuracy.