降雨引發坡地淺崩塌之區域性風險分析研究

Abstract

降雨引致之淺崩塌為常見之大規模天然災害之ㄧ。以格網點為計算單元並基於無限邊坡理論與可靠度分析所建立之邊坡穩定分析方法，由於具有根基於力學基礎且同時考量地質參數不確定性等優點，近年來已廣泛地應用於相關研究中(Baum et al. 2002)。然對於具數個格網點之分析區域而言，多數研究皆僅探討各格網點之可靠度而忽略鄰近格網點之影響，並無法定量地評估分析區域之整體崩塌潛勢，因此本研究將考慮各格網點間之空間相關性，以系統之觀點提出區域可靠度之分析方法。 依據蘇歆婷(2007)，本研究選定凝聚力、摩擦角、土壤飽和單位重與飽和水力傳導係數等為具不確定性之地質參數，並假設地質參數之空間變異性符合二階定常性且共變異函數為指數型態據以計算各地質參數在不同格網點間之相關係數。接著再以Tsai and Yang(2006)所發展之「降雨引發坡地淺崩塌定率評估模式」為基礎，配合一階二次矩法計算各格網點安全係數之統計特性，包含期望值、標準差與相關係數等。最後再假設安全係數之結合機率函數為多變量常態分佈，進一步利用串聯系統之概念求解坡地穩定之區域可靠度。 為了評估區域可靠度分析方法之正確性，本研究以假設之案例配合蒙地卡羅模擬進行測試。測試結果顯示無論地質參數之不確定性程度為何，安全係數之結合機率函數皆可合理地假設為屬於多變量常態分佈，且一階二次矩法與蒙地卡羅模擬所計算之區域可靠度差異不大，顯示本研究利用一階二次矩法評估區域性崩塌風險之合理性。 經測試後，本研究以石門水庫集水區進行實際案例之探討。模擬結果顯示，相較於傳統僅計算單一格網點可靠度之邊坡穩定分析方法，本研究所提出之區域可靠度因同時考慮區域內地質參數之空間變異性與各格網點可靠度之分散程度，故更能呈現區域整體之崩塌趨勢。此外，依據區域可靠度之不同，其亦可作為決策者擬定各區域治理工程優先順序之參考。

Rainfall-triggered shallow landslide is one of the major natural hazards. Recently, the infinite slope theory combining reliability analysis was widely applied to assess the grid-based regional slope stability (Baum et al. 2002). The advantages of above method are based on sound physical mechanic and accounting the uncertainties of hydrogeological parameters, simultaneously. However, for a specified region consisting of several grid points, most researches accounted for the slope reliability of each individual point, and ignored the influence of its neighboring points, thus, the overall landslide potential for whole region cannot be quantified. In this study, a framework to evaluate the regional reliability during rainstorm event is presented which explicitly incorporating the spatial correlation between each grid points. According to Su (2007), the cohesion, friction angle, unit weight of saturated soil, and saturated hydraulic conductivity are considered as the random hydrogeological parameters in this study. Based on the assumption that the spatial variability of random hydrogeological parameters are second-order stationary with exponential covariance function, the spatial correlation of uncertain parameters between each grid points inside the pre-specified region are accounted firstly. From the “Rainfall-Triggered Shallow Landslide Model” developed by Tsai and Yang (2006) along with the first-order second-moment method (FOSM), the statistical properties of safety factor (FS), including expectation, standard deviation, and correlation coefficients, are quantified. Furthermore, based on the assumption that the joint probability function for safety factors is multivariate normal distribution, the concept of “series system” is adopted to obtain the regional reliability (i.e. the reliability that all the grid points do not failure during rainstorm event). To examine the accuracy of proposed framework, a hypothetical example is utilized. The examination is conducted through the comparison of the regional reliability calculated by the proposed framework and Monte Carlo simulation (MCS). The results indicate that the multivariate normal distribution assumption of safety factors and the FOSM are applicable for risk assessment of landslide, regardless of the uncertainties degrees of hydrogeologic parameters. After the proposed framework has been examined, it is applied to the Shihmen reservoir watershed. From the application results, comparing with the traditional methods which determine the reliabilities for each individual grid points, the regional reliability is more suitable to assess the overall landslide potential for whole region because it incorporate the spatial variability of hydrogeological parameters and the spread of reliabilities among all the grid points simultaneously. Thus, the proposed framework could assist the engineers outline the management priorities for different regions according to various degrees of regional reliabilities.