邊坡穩定性及邊坡變形是一個動態變化過程，在現階段針對邊坡地質災害的研究主要分為兩種極端，一種是套用確定、靜態模式方法，主要是極限平衡法和彈塑性數值分析方法(如有限元素法等)，只能考慮瞬間的邊坡穩定狀態，沒有考慮時間因素；另一種則是透過監測方法收集數據資料，利用齋藤法等模式來預測邊坡破壞時間，雖然有考慮時間因素，但並非所有邊坡都適用此模式，無法針對差異性加以定性、定量，因此，迫切需要研究具有變形時效實際意義的邊坡穩定性評價方法、邊坡失穩預測預報方法以及邊坡變形分析理論等。
本研究即是以「邊坡位移時間序列」資料為出發點，來重新建構邊坡系統發展之變化特徵與趨勢，並預測邊坡位移及破壞可能時間點。邊坡位移在時間軸上可視為一非線性動力系統，位移序列是一個非線性動態行為，因此描述邊坡位移的動態行為可更完整瞭解邊坡演化至破壞的特性。本研究主要是利用Hurst(1965)提出的R/S分析法(Rescaled Range Analysis)與BDS檢定方式(獨立一致性檢定)，來判斷邊坡位移資料的基本特性，檢視是否對應邊坡位移物理量之原始特徵，再者為了後續邊坡預測分析模式的選擇，利用切線角法與加卸載響應比(Load and Unload Response Ratio，簡稱LURR )理論來判斷邊坡變形階段；另外在論文中亦引用混沌理論，透過計算Lyapunov exponent、相關維度等特徵量來探討邊坡非線性動力系統之相關特性與動態行為，並利用混沌時間序列預測模型及非線性時間序列預測法之結果來比較。而本研究最終目的則是希望藉由這些分析過程建立預測與預報邊坡破壞之時間，進而達成防災與管理之目標。
本研究以梨山地滑區的案例來進行一系列的分析與建模，發現此地滑區的六個滑坡體(主要在東南區)滑動變形過程互異，不過均處於初始變形階段，透過統計分析發現其位移的產生過程具有長期記憶效應，且均具有非線性結構，但混沌效應不一(B1、B9與C1滑坡體存在弱混沌，其餘則無)，綜合滑坡體的演化特性定量判斷之後，以B1與B4滑坡體為例，選擇適當的預測模式來預測後續位移量變化，位移量的變化幅度不大，邊坡狀態均維持相同情況(初始變形階段)。

Slope stability problem involved multiple aspects is a complex nonlinear dynamic system under the influence of geological conditions, underground water, earthquake, and human activities etc. The key feature of slope failure mechanism is so complexity that it is very difficult to predict the tendency of landslide or hazard. With developing of the non-linear science such as chaos theory and fractal theory, whole new theory and methods are offered a powerful theoretical basis for study the non-linear problems in slope instability.

We have presented a general framework to perform the thinking based the non-linear science. In this study, we just only need one kind of data which is collected from in-situ monitoring. Displacement time series contained extensive information of slope deformation process is a kind of monitoring data which we can easily get. It is significant to acquire slope failure evolution information and build predicting model. In order to make the most of monitoring data and obtain useful information from it so we can make some valuable prediction. This study may lead to a better understanding of characteristics mechanism in slope natural system.

Therefore, the aim of this dissertation attempts to explore how to use one variable data (displacement) to reveal slope failure mechanism related the deformation process by non-linear dynamic methods. To address this issue, a series procedure was conducted. This research involved a lot of analyses conclude time series analysis (R/S method and BDS statistical testing), the quantitative determination of slope deformation stages, chaotic effect analysis and prediction models proposed. According to chaos theory, the phase reconstruction of time series is performed. The chaotic invariants of measured time series of Li-San landslide such as correlation dimension, the Lyapunov exponent are calculated. The results show that the monitoring data obtained in Li-San landslide (B1, B9 and C1) is a chaotic time series; in Li-San landslide (B4, B5 and B13) is non-linear time series. In consideration of the chaotic character and non-linear of displacement time series, then the prediction models that fit for landslide displacement time series were built, which provide new method for landslide prediction. The results are valuable but future work is obviously required.

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