A Study on Slope Stability Analysis Using Shear Strength Reduction Technique

分析邊坡穩定問題，基本上可分為二種方法，其一為與土壤應變行為無任何關連之極限平衡方法(Bishop, 1955; Morgenstern and Price, 1965; Spencer, 1967; Janbu, 1973)，另則為採用土壤應力應變關係之數值分析方法(Brown and King, 1966; Dunlop and Duncan, 1970; Wright等人, 1973; Giam and Donald, 1988; Huang and Yamasaki, 1993; Zou等人, 1995)。極限平衡方法之所以能為工程界所接受並加以使用，主要是簡易且可得到不錯之結果，但其基本上都存在有極限狀態簡化假設之缺失(Wright等人, 1973)。隨著有限元素方法與電腦的快速發展，對於已知邊坡的材料性質及幾何形狀，利用應力應變分析方法計算出坡體內之應力與應變後分析其變形及安全性已並無困難。有限元素法與傳統極限平衡法相比較，其主要優點為無需預先假設切片間的側向力與破壞面的形狀或位置，破壞自然地發生在土壤的抗剪強度不能抵抗其剪應力的地帶(Wong, 1984)。 至於將有限元素分析結果轉換為安全係數值，主要也有兩類程序，其一為針對潛在破壞面考量其作用應力(Wright el al., 1973; Giam and Donald, 1988; Huang and Yamasaki, 1993)，另則為剪力強度折減技巧(Zienkiewicz等人, 1975; Donald and Giam, 1988; Ugai, 1989; Matsui and San, 1992; Griffiths and Lane, 1999; Manzari and Nour, 2000)。前者一般採用與極限平衡法相同之搜尋程序，須藉由分析所得之應力狀態再進一步進行更多的滑動面搜尋，安全係數定義為滑動面上所提供的剪力強度與作用剪應力總和之比值，而相應最小安全係數之滑動面則為臨界滑動面。嚴格來說，此分析方法較優於傳統極限平衡方法在於能夠提供可靠邊坡之應力狀態。 Duncan (1996)指出邊坡穩定安全係數可視為將土壤剪力強度降低至邊坡達到破壞之因子，因此配合數值分析方法，利用剪力強度折減技巧逐漸降低土壤剪力強度直到產生破壞為止，則此降低因子即為安全係數。以剪力強度折減技巧評估邊坡破壞方式有節點位移法(Donald and Giam, 1988)與數值解的非收斂性方法(Griffiths and Lane, 1999)。相較於傳統極限平衡方法，此分析方法不必經由繁雜之邊坡破壞面搜尋程序以求取安全係數與相應之滑動面，可透過為數不多的剪力強度折減階段，直接求得邊坡之安全係數。然而在判斷邊坡發生破壞時，從變位與剪力強度折減因子曲線中，無法完全描述轉折點之位置，亦即無法明確決定安全係數之臨界值。 本研究提出一種利用剪力強度折減因子之有限元素方法，配合破壞準則的定義及計算結果圖顯塑性區生成的方式，尋求邊坡臨界滑動面與相應之安全係數。以Drucker-Prager非線性應力應變關係之彈塑性有限元素法進行邊坡內之有效應力計算，塑性變形為一非關連流動準則；採一次填築方式形成邊坡，而土層自重則是以節點作用力方式一次施加完成，並基於Mohr-Coulomb破壞準則來估算土壤的剪力強度。當邊坡內部之降伏區擴展形成一完整滑動面時，則認定此時之邊坡已達破壞，而其相應之強度折減因子SRF即為邊坡穩定之安全係數。本研究方法可明確地決定邊坡之破壞與其漸進破壞過程，所獲得之臨界滑動面並非唯一，而是一狹窄之屈伏帶，所有經由此區域之滑動面均可視為邊坡之滑動面。研究結果顯示，本研究方法所獲得之安全係數與Bishop簡化法及Spencer切片法有良好之關連性，惟本研究方法可提供設計者在邊坡穩定分析上較多之實質性基本觀念。In the stability analysis of soil slopes, there are basically two deterministic approaches. The first is the limit equilibrium method (Bishop, 1955; Morgenstern and Price, 1965; Spencer, 1967; Janbu, 1973) and the second is stress-strain analysis (Brown and King, 1966; Dunlop and Duncan, 1970; Wright et al., 1973; Giam and Donald, 1988; Huang and Yamasaki, 1993; Zou et al., 1995). The limit equilibrium method is concerned with limit state analysis and has received wide acceptance because of its simplicity. However, this method has some theoretical shortcomings (Wright el al., 1973). With the advent of the finite element technique and powerful computers, given the material properties and the geometry of the slope, it is not difficult to analyze the soil slope for deformation and safety by computing the stress and strain in the slope using stress-strain analysis. The main advantages of the finite element approach to slope stability analysis over the traditional limit equilibrium method are that no assumption needs to be made in advance about slice side forces, or the location or shape of the slip surface. Failure occurs “naturally” through the zones within the soil slope in which the soil shear strength is unable to sustain the acting shear stresses (Wong, 1984). As for the attempt to convert the finite element analysis into a safety factor calculation, there are mainly two types of procedure. One is the consideration of stress level on the potential failure surface (Wright el al., 1973; Giam and Donald, 1988; Huang and Yamasaki, 1993). The other is the strength reduction technique (Zienkiewicz, et al. 1975; Donald and Giam, 1988; Ugai, 1989; Matsui and San, 1992; Griffiths and Lane, 1999; Manzari and Nour, 2000). In the former, a searching scheme as commonly adopted in the limit equilibrium method is needed to search for many slip surfaces through analysis of stress states. The safety factor is defined as the ratio of the sum of the shear strength available to the shear stress acting over the slip surface. The critical slip surface is the one corresponding to the minimum safety factor value. In a strict sense, the merits of this method over the traditional limit equilibrium method lie in the reliable estimation of stress states in the soil slope. In the strength reduction technique, the original shear strength parameters are divided in order to bring the slope to failure (Duncan, 1996). The evaluation of slope failure may use the bulging extended through the verge of instability localized in a narrow zone of the deformed shape (Donald and Giam, 1988) or non-convergence of the solution in a mathematical manner (Griffiths and Lane, 1999). Compared with the former method, only limited steps of analysis are needed to determine the critical slip surface and the corresponding safety factor using the strength reduction technique. However, the sharp bend of displacement in the instability region near the failure site may continue for several steps during the reduction process of shear strength for the existing procedure. There will be no perfectly delineated break-off point in the curve of displacement versus strength reduction factor (SRF) for determining the critical value of safety factor. In this study, an approach using the strength reduction technique of finite element analysis, with the provision of a failure criterion, and incorporation of graphical output, to examine the failure zone developed, was used in order to determine the slope failure and the corresponding safety factor. The state of the effective stresses in a slope is calculated by the finite element method using eight-node quadrilateral elements of elastic-plastic soil with the Drucker-Prager nonlinear stress-strain relationship and a nonassociated flow rule. The soil's self-weight is modeled by a gravity “turn-on” procedure (Smith and Griffiths, 1988) with nodal loads added in a single increment. The shear strength of soil is estimated based on the Mohr-Coulomb failure criterion. Slope failure occurs when the yield zone spreads over the entire slip surface and the corresponding SRF is the safety factor of the soil slope. The slope failure could be clearly defined and progressive failure was also observed. It should be kept in mind that the critical slip surface is not unique. A narrow yielding zone was developed when the slope started to fail and any slip surface passing through the yield zone could be the failure surface. The factor of safety obtained by the proposed procedure is in good agreement with that determined by Bishop's and Spencer's methods. However, the proposed procedure can provide the designers a more solidly based concept in slope stability analysis.誌謝 I 摘要 II 英文摘要 IV 目錄 VI 表目錄 X 圖目錄 XI 符號說明 XVI 第一章 緒論 1 1.1 前言 1 1.2 研究動機 3 1.3 研究方法 4 1.4 內容編排及研究流程 6 第二章 前人相關研究 8 2.1 極限平衡法 8 2.1.1 滑動面之搜尋程序 19 2.2 極限分析方法 22 2.3 有限元素分析方法 24 2.3.1 應力─應變分析方法 25 2.3.2 剪力強度折減方法 28 第三章 剪力強度折減之彈塑性有限元素分析模式 30 3.1 剪力強度折減技巧 30 3.2 黏塑性有限元素法簡介 32 3.2.1 黏塑性 32 3.2.2黏塑性應變增量 33 3.2.3應力增量 34 3.2.4 平衡方程式 34 3.2.5時間步長的決定 35 3.3 強度驅動率的定義 36 3.4 邊坡破壞及臨界滑動面的認定 38 3.5 土壤的組構模式 41 3.6 土壤模型及邊坡形成 43 第四章 二維度邊坡穩定範例分析 45 4.1邊坡範例驗證 45 4.2 邊坡範例進一步分析應用 51 4.2.1承受水平地震力作用 51 4.2.2 定額比例孔隙水壓力的作用 53 4.2.3 自由水面與蓄水加載的情況 55 4.2.4 非均質邊坡的情況 64 4.3 雙邊土堤分析 67 4.4 土壤膨脹性之影響 69 4.4.1 土壤膨脹性簡介 69 4.4.2 膨脹角對安全係數的影響 69 4.5 強度參數對邊坡穩定之影響 78 4.5.1 1:1土壤邊坡 80 4.5.2 1:2土壤邊坡 91 4.5.3 2:1土壤邊坡 93 4.5.3.1 彈性模數E值之影響 95 4.5.3.2 不同數值積分方式之影響 98 4.5.3.3 與Griffiths等人之研究成果比較 105 4.6 綜合討論 108 第五章 三維度邊坡穩定範例分析 109 5.1 三維度之極限平衡法 109 5.2 三維度之強度折減有限元素法 110 5.3 三維(3D)邊坡穩定之範例研究 113 第六章 結論與建議 133 參考文獻 136 附錄1 14