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姓名 黃柏霖(Bo-Lin Huang) 查詢紙本館藏 畢業系所 土木工程學系 論文名稱 根據切片法原理建立穩定數圖表進行邊坡穩定性分析 相關論文 檔案 [Endnote RIS 格式]
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摘要(中) 大地工程設計上，安全係數的設計上往往包含了公式模型、參數的不確定性
(Aleatory Uncertainty and Epistemic Uncertainty)所帶來的影響，然而這兩種不確定性是基
於對大地工程上知識的不完美、取樣現地土壤於大地中的自然隨機性。然而，現地土壤
自然的隨機性往往會造成參數的不確定性，也是影響工程設計的主要原因。
Taylor (1937)提出穩定數原理，是由整體法(摩擦圓法)推估均質有限邊坡之穩定數，藉由
事前一系列計算，將不同坡角、摩擦角下之穩定數計算出來，最後可由穩定數來回推邊
坡之安全係數。
本研究透過SLOPE/W 內建六種切片分析法(Bishop、Morgenstern-Price、Ordinary、
Spencer、Janbu、Sarma)結合穩定數原理計算不同坡角(β = 20。~ 80。)、摩擦角(ψ = 5。
~ 45。)共54 種組合下之穩定數，記錄其研究數據，並繪製成六種由不同切片分析法下
所生成的穩定數圖表。同時，提出平均六種切片分析法邊坡安全係數之穩定數圖表，以
及六種方法下最保守安全係數之設計圖表。最後，透過案例的運算、點估計法的運用分
別驗證圖表的正確性，量化公式模型以及參數的不確定性下對邊坡安全係數的影響。
實驗結果顯示，本研究提出之穩定數圖表，透過穩定數的分析可以正確地替代切片
分析法，在未來便可更快速地計算有限邊坡安全係數而不必透過電腦的運算;而由點估
計法的計算結果可知，土壤的參數不確定性相較於公式模型的不確定性，前者對邊坡安
全係數影響較大。摘要(英) In the design of engineering, the factor of safety often includes the influence of aleatory and
epistemic uncertainty. These two uncertainties are based on imperfect knowledge of engineering and
the randomness of soil in the soil layer. At the same time, the natural randomness uncertainty is the
main factor that affects the engineering design.
Taylor (1937) proposed the principle of stability number, using the friction circle method to
estimate the stability number at homogeneous finite slope. The stability number chart was proposed
through a series of calculations in different slope angles and friction angle of soil. Finally, we can use
the stability number to estimate the factor of safety at finite slope.
In this study, I use six types method of slices (Bishop、Morgenstern-Price、Ordinary、Spencer、
Janbu、Sarma) and combine with the principle of stability number to calculate stability number in
different slope angles (β = 20。~ 80。) and friction angles (ψ = 20。~ 80。). Moreover, I draw six kinds
of stability number charts by different methods of slices. Besides, I average m value (stability number)
from the results to make the average chart and select the maximum m value to propose a design chart
for estimating the most conservative factor of safety in six methods.
Finally, through the calculation of cases and the application of the Rosenblueth method, we can
verify the correctness of charts and quantify the influence of aleatory and epistemic uncertainty in the
factor of safety.
The simulation results show that the stability number charts proposed in this study can correctly
replace the method of slices so that we can more quickly calculate the factor of safety without
computer soft. From the calculation results of the Rosenblueth method, it can be seen that the
epistemic uncertainty has greater influence on the factor of safety than aleatory uncertainty.關鍵字(中) ★ 有限邊坡
★ 切片分析法
★ 穩定數圖表
★ 點估計法關鍵字(英) ★ Finite slope
★ Method of slices
★ Stability number chart
★ Point estimation論文目次 目錄
摘要 ..................................................................... i
Abstract ................................................................... i
目錄 .................................................................... iv
圖目錄 ................................................................... iv
表目錄 ................................................................... iv
第一章 緒論 .............................................................. 1
1-1 研究動機 .......................................................... 1
1-2 研究目的 .......................................................... 2
1-3 論文架構 .......................................................... 3
第二章 文獻回顧 .......................................................... 4
2-1 邊坡破壞之模式 .................................................... 4
2-2 無限邊坡 (Infinite slope) ............................................. 7
2-3 邊坡安全係數 (Factor of Safety) ..................................... 10
2-4 有限邊坡 (Finite slope) ............................................. 12
2-4-1 平面破壞面 (Planar surface analysis) ............................ 12
2-4-2 圓弧破壞面 (Circular surface analysis) ........................... 15
2-5 極限平衡法 (Limit equilibrium method) ................................ 16
2-6 邊坡穩定性分析 ................................................... 17
2-7 整體法 (Mass procedure) ............................................ 18
2-7-1 整體法 (均勻黏土層邊坡ψ = 0) .............................. 18
2-7-2 整體法 (c-ψ均勻土壤中之邊坡) ............................... 22
2-8 切片法 (Method of slices) ........................................... 26
2.8-1 一般切片法 (Ordinary method of slices, OMS) .................... 26
2-8-2 Bishop 簡化法(Bishop’s simplified method) ....................... 29
2-8-3 Janbu 簡化法 (Janbu simplified method) .......................... 31
2-8-4 Spencer 法(Spencer’s method) .................................. 32
2-8-5 Morgenstern-Price 法 (Morgenstern-Price’s method) ................. 33
2-9 參數的不確定性 (Aleatory uncertainty) ................................ 35
2.10 認知的不確定性 (Epistemic uncertainty) .............................. 35
2.11 變異係數(Coefficient of variation, COV) .............................. 36
第三章 穩定數圖表的建立 ................................................. 38
3-1 模擬方法 ......................................................... 38
3-2 試驗模型與土壤參數 ............................................... 39
3-3 Geostudio 簡介及SLOPE/W 相關研究 ................................. 42
3-4 Excel VBA (Visual Basic for Applications) 程式應用與檢驗 ................ 43
3-5 SLOPE/W 模擬流程 ................................................ 44
3-6 穩定數圖表的建立 ................................................. 49
第四章 研究結果與討論 ................................................... 50
4-1 六種切片法下之穩定數圖表 ......................................... 50
4-2 平均穩定數圖表 (Average stability chart) .............................. 55
4-3 最保守穩定數設計圖表 (Conservative design chart) ...................... 56
4-4 穩定數圖表的驗證 ................................................. 57
4-5 有限邊坡試算 (100 組案例) ........................................ 61
4-6 臨界坡高表格試算 ................................................. 67
4-7 邊坡穩定性分析探討參數的不確定性和公式模型的不確定性 ............. 81
第五章 結論與建議 ....................................................... 87
5-1 結論 ............................................................. 90
5-2 建議 ............................................................. 91
第六章 參考文獻 ......................................................... 92參考文獻 [1] Abramson, L. W., Lee, T. S., Sharma, S., and Boyce, G. M., Slope stability and
stabilization methods, John Wiley & Sons (2001).
[2] Das, B., and Sobhan, K., Principle of Geotechnical Engineering, 9th edition., Cengage
Learning (2016).
[3] 王崧竹，「利用程式化穩定數分析邊坡在地震力作用下之安全係數」，私立義守大
學，碩士論文，高雄(2011)。
[4] 林唯庭，「廬山邊坡破壞機率研究」，國立中興大學，碩士論文，台中(2019)。
[5] 楊沛漳，「利用Rosenblueth 點估計建立考量土壤參數不確定性之降雨引發無限邊
坡破壞機率模式」，國立嘉義大學，碩士論文，嘉義(2011)。
[6] Ang, A. H-S., and Tang, W. H., Probability Concepts In Engineering, 2nd edition.,
Wiley (2007).
[7] Cho, S. E., “Effects of spatial variability of soil properties slope stability.” Engineering
Geology, Vol. 92. pp. 97-109 (2007).
[8] 王友為，「以離心模型試驗探討凹型邊坡之穩定性」，國立中央大學，碩士論文，
桃園(2020)。
[9] Taylor, D. W., 1937. “Stability of Earth Slopes.” Journal of the Boston Society of Civil
Engineers, Vol. 24, pp. 197-246.
[10] Vanmarcke, E. H., 1980. “Probability stability analysis of earth slopes.” Engineering
Geology, Vol. 16, pp. 29-50.
[11] EI-Ramly, H., Morgenstern, N. R. and Cruden, D. M., 2002. “Probability slope stability
analysis for practice.” Canadian Geotechnical Journal, Vol. 39(3), pp. 665-683.
[12] Rosenblueth, E., 1975. “Point Estimates for Probability Moment.” Proceedings of the
National Academy of Science, Mathematics, Vol. 72, No. 10, pp. 3812-3814.
[13] Duncan, J. M., 2000. “Factors of safety and reliability in geotechnical engineering.”
ASCE, Vol. 126:307-316.指導教授 王瑞斌(Jui-Pin Wang) 審核日期 2021-8-27 推文 plurk
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