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。

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.

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