在大地工程也開始逐漸步入可靠度分析與設計(Reliability Analysis & Reliability-based Design)後,基於部分係數設計法(Partial Factors Design)的缺陷,卿建業和方國光在2011年提出了分位數值法(Quantile Value Method, QVM)改善常數部分係數在變動的系統變異下之問題。而大地工程中另一特色為層狀土壤,而由於不同土層所提供之強度變化大,因此必須將每一土層視為一強度來源之隨機變數(Random variables)。最近我們發現使用常數的分位數之QVM在變動的土層當中表現並不良好,因此本研究提出一改良方案,以有效隨機維度(Effective Random Dimension, ERD)來改善QVM的問題。 本文首先將會闡述ERD、破壞機率與機率門檻(Probability threshold, η)三者的關係,說明ERD為何能影響系統,並以一於標準常態下推導得之關係式作為本研究之主體,利用此關係式進行可靠度分析與設計。在本研究中將會使用三個常見的大地工程案例來探討,並加入傳統安全係數設計(Safety Factor Design)、一階二次矩法(First Order Second Moment Method, FOSM)與QVM於不同設計情景下做分析,隨後則利用設計指標預測可靠度指標(Reliability Index, β)來進行比較,其中即加入ERD來觀察是否能夠改善QVM。最後本文則建立一套ERD的預測式,比較傳統QVM與加入ERD後的QVM於可靠度設計之差別。
The Reliability Analysis (RA) and Reliability-based Design (RBD) are gradually used in Geotechnical engineering society. However, Using Partial Factor Design which has generally applied in structure engineering in geotechnical engineering is not a good way due to variable varieties. Ching and Phoon proposed a novel simplified RBD method called “Quantile Value Method, QVM” in 2011 in respond to this problem. Furthermore, another characteristic of Geotech is variable sources of resistance such as a single pile embedded in multiple soil layers. According to recent research, the constant η quantile could not maintain a uniform reliability in the practices of variable strata. This paper proposes an improvement adopting the concept called “Effective Random Dimension, ERD” to enhance QVM’s performance. The focus of this research is to explain the role of ERD and the effect of using ERD in QVM. This paper will discuss the relationship among ERD, probability of failure and Probability Threshold at first. How the ERD affects the whole system is the main point and a formula derived from standard normal distribution would be demonstrated. To present the advantage of using ERD, we will use three common geotechnical examples to statistically compare the information content of three design method, Safety Factor Design, First Order Second Moment Method and QVM. Here will show a simple comparison of three types of design indices, then a regression predicting ERD will be established in order to take the ERD into account in RA and RBD. At the end the results of QVM and ERD-based QVM will be discussed.
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