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  • 學位論文

大地工程多維度設計中之特性值估計

Estimation of multivariate characteristic values in geotechnical design

指導教授 : 卿建業

摘要


特性值指工程設計中影響安全與使用性之大地工程參數的謹慎估計值。其定義主要由兩個部份組成:影響極限狀態發生的值以及謹慎的估計值。本文著重於謹慎估計值的探討,並令符合影響極限狀態發生的大地工程參數稱之為“驅動參數”。 歐洲規範希望驅動參數的估計值,應是謹慎的估計且具有95%的信心區間,並建議此謹慎的估計值可為5%分位數,然而目前有限文獻以及歐洲規範本身,並沒有清楚的解釋:5%的分位數是應用於每個驅動參數,或是5%的分位數應用於極限狀態函數(G)。本文的首要議題;確定解釋1(各別驅動參數符合5%的分位數)及解釋2(極限狀態函數(G)符合5%的分位數),哪一個較能符合歐洲規範的宗旨。 歐洲規範希望驅動參數的謹慎估計值具有95%的信心區間,意旨現地強度參數值小於估計值的機率應控制為5%,本研究經由解釋1及解釋2之理念模擬構造物之設計,了解兩種不同解釋所設計出之構造物破壞機率,並加以利用莫爾庫倫破壞包絡線進行模擬,發現解釋1,產生之破壞機率具有高度的變異性,且特性破壞包絡線不隨著系統的變化(維度、相關性)而改變,甚至沒有任何破壞包絡線小於特性破壞包絡線,解釋2並無此問題,所產生之破壞機率皆為0.05,且模擬的包絡線小於特性破壞包絡線的機率大約為5%,較能符合歐洲規範之期望。 然而要使得極限狀態函數(G)符合5%的分位數,需要控制極限狀態函數的CDF(累積機率密度函數),這將牽扯到複雜的機率運算,非常不切實際。本研究希望建議一個簡易的近似式,實現解釋2(極限狀態函數符合5%的分位數),而不需牽扯到複雜的MCS或極限狀態函數的CDF的控制。

並列摘要


The definition of characteristic value has two different parts. First of all, the value affecting the occurrence of the limit state and cautious estimate. In this research, cautious estimate is the core issue. Moreover, the geotechinical parameter which conform in affecting the occurrence of the limit state is called mobilized value. Eurocode 7 hopes the estimate of mobilized value supposed to locate in confidence level of 95%. This cautious estimate is about 5% fractile. However, there are two possible interpretations for the 5% quantile for the characteristic value in Eurocode 7. The first interpretation is that the 5% quantile is on the input geotechnical parameters. The second interpretation is that the 5% quantile is on the output limit state G. The major issue of this research explains the two ideas above which is the closest to Eurocod 7’s purpose. According to Eurocode 7’s purpose, the probability value of estimate should be controlled in 5% which is lower than genuine in-situ strength parameter. By going through first and second interpretation, structure deisgn would be simulated. Figuring out the probabilty of structur failure, First interpretation is found that probaility of failure has highly variable and the failure probability is very small. However, second interpretation does not has those problems. However, second interpretation requires the CDF of the limit state G and the ability to control this CDF. The two requirements are very unrealistic for engineer. This research hope to propose an approximate fulfilling second interpretation.

參考文獻


[1]. Bond, A. and Harris, A. (2008). Decoding Eurocode 7, Taylor & Francis, London.
[2]. Ching, J. and Phoon, K.K. (2011). A quantile-based approach for calibrating reliability-based partial factors, Structural Safety, 33, 275-285.
[3]. Ching, J. and Phoon, K.K. (2013). Quantile value method versus design value method for calibration of reliability-based geotechnical codes, Structural Safety, 44, 47-58.
[4]. Ching, J. Y. and Phoon, K. K. (2015). Role of redundancy in simplified geotechnical reliability-based design – A quantile value method perspective, Structural Safety, 55, 37-48.
[5]. Ching, J., Hu, Y.G., and Phoon, K.K. (2017). Effective Young’s modulus of a spatially variable soil mass under a footing, Structural Safety, under review.

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