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研究生:吳采容
研究生(外文):Tsai-Jung Wu
論文名稱:以有限圓錐貫入試驗估計水平向關聯性長度
論文名稱(外文):Estimating horizontal scale of fluctuation with limited CPT soundings
指導教授:卿建業卿建業引用關係
口試日期:2017-07-17
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:土木工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:中文
論文頁數:64
中文關鍵詞:大地工程現地調查空間變異性水平關聯性長度
外文關鍵詞:geotechnical engineeringsite characterizationspatial variabilityhorizontal scale of fluctuation
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關聯性長度是大地工程中描述空間中資料相關性的一個重要參數,關聯性長度大反應出的實際情況為地層為接近均質情形。本研究將以圓錐貫入試驗 (cone penetration test, CPT) 的修正之錐尖阻抗 (qt) 資料做為討論對象,著重探討利用圓錐貫入試驗資料估計水平向關聯性長度。相比於垂直向關聯性長度,水平向關聯性長度的估計較為困難,原因為水平方向上的資訊豐富程度遠低於垂直方向,以施作單一孔位CPT作為說明,CPT在施作時是以垂直方向進行,故在垂直方向上有大量的資訊,而沒有任何水平方向的資料,故較難有效的估計出水平關聯性長度。面對在水平方向上有限的資訊,本研究採用以貝氏分析為基礎的漸進式馬可夫鏈蒙地卡羅法 (transitional Markov chain Monte Carlo, TMCMC; Ching and Chen, 2007) 作為估計水平方向的隨機場參數的方法,且於研究過程中發現,自關聯性模型的選擇會對關聯性長度評估有很大的影響,故進一步將自關聯性模型類型一併納入考量,所用的自關聯性模型為Stein於1999年提出的Whittle-Matérn模型,此模型可平滑參數以及關聯性長度同時納入考量。在上述二種工具的使用下,本研究欲以有限(少於十孔)的CPT孔數估計水平關聯性長度,最後將以實際案例說明估計水平關聯性長度之流程。
The scale of fluctuation (SOF) is an important parameter to characterize the spatial correlation of soil or rock property. The large SOF indicates that the soil or rock is close to homogeneous situation. This study will focus on the estimation of horizontal SOF based on the cone penetration test (CPT) soundings. Compare to the vertical SOF, determining the horizontal scale of fluctuation is challenging, because a single CPT sounding contains abundant information, but no information in the horizontal direction. In current study, it demonstrates that it is possible to estimate the horizontal SOF base on the limited CPT soundings which separation distances are chosen suitably and probability analysis framework. The study also shows that the Whittle-Matérn auto-correlation model should be adopted to obtain a consistent estimation of horizontal SOF. The proposed approach will be applied to a real case study finally.
致謝 I
中文摘要 II
ABSTRACT III
目錄 IV
圖目錄 VI
表目錄 VIII
第一章 緒論 1
1.1 研究動機與目的 1
1.2 研究方法 4
1.3 本文內容 5
第二章 文獻回顧 6
2.1 隨機場 (random field) 6
2.1.1 穩態隨機場 (stationary random field) 6
2.1.2 自關聯性模型 (auto-correlation function) 8
2.2 Whittle-Matérn 模型 12
2.3 馬可夫鏈蒙地卡羅法 14
2.4 漸進式馬可夫鏈蒙地卡羅法 16
2.5估計方法一致性探討 18
第三章 研究方法 20
3.1 資料模擬 20
3.1.1 隨機場參數對模擬資料的影響 20
3.1.2 三維零均震盪項之模擬 23
3.2 漸進式馬可夫鏈蒙地卡羅法於估計隨機場參數之表現 25
3.2.1 辨識模型已知情況 26
3.2.2 辨識模型未知情況 29
3.3 Whittle-Matérn 模型之納用 33
3.4 影響水平關聯性長度辨識因子 35
3.4.1 孔位數量/佈置的影響 36
3.4.2 厚度(nD)的影響 39
3.5 討論與小結 42
第四章 現地案例討論 43
4.1 案例地點 43
4.2 TMCMC估計隨機場參數流程 45
4.3 參數辨識成果 46
4.3.1 參數辨識成果一 47
4.3.2 參數辨識成果二 50
4.3.3 參數辨識結果三 51
4.3.4 參數辨識結果四 52
第五章 結論與建議 54
參考文獻 56
附錄A 提問與答覆 62
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