無凝聚性土壤參數間之轉換及其相關性探討

Transformations and correlations among some parameters of cohesionless soils

林冠宏(Guan-Hong Lin)

指導教授 ： 卿建業

國立臺灣大學/工學院/土木工程學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201601230

摘要

不確定性(uncertainty)普遍存在於大地工程中，且在可靠度設計中是一個重要的指標，然而目前業界使用的安全係數設計法雖然具有方便且迅速的優點，但因其無法準確量化不確定性因子，可能導致過於保守的設計。因此本研究的目的即是有效利用現場工址調查的資訊來預測無凝聚性土壤之Dr及ϕ'的機率分佈情形並結合不僅僅只單一參數的資訊來降低其不確定性。首先，藉由文獻回顧蒐集前人對無凝聚性土壤(cohesionless soil)經實驗室試驗或現地試驗的所得之土壤參數資料，建立一龐大的資料庫，於其中篩選出我們認為與土壤強度有密切關聯的參數，包含：(1)均勻係數(coefficient of uniformity, Cu)；(2)平均粒徑(mean particle size, D50)；(3)相對密度(relative density, Dr)；(4)正規化後有效垂直應力(effective vertical stress, 'v/Pa)；(5)土壤有效摩擦角(ϕ')；(6) 修正後的CPT錐尖阻抗qt1；(7) 修正後的SPT-N值((N1)60)。計算得到這七個參數間的相關係數矩陣，了解參數間彼此的關係。再來，利用Johnson分佈系統將參數轉換為標準常態分佈，利用常態空間下的相關係數矩陣推導後續貝氏分析(Bayesian analysis)的演算法，最後得出在不同參數條件下、更新後土壤摩擦角的事後機率分佈函數(posterior PDF)。當代入的已知資訊愈多，標準偏差越小，所估出來的Dr或ϕ'也就愈準確，我們便能更清楚知道此兩種土壤參數分佈的範圍，於可靠度概念下能更準確地設計結構物，適度地節省工程材料成本。

關鍵字

無凝聚性土壤 ； SAND/7/2794 ； 相關性 ； 貝氏分析 ； 多變數機率分佈模型

並列摘要

Comparing with safety factor method, reliability-based design method can quantify the uncertainty to design geotechnical structure in a more systematical and economical way. In this study, a multivariate probability distribution model for seven parameters of cohesionless soils is constructured based on the SAND/7/2794 database. These seven parameters are: (1)coefficient of uniformity (Cu); (2)mean particle size (D50); (3)relative density (Dr); (4)normalized vertical effective stress ('v/Pa); (5)effective friction angle (ϕ'); (6)corrected CPT cone tip resistance (qt1); (7)corrected SPT-N value [(N1)60]. Consistency is shown that the multivariate probability distribution captures the correlation behaviors in the database among the seven parameters. According to the conditioning concept of Bayesian analysis, the original distributions of the design soil parameters (Dr, ϕ') serve as prior distributions and can be updated into the posterior distributions by using different multivariate site-specific information. The forms of posterior distributions were summarized into tables so that detailed Bayesian analysis would not be conducted. From the results, the transformation uncertainty of predicted posterior distribution can be effectively reduced as the multivariate site-specific information increases. With smaller uncertainty, reliability-based design can deduce more economical design.

並列關鍵字

cohesionless soils ； SAND/7/2794 ； Bayesian analysis ； multivariate probability distribution

參考文獻

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