黏土參數聯合機率分佈的建置

Abstract

大地工程中，普遍存在著不確定性，且為可靠度設計中不可缺少的要素之一，雖然目前業界仍然使用安全係數法，但因他無法準確地量化不確定性，進而導致過度保守之設計。故本研究之目的為：有效利用現地調查所得來之資訊去預測不排水楊氏模數E50及靜止有效土壓力係數K0的機率分佈情形，並且結合其它參數的資訊去降低其不確定性。 首先，藉由文獻回顧去蒐集前人對飽和黏土所做阿太堡試驗、不排水等向性(異向性)三軸拉(壓)試驗以及其他試驗而測得之土壤參數去建立龐大資料庫，再篩選出我們認為有能探討之相關性的參數，包含： (1)液性限度(liquid limit, LL)；(2)塑性指數(plastic index, PI)；(3)液性指數(liquid index, LI)；(4)垂直有效應力(vertical effective stress, σv’/pa)；(5)過去垂直最大有效應力(vertical effective maximum stress, σp’/pa)；(6)靈敏度(sensitivity, St)；(7)正規化之不排水剪力強度(normalize undrained shear strength, su)；(8)靜止有效土壓力係數(the coefficient of earth pressure at rest, K0)；(9)正規化之不排水楊氏模數(undrained modulus, Eu50/su(mob))；(10)試驗量測求得孔隙水壓力常數(Bq)；(11)試驗量測求得正規化修正後總錐尖阻抗((qT-σv)/σv’)；(12)試驗量測求得正規化修正後有效錐尖阻抗((qT-u2)/σv’))。 先用Johnson分佈系統將參數轉至標準常態空間，再使用吉普斯取樣法搭配共軛條件計算得到這十二個參數之間的共變異數矩陣、期望值向量以及填補資料庫的空洞；可利用標準常態空間下的共變異數矩陣及貝氏分析(Bayesian analysis)的演算法，得到在不同參數條件下，更新後不排水楊氏模數和靜止有效土壓力係數的後驗機率分佈函數。當代入的已知資訊愈多，標準偏差越小，所能估出來參數就越準確，我們便能更清楚知道此兩種黏土參數分佈的範圍，於可靠度觀念下能更加準確地去設計大地結構物並且節省工程材料成本。

Comparing with safety factor method, reliability-based design method can quantify the uncertainty to design geotechnical structure in a more systematical and economical design. In this study, a multivariate probability distribution model for twelve parameters of clay is constructed based on the CLAY/12/8198 database. These twelve parameters are:(1)liquid limit, LL; (2)plastic index, PI; (3)liquid index, LI; (4)vertical effective stress, σv’/pa; (5)vertical effective maximum stress, σp’/pa; (6)sensitivity, St; (7)normalize undrained shear strength, su; (8)the coefficient of earth pressure at rest, K0; (9)undrained modulus, Eu50/su(mob); (10)Bq; (11)(qT-σv)/σv’; (12)(qT-u2)/σv’. Using Johnson distribution system to transform those distributions to standard normal distribution, then applying Gibbs sampler method under condition of conjugation let us get those 12 covariance matrix, mean vector and non-vacancy databases. Afterwards, using the Bayesian analysis framework, the original distributions of the design clay parameters (E50, K0) would serve as prior distributions and can be updated into posterior distributions by using different multivariate site-specific information. 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 be more economical.