黏土壓密參數多變數分布模型的建置

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，但因它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壓縮指數Cc、回脹指數Cs及壓密係數cv的機率分布情形，並且結合其它黏土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、壓密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(plasticity index, PI)；(3)含水量(water content, wn)；(4)孔隙比(void ratio, e0)；(5)垂直有效應力(vertical effective stress, σv’)；(6)壓縮指數(compression index, Cc)；(7)回脹指數(swelling index, Cs)；(8)壓密係數(coefficient of consolidation, cv)。 先用Johnson分布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八個參數之間的期望值向量、共變異數矩陣建立多變數分布模型，接著在貝氏分析(Bayesian analysis)的架構下，藉由得到不同的現地參數條件，更新壓縮指數、回脹指數和壓密係數的後驗機率分布函數。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三種黏土參數分布的範圍，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 distribution model for ten parameters of clay is constructed based on the database. These eight parameters are：(1) liquid limit, LL；(2) plasticity index, PI；(3)water content, wn；(4) void ratio, e0；(5) vertical effective stress, σv’；(6) compression index, Cc；(7)swelling index, Cs；(8) coefficient of consolidation, cv. Using Johnson distribution system to transform those distributions to standard normal distributions, then applying Gibbs sampler method under condition of conjugation let us get those 8 mean vector and covariance matrix to construst multivariate distribution model. Under the Bayesian analysis framework, the original distributions of the design clay parameters (Cc、Cs, and cv) 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.