基於全球性資料庫與階層式貝氏模型之液化沉陷預測模式

Abstract

當地震波傳遞至鬆散且飽和水分的砂質土層時，可能引發土壤液化現象，導致地層表現如液體般流動，進而造成嚴重的地層下陷與結構損壞。台灣於 1999 年九二一集集大地震期間，即曾出現此類災害案例。準確預測液化後地層下陷量，對於災害防減工作而言至關重要。 本研究旨在建立一套針對砂質土壤液化後地層下陷的預測模式，結合階層式貝氏模型（Hierarchical Bayesian Model, HBM）與經驗公式（Ishihara and Yoshimine 1992），以克服場址間差異性與觀測資料不完整所造成的不確定性。研究首先建構一個全球砂質土壤資料庫，涵蓋六組與 r D 具相關性的參數，並以 Johnson 轉換將其轉換至標準常態空間，以符合 HBM 建模需求。 預測流程分為兩條路徑：其一為 HBM 推估 rD ，再利用經驗模型估算體積應變與下陷量；其二則為直接套用經驗公式進行沉陷預測。模型透過 Gibbs 抽樣進行參數推論與模擬，並應用於東日本大地震等五個實地案例，比較其預測結果與實測值的一致性。 研究結果顯示， HBM 具備良好的多場址整合能力與條件推論能力，且可提供信賴區間評估不確定性。在資料有限的情況下， HBM 仍能預測 r D 與沉陷量，並對於液化區與非液化區展現不同預測特性。與 Ishihara 經驗模式相比，雖預測準確度略遜，但 HBM 提供了更強的彈性與不確定性表徵能力，對於地震後快速判讀與資料補值具有潛在應用價值。

Soil liquefaction occurs when seismic waves cause loose, water-saturated sandy soils to behave like a liquid, leading to significant ground subsidence and structural damage, as evidenced by the 1999 Chi-Chi Earthquake in Taiwan. Accurate prediction of postliquefaction subsidence is essential for disaster mitigation. This study develops a predictive framework for ground settlement induced by soil liquefaction in sandy deposits, integrating a Hierarchical Bayesian Model (HBM) with empirical formulations (Ishihara and Yoshimine 1992) to address site variability and incomplete data. A global database was constructed with six influencing parameters, and all inputs were transformed using the Johnson distribution system to fit the HBM's Gaussian assumptions. The predictive framework includes two steps: one that estimates r D via HBM and computes settlement using empirical models; and another that directly applies empirical formulas. Inference and simulation were performed using Gibbs sampling, and the approach was validated using five real-world sites affected by the 2011 Tohoku earthquake. Results indicate that the HBM exhibits strong multi-site integration, conditional inference capability, and uncertainty quantification through credible intervals. Even under sparse data conditions, the HBM effectively predicts r D and settlement. While the accuracy may be slightly inferior to Ishihara’s empirical model, the HBM offers greater flexibility and interpretability—making it a valuable tool for post-earthquake assessment and data imputation under uncertainty.