基于Gross方程的飽和砂土液化后流動特性模型

吳海清

摘要：將液化后的飽和砂土視為一種流體，其流動特性表現出類似剪切稀化非牛頓流體的特性。根據非牛頓流體力學理論分析液化后飽和砂土的流動特性發現，當處于零有效應力狀態時，可以用純粘性流動本構模型較好地描述砂土的剪應變率表觀黏度關系。通過擬合動扭剪試驗結果的流變曲線，對比分析了幾種常用的純粘性流動本構模型，發現Gross模型可以較好且較簡潔地描述液化后砂土零有效應力狀態時的流動特性。通過對擬合參數的分析，建立了基于Gross模型的液化后飽和砂土零有效應力狀態的流動本構模型，得到時間量綱下的參數K以及零剪切表觀黏度η0和極限剪切表觀黏度η∞的函數關系。考慮相對密實度、固結應力和應力歷史對模型參數的影響，闡釋了模型參數的函數關系以及物理意義。

關鍵詞：飽和砂土;剪切稀化;零有效應力;流動本構模型;剪應變率表觀黏度

中圖分類號：TU447 文獻標志碼：A 文章編號：20966717（2020）03003208

Abstract：

When the liquefied watersaturated sand is regarded as a fluid， it can be idealized as a kind of shear thinning nonNewtonian fluid. Based on nonNewtonian fluid mechanics， the theoretical analysis was conducted on the liquefied watersaturated sand. According to this， the relationship between the shear strain rate and the viscosity under zero effective stress state can be properly described by pure viscous flow constitutive model. The Gross model of liquefied watersaturated sand is established by fitting the flow curve of the dynamic torsional shear test results on the basis of predictions obtained from several commonly used pure viscous flow constitutive models. The representative model parameters include the relative density， the consolidation stress and the impact of stress history. The functional relationships among time dimension K， zero shear apparent viscosity η0 and limit shear apparent viscosity η∞ are fitted based on the dynamic torsional shear test results， and the physical meanings of the parameters are introduced in the composed function. The research landmarks a theoretical foundation for further analysis of large deformation of liquefied flows based on fluid mechanics theory.

Keywords：watersaturated sand; shear thinning; zero effective stress; flow constitutive model; shear strain rateapparent viscosity

地震是人類面臨的主要自然災害之一。近年來，世界范圍內地震活動頻繁，如2008年中國“5·12”汶川大地震（里氏震級M=8.0）[1]，2010年智利“2·27”大地震（里氏震級M=8.8）以及2011年日本“3·11”本州島海域大地震（里氏震級M=9.0）[2]，2018年印尼“9·28”大地震（里氏震級M=7.4）等，這些大地震中均存在因飽和砂土液化而引起的震害，因此，地震液化問題的研究仍然是土動力學與巖土地震工程領域重要的課題之一。

Seed等[3]把不排水循環剪切試驗中有效應力第一次為0的狀態稱為“初始液化”，從而將液化過程分為“液化前（初始液化前）”和“液化后（初始液化后）”兩個階段。……