汎用三次元FEMに二相系支配方程式を導入した液状化解析手法
その１ 支配方程式の定式化と液状化地盤の弾塑性構成モデル
南海トラフ地震や首都直下地震等の大規模地震の発生が切迫している。大規模地震時に予想される液状化被害に対し，効果的な対策工や合理的な基礎形式を検討するには，液状化地盤の変形を詳細に評価することが重要となる。液状化に伴う地盤変形において，そのメカニズムは飽和土が土骨格と間隙水の二相の連続体で構成されると仮定したBiotの飽和多孔質体理論によって精緻に捉えられる。このことから，筆者らは汎用三次元FEMプログラムTDAPIIIに本理論に基づく二相系有効応力解析機能を導入した。本研究の内容は二編の論文によって報告する。本報文では，解析機能の骨子として，u-w定式化による二相系支配方程式と砂質土の挙動を表現するためのStress-Densityモデルについて述べる。さらに，土柱モデルによる基本的なシミュレーションを実施し，液状化地盤の一般的な挙動と定性的に調和的な解析結果が得られることを示している。
キーワード：液状化，三次元，有効応力解析，u-w定式化，弾塑性構成則，Stress-Densityモデル
＊１ 技術センター 社会基盤技術研究部 地盤研究室
＊２ 技術センター 都市基盤技術研究部 防災研究室
＊３ （株）アーク情報システム
Liquefaction Analysis Method by Introducing Governing Equations of Two-Phase System into General-Purpose 3D-FEM
Part 1: Formulation of Governing Equations and Elasto-Plastic Constitutive Model of Liquefiable Soil
The occurrence of large earthquakes such as the Nankai Trough earthquake and the Tokyo inland earthquake is imminent. In order to examine effective countermeasures and rational foundations considering liquefaction-induced damage expected during the large earthquakes, it is important to evaluate the deformation of liquefiable ground in detail. The mechanism of its deformation is precisely accounted for by the Biot's theory of saturated porous media, which assumes that a saturated soil consists of two-phase continua of soil skeleton and pore water.
Therefore, we introduced the function for effective stress analysis based on the two-phase system devised in this theory to a general-purpose 3D-FEM program, TDAPIII. The contents of this study are reported in two papers. In this paper, the governing equations using the u-w formulation technique and the Stress-Density model for expressing behaviors of sandy soils are described as the key point of the introduced analysis function. Moreover, a basic simulation using a soil-columnar model is carried out, and it is shown that the numerical results are qualitatively harmonious with the general behaviors observed in liquefiable ground.
Keywords: liquefaction, three dimensions, effective stress analysis, u-w formulation, elasto-plastic constitutive law, Stress-Density model
*1 Geotechnical Research Section, Infrastructure Technology Research Department, Taisei Advanced Center of Technology
*2 Disaster Prevention Research Section, Urban Engineering Research Department, Taisei Advanced Center of Technology
*3 ARK Information Systems, INC.