二相系u-U定式化に基づく水－土連成有限要素解析の精度向上
間隙率の新たな空間離散化手法の提案と妥当性確認
間隙が水で飽和した地盤の挙動を表現するための支配方程式は，飽和土を固相と液相の二相系からなると仮定したBiotの飽和多孔質体理論（例えば，Biot, 1962）によって導かれる。支配方程式に対するいくつかの定式化のうち，本研究では固相の変位uと液相の変位Uを未知数とするu-U定式化に着目する。一方，有限要素法による飽和地盤のモデル化では，地層の種類や密度の違いによって要素間の間隙率の変化が不連続となる場合がある。このような場合にu-U定式化を適用すると，要素間の隣接面上の流量と間隙水圧に連続性が成立せず，解析精度が低下するという課題がある。本研究では，隣接面上の流量と間隙水圧の連続性を改良したu-U定式化に基づく有限要素解析を提案するとともに，間隙率の不連続面を含む1次元地盤の準静的あるいは動的挙動に関するケーススタディを通じて妥当性を確認した。
キーワード：飽和多孔質体理論，u-U定式化，間隙率，流量，間隙水圧，連続性
＊１ 技術センター 社会基盤技術研究部 地盤研究室
Improvement in Accuracy of a Soil-Water Coupled Finite Element Analysis Based on the u-U Formulation
Proposal of a New Method for the Space Discretization of Porosity and Its Validation
The governing equation for the behavior of saturated ground is derived from the theory of saturated porous media (e.g. Biot, 1962). The u-U formulation is well-known as one of the formulations for the governing equation, and a finite element analysis based on the u-U formulation is often used for simulations of soil-water coupled phenomena (consolidation, liquefaction and others). However, in modeling of saturated ground by the finite element method, differences in stratum and density can cause that the change in porosity is discontinuous between elements. When the conventional analysis based on the u-U formulation is applied in such cases, continuities of discharge flow rate and pore water pressure are not reproduced on boundary surfaces between adjacent elements, and this has the problem that the analysis accuracy is reduced. In this paper, a new finite element analysis focused on the space discretization of porosity is proposed for the u-U formulation in order to improve the continuities of discharge flow rate and pore water pressure between the adjacent elements, and its validity is discussed through case studies on one-dimensional quasi-static or dynamic behavior of the ground including the boundary surfaces on which the porosity varies discontinuously.
Keywords: theory of saturated porous media, u-U formulation, porosity, discharge flow rate, pore water pressure, continuity
*1 Geotechnical Research Section, Infrastructure Technology Research Department, Taisei Advanced Center of Technology