饱和土体动力分析的双重网格插值算法

饱和土体作为液固两相介质常用Biot方程来分析土体颗粒与孔隙水间的相互作用.但对于不排水不可压缩饱和土体,由于受Babuska-Brezzi稳定条件的限制,用常规的等插值u-p混合有限元法求解基本控制方程将导致孔隙压力紊乱.针对上述情况,提出双重网格插值算法,通过对细网格中压力自由度运用插值技术,可使得独立位移自由度阶数高于独立压力自由度阶数,从而满足Babuska-Brezzi稳定条件,使得位移场和压力场单元插值阶数保持一致,并通过典型算例验证了该方法的正确性.

Double-mesh interpolation method for dynamic analysis of saturated soil

Biot equation is often used for analysis of the interaction between soil skeleton and pore water of saturated soil,which is taken as a fluid-solid two-phase media.On the other hand,under the restriction of Babuska-Brezzi stability condition,the conventional FEM based on u-p formula of equal-interval interpolation will lead to spurious oscillation of pore pressure when it is used for dealing with undrained-incompressible saturated soil.In consideration of the above fact,a double-mesh interpolation method was proposed.The application of the interpolation technique to degree of freedom(DOF) of pore pressure in fine meshes makes the order of DOF of independent displacement higher than that of independent pressure,so that the BabuskaBrezzi stability condition can be satisfied,and the orders of element interpolation for displacement field and pressure field are in agreement with each other. The correctness of the present method is verified by a typical calculation example.