平面应变Biot固结的解析层元

ANALYTICAL LAYER-ELEMENT OF PLANE STRAIN BIOT'S CONSOLIDATION

提出用解析层元法有效地解决任意深度单层土的平面应变Biot固结问题.从Biot固结问题的控制方程出发,采用特征值法在Laplace-Fourier变换域内推导出一个精确对称的解析层元刚度矩阵.通过表示单层土广义力和广义位移之间关系的解析层元,并结合土层的边界条件,推导出土层任意点的解答;物理域内的真实解可以通过Laplace-Fourier数值逆变换进一步获得.通过数值计算验证理论的正确性,研究了土层性质及时间因素对固结的影响.

An efficient algorithm is presented to solve plane strain Blot＇s consolidation of a single sou layer with an arbitrary depth. Starting from the governing equations of Blot＇s consolidation, an exactly symmetric stiffness matrix, i.e. the analytical layer-element, is deduced in Laplace-Fourier transformed domain by using the eigenvalue approach. According to the relationship between generalized displacements and stresses of a single layer in the transformed domain described by the matrix, and the boundary conditions of the soil layer, the solutions of any point can be obtainedl The actual solutions in the physical domain can further be acquired by inverting the Laplace^Fourier transform. Finally, numerical examples are presented to verify the theory and study the influence of the soil properties and time history on the consolidation behavior.