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中文摘要：
基于直角坐标系下Biot固结的基本控制方程,并考虑软土土骨架的黏弹性特性,通过Fourier-Laplace积分变换、解耦变换、微分方程组理论和矩阵理论,推导了黏弹性地基Biot固结三维空间问题和平面应变问题在积分变换域的解析解,进而得到对应问题的单元刚度矩阵.然后根据对号入座原则组装得到层状黏弹性地基Biot固结对应问题的总体刚度矩阵.通过求解总体刚度矩阵形成的线性代数方程,得到层状黏弹性地基Biot固结对应问题在积分变换域内的解答.最后应用Fourier-Laplace逆变换得到其物理域内的解.对比求解黏弹性Biot固结问题退化的弹性Biot固结问题与已有解答,验证了刚度矩阵计算方法的正确性,为层状黏弹性地基Biot固结问题提供了理论基础.
英文摘要：
Based on the basic viscoelastic equations of Biot consolidation in the Cartesian coordinate system and in view of the viscoelasticity of soft soil skeleton,the analytical solutions to 3D problems and plane strain problems of Biot consolidation in the integral transform domain were obtained through the Fourier-Laplace transform and the decoupling transform according to the differential equation theory and the matrix theory,and in turn the corresponding element stiffness matrixes were derived.The global stiffness matrixes for Biot consolidation 3D problems and plane strain problems of multilayered viscoelastic foundations were assembled with the matrix matching method,and the solutions to the corresponding problems of multilayered viscoelastic foundations in the transform domain were obtained in the solution of the algebraic equations for the global stiffness matrixes.The solutions in the physical domain were acquired through the inverse Fourier-Laplace transform.The validity of the proposed method was examined in the comparison of the present results of 2 examples,where viscoelastic Biot consolidation was reduced to elastic Biot consolidation,with the previous reference solutions.The analytical stiffness matrixes provide a theoretical base for Biot consolidation of multilayered viscoelastic foundations.
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