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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.
Based on the basic governing equations of Biot consolidation in Cartesian coordinates and considering the viscoelastic properties of soft soil soils, the Biot solid of viscoelastic foundation is deduced by Fourier-Laplace integral transformation, decoupling transformation, differential equations and matrix theory The three-dimensional space problem and the plane strain problem in the integral transform domain are solved analytically to get the element stiffness matrix of the corresponding problem.According to the colony seating principle, the global stiffness matrix of the Biot consolidation response problem for the layered viscoelastic foundation is obtained by solving the total stiffness Matrix linear algebraic equations to obtain the solution of the Biot consolidation response of the layered viscoelastic foundation in the integral transform domain.Finally, the solution of the physical domain is obtained by Fourier-Laplace inverse transformation.Compared with the degenerated elasticity of viscoelastic Biot consolidation problem Biot’s consolidation problem and existing solutions verify the correctness of the stiffness matrix calculation method and provide a theoretical basis for the Biot consolidation problem of layered viscoelastic foundation.