承压水降压引起上覆层状土体二维黏弹性固结分析
Two-Dimensional Viscoelastic Consolidation Analysis of Overlying Layered Soil Caused by Pressure Drop of Confined Water
摘要: 针对承压层的水位下降引起的上覆多层结构土体沉降问题，结合二维固结方程、Merchant流变模型与水位变化边界条件，提出了考虑土骨架黏弹性的多层弱透水层二维渗流固结数学模型。针对该模型，由Fourier-Laplace变换推导了Fourier-Laplace变换域内问题的解析解，利用Stehfest数值反演方法得到了问题在在时域内的真实解。在此基础上，对本文给出的多层弱透水层固结度、沉降量解答与已有一维解析解、二维有限单元数值解进行了对比，验证了本文方法的正确性。通过进一步的算例分析，研究了土体黏滞性、刚度比、以及承压层水位下降幅度对固结过程的影响规律。
Abstract: For the settlement problem of the overlying multi-layer soil caused by the water level drawdown in the confined layer, a two-dimensional seepage consolidation mathematical model of the multi-layer aquitard considering the viscoelasticity of the soil skeleton is proposed in combination with the two-dimensional consolidation equation, the Merchant rheological model and the boundary condition of water level change. For this model, the analytical solution of the problem in the Fourier Laplace transform domain is derived from the Fourier Laplace transform, and the real solution of the problem in the time domain is obtained using the Stehfest numerical inversion method. On this basis, the consolidation degree and settlement of multi-layer aquitard given in this paper are compared with the existing one-dimensional analytical solution and two-dimensional finite element numerical solution, and the correctness of this method is verified. The influence of viscosity, stiffness ratio and amplitude of the water level drawdown on consolidation process is studied through further analysis of several examples.
文章引用：刘磊. 承压水降压引起上覆层状土体二维黏弹性固结分析[J]. 理论数学, 2023, 13(2): 189-197. https://doi.org/10.12677/PM.2023.132022

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