半透水边界下饱和黏土地基的一维黏弹性固结分析

One-dimensional Viscoelastic Consolidation Analysis of Saturated Clay Layer with Semi-permeable Boundary

为了深入探讨饱和黏土的流变特性,引入Koeller弹壶元件修正的分数阶Merchant模型描述土的黏弹性变形特性,并采用非牛顿指数描述的非Darcy渗流方程来描述土体固结过程中孔隙水的流动,重新推导了半透水边界下的饱和黏土一维流变固结方程。采用隐式有限差分法求出了固结方程的数值解。通过与有关文献中退化模型结果对比,验证了数值解法的有效性。在此基础上,分析了半透水边界参数、非Darcy渗流模型参数以及分数阶Merchant流变模型参数对流变固结过程的影响。结果表明:增大半透水边界参数能加快地基内孔压的整体消散速率以及地基沉降速率;分数阶Merchant模型参数中分数阶数和黏滞系数对地基沉降速率的影响更为显著,且对地基沉降速率的影响主要集中在固结进程的中后期;Kelvin体与独立弹簧的模量之比对固结进程的影响也主要在中后期,且随着模量比的增大,地基的固结进程逐渐加快;非Darcy渗流延缓了土层的固结速率,且随着非牛顿指数的增大,地基的固结逐渐变慢。

In order to further explore the rheological properties of saturated clay,the fraction-order Merchant model modified by Koeller's spring-pot element was introduced to describe the viscoelastic deformation of soil,and the non-Darcy flow equation described by non-Newtonion index was introduced to describe the pore water flow during consolidation.The one-dimensional rheological consolidation equation of saturated clay under semi-permeable boundary was re-derived.The numerical solution of consolidation equation was obtained by the implicit finite difference method.The effectiveness of the numerical method was verified by comparing with the results of degradation models in related literature.On this basis,the effects of the parameters of semi-permeable boundary,non-Darcy flow and fractional-order Merchant's rheological model on rheological consolidation process were investigated.The calculation results illustrated that the increase of semi-permeable boundary parameter could accelerate the dissipation of pore pressure and settlement of foundation.In the parameters of the fractional-order Merchant model,the order of fractional derivative and the viscosity coefficient have more significant effects on the settlement rate of foundation,and the influence on the settlement rate of foundation is mainly concentrated in the middle and late stages of consolidation process.The ratio of modulus of Kelvin's body to independent spring had a major effect on the consolidation process in the middle stage,and with the increase of modulus ratio,the consolidation process of foundation gradually accelerated.In addition,the consolidation rate of soil layer was delayed by non-Darcy flow,and the consolidation of layer was gradually slowed down with the increase of non-Newtonian index.