饱和黏土地基三维非轴对称流变固结的半解析解

SEMI ANALYTICAL SOLUTION FOR 3D NON AXISYMMETRIC RHEOLOGICAL CONSOLIDATION OF SATURATED CLAY

  • 摘要: 流变性使土体应力-应变关系具有时间效应,对土体固结过程中的孔压消散和变形发展产生显著影响。利用分数阶导数Merchant流变本构,考虑土骨架应力-应变关系的时间效应;结合Biot固结理论,构建饱和土地基在矩形分布荷载作用下的三维非轴对称流变固结模型。在三维直角坐标系中建立半空间饱和土地基的固结控制方程;通过双重Fourier变换和Laplace变换,将控制方程转化为常微分方程;利用常微分方程理论,推导出变换域的解析解;再通过数值反演,得到地基中任意位置处的时域响应,并进行算例分析。研究结果表明,土骨架流变性对加载时的瞬时固结响应具有显著影响,瞬时孔压和变形都明显减小,而且在加载初期出现较长时间的孔压递增阶段;土骨架流变性只影响土体固结过程中孔压递增和消散的时间路径,而对孔压峰值无影响;土骨架流变性使深层土体固结响应的滞后性增大,使不同深度处土体固结时的孔压差减小。

     

    Abstract: Rheological properties cause the stress-strain relationship of soil to have a time effect, which has a significant impact on the dissipation of pore pressure and the development of deformation during soil consolidation. Using the fractional derivative Merchant rheological constitutive model to consider the time effect of the stress-strain relationship of the soil skeleton, combined with Biot consolidation theory, a three-dimensional non-axisymmetric rheological consolidation model of saturated soil foundation under rectangular distributed load is constructed. The consolidation control equation of a half-space saturated soil foundation is established in a three-dimensional rectangular coordinate system. The control equation is transformed into an ordinary differential equation through double Fourier transform and Laplace transform. The analytical solution in the transformed domain is derived using the theory of ordinary differential equations, and the time-domain response at any location in the foundation is obtained through numerical inversion. The results show that the rheological properties of the soil skeleton have a significant impact on the instantaneous consolidation response during loading, with both instantaneous pore pressure and deformation significantly reduced, and a long period of pore pressure growth occurs during the initial loading stage. The rheological properties of the soil skeleton only affect the time path of the increase and dissipation of pore pressure during consolidation, but have no effect on the peak value of pore pressure. The rheological properties of the soil skeleton increase the lag in consolidation response of deep soil, which reduces the pore pressure difference when the soil is consolidated at different depths.

     

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