半透水边界下分数阶黏弹性饱和土一维固结特性分析

Analysis of one-dimensional consolidation of fractional viscoelastic saturated soils with semi-permeable boundary

为描述饱和土体的流变特性,引入分数阶导数Kelvin-Voigt黏弹性模型,采用解析方法对半透水边界下的分数阶黏弹性饱和土一维固结特性进行了研究。分别对骤加恒载下饱和土一维固结微分方程和分数阶Kelvin-Voigt黏弹性本构方程进行Laplace变换,并联立求解得到了双边半透水边界条件下分数阶黏弹性饱和土在Laplace变换域内的解析表达式。通过Crump方法实现Laplace数值反演,得到时间域内的半解析解。将所得到的解分别退化为分数阶黏弹性饱和土一维固结半解析解和双边半透水黏弹性饱和土一维固结半解析解,结果与已有文献半解析解相同,验证了提出的双边半透水边界条件下分数阶黏弹性饱和土一维固结解的可靠性。通过算例考察了半透水边界条件和分数阶黏弹性饱和土参数对一维固结特性的影响。研究表明,双边半透水边界下分数阶黏弹性饱和土一维固结发展过程与半透水边界条件、分数阶次和黏滞系数有关,且土体的压缩模量对饱和土一维固结最终沉降量有显著影响。

The fractional Kelvin-Voigt viscoelastic model is introduced to describe the rheological characteristics of saturated soils. One-dimensional consolidation characteristics of saturated soils with fractional viscoelastic model under symmetric semi-permeable boundaries is studied. By applying these two models, the analytical solution to the one-dimensional consolidation is obtained in the Laplace transform domain. Crump’s method is adopted to perform the inverse Laplace transform to obtain semi-analytical solutions in the time domain. By reducing the proposed solution to one dimensional consolidation equation of saturated soils under symmetric semi-permeable boundaries using these two models, it is shown that the present solution is reliable and in a good agreement with the existing solutions from literatures. Finally, several numerical examples are provided to investigate the consolidation behavior of saturated soils with the fractional viscoelastic model under symmetric semi-permeable boundaries. It can be found that the one-dimensional consolidation process is affected by the semi-permeable boundary parameters, fractional order and viscosity coefficient, and the modulus of compressibility has a significant effect on the final settlement of saturated soil.