双层非饱和土地基一维固结半解析解

Semi-analytical solution to one-dimensional consolidation of double-layered unsaturated ground

基于Fredlund和Hasan的非饱和土一维固结理论,将非饱和地基假定为双层,引入层间渗流连续条件,得到双层非饱和土地基一维固结控制方程。采用Laplace变换将偏微分方程组转化为常微分方程组,求解得到双层非饱和土地基在单面、双面渗透边界条件下超孔隙压力和沉降在Laplace域内的解;并利用Crump数值方法实现Laplace逆变换,最终得到时间域内双层非饱和土地基一维固结的半解析解。通过与已有文献和有限差分解的结果比较,验证了所得半解析解的有效性。基于得到的解答,结合算例考察了不同层间渗透系数比下,双层非饱和土地基中超孔隙压力的分布规律;并通过参数分析讨论了土层厚度比和层间渗透系数比对双层非饱和土地基沉降的影响。

Combining the one-dimensional(1D) consolidation theory of unsaturated soils proposed by Fredlund and Hasan and the interfacial continuity conditions during the consolidation,the 1D consolidation model for a double-layered unsaturated ground is obtained in this study.The Laplace transformation is adopted to convert the partial differential equations into the ordinary ones,and the solutions to the excess pore pressures and settlements in the Laplace domain can be acquired.The semi-analytical solution to 1D consolidation of the double-layered unsaturated ground in the time domain is calculated after taking the inverse Laplace transformation by numerical Crump method.A comparison with the finite difference solution and the available analytical solution illustrates that the proposed solution is effective.Based on the proposed semi-analytical solution,the distribution of the excess pore pressures with ratio of various permeability coefficients in the two-layered unsaturated ground is studied,and the parametric studies are made to investigate the influences of the thickness ratio of the soil layer and the ratio of permeability coefficients on the settlement of the double-layered unsaturated ground.