基于指数形式渗流的成层地基一维固结半解析解

为了计算基于指数形式渗流的成层地基一维固结变形,将指数形式的渗流模型引入传统的成层地基一维固结理论,建立了变荷载条件下的控制微分方程;采用解析法与数值离散相结合的半解析法对控制方程进行求解;在指数形式渗流退化为达西渗流的条件下,将半解析法的计算结果与解析解进行比较,验证了半解析法计算结果的可靠性.最后,结合某双层地基固结实例对不同参数时的固结性状进行了分析.结果表明:用半解析法计算基于指数形式渗流的成层地基一维固结简便、可靠;上层土比下层土的渗流指数对固结速率的影响显著;压缩性小、渗透性大的土层越厚,成层地基的固结速率越快;加载速率越快,固结速率越快. 

Semi-analytical Solutions for One-Dimensional Consolidation of Layered Soil Obeying Exponential Flow Law

To calculate one-dimensional consolidation settlement of layered soil obeying an exponential flow law,an exponential flow law model was introduced into the classical consolidation theory for layered soil.The governing equation for one-dimensional consolidation of layered soil was established by considering the exponential flow law and time-dependent loading.A semi-analytical method combining the analytical method with numerical discretization was adopted to solve the governing equation.On condition that the exponential flow law is degenerated into the Darcy’s flow law,the reliability of semi-analytical solutions was verified by comparing the results of the semi-analytical method with those of the analytical method.Finally,consolidation behaviors under different parameters were analyzed by combining with a case study of the consolidation of double-layered soil obeying an exponential flow law.The results show that it is simple and reliable to apply the semi-analytical method to the one-dimensional consolidation of layered soil obeying an exponential flow law;compared with the bottom soil layer,the flow exponent of upper soil layer has a great effect on the rate of consolidation;the consolidation rate increases with increasing the thickness of soil layer with low compressibility and high permeability;and the faster the loading rate,the faster the rate of consolidation.