圆柱土样Biot固结模型的Green函数及其土体体积应变规律

The Green Function and the Law of Volumetric Strain for Biot Consolidation of Columnar Soil-sample

通过建立横观各向同性圆柱土样轴对称Biot固结问题的Green·函数,得到了用Green函数表示的径向位移分布表达式和相应的空隙水压力的精确解析解.该方法不仅避免了将问题的解分解为弹性静力学解和渗流拟动态解的叠加的过程和复杂的积分变换,而且问题的级数解形式简洁,收敛速度较快,便于数值计算和圆柱土样的全场渗流固结规律的分析.最后以此结果具体分析了Mandel-Cryer效应在圆柱土样不同位置的强弱程度和土的泊松比对Mandel-Cryer效应的影响,表明本文方法的正确性.

The expression of radial displacement which expressed by Green function for Biot consolidation of columnar cross-isotropic soil--sample is obtained by building Green function. Correspondingly, exact analytical solutions for volumetric strain and pore water pressure are obtained also. This method not only avoid the process of decomposing solution of the Biot consolidation of columnar cross-isotropic soil--sample into the elasticity static＇s solution and quasi--dynamic solution of fluids, but also easy to numerical calculation and analyzing the full-court filtration concretion law for columnar cross-isotropic soil-sample. In the end of this paper, with this result, we particularly analyze the law of volumetric strain of soils and the degree of the Mandel-Cryer effect in different position of soil-sample and the influence of Poisson＇s ratio on the Mandel-Cryer effect.