层状地质材料弹性张量求解及应用

RESEARCH ON ELASTIC TENSOR RESOLUTION IN STRATIFIED GEOMATERIAL AND ITS APPLICATION

有效弹性张量的确定是土木工程研究者一个重要课题,正确决定宏观有效弹性张量往往是计算结果是否成功的关键。现行主要流行的方法主要有:对弹性张量各元素采用简单体积平均法(方法一)、自洽法(方法二)、Hashin-Strikman法上限(方法三)和Hashin-Strikman法下限(方法四)。利用均匀化技术,在横观各向同性成层地质材料满足位移和应力相等的条件下,获得了宏观弹性张量的具体表达形式(方法五)。在特殊条件下,该表达方程可以简化为自洽法和简单的体积平均法。在实例和应用研究的基础上,对5种方法进行了对比分析。研究结果表明,所提出的方法可以综合描述平行流模型和系列流模型,且弹性张量各组成部分上、下限值不是Hashin-Strikman上下限法所指定的范围,其下限应为自洽法的结果;除元素Ceff1133外,其上限应为Hashin-Strikman上限法结果。这种研究对边坡、坝基等土木工程的计算和分析具有重要作用。

The determination of effective elastic tensor is very important for civil engineering researchers; and it is essential to calculate the effective elastic tensor in order to obtain the rational results. Four kinds of methods for current effective elastic tensor determination are shown： volumetrical average method, self-consist method, Hashin-Strikman method（upper limit method） and Hashin-Strikman method（lower limit method） for every component in the effective elastic tensor. Based on the homogenization technology, the formulae of macroscopic effective elastic tensor are obtained for stratified isotropic geomaterial under the condition that the displacement and stress are equal in the everywhere in the element. And the proposed equation can be simplified as the formulae of volumetrical average method and self-consist method under some special cases. The comparative analyses of five different methods are performed; and the calculation results show the proposed method can describe the parallel flow model and series flow model. The upper-lower limit values of every component of effective elastic tensor are not determined by Hashin-Strikman method： and the lower limit scope can be decided by self-consist method. However, the upper limit scope can be determined by Hashin-Strikman method except C1133^eff. The obtained results are very important for calculation and analysis of rock slope and dam foundation engineering.