基于Eshelby张量和Mori-Tanaka等效方法的砂卵石土等效弹性模量研究  

Study of equivalent elastic modulus of sand gravel soil with Eshelby tensor and Mori-Tanaka equivalent method

作　　者：胡敏[1] 徐国元[1] 胡盛斌[1] 

机构地区：[1]华南理工大学土木与交通学院,广州510641

出　　处：《岩土力学》2013年第5期1437-1442,1448,共7页Rock and Soil Mechanics

基　　金：国家自然科学基金项目(No.51078151)

摘　　要：砂卵石土是物理力学性质既不同于砂土也不同于完整岩体的离散体,将其简化为砂土为基体,卵石为椭球形夹杂的两相复合材料。在小变形条件下,考虑卵石的含量和分布,采用Eshelby张量和Mori-Tanaka等效方法,运用替换迭代方式,从理论上推导出等效柔度张量一般性计算方程;重点研究卵石为球形时(椭球的一种特殊情况)砂卵石土等效弹性模量,通过编写程序求得其数值解,并与相关数值试验和理论进行对比。结果表明,此理论计算方法精度较以前的理论计算方法精度有大幅提高,当卵石体积分数小于50%时,理论计算结果与数值试验结果吻合较好,其结果可用于判断砂卵石土宏观力学特性,有利于地下工程应用;当体积分数大于50%时,理论计算结果和数值试验结果有一定误差。Sandy pebble soil is a granular media, and the physico-mechanical properties of sandy pebble soil are different from those of sandy soil and intact rock mass. Here sandy pebble soil is considered as a simplified material, namely a two-phase composite material consists of sandy soil as matrix and pebble as ellipsoid inclusion. This paper presents the theoretical derivation of equivalent elastic matrix calculation equation. The derivation process is based on Eshelby tensors and Mori-Tanaka equivalent method within small deformation condition. The process is also considered pebble＇s content and distribution, using replacement iterative method. This paper focuses on the calculation of sandy pebble soil equivalent elastic modulus using numerical solution through compile program. Comparison is made between numerical solution and theoretical result. The result shows that the theoretical calculation method has better calculation accuracy than the earlier calculation methods of previous experiment and theory. When the pebble volume fraction less than 50%, the result of theoretical calculation coincides with experiment result, thus the presented method can be used to predict sandy pebble soil＇s macroscopic mechanical properties, and it is beneficial to underground engineering application; when the volume fraction more than 50%, the theoretical calculation result may have some error with the experiment result.

关 键 词：砂卵石土 等效弹性模量 自洽理论 Eshelby张量 等效应力 

分 类 号：P584[天文地球—岩石学]