Biot固结理论中连续性方程形式的讨论  

Discussion on forms of continuum equation for Biot’s consolidation

作　　者：张凯[1] 周辉[1] 冯夏庭[1] 房敬年[1] 张元刚[2] 

机构地区：[1]中国科学院武汉岩土力学研究所岩土力学国家重点实验室,武汉430071 [2]兖州煤业股份有限公司,山东邹城273500

出　　处：《岩土力学》2009年第11期3273-3277,共5页Rock and Soil Mechanics

基　　金：国家自然科学基金委员会;二滩水电开发有限责任公司雅砻江水电开发联合研究基金项目(No.50539090;50579091);国家自然科学基金项目(No.10772190);国家技术支撑计划项目(No.2006BAB04A06)

摘　　要：对于Biot固结方程中的连续性方程形式,不同的研究者存在分歧。在详细分析了Biot推导固结方程的过程后,发现其在推导固结方程时用到的弹性应变能密度函数存在错误。为了得到正确的连续性方程,采用两种思路进行了分析:①通过对土体单元变形的分析,得到了考虑土体颗粒和流体可压缩性的连续性方程;②按照Biot推导固结方程的思路,通过修正推导过程中用到的弹性应变能密度函数得到了连续性方程。上述两种思路得到的连续性方程是等价的,同时将上述连续性方程和其他研究者通过质量守恒得到的连续方程进行了对比,结果是一致的,从而确定了连续性方程的正确形式,并澄清了目前在Biot固结方程中的连续性方程上存在的分歧,所得结论可为固结方程的解析或数值计算提供依据。When solving Biot＇s consolidation equations, different researchers used different continuum equations. The methods Biot M.A. used to deduce the consolidation equations are firstly reviewed. It can be seen that some mistakes exist in the strain energy density function. In order to derive the correct form of continuum equation, two methods are used here. Firstly, based on the analysis of the deformation of the representative element volume （REV） of the soil, a fluid continuum equation which can take the compressibility of grain and fluid into account is derived. Secondly, based on the method Biot M.A. used with modified strain energy density, another continuum equation is derived. The continuum equations deduced from the two methods listed above are found to be equivalent. In addition, the equations are compared to the continuum equation derived by other researchers based on mass conservation law, and they are found to be coincident. Then, the right form of fluid continuum equation is proved and the result can provide theoretical support to consolidation calculation.

关 键 词：BIOT固结方程 连续性方程 应变能密度 变质量系统 

分 类 号：O341[理学—固体力学] TU43[理学—力学]