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浙江大学学报(工学版)
浙江大学学报(工学版)
土木与交通工程     
非饱和多孔岩石的热力学本构理论
胡亚元
浙江大学 滨海和城市岩土工程研究中心 浙江 杭州 310027
Thermodynamics-based constitutive theory for unsaturated porous rock
HU Ya yuan
Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou, 310058, China
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摘要：

为了在本构模型中同时考虑岩石材料和多孔岩石的非线性和不可逆变形,提出非饱和多孔岩石工程力学理论.应用体积分数概念和混合物理论,凭借均匀化响应原理,获得由孔隙应变张量、饱和度和各组分材料体应变5个状态变量表示的能量平衡方程.利用自由能确定的5个弹性方程,加上体积分数之和等于1这个方程组成6个本构方程.根据这些方程可以求解非饱和岩石本构模型的全部6个未知变量（3个位移矢量和3个体积分数）.根据不可逆热力学理论,基于熵产公式提出用内变量表示的耗散率势函数,获得能够反映黏性和塑性不可逆变形特性的耗散本构方程.结果表明,自由能和耗散率2个势函数分别反映了岩石弹性和非弹性变形规律,共同构成了非饱和多孔岩石的热力学本构理论框架.
Abstract:

An engineering mechanics of unsaturated porous rock was proposed in order to consider the nonlinear and irreversible deformations of both rock material and porous rock. Firstly, with using the volume fraction concept and mixture theory, the equation of energy balance in terms of five state variables was obtained in virtue of the mixture homogenous response principle, which were called void strain tensor, degree of saturation and the material volume strain of each constituent. The five elastic equations which were determined by free energy and the one equation that the sum of all volume fractions was equal to unity compose six constitutive equations. Based on these equations, all six unknown variables (three displace vectors and three volume fractions) could be solved in the constitutive model of unsaturated rock. Secondly, according to the irreversible thermodynamics, the potential of dissipative rate in terms of internal variables was proposed on the basis of entropy production formula. Thus, the dissipative constitutive equations were derived to describe the irreversible deformation behaviors such as viscosity or plasticity. Results show that, the two potential functions of free energy and dissipative rate can depict the discipline of elastic and inelastic deformations, respectively, which both form the constitutive theoretical framework of unsaturated porous rock.
出版日期: 2017-03-06
CLC:  TU 47  
基金资助:

国家自然科学基金资助项目（51178419）.
作者简介: 胡亚元（1968—），男，副教授，从事地基处理和土的本构关系等研究.ORCID:0000-0002-5422-7679. E-mail: huyayuan@zju.edu.cn
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胡亚元. 非饱和多孔岩石的热力学本构理论[J]. 浙江大学学报(工学版), 10.3785/j.issn.1008-973X.2017.02.005.

HU Ya yuan. Thermodynamics-based constitutive theory for unsaturated porous rock. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 10.3785/j.issn.1008-973X.2017.02.005.

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