非饱和双重孔隙介质的势函数本构方程及应用

Potential constitutive equation of unsaturated double-porosity media and its application

为了分析复杂岩土工程多场多相耦合效应,需要建立非饱和双重孔隙介质的一般本构理论框架。把双重孔隙介质视为两个单重孔隙介质的嵌套叠加,利用各组分应变与孔隙变形之间的内在联系,从经典混合物理论出发推导了非饱和双重孔隙介质的能量守恒方程。通过功共轭对之间的力学性质建立了小应变条件下非饱和双重孔隙介质的一般势函数本构方程。作为一般势函数本构方程的应用,把势函数取为应变量的二次多项式,假定各共轭量之间相互独立,获得了非饱和双重孔隙介质的各向同性线弹性模型,并根据试验数据确定了模型参数。当非饱和双重孔隙介质退化为饱和双重孔隙介质或非饱和单重孔隙介质时,本文模型退化为已有的相应模型。本文获得的一般势函数本构方程可以指导非饱和双重孔隙介质的具体建模工作,线弹性本构方程可用于建立相应的固结控制方程。

To analyze the multi-physical field and multi-phase coupling effects in complex geotechnical engineering,it is necessary to construct a general constitutive theoretical framework for unsaturated double-porosity media.First,double-porosity media was regarded as the nested superposition of two single-porosity media,and an energy conservation equation for unsaturated double-porosity media was derived from classical mixture theory based on the internal relations between strain and pore deformation of each component.Then,the general potential constitutive equations were established under small strain condition for unsaturated double-porosity media on the basis of the mechanical behaviors of conjugate quantity pair.As an application of the general potential constitutive equation,the potential function was adopted as a quadratic polynomial of strains,and it was supposed that each conjugate quantity was independent of each other.Thus,an isotropic linear elastic model of unsaturated double-porosity media was established,and model parameters were determined by experimental data.When unsaturated double-porosity media was degenerated into saturated double-porosity or unsaturated single-porosity media,the proposed model was degenerated into corresponding existing model.The general potential constitutive equation obtained in this paper can provide guidance for the specific modeling of unsaturated double-porosity media,and the linear elastic constitutive model can be used to formulate corresponding consolidation governing equation.