横观各向同性岩体内时损伤本构模型研究

Endchronic damage constitutive model of transversely isotropic rock

层状岩体一般视作横观各向同性体,其力学特性在不同的层面倾角下存在较大的差异。为了解决这一问题并研究层面倾角与力学特性之间的内在联系,引入横观各向同性体体积模量和剪切模量与层面倾角的函数关系式。从内时理论出发,通过内蕴时间的重新构造,在Helmholtz自由能中引入损伤变量,利用不可逆热力学的基本原理推导出横观各向同性岩体的内时损伤本构方程,并给出确定本构模型中各参数的方法。对该方程在单轴应力条件下进行求解、分析与验证。研究结果表明:该本构方程能很好地描述横观各向同性岩体在损伤发生前后的变形特点,并能有效地反映横观各向同性岩体的非线性和剪胀扩容等物理力学现象。

The layered rock is generally treated as a transversely isotropic body,but its mechanical characteristics are significantly different under different levels of inclination.First of all,to solve such problems and further investigate the inter-connections among these models,the functional relationships for transversely isotropy among bulk modulus,shear modulus,and the bedding angle were introduced.Second,starting from the endochronic theory,by rebuilding intrinsic time and introducing a damage variable into the Helmholtz free energy,a new set of endochronic damage constitutive equations for transversely isotropic rock were deduced using the fundamental principles of the irreversible thermodynamics of continuum media.Furthermore,the method for determining parameters of the constitutive model was also presented.Finally,solution analysis and experimental validation of the equations for transversely isotropic rock under uniaxial stress condition were performed.The results show that the endochronic damage constitutive equations can describe accurately the properties of coal containing gas before and after damage and also can reflect effectively the nonlinear and shear expansion mechanical phenomena of coal containing gas.