岩石结构超塑性损伤本构理论及热力学框架

Constitutive theory and thermodynamic framework for hyperplastic damage of deep rock structure

基于热力学势函数引入损伤理论,建立适用于深部岩体的新结构超塑性损伤本构框架。通过定义新内变量对:应变(损伤积累应变,结构重排应变)及相应广义应力、温度和熵,用4种热力学能量函数:内能,Helmholtz自由能,焓和Gibbs自由能描述岩石结构超塑性本构关系。本理论框架即能满足热力学定律具有严格物理意义又能对结构性进行较合理考虑。通过Legendre变换建立各能量形式间的转换。利用运动内变量参数及其共轭变量(广义应力)引出耗散势。给出承压变温条件下深部岩体的塑形耗散函数或屈服函数形式,可反映损伤并考虑结构重排的体变行为,两者通过Legendre变换的退化特例进行联系。构建适用深部岩体热力学本构理论框架下具体的应力–应变增量本征关系及其新应用实例,并提供应用性的判断依据。该理论对深部地下工程实践中岩石的力学分析具有借鉴意义。

The damage theory was introduced based on the thermodynamic potential function and a new damage constitutive theory for hyperplastic structure of deep rock was established. The new internal variable pairs：strain（including damage accumulate strain and structural rearranged strain） and the corresponding generalized stress,the temperature and entropy were defined and four kinds of thermal energy function： Internal energy,Helmholtz free energy,enthalpy and Gibbs free energy were used to describe the hyperplastic constitutive theory of rock structure. The rock constitutive theory obtained satisfies the laws of thermodynamics. The framework has a strict physical meaning and can reasonably consider the structural characteristics of rock. The links between the different energy functions were established by using the Legendre transformations. Dissipative functions were introduced through the kinematic internal parameters and their conjugate variables（generalized stresses）. The plastic dissipation function or yielding function of deep rock was given for the various conditions of pressure and temperature. It can reflect the damage character and structural rearrangement of the volume changes at the same time,which could be related through a degenerate case of Legendre transformation. The incremental stress-strain relation and new application examples were constructed for the deep rock structure. The criterion of application was provided.