基于内变量热力学的岩石蠕变与应力松弛研究

CREEP AND RELAXATION OF ROCK MASS BASED ON THERMODYNAMICS WITH INTERNAL STATE VARIBALES

蠕变和应力松弛是岩石材料固有的时效特性,与岩石工程的长期稳定性密切相关。基于Rice不可逆内变量热力学理论对岩石蠕变和松弛本质上的一致性问题进行研究。给定余能密度函数和内变量演化方程建立基本热力学方程,通过不同约束条件构建黏弹–黏塑性蠕变和应力松弛本构方程。黏弹性本构方程具有普遍性,能包含经典元件组合模型的黏弹性本构方程;黏塑性本构方程考虑材料变形过程中的硬化效应,更加符合实际情况。蠕变和松弛是岩石材料在不同约束下的外在表现,但两者具有相同的非平衡演化规律,本质上具有一致性。蠕变与应力松弛本构方程基于相同的基本热力学方程,可以相互转化,且方程参数相同,因此可以通过蠕变方程和蠕变试验结果对材料的松弛特性进行分析。最后通过模型相似材料单轴蠕变加卸载试验和应力松弛试验对这一思想进行验证。

Creep and stress relaxation are the intrinsic time-dependent properties of rock mass,and are closely linked to the long term stability of rock. The creep and stress relaxation was discussed based on the irreversible thermodynamics with internal state variables proposed by Rice. The fundamental thermodynamic equations were derived by proposing a specific function of complementary energy and a kinetic equation of internal state variables. The constitutive equation describing the creep and stress relaxation was established based on the fundamental thermodynamic equations under different constraint conditions. Some classical viscoelastic equations from component models were contained in the proposed viscoelastic constitutive equation and the hardening effect was considered in the viscoplasctic creep equation. The creep and stress relaxation were found to be the result of the same non-equilibrium evolution of microstructure within material and were consistent in essence. The creep and stress relaxation equations can be transformed into each other and the parameters in these two equations are all the same. So the relaxation properties can be analyzed through creep constitutive equation and creep test. This point was validated by the uniaxial creep and stress relaxation tests of similar materials used in geomechanical model test.