盐岩流变损伤特性及本构模型研究

借助盐岩单轴流变-声发射试验，分析了流变3个特征阶段与声发射事件数的对应关系，并基于Weibull分布构建了声发射事件数随加载时间的关系式，进而获得了损伤变量的演化关系式。对盐岩流变-声发射试验及流变-超声波试验数据拟合分析表明，该损伤变量表达式具有很好的适用性。进一步对损伤表达式中的参数进行了敏感性分析，揭示了形状参数、尺度参数对损伤值的影响规律。引入分数阶微积分理论及损伤理论，构建了基于损伤的Abel黏壶本构关系，通过替代西原模型中Newton黏壶的方法，求解获得了盐岩分数阶流变本构模型。由盐岩单轴流变试验曲线拟合分析可知，分数阶流变模型能很好地描述盐岩流变的3个特征阶段，尤其是加速流变阶段，且验证了西原模型为分数阶流变模型的一种特殊形式。

Characters of rheological damage and constitutive model of salt rock

This paper analyzes the correlations between three regions of rheology and numbers of acoustic emission (AE) events with the application of the rheology-AE test for salt rock under the condition of uniaxial compression. On the basis of the relationship between AE events and loading time, which is obtained from Weibull distribution, the function of damage variable with time is proposed. By comparing the fitting results with data obtained from the rheology-AE test and the rheology-ultrasonic test of salt rock, it is found that the function of damage variable with time has an excellent applicability. In addition, this paper conducts the sensitivity analysis of parameters in the function of damage variable with time and reveals the effects of shape parameters and scale parameters on the damage variable of salt rock. The theories of fractional calculus and damage are introduced to build the constitutive model of the variable-viscosity Abel dashpot. By replacing the Newton dashpot in the Nishihara model with the variable-viscosity Abel dashpot, the fractional rheological model of salt rock is proposed. The fitting analysis of uniaxial rheological test curves of salt rock suggests that the fractional rheological model is evidently superior to Nishihara model in describing three regions of rheology, especially the accelerating one. Furthermore, the Nishihara model is proved to be a special case of the fractional rheological model.