基于Weibull分布的盐岩分数阶蠕变本构模型研究

采用流变程控仪对湖北江汉油田盐岩试样进行了三轴蠕变实验。基于Weibull随机分布获得岩石损伤变量随加载时间的变化形式，构建了变黏性系数Abel粘壶本构关系。基于分数阶微分理论，采用将变黏性系数Abel粘壶替代西原正夫模型中Newton粘壶的方法，建立了盐岩蠕变损伤本构模型，并采用最小二乘法拟合获得了该本构模型中的参数。通过拟合曲线对比发现，本文提出的盐岩分数阶蠕变本构模型在描述盐岩的蠕变全过程，尤其是加速蠕变过程中具有较明显的优势，并且验证了西元正夫模型为本文所提出的本构模型的一个特例。

THE FRACTIONAL DERIVATIVE APPROACH TO CREEP CONSTITUTIVE MODEL OF SALT ROCK BASED ON WEIBULL DISTRIBUTION

A computer-controlled creep setup is applied to the triaxial creep tests of the salt rock specimens, which are taken from the Jianghan Oilfield, Hubei Province. Based on the definition of damage variable of rock, which is changing with loading time and obtained from Weibull distribution, a new variable-viscosity Abel dashpot has been proposed. Based on the theory of fractional calculus, the creep damage constitutive model of salt rock is proposed by replacing the Newtonian dashpot in the classical Nishihara model with the new Abel dashpot. Also, parameters in the new constitutive model can be determined by the least-squares fitting analysis. In comparison of fitted curves, it can be manifested that the fractional derivative creep constitutive model proposed in this paper is evidently superior to describe the three creep stages of salt rock, especially the tertiary one. Furthermore, the classical Nishihara model has been proved as a special case of the constitutive model proposed in this paper