基于Weibull分布的盐岩分数阶蠕变本构模型研究  

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

作　　者：丁靖洋[1] 周宏伟[1] 李潮[1] 王春萍[1] 武志德[2] 

机构地区：[1]中国矿业大学(北京)煤炭资源与安全开采国家重点实验室,北京100083 [2]中国石油勘探开发研究院廊坊分院,廊坊067005

出　　处：《固体力学学报》2013年第5期473-480,共8页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(11172318和51120145001);国家973项目(2009CB724602);科技部国际科技合作项目(2010DFA64560)资助

摘　　要：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,论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论文所提出的本构模型的一个特例.A computer-controlled creep setup was applied to the triaxial creep tests of the salt rock specimens,which were taken from the Jianghan Oilfield,Hubei Province.Based on the definition of damage variable of rock,which varies with loading time and obtained randomly from Weibull distribution,a new variable-viscosity Abel dashpot was proposed.Based on the theory of fractional calculus,the creep damage constitutive model of salt rock was developed 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 was proved as a special case of the present constitutive model.

关 键 词：盐岩三轴蠕变 WEIBULL分布 新Abel粘壶 分数阶微分理论 

分 类 号：TU452[建筑科学—岩土工程]