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基于分数阶微积分的岩石蠕变损伤本构模型

刘峻松,黄海峰,黄敏,杨豪,蓝康文   

  • 出版日期:2018-04-14 发布日期:2018-04-14

Creep damage constitutive model of rock mass based on fractional calculus

LIU Junsong, HUANG Haifeng, HUANG Min, YANG Hao, LAN Kangwen   

  • Online:2018-04-14 Published:2018-04-14

摘要: 为了反映岩石蠕变特性,采用YSJ-01-00岩石三轴流变试验机进行砂岩三轴压缩蠕变试验,基于岩石蠕变的阶段特征,提出通过弹性体、基于分数阶微积分的软体元件和黏塑性体分别描述岩石蠕变的弹性应变、黏弹性应变和黏塑性应变。依据连续损伤理论对弹性体和分数阶黏塑性体进行改进,通过SN元件改进分数阶软体。利用综合改进后的考虑时效损伤的弹性体和基于分数阶微积分的非定常黏滞体和非定常黏塑性体,构建了新的三元件蠕变损伤本构模型,并用遗传算法得到了模型参数。对比试验曲线和模型拟合曲线,表明所建模型具有合理性和适用性,可为红层边坡流变特性的研究提供一定参考。

关键词: 分数阶微积分, 岩石蠕变, 损伤, 本构模型, SN元件

Abstract: In order to reflect the characters of rock creep, the triaxial compression creep test of sandstone was carried out by using YSJ-01-00 rock triaxial creep testing machine. Based on the characteristics of rock creep, the elastomer, software components and visco plastic body based on fractional calculus are used to describe the elastic, viscoelastic and viscoplastic strain of rock respectively. The elastic and viscoplastic body are improved based on the continuous damage theory, and the fractional software component is improved by SN component. A new constitutive model of three elements for creep damage is established, which is composed of an elastic body considering the time-dependent damage and an unsteady viscous and viscoplastic body based on fractional calculus. The rationality and applicability of the presented model is proved by comparing the test curves and the fitting curves.

Key words: fractional calculus, rock creep, damage, constitutive model, SN component